CFD ANALYSIS OF TURBULENT SLURRY FLOW
THROUGH THE SENSING REGION OF NEAR IR
DIFFUSE TRANSMISSION AND REFLECTANCE
PROBES MOUNTED IN A PIPE FLOW
By
GAURAV SHARMA
Bachelor of Engineering in Mechanical Engineering
Madhav Institute of Technology and Science
Gwalior, India
2006
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
May, 2010
ii
CFD ANALYSIS OF TURBULENT SLURRY FLOW
THROUGH THE SENSING REGION OF NEAR IR
DIFFUSE TRANSMISSION AND REFLECTANCE
PROBES MOUNTED IN A PIPE FLOW
Thesis Approved:
Dr. Frank W. Chambers
Thesis Adviser
Dr. David G. Lilley
Dr. Andrew S. Arena
Dr. A. Gordon Emslie
Dean of the Graduate College
iii
ACKNOWLEDGMENTS
First of all, I wish to extend sincere gratitude to my Adviser Dr. Frank Chambers
for his esteemed guidance and untiring supervision. I extremely appreciate his caring
attitude towards his students. Also, I would like to thank him for his precious suggestions
during my research work. I am grateful to him for providing me the privilege to work on
this research opportunity.
I also wish to extend my appreciation to Dr. A. Arena and Dr. D.G. Lilley for serving as
the members of my Thesis committee. I wish to say thanks to my dear parents and my
brothers Saurav and Pushkar for boosting me up with their love.
I would like to express my regards to my research group members Netaji, Krishna and
Vamsee for their suggestions during my research study. At last, I am indebted to my
friends Vineet, Ashish, Sam and Janae for their love and encouragement.
I am also thankful to all those people who directly or indirectly helped me through my
thesis work.
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TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION ...................................................…………………………………….1
1.1 Background ....................................................................................................................1
1.2 Importance of computational methods...........................................................................2
1.3 Fluent and Gambit as CFD tools ....................................................................................3
1.4 Aims and objectives to accomplish ................................................................................4
II. REVIEW OF LITERATURE..........................................................................................5
2.1 Introduction ....................................................................................................................5
2.2 Numerical simulation studies in two phase flow ...........................................................5
2.3 Studies of two phase slurries in pipes ............................................................................7
2.4 Other Studies focusing on two phase ...........................................................................16
2.5 Fourier Transformed Infrared (FTIR) spectroscopy ....................................................25
2.5.1 Studies related to FTIR/NIR spectroscopy ...............................................................26
3.1 Conclusions ..................................................................................................................33
III. NUMERICAL APPROACH .......................................................................................34
3.1 Introduction ..................................................................................................................34
3.2 Governing Equations ...................................................................................................37
3.3 Numerical methods in CFD .........................................................................................39
3.4 Selection of turbulence model .....................................................................................42
3.5 Modeling the multiphase flow .....................................................................................45
3.5.1 Modeling with mixture multiphase model ....................................................47
3.5.2 Equations used in mixture model ..................................................................48
3.5.3 Limitations and assumptions of mixture model ............................................51
3.5.4 K-ε equations used in mixture model ..........................................................52
3.6 Incorporation of sensor and pipe geometry using Gambit meshing
and formulation ...........................................................................................................53
3.7 Simulations in Fluent ...................................................................................................56
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Chapter Page
IV. RESULTS AND DISCUSSION ..................................................................................62
4.1 Brief recapitulation ......................................................................................................62
