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DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS REBECCA ANN OSTERMANN Bachelor of Science Oklahoma State University Stillwater, Oklahoma 2000 Submitted to the Faculty of the Graduate College of Oklahoma State University in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE December, 2005 ii DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS Thesis Approved: Dr. Timothy Bowser Thesis Advisor Dr. William McGlynn Dr. Paul Weckler Dr. A. Gordon Emslie Dean of the Graduate College iii TABLE OF CONTENTS Page List of Tables ........................................................................................................ v List of Figures.......................................................................................................vi List of Nomenclature........................................................................................... viii Acknowledgements .............................................................................................. x I. Introduction................................................................................................ 1 II. Literature Review....................................................................................... 3 Thermal processing of liquid food products..................................... 3 Direct steam injection heating ......................................................... 4 Condensationinduced water hammer ............................................ 9 Objectives of research .................................................................. 11 III. Research Methodology............................................................................ 12 Products tested ............................................................................. 12 Experimental setup ....................................................................... 13 Data Collection.............................................................................. 14 Testing procedures ....................................................................... 17 IV. Error Analysis .......................................................................................... 24 Instrumental error.......................................................................... 24 Methodological error ..................................................................... 25 Model error.................................................................................... 26 V. Results and Discussion............................................................................ 29 VI. Summary and Conclusions...................................................................... 40 Observations from research.......................................................... 40 Conclusions from analysis of data................................................. 41 Recommendations for further research......................................... 42 Summary....................................................................................... 46 Bibliography .................................................................................................. 47 iv Appendices Appendix A: Pump calibration curve ............................................. 51 Appendix B: Thermal diffusivity calculations ................................. 53 Appendix C: Collected data........................................................... 57 Appendix D: Calculation of methodological error associated with the final temperature ........................................ 60 Appendix E: Tabular results of the calculation of dimensionless parameters .............................................................. 63 Appendix F: Results of linear regression for grouped and averaged data .................................................... 67 Appendix G: Results of regression analysis using logarithmic, exponential, and power relationships....................... 71 Appendix H: Results of regression analysis for portions of data set................................................................ 90 Vita Abstract v LIST OF TABLES Table Number Table Title Page Table 1 Constants for use in determining the saturation temperature of water 16 Table 2 Measurement error 25 Table 3 Contributions to model uncertainty 28 Table 4 Range of parameters tested within the study 30 Table 5 Adherence to the predictive equation based on product 33 Table 6 Descriptive statistics of dimensionless parameters tested 33 Table 7 Averaged RT and dimensionless parameter values for data analysis 37 Table 8 Coefficient of determination values for all analyses 39 Table B1 Coefficients to estimate food physical properties 54 Table B2 Physical properties of the products tested 55 Table C1 Collected data 58 Table D1 Variation in final temperature values 62 Table E1 Calculated dimensionless numbers 64 vi LIST OF FIGURES Figure Number Figure Title Page Figure 1 Single orifice venturi direct steam injector 5 Figure 2 Pilot scale steam injection heater 6 Figure 3 Disassembled view of the multiorifice steam injector heater body used in this study 6 Figure 4 Experimental setup 14 Figure 5 Example of determination of Tf based on temperatures recorded by the data logger 20 Figure 6 Analysis of test results for water and sugar solution compared to the predictive equation 31 Figure 7 Comparison of results of tests of beef stock and starch to the predictive equation. 32 Figure 8 Linear regression of the relationship between Thermodynamic Ratio and Reynolds Number 34 Figure 9 Linear regression of the relationship between Thermodynamic Ratio and Prandtl Number 35 Figure 10 Linear regression of the relationship between Thermodynamic Ratio and Nusselt Number 35 Figure 11 Linear regression of the relationship between Thermodynamic Ratio and Stanton Number 36 Figure 12 Linear regression of the relationship between Thermodynamic Ratio and Jacobs Number 36 Figure 13 Data logger output of Ti and Tf over time showing system pressure adjustments during testing 44 Figure A1 Pump calibration curve for Waukesha Cherry Burrell, Delavan, WI, Model 15 positive displacement pump 52 Figure D1 Example of methodological error in final temperature determination 61 Figure F1 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Reynolds Number 68 Figure F2 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Prandtl Number 68 Figure F3 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Nusselt Number 69 vii Figure Number Figure Title Page Figure F4 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Stanton Number 69 Figure F5 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Jacobs Number 70 Figures G136 Regression analysis using logarithmic, exponential, and power relationships 71 Figures H136 Regression analysis for portions of data set 90 viii LIST OF NOMENCLATURE A0A8 Psychometric Constants A Cross Sectional Flow Area, m2 cP Specific Heat, kJkg1C1 CWH Condensation Induced Water Hammer d Diameter of Interior Concentric Pipe, m D Diameter of Exterior Concentric Pipe, m dc Characteristic Dimension, m dh Hydraulic Diameter, m DSI Direct Steam Injection E Error FAPC Food and Agricultural Products Center h Convective Heat Transfer Coefficient, Wm2C1 hLG Enthalpy of Evaporation, Ja Jacob Number k Thermal Conductivity, Wm1C1 L Characteristic Length of Flow Geometry, m N Model Output n Number of Components to be Summed Nu Nusselt Number P Wetted Perimeter, m Pe Peclet Number Pr Prandtl Number Ps System Operating Pressure, psi q Heat Flux, Btuhr1ft2 R2 Coefficient of Determination Re Reynolds Number rh Hydraulic Radius, m RT Thermodynamic Ratio RTD Resistive Thermal Device St Stanton Number T? Liquid Temperature, °C ix tiw Initial Temperature of the Wall, F Tf Final Temperature of the Product at onset of CWH, K Ti Initial Temperature of the Product, K Tsat Saturation Temperature of the Product, K tvs Saturation Temperature of the Steam, F u Product Velocity, ms1 ui Model Input Variables V Product Velocity, ms1 Xi Mass Fraction of the ith Component Thermal Diffusivity, m2s1 μ Product Viscosity, cP Product Density, kgm3 G Density of Gas, kgm3 L Density of Liquid, kgm3 x ACKNOWLEDGEMENTS My thanks goes first and foremost to God for giving me patience and my family for giving me encouragement throughout this process. I would also like to thank the following people: • My committee members, Drs Bowser, McGlynn, and Weckler for providing to me the opportunity to conduct this research. • Jana Moore for all of her assistance over the years and for being a great friend. • Dave Moe and Joe at the Food and Agricultural Products Center without whom I would not have been able to collect the data. • The entire faculty and staff of the Biosystems Engineering department for allowing me to serve in the Recruiter position, which not only gave me the opportunity to pursue a Masters degree, but also allowed me to contribute to the success of a department that I love. 1 CHAPTER I INTRODUCTION Heating of food products can cause many useful changes to a product’s taste, texture, and appearance. In addition to these changes, many of the most useful impacts of thermal processing on the food product occur on a cellular level, including the inactivation of enzymes and the destruction of pathogens that can cause spoilage. Pasteur’s discovery that microbial metabolism is the driving force behind the fermentations that spoil food products (Lewis and Heppell, 2000) brought to light the importance of the commercial sterilization of food products. There are many methods of thermal processing used in the food industry. Techniques range from batch processing to continuous processing and from indirect heat exchange to direct heat transfer. Direct Steam Injection (DSI) heating, the thermal processing method that is the focus of this research, has not found widespread acceptance in the industry. Despite the benefits of highly efficient heat transfer in a continuous flow system, the occurrence of Condensationinduced Water Hammer (CWH) and the associated noise, system damage, and operator hazards have deterred processors from using DSI systems (Lewis and Heppell, 2000; Schroyer, 1997). The purpose of the research described herein, was to examine relationships between the operating conditions of a DSI system, the physical 2 properties of liquid food products, and the occurrence of CWH. The goal was to investigate a mathematical relationship that processing plant managers and DSI system operators could use to predict safe operating conditions. Such an equation was developed by Bowser et al. (2003) based on the thermodynamic ratio (RT) and the Peclet Number (Pe) using data collected in tests of water and sugar water. The following research first repeated the experiments reported by Bowser et al. (2003) testing water and sugar solution, then examined the applicability of the relationship determined by Bowser et al. to beef stock and corn starch, and finally looked at the use of other dimensionless parameters that are commonly used to describe heat transfer and fluid flow to see if another relationship could be defined. 3 CHAPTER II LITERATURE REVIEW Thermal Processing of Liquid Food Products Batch processing is an inexpensive and flexible method for heating foods. In batch processing, a unit of product is introduced into the heating apparatus, brought up to temperature, held for sterilization time if required, and removed from the heater. This method, used in steamjacketed kettles and retorts, can be applied to virtually any food product (Lewis and Heppell, 2000). In heat transfer, temperature is a function of location and time (Singh and Heldman, 2001). Therefore, the distance from the heating source to the center of the product determines the time that a product must be exposed to high temperatures. While heating can have beneficial effects on the food product, prolonged exposure to heat or heating at high temperatures can have adverse effects on the taste, texture, appearance, and nutritional characteristics of a product (Lewis and Heppell, 2000). Therefore, processors have turned to continuous heating techniques over batch processing for pumpable products in order to reduce the distance from the heat source to the center of the product and therefore the reduce time required for heating. In continuous processing, heat is transferred to a product as it flows through a heat exchanger, with the hold time required for reducing microbial activity determined by the product flow rate and the equipment properties 4 including tube diameter and length. The thermal death time of microbes decreases as temperature increases, and because the desired temperature can be reached faster in continuous processing than in batch processing, the product is not required to be at a high temperature for a prolonged period. In addition to the increased product quality that results from a shorter exposure to high temperatures, continuous processing may have economic benefits from a higher production rate and less materials handling (Kundra and Strumillo, 1998). Continuous thermal processing techniques include methods that employ electrical energy for heating and methods that utilize heat from hot water or steam, with the later method being of interest for this research. Processes that use hot water or steam for heat transfer can be further divided into indirect methods and direct heating methods. Indirect methods are those in which there is a heat exchange surface separating the heating medium from the product to be heated, for example plate, tubular, and scraped surface heat exchangers. Direct methods such as steam infusion or steam injection have direct mixing of the heating medium and the product (Kudra and Strumillo, 1998). Direct Steam Injection Heating In a direct steam injection system, food grade steam is injected directly into the food product. This can be done simply through a singleorifice venturi as shown in Figure 1. However, this method must have high velocity steam and a long stretch of straight pipe downstream in order to ensure proper mixing and there is a large pressure drop across the device (Lewis and Heppell, 2000). 5 Figure 1: Single orifice venturi direct steam injector (Perry, 1998). A multipleorifice DSI heater is an improvement over the singleorifice models for food processing applications. In this design, steam is injected into the product through many small holes in a central tube. The central tube contains a spring loaded piston that regulates the steam pressure in relation to the product pressure. Helical flights aid in mixing the steam with the product within the mixing chamber. The DSI heater used in this research is shown in Figure 2 (Pick Heaters, West Bend, WI Model SC23). A disassembled view of the heater body is shown in Figure 3. The small holes in the injector tube ensure that the steam is introduced into the product in the form of small bubbles, which produces a more rapid condensation and thus virtually instantaneous heating. In fact, Burton et al. (1977) found that full temperature could be reached just 0.9 seconds after steam injection. Rapid condensation is also important to minimize uncondensed steam bubbles in downstream piping, and maximize product throughput. Rapid condensation can also be encouraged by providing product backpressure on the injector greater than the pressure required to prevent boiling (Lewis and Heppell, 2000). 6 Figure 2: Pilot scale steam injection heater (Pick Heaters, West Bend, WI Model SC23) (photo courtesy of the Food and Agricultural Products Center, Oklahoma State University, Stillwater, OK). Figure 3: Disassembled view of the multiorifice steam injection heater body used in this study (photo courtesy of the Food and Agricultural Products Center, Oklahoma State University, Stillwater, OK). Injector tube Spring plunger Static mixer Housing 7 When the steam is injected into the product, it condenses, giving up some of its sensible heat and its latent heat of vaporization. This condensate can cause considerable dilution, with a 60°C increase in product temperature adding about 11% of water to the product (Lewis and Heppell, 2000). In many food processing applications, dilution is acceptable; but for applications where additional water is not desirable, the condensate can be removed from the product after heating using a vacuum chamber. Direct heating is a much more efficient heating method than indirect heating. Indirect heating only utilizes sensible heat, meaning that, when using hot water as the heating medium, only 4.2kJ of heat is available per kilogram of water for every degree difference between the temperature of the product and the temperature of the heating water. However, DSI heating employs the latent heat of vaporization of steam (2260 kJ kg1), in addition to the sensible heat. On a perdegreebasis, the heat content of steam is 540 times that of water (Alverez et al., 2000). In fact, Jones and Larner (1968) found that the heat transfer coefficient of a DSI system was 60 times greater than of indirect steam heating systems. This high efficiency leads to energy savings for producers; Sutter (1997) found that a DSI systems used 7.9% less energy than a shell and tube heat exchanger when heating water and Schroyer (1997) stated that reductions in energy demands of 2025% were common. Precise and flexible temperature control is another major benefit to steam injection heating. DSI units can be used for raising product temperature by as little as 5.5°C to much larger increases of 96.7°C just by varying the amount of 8 steam added to the product (Singh and Heldman, 2001). In addition, product heating begins as soon as the steam valve is opened and ends as soon as it is closed, so DSI systems do not require a long warmup period and have fewer problems with overshooting the set point temperature due to residual heat in the system (Schroyer, 1997). Finally, Alverez et al. (2000) found that when heating beer mash, DSI was preferred over batch processing. He found there was a reduced risk of scorching the mash, because the steam remained at a constant temperature, limiting the temperature of the final product. In addition to the high efficiency, instantaneous heating, and precise temperature control of DSI, benefits over indirect heat exchangers include less space requirements, no need for condensate return systems (Schroyer, 1997), increased temperature control (Sutter, 1997), the ability to process moreviscous products, and less fouling (Lewis and Heppell, 2000). Steam injection heating has found utility in a wide variety of applications. In the field of biotechnology, it has been found that steam injection heating does not require a product to be held at high temperatures for as long as batch processing does to achieve the same result. Biotechnology products that benefit from a shorter exposure to high heat include thermolabile biomaterials, applications that require constant dry matter content after heating, and biomaterial broths that contain starch that otherwise could be gelatinized. (Kudra and Strumillo, 1998). Industrial facilities that already posses a steam supply have found that steam injection heating is an efficient means of producing hot water for use throughout the facility. For example, steam heated hot water can be 9 used instead of steam in a jacketed kettle to produce more even heating and better temperature control of the product (Sutter, 1997). In the food processing arena, steam injection can be used to heat almost any pumpable product. Some designers advocate that it is most applicable to low viscosity and homogenous products such as milk and juices (Richardson, 2001). However, it has also been employed to heat soups, chocolate, processed cheeses, ice cream mixes, puddings, fruit pie fillings (Singh and Heldman, 2001), jams, cheeses, salsa, pet foods, sugar and starch candy mixtures (Pick Heaters, 2004), beer mash (Alverez et al, 2000), baby food, and texturized proteins (Bowser et al, 2003). CondensationInduced Water Hammer Condensationinduced water hammer is a major drawback of DSI heating systems. This phenomenon can occur when a high pressure steam bubble is surrounded by product. As the steam condenses due to heat loss to the product, the volume of the condensate is much less than the volume of the steam. The pressure within the bubble drops drastically causing the bubble to collapse. Bubble collapse can cause large pressure surges that propagate within the system and cause loud noise (Van Duyne et al., 1989). Lewis and Heppell (2000) suggested that “some form of sound absorption may be necessary” to cover up this problem. However, the issue goes beyond simple noise. The forces on the system piping and valves can be large enough to cause costly damage and may be hazardous to operators. Therefore, it is important to define the operating conditions under which CWH will occur so as to allow processors to implement DSI systems and avoid the undesirable effects of CWH. 10 Bowser, et al. (2003) addressed the concern of designing DSI systems to decrease the occurrence of CWH. In this research, water and aqueous sugar solutions of various concentrations were heated under a variety of operating conditions. A relationship between the thermodynamic ratio and the Peclet number was established that could effectively predict a CWH event. The thermodynamic ratio (RT) is a dimensionless number that was first identified by Block et al. (1977) in the research of water hammer in steam power generators. The simplified expression for thermodynamic ratio, which assumes that heat transfer from the steam to the product is 100% efficient and that the mass of the steam added to the product is negligible is: f i sat i T T T R T T = Equation 1 where Tsat is the saturation temperature of the product (K), Ti is the initial product temperature (K), and Tf is the final product temperature at the onset of CWH (K). The Peclet number (Pe) is a dimensionless heat transfer parameter, named for Jean Claude Eugene Peclet (17931857), that gives the ratio of bulk heat transfer to conductive heat transfer (Incropera and De Witt, 1985). It is defined by Equation 2. Pe = uL Equation 2 where u is the product velocity (ms1), L is the characteristic length of the flow geometry (m), and is the thermal diffusivity of the product (m2s1). 11 Bowser, et al. found that CWH would be avoided 90% of the time if the thermodynamic ratio could be maintained above a given value as shown in Equation 3. RT > 1.5× (2.4×10 5 Pe +1.25) Equation 3 Objectives of Research The overall goal of this research was to develop a greater understanding of the safe operating conditions for a DSI heater. Two specific objectives for accomplishing this goal were: 1. To evaluate the validity and limitations of the equation developed by Bowser et al. (2003), which were based on tests with water and sugar solution, to additional liquid food products. 2. To investigate if another correlation between the physical properties of liquid food products and the temperature at which CWH occurs could be developed using common heat transfer and fluid flow parameters. This investigation was meant to be a general screening of parameters using the available data, not a focused study of any particular parameter. 