4.2 Flow of Xylene (WITHOUT particles) in 7.112m length pipe ...................................63
4.3 Flow of ADP particles with Xylene in 280” (7.112m, L/D=70) length pipe...............67
4.3.1 Plots of velocity profiles ...............................................................................68
4.3.2 Plots of particle volume fraction ...................................................................75
4.3.3 Z velocity of slurry/mixture along the vertical and horizontal (axial) axes.
.......................................................................................................................80
4.3.4 Visualization of the flow of ADP particles with Xylene ..............................87
4.3.5 Comparison of Volume fraction profiles obtained for two different
particle sizes ..................................................................................................95
4.4 Comparison of the velocity profiles obtained for ADP and Xylene slurry to that of
calcium carbonate and water slurry .................................................................................101
V. CONCLUSION ..........................................................................................................105
5.1 Summary ....................................................................................................................105
5.2 Conclusions ................................................................................................................105
5.3 Recommendations ......................................................................................................108
REFERENCES ................................................................................................................109
APPENDICES .................................................................................................................112
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LIST OF TABLES
Table
Page
2.1 Cases as identified by Xu et al. (2004) ........................................................................18
3.1 Input materials in Fluent ..............................................................................................57
3.2 Input materials phase in Fluent ....................................................................................58
3.3 Input variables and their magnitudes ...........................................................................59
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LIST OF FIGURES
Figure Page
2.1 Test loop used by Kaushal et al. (2005 ..........................................................................9
2.2 Evolution of volume fraction of silica sand at the vertical central plane of the pipe’s
cross section (Source: Lin et al (2007)) .............................................................................13
2.3 Velocity profiles of single and double species slurry flow along the vertical centerline
from the entrance region to fully developed slurry flow region (volume fraction=20%,
particle diameter =100 microns, pipe diameter = 0.0221m (Source: Lin et al (2007)) .....14
2.4.Contour of particle volume fraction in the channels for different particle sizes at
elapsed time t=2 s. (Influx particle volume fraction αp,0=19.0%, flow velocity )
..........................................................................................................................................19
2.5 Particle volume fractions at intersection of surfaces y=0.01 m and z=0 m for different
particle sizes at elapsed time t=2 s. (Influx particle volume fraction αp,0=19.0%, flow
velocity m/s .......................................................................................................19
2.6 (a) Experimental velocity profile (b). Simulation velocity profile. Both are in
r-z plane .............................................................................................................................21
2.7 Comparison of simulated velocity between spherical and slender par ........................22
2.8. Inner and outer zones in modified inner outer iterative method. (Source: Wang
et al. (2003) ........................................................................................................................23
2.9.Computational grid of ‘inner’ and ‘outer’ domains (Source: Wang et al. (2003)) ......24
2.10.Experimental set up. 1 Personal computer, 2 NIR instrument, 3 Fiber optics cable, 4
Transflectance probe, 5 Stirrer motor, 6, Temperature probe,7 Reactor temperature
control, 8 Stirrer, 9 glass jacketed reactor (500 ml),10 Condenser....................................27
2.11 Raw NIR spectra of slurries of α-form L-GA crystals of different particle sizes,
under fixed temperature and solid concentration ...............................................................28
2.12. α-form spectra at varied solid concentrations but fixed particle size (70 μm) and
temperature (40 °C) ...........................................................................................................28
2.13.Experimental set up with the measurement locations and cook ups at S1, S2, S3
and S4................................................................................................................................30
viii
2.14 Predicted velocity vectors and CO2 mass fraction contours at the centre y plane for
an air flow rate of 2.4 ACH ...............................................................................................31
3.1 Rectangular cell control volume ..................................................................................42
3.2 Extent of resolution of turbulence scales and modeling in different turbulence
models ...............................................................................................................................44
3.3 Fourier Transformed Infrared Reflectance probe ........................................................53
3.4 Boundary types shown in Gambit ................................................................................54
3.5 The meshed pipe and probe assembly in Gambit ........................................................54
3.6 Solution strategy in Fluent ...........................................................................................61
4.1(a) Pipe coordinate system (plain pipe). (b) Z velocity of Xylene varying along
centerline of the pipe ..........................................................................................................64
4.2 Pipe section showing the location of planes and the respective axes along which Z
velocity are plotted. Inlet (shown in blue) is near Z= -1 plane and oulet (shown in red)
lies near to Z= -7 plane. Flow direction shown by arrow ..................................................64
4.3 Z velocity profiles along vertical axes in (a) Z= -1 (Z/D=9.84), (b) Z= -2
(Z/D=19.685), (c) Z= -3.5 (Z/D=34.45), (d) Z= -5 (Z/D=49.2) and (e) Z= -7 (Z/D= 68.89)
cross sectional planes as shown .........................................................................................65
4.3 (f) 4.3 (f) Comparison of velocity profile in radial direction with power law profile
(n=7) shown in red with the fluent profile in blue at Z/D=35 ...........................................66
4.4 Particle Z velocity profile along centerline of the plain pipe.......................................66
Fig. 4.5 (a1) Probe and pipe assembly with the directional coordinate system (a2) Axis
of the pipe (b) Particle phase Z velocity variation along the centerline (c)Flow along the
probe vicinity shown between parallel lines ......................................................................70
Fig. 4.6 (a) Axis (b) Particle phase Z velocity variation along the axis parallel to the
centerline.(c)Flow along the probe vicinity shown between parallel lines ........................71
Fig. 4.7(a) Axis. (b) Particle phase Z velocity variation along the axis parallel to the
centerline but passing through the lower solid end of the probe. (c)Flow along the probe
vicinity shown between parallel lines ................................................................................73
Fig. 4.8(a) Axes in Y direction and along the lines to the left and to the right of it
(b)Particle Z velocity vs. Y axis (Along the line through the center of the probe slot
circular section, along the lines to the left and to the right of it ........................................75
ix
Fig. 4.9(a) Axes in Y direction and along the lines to the left and to the right of it (b)
Particle volume fraction vs. Y axis (Along the line through the center of the probe slot
circular section, along the lines to the left and to the right of it ........................................77
4.10 (a) Axes (b) Particle volume fraction variation along the axis behind the Y axis
through probe. The axis is shown in Fig. (a) .....................................................................78
4.11 Particle volume fraction variation along the axis in front of Y axis .... through probe.
The axis is shown in Fig. 4.10 (a) ......................................................................................79
4.12Particle volume fraction variation along the axes shown in Fig. 4.10 (a) ..................80
4.13 (a) Probe and pipe assembly with the planes Z=3, 2, 1,-1,-2(b) Particle Z velocity
along a vertical line in the cross sectional plane Z=3, Z/D=29.527 ..................................81
4.14 Particle Z velocity along a vertical line in the cross sectional plane Z=2,
Z/D=19.685 ........................................................................................................................82
4.15 Particle Z velocity along a vertical line in the cross sectional plane Z= 1, Z/D=9.84
................................................................................................................................83
4.16 Particle Z velocity along a vertical line in the cross sectional plane Z= -1, Z/D= -
9.84....................................................................................................................................84
4.17 Particle Z velocity along a vertical line in the cross sectional plane Z= -2, Z/D = -
19.685................................................................................................................................84
4.18 (a’) Axes. Z velocity profiles along the axial lines through probe slot. (a)Slot line 1,
y/R= 0.74 (b) Slot line 2, y/R= 0.69(c) Slot line 3, y/R= 0.625 (d) Slot line 4, y/R=0.56
(e) Slot line 5, y/R=0.51. Axes are shown in (a’) .............................................................86
4.19 Volume fraction profiles along the axial lines through probe slot .............................87
4.20 (a) Plane Y=0.02 (b) Contours of Z velocity of slurry along the plan Y=0.02,
Y/R=0.39 ............................................................................................................................88
4.21 (a) Plane Y=0.03 (b) Contours of Z velocity of slurry along the plan Y=0.03,
Y/R=0.59 ............................................................................................................................89
4.22 Contours of velocity Z velocity of slurry along the plane X=0 (X/R=0) which the
passes right in the middle through the probe section as well as the probe slot ..................90
4.23 Contours of velocity Z velocity of slurry along the plane X=0 (closer view) ...........91
x
4.24 Contours of velocity Z velocity of slurry along the plane X=0, closer look of probe