12 CHAPTER III RESEARCH METHODOLOGY Products Tested Products were selected to both reflect the previous tests of Bowser et al. (2003) and to study the effects of CWH on products with a wider range of rheological properties. First, water was tested in order to benchmark the system performance. Second, aqueous sugar solutions at concentrations ranging from 49.2 to 68.3 degrees brix were tested. Sugar solution was the product used by Bowser, et al., so it provided a standard of comparison to ensure that research and calculation methodologies of this study produced similar results as the previous research did. Third, concentrated beef bone stock (CJ NutraCon, Guymon, OK), a highly viscous paste composed of approximately 42% water, 29% protein, 20% fat, and 9% ash, was tested. This product was chosen for its rheological properties: the viscosity decreases greatly with heating. Finally, a corn starch slurry was selected for testing because of its widespread use in the food processing industry. Corn starch test samples were made by combining Pure Food Powder (Tate and Lyle  AE Staley Manufacturing Company, Decatur, IL), which is approximately 90% carbohydrate and 10% water, with water and heating to the gelatinization temperature of 160°F in a continuousstir steam jacketed kettle. Without gelatinization, the starch and water mix is simply a 13 solution that has physical properties similar to water, but gelatinizing the starch forms a highly viscous material. Experimental Setup Testing was performed at the Food and Agricultural Products Center (FAPC) at Oklahoma State University using an approach similar to that of Bowser et al. (2003). A schematic of the system is shown in Figure 4. Steam, supplied from the boiler at 414 kPa (60 psi), was conditioned by a steam separator and a carbon filter before entering the pilot scale steam injection heater (Pick Heaters, West Bend, WI Model SC23). For tests involving sugar water, beef broth, and corn starch, the product was stored in a stainless steal sanitary tank and was supplied to the heater using a positive displacement pump (Waukesha CherryBurrell, Delavan, WI, Model 15). After heating, the product was returned to a separate tank to await further testing or disposal. This setup was modified slightly for tests in which water was heated. Because the pump’s hotclearance rotors experienced slippage for water, the pump shown in Figure 4 was not used. Instead, a potable water supply was connected directly to the steam injection heater’s inlet, and the heated water was discharged directly to a floor drain. 14 Figure 4: Experimental setup Data Collection To evaluate Bowser's equation, the variables used to calculate the Peclet number and the thermodynamic ratio needed to be quantified. For Equation 1 these variables were Ti, Tf, and Tsat; for Equation 2 the variables were L, u, and . The method used to determine each of these variables is outlined below. The characteristic length (L) is simply defined in textbooks as the inside diameter of the pipe for indirect heat transfer systems. However, in the DSI system tested, the product did not flow through an open pipe. Rather it flowed through the annular section between the heater body and the injector tube from which pressurized steam emanated. Therefore, the characteristic length was defined as the hydraulic diameter. Direct Steam Injection Ti Heater Tf Pf Pi DP Steam Product In Product Out Data Logger steam trap filter separator μ 15 The product velocity (u) was determined by two different methods. For the experiments with water, a catchcan test using a stopwatch and scale was used to calculate the flow rate from which velocity was calculated. For all other tests, the pump calibration curve (Appendix A) was used to determine product flow rate. To convert this flow rate into a velocity, it was divided by the flow area. It was assumed that the flow area was the annular space between the injector tube and the heater housing. The thermal diffusivities ( ) of the products were calculated based on the composition of the product using Equation 4. = = n i iXi 1 Equation 4 where n is the number of components, i is the thermal diffusivity of the ith component, and Xi is the mass fraction of the ith component (Singh and Heldman, 2001). Details of these calculations and a table of thermal diffusivity values used are given in Appendix B. Ti and Tf were both measured using sanitary resistive thermal devices (RTD) (Anderson Instruments, Fulton, NY Model SA510040370000). These values were then recorded using a digital data logger (Fluke, Everett, WA Model 2635A). To find the saturation temperature of the product, the saturation temperature of pure water at the operating pressure was calculated using the psychometric data published by the American Society of Agricultural Engineers (ASAE, 1999), which is defined by the relationship in Equation 5. 16 ( ) [ ] = 8 0 ln 10 i i i T Ai Ps Equation 5 where A0 through A8 are constants found in Table 1 and Ps is the system operating pressure (psi). Table 1: Constants for use in determining the saturation temperature of water (Equation 5). Constant Value A0 35.1579 A1 24.5926 A2 2.11821 A3 0.341447 A4 0.157416 A5 0.0313296 A6 0.00386583 A7 0.000249018 A8 6.84016E06 To account for the effect of solutes, a boiling point rise value was then added to the saturation temperature of water to find the saturation temperature of the product at the system pressure. The boiling point rise of the sugar solutions was found in Hoynak and Bollenback (1966). For the beef bone stock and starch, the boiling point rise was determined using Duhring’s rule based on the salt content of the product. In order to perform a boiling point rise calculation, the system pressure had to be monitored and recorded. The pressure of the product both before and after the heater was monitored using sanitary pressure sensors (Anderson Instruments, Fulton, NY Model SR032C004G1105). In addition to facilitating an accurate calculation of Tsat, monitoring the system pressure was the primary method for determining when a CWH event occurred. 17 Because the purpose of this research was not only to examine the results of the research of Bowser et al. (2003), but to evaluate alternative relationships between food product properties and CWH, it was desired to know the viscosity of the product immediately prior to heating. The viscosity of water varied with temperature and was found from Table A.4.1 of Singh and Heldman (2001). For tests involving sugar water, literature sources were used to relate the Brix value with viscosity (ICUMSA, 1979). For both beef broth and corn starch, viscosity was measured using a Brookfield inline viscometer (Brookfield Engineering, Middleboro, MD Model TT100). Testing Procedures In general, the following steps were taken in conducting the tests. 1. The product supply valve was opened allowing product to flow through the entire system, purging any air or water in the system. The unheated product was not recirculated during this step, but was sent directly to the outflow tank for potential use in additional tests. 2. Product flow rate was set and system pressure was controlled using a gate valve that was placed after the steam injection heater. 3. The steam valve controller was opened rapidly to 30% (previous tests correlating controller settings to steam pressure out of the valve showed that prior to 30%, the valve was not actually open). From this value, the controller was slowly opened (approximately 1% every 30 seconds) while the system was observed for signs of CWH. 18 4. When a CWH event was observed the approximate system pressure and outlet product temperature were recorded. These recorded values were considered as approximate, because as the system approached CWH, the system pressure, inlet product temperature, and outlet product temperature all fluctuated. 5. After recording these values, the steam valve was closed and the system parameters were reset for the next test. In some instances, the valve was merely closed enough for the CWH to cease, and then was reopened to collect another data point using the same system parameters. System pressure fluctuations greater than 41.4 kPa (6 psi), were used as a qualitative indicator to establish the occurrence of CWH. However, other indicators such as loud noise and movement of system piping were also observed. When testing beef broth and starch, some modifications were made to the procedure outlined above. First, in order to conserve product, the steam controller value was increased to 30% while the product was pumped at a very low flow rate, then the flow rate was increased to the test value and the steam controller setting was increased at a rate of 1% every 10 seconds until initial system pressure fluctuations of 13.8 kPa (2 psi) were observed at which time the rate of controller increase was slowed to the standard 1% every 30 seconds. The second modification was in the regulation of system pressure to maintain steady state operating conditions. The system pressure dropped significantly during testing of beef stock due to the decreased viscosity of the heated product. 19 This decrease in viscosity was not quantified, but was detected visually. During tests with starch, the system pressure increased. To maintain a steady system pressure during tests with both beef stock and starch, the gate valve was periodically adjusted during the test. When initial indications of CWH were observed, the researcher stopped adjusting the valve so that the final indication of a 41.1 kPa (6 psi) fluctuation in system pressure would not be affected. After testing, the observed final temperature was compared to the temperatures recorded by the data logger and refined. This refinement was required because of the inherent instability of the output temperature during a CWH event. The final temperature may have oscillated at the moment it was observed, and therefore may not have accurately reflected the final temperature that should be used in calculating the threshold RT value. The following method was used to hone the estimate of final temperature. 1. Fluctuations in the logged outlet temperatures were assumed to correspond to the large pressure fluctuations used to define a CWH event. 2. If the observed final temperature value was logged at the beginning of a drop in the recorded temperature, it was used as the final temperature for calculations. 3. If temperature drops occurred immediately (within 30 seconds – the time between increases in the steam valve opening) prior to the observed final temperature, it was assumed that the temperature was observed during an oscillation. A revised final temperature that corresponded to the 20 highest temperature reached prior to the oscillations within that time period was used. The recorded temperature values shown in Figure 5 for test 12 of beef stock are used to illustrate this method. The observed final temperature for this test was 70 °C. Because there were temperature fluctuations that preceded this value, step 3 was used to revise the final temperature. There were two drops in temperature that occurred within the 30 seconds prior to the observed value. The highest temperature before either of these drops was 63 °C, which was used as the final temperature in calculations. Beef Stock Test 12 50 55 60 65 70 75 Time (point collected every 2 seconds) Temperature (C) Product Inlet Temperature Product Outlet Temperature Observed Final Temperature 70 °C Final Temperature For Calculations 63 °C 30 Seconds Figure 5: Example of determination of Tf based on temperatures recorded by the data logger. The final step in the research process was to calculate dimensionless parameters that could potentially be used to predict CWH. First, the 21 thermodynamic ratio and Peclet number were calculated for each test for use in comparing to the predictive equation developed by Bowser, et al. Second, five additional dimensionless parameters: the Reynolds, Prandtl, Nusselt, Stanton, and the Jacob numbers were calculated for use in the screening investigation. The Reynolds number, defined by Equation 6, described the flow characteristics of the product. μ Re = VL Equation 6 where is product density (kgm3), V is product velocity (ms1), L is the characteristic length (m), and μ is product viscosity (cP). This parameter can also be described as a ratio of the inertial forces of the fluid to the viscous forces of the fluid (Incropera and De Witt, 1985). When Re is less than 2100 the flow is classified as laminar, when it is between 2100 and 4000 the flow is considered transitional, and when Re is greater than 4000 the flow is turbulent (Singh and Heldman, 2001). This parameter impacts steam injection heating, because as when the Reynolds number increases, more mixing occurs in the fluid, which should help to incorporate the steam into the product, reducing the opportunity for CWH to occur. The Prandtl number is a ratio of the molecular diffusivity of momentum to the molecular diffusivity of heat for forced convection (Incropera and De Witt, 1985). It is defined as: k Pr = μ cp Equation 7 22 where μ is the viscosity (cP), cp is the specific heat (kJkg1C1), and k is the thermal conductivity (Wm2C1). The Nusselt number relates the rate of heat transfer due to convection to the rate of heat transfer due to conduction (Incropera and De Witt, 1985). It is defined as: k Nu = hdc Equation 8 where h is the convective heat transfer coefficient (Wm2C1), dc is the characteristic dimension (m), and k is the thermal conductivity (Wm1C1). The value of Nu relates to the magnitude by which convection increases the amount of heat transferred, so a Nusselt value of 3 means that the heat transfer due to convection is 3 times the amount due solely to conduction (Singh and Heldman, 2001). The Nusselt number is intended to be used to describe indirect heat transfer, but DSI heating does not employee a heat transfer surface. An attempt to account for this difference was made by using Equation 9 found in the work of Goodykoontz and Dorshe (1966) to quantify the convective heat transfer component of the Nusselt number. vs iw i t t h q = Equation 9 where qi is the heat flux (Wm2) based on the heat flux area calculated using the pipe inside diameter, tvs is the saturation temperature of the steam (C), and tiw is the initial temperature of the wall (C). Goodykoontz and Dorshe applied this 23 equation to film condensation, but it was assumed in this research to also be applicable to droplet condensation. The Stanton number simply relates the previous three coefficients (Incropera and De Witt, 1985). Pr St = NuRe Equation 10 Finally, the Jacob number was calculated using Equation 11. G LG L pL sat h Ja c T T = ( ) Equation 11 where L is the density of the liquid (kgm3), cpL is the specific heat of the liquid (m2s2K1), Tsat is the saturation temperature of the steam (°C), T? is the liquid temperature (°C), G is the density of the gas (kgm3), and hLG is the enthalpy of evaporation (m2s2). The Jacob number is part of a theoretical model that is used to describe heat transfer in bubble type condensers based on transient conduction (Hewitt et al., 1994). 24 CHAPTER IV ERROR ANALYSIS All measurable quantities are subject to error  the difference between the measured value and the true value of the parameter. The two main contributors to error are instrumental error and methodological error. Instrumental Error Instrumental error is due to the cumulative effects of imperfections in the measuring equipment and human imprecision in reading the measurement (Bevington, 1969). In the error analysis for this research, human imprecision from reading the value off of the instrument was considered insignificant, because all of the sensors used were digital (Rabinovich, 2000). The instrument’s accuracy, which quantifies the inherent error associated with it, was found in the literature that accompanied each instrument. Another aspect of the instrumental error is the number of significant digits to which an instrument is read, referred to as data collection precision. The contributions to the error for the DSI system tested are shown in Table 2. The larger of the two values, instrument accuracy and data collection precision, was the observational uncertainty for that instrument. Another contribution to the uncertainty associated with the instrumentation was the assumption that each instrument used was properly calibrated, the viscometer at the factory and the pressure and temperature sensors during previous research. This assumption was correct for 25 the viscometer, but incorrect for the temperature and pressure sensors, adding an unknown error to the data. Table 2:Measurement Error Instrument Property Measured Instrument Accuracy Data Collection Precision RTD Tp,I & Tp,f 0.66 C 0.01 Analog transmitter N/A ±0.18 C N/A Data logger Temperature N/A ±0.10 C N/A Viscometer Viscosity 20cP 0.01cP Data logger Viscosity N/A ±0.5cp N/A Pump Flow rate 0.11 gpm N/A Methodological Error Methodological error is due to human imprecision in selecting the correct value of the measured parameter. In this research there were methodological errors associated with the final temperature values and the characteristic length. The error associated with selecting the Tf value used in calculations was based on the range of temperature values in the oscillations surrounding the selected final temperature, resulting in a methodological error of 5 °C for Tf. The method and results of this assessment are provided in Appendix D. The characteristic length also has methodological error associated with it. This is due to the ambiguity in the definition of L for DSI heaters. This error was defined as the difference between the two possible values of L, the hydraulic radius and the hydraulic diameter, which has a value of 0.0255 m. 26 Model Error Errors in the determination of variable values are consequential when considering the validity of a model. For this reason, the technique presented by Doebelin (1966) was used to find the absolute error of the model presented by Bowser et. al (2003) for the instruments and techniques used in this analysis. This techniques says that, if a model's output depends on multiple input variables (Equation 12), then the absolute error of the model output is proportional to the errors of each variable (Doebelin, 1966). In other words, the error in N is approximately the error in a variable multiplied by the effect that the variable has on the final value of N, summed for all variables in the model (Bevington, 1969). This concept can be expressed mathematically using the Taylor series expansion in Equation 13. The higherorder terms in Taylor's expansion are neglected, because all of the individual errors are small (Bevington, 1969). N = f (u1,u2 ,u3...ui ) Equation 12 where N is the model output and the ui's are the model input variables. + + + + = i i u u N u u N u u N u E N u N ( ) ... 3 3 2 2 1 1 Equation 13 Since the original goal of this research was to examine the applicability of the equation developed by Bowser et al. (2003), the model error will be examined by applying Equation 13 to Equations 1 and 2, the result of which is given in Equations 14 and 15. + + = p f p f p i p i Tp sat p sat T T T T T T T T T u u R u u R u E R u R , , , , , , ( ) Equation 14 27 + + = u u Pe u u Pe u E Pe u Pe L L u ( ) u Equation 15 The partial derivates for use in Equations 14 and 15 are calculated in Equations 1619. L u Pe u = Equation 16 u u Pe L = Equation 17 2 , , , , ( ) , p f p i p sat p f T T T T T T u R p i + = Equation 18 2 , , , , , ( p f p i ) p in p sat p f T T T T T u R = Equation 19 By combining all of the instrumental errors and the methodological error that contribute to each variable, the variable’s uncertainty can be determined. The uncertainties for each variable in the model of Bowser, et al. are given in Table 3. 28 Table 3: Contributions to model uncertainty Variable Contributions to Uncertainty Variable Uncertainty velocity, u pump calibration curve error 0.0063 ms1 characteristic length, L multiple definitions that can be applied to a single variable 0.0255 m thermal diffusivity, Insignificant initial product temperature, Ti RTD, analog transmitter, data logger 1.22 C final product temperature, Tf RTD, analog transmitter, data logger, methodological error 6.22 C product saturation temperature, Tsat Insignificant Substituting these uncertainty values and the partial derivatives in Equations 1819 into Equation 14 gives an average error in thermodynamic ratio of 0.75. 29 CHAPTER V RESULTS AND DISCUSSION The first objective of the research was to evaluate the applicability of the equation developed by Bowser et al. (2003), based on tests with water and sugar solution, to additional liquid food products. This equation stated that CWH would be avoided 90% of the time if RT > 1.5× (2.4×10 5 Pe +1.25) Equation 3 A total of 41 individual test runs were conducted during this study. For the data analysis, these results were combined with data collected from 24 tests that were conducted by Bowser, et al. (2003). Of the 65 test runs, 14 were water, 23 were sugar solution, 22 were beef stock, and 6 were corn starch slurry. It would have been desirable to have a larger number of data points over a wider range of conditions for the corn starch; however, samples were limited due to time constraints. The system parameters that could be varied for each test were the product flow rate, system pressure, initial product temperature, and product viscosity prior to heating. Table 4 shows the range of these parameters tested within this study. For each test the values of these parameters as well as the final product temperature were recorded and are provided in Appendix C. 30 Table 4: Range of parameters tested within the study Product Flow rates gpm System pressures psi Initial product temperatures °C Viscosities cP Water 0.233.80 14.035.0 13.7221.94 0.951.18 Sugar Solution 0.482.89 10.533.0 15.0043.89 7174 Beef stock 0.962.41 12.035.0 11.7533.72 3533463 Starch 0.962.17 17.032.0 35.4045.47 3121554 All products 0.233.80 10.535.0 11.7545.47 13463 The first analysis performed on the data was to determine if the system behavior with respect to CWH during each test adhered to the predictive equation of Bowser, et al. The threshold value of RT and the Peclet number were calculated for each test run (see Appendix E for calculated values). Figure 6 shows the results of tests performed using water and sugar solution, the products used in the development of the equation. 31 Thermodynamic Ratio vs. Peclet Number Tests of Water and Sugar Solution 0 1 2 3 4 0 10000 20000 30000 40000 50000 60000 Pe RT SugarOstermann WaterOstermann SugarBowser WaterBowser Bowsers Equation Figure 6: Analysis of test results for water and sugar solution compared to the predictive equation. As Figure 6 shows, the data collected for water and sugar solution in this research support the predictive equation developed by Bowser, et al. Of the combined data set, CWH occurred as predicted for 100% of the water tests and 96% of the sugar solution tests. The second analysis was to see if Bowser’s equation was equally applicable to the tests with beef stock and corn starch. The results of this analysis are shown in Figure 7 and presented in Table 5. It may be observed from Figure 7 that the data is not spread evenly across the range of Pe numbers. This was due to varying inputs of pressure, initial temperature, and flow rate randomly without designing the experiments to target specific Pe values. In addition, redundant experiments (shown in example areas A, B, and C enclosed 32 in dashed lines in Figure 7) resulted in a wider than expected range of Rt values as indicated by error bars that did not overlap. This indicated that some experimental error or other factor was present that was not accounted for in the error analysis. This error could be from many sources including the calculation of the products’ physical properties, the regulation of pressure during testing, uncalibrated sensors, or heater inefficiency due to improper cleaning. An improved approach to data collection is given in the Conclusions section. Thermodynamic Ratio vs. Peclet Number Error Bars for RT 0 1 2 3 4 5 6 7 8 9 10 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 40000 44000 48000 Pe RT Beef Starch Bowser's Equation A B C Figure 7: Comparison of results of tests of beef stock and starch to the predictive equation. 