region ................................................................................................................................91
4.25 Vertical plane passing through the probe slot shown in grey with the probe shown
in green..............................................................................................................................92
4.26 Contours of velocity magnitude of slurry/mixture along the plane X=0, X/R=0
which passes right in the middle of the probe slot .............................................................93
4.27 Contours of Z velocity of slurry/mixture along the plane Z=0, where Z/D=0 ..........93
4.28 Contours of velocity colored by particle volume fraction in the plane X=0, where
X/R=0 ................................................................................................................................94
4.29 Comparison of volume fraction along Y axis lying in the probe slot ........................95
4.30 Comparison of volume fraction along line parallel to Y axis lying in the probe slot
but to the left of it...............................................................................................................96
4.31 Comparison of volume fraction along line parallel to Y axis lying in the probe slot
but to the right of it ............................................................................................................97
4.32 (a) Axes along the probe slot (b) Comparison of volume fraction along line parallel
to Y axis but behind it (shown by Red line in Fig. (a)). (c) Comparison of volume fraction
along line parallel to Y axis but in front of it (shown by green line in Fig. (a)) ................98
Fig. 4.33 Comparison of volume fraction for different particle size along (b) Slot line A,
y/R= 0.69 (c) Slot line B, y/R= 0.625 (d) Slot line C, y/R=0.56, as shown in Fig. (a) ...100
4.34 Comparison of ADP and CaC03 particles Z velocity profile along centerline of the
pipe. (Probe vicinity shown between parallel lines with 0.09<Z/D< 0.09) .....................101
4.35 Comparison of ADP and CaC03 particles Z velocity profile along the axis parallel to
the centerline and passing through the probe slot. (Probe vicinity shown between parallel
lines with 0.09 < Z/D < 0.09) ...........................................................................................102
4.36 Comparison of Z velocity along the line through the center of the probe slot circular
section in Y direction. (Probe slot lying between 0.5<y/R<0.75) ...................................103
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NOMENCLATURE
a Acceleration in m/sec
f Body forces
g Acceleration due to gravity
I Identity matrix
k Turbulent Kinetic energy
L Litres
m Mass in Kg.
p Pressure
r Radial coordinate
R Radius in meters.
Re Reynolds number
ReP Particle Reynolds number
Δp Pressure drop
t Time in secs.
T Temperature
u Velocity in X direction
v Velocity in Y direction
w Velocity in Z direction
X X-axis
xii
Y Y-axis
Z Z-axis
Volume fraction
ε Turbulence dissipation
κ Log-law coefficient
ρ Fluid density
τ Stress tensor
μ Dynamic viscosity
ν Kinematic viscosity
Τurbulent viscosity
ω Specific dissipation rate
∇ Del operator
Angular distance
xiii
ABBREVIATIONS
ACH Air Changes per Hour
AR Aspect Ratio
ADP 2, Amino, 4, 6 Dimethyl Pyrimidine
ASM Algebraic Slip Model
CFD Computational Fluid Dynamics
DES Detached Eddy Simulation
DNS Direct Numerical Simulation
FTIR Fourier Transformed Infrared Reflectance
LES Large Eddy Simulation
LIF Laser Induced Fluorescence
N-S Navier Stokes
NIR Near Infrared
NIRA Near Infrared Reflectance Analysis
PDE Partial Differential Equation
PEPT Positron Emission Particle Technique
PIV Particle Image Velocimetry
RANS Reynolds Averaged Navier Stokes
RNG Renormalization Group
RSM Reynolds Stress Model
SA Spalart Allmaras
S k- Standard k-
SKW Standard k-omega
xiv
SST Shear Stress Transport k- omega
TI Turbulent Intensity
1
CHAPTER I
INTRODUCTION
1.1 Background:
The flow of liquids through pipelines is a common process in industries as well as
the households. The supply of water for household purposes involves the transport of
water through pipes which have small diameters. In industries the water and other fluids
supply is done through pipelines with comparatively larger diameter. The mechanics of
the flow of fluids depends on the properties of the fluids being transported. These fluid
properties include density, viscosity and surface tension. The mechanics of fluid flow is
simpler when there is only one phase. Complexities in the flow are introduced when more
than one number of phases is participating in the flow. The flow in which more than one
phases is flowing together is known as multiphase flow. Examples of multiphase flow
can be bubble or droplet flow, slug flow, pneumatic transport, hydrotransport or slurry
flows. The multiphase flow of solid particles with liquids such that the presence of solid
particles in the flow is considerable is termed slurry flow
Multiphase flows are complex flows and their complexity can be attributed to the
interaction between the participating phases. Apart from this, there can be other sources
which contribute to the complexity of the flow. These may include the physical aspects
2
like transition between different flow regimes, turbulent flow and the presence of some
disturbed interface such as surface waves on a film to name a few. In the case of slurry
flows liquid- particle interaction and turbulent characteristics of the flow are the factors
which require special attention. In industrial applications, along with single phase flows,
there are many multiphase flows in the form of particles and liquid flowing together.
Most of the pharmaceutical and petrochemical industries involve the transportation of
slurries through pipes using different type of pumping devices. These slurries have a
complex composition consisting of chemical particles flowing in organic or inorganic
solutions. The methods or the processes applied in the handling of slurries should be
effective and efficient. The current research focus is to design better sampling techniques
for measuring these chemical slurries used for industrial purposes. This study aims at
providing a new methodology for the analysis of complex samples under industrial
conditions. In the current study the flow of some specific slurries has been simulated
using a CFD commercial software package.
1.2 Importance of computational methods: Experimental methods have always found
wide applications in order to visualize the flow fields and the feature which are of real
concern. Some of the flows can be very well described using experimental methods.
However, it could be difficult to set up a multiphase flow experiment with the necessary
degree of control. Such situations arise, for example, in the case of the breakup of a drop
in a turbulent flow or precise characterization of the bubble or drop size distribution.
There are many experimental techniques that can be easily implemented for single phase
flows while multiphase flow systems poses severe difficulties. For example, bubbly flow
may become opaque resulting in poor visualization even at low volume fractions. The
3
clustering of particles suspended in a slurry flow depends on the small scale details which
are difficult to be resolved through experiments. In all these situations, numerical
simulation stands out as an important tool for the study of multiphase flow systems.
Computation techniques may be the best tools in some conditions. These conditions may
be attributed to the presence of forces of gravity and surface tension. In case of
experimental techniques, these aspects may be immeasurable. In the case of multiphase
flows, there is always a requirement of reduced descriptions for modeling which is given
sometimes through averaged equations. Thus such reduced models are greatly benefitted
from the computational techniques.
1.3 Fluent and Gambit as CFD tools: As discussed in the preceding paragraphs
computational methods have an edge over experimental techniques not only because of
the ease of obtaining the end results but also because they are economical compared to
the experimental set ups. In the present study, Fluent has been employed as the
commercial software package in order to facilitate the analysis of chemical slurry flow
through pipes with FTIR (Fourier transformed infrared reflectance) probes. Gambit has
been used as the preprocessor used to construct and mesh the pipe and probe assembly.
The meshed geometry is exported to Fluent for the actual analysis. The pipe Reynolds
number for the flow is of the order of 100,000. The mixture model has been employed as
the multiphase flow model while K-ε model has been used to account for the turbulence
effects of the flow. Two different types of slurries have been considered for analysis. The
first one is the flow of ADP particles in Xylene as the liquid and another is the Calcium
Carbonate particles in water as the flowing liquid.
4
1.4 Aims and objectives to accomplish: The present study aims at the following tasks:
- To apply CFD to visualize the flow over and through the sensing gap of the FTIR probe.
- To determine the volume fraction profiles of the particles flowing through the sensing
gap.
- To determine the velocity profiles of the particles flowing through the sensing gap.
5
CHAPTER II
REVIEW OF LITERATURE
2.1 Introduction:
This chapter deals with the studies and investigations done by researchers and
scientists around the world in the field of Computational Fluid Dynamics (CFD). The
discussion in the current study will be focusing on the multiphase flow consisting of solid
particles and liquid fluids with turbulent characteristics. This chapter will also deal with a
little discussion about the Fourier transformed infrared spectroscopic studies. In the
current study the area to be given attention is the CFD simulations of turbulent slurry
flows through pipe, hence major stress has been given on these keywords. Therefore this
chapter includes the review of most relevant literature available. In the first part of the
chapter, studies related to the CFD have been covered while the later part deals in brief
about Fourier transformed spectroscopic studies and some of their applications.