33 Table 5: Adherence to predictive equation based on product Product Test Runs Occurrences of CWH Percentage of Tests that Adhere to the Predictive Equation Water 14 0 100% Sugar Solution 23 1 96% Beef Stock 22 14 36% Starch 6 5 17% All Products 65 20 69% Because the behavior of the system when testing beef stock and starch did not appear to follow the predictive equation, data analysis was conducted for the final objective of this research: to investigate if another correlation between the physical properties of liquid food products and the temperature at which CWH occurs could be developed using common heat transfer and fluid flow dimensionless parameters. As previously stated, the parameters that were selected for examination were the Reynolds, Prandtl, Nusselt, Stanton, and the Jacob numbers. The values of these parameters for each test are provided in Appendix E, and Table 6 shows the minimum, maximum, average and standard deviation of each of the dimensionless parameters tested. Table 6: Descriptive statistics of dimensionless parameters tested. Maximum Minimum Average Standard Deviation Thermodynamic Ratio 6.54 1.24 2.72 1.22 Peclet Number 52815.79 3016.69 26479.02 11395 Prandtl Number 27037.22 6.54 5304.72 7559.97 Reynolds Number 7605.12 0.89 679.75 1444.15 Nusselt Number 17147.70 1901.84 9043.62 3878.49 Stanton Number 1.44E+07 1.69E01 9.48E+05 2.64E+06 Jacob Number 95.98 62.49 78.03 9.03 Because the purpose in developing a predictive equation is to provide operators with a simple guideline for setting the operating temperature of steam injection heaters, the first analysis that was performed for this objective was to 34 see if a relationship could be defined using only linear regression to relate the thermodynamic ratio to each of the dimensionless parameters. Figures 812 show the linear relationship between the thermodynamic ratio and each of the dimensionless parameters studied. Thermodynamic Ratio vs. Reynolds Number y = 0.0002x + 2.8231 0 1 2 3 4 5 6 7 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure 8: Linear regression of the relationship between thermodynamic ratio and Reynolds number. 35 Thermodynamic Ratio vs. Prandtl Number y = 8E05x + 2.2799 0 1 2 3 4 5 6 7 0 5000 10000 15000 20000 25000 30000 Pr RT Figure 9: Linear regression of the relationship between thermodynamic ratio and Prandtl number. Thermodynamic Ratio vs. Nusslet Number y = 0.0001x + 3.8663 0 1 2 3 4 5 6 7 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure 10: Linear regression of the relationship between thermodynamic ratio and Nusselt number. 36 Thermodynamic Ratio vs. Stanton Number y = 5E08x + 2.7674 0 1 2 3 4 5 6 7 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 St RT Figure 11: Linear regression of the relationship between thermodynamic ratio and Stanton number. Thermodynamic Ratio vs. Jacobs Number y = 0.0281x + 4.9161 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure 12: Linear regression of the relationship between thermodynamic ratio and Jacobs number. 37 As previously mentioned, the research was not properly designed to ensure a broad range of data points across all dimensionless parameters, resulting in redundant data. To reduce the influence of this redundancy, a second analysis was performed. For this investigation, all data points were grouped by RT value (based on tenths). For each group, both the RT and the dimensionless parameter values were averaged. The results of this data manipulation are shown in Table 7. These relationships were then graphed, the results of which are provided in Appendix F. Table 7: Averaged RT and dimensionless parameter values for data analysis. RT Pe Pr Re Nu St Ja 1.24 8772.17 488.55 17.93 6044.19 2.22E+02 74.75 1.36 4786.00 6.96 674.26 3000.31 3.14E+05 91.43 1.40 15706.79 7.53 2086.15 9902.69 2.74E+06 93.46 1.54 18614.43 141.36 1549.04 10892.65 2.81E+06 84.24 1.63 17773.87 56.40 1660.01 9949.28 2.27E+06 84.37 1.74 16688.95 176.39 562.95 8252.31 5.29E+05 76.83 1.92 19067.73 257.04 681.72 8577.38 5.94E+05 80.86 2.02 23549.02 4018.14 1075.07 9985.53 1.44E+06 79.62 2.12 24464.12 10832.06 62.64 9724.12 6.02E+03 76.82 2.26 37470.16 4335.44 770.57 14133.92 9.20E+05 80.00 2.36 33777.12 2050.59 317.46 11819.07 7.95E+04 71.54 2.44 29910.78 2988.80 1275.71 10711.88 2.42E+06 76.53 2.55 37190.94 86.58 429.43 13543.86 6.72E+04 76.78 2.67 38918.62 8917.68 127.46 12108.62 9.95E+03 80.52 2.99 26334.43 27037.22 0.97 7421.43 2.67E01 79.98 3.14 19404.06 10568.35 1.87 5369.20 9.82E01 72.22 3.38 23683.37 7093.64 5.09 5803.94 8.04E+00 71.02 3.42 36451.86 8945.30 37.59 9158.13 9.22E+02 74.97 3.56 25592.47 4235.09 6.04 6025.86 8.59E+00 66.70 3.60 51099.48 6.70 7605.12 12680.30 1.44E+07 90.68 3.74 49912.64 147.73 337.48 10868.05 2.48E+04 64.35 3.94 24717.58 4666.30 7.57 5361.60 1.69E+01 73.57 4.09 27815.18 15970.11 1.74 5820.41 6.34E01 74.74 4.69 25915.86 10453.41 2.48 4993.05 1.18E+00 73.12 4.82 16042.30 4419.19 3.63 2891.87 2.38E+00 75.10 5.50 23750.62 23327.16 1.02 3874.04 1.69E01 79.58 6.26 43935.66 20677.57 2.13 5733.39 5.90E01 78.72 6.48 35165.19 18991.48 1.85 4678.95 4.56E01 78.49 6.54 19442.14 10387.40 1.91 2446.76 4.50E01 79.30 38 The third step in the data analysis was to investigate if the relationship between the thermodynamic ratio and each dimensionless parameter could be better explained using a different type of curve to define the data. For each dimensionless parameter, regression equations were defined using logarithmic, exponential, and power equations for all of the tests and for the averaged values. The graphs of this analysis are included in Appendix G. The final step in the data analysis was to determine for each dimensionless parameter if a stronger relationship existed for a portion of the data than that of the entire data set. The segmentation of the data was done by visually inspecting the graphs of thermodynamic ratio verses each of the dimensionless parameters. Appendix H show the results of this analysis. For each of the analyses described above, a coefficient of correlation (r2) was determined. The r2 value describes the percentage of the data points that can be described by the regression equation and was used in drawing conclusions about the applicability of each relationship studied. Table 8 lists all of these r2 values. 39 Table 8: Coefficient of determination values for all analysis. Linear Log Exponential Power Pe 0.0906 0.1140 0.1595 0.2033 Pr 0.2620 0.3107 0.2621 0.3600 Re 0.0321 0.2587 0.0328 0.2822 Nu 0.1612 0.1782 0.1023 0.1063 St 0.0117 0.3074 0.0105 0.3342 All Tests Ja 0.0431 0.0350 0.0767 0.0657 Pe 0.1288 0.1618 0.2167 0.2785 Pr 0.4111 0.3307 0.4040 0.3915 Re 0.0395 0.5064 0.0333 0.4955 Nu 0.2954 0.3300 0.2019 0.2240 St 0.0149 0.5682 0.0099 0.5546 Averaged Tests Ja 0.0765 0.0708 0.1474 0.1402 RT<5 Pe 0.1220 0.1553 0.1910 0.2427 Pr<500 Pr 0.0099 0.0444 0.0064 0.0514 Pr>500 Pr 0.0386 0.0545 0.0271 0.0468 Re<500 Re 0.0934 0.2139 0.0941 0.2256 Re>500 Re 0.6115 0.3690 0.5539 0.3537 RT<5 Nu 0.0664 0.0596 0.0286 0.0214 St<100,000 St 0.0355 0.2575 0.0243 0.2618 St>100,000 St 0.5712 0.2643 0.5187 0.2770 Outliers Deleted RT<5 Ja 0.1138 0.1045 0.1329 0.1224 40 CHAPTER VI SUMMARY AND CONCLUSIONS Observations from Research In conducting this research, the challenges of operating a DSI heater were very apparent. It was found that Schroyer’s (1997) assertion, that a warmup period is not needed because heating begins as soon as the steam valve is opened, does not truly capture the operating conditions. Instead, to start the system, product had to be flowing through the system and the steam valve had to be opened slowly. If the steam valve was opened too rapidly, CWH occurred prematurely. This startup procedure caused a substantial amount of wasted product. However, attempting to mitigate for this waste by recycling the product was not desirable because the testing required steady state conditions, and recycling product would have caused variation in both the product inflow temperature and the product inflow viscosity during testing. In addition, recycling would not have reflected a typical production situation. A second insight received was that, because some products become less viscous during heating, the system pressure can drop drastically resulting in CWH at lower than expected temperatures. Finally, it was found that using very viscous products such as the starch was also difficult. Prior to conducting tests, it was observed that the high viscosity of the starch could cause large system pressures resulting in hose 41 blowouts upstream of the heater. These high pressures were reduced for testing by limiting the flow rate and opening the gate valve. Conclusions from Analysis of Data The first objective of this research was to determine the validity of the equation developed by Bowser, et al. (Equation 3) when applied to additional food products. This equation was developed using water and sugar solution, and it was found that for the new data points collected in this research using water and sugar solution, it adequately defined the threshold thermodynamic ratio for CWH. The results for beef stock and corn starch were inconclusive due to experimental error and insufficient data. The second objective for this research was to examine if the relationship between the physical properties of a product, the system operating conditions, and the threshold RT value could be better predicted by a different equation. Based on the coefficient of variation values shown in Table 8, the following conclusions can be made. 1. The Jacob number should not be used to develop a relationship between by which to predict safe operating conditions for a DSI system. None of the equations developed for this parameter were able to explain more than 7% of the data. 2. Power and logarithmic relationships should receive greater attention for use in defining a relationship between product physical properties, system operating conditions and the threshold thermodynamic ratio. The highest coefficient of determination for both the entire data set analysis and the 42 averaged data set analysis corresponded to one of these two relationships. The only exception being, the averaged analysis for Pr which had an r2 value 0.02 higher for the linear relationship than the power relationship. 3. Further investigation should focus on the Prandtl, Reynolds, and Stanton numbers which had the highest r2 values for both the entire data set analysis and the averaged data set analysis. In addition, the Peclet number should not be excluded from further investigation, because it is the product of the Reynolds and Prandtl numbers. 4. Based on the error analysis, the above conclusions should not be considered definitive. Not only was there an abundance of quantifiable errors, but it was also found from the results of redundant experiments that fell outside of the expected range of error, that some unknown error existed in the experimental setup and/or technique. The steps proposed in the following section should be taken to reduce model error in further research. Recommendations for Further Research In order to collect a more reliable data set and reduce the influence of errors, modifications must be made to the experimental setup and research techniques. The experimental setup should be altered and improved to allow for better accuracy in determining the temperature at which CWH occurs. One way that this can be accomplished is by using the data logger to record the system 43 pressure in addition to recording the product temperature and viscosity. This would eliminate the methodological error associated with the determination of Tf, because the first instance of 41.1 kPa (6psi) pressure fluctuation could be compared directly to the outlet temperature. In addition, all instruments should be properly calibrated immediately prior to use. Finally, equipment that monitors sound and/or vibration could be incorporated into the system setup. For this research only a quantitative criterion was used to indicate a CWH event. This criterion was pressure fluctuations of 41 kPa (6 psi), which was a lower value than the criterion of 60 kPa used by Bowser et al. (2003), because it was found that system stability was difficult to maintain up to 60 kPa. Installing sound and vibration monitors recognizes that requiring a specific value of pressure oscillation to indicate CWH may not be appropriate. It would allow qualitative indicators used by Bowser, such as shaking of system piping and gasps of collapsing steam voids, to be accounted for in a quantitative manner. The second suggested modification is to minimize the potential for unknown errors. A potential source of unknown error was the manual regulation of the system pressure during testing of beef broth in an attempt to maintain steady state operating conditions. Figure 13 shows the recorded temperature values and the impact of the reduction in system pressure due to the change in the viscous properties of beef stock during heating. The product went from a thick sticky paste to a thin watery liquid causing the system pressure to drop, by as much as 170 kPa (25 psi). System pressure drops resulted in premature occurrence of CWH, which caused blowouts of system hoses. Even though 44 every effort was made to adjust the pressure as little as possible when signs of approaching CWH were observed, any adjustment would affect the reliability of the data set. A pressure regulating valve would enable the system pressure to be maintained at a steady state. In addition, a pressure relief valve and use of rigid pipes instead of flexible hoses could help prevent blowouts. Beef Stock Test 1 0 10 20 30 40 50 60 70 80 Time (a point collected every two seconds) Temperature Product Inlet Temperature Product Outlet Temperature Figure 13: Data logger output of Ti and Tf over time showing system pressure adjustments during testing. A second potential source of unknown error was the maintenance of the heater during testing. The heater was cleaned by running water through the heater until it flowed clear. However, disassembly of the heater after the research was conducted showed that this was not a sufficient cleaning method. In future research, the apparatus should be disassembled and cleaned after each round of tests and between tests on different products. Pressure Adjustments 45 The third suggestion for future research is to develop a better understanding of how to define the characteristic length for a DSI heater. One definition of characteristic length is the hydraulic radius defined in Equation 20. P r A h = Equation 20 where A is the crosssectional flow area (m2) and P is the wetted perimeter (m). Other researchers choose to use the hydraulic diameter, calculated for two concentric pipes as shown in Equation 21. D d D d D d dh = + = 4 4 4 2 2 Equation 21 where D is the diameter of the exterior pipe (m) and d is the diameter of the interior pipe (m). The value of hydraulic radius for this heater was 0.0085 m and the hydraulic diameter was 0.034 m. While the hydraulic diameter was selected for use in this study, being able to characterize this value with certainty would allow for a better defined relationship for predicting safe operating conditions for a DSI heater. Finally, it is recommended that the research techniques be modified to collect data that will define the entire spectrum of each parameter of interest. Because this research was to serve as a general screening of dimensionless parameters, an effort was not made to tailor system operating conditions to collect data for any particular parameter. If research were to progress based on these results, boundary conditions should be established for the Re, Pr, and St numbers, and data should be collected to fill in the gaps of this research. For 46 example, more data should be collected for Reynolds numbers between 10 and 100, for Prandtl numbers between 10 and 100 as well as between 1000 and 2500, and for Stanton numbers between 10 and 500. Summary There is still much research to be done in the field of direct contact heat exchange. But, with the effort of food engineers, approaches for the safe design and use of DSI heating for liquid food products may yet be developed. 47 BIBLIOGRAPHY Alverez, E., J.M. Correa, M.M. Navaza, and C. Riverol. 2000. 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Relationship between data from capillary tube experiments and from UHT sterilizers. Journal of Food Technology. 12:149161. Doebelin, E.O. 1966. Measurement Systems: Application and Design. New York, NY: McGrawHill Book Company. Goodykoontz, J.H. and R.G. Dorsch. 1966. Local heat transfer coefficients for condensation of steam in vertical downflow within a 5/8Inch diameter tube. Lewis Research Center, National Aeronautics and Space Administration. Cleveland, OH. Hewitt, G.F., G.L. Shires, and T.R. Bott. 1994. Process Heat Transfer. Boca Raton, FL: CRC Press. 48 Hoynak, P.X. and G.N. Bollenback. 1966. This is Liquid Sugar. 2nd ed. Yonkers, N.Y.: Refined Syrups & Sugars, Inc. ICUMSA. 1979. Sugar Analysis, General Methods. ICUMSA Pub., Peterborough, UK. Incropera, F.P. and D.P. DeWitt. 1985. Fundamentals of Heat and Mass Transfer. New York, NY: John Wiley & Sons, Inc. Jones, M.C. and G.S. Larner. 1968. 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American Society of Mechanical Engineers, New York. 50 APPENDICES 51 APPENDIX A PUMP CALIBRATION CURVE 52 Pump speed (Hz) vs. Flow (gpm) 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 40 50 60 70 Pump Speed (Hz) Flow (gpm) Figure A 1: Pump calibration curve for Waukesha CherryBurrell, Delavan, WI, Model 15 positive displacement pump. 53 APPENDIX B THERMAL DIFFUSIVITY CALCULATIONS 54 For food products the physical properties at various temperatures can be determined based on the amounts of protein, fat, carbohydrate, fiber, ash, water, and ice in the product using Equation B1 and the temperature functions in Table B1. = = n i k kiXi 1 Equation B1 where n is the number of components, ki is the thermal conductivity of the ith component, and Xi is the mass fraction of the ith component (Singh and Heldman, 2001). Equation B1 is equally applicable to density, specific heat, and thermal diffusivity. Table B 1: Coefficients to estimate food physical properties (Singh and Heldman, 2001). Property Component Temperature Function k Protein k=1.7881x101 + 1.1958x103T  2.7178x106T2 Fat k=1.8071x101 – 2.7604x103T  1.7749x106T2 Carbohydrate k=2.0141x101 + 1.3874x103T  4.3312x106T2 Ash k=3.2962x101 + 1.4011x103T  2.9069x106T2 Water k=5.7109x101 + 1.7625x103T  6.7036x106T2 Protein =1.3299x103  5.1840x101T Fat =9.2559x102  4.1757x101T Carbohydrate =1.5991x103  3.1046x101T Ash =2.4238x103  2.8063x101T Water =9.9718x102 + 3.1439x103T  3.7574x103T2 cp Protein cp=2.0082 + 1.2089x103T – 1.3129x106T2 Fat =1.9842 + 1.4733x103T – 4.8008x106T2 Carbohydrate =1.5488 + 1.9625x103T – 5.9399x106T2 Ash =1.0926 + 1.8896x103T – 3.6817x106T2 Water =4.1762 – 9.0864x105T + 5.4731x106T2 55 cp k = Equation B2 (Singh and Heldman, 2001) where is thermal diffusivity (m2s1), k is thermal conductivity (Wm1C1), is density (kgm3), and cp is specific heat (kJkg1K1) Table B 2: Physical properties of the products tested. Tester Product Test Ti ºC kg/m3 m2/s cp kJ/(kgC) k W/m/C Ostermann Beef Stock 1 23.19 1198.19 1.08E07 2.8514 0.370 Ostermann Beef Stock 2 24.20 1197.85 1.08E07 2.8522 0.370 Ostermann Beef Stock 3 19.69 1199.35 1.08E07 2.8486 0.368 Ostermann Beef Stock 4 12.41 1201.58 1.07E07 2.8428 0.365 Ostermann Beef Stock 5 20.43 1199.09 1.08E07 2.8492 0.369 Ostermann Beef Stock 6 17.62 1199.99 1.08E07 2.8469 0.367 Ostermann Beef Stock 7 14.21 1201.04 1.07E07 2.8442 0.366 Ostermann Beef Stock 8 17.87 1199.91 1.08E07 2.8471 0.368 Ostermann Beef Stock 9 23.12 1198.21 1.08E07 2.8513 0.370 Ostermann Beef Stock 10 23.62 1198.05 1.08E07 2.8517 0.370 Ostermann Beef Stock 11 11.95 1201.72 1.07E07 2.8424 0.364 Ostermann Beef Stock 12 12.50 1201.56 1.07E07 2.8429 0.365 Ostermann Beef Stock 13 11.75 1201.78 1.07E07 2.8423 0.364 Ostermann Beef Stock 14 13.83 1201.16 1.07E07 2.8439 0.365 Ostermann Beef Stock 15 15.76 1200.57 1.07E07 2.8455 0.366 Ostermann Beef Stock 16 23.25 1198.17 1.08E07 2.8514 0.370 Ostermann Beef Stock 17 28.15 1196.51 1.09E07 2.8554 0.372 Ostermann Beef Stock 18 21.89 1198.62 1.08E07 2.8504 0.370 Ostermann Beef Stock 19 22.39 1198.45 1.08E07 2.8508 0.370 Ostermann Beef Stock 20 25.97 1197.26 1.09E07 2.8536 0.371 Ostermann Beef Stock 21 33.72 1194.52 1.10E07 2.8599 0.375 Ostermann Beef Stock 22 33.46 1194.62 1.10E07 2.8597 0.375 Ostermann Corn Starch 1 36.55 1039.17 1.44E07 3.9780 0.597 Ostermann Corn Starch 2 45.47 1036.44 1.47E07 3.9820 0.607 Ostermann Corn Starch 4 41.30 1037.79 1.46E07 3.9800 0.602 Ostermann Corn Starch 5 45.28 1036.51 1.47E07 3.9819 0.607 Ostermann Corn Starch 6 43.47 1037.10 1.47E07 3.9810 0.605 Ostermann Corn Starch 7 35.40 1056.90 1.44E07 3.9024 0.584 56 Table B 2: Physical properties of products tested, continued Tester Product Test Ti ºC kg/m3 m2/s cp kJ/(kgC) k W/m/C Ostermann Sugar Water 2 16.80 1302.38 1.10E07 2.8462 0.407 Ostermann Sugar Water 5 23.60 1299.61 1.12E07 2.8578 0.416 Ostermann Sugar Water 6 27.60 1295.03 1.14E07 2.8771 0.424 Ostermann Sugar Water 10 15.00 1297.98 1.09E07 2.8653 0.407 Ostermann Sugar Water 12 23.00 1292.60 1.13E07 2.8883 0.420 Ostermann Sugar Water 13 23.70 1292.43 1.13E07 2.8889 0.421 Bowser Sugar Water 1 34.17 1399.75 1.07E07 2.4235 0.364 Bowser Sugar Water 2 21.50 1390.19 1.04E07 2.4650 0.357 Bowser Sugar Water 3 43.06 1368.94 1.12E07 2.5545 0.392 Bowser Sugar Water 4 43.06 1368.94 1.12E07 2.5545 0.392 Bowser Sugar Water 5 43.06 1368.94 1.12E07 2.5545 0.392 Bowser Sugar Water 6 23.72 1366.15 1.07E07 2.5695 0.375 Bowser Sugar Water 7 23.72 1366.15 1.07E07 2.5695 0.375 Bowser Sugar Water 8 23.72 1366.15 1.07E07 2.5695 0.375 Bowser Sugar Water 9 41.56 1353.51 1.13E07 2.6213 0.401 Bowser Sugar Water 10 41.56 1353.51 1.13E07 2.6213 0.401 Bowser Sugar Water 11 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 12 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 13 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 14 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 15 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 16 26.67 1334.97 1.10E07 2.7044 0.398 Bowser Sugar Water 17 43.89 1294.85 1.18E07 2.8727 0.440 Ostermann Water 1 17.00 996.15 1.44E07 4.1762 0.599 Ostermann Water 2 16.90 996.16 1.44E07 4.1762 0.599 Ostermann Water 3 17.10 996.14 1.44E07 4.1762 0.599 Ostermann Water 5 18.31 995.98 1.45E07 4.1764 0.601 Ostermann Water 6 18.38 995.97 1.45E07 4.1764 0.601 Ostermann Water 7 17.70 996.06 1.44E07 4.1763 0.600 Ostermann Water 8 17.50 996.08 1.44E07 4.1763 0.600 Bowser Water 1 20.83 995.62 1.45E07 4.1767 0.605 Bowser Water 2 13.72 996.52 1.43E07 4.1760 0.594 Bowser Water 3 18.61 995.94 1.45E07 4.1764 0.602 Bowser Water 4 18.67 995.93 1.45E07 4.1764 0.602 Bowser Water 5 18.72 995.92 1.45E07 4.1764 0.602 Bowser Water 6 21.17 995.56 1.46E07 4.1767 0.605 Bowser Water 7 21.94 995.44 1.46E07 4.1768 0.607 57 APPENDIX C COLLECTED DATA 58 Table C1: Collected Data Tester Product Test Flow rate gpm Viscosity cP Pressure psi Ti ºC Tf ºC Tsat ºC Ostermann Beef Stock 1 1.20 1236.5 20 23.19 64.90 126.2 Ostermann Beef Stock 2 1.20 1155.3 15 24.20 72.60 121.2 Ostermann Beef Stock 3 1.44 1485.2 20 19.69 51.10 126.2 Ostermann Beef Stock 4 1.30 2995.08 25 12.41 33.90 130.6 Ostermann Beef Stock 5 1.54 2068.29 20 20.43 46.30 126.2 Ostermann Beef Stock 6 1.69 1796.45 15 17.62 65.90 121.2 Ostermann Beef Stock 7 1.93 2443.88 20 14.21 31.50 126.2 Ostermann Beef Stock 8 1.20 2110.79 15 17.87 48.30 121.2 Ostermann Beef Stock 9 1.44 1356.49 27 23.12 46.40 132.3 Ostermann Beef Stock 10 1.44 1009.65 20 23.62 66.90 126.2 Ostermann Beef Stock 11 2.17 3105.06 12 11.95 58.70 117.8 Ostermann Beef Stock 12 1.20 3163.18 14 12.50 63.10 120.1 Ostermann Beef Stock 13 1.44 3462.53 17 11.75 49.00 123.3 Ostermann Beef Stock 14 2.41 2653.86 14 13.83 30.80 120.1 Ostermann Beef Stock 15 1.69 2270.15 16 15.76 55.80 122.2 Ostermann Beef Stock 16 1.20 1636.46 19 23.25 55.40 125.2 Ostermann Beef Stock 17 1.44 1109.64 20 28.15 53.30 126.2 Ostermann Beef Stock 18 1.93 1300.25 35 21.89 56.10 138.3 Ostermann Beef Stock 19 1.69 1327.74 17 22.39 72.80 123.3 Ostermann Beef Stock 20 0.96 1108.39 27 25.97 60.11 132.3 Ostermann Beef Stock 21 1.44 555.32 20 33.72 59.70 126.2 Ostermann Beef Stock 22 1.20 352.84 15 33.46 59.50 121.2 Ostermann Corn Starch 1 2.17 312.22 20 36.55 59.00 126 Ostermann Corn Starch 2 1.44 518.45 30 45.47 68.00 134.5 Ostermann Corn Starch 4 1.20 668.43 25 41.30 59.80 130.4 Ostermann Corn Starch 5 1.20 706.55 32 45.28 87.80 136 Ostermann Corn Starch 6 0.96 775.92 20 43.47 77.70 126 Ostermann Corn Starch 7 1.44 1554.49 17 35.40 48.80 123.1 59 Table C1: Collected Data, continued Tester Product Test Flow rate gpm Viscosity cP Pressure psi Ti ºC Tf ºC Tsat ºC Ostermann Sugar 2 2.65 26.58 14.80 16.80 56.30 122.76 Ostermann Sugar 5 1.69 17.55 17.60 23.60 72.30 125.64 Ostermann Sugar 6 2.17 12.76 29.30 27.60 70.00 135.84 Ostermann Sugar 10 1.69 24.20 19.40 15.00 62.50 127.34 Ostermann Sugar 12 1.93 14.12 28.20 23.00 68.70 134.92 Ostermann Sugar 13 1.93 13.59 22.90 23.70 71.30 130.49 Bowser Sugar 1 1.44 141.20 10.50 34.17 77.22 120.39 Bowser Sugar 2 2.17 173.90 29.50 21.50 73.22 138.28 Bowser Sugar 3 1.44 31.40 33.00 43.06 103.90 140.39 Bowser Sugar 4 2.17 31.40 22.00 43.06 79.44 131.52 Bowser Sugar 5 2.17 31.40 10.50 43.06 75.00 119.54 Bowser Sugar 6 2.89 71.30 13.00 23.72 52.22 122.22 Bowser Sugar 7 0.96 71.30 18.00 23.72 77.22 127.50 Bowser Sugar 8 0.48 71.30 17.00 23.72 106.70 126.50 Bowser Sugar 9 2.89 22.60 15.90 41.56 63.89 125.15 Bowser Sugar 10 1.20 22.60 23.00 41.56 92.22 131.94 Bowser Sugar 11 0.57 40.30 11.80 24.89 80.56 120.34 Bowser Sugar 12 0.82 40.30 17.80 24.89 91.11 126.80 Bowser Sugar 13 1.20 40.30 16.00 24.89 82.78 124.97 Bowser Sugar 14 1.44 40.30 16.00 24.89 76.67 124.97 Bowser Sugar 15 1.93 40.30 16.00 24.89 69.44 124.97 Bowser Sugar 16 2.51 27.70 13.20 26.67 68.33 121.66 Bowser Sugar 17 2.51 7.00 19.00 43.89 80.00 127.00 Ostermann Water 1 1.91 1.08 35.00 17.00 77.30 138.12 Ostermann Water 2 3.25 1.08 21.40 16.90 61.70 127.28 Ostermann Water 3 1.16 1.08 23.00 17.10 97.10 128.71 Ostermann Water 5 1.03 1.04 29.00 18.31 73.50 133.68 Ostermann Water 6 1.03 1.04 29.50 18.38 79.20 134.07 Ostermann Water 7 0.48 1.06 20.20 17.70 96.80 126.17 Ostermann Water 8 1.66 1.06 32.00 17.50 94.10 135.96 Bowser Water 1 3.80 0.97 26.00 20.83 51.50 131.27 Bowser Water 2 2.35 1.18 14.00 13.72 61.11 119.89 Bowser Water 3 1.06 1.03 28.00 18.61 84.72 132.89 Bowser Water 4 1.15 1.03 24.00 18.67 87.89 129.58 Bowser Water 5 1.80 1.03 23.00 18.72 83.89 128.71 Bowser Water 6 0.48 0.97 26.00 21.17 88.89 131.27 Bowser Water 7 0.23 0.95 20.00 21.94 98.89 125.98 60 APPENDIX D CALCULATION OF METHODOLOGICAL ERROR ASSOCIATED WITH THE FINAL TEMPERATURE 61 The error associated with selecting the Tf value used in calculations was based on the range of temperature values in the oscillations surrounding the selected final temperature. An example of this range is shown in Figure D1 for test 12 of beef stock. Table D1 shows the range of Tf values for tests using beef stock and corn starch, with the average range being 5 °C. This average was assumed to be the methodological error for Tf. Beef Stock Test 12 50 55 60 65 70 75 Time (point collected every 2 seconds) Temperature (C) Product Inlet Temperature Product Outlet Temperature High Value of Range 70 °C Low Value of Range Observed Tf Figure D1: Example of methodological error in final temperature determination 62 Table D1: Variation in final temperature values Product Test Tf ºC Low High Difference Between Low and High Beef Stock 1 64.90 63.10 67.60 4.5 Beef Stock 2 72.60 71.90 75.20 3.3 Beef Stock 3 51.10 50.00 52.40 2.4 Beef Stock 4 33.90 33.30 34.60 1.3 Beef Stock 5 46.30 44.90 48.00 3.1 Beef Stock 6 65.90 63.90 67.20 3.3 Beef Stock 7 31.50 27.90 38.06 10.2 Beef Stock 8 48.30 NA NA 0.0 Beef Stock 9 46.40 43.80 46.40 2.6 Beef Stock 10 66.90 65.40 71.30 5.9 Beef Stock 11 58.70 56.10 65.40 9.3 Beef Stock 12 63.10 59.00 71.10 12.1 Beef Stock 13 49.00 NA NA 0.0 Beef Stock 14 30.80 27.00 37.00 10.0 Beef Stock 15 55.80 NA NA 0.0 Beef Stock 16 55.40 NA NA 0.0 Beef Stock 17 53.30 50.30 60.70 10.4 Beef Stock 18 56.10 54.50 57.40 2.9 Beef Stock 19 72.80 NA NA 0.0 Beef Stock 20 60.11 58.80 60.11 1.3 Beef Stock 21 59.70 58.20 60.70 2.5 Beef Stock 22 59.50 NA NA 0.0 Corn Starch 1 59.00 49.00 64.00 15.0 Corn Starch 2 68.00 66.40 73.10 6.7 Corn Starch 4 59.80 58.30 66.90 8.6 Corn Starch 5 87.80 84.30 94.40 10.1 Corn Starch 6 77.70 73.10 81.40 8.3 Corn Starch 7 48.80 45.70 54.70 9.0 63 APPENDIX E TABULAR RESULTS OF THE CALCULATION OF DIMENTIONLESS PARAMETERS 64 Table E1: Calculated Dimensionless Parameters Tester Product Test RT Pe Pr Re Nu St Ja Ostermann Beef Stock 1 2.47 21594 9529.07 2.27 7459 1.77 73.08 Ostermann Beef Stock 2 2.00 21567 8905.80 2.43 8729 2.38 72.46 Ostermann Beef Stock 3 3.39 26034 11496.58 2.27 6587 1.30 75.19 Ostermann Beef Stock 4 5.50 23751 23327.16 1.02 3874 0.17 79.58 Ostermann Beef Stock 5 4.09 27815 15970.11 1.74 5820 0.63 74.74 Ostermann Beef Stock 6 2.15 30641 13935.46 2.20 11718 1.85 76.44 Ostermann Beef Stock 7 6.48 35165 18991.48 1.85 4679 0.46 78.49 Ostermann Beef Stock 8 3.40 21750 16330.52 1.33 5240 0.43 76.29 Ostermann Beef Stock 9 4.69 25916 10453.41 2.48 4993 1.18 73.12 Ostermann Beef Stock 10 2.37 25899 7781.67 3.33 9321 3.99 72.81 Ostermann Beef Stock 11 2.26 39674 24246.77 1.64 14057 0.95 79.86 Ostermann Beef Stock 12 2.13 21920 24637.27 0.89 8426 0.30 79.53 Ostermann Beef Stock 13 2.99 26334 27037.22 0.97 7421 0.27 79.98 Ostermann Beef Stock 14 6.26 43936 20677.57 2.13 5733 0.59 78.72 Ostermann Beef Stock 15 2.66 30723 17649.49 1.74 9603 0.95 77.56 Ostermann Beef Stock 16 3.17 21593 12611.36 1.71 5752 0.78 73.04 Ostermann Beef Stock 17 3.90 25755 8517.38 3.03 5598 1.99 70.07 Ostermann Beef Stock 18 3.40 34790 10016.84 3.47 9735 3.37 73.86 Ostermann Beef Stock 19 2.00 30444 10230.06 2.97 12613 3.67 73.56 Ostermann Beef Stock 20 3.11 17215 8525.34 2.02 4986 1.18 71.39 Ostermann Beef Stock 21 3.56 25592 4235.09 6.04 6026 8.59 66.70 Ostermann Beef Stock 22 3.37 21333 2690.71 7.92 5021 14.78 66.86 Ostermann Corn Starch 1 3.98 29317 2080.42 14.08 6121 41.44 78.64 Ostermann Corn Starch 2 3.95 19081 3401.10 5.61 4365 7.20 71.99 Ostermann Corn Starch 4 4.82 16042 4419.19 3.63 2892 2.38 75.10 Ostermann Corn Starch 5 2.13 15907 4634.94 3.43 6852 5.07 72.14 Ostermann Corn Starch 6 2.41 12774 5105.68 2.50 4350 2.13 73.48 Ostermann Corn Starch 7 6.54 19442 10387.40 1.91 2447 0.45 79.30 65 Table E1: Calculated Dimensionless Numbers, continued Tester Product Test RT Pe Pr Re Nu St Ja Ostermann Sugar Water 2 2.68 47115 185.88 253.18 14614 19905 83.48 Ostermann Sugar Water 5 2.10 29388 120.56 244.02 11900 24085 79.17 Ostermann Sugar Water 6 2.55 37191 86.58 429.43 13544 67173 76.78 Ostermann Sugar Water 10 2.36 30110 170.37 176.74 11088 11502 84.94 Ostermann Sugar Water 12 2.45 33436 97.10 344.50 12634 44824 79.98 Ostermann Sugar Water 13 2.24 33366 93.25 357.89 13206 50680 79.52 Bowser Sugar Water 1 2.00 26141 940.10 27.83 10257 304 65.96 Bowser Sugar Water 2 2.26 40636 1200.74 33.82 17148 483 74.32 Bowser Sugar Water 3 1.60 25047 204.62 122.41 15097 9032 62.49 Bowser Sugar Water 4 2.43 37745 204.62 184.47 13604 12264 62.49 Bowser Sugar Water 5 2.39 37745 204.62 184.47 11944 10767 62.49 Bowser Sugar Water 6 3.46 52816 488.55 107.97 12499 2762 74.75 Bowser Sugar Water 7 1.94 17544 488.55 35.87 7794 572 74.75 Bowser Sugar Water 8 1.24 8772 488.55 17.93 6044 222 74.75 Bowser Sugar Water 9 3.74 49913 147.73 337.48 10868 24827 64.35 Bowser Sugar Water 10 1.78 20725 147.73 140.13 10238 9711 64.35 Bowser Sugar Water 11 1.71 10238 275.34 37.16 4782 645 75.32 Bowser Sugar Water 12 1.54 14729 275.34 53.46 8183 1589 75.32 Bowser Sugar Water 13 1.73 21554 275.34 78.23 10468 2974 75.32 Bowser Sugar Water 14 1.93 25865 275.34 93.87 11236 3831 75.32 Bowser Sugar Water 15 2.25 34667 275.34 125.82 12957 5921 75.32 Bowser Sugar Water 16 2.28 44446 188.22 235.87 15763 19753 75.00 Bowser Sugar Water 17 2.30 41355 45.70 905.31 14924 295626 65.93 66 Table E1: Calculated Dimensionless Numbers, continued Tester Product Test RT Pe Pr Re Nu St Ja Ostermann Water 1 2.01 25799 7.53 3426.67 12251 5575180 93.54 Ostermann Water 2 2.46 44005 7.53 5844.80 15512 12041250 93.61 Ostermann Water 3 1.40 15707 7.53 2086.15 9903 2743604 93.46 Ostermann Water 5 2.09 13794 7.23 1915.43 6078 1610982 92.56 Ostermann Water 6 1.90 13794 7.23 1915.41 6702 1776274 92.51 Ostermann Water 7 1.37 6555 7.38 887.02 4099 492770 93.02 Ostermann Water 8 1.55 22500 7.38 3044.63 13603 5613169 93.17 Bowser Water 1 3.60 51099 6.70 7605.12 12680 14400782 90.68 Bowser Water 2 2.24 32032 8.30 3868.36 11673 5443280 95.98 Bowser Water 3 1.73 14238 7.15 1996.28 7521 2101146 92.34 Bowser Water 4 1.60 15464 7.15 2168.15 8557 2596328 92.30 Bowser Water 5 1.69 24205 7.15 3393.60 12614 5990632 92.25 Bowser Water 6 1.63 6379 6.70 955.88 3529 503758 90.43 Bowser Water 7 1.35 3017 6.54 461.50 1902 134267 89.85 67 APPENDIX F RESULTS OF LINEAR REGRESSION FOR GROUPED AND AVERAGED DATA VALUES 68 Thermodynamic Ratio vs. Reynolds Number For Averaged Values y = 0.0002x + 3.3631 0 1 2 3 4 5 6 7 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure F1: Linear regression of the relationship between averaged thermodynamic ratio and averaged Reynolds number. Thermodynamic Ratio vs. Prandtl Number For Averaged Values y = 0.0001x + 2.3252 0 1 2 3 4 5 6 7 0 5000 10000 15000 20000 25000 30000 Pr RT Figure F2: Linear regression of the relationship between averaged thermodynamic ratio and averaged Prandtl number. 69 Thermodynamic Ratio vs. Nusslet Number For Averaged Values y = 0.0003x + 5.2366 0 1 2 3 4 5 6 7 0 2000 4000 6000 8000 10000 12000 14000 16000 Nu RT Figure F3: Linear regression of the relationship between averaged thermodynamic ratio and averaged Nusselt number. Thermodynamic Ratio vs. Stanton Number For Averaged Values y = 7E08x + 3.2903 0 1 2 3 4 5 6 7 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 St RT Figure F4: Linear regression of the relationship between averaged thermodynamic ratio and averaged Stanton number 70 Thermodynamic Ratio vs. Jacobs Number For Averaged Values y = 0.0656x + 8.3305 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure F5: Linear regression of the relationship between averaged thermodynamic ratio and averaged Jacobs number 71 APPENDIX G RESULTS OF REGRESSION ANALYSIS USING LOGRITHMIC, EXPONENTIAL, AND POWER RELATIONSHIPS 72 Thermodynamic Ratio vs. Peclet Number Logarithmic y = 0.7811Ln(x)  5.1462 0 1 2 3 4 5 6 7 1000 10000 100000 Pe RT Figure G 1 Thermodynamic Ratio vs. Peclet Number Exponential y = 1.736e1E05x 1 10 0 10000 20000 30000 40000 50000 60000 Pe RT Figure G 1 73 Thermodynamic Ratio vs. Peclet Number Power y = 0.085x0.336 1 10 1000 10000 100000 Pe RT Figure G 2 Thermodynamic Ratio vs. Reynolds Number Logarithmic y = 0.22Ln(x) + 3.5496 0 1 2 3 4 5 6 7 0 1 10 100 1000 10000 Re RT Figure G 3 74 Thermodynamic Ratio vs. Reynolds Number Exponential y = 2.5904e5E05x 1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure G 4 Thermodynamic Ratio vs. Reynolds Number Power y = 3.3112x0.074 1 10 0 1 10 100 1000 10000 Re RT Figure G 5 75 Thermodynamic Ratio vs. Prandtl Number Logarithmic y = 0.235Ln(x) + 1.2394 0 1 2 3 4 5 6 7 1 10 100 1000 10000 100000 Pr RT Figure G 6 Thermodynamic Ratio vs. Prandtl Number Exponential y = 2.1739e3E05x 1 10 0 5000 10000 15000 20000 25000 30000 Pr RT Figure G 7 76 Thermodynamic Ratio vs. Prandtl Number Power y = 1.4994x0.0815 1 10 1 10 100 1000 10000 100000 Pr RT Figure G 8 Thermodynamic Ratio vs. Nusslet Number Logarithmic y = 1.0373Ln(x) + 12.056 0 1 2 3 4 5 6 7 1000 10000 100000 Nu RT Figure G 9 77 Thermodynamic Ratio vs. Nusslet Number Exponential y = 3.3612e3E05x 1 10 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure G 10 Thermodynamic Ratio vs. Nusslet Number Power y = 25.545x0.258 1 10 1000 10000 100000 Nu RT Figure G 11 78 Thermodynamic Ratio vs. Stanton Number Logarithmic y = 0.1151Ln(x) + 3.4651 0 1 2 3 4 5 6 7 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 12 Thermodynamic Ratio vs. Stanton Number Exponential y = 2.5414e2E08x 1 10 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure G 13 79 Thermodynamic Ratio vs. Stanton Number Power y = 3.2171x0.0387 1 10 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 14 Thermodynamic Ratio vs. Jacobs Number Logarithmic y = 2.0034Ln(x) + 11.436 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure G 15 80 Thermodynamic Ratio vs. Jacobs Number Exponential y = 6.4374e0.0121x 1 10 55 65 75 85 95 105 Ja RT Figure G 16 Thermodynamic Ratio vs. Jacobs Number Power y = 116.88x0.8833 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure G 17 81 Thermodynamic Ratio vs. Peclet Number For Averaged Values Logarithmic y = 1.2559Ln(x)  9.4537 0 1 2 3 4 5 6 7 1000 10000 100000 Pe RT Figure G 18 Thermodynamic Ratio vs. Peclet Number For Averaged Values Exponential y = 1.6791e2E05x 1 10 0 10000 20000 30000 40000 50000 60000 Pe RT Figure G 19 82 Thermodynamic Ratio vs. Peclet Number For Averaged Values Power y = 0.0164x0.512 1 10 1000 10000 100000 Pe RT Figure G 20 Thermodynamic Ratio vs. Reynolds Number For Averaged Values Logarithmic y = 0.382Ln(x) + 4.7425 0 1 2 3 4 5 6 7 0.1 1 10 100 1000 10000 Re RT Figure G 21 83 Thermodynamic Ratio vs. Reynolds Number For Averaged Values Exponential y = 2.9983e6E05x 1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure G 22 Thermodynamic Ratio vs. Reynolds Number For Averaged Values Power y = 4.596x0.1174 1 10 0.1 1 10 100 1000 10000 Re RT Figure G 23 84 Thermodynamic Ratio vs. Prandtl Number For Averaged Values Logarithmic y = 0.3448Ln(x) + 0.694 0 1 2 3 4 5 6 7 1 10 100 1000 10000 100000 Pr RT Figure G 24 Thermodynamic Ratio vs. Prandtl Number For Averaged Values Exponential y = 2.1849e4E05x 1 10 0 5000 10000 15000 20000 25000 30000 Pr RT Figure G 25 85 Thermodynamic Ratio vs. Prandtl Number For Averaged Values Power y = 1.2251x0.1166 1 10 1 10 100 1000 10000 100000 Pr RT Figure G 26 Thermodynamic Ratio vs. Nusslet Number For Averaged Values Logarithmic y = 1.8559Ln(x) + 19.71 0 1 2 3 4 5 6 7 1000 10000 100000 Nu RT Figure G 27 86 Thermodynamic Ratio vs. Nusslet Number For Averaged Values Exponential y = 4.8327e6E05x 1 10 0 2000 4000 6000 8000 10000 12000 14000 16000 Nu RT Figure G 28 Thermodynamic Ratio vs. Nusslet Number For Averaged Values Power y = 196.13x0.4751 1 10 1000 10000 100000 Nu RT Figure G 29 87 Thermodynamic Ratio vs. Stanton Number For Averaged Values Logarithmic y = 0.1821Ln(x) + 4.5253 0 1 2 3 4 5 6 7 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 30 Thermodynamic Ratio vs. Stanton Number For Averaged Values Exponential y = 2.9303e2E08x 1 10 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure G 31 88 Thermodynamic Ratio vs. Stanton Number For Averaged Values Power y = 4.297x0.0559 1 10 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 32 Thermodynamic Ratio vs. Jacobs Number For Averaged Values Logarithmic y = 4.9669Ln(x) + 24.84 0 1 2 3 4 5 6 7 10 100 Ja RT Figure G 33 89 Thermodynamic Ratio vs. Jacobs Number For Averaged Values Exponential y = 26.083e0.0283x 1 10 55 65 75 85 95 105 Ja RT Figure G 34 Thermodynamic Ratio vs. Jacobs Number For Averaged Values Power y = 36751x2.1721 1 10 10 100 Ja RT Figure G 35 90 APPENDIX H RESULTS OF REGRESSION ANALYSIS FOR PORTIONS OF DATA SET 91 Thermodynamic Ratio vs. Peclet Number Rt<5 Linear y = 3E05x + 1.8076 0 1 2 3 4 5 6 0 10000 20000 30000 40000 50000 60000 Pe RT Figure H 2 Thermodynamic Ratio vs. Peclet Number Rt<5 Logarithmic y = 0.6263Ln(x)  3.8069 0 1 2 3 4 5 6 1000 10000 100000 Pe RT Figure H 3 92 Thermodynamic Ratio vs. Peclet Number Rt<5 Exponential y = 1.6992e1E05x 1 10 0 10000 20000 30000 40000 50000 60000 Pe RT Figure H 4 Thermodynamic Ratio vs. Peclet Number Rt<5 Power y = 0.1148x0.3006 1 10 1000 10000 100000 Pe RT Figure H 5 93 Thermodynamic Ratio vs. Prandtl Number Pr<500 Linear y = 0.0004x + 2.0387 0 1 1 2 2 3 3 4 4 0 100 200 300 400 500 600 Pr RT Figure H 6 Thermodynamic Ratio vs. Prandtl Number Pr<500 Logarithmic y = 0.0752Ln(x) + 1.7984 0 1 1 2 2 3 3 4 4 1 10 100 1000 Pr RT Figure H 7 94 Thermodynamic Ratio vs. Prandtl Number Pr<500 Exponential y = 1.9789e0.0001x 1 10 0 100 200 300 400 500 600 Pr RT Figure H 8 Thermodynamic Ratio vs. Prandtl Number Pr<500 Power y = 1.7508x0.0362 1 10 1 10 100 1000 Pr RT Figure H 9 95 Thermodynamic Ratio vs. Prandtl Number Pr>500 Linear y = 4E05x + 3.0435 0 1 2 3 4 5 6 7 0 5000 10000 15000 20000 25000 30000 Pr RT Figure H 10 Thermodynamic Ratio vs. Prandtl Number Pr>500 Logarithmic y = 0.3624Ln(x) + 0.1705 0 1 2 3 4 5 6 7 100 1000 10000 100000 Pr RT Figure H 11 96 Thermodynamic Ratio vs. Prandtl Number Pr>500 Exponential y = 2.9378e8E06x 1 10 0 5000 10000 15000 20000 25000 30000 Pr RT Figure H 12 Thermodynamic Ratio vs. Prandtl Number Pr>500 Power y = 1.4162x0.0908 1 10 100 1000 10000 100000 Pr RT Figure H 13 97 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Linear y = 0.0031x + 3.1813 0 1 2 3 4 5 6 7 0 50 100 150 200 250 300 350 400 450 500 Re RT Figure H 14 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Logarithmic y = 0.2795Ln(x) + 3.674 0 1 2 3 4 5 6 7 0 1 10 100 1000 Re RT Figure H 15 98 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Exponential y = 2.9227e0.001x 1 10 0 50 100 150 200 250 300 350 400 450 500 Re RT Figure H 16 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Power y = 3.4218x0.0884 1 10 0 1 10 100 1000 Re RT Figure H 17 99 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Linear y = 0.0002x + 1.295 0 1 2 3 4 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure H 18 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Logarithmic y = 0.5364Ln(x)  2.1945 0 1 2 3 4 100 1000 10000 Re RT Figure H 19 100 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Exponential y = 1.4292e0.0001x 1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure H 20 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Power y = 0.3078x0.2348 1 10 100 1000 10000 Re RT Figure H 21 101 Thermodynamic Ratio vs. Nusselt Number Rt<5 Linear y = 6E05x + 3.0375 0 1 2 3 4 5 6 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure H 22 Thermodynamic Ratio vs. Nusselt Number Rt<5 Logarithmic y = 0.4422Ln(x) + 6.4925 0 1 2 3 4 5 6 1000 10000 100000 Nu RT Figure H 23 102 Thermodynamic Ratio vs. Nusselt Number Rt<5 Exponential y = 2.7087e1E05x 1 10 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure H 24 Thermodynamic Ratio vs. Nusselt Number Rt<5 Power y = 5.9287x0.1018 1 10 1000 10000 100000 Nu RT Figure H 25 103 Thermodynamic Ratio vs. Stanton Number St<100,000 Linear y = 2E05x + 3.068 0 1 2 3 4 5 6 7 0 10000 20000 30000 40000 50000 60000 70000 80000 St RT Figure H 26 Thermodynamic Ratio vs. Stanton Number St<100,000 Logarithmic y = 0.1485Ln(x) + 3.5582 0 1 2 3 4 5 6 7 0 1 10 100 1000 10000 100000 St RT Figure H 27 104 Thermodynamic Ratio vs. Stanton Number St<100,000 Exponential y = 2.8153e4E06x 1 10 0 10000 20000 30000 40000 50000 60000 70000 80000 St RT Figure H 28 Thermodynamic Ratio vs. Stanton Number St<100,000 Power y = 3.2898x0.0453 1 10 0 1 10 100 1000 10000 100000 St RT Figure H 29 105 Thermodynamic Ratio vs. Stanton Number St>100,000 Linear y = 1E07x + 1.5072 0 1 2 3 4 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure H 30 Thermodynamic Ratio vs. Stanton Number St>100,000 Logarithmic y = 0.2173Ln(x)  1.2367 0 1 2 3 4 1.E+05 1.E+06 1.E+07 1.E+08 St RT Figure H 31 106 Thermodynamic Ratio vs. Stanton Number St>100,000 Exponential y = 1.55e4E08x 1 10 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure H 32 Thermodynamic Ratio vs. Stanton Number St>100,000 Power y = 0.4248x0.1014 1 10 1.E+05 1.E+06 1.E+07 1.E+08 St RT Figure H 33 107 Thermodynamic Ratio vs. Jacob Number Rt<5 Linear y = 0.0309x + 4.9025 0 1 2 3 4 5 6 50 55 60 65 70 75 80 85 90 95 100 Ja RT Figure H 34 Thermodynamic Ratio vs. Jacob Number Rt<5 Logarithmic y = 2.3403Ln(x) + 12.671 0 1 2 3 4 5 6 10 100 Ja RT Figure H 35 108 Thermodynamic Ratio vs. Jacob Number Rt<5 Exponential y = 6.4189e0.0128x 1 10 50 55 60 65 70 75 80 85 90 95 100 Ja RT Figure H 36 Thermodynamic Ratio vs. Jacob Number Rt<5 Power y = 161.99x0.9722 1 10 10 100 Ja RT Figure H 37 VITA Rebecca Ann Ostermann Candidate for the Degree of Master of Science Thesis: DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS Major Field: Biosystems Engineering Biographical: Personal Data: Born in Colorado Springs, Colorado on May 16, 1977 the daughter of Tom and Jeanne Ostermann. Education: Graduated from Poudre High School, Fort Collins, Colorado in April, 1995; received a Bachelor of Science degree in Biosystems Engineering from Oklahoma State University, Stillwater, Oklahoma in May, 2000. Completed the requirements for the Master of Science degree with a major in Biosystems Engineering from Oklahoma State University in December, 2005. Professional Experience: Water Resource Engineer, CH2M Hill, Inc. September 2004Present Professional Memberships: American Society of Agricultural and Biological Engineers Name: Rebecca Ann Ostermann Date of Degree: December, 2005 Institution: Oklahoma State University Location: Stillwater, Oklahoma Title of Study: DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS Pages in Study: 108 Candidate for the Degree of Master of Science Major Field: Biosystems Engineering Scope and Method of Study: The purpose of this research was to investigate a correlation between flow characteristics and physical properties of liquid food products and the occurrence of condensationinduced water hammer in direct steam injection heating. A linear relationship developed by Bowser et al. (2003) between the thermodynamic ratio and the Peclet number was examined for applicability to results from tests performed using water, sugar solution, beef bone stock, and corn starch. Five other dimensionless parameters were screened for potential relationships to the thermodynamic ratio that could be used to define safe operating conditions for a steam injection heater. Findings and Conclusions: It was verified that a linear relationship between the thermodynamic ratio and the Peclet number for predicting CWH applied well to water and sugar water. Results for other food products tested in this study were inconclusive. Of the six dimensionless parameters investigated, four, the Prandlt, Reynolds, Peclet, and Stanton numbers, merited further investigation. It was also found that power and logarithmic equations may better describe a relationship to predict condensationinduced water hammer than a linear equation. ADVISER’S APPROVAL: Dr. Timothy Bowser
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Title  Direct Steam Injection Heating of Liquid Food Products 
Date  20051201 
Author  Ostermann, Rebecca 
Department  Biosystems & Agricultural Engineering 
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Full Text Type  Open Access 
Abstract  The purpose of this research was to investigate a correlation between flow characteristics and physical properties of liquid food products and the occurrence of condensationinduced water hammer in direct steam injection heating. A linear relationship developed by Bowser et al. (2003) between the thermodynamic ratio and the Peclet number was examined for applicability to results from tests performed using water, sugar solution, beef bone stock, and corn starch. Five other dimensionless parameters were screened for potential relationships to the thermodynamic ratio that could be used to define safe operating conditions for a steam injection heater. It was verified that a linear relationship between the thermodynamic ratio and the Peclet number for predicting CWH applied well to water and sugar water. Results for other food products tested in this study were inconclusive. Of the six dimensionless parameters investigated, four, the Prandlt, Reynolds, Peclet, and Stanton numbers, merited further investigation. It was also found that power and logarithmic equations may better describe a relationship to predict condensationinduced water hammer than a linear equation. 