2.2 Numerical simulation studies in two phase flow: As the present study deals with
the flow of ADP particles with Xylene as the liquid fluid hence it is necessary that the
particles should remain in suspension with the liquid while during the flow. Various
studies have been conducted in order to determine the factors that are responsible to make
the particles flow with the liquid fluid. This section will cover the previous studies and
6
researches made in order to discuss the effects of governing parameters on the flow
characteristics and its behavior in a two phase flow. These parameters are particle size,
particle concentration and particle velocities to name a few. Xu et al. (2004) have
conducted numerical simulations in order to simulate the flow of solid hydrogen particles
in liquid helium. They concluded that the flow must be turbulent else the hydrogen
particles will form a sliding layer over the helium layer. The concentration profiles of
hydrogen particles have been found to be dependent upon the size of particles, the
velocity of flow and the inlet volume fraction of the hydrogen particles.
Similarly Oey et al. (2001) have simulated the flow of gas-liquid and solid flow in
an internal loop airlift reactor. They have made use of the two phase flow approach in
order to simulate a three phase mixture of solid, liquid and gas by treating the airlift loop
as two phase system i.e. a gas-liquid two phase system. They were able to detect different
flow regimes by varying the gas flow rate. They also concluded that turbulent dispersion
of the solid particles is needed in order to prevent them from settling down at the dead
corners. The solid particle distribution is found to be smooth with higher volume fraction
of solids in the lower part of the lower comers when the turbulent dispersion is taken into
consideration. When turbulent dispersion is taken into account equilibrium between
settling and dispersion is found.
Kasat et al. (2008) developed a CFD model in order to evaluate the complex
interaction between the solid particles and the liquid phase mixing in a stirred slurry
reactor. They studied the characteristic behavior of mixing time of the solid liquid
suspension as a function of the impeller speed. According to them the mixing time
increases with the increment in impeller speed and then reaches a maximum value and
7
further increment in impeller speed brings a gradual decrease in the mixing time. They
have attributed the delayed mixing of the solid and liquid phases to the low velocities in
the upper clear liquid region in the reactor. Their CFD model can be used for large scale
industrial studies which involve the suspension and mixing of solid particles into liquids.
2.3 Studies of two phase slurries in pipes: In this portion of the chapter, discussion is
primarily focused on studies involving solid-liquid flow through pipelines.
Brown (1999) studied the abrasive nature of a slurry consisting of bauxite
particles flowing with caustic liquid by predicting the erosion taking place in the
pipelines. He developed a three dimensional CFD model bases on Eulerian- Eulerian
continuum approach. He has used K-ε model to account for the turbulence effects at the
Tee section. A swirling inlet flow condition has been preferred to be used to accurately
predict the accumulation of particles and the position of accumulation. They have
employed a multiphase model with the help of which a solution for the erosion problem
has been obtained. The problem of erosion has been found to be decreased by using a
pivoted elbow design in place of a Tee junction. They have shown the ability of
applications of CFD to the industrial problems which occur due to erosion phenomenon.
It has been observed that deposition critical velocity plays an important role in the
design of the pipelines made for the slurry flows. It is the magnitude of minimum flow
velocity at which the flow of slurries can remain suspended in the pipeline. It has been
found that the deposition velocity of flow depends on several factors including the size of
the particles, the density of particles, the diameter of pipe and the solid concentration of
the slurries. Kaushal et al. (2002) have conducted experiments to measure the
8
concentration at the pipe bottom at deposition velocity. They have utilized the data
studied by Kaushal et al. (1995), Mukhtar et al. (1991), Seshadri et al. (1975) and
Seshadri et al. (1980) with variable size iron ore particles, copper tailings and zinc
tailings slurries flowing through pipes. The diameters of the pipelines which were
considered are 55 mm and 105 mm. They have made modifications to Karabela’s model
(1977) on the basis of their studies. The original Karabela’s model determines the solid
concentration profiles in a slurry consisting of multisized particles with help of an
equation. The Karabela’s equation take into account the particle diffusivity, the particle
size, and settling velocity. There are two assumptions involved in determining the solid
concentration profiles in Karabela’s model. Firstly, the dimensionless eddy diffusivity is
taken constant and is independent of space coordinates and solid concentration. Second,
the solid concentration is assumed to depend only on vertical coordinate. It has been
found that the overall concentration profiles predicted by the modified Karabelas model
for 30 sets of experimental data holds good agreement for almost all of them. The
original Karabelas model gives large deviations particularly for higher concentrations.
Thus it has been concluded that the modified Karabelas model is more accurate. This is
due to incorporating the solid concentration effects on settling of particles and the
turbulent eddy diffusivity. Thus it has been proved that turbulence is affected by solid
concentration. Further, the deposition velocity can be obtained using the ratio of
concentration at the bottom and static settled concentration. Also deposition takes place
when solid concentration at the bottom becomes equal to three times the product of efflux
concentration and static settled concentration.
9
Deposition critical velocity plays an important role in the flow of slurries through
pipelines. However designing a pipeline also requires lot of parameters which needs to be
considered. Pressure drop through the pipeline is one of the important factors that should
be given importance. In order to design a pipeline carrying slurries it is necessary to
know the pressure drop. Also it helps to choose the power of the pumping device.
Kaushal et al. (2005) made an attempt to measure the pressure drop and concentration
profiles in horizontal, vertical and 45o inclined planes including the axis of the pipe. The
diameter of the pipe was 54.9 mm. The concentration profiles were obtained by
traversing isokinetic sampling probes. They have used two types of glass bead particles
with mean diameters 440μ m and 125 μ m respectivelly. They have developed the
experimental set up as shown in the figure 2.1.
Fig. 2.1 Test loop used by Kaushal et al. (2005)
Pipe diameter is 54.9 mm while the rig has a 22 m long recirculating pipe loop with
slurry tank having capacity of 200 L. It also consists of 150 L capacity water tank along
with a centrifugal pump to maintain the flow of slurry. The supply of slurry is done
through tank 7 (Fig. 2.1) where proper mixing of water and solid particles are done
10
mechanically using an electric mixer. It is ensured with the help of the mixer that
distribution of particles should be homogenous. The outlet of the tank is situated at 10 cm
above the bottom i.e. almost 10 cm below the impeller. There is an additional water tank
10 (as shown in Fig. 2.1) connected in parallel with the slurry tank which has been
employed to reduce the variation of mixture level in the tank at start up and shut down.
The circulation of slurry in the loop is done with a centrifugal pump with the operating
conditions of – 15 kW with a rate of 0.6 cubic meters per min at 22 m head. Slurry
volumetric flow rate is measured with the help of an electromagnetic flow meter 2 (as
shown in Fig. 2.1). A sampling probe 3 (as shown in Fig. 2.1) is used to measure the
concentration profiles. It has a rectangular slot of area 5 mm x 6 mm which is 3 mm
above the end. Samples were collected in horizontal, vertical and 45o inclined planes at
different locations ensuring the slurry flow is uniform and uninterrupted. On the basis of
their results they have concluded that variation in flow velocity does not bring any
significant variation in the concentration in horizontal plane. They have obtained a
unique change of concentration profile for 440 μ m particles which indicated a sliding
bed regime. They also found that high frictional losses are associated with narrow
grading particles (small diameter) and broad grading particles (larger diameter) have low
frictional losses at higher concentrations.
In another study, Kaushal et al. (2002) have modified the model for solids
concentration profiles and composites proposed by Kaushal and Tomita (2002). They
have included the effect of particle size and efflux concentration of particle diffusivity.
They have calculated the ratio of homogeneously distributed concentration and
heterogeneously distributed concentration for each size of particles present in the slurry.
11
They have calculated the total pressure drop in the pipe by adding the pressure drop
through the homogenously distributed and heterogeneously distributed portions of all the
particle sizes. They have also done the experiments to calculate the pressure drop to
validate the results. These pressure drop results obtained are found to be more accurate
than those obtained by previous researchers and were found to be in good agreement with
the experimental results. They calculated the mean square difference values between
predicted and experimental values and have expressed as percentage of the measured
value. Their comparison statistics have shown the variation for different models as Wasp
et al. (1977) with 5-21.8%, Gillies model (1991) with 6-9.2 %, Kaushal and Tomita
model (2002) with 1.7-3.5 % and the proposed model with just 1.6-2.0 %.
Kumar et al (2003) have also conducted studies with varied range of efflux
concentration and particle size through slurry pipelines carrying liquid solid flows. They
have measured the pressure drop and distribution of solid concentration. They have
measured the particle size effects on pressure drop utilizing the solid distribution in the
pipe. They have employed an integral flow model to determine the optimum particle size