Note  Thesis 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS REBECCA ANN OSTERMANN Bachelor of Science Oklahoma State University Stillwater, Oklahoma 2000 Submitted to the Faculty of the Graduate College of Oklahoma State University in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE December, 2005 ii DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS Thesis Approved: Dr. Timothy Bowser Thesis Advisor Dr. William McGlynn Dr. Paul Weckler Dr. A. Gordon Emslie Dean of the Graduate College iii TABLE OF CONTENTS Page List of Tables ........................................................................................................ v List of Figures.......................................................................................................vi List of Nomenclature........................................................................................... viii Acknowledgements .............................................................................................. x I. Introduction................................................................................................ 1 II. Literature Review....................................................................................... 3 Thermal processing of liquid food products..................................... 3 Direct steam injection heating ......................................................... 4 Condensationinduced water hammer ............................................ 9 Objectives of research .................................................................. 11 III. Research Methodology............................................................................ 12 Products tested ............................................................................. 12 Experimental setup ....................................................................... 13 Data Collection.............................................................................. 14 Testing procedures ....................................................................... 17 IV. Error Analysis .......................................................................................... 24 Instrumental error.......................................................................... 24 Methodological error ..................................................................... 25 Model error.................................................................................... 26 V. Results and Discussion............................................................................ 29 VI. Summary and Conclusions...................................................................... 40 Observations from research.......................................................... 40 Conclusions from analysis of data................................................. 41 Recommendations for further research......................................... 42 Summary....................................................................................... 46 Bibliography .................................................................................................. 47 iv Appendices Appendix A: Pump calibration curve ............................................. 51 Appendix B: Thermal diffusivity calculations ................................. 53 Appendix C: Collected data........................................................... 57 Appendix D: Calculation of methodological error associated with the final temperature ........................................ 60 Appendix E: Tabular results of the calculation of dimensionless parameters .............................................................. 63 Appendix F: Results of linear regression for grouped and averaged data .................................................... 67 Appendix G: Results of regression analysis using logarithmic, exponential, and power relationships....................... 71 Appendix H: Results of regression analysis for portions of data set................................................................ 90 Vita Abstract v LIST OF TABLES Table Number Table Title Page Table 1 Constants for use in determining the saturation temperature of water 16 Table 2 Measurement error 25 Table 3 Contributions to model uncertainty 28 Table 4 Range of parameters tested within the study 30 Table 5 Adherence to the predictive equation based on product 33 Table 6 Descriptive statistics of dimensionless parameters tested 33 Table 7 Averaged RT and dimensionless parameter values for data analysis 37 Table 8 Coefficient of determination values for all analyses 39 Table B1 Coefficients to estimate food physical properties 54 Table B2 Physical properties of the products tested 55 Table C1 Collected data 58 Table D1 Variation in final temperature values 62 Table E1 Calculated dimensionless numbers 64 vi LIST OF FIGURES Figure Number Figure Title Page Figure 1 Single orifice venturi direct steam injector 5 Figure 2 Pilot scale steam injection heater 6 Figure 3 Disassembled view of the multiorifice steam injector heater body used in this study 6 Figure 4 Experimental setup 14 Figure 5 Example of determination of Tf based on temperatures recorded by the data logger 20 Figure 6 Analysis of test results for water and sugar solution compared to the predictive equation 31 Figure 7 Comparison of results of tests of beef stock and starch to the predictive equation. 32 Figure 8 Linear regression of the relationship between Thermodynamic Ratio and Reynolds Number 34 Figure 9 Linear regression of the relationship between Thermodynamic Ratio and Prandtl Number 35 Figure 10 Linear regression of the relationship between Thermodynamic Ratio and Nusselt Number 35 Figure 11 Linear regression of the relationship between Thermodynamic Ratio and Stanton Number 36 Figure 12 Linear regression of the relationship between Thermodynamic Ratio and Jacobs Number 36 Figure 13 Data logger output of Ti and Tf over time showing system pressure adjustments during testing 44 Figure A1 Pump calibration curve for Waukesha Cherry Burrell, Delavan, WI, Model 15 positive displacement pump 52 Figure D1 Example of methodological error in final temperature determination 61 Figure F1 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Reynolds Number 68 Figure F2 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Prandtl Number 68 Figure F3 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Nusselt Number 69 vii Figure Number Figure Title Page Figure F4 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Stanton Number 69 Figure F5 Linear regression of the relationship between averaged Thermodynamic Ratio and averaged Jacobs Number 70 Figures G136 Regression analysis using logarithmic, exponential, and power relationships 71 Figures H136 Regression analysis for portions of data set 90 viii LIST OF NOMENCLATURE A0A8 Psychometric Constants A Cross Sectional Flow Area, m2 cP Specific Heat, kJkg1C1 CWH Condensation Induced Water Hammer d Diameter of Interior Concentric Pipe, m D Diameter of Exterior Concentric Pipe, m dc Characteristic Dimension, m dh Hydraulic Diameter, m DSI Direct Steam Injection E Error FAPC Food and Agricultural Products Center h Convective Heat Transfer Coefficient, Wm2C1 hLG Enthalpy of Evaporation, Ja Jacob Number k Thermal Conductivity, Wm1C1 L Characteristic Length of Flow Geometry, m N Model Output n Number of Components to be Summed Nu Nusselt Number P Wetted Perimeter, m Pe Peclet Number Pr Prandtl Number Ps System Operating Pressure, psi q Heat Flux, Btuhr1ft2 R2 Coefficient of Determination Re Reynolds Number rh Hydraulic Radius, m RT Thermodynamic Ratio RTD Resistive Thermal Device St Stanton Number T? Liquid Temperature, °C ix tiw Initial Temperature of the Wall, F Tf Final Temperature of the Product at onset of CWH, K Ti Initial Temperature of the Product, K Tsat Saturation Temperature of the Product, K tvs Saturation Temperature of the Steam, F u Product Velocity, ms1 ui Model Input Variables V Product Velocity, ms1 Xi Mass Fraction of the ith Component Thermal Diffusivity, m2s1 μ Product Viscosity, cP Product Density, kgm3 G Density of Gas, kgm3 L Density of Liquid, kgm3 x ACKNOWLEDGEMENTS My thanks goes first and foremost to God for giving me patience and my family for giving me encouragement throughout this process. I would also like to thank the following people: • My committee members, Drs Bowser, McGlynn, and Weckler for providing to me the opportunity to conduct this research. • Jana Moore for all of her assistance over the years and for being a great friend. • Dave Moe and Joe at the Food and Agricultural Products Center without whom I would not have been able to collect the data. • The entire faculty and staff of the Biosystems Engineering department for allowing me to serve in the Recruiter position, which not only gave me the opportunity to pursue a Masters degree, but also allowed me to contribute to the success of a department that I love. 1 CHAPTER I INTRODUCTION Heating of food products can cause many useful changes to a product’s taste, texture, and appearance. In addition to these changes, many of the most useful impacts of thermal processing on the food product occur on a cellular level, including the inactivation of enzymes and the destruction of pathogens that can cause spoilage. Pasteur’s discovery that microbial metabolism is the driving force behind the fermentations that spoil food products (Lewis and Heppell, 2000) brought to light the importance of the commercial sterilization of food products. There are many methods of thermal processing used in the food industry. Techniques range from batch processing to continuous processing and from indirect heat exchange to direct heat transfer. Direct Steam Injection (DSI) heating, the thermal processing method that is the focus of this research, has not found widespread acceptance in the industry. Despite the benefits of highly efficient heat transfer in a continuous flow system, the occurrence of Condensationinduced Water Hammer (CWH) and the associated noise, system damage, and operator hazards have deterred processors from using DSI systems (Lewis and Heppell, 2000; Schroyer, 1997). The purpose of the research described herein, was to examine relationships between the operating conditions of a DSI system, the physical 2 properties of liquid food products, and the occurrence of CWH. The goal was to investigate a mathematical relationship that processing plant managers and DSI system operators could use to predict safe operating conditions. Such an equation was developed by Bowser et al. (2003) based on the thermodynamic ratio (RT) and the Peclet Number (Pe) using data collected in tests of water and sugar water. The following research first repeated the experiments reported by Bowser et al. (2003) testing water and sugar solution, then examined the applicability of the relationship determined by Bowser et al. to beef stock and corn starch, and finally looked at the use of other dimensionless parameters that are commonly used to describe heat transfer and fluid flow to see if another relationship could be defined. 3 CHAPTER II LITERATURE REVIEW Thermal Processing of Liquid Food Products Batch processing is an inexpensive and flexible method for heating foods. In batch processing, a unit of product is introduced into the heating apparatus, brought up to temperature, held for sterilization time if required, and removed from the heater. This method, used in steamjacketed kettles and retorts, can be applied to virtually any food product (Lewis and Heppell, 2000). In heat transfer, temperature is a function of location and time (Singh and Heldman, 2001). Therefore, the distance from the heating source to the center of the product determines the time that a product must be exposed to high temperatures. While heating can have beneficial effects on the food product, prolonged exposure to heat or heating at high temperatures can have adverse effects on the taste, texture, appearance, and nutritional characteristics of a product (Lewis and Heppell, 2000). Therefore, processors have turned to continuous heating techniques over batch processing for pumpable products in order to reduce the distance from the heat source to the center of the product and therefore the reduce time required for heating. In continuous processing, heat is transferred to a product as it flows through a heat exchanger, with the hold time required for reducing microbial activity determined by the product flow rate and the equipment properties 4 including tube diameter and length. The thermal death time of microbes decreases as temperature increases, and because the desired temperature can be reached faster in continuous processing than in batch processing, the product is not required to be at a high temperature for a prolonged period. In addition to the increased product quality that results from a shorter exposure to high temperatures, continuous processing may have economic benefits from a higher production rate and less materials handling (Kundra and Strumillo, 1998). Continuous thermal processing techniques include methods that employ electrical energy for heating and methods that utilize heat from hot water or steam, with the later method being of interest for this research. Processes that use hot water or steam for heat transfer can be further divided into indirect methods and direct heating methods. Indirect methods are those in which there is a heat exchange surface separating the heating medium from the product to be heated, for example plate, tubular, and scraped surface heat exchangers. Direct methods such as steam infusion or steam injection have direct mixing of the heating medium and the product (Kudra and Strumillo, 1998). Direct Steam Injection Heating In a direct steam injection system, food grade steam is injected directly into the food product. This can be done simply through a singleorifice venturi as shown in Figure 1. However, this method must have high velocity steam and a long stretch of straight pipe downstream in order to ensure proper mixing and there is a large pressure drop across the device (Lewis and Heppell, 2000). 5 Figure 1: Single orifice venturi direct steam injector (Perry, 1998). A multipleorifice DSI heater is an improvement over the singleorifice models for food processing applications. In this design, steam is injected into the product through many small holes in a central tube. The central tube contains a spring loaded piston that regulates the steam pressure in relation to the product pressure. Helical flights aid in mixing the steam with the product within the mixing chamber. The DSI heater used in this research is shown in Figure 2 (Pick Heaters, West Bend, WI Model SC23). A disassembled view of the heater body is shown in Figure 3. The small holes in the injector tube ensure that the steam is introduced into the product in the form of small bubbles, which produces a more rapid condensation and thus virtually instantaneous heating. In fact, Burton et al. (1977) found that full temperature could be reached just 0.9 seconds after steam injection. Rapid condensation is also important to minimize uncondensed steam bubbles in downstream piping, and maximize product throughput. Rapid condensation can also be encouraged by providing product backpressure on the injector greater than the pressure required to prevent boiling (Lewis and Heppell, 2000). 6 Figure 2: Pilot scale steam injection heater (Pick Heaters, West Bend, WI Model SC23) (photo courtesy of the Food and Agricultural Products Center, Oklahoma State University, Stillwater, OK). Figure 3: Disassembled view of the multiorifice steam injection heater body used in this study (photo courtesy of the Food and Agricultural Products Center, Oklahoma State University, Stillwater, OK). Injector tube Spring plunger Static mixer Housing 7 When the steam is injected into the product, it condenses, giving up some of its sensible heat and its latent heat of vaporization. This condensate can cause considerable dilution, with a 60°C increase in product temperature adding about 11% of water to the product (Lewis and Heppell, 2000). In many food processing applications, dilution is acceptable; but for applications where additional water is not desirable, the condensate can be removed from the product after heating using a vacuum chamber. Direct heating is a much more efficient heating method than indirect heating. Indirect heating only utilizes sensible heat, meaning that, when using hot water as the heating medium, only 4.2kJ of heat is available per kilogram of water for every degree difference between the temperature of the product and the temperature of the heating water. However, DSI heating employs the latent heat of vaporization of steam (2260 kJ kg1), in addition to the sensible heat. On a perdegreebasis, the heat content of steam is 540 times that of water (Alverez et al., 2000). In fact, Jones and Larner (1968) found that the heat transfer coefficient of a DSI system was 60 times greater than of indirect steam heating systems. This high efficiency leads to energy savings for producers; Sutter (1997) found that a DSI systems used 7.9% less energy than a shell and tube heat exchanger when heating water and Schroyer (1997) stated that reductions in energy demands of 2025% were common. Precise and flexible temperature control is another major benefit to steam injection heating. DSI units can be used for raising product temperature by as little as 5.5°C to much larger increases of 96.7°C just by varying the amount of 8 steam added to the product (Singh and Heldman, 2001). In addition, product heating begins as soon as the steam valve is opened and ends as soon as it is closed, so DSI systems do not require a long warmup period and have fewer problems with overshooting the set point temperature due to residual heat in the system (Schroyer, 1997). Finally, Alverez et al. (2000) found that when heating beer mash, DSI was preferred over batch processing. He found there was a reduced risk of scorching the mash, because the steam remained at a constant temperature, limiting the temperature of the final product. In addition to the high efficiency, instantaneous heating, and precise temperature control of DSI, benefits over indirect heat exchangers include less space requirements, no need for condensate return systems (Schroyer, 1997), increased temperature control (Sutter, 1997), the ability to process moreviscous products, and less fouling (Lewis and Heppell, 2000). Steam injection heating has found utility in a wide variety of applications. In the field of biotechnology, it has been found that steam injection heating does not require a product to be held at high temperatures for as long as batch processing does to achieve the same result. Biotechnology products that benefit from a shorter exposure to high heat include thermolabile biomaterials, applications that require constant dry matter content after heating, and biomaterial broths that contain starch that otherwise could be gelatinized. (Kudra and Strumillo, 1998). Industrial facilities that already posses a steam supply have found that steam injection heating is an efficient means of producing hot water for use throughout the facility. For example, steam heated hot water can be 9 used instead of steam in a jacketed kettle to produce more even heating and better temperature control of the product (Sutter, 1997). In the food processing arena, steam injection can be used to heat almost any pumpable product. Some designers advocate that it is most applicable to low viscosity and homogenous products such as milk and juices (Richardson, 2001). However, it has also been employed to heat soups, chocolate, processed cheeses, ice cream mixes, puddings, fruit pie fillings (Singh and Heldman, 2001), jams, cheeses, salsa, pet foods, sugar and starch candy mixtures (Pick Heaters, 2004), beer mash (Alverez et al, 2000), baby food, and texturized proteins (Bowser et al, 2003). CondensationInduced Water Hammer Condensationinduced water hammer is a major drawback of DSI heating systems. This phenomenon can occur when a high pressure steam bubble is surrounded by product. As the steam condenses due to heat loss to the product, the volume of the condensate is much less than the volume of the steam. The pressure within the bubble drops drastically causing the bubble to collapse. Bubble collapse can cause large pressure surges that propagate within the system and cause loud noise (Van Duyne et al., 1989). Lewis and Heppell (2000) suggested that “some form of sound absorption may be necessary” to cover up this problem. However, the issue goes beyond simple noise. The forces on the system piping and valves can be large enough to cause costly damage and may be hazardous to operators. Therefore, it is important to define the operating conditions under which CWH will occur so as to allow processors to implement DSI systems and avoid the undesirable effects of CWH. 10 Bowser, et al. (2003) addressed the concern of designing DSI systems to decrease the occurrence of CWH. In this research, water and aqueous sugar solutions of various concentrations were heated under a variety of operating conditions. A relationship between the thermodynamic ratio and the Peclet number was established that could effectively predict a CWH event. The thermodynamic ratio (RT) is a dimensionless number that was first identified by Block et al. (1977) in the research of water hammer in steam power generators. The simplified expression for thermodynamic ratio, which assumes that heat transfer from the steam to the product is 100% efficient and that the mass of the steam added to the product is negligible is: f i sat i T T T R T T = Equation 1 where Tsat is the saturation temperature of the product (K), Ti is the initial product temperature (K), and Tf is the final product temperature at the onset of CWH (K). The Peclet number (Pe) is a dimensionless heat transfer parameter, named for Jean Claude Eugene Peclet (17931857), that gives the ratio of bulk heat transfer to conductive heat transfer (Incropera and De Witt, 1985). It is defined by Equation 2. Pe = uL Equation 2 where u is the product velocity (ms1), L is the characteristic length of the flow geometry (m), and is the thermal diffusivity of the product (m2s1). 11 Bowser, et al. found that CWH would be avoided 90% of the time if the thermodynamic ratio could be maintained above a given value as shown in Equation 3. RT > 1.5× (2.4×10 5 Pe +1.25) Equation 3 Objectives of Research The overall goal of this research was to develop a greater understanding of the safe operating conditions for a DSI heater. Two specific objectives for accomplishing this goal were: 1. To evaluate the validity and limitations of the equation developed by Bowser et al. (2003), which were based on tests with water and sugar solution, to additional liquid food products. 2. To investigate if another correlation between the physical properties of liquid food products and the temperature at which CWH occurs could be developed using common heat transfer and fluid flow parameters. This investigation was meant to be a general screening of parameters using the available data, not a focused study of any particular parameter. 12 CHAPTER III RESEARCH METHODOLOGY Products Tested Products were selected to both reflect the previous tests of Bowser et al. (2003) and to study the effects of CWH on products with a wider range of rheological properties. First, water was tested in order to benchmark the system performance. Second, aqueous sugar solutions at concentrations ranging from 49.2 to 68.3 degrees brix were tested. Sugar solution was the product used by Bowser, et al., so it provided a standard of comparison to ensure that research and calculation methodologies of this study produced similar results as the previous research did. Third, concentrated beef bone stock (CJ NutraCon, Guymon, OK), a highly viscous paste composed of approximately 42% water, 29% protein, 20% fat, and 9% ash, was tested. This product was chosen for its rheological properties: the viscosity decreases greatly with heating. Finally, a corn starch slurry was selected for testing because of its widespread use in the food processing industry. Corn starch test samples were made by combining Pure Food Powder (Tate and Lyle  AE Staley Manufacturing Company, Decatur, IL), which is approximately 90% carbohydrate and 10% water, with water and heating to the gelatinization temperature of 160°F in a continuousstir steam jacketed kettle. Without gelatinization, the starch and water mix is simply a 13 solution that has physical properties similar to water, but gelatinizing the starch forms a highly viscous material. Experimental Setup Testing was performed at the Food and Agricultural Products Center (FAPC) at Oklahoma State University using an approach similar to that of Bowser et al. (2003). A schematic of the system is shown in Figure 4. Steam, supplied from the boiler at 414 kPa (60 psi), was conditioned by a steam separator and a carbon filter before entering the pilot scale steam injection heater (Pick Heaters, West Bend, WI Model SC23). For tests involving sugar water, beef broth, and corn starch, the product was stored in a stainless steal sanitary tank and was supplied to the heater using a positive displacement pump (Waukesha CherryBurrell, Delavan, WI, Model 15). After heating, the product was returned to a separate tank to await further testing or disposal. This setup was modified slightly for tests in which water was heated. Because the pump’s hotclearance rotors experienced slippage for water, the pump shown in Figure 4 was not used. Instead, a potable water supply was connected directly to the steam injection heater’s inlet, and the heated water was discharged directly to a floor drain. 14 Figure 4: Experimental setup Data Collection To evaluate Bowser's equation, the variables used to calculate the Peclet number and the thermodynamic ratio needed to be quantified. For Equation 1 these variables were Ti, Tf, and Tsat; for Equation 2 the variables were L, u, and . The method used to determine each of these variables is outlined below. The characteristic length (L) is simply defined in textbooks as the inside diameter of the pipe for indirect heat transfer systems. However, in the DSI system tested, the product did not flow through an open pipe. Rather it flowed through the annular section between the heater body and the injector tube from which pressurized steam emanated. Therefore, the characteristic length was defined as the hydraulic diameter. Direct Steam Injection Ti Heater Tf Pf Pi DP Steam Product In Product Out Data Logger steam trap filter separator μ 15 The product velocity (u) was determined by two different methods. For the experiments with water, a catchcan test using a stopwatch and scale was used to calculate the flow rate from which velocity was calculated. For all other tests, the pump calibration curve (Appendix A) was used to determine product flow rate. To convert this flow rate into a velocity, it was divided by the flow area. It was assumed that the flow area was the annular space between the injector tube and the heater housing. The thermal diffusivities ( ) of the products were calculated based on the composition of the product using Equation 4. = = n i iXi 1 Equation 4 where n is the number of components, i is the thermal diffusivity of the ith component, and Xi is the mass fraction of the ith component (Singh and Heldman, 2001). Details of these calculations and a table of thermal diffusivity values used are given in Appendix B. Ti and Tf were both measured using sanitary resistive thermal devices (RTD) (Anderson Instruments, Fulton, NY Model SA510040370000). These values were then recorded using a digital data logger (Fluke, Everett, WA Model 2635A). To find the saturation temperature of the product, the saturation temperature of pure water at the operating pressure was calculated using the psychometric data published by the American Society of Agricultural Engineers (ASAE, 1999), which is defined by the relationship in Equation 5. 16 ( ) [ ] = 8 0 ln 10 i i i T Ai Ps Equation 5 where A0 through A8 are constants found in Table 1 and Ps is the system operating pressure (psi). Table 1: Constants for use in determining the saturation temperature of water (Equation 5). Constant Value A0 35.1579 A1 24.5926 A2 2.11821 A3 0.341447 A4 0.157416 A5 0.0313296 A6 0.00386583 A7 0.000249018 A8 6.84016E06 To account for the effect of solutes, a boiling point rise value was then added to the saturation temperature of water to find the saturation temperature of the product at the system pressure. The boiling point rise of the sugar solutions was found in Hoynak and Bollenback (1966). For the beef bone stock and starch, the boiling point rise was determined using Duhring’s rule based on the salt content of the product. In order to perform a boiling point rise calculation, the system pressure had to be monitored and recorded. The pressure of the product both before and after the heater was monitored using sanitary pressure sensors (Anderson Instruments, Fulton, NY Model SR032C004G1105). In addition to facilitating an accurate calculation of Tsat, monitoring the system pressure was the primary method for determining when a CWH event occurred. 17 Because the purpose of this research was not only to examine the results of the research of Bowser et al. (2003), but to evaluate alternative relationships between food product properties and CWH, it was desired to know the viscosity of the product immediately prior to heating. The viscosity of water varied with temperature and was found from Table A.4.1 of Singh and Heldman (2001). For tests involving sugar water, literature sources were used to relate the Brix value with viscosity (ICUMSA, 1979). For both beef broth and corn starch, viscosity was measured using a Brookfield inline viscometer (Brookfield Engineering, Middleboro, MD Model TT100). Testing Procedures In general, the following steps were taken in conducting the tests. 1. The product supply valve was opened allowing product to flow through the entire system, purging any air or water in the system. The unheated product was not recirculated during this step, but was sent directly to the outflow tank for potential use in additional tests. 2. Product flow rate was set and system pressure was controlled using a gate valve that was placed after the steam injection heater. 3. The steam valve controller was opened rapidly to 30% (previous tests correlating controller settings to steam pressure out of the valve showed that prior to 30%, the valve was not actually open). From this value, the controller was slowly opened (approximately 1% every 30 seconds) while the system was observed for signs of CWH. 18 4. When a CWH event was observed the approximate system pressure and outlet product temperature were recorded. These recorded values were considered as approximate, because as the system approached CWH, the system pressure, inlet product temperature, and outlet product temperature all fluctuated. 5. After recording these values, the steam valve was closed and the system parameters were reset for the next test. In some instances, the valve was merely closed enough for the CWH to cease, and then was reopened to collect another data point using the same system parameters. System pressure fluctuations greater than 41.4 kPa (6 psi), were used as a qualitative indicator to establish the occurrence of CWH. However, other indicators such as loud noise and movement of system piping were also observed. When testing beef broth and starch, some modifications were made to the procedure outlined above. First, in order to conserve product, the steam controller value was increased to 30% while the product was pumped at a very low flow rate, then the flow rate was increased to the test value and the steam controller setting was increased at a rate of 1% every 10 seconds until initial system pressure fluctuations of 13.8 kPa (2 psi) were observed at which time the rate of controller increase was slowed to the standard 1% every 30 seconds. The second modification was in the regulation of system pressure to maintain steady state operating conditions. The system pressure dropped significantly during testing of beef stock due to the decreased viscosity of the heated product. 19 This decrease in viscosity was not quantified, but was detected visually. During tests with starch, the system pressure increased. To maintain a steady system pressure during tests with both beef stock and starch, the gate valve was periodically adjusted during the test. When initial indications of CWH were observed, the researcher stopped adjusting the valve so that the final indication of a 41.1 kPa (6 psi) fluctuation in system pressure would not be affected. After testing, the observed final temperature was compared to the temperatures recorded by the data logger and refined. This refinement was required because of the inherent instability of the output temperature during a CWH event. The final temperature may have oscillated at the moment it was observed, and therefore may not have accurately reflected the final temperature that should be used in calculating the threshold RT value. The following method was used to hone the estimate of final temperature. 1. Fluctuations in the logged outlet temperatures were assumed to correspond to the large pressure fluctuations used to define a CWH event. 2. If the observed final temperature value was logged at the beginning of a drop in the recorded temperature, it was used as the final temperature for calculations. 3. If temperature drops occurred immediately (within 30 seconds – the time between increases in the steam valve opening) prior to the observed final temperature, it was assumed that the temperature was observed during an oscillation. A revised final temperature that corresponded to the 20 highest temperature reached prior to the oscillations within that time period was used. The recorded temperature values shown in Figure 5 for test 12 of beef stock are used to illustrate this method. The observed final temperature for this test was 70 °C. Because there were temperature fluctuations that preceded this value, step 3 was used to revise the final temperature. There were two drops in temperature that occurred within the 30 seconds prior to the observed value. The highest temperature before either of these drops was 63 °C, which was used as the final temperature in calculations. Beef Stock Test 12 50 55 60 65 70 75 Time (point collected every 2 seconds) Temperature (C) Product Inlet Temperature Product Outlet Temperature Observed Final Temperature 70 °C Final Temperature For Calculations 63 °C 30 Seconds Figure 5: Example of determination of Tf based on temperatures recorded by the data logger. The final step in the research process was to calculate dimensionless parameters that could potentially be used to predict CWH. First, the 21 thermodynamic ratio and Peclet number were calculated for each test for use in comparing to the predictive equation developed by Bowser, et al. Second, five additional dimensionless parameters: the Reynolds, Prandtl, Nusselt, Stanton, and the Jacob numbers were calculated for use in the screening investigation. The Reynolds number, defined by Equation 6, described the flow characteristics of the product. μ Re = VL Equation 6 where is product density (kgm3), V is product velocity (ms1), L is the characteristic length (m), and μ is product viscosity (cP). This parameter can also be described as a ratio of the inertial forces of the fluid to the viscous forces of the fluid (Incropera and De Witt, 1985). When Re is less than 2100 the flow is classified as laminar, when it is between 2100 and 4000 the flow is considered transitional, and when Re is greater than 4000 the flow is turbulent (Singh and Heldman, 2001). This parameter impacts steam injection heating, because as when the Reynolds number increases, more mixing occurs in the fluid, which should help to incorporate the steam into the product, reducing the opportunity for CWH to occur. The Prandtl number is a ratio of the molecular diffusivity of momentum to the molecular diffusivity of heat for forced convection (Incropera and De Witt, 1985). It is defined as: k Pr = μ cp Equation 7 22 where μ is the viscosity (cP), cp is the specific heat (kJkg1C1), and k is the thermal conductivity (Wm2C1). The Nusselt number relates the rate of heat transfer due to convection to the rate of heat transfer due to conduction (Incropera and De Witt, 1985). It is defined as: k Nu = hdc Equation 8 where h is the convective heat transfer coefficient (Wm2C1), dc is the characteristic dimension (m), and k is the thermal conductivity (Wm1C1). The value of Nu relates to the magnitude by which convection increases the amount of heat transferred, so a Nusselt value of 3 means that the heat transfer due to convection is 3 times the amount due solely to conduction (Singh and Heldman, 2001). The Nusselt number is intended to be used to describe indirect heat transfer, but DSI heating does not employee a heat transfer surface. An attempt to account for this difference was made by using Equation 9 found in the work of Goodykoontz and Dorshe (1966) to quantify the convective heat transfer component of the Nusselt number. vs iw i t t h q = Equation 9 where qi is the heat flux (Wm2) based on the heat flux area calculated using the pipe inside diameter, tvs is the saturation temperature of the steam (C), and tiw is the initial temperature of the wall (C). Goodykoontz and Dorshe applied this 23 equation to film condensation, but it was assumed in this research to also be applicable to droplet condensation. The Stanton number simply relates the previous three coefficients (Incropera and De Witt, 1985). Pr St = NuRe Equation 10 Finally, the Jacob number was calculated using Equation 11. G LG L pL sat h Ja c T T = ( ) Equation 11 where L is the density of the liquid (kgm3), cpL is the specific heat of the liquid (m2s2K1), Tsat is the saturation temperature of the steam (°C), T? is the liquid temperature (°C), G is the density of the gas (kgm3), and hLG is the enthalpy of evaporation (m2s2). The Jacob number is part of a theoretical model that is used to describe heat transfer in bubble type condensers based on transient conduction (Hewitt et al., 1994). 24 CHAPTER IV ERROR ANALYSIS All measurable quantities are subject to error  the difference between the measured value and the true value of the parameter. The two main contributors to error are instrumental error and methodological error. Instrumental Error Instrumental error is due to the cumulative effects of imperfections in the measuring equipment and human imprecision in reading the measurement (Bevington, 1969). In the error analysis for this research, human imprecision from reading the value off of the instrument was considered insignificant, because all of the sensors used were digital (Rabinovich, 2000). The instrument’s accuracy, which quantifies the inherent error associated with it, was found in the literature that accompanied each instrument. Another aspect of the instrumental error is the number of significant digits to which an instrument is read, referred to as data collection precision. The contributions to the error for the DSI system tested are shown in Table 2. The larger of the two values, instrument accuracy and data collection precision, was the observational uncertainty for that instrument. Another contribution to the uncertainty associated with the instrumentation was the assumption that each instrument used was properly calibrated, the viscometer at the factory and the pressure and temperature sensors during previous research. This assumption was correct for 25 the viscometer, but incorrect for the temperature and pressure sensors, adding an unknown error to the data. Table 2:Measurement Error Instrument Property Measured Instrument Accuracy Data Collection Precision RTD Tp,I & Tp,f 0.66 C 0.01 Analog transmitter N/A ±0.18 C N/A Data logger Temperature N/A ±0.10 C N/A Viscometer Viscosity 20cP 0.01cP Data logger Viscosity N/A ±0.5cp N/A Pump Flow rate 0.11 gpm N/A Methodological Error Methodological error is due to human imprecision in selecting the correct value of the measured parameter. In this research there were methodological errors associated with the final temperature values and the characteristic length. The error associated with selecting the Tf value used in calculations was based on the range of temperature values in the oscillations surrounding the selected final temperature, resulting in a methodological error of 5 °C for Tf. The method and results of this assessment are provided in Appendix D. The characteristic length also has methodological error associated with it. This is due to the ambiguity in the definition of L for DSI heaters. This error was defined as the difference between the two possible values of L, the hydraulic radius and the hydraulic diameter, which has a value of 0.0255 m. 26 Model Error Errors in the determination of variable values are consequential when considering the validity of a model. For this reason, the technique presented by Doebelin (1966) was used to find the absolute error of the model presented by Bowser et. al (2003) for the instruments and techniques used in this analysis. This techniques says that, if a model's output depends on multiple input variables (Equation 12), then the absolute error of the model output is proportional to the errors of each variable (Doebelin, 1966). In other words, the error in N is approximately the error in a variable multiplied by the effect that the variable has on the final value of N, summed for all variables in the model (Bevington, 1969). This concept can be expressed mathematically using the Taylor series expansion in Equation 13. The higherorder terms in Taylor's expansion are neglected, because all of the individual errors are small (Bevington, 1969). N = f (u1,u2 ,u3...ui ) Equation 12 where N is the model output and the ui's are the model input variables. + + + + = i i u u N u u N u u N u E N u N ( ) ... 3 3 2 2 1 1 Equation 13 Since the original goal of this research was to examine the applicability of the equation developed by Bowser et al. (2003), the model error will be examined by applying Equation 13 to Equations 1 and 2, the result of which is given in Equations 14 and 15. + + = p f p f p i p i Tp sat p sat T T T T T T T T T u u R u u R u E R u R , , , , , , ( ) Equation 14 27 + + = u u Pe u u Pe u E Pe u Pe L L u ( ) u Equation 15 The partial derivates for use in Equations 14 and 15 are calculated in Equations 1619. L u Pe u = Equation 16 u u Pe L = Equation 17 2 , , , , ( ) , p f p i p sat p f T T T T T T u R p i + = Equation 18 2 , , , , , ( p f p i ) p in p sat p f T T T T T u R = Equation 19 By combining all of the instrumental errors and the methodological error that contribute to each variable, the variable’s uncertainty can be determined. The uncertainties for each variable in the model of Bowser, et al. are given in Table 3. 28 Table 3: Contributions to model uncertainty Variable Contributions to Uncertainty Variable Uncertainty velocity, u pump calibration curve error 0.0063 ms1 characteristic length, L multiple definitions that can be applied to a single variable 0.0255 m thermal diffusivity, Insignificant initial product temperature, Ti RTD, analog transmitter, data logger 1.22 C final product temperature, Tf RTD, analog transmitter, data logger, methodological error 6.22 C product saturation temperature, Tsat Insignificant Substituting these uncertainty values and the partial derivatives in Equations 1819 into Equation 14 gives an average error in thermodynamic ratio of 0.75. 29 CHAPTER V RESULTS AND DISCUSSION The first objective of the research was to evaluate the applicability of the equation developed by Bowser et al. (2003), based on tests with water and sugar solution, to additional liquid food products. This equation stated that CWH would be avoided 90% of the time if RT > 1.5× (2.4×10 5 Pe +1.25) Equation 3 A total of 41 individual test runs were conducted during this study. For the data analysis, these results were combined with data collected from 24 tests that were conducted by Bowser, et al. (2003). Of the 65 test runs, 14 were water, 23 were sugar solution, 22 were beef stock, and 6 were corn starch slurry. It would have been desirable to have a larger number of data points over a wider range of conditions for the corn starch; however, samples were limited due to time constraints. The system parameters that could be varied for each test were the product flow rate, system pressure, initial product temperature, and product viscosity prior to heating. Table 4 shows the range of these parameters tested within this study. For each test the values of these parameters as well as the final product temperature were recorded and are provided in Appendix C. 30 Table 4: Range of parameters tested within the study Product Flow rates gpm System pressures psi Initial product temperatures °C Viscosities cP Water 0.233.80 14.035.0 13.7221.94 0.951.18 Sugar Solution 0.482.89 10.533.0 15.0043.89 7174 Beef stock 0.962.41 12.035.0 11.7533.72 3533463 Starch 0.962.17 17.032.0 35.4045.47 3121554 All products 0.233.80 10.535.0 11.7545.47 13463 The first analysis performed on the data was to determine if the system behavior with respect to CWH during each test adhered to the predictive equation of Bowser, et al. The threshold value of RT and the Peclet number were calculated for each test run (see Appendix E for calculated values). Figure 6 shows the results of tests performed using water and sugar solution, the products used in the development of the equation. 31 Thermodynamic Ratio vs. Peclet Number Tests of Water and Sugar Solution 0 1 2 3 4 0 10000 20000 30000 40000 50000 60000 Pe RT SugarOstermann WaterOstermann SugarBowser WaterBowser Bowsers Equation Figure 6: Analysis of test results for water and sugar solution compared to the predictive equation. As Figure 6 shows, the data collected for water and sugar solution in this research support the predictive equation developed by Bowser, et al. Of the combined data set, CWH occurred as predicted for 100% of the water tests and 96% of the sugar solution tests. The second analysis was to see if Bowser’s equation was equally applicable to the tests with beef stock and corn starch. The results of this analysis are shown in Figure 7 and presented in Table 5. It may be observed from Figure 7 that the data is not spread evenly across the range of Pe numbers. This was due to varying inputs of pressure, initial temperature, and flow rate randomly without designing the experiments to target specific Pe values. In addition, redundant experiments (shown in example areas A, B, and C enclosed 32 in dashed lines in Figure 7) resulted in a wider than expected range of Rt values as indicated by error bars that did not overlap. This indicated that some experimental error or other factor was present that was not accounted for in the error analysis. This error could be from many sources including the calculation of the products’ physical properties, the regulation of pressure during testing, uncalibrated sensors, or heater inefficiency due to improper cleaning. An improved approach to data collection is given in the Conclusions section. Thermodynamic Ratio vs. Peclet Number Error Bars for RT 0 1 2 3 4 5 6 7 8 9 10 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 40000 44000 48000 Pe RT Beef Starch Bowser's Equation A B C Figure 7: Comparison of results of tests of beef stock and starch to the predictive equation. 33 Table 5: Adherence to predictive equation based on product Product Test Runs Occurrences of CWH Percentage of Tests that Adhere to the Predictive Equation Water 14 0 100% Sugar Solution 23 1 96% Beef Stock 22 14 36% Starch 6 5 17% All Products 65 20 69% Because the behavior of the system when testing beef stock and starch did not appear to follow the predictive equation, data analysis was conducted for the final objective of this research: to investigate if another correlation between the physical properties of liquid food products and the temperature at which CWH occurs could be developed using common heat transfer and fluid flow dimensionless parameters. As previously stated, the parameters that were selected for examination were the Reynolds, Prandtl, Nusselt, Stanton, and the Jacob numbers. The values of these parameters for each test are provided in Appendix E, and Table 6 shows the minimum, maximum, average and standard deviation of each of the dimensionless parameters tested. Table 6: Descriptive statistics of dimensionless parameters tested. Maximum Minimum Average Standard Deviation Thermodynamic Ratio 6.54 1.24 2.72 1.22 Peclet Number 52815.79 3016.69 26479.02 11395 Prandtl Number 27037.22 6.54 5304.72 7559.97 Reynolds Number 7605.12 0.89 679.75 1444.15 Nusselt Number 17147.70 1901.84 9043.62 3878.49 Stanton Number 1.44E+07 1.69E01 9.48E+05 2.64E+06 Jacob Number 95.98 62.49 78.03 9.03 Because the purpose in developing a predictive equation is to provide operators with a simple guideline for setting the operating temperature of steam injection heaters, the first analysis that was performed for this objective was to 34 see if a relationship could be defined using only linear regression to relate the thermodynamic ratio to each of the dimensionless parameters. Figures 812 show the linear relationship between the thermodynamic ratio and each of the dimensionless parameters studied. Thermodynamic Ratio vs. Reynolds Number y = 0.0002x + 2.8231 0 1 2 3 4 5 6 7 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure 8: Linear regression of the relationship between thermodynamic ratio and Reynolds number. 35 Thermodynamic Ratio vs. Prandtl Number y = 8E05x + 2.2799 0 1 2 3 4 5 6 7 0 5000 10000 15000 20000 25000 30000 Pr RT Figure 9: Linear regression of the relationship between thermodynamic ratio and Prandtl number. Thermodynamic Ratio vs. Nusslet Number y = 0.0001x + 3.8663 0 1 2 3 4 5 6 7 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure 10: Linear regression of the relationship between thermodynamic ratio and Nusselt number. 36 Thermodynamic Ratio vs. Stanton Number y = 5E08x + 2.7674 0 1 2 3 4 5 6 7 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 St RT Figure 11: Linear regression of the relationship between thermodynamic ratio and Stanton number. Thermodynamic Ratio vs. Jacobs Number y = 0.0281x + 4.9161 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure 12: Linear regression of the relationship between thermodynamic ratio and Jacobs number. 37 As previously mentioned, the research was not properly designed to ensure a broad range of data points across all dimensionless parameters, resulting in redundant data. To reduce the influence of this redundancy, a second analysis was performed. For this investigation, all data points were grouped by RT value (based on tenths). For each group, both the RT and the dimensionless parameter values were averaged. The results of this data manipulation are shown in Table 7. These relationships were then graphed, the results of which are provided in Appendix F. Table 7: Averaged RT and dimensionless parameter values for data analysis. RT Pe Pr Re Nu St Ja 1.24 8772.17 488.55 17.93 6044.19 2.22E+02 74.75 1.36 4786.00 6.96 674.26 3000.31 3.14E+05 91.43 1.40 15706.79 7.53 2086.15 9902.69 2.74E+06 93.46 1.54 18614.43 141.36 1549.04 10892.65 2.81E+06 84.24 1.63 17773.87 56.40 1660.01 9949.28 2.27E+06 84.37 1.74 16688.95 176.39 562.95 8252.31 5.29E+05 76.83 1.92 19067.73 257.04 681.72 8577.38 5.94E+05 80.86 2.02 23549.02 4018.14 1075.07 9985.53 1.44E+06 79.62 2.12 24464.12 10832.06 62.64 9724.12 6.02E+03 76.82 2.26 37470.16 4335.44 770.57 14133.92 9.20E+05 80.00 2.36 33777.12 2050.59 317.46 11819.07 7.95E+04 71.54 2.44 29910.78 2988.80 1275.71 10711.88 2.42E+06 76.53 2.55 37190.94 86.58 429.43 13543.86 6.72E+04 76.78 2.67 38918.62 8917.68 127.46 12108.62 9.95E+03 80.52 2.99 26334.43 27037.22 0.97 7421.43 2.67E01 79.98 3.14 19404.06 10568.35 1.87 5369.20 9.82E01 72.22 3.38 23683.37 7093.64 5.09 5803.94 8.04E+00 71.02 3.42 36451.86 8945.30 37.59 9158.13 9.22E+02 74.97 3.56 25592.47 4235.09 6.04 6025.86 8.59E+00 66.70 3.60 51099.48 6.70 7605.12 12680.30 1.44E+07 90.68 3.74 49912.64 147.73 337.48 10868.05 2.48E+04 64.35 3.94 24717.58 4666.30 7.57 5361.60 1.69E+01 73.57 4.09 27815.18 15970.11 1.74 5820.41 6.34E01 74.74 4.69 25915.86 10453.41 2.48 4993.05 1.18E+00 73.12 4.82 16042.30 4419.19 3.63 2891.87 2.38E+00 75.10 5.50 23750.62 23327.16 1.02 3874.04 1.69E01 79.58 6.26 43935.66 20677.57 2.13 5733.39 5.90E01 78.72 6.48 35165.19 18991.48 1.85 4678.95 4.56E01 78.49 6.54 19442.14 10387.40 1.91 2446.76 4.50E01 79.30 38 The third step in the data analysis was to investigate if the relationship between the thermodynamic ratio and each dimensionless parameter could be better explained using a different type of curve to define the data. For each dimensionless parameter, regression equations were defined using logarithmic, exponential, and power equations for all of the tests and for the averaged values. The graphs of this analysis are included in Appendix G. The final step in the data analysis was to determine for each dimensionless parameter if a stronger relationship existed for a portion of the data than that of the entire data set. The segmentation of the data was done by visually inspecting the graphs of thermodynamic ratio verses each of the dimensionless parameters. Appendix H show the results of this analysis. For each of the analyses described above, a coefficient of correlation (r2) was determined. The r2 value describes the percentage of the data points that can be described by the regression equation and was used in drawing conclusions about the applicability of each relationship studied. Table 8 lists all of these r2 values. 39 Table 8: Coefficient of determination values for all analysis. Linear Log Exponential Power Pe 0.0906 0.1140 0.1595 0.2033 Pr 0.2620 0.3107 0.2621 0.3600 Re 0.0321 0.2587 0.0328 0.2822 Nu 0.1612 0.1782 0.1023 0.1063 St 0.0117 0.3074 0.0105 0.3342 All Tests Ja 0.0431 0.0350 0.0767 0.0657 Pe 0.1288 0.1618 0.2167 0.2785 Pr 0.4111 0.3307 0.4040 0.3915 Re 0.0395 0.5064 0.0333 0.4955 Nu 0.2954 0.3300 0.2019 0.2240 St 0.0149 0.5682 0.0099 0.5546 Averaged Tests Ja 0.0765 0.0708 0.1474 0.1402 RT<5 Pe 0.1220 0.1553 0.1910 0.2427 Pr<500 Pr 0.0099 0.0444 0.0064 0.0514 Pr>500 Pr 0.0386 0.0545 0.0271 0.0468 Re<500 Re 0.0934 0.2139 0.0941 0.2256 Re>500 Re 0.6115 0.3690 0.5539 0.3537 RT<5 Nu 0.0664 0.0596 0.0286 0.0214 St<100,000 St 0.0355 0.2575 0.0243 0.2618 St>100,000 St 0.5712 0.2643 0.5187 0.2770 Outliers Deleted RT<5 Ja 0.1138 0.1045 0.1329 0.1224 40 CHAPTER VI SUMMARY AND CONCLUSIONS Observations from Research In conducting this research, the challenges of operating a DSI heater were very apparent. It was found that Schroyer’s (1997) assertion, that a warmup period is not needed because heating begins as soon as the steam valve is opened, does not truly capture the operating conditions. Instead, to start the system, product had to be flowing through the system and the steam valve had to be opened slowly. If the steam valve was opened too rapidly, CWH occurred prematurely. This startup procedure caused a substantial amount of wasted product. However, attempting to mitigate for this waste by recycling the product was not desirable because the testing required steady state conditions, and recycling product would have caused variation in both the product inflow temperature and the product inflow viscosity during testing. In addition, recycling would not have reflected a typical production situation. A second insight received was that, because some products become less viscous during heating, the system pressure can drop drastically resulting in CWH at lower than expected temperatures. Finally, it was found that using very viscous products such as the starch was also difficult. Prior to conducting tests, it was observed that the high viscosity of the starch could cause large system pressures resulting in hose 41 blowouts upstream of the heater. These high pressures were reduced for testing by limiting the flow rate and opening the gate valve. Conclusions from Analysis of Data The first objective of this research was to determine the validity of the equation developed by Bowser, et al. (Equation 3) when applied to additional food products. This equation was developed using water and sugar solution, and it was found that for the new data points collected in this research using water and sugar solution, it adequately defined the threshold thermodynamic ratio for CWH. The results for beef stock and corn starch were inconclusive due to experimental error and insufficient data. The second objective for this research was to examine if the relationship between the physical properties of a product, the system operating conditions, and the threshold RT value could be better predicted by a different equation. Based on the coefficient of variation values shown in Table 8, the following conclusions can be made. 1. The Jacob number should not be used to develop a relationship between by which to predict safe operating conditions for a DSI system. None of the equations developed for this parameter were able to explain more than 7% of the data. 2. Power and logarithmic relationships should receive greater attention for use in defining a relationship between product physical properties, system operating conditions and the threshold thermodynamic ratio. The highest coefficient of determination for both the entire data set analysis and the 42 averaged data set analysis corresponded to one of these two relationships. The only exception being, the averaged analysis for Pr which had an r2 value 0.02 higher for the linear relationship than the power relationship. 3. Further investigation should focus on the Prandtl, Reynolds, and Stanton numbers which had the highest r2 values for both the entire data set analysis and the averaged data set analysis. In addition, the Peclet number should not be excluded from further investigation, because it is the product of the Reynolds and Prandtl numbers. 4. Based on the error analysis, the above conclusions should not be considered definitive. Not only was there an abundance of quantifiable errors, but it was also found from the results of redundant experiments that fell outside of the expected range of error, that some unknown error existed in the experimental setup and/or technique. The steps proposed in the following section should be taken to reduce model error in further research. Recommendations for Further Research In order to collect a more reliable data set and reduce the influence of errors, modifications must be made to the experimental setup and research techniques. The experimental setup should be altered and improved to allow for better accuracy in determining the temperature at which CWH occurs. One way that this can be accomplished is by using the data logger to record the system 43 pressure in addition to recording the product temperature and viscosity. This would eliminate the methodological error associated with the determination of Tf, because the first instance of 41.1 kPa (6psi) pressure fluctuation could be compared directly to the outlet temperature. In addition, all instruments should be properly calibrated immediately prior to use. Finally, equipment that monitors sound and/or vibration could be incorporated into the system setup. For this research only a quantitative criterion was used to indicate a CWH event. This criterion was pressure fluctuations of 41 kPa (6 psi), which was a lower value than the criterion of 60 kPa used by Bowser et al. (2003), because it was found that system stability was difficult to maintain up to 60 kPa. Installing sound and vibration monitors recognizes that requiring a specific value of pressure oscillation to indicate CWH may not be appropriate. It would allow qualitative indicators used by Bowser, such as shaking of system piping and gasps of collapsing steam voids, to be accounted for in a quantitative manner. The second suggested modification is to minimize the potential for unknown errors. A potential source of unknown error was the manual regulation of the system pressure during testing of beef broth in an attempt to maintain steady state operating conditions. Figure 13 shows the recorded temperature values and the impact of the reduction in system pressure due to the change in the viscous properties of beef stock during heating. The product went from a thick sticky paste to a thin watery liquid causing the system pressure to drop, by as much as 170 kPa (25 psi). System pressure drops resulted in premature occurrence of CWH, which caused blowouts of system hoses. Even though 44 every effort was made to adjust the pressure as little as possible when signs of approaching CWH were observed, any adjustment would affect the reliability of the data set. A pressure regulating valve would enable the system pressure to be maintained at a steady state. In addition, a pressure relief valve and use of rigid pipes instead of flexible hoses could help prevent blowouts. Beef Stock Test 1 0 10 20 30 40 50 60 70 80 Time (a point collected every two seconds) Temperature Product Inlet Temperature Product Outlet Temperature Figure 13: Data logger output of Ti and Tf over time showing system pressure adjustments during testing. A second potential source of unknown error was the maintenance of the heater during testing. The heater was cleaned by running water through the heater until it flowed clear. However, disassembly of the heater after the research was conducted showed that this was not a sufficient cleaning method. In future research, the apparatus should be disassembled and cleaned after each round of tests and between tests on different products. Pressure Adjustments 45 The third suggestion for future research is to develop a better understanding of how to define the characteristic length for a DSI heater. One definition of characteristic length is the hydraulic radius defined in Equation 20. P r A h = Equation 20 where A is the crosssectional flow area (m2) and P is the wetted perimeter (m). Other researchers choose to use the hydraulic diameter, calculated for two concentric pipes as shown in Equation 21. D d D d D d dh = + = 4 4 4 2 2 Equation 21 where D is the diameter of the exterior pipe (m) and d is the diameter of the interior pipe (m). The value of hydraulic radius for this heater was 0.0085 m and the hydraulic diameter was 0.034 m. While the hydraulic diameter was selected for use in this study, being able to characterize this value with certainty would allow for a better defined relationship for predicting safe operating conditions for a DSI heater. Finally, it is recommended that the research techniques be modified to collect data that will define the entire spectrum of each parameter of interest. Because this research was to serve as a general screening of dimensionless parameters, an effort was not made to tailor system operating conditions to collect data for any particular parameter. If research were to progress based on these results, boundary conditions should be established for the Re, Pr, and St numbers, and data should be collected to fill in the gaps of this research. For 46 example, more data should be collected for Reynolds numbers between 10 and 100, for Prandtl numbers between 10 and 100 as well as between 1000 and 2500, and for Stanton numbers between 10 and 500. Summary There is still much research to be done in the field of direct contact heat exchange. But, with the effort of food engineers, approaches for the safe design and use of DSI heating for liquid food products may yet be developed. 47 BIBLIOGRAPHY Alverez, E., J.M. Correa, M.M. Navaza, and C. Riverol. 2000. Injection of steam into the mashing process as alternative method for the temperature control and lowcost of production. Journal of Food Engineering. 43: 193 196. American Society of Agricultural Engineers. 1999. Psychometric Data. ASAE Standard D271.2 DEC99. Bevington, P.R. Data Reduction and Error Analysis for the Physical Sciences. New York, N.Y.: McGrawHill Book Company. Block, J.A. et al. 1977. An evaluation of power steam generator waterhammer. TN251, Creare, Inc. NUREG0291, U.S. Nuclear Regulatory Commission. Bowser, T.J., P.R. Weckler, and R. Jayasekara. 2003. Design parameters for operation of a steam injection heater without water hammer when processing viscous food and agricultural products. Applied Engineering in Agriculture. 19(4): 447451. Burton, H., A.G. Perkins, F.L. Davies, and H.M. Underwood. 1977. Thermal death kinetics of Bacillus Stearothermophilus spores at ultra high temperatures. III. Relationship between data from capillary tube experiments and from UHT sterilizers. Journal of Food Technology. 12:149161. Doebelin, E.O. 1966. Measurement Systems: Application and Design. New York, NY: McGrawHill Book Company. Goodykoontz, J.H. and R.G. Dorsch. 1966. Local heat transfer coefficients for condensation of steam in vertical downflow within a 5/8Inch diameter tube. Lewis Research Center, National Aeronautics and Space Administration. Cleveland, OH. Hewitt, G.F., G.L. Shires, and T.R. Bott. 1994. Process Heat Transfer. Boca Raton, FL: CRC Press. 48 Hoynak, P.X. and G.N. Bollenback. 1966. This is Liquid Sugar. 2nd ed. Yonkers, N.Y.: Refined Syrups & Sugars, Inc. ICUMSA. 1979. Sugar Analysis, General Methods. ICUMSA Pub., Peterborough, UK. Incropera, F.P. and D.P. DeWitt. 1985. Fundamentals of Heat and Mass Transfer. New York, NY: John Wiley & Sons, Inc. Jones, M.C. and G.S. Larner. 1968. The use of steam injection as a means of rapid heating and sterilization of liquid food. The Chemical Engineer. Jan/Feb CE4CE9. Kreith, F. and R.F. Boehm. 1988. DirectContact Heat Transfer. Washington DC: Hemisphere Publishing Corporation. Kudra, T. and C. Strumillo. 1998. Thermal Processing of BioMaterials. Amsterdam, Netherlands: Gordon and Breach Science Publishers. Lewis, M. and N. Heppell. 2000. Continuous Thermal Processing of Foods: Pasteurization and UHT Sterilization. Gaithersburg, MD: Aspen Publishers, Inc. Perry, J.A. Accessed July 14, 2004. Process Heating by Direct Steam Injection. Posted October 1,1998. www.processheating.com Pick Heaters. Accessed April 16, 2004. www.pickheaters.com/sanitary_specshtm.htm Rabinovich, S.G. 2000. Measurement Errors and Uncertainties. 2nd ed. New York, N.Y.: SpringerVerlag. Richardson, P. 2001. Thermal Technologies in Food Processing. Cambridge, England: Woodhead Publishing Limited. Schroyer, J.A. 1997. Understand the basics of steam injection heating. Chemical Engineering Progress. pg 5255. Singh, R.P. and D.R. Heldman. 2001. Introduction to Food Engineering. 3rd ed. London, England: Academic Press. Sutter, P.J. 1997. Heat Water for Jacketed Vessels by Direct Steam Injection. Chemical Engineering Progress. pg 4043 49 Van Duyne, D.A., W. Yow, H.H. Safwat, A.H. Arastu, and M. Merilo. 1989. Water hammer events under twophase flow conditions. Proceedings of the Second International Multiphase Fluid Transient Symposium, FEDVol. 87. M. Braun, editor. American Society of Mechanical Engineers, New York. 50 APPENDICES 51 APPENDIX A PUMP CALIBRATION CURVE 52 Pump speed (Hz) vs. Flow (gpm) 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 40 50 60 70 Pump Speed (Hz) Flow (gpm) Figure A 1: Pump calibration curve for Waukesha CherryBurrell, Delavan, WI, Model 15 positive displacement pump. 53 APPENDIX B THERMAL DIFFUSIVITY CALCULATIONS 54 For food products the physical properties at various temperatures can be determined based on the amounts of protein, fat, carbohydrate, fiber, ash, water, and ice in the product using Equation B1 and the temperature functions in Table B1. = = n i k kiXi 1 Equation B1 where n is the number of components, ki is the thermal conductivity of the ith component, and Xi is the mass fraction of the ith component (Singh and Heldman, 2001). Equation B1 is equally applicable to density, specific heat, and thermal diffusivity. Table B 1: Coefficients to estimate food physical properties (Singh and Heldman, 2001). Property Component Temperature Function k Protein k=1.7881x101 + 1.1958x103T  2.7178x106T2 Fat k=1.8071x101 – 2.7604x103T  1.7749x106T2 Carbohydrate k=2.0141x101 + 1.3874x103T  4.3312x106T2 Ash k=3.2962x101 + 1.4011x103T  2.9069x106T2 Water k=5.7109x101 + 1.7625x103T  6.7036x106T2 Protein =1.3299x103  5.1840x101T Fat =9.2559x102  4.1757x101T Carbohydrate =1.5991x103  3.1046x101T Ash =2.4238x103  2.8063x101T Water =9.9718x102 + 3.1439x103T  3.7574x103T2 cp Protein cp=2.0082 + 1.2089x103T – 1.3129x106T2 Fat =1.9842 + 1.4733x103T – 4.8008x106T2 Carbohydrate =1.5488 + 1.9625x103T – 5.9399x106T2 Ash =1.0926 + 1.8896x103T – 3.6817x106T2 Water =4.1762 – 9.0864x105T + 5.4731x106T2 55 cp k = Equation B2 (Singh and Heldman, 2001) where is thermal diffusivity (m2s1), k is thermal conductivity (Wm1C1), is density (kgm3), and cp is specific heat (kJkg1K1) Table B 2: Physical properties of the products tested. Tester Product Test Ti ºC kg/m3 m2/s cp kJ/(kgC) k W/m/C Ostermann Beef Stock 1 23.19 1198.19 1.08E07 2.8514 0.370 Ostermann Beef Stock 2 24.20 1197.85 1.08E07 2.8522 0.370 Ostermann Beef Stock 3 19.69 1199.35 1.08E07 2.8486 0.368 Ostermann Beef Stock 4 12.41 1201.58 1.07E07 2.8428 0.365 Ostermann Beef Stock 5 20.43 1199.09 1.08E07 2.8492 0.369 Ostermann Beef Stock 6 17.62 1199.99 1.08E07 2.8469 0.367 Ostermann Beef Stock 7 14.21 1201.04 1.07E07 2.8442 0.366 Ostermann Beef Stock 8 17.87 1199.91 1.08E07 2.8471 0.368 Ostermann Beef Stock 9 23.12 1198.21 1.08E07 2.8513 0.370 Ostermann Beef Stock 10 23.62 1198.05 1.08E07 2.8517 0.370 Ostermann Beef Stock 11 11.95 1201.72 1.07E07 2.8424 0.364 Ostermann Beef Stock 12 12.50 1201.56 1.07E07 2.8429 0.365 Ostermann Beef Stock 13 11.75 1201.78 1.07E07 2.8423 0.364 Ostermann Beef Stock 14 13.83 1201.16 1.07E07 2.8439 0.365 Ostermann Beef Stock 15 15.76 1200.57 1.07E07 2.8455 0.366 Ostermann Beef Stock 16 23.25 1198.17 1.08E07 2.8514 0.370 Ostermann Beef Stock 17 28.15 1196.51 1.09E07 2.8554 0.372 Ostermann Beef Stock 18 21.89 1198.62 1.08E07 2.8504 0.370 Ostermann Beef Stock 19 22.39 1198.45 1.08E07 2.8508 0.370 Ostermann Beef Stock 20 25.97 1197.26 1.09E07 2.8536 0.371 Ostermann Beef Stock 21 33.72 1194.52 1.10E07 2.8599 0.375 Ostermann Beef Stock 22 33.46 1194.62 1.10E07 2.8597 0.375 Ostermann Corn Starch 1 36.55 1039.17 1.44E07 3.9780 0.597 Ostermann Corn Starch 2 45.47 1036.44 1.47E07 3.9820 0.607 Ostermann Corn Starch 4 41.30 1037.79 1.46E07 3.9800 0.602 Ostermann Corn Starch 5 45.28 1036.51 1.47E07 3.9819 0.607 Ostermann Corn Starch 6 43.47 1037.10 1.47E07 3.9810 0.605 Ostermann Corn Starch 7 35.40 1056.90 1.44E07 3.9024 0.584 56 Table B 2: Physical properties of products tested, continued Tester Product Test Ti ºC kg/m3 m2/s cp kJ/(kgC) k W/m/C Ostermann Sugar Water 2 16.80 1302.38 1.10E07 2.8462 0.407 Ostermann Sugar Water 5 23.60 1299.61 1.12E07 2.8578 0.416 Ostermann Sugar Water 6 27.60 1295.03 1.14E07 2.8771 0.424 Ostermann Sugar Water 10 15.00 1297.98 1.09E07 2.8653 0.407 Ostermann Sugar Water 12 23.00 1292.60 1.13E07 2.8883 0.420 Ostermann Sugar Water 13 23.70 1292.43 1.13E07 2.8889 0.421 Bowser Sugar Water 1 34.17 1399.75 1.07E07 2.4235 0.364 Bowser Sugar Water 2 21.50 1390.19 1.04E07 2.4650 0.357 Bowser Sugar Water 3 43.06 1368.94 1.12E07 2.5545 0.392 Bowser Sugar Water 4 43.06 1368.94 1.12E07 2.5545 0.392 Bowser Sugar Water 5 43.06 1368.94 1.12E07 2.5545 0.392 Bowser Sugar Water 6 23.72 1366.15 1.07E07 2.5695 0.375 Bowser Sugar Water 7 23.72 1366.15 1.07E07 2.5695 0.375 Bowser Sugar Water 8 23.72 1366.15 1.07E07 2.5695 0.375 Bowser Sugar Water 9 41.56 1353.51 1.13E07 2.6213 0.401 Bowser Sugar Water 10 41.56 1353.51 1.13E07 2.6213 0.401 Bowser Sugar Water 11 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 12 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 13 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 14 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 15 24.89 1347.36 1.09E07 2.6509 0.388 Bowser Sugar Water 16 26.67 1334.97 1.10E07 2.7044 0.398 Bowser Sugar Water 17 43.89 1294.85 1.18E07 2.8727 0.440 Ostermann Water 1 17.00 996.15 1.44E07 4.1762 0.599 Ostermann Water 2 16.90 996.16 1.44E07 4.1762 0.599 Ostermann Water 3 17.10 996.14 1.44E07 4.1762 0.599 Ostermann Water 5 18.31 995.98 1.45E07 4.1764 0.601 Ostermann Water 6 18.38 995.97 1.45E07 4.1764 0.601 Ostermann Water 7 17.70 996.06 1.44E07 4.1763 0.600 Ostermann Water 8 17.50 996.08 1.44E07 4.1763 0.600 Bowser Water 1 20.83 995.62 1.45E07 4.1767 0.605 Bowser Water 2 13.72 996.52 1.43E07 4.1760 0.594 Bowser Water 3 18.61 995.94 1.45E07 4.1764 0.602 Bowser Water 4 18.67 995.93 1.45E07 4.1764 0.602 Bowser Water 5 18.72 995.92 1.45E07 4.1764 0.602 Bowser Water 6 21.17 995.56 1.46E07 4.1767 0.605 Bowser Water 7 21.94 995.44 1.46E07 4.1768 0.607 57 APPENDIX C COLLECTED DATA 58 Table C1: Collected Data Tester Product Test Flow rate gpm Viscosity cP Pressure psi Ti ºC Tf ºC Tsat ºC Ostermann Beef Stock 1 1.20 1236.5 20 23.19 64.90 126.2 Ostermann Beef Stock 2 1.20 1155.3 15 24.20 72.60 121.2 Ostermann Beef Stock 3 1.44 1485.2 20 19.69 51.10 126.2 Ostermann Beef Stock 4 1.30 2995.08 25 12.41 33.90 130.6 Ostermann Beef Stock 5 1.54 2068.29 20 20.43 46.30 126.2 Ostermann Beef Stock 6 1.69 1796.45 15 17.62 65.90 121.2 Ostermann Beef Stock 7 1.93 2443.88 20 14.21 31.50 126.2 Ostermann Beef Stock 8 1.20 2110.79 15 17.87 48.30 121.2 Ostermann Beef Stock 9 1.44 1356.49 27 23.12 46.40 132.3 Ostermann Beef Stock 10 1.44 1009.65 20 23.62 66.90 126.2 Ostermann Beef Stock 11 2.17 3105.06 12 11.95 58.70 117.8 Ostermann Beef Stock 12 1.20 3163.18 14 12.50 63.10 120.1 Ostermann Beef Stock 13 1.44 3462.53 17 11.75 49.00 123.3 Ostermann Beef Stock 14 2.41 2653.86 14 13.83 30.80 120.1 Ostermann Beef Stock 15 1.69 2270.15 16 15.76 55.80 122.2 Ostermann Beef Stock 16 1.20 1636.46 19 23.25 55.40 125.2 Ostermann Beef Stock 17 1.44 1109.64 20 28.15 53.30 126.2 Ostermann Beef Stock 18 1.93 1300.25 35 21.89 56.10 138.3 Ostermann Beef Stock 19 1.69 1327.74 17 22.39 72.80 123.3 Ostermann Beef Stock 20 0.96 1108.39 27 25.97 60.11 132.3 Ostermann Beef Stock 21 1.44 555.32 20 33.72 59.70 126.2 Ostermann Beef Stock 22 1.20 352.84 15 33.46 59.50 121.2 Ostermann Corn Starch 1 2.17 312.22 20 36.55 59.00 126 Ostermann Corn Starch 2 1.44 518.45 30 45.47 68.00 134.5 Ostermann Corn Starch 4 1.20 668.43 25 41.30 59.80 130.4 Ostermann Corn Starch 5 1.20 706.55 32 45.28 87.80 136 Ostermann Corn Starch 6 0.96 775.92 20 43.47 77.70 126 Ostermann Corn Starch 7 1.44 1554.49 17 35.40 48.80 123.1 59 Table C1: Collected Data, continued Tester Product Test Flow rate gpm Viscosity cP Pressure psi Ti ºC Tf ºC Tsat ºC Ostermann Sugar 2 2.65 26.58 14.80 16.80 56.30 122.76 Ostermann Sugar 5 1.69 17.55 17.60 23.60 72.30 125.64 Ostermann Sugar 6 2.17 12.76 29.30 27.60 70.00 135.84 Ostermann Sugar 10 1.69 24.20 19.40 15.00 62.50 127.34 Ostermann Sugar 12 1.93 14.12 28.20 23.00 68.70 134.92 Ostermann Sugar 13 1.93 13.59 22.90 23.70 71.30 130.49 Bowser Sugar 1 1.44 141.20 10.50 34.17 77.22 120.39 Bowser Sugar 2 2.17 173.90 29.50 21.50 73.22 138.28 Bowser Sugar 3 1.44 31.40 33.00 43.06 103.90 140.39 Bowser Sugar 4 2.17 31.40 22.00 43.06 79.44 131.52 Bowser Sugar 5 2.17 31.40 10.50 43.06 75.00 119.54 Bowser Sugar 6 2.89 71.30 13.00 23.72 52.22 122.22 Bowser Sugar 7 0.96 71.30 18.00 23.72 77.22 127.50 Bowser Sugar 8 0.48 71.30 17.00 23.72 106.70 126.50 Bowser Sugar 9 2.89 22.60 15.90 41.56 63.89 125.15 Bowser Sugar 10 1.20 22.60 23.00 41.56 92.22 131.94 Bowser Sugar 11 0.57 40.30 11.80 24.89 80.56 120.34 Bowser Sugar 12 0.82 40.30 17.80 24.89 91.11 126.80 Bowser Sugar 13 1.20 40.30 16.00 24.89 82.78 124.97 Bowser Sugar 14 1.44 40.30 16.00 24.89 76.67 124.97 Bowser Sugar 15 1.93 40.30 16.00 24.89 69.44 124.97 Bowser Sugar 16 2.51 27.70 13.20 26.67 68.33 121.66 Bowser Sugar 17 2.51 7.00 19.00 43.89 80.00 127.00 Ostermann Water 1 1.91 1.08 35.00 17.00 77.30 138.12 Ostermann Water 2 3.25 1.08 21.40 16.90 61.70 127.28 Ostermann Water 3 1.16 1.08 23.00 17.10 97.10 128.71 Ostermann Water 5 1.03 1.04 29.00 18.31 73.50 133.68 Ostermann Water 6 1.03 1.04 29.50 18.38 79.20 134.07 Ostermann Water 7 0.48 1.06 20.20 17.70 96.80 126.17 Ostermann Water 8 1.66 1.06 32.00 17.50 94.10 135.96 Bowser Water 1 3.80 0.97 26.00 20.83 51.50 131.27 Bowser Water 2 2.35 1.18 14.00 13.72 61.11 119.89 Bowser Water 3 1.06 1.03 28.00 18.61 84.72 132.89 Bowser Water 4 1.15 1.03 24.00 18.67 87.89 129.58 Bowser Water 5 1.80 1.03 23.00 18.72 83.89 128.71 Bowser Water 6 0.48 0.97 26.00 21.17 88.89 131.27 Bowser Water 7 0.23 0.95 20.00 21.94 98.89 125.98 60 APPENDIX D CALCULATION OF METHODOLOGICAL ERROR ASSOCIATED WITH THE FINAL TEMPERATURE 61 The error associated with selecting the Tf value used in calculations was based on the range of temperature values in the oscillations surrounding the selected final temperature. An example of this range is shown in Figure D1 for test 12 of beef stock. Table D1 shows the range of Tf values for tests using beef stock and corn starch, with the average range being 5 °C. This average was assumed to be the methodological error for Tf. Beef Stock Test 12 50 55 60 65 70 75 Time (point collected every 2 seconds) Temperature (C) Product Inlet Temperature Product Outlet Temperature High Value of Range 70 °C Low Value of Range Observed Tf Figure D1: Example of methodological error in final temperature determination 62 Table D1: Variation in final temperature values Product Test Tf ºC Low High Difference Between Low and High Beef Stock 1 64.90 63.10 67.60 4.5 Beef Stock 2 72.60 71.90 75.20 3.3 Beef Stock 3 51.10 50.00 52.40 2.4 Beef Stock 4 33.90 33.30 34.60 1.3 Beef Stock 5 46.30 44.90 48.00 3.1 Beef Stock 6 65.90 63.90 67.20 3.3 Beef Stock 7 31.50 27.90 38.06 10.2 Beef Stock 8 48.30 NA NA 0.0 Beef Stock 9 46.40 43.80 46.40 2.6 Beef Stock 10 66.90 65.40 71.30 5.9 Beef Stock 11 58.70 56.10 65.40 9.3 Beef Stock 12 63.10 59.00 71.10 12.1 Beef Stock 13 49.00 NA NA 0.0 Beef Stock 14 30.80 27.00 37.00 10.0 Beef Stock 15 55.80 NA NA 0.0 Beef Stock 16 55.40 NA NA 0.0 Beef Stock 17 53.30 50.30 60.70 10.4 Beef Stock 18 56.10 54.50 57.40 2.9 Beef Stock 19 72.80 NA NA 0.0 Beef Stock 20 60.11 58.80 60.11 1.3 Beef Stock 21 59.70 58.20 60.70 2.5 Beef Stock 22 59.50 NA NA 0.0 Corn Starch 1 59.00 49.00 64.00 15.0 Corn Starch 2 68.00 66.40 73.10 6.7 Corn Starch 4 59.80 58.30 66.90 8.6 Corn Starch 5 87.80 84.30 94.40 10.1 Corn Starch 6 77.70 73.10 81.40 8.3 Corn Starch 7 48.80 45.70 54.70 9.0 63 APPENDIX E TABULAR RESULTS OF THE CALCULATION OF DIMENTIONLESS PARAMETERS 64 Table E1: Calculated Dimensionless Parameters Tester Product Test RT Pe Pr Re Nu St Ja Ostermann Beef Stock 1 2.47 21594 9529.07 2.27 7459 1.77 73.08 Ostermann Beef Stock 2 2.00 21567 8905.80 2.43 8729 2.38 72.46 Ostermann Beef Stock 3 3.39 26034 11496.58 2.27 6587 1.30 75.19 Ostermann Beef Stock 4 5.50 23751 23327.16 1.02 3874 0.17 79.58 Ostermann Beef Stock 5 4.09 27815 15970.11 1.74 5820 0.63 74.74 Ostermann Beef Stock 6 2.15 30641 13935.46 2.20 11718 1.85 76.44 Ostermann Beef Stock 7 6.48 35165 18991.48 1.85 4679 0.46 78.49 Ostermann Beef Stock 8 3.40 21750 16330.52 1.33 5240 0.43 76.29 Ostermann Beef Stock 9 4.69 25916 10453.41 2.48 4993 1.18 73.12 Ostermann Beef Stock 10 2.37 25899 7781.67 3.33 9321 3.99 72.81 Ostermann Beef Stock 11 2.26 39674 24246.77 1.64 14057 0.95 79.86 Ostermann Beef Stock 12 2.13 21920 24637.27 0.89 8426 0.30 79.53 Ostermann Beef Stock 13 2.99 26334 27037.22 0.97 7421 0.27 79.98 Ostermann Beef Stock 14 6.26 43936 20677.57 2.13 5733 0.59 78.72 Ostermann Beef Stock 15 2.66 30723 17649.49 1.74 9603 0.95 77.56 Ostermann Beef Stock 16 3.17 21593 12611.36 1.71 5752 0.78 73.04 Ostermann Beef Stock 17 3.90 25755 8517.38 3.03 5598 1.99 70.07 Ostermann Beef Stock 18 3.40 34790 10016.84 3.47 9735 3.37 73.86 Ostermann Beef Stock 19 2.00 30444 10230.06 2.97 12613 3.67 73.56 Ostermann Beef Stock 20 3.11 17215 8525.34 2.02 4986 1.18 71.39 Ostermann Beef Stock 21 3.56 25592 4235.09 6.04 6026 8.59 66.70 Ostermann Beef Stock 22 3.37 21333 2690.71 7.92 5021 14.78 66.86 Ostermann Corn Starch 1 3.98 29317 2080.42 14.08 6121 41.44 78.64 Ostermann Corn Starch 2 3.95 19081 3401.10 5.61 4365 7.20 71.99 Ostermann Corn Starch 4 4.82 16042 4419.19 3.63 2892 2.38 75.10 Ostermann Corn Starch 5 2.13 15907 4634.94 3.43 6852 5.07 72.14 Ostermann Corn Starch 6 2.41 12774 5105.68 2.50 4350 2.13 73.48 Ostermann Corn Starch 7 6.54 19442 10387.40 1.91 2447 0.45 79.30 65 Table E1: Calculated Dimensionless Numbers, continued Tester Product Test RT Pe Pr Re Nu St Ja Ostermann Sugar Water 2 2.68 47115 185.88 253.18 14614 19905 83.48 Ostermann Sugar Water 5 2.10 29388 120.56 244.02 11900 24085 79.17 Ostermann Sugar Water 6 2.55 37191 86.58 429.43 13544 67173 76.78 Ostermann Sugar Water 10 2.36 30110 170.37 176.74 11088 11502 84.94 Ostermann Sugar Water 12 2.45 33436 97.10 344.50 12634 44824 79.98 Ostermann Sugar Water 13 2.24 33366 93.25 357.89 13206 50680 79.52 Bowser Sugar Water 1 2.00 26141 940.10 27.83 10257 304 65.96 Bowser Sugar Water 2 2.26 40636 1200.74 33.82 17148 483 74.32 Bowser Sugar Water 3 1.60 25047 204.62 122.41 15097 9032 62.49 Bowser Sugar Water 4 2.43 37745 204.62 184.47 13604 12264 62.49 Bowser Sugar Water 5 2.39 37745 204.62 184.47 11944 10767 62.49 Bowser Sugar Water 6 3.46 52816 488.55 107.97 12499 2762 74.75 Bowser Sugar Water 7 1.94 17544 488.55 35.87 7794 572 74.75 Bowser Sugar Water 8 1.24 8772 488.55 17.93 6044 222 74.75 Bowser Sugar Water 9 3.74 49913 147.73 337.48 10868 24827 64.35 Bowser Sugar Water 10 1.78 20725 147.73 140.13 10238 9711 64.35 Bowser Sugar Water 11 1.71 10238 275.34 37.16 4782 645 75.32 Bowser Sugar Water 12 1.54 14729 275.34 53.46 8183 1589 75.32 Bowser Sugar Water 13 1.73 21554 275.34 78.23 10468 2974 75.32 Bowser Sugar Water 14 1.93 25865 275.34 93.87 11236 3831 75.32 Bowser Sugar Water 15 2.25 34667 275.34 125.82 12957 5921 75.32 Bowser Sugar Water 16 2.28 44446 188.22 235.87 15763 19753 75.00 Bowser Sugar Water 17 2.30 41355 45.70 905.31 14924 295626 65.93 66 Table E1: Calculated Dimensionless Numbers, continued Tester Product Test RT Pe Pr Re Nu St Ja Ostermann Water 1 2.01 25799 7.53 3426.67 12251 5575180 93.54 Ostermann Water 2 2.46 44005 7.53 5844.80 15512 12041250 93.61 Ostermann Water 3 1.40 15707 7.53 2086.15 9903 2743604 93.46 Ostermann Water 5 2.09 13794 7.23 1915.43 6078 1610982 92.56 Ostermann Water 6 1.90 13794 7.23 1915.41 6702 1776274 92.51 Ostermann Water 7 1.37 6555 7.38 887.02 4099 492770 93.02 Ostermann Water 8 1.55 22500 7.38 3044.63 13603 5613169 93.17 Bowser Water 1 3.60 51099 6.70 7605.12 12680 14400782 90.68 Bowser Water 2 2.24 32032 8.30 3868.36 11673 5443280 95.98 Bowser Water 3 1.73 14238 7.15 1996.28 7521 2101146 92.34 Bowser Water 4 1.60 15464 7.15 2168.15 8557 2596328 92.30 Bowser Water 5 1.69 24205 7.15 3393.60 12614 5990632 92.25 Bowser Water 6 1.63 6379 6.70 955.88 3529 503758 90.43 Bowser Water 7 1.35 3017 6.54 461.50 1902 134267 89.85 67 APPENDIX F RESULTS OF LINEAR REGRESSION FOR GROUPED AND AVERAGED DATA VALUES 68 Thermodynamic Ratio vs. Reynolds Number For Averaged Values y = 0.0002x + 3.3631 0 1 2 3 4 5 6 7 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure F1: Linear regression of the relationship between averaged thermodynamic ratio and averaged Reynolds number. Thermodynamic Ratio vs. Prandtl Number For Averaged Values y = 0.0001x + 2.3252 0 1 2 3 4 5 6 7 0 5000 10000 15000 20000 25000 30000 Pr RT Figure F2: Linear regression of the relationship between averaged thermodynamic ratio and averaged Prandtl number. 69 Thermodynamic Ratio vs. Nusslet Number For Averaged Values y = 0.0003x + 5.2366 0 1 2 3 4 5 6 7 0 2000 4000 6000 8000 10000 12000 14000 16000 Nu RT Figure F3: Linear regression of the relationship between averaged thermodynamic ratio and averaged Nusselt number. Thermodynamic Ratio vs. Stanton Number For Averaged Values y = 7E08x + 3.2903 0 1 2 3 4 5 6 7 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 St RT Figure F4: Linear regression of the relationship between averaged thermodynamic ratio and averaged Stanton number 70 Thermodynamic Ratio vs. Jacobs Number For Averaged Values y = 0.0656x + 8.3305 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure F5: Linear regression of the relationship between averaged thermodynamic ratio and averaged Jacobs number 71 APPENDIX G RESULTS OF REGRESSION ANALYSIS USING LOGRITHMIC, EXPONENTIAL, AND POWER RELATIONSHIPS 72 Thermodynamic Ratio vs. Peclet Number Logarithmic y = 0.7811Ln(x)  5.1462 0 1 2 3 4 5 6 7 1000 10000 100000 Pe RT Figure G 1 Thermodynamic Ratio vs. Peclet Number Exponential y = 1.736e1E05x 1 10 0 10000 20000 30000 40000 50000 60000 Pe RT Figure G 1 73 Thermodynamic Ratio vs. Peclet Number Power y = 0.085x0.336 1 10 1000 10000 100000 Pe RT Figure G 2 Thermodynamic Ratio vs. Reynolds Number Logarithmic y = 0.22Ln(x) + 3.5496 0 1 2 3 4 5 6 7 0 1 10 100 1000 10000 Re RT Figure G 3 74 Thermodynamic Ratio vs. Reynolds Number Exponential y = 2.5904e5E05x 1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure G 4 Thermodynamic Ratio vs. Reynolds Number Power y = 3.3112x0.074 1 10 0 1 10 100 1000 10000 Re RT Figure G 5 75 Thermodynamic Ratio vs. Prandtl Number Logarithmic y = 0.235Ln(x) + 1.2394 0 1 2 3 4 5 6 7 1 10 100 1000 10000 100000 Pr RT Figure G 6 Thermodynamic Ratio vs. Prandtl Number Exponential y = 2.1739e3E05x 1 10 0 5000 10000 15000 20000 25000 30000 Pr RT Figure G 7 76 Thermodynamic Ratio vs. Prandtl Number Power y = 1.4994x0.0815 1 10 1 10 100 1000 10000 100000 Pr RT Figure G 8 Thermodynamic Ratio vs. Nusslet Number Logarithmic y = 1.0373Ln(x) + 12.056 0 1 2 3 4 5 6 7 1000 10000 100000 Nu RT Figure G 9 77 Thermodynamic Ratio vs. Nusslet Number Exponential y = 3.3612e3E05x 1 10 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure G 10 Thermodynamic Ratio vs. Nusslet Number Power y = 25.545x0.258 1 10 1000 10000 100000 Nu RT Figure G 11 78 Thermodynamic Ratio vs. Stanton Number Logarithmic y = 0.1151Ln(x) + 3.4651 0 1 2 3 4 5 6 7 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 12 Thermodynamic Ratio vs. Stanton Number Exponential y = 2.5414e2E08x 1 10 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure G 13 79 Thermodynamic Ratio vs. Stanton Number Power y = 3.2171x0.0387 1 10 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 14 Thermodynamic Ratio vs. Jacobs Number Logarithmic y = 2.0034Ln(x) + 11.436 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure G 15 80 Thermodynamic Ratio vs. Jacobs Number Exponential y = 6.4374e0.0121x 1 10 55 65 75 85 95 105 Ja RT Figure G 16 Thermodynamic Ratio vs. Jacobs Number Power y = 116.88x0.8833 0 1 2 3 4 5 6 7 55 65 75 85 95 105 Ja RT Figure G 17 81 Thermodynamic Ratio vs. Peclet Number For Averaged Values Logarithmic y = 1.2559Ln(x)  9.4537 0 1 2 3 4 5 6 7 1000 10000 100000 Pe RT Figure G 18 Thermodynamic Ratio vs. Peclet Number For Averaged Values Exponential y = 1.6791e2E05x 1 10 0 10000 20000 30000 40000 50000 60000 Pe RT Figure G 19 82 Thermodynamic Ratio vs. Peclet Number For Averaged Values Power y = 0.0164x0.512 1 10 1000 10000 100000 Pe RT Figure G 20 Thermodynamic Ratio vs. Reynolds Number For Averaged Values Logarithmic y = 0.382Ln(x) + 4.7425 0 1 2 3 4 5 6 7 0.1 1 10 100 1000 10000 Re RT Figure G 21 83 Thermodynamic Ratio vs. Reynolds Number For Averaged Values Exponential y = 2.9983e6E05x 1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure G 22 Thermodynamic Ratio vs. Reynolds Number For Averaged Values Power y = 4.596x0.1174 1 10 0.1 1 10 100 1000 10000 Re RT Figure G 23 84 Thermodynamic Ratio vs. Prandtl Number For Averaged Values Logarithmic y = 0.3448Ln(x) + 0.694 0 1 2 3 4 5 6 7 1 10 100 1000 10000 100000 Pr RT Figure G 24 Thermodynamic Ratio vs. Prandtl Number For Averaged Values Exponential y = 2.1849e4E05x 1 10 0 5000 10000 15000 20000 25000 30000 Pr RT Figure G 25 85 Thermodynamic Ratio vs. Prandtl Number For Averaged Values Power y = 1.2251x0.1166 1 10 1 10 100 1000 10000 100000 Pr RT Figure G 26 Thermodynamic Ratio vs. Nusslet Number For Averaged Values Logarithmic y = 1.8559Ln(x) + 19.71 0 1 2 3 4 5 6 7 1000 10000 100000 Nu RT Figure G 27 86 Thermodynamic Ratio vs. Nusslet Number For Averaged Values Exponential y = 4.8327e6E05x 1 10 0 2000 4000 6000 8000 10000 12000 14000 16000 Nu RT Figure G 28 Thermodynamic Ratio vs. Nusslet Number For Averaged Values Power y = 196.13x0.4751 1 10 1000 10000 100000 Nu RT Figure G 29 87 Thermodynamic Ratio vs. Stanton Number For Averaged Values Logarithmic y = 0.1821Ln(x) + 4.5253 0 1 2 3 4 5 6 7 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 30 Thermodynamic Ratio vs. Stanton Number For Averaged Values Exponential y = 2.9303e2E08x 1 10 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure G 31 88 Thermodynamic Ratio vs. Stanton Number For Averaged Values Power y = 4.297x0.0559 1 10 1.0E01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 St RT Figure G 32 Thermodynamic Ratio vs. Jacobs Number For Averaged Values Logarithmic y = 4.9669Ln(x) + 24.84 0 1 2 3 4 5 6 7 10 100 Ja RT Figure G 33 89 Thermodynamic Ratio vs. Jacobs Number For Averaged Values Exponential y = 26.083e0.0283x 1 10 55 65 75 85 95 105 Ja RT Figure G 34 Thermodynamic Ratio vs. Jacobs Number For Averaged Values Power y = 36751x2.1721 1 10 10 100 Ja RT Figure G 35 90 APPENDIX H RESULTS OF REGRESSION ANALYSIS FOR PORTIONS OF DATA SET 91 Thermodynamic Ratio vs. Peclet Number Rt<5 Linear y = 3E05x + 1.8076 0 1 2 3 4 5 6 0 10000 20000 30000 40000 50000 60000 Pe RT Figure H 2 Thermodynamic Ratio vs. Peclet Number Rt<5 Logarithmic y = 0.6263Ln(x)  3.8069 0 1 2 3 4 5 6 1000 10000 100000 Pe RT Figure H 3 92 Thermodynamic Ratio vs. Peclet Number Rt<5 Exponential y = 1.6992e1E05x 1 10 0 10000 20000 30000 40000 50000 60000 Pe RT Figure H 4 Thermodynamic Ratio vs. Peclet Number Rt<5 Power y = 0.1148x0.3006 1 10 1000 10000 100000 Pe RT Figure H 5 93 Thermodynamic Ratio vs. Prandtl Number Pr<500 Linear y = 0.0004x + 2.0387 0 1 1 2 2 3 3 4 4 0 100 200 300 400 500 600 Pr RT Figure H 6 Thermodynamic Ratio vs. Prandtl Number Pr<500 Logarithmic y = 0.0752Ln(x) + 1.7984 0 1 1 2 2 3 3 4 4 1 10 100 1000 Pr RT Figure H 7 94 Thermodynamic Ratio vs. Prandtl Number Pr<500 Exponential y = 1.9789e0.0001x 1 10 0 100 200 300 400 500 600 Pr RT Figure H 8 Thermodynamic Ratio vs. Prandtl Number Pr<500 Power y = 1.7508x0.0362 1 10 1 10 100 1000 Pr RT Figure H 9 95 Thermodynamic Ratio vs. Prandtl Number Pr>500 Linear y = 4E05x + 3.0435 0 1 2 3 4 5 6 7 0 5000 10000 15000 20000 25000 30000 Pr RT Figure H 10 Thermodynamic Ratio vs. Prandtl Number Pr>500 Logarithmic y = 0.3624Ln(x) + 0.1705 0 1 2 3 4 5 6 7 100 1000 10000 100000 Pr RT Figure H 11 96 Thermodynamic Ratio vs. Prandtl Number Pr>500 Exponential y = 2.9378e8E06x 1 10 0 5000 10000 15000 20000 25000 30000 Pr RT Figure H 12 Thermodynamic Ratio vs. Prandtl Number Pr>500 Power y = 1.4162x0.0908 1 10 100 1000 10000 100000 Pr RT Figure H 13 97 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Linear y = 0.0031x + 3.1813 0 1 2 3 4 5 6 7 0 50 100 150 200 250 300 350 400 450 500 Re RT Figure H 14 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Logarithmic y = 0.2795Ln(x) + 3.674 0 1 2 3 4 5 6 7 0 1 10 100 1000 Re RT Figure H 15 98 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Exponential y = 2.9227e0.001x 1 10 0 50 100 150 200 250 300 350 400 450 500 Re RT Figure H 16 Thermodynamic Ratio vs. Reynolds Number Just Re<500 Power y = 3.4218x0.0884 1 10 0 1 10 100 1000 Re RT Figure H 17 99 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Linear y = 0.0002x + 1.295 0 1 2 3 4 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure H 18 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Logarithmic y = 0.5364Ln(x)  2.1945 0 1 2 3 4 100 1000 10000 Re RT Figure H 19 100 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Exponential y = 1.4292e0.0001x 1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 Re RT Figure H 20 Thermodynamic Ratio vs. Reynolds Number Just Re>500 Power y = 0.3078x0.2348 1 10 100 1000 10000 Re RT Figure H 21 101 Thermodynamic Ratio vs. Nusselt Number Rt<5 Linear y = 6E05x + 3.0375 0 1 2 3 4 5 6 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure H 22 Thermodynamic Ratio vs. Nusselt Number Rt<5 Logarithmic y = 0.4422Ln(x) + 6.4925 0 1 2 3 4 5 6 1000 10000 100000 Nu RT Figure H 23 102 Thermodynamic Ratio vs. Nusselt Number Rt<5 Exponential y = 2.7087e1E05x 1 10 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Nu RT Figure H 24 Thermodynamic Ratio vs. Nusselt Number Rt<5 Power y = 5.9287x0.1018 1 10 1000 10000 100000 Nu RT Figure H 25 103 Thermodynamic Ratio vs. Stanton Number St<100,000 Linear y = 2E05x + 3.068 0 1 2 3 4 5 6 7 0 10000 20000 30000 40000 50000 60000 70000 80000 St RT Figure H 26 Thermodynamic Ratio vs. Stanton Number St<100,000 Logarithmic y = 0.1485Ln(x) + 3.5582 0 1 2 3 4 5 6 7 0 1 10 100 1000 10000 100000 St RT Figure H 27 104 Thermodynamic Ratio vs. Stanton Number St<100,000 Exponential y = 2.8153e4E06x 1 10 0 10000 20000 30000 40000 50000 60000 70000 80000 St RT Figure H 28 Thermodynamic Ratio vs. Stanton Number St<100,000 Power y = 3.2898x0.0453 1 10 0 1 10 100 1000 10000 100000 St RT Figure H 29 105 Thermodynamic Ratio vs. Stanton Number St>100,000 Linear y = 1E07x + 1.5072 0 1 2 3 4 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure H 30 Thermodynamic Ratio vs. Stanton Number St>100,000 Logarithmic y = 0.2173Ln(x)  1.2367 0 1 2 3 4 1.E+05 1.E+06 1.E+07 1.E+08 St RT Figure H 31 106 Thermodynamic Ratio vs. Stanton Number St>100,000 Exponential y = 1.55e4E08x 1 10 0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07 1.E+07 1.E+07 2.E+07 St RT Figure H 32 Thermodynamic Ratio vs. Stanton Number St>100,000 Power y = 0.4248x0.1014 1 10 1.E+05 1.E+06 1.E+07 1.E+08 St RT Figure H 33 107 Thermodynamic Ratio vs. Jacob Number Rt<5 Linear y = 0.0309x + 4.9025 0 1 2 3 4 5 6 50 55 60 65 70 75 80 85 90 95 100 Ja RT Figure H 34 Thermodynamic Ratio vs. Jacob Number Rt<5 Logarithmic y = 2.3403Ln(x) + 12.671 0 1 2 3 4 5 6 10 100 Ja RT Figure H 35 108 Thermodynamic Ratio vs. Jacob Number Rt<5 Exponential y = 6.4189e0.0128x 1 10 50 55 60 65 70 75 80 85 90 95 100 Ja RT Figure H 36 Thermodynamic Ratio vs. Jacob Number Rt<5 Power y = 161.99x0.9722 1 10 10 100 Ja RT Figure H 37 VITA Rebecca Ann Ostermann Candidate for the Degree of Master of Science Thesis: DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS Major Field: Biosystems Engineering Biographical: Personal Data: Born in Colorado Springs, Colorado on May 16, 1977 the daughter of Tom and Jeanne Ostermann. Education: Graduated from Poudre High School, Fort Collins, Colorado in April, 1995; received a Bachelor of Science degree in Biosystems Engineering from Oklahoma State University, Stillwater, Oklahoma in May, 2000. Completed the requirements for the Master of Science degree with a major in Biosystems Engineering from Oklahoma State University in December, 2005. Professional Experience: Water Resource Engineer, CH2M Hill, Inc. September 2004Present Professional Memberships: American Society of Agricultural and Biological Engineers Name: Rebecca Ann Ostermann Date of Degree: December, 2005 Institution: Oklahoma State University Location: Stillwater, Oklahoma Title of Study: DIRECT STEAM INJECTION HEATING OF LIQUID FOOD PRODUCTS Pages in Study: 108 Candidate for the Degree of Master of Science Major Field: Biosystems Engineering Scope and Method of Study: The purpose of this research was to investigate a correlation between flow characteristics and physical properties of liquid food products and the occurrence of condensationinduced water hammer in direct steam injection heating. A linear relationship developed by Bowser et al. (2003) between the thermodynamic ratio and the Peclet number was examined for applicability to results from tests performed using water, sugar solution, beef bone stock, and corn starch. Five other dimensionless parameters were screened for potential relationships to the thermodynamic ratio that could be used to define safe operating conditions for a steam injection heater. Findings and Conclusions: It was verified that a linear relationship between the thermodynamic ratio and the Peclet number for predicting CWH applied well to water and sugar water. Results for other food products tested in this study were inconclusive. Of the six dimensionless parameters investigated, four, the Prandlt, Reynolds, Peclet, and Stanton numbers, merited further investigation. It was also found that power and logarithmic equations may better describe a relationship to predict condensationinduced water hammer than a linear equation. ADVISER’S APPROVAL: Dr. Timothy Bowser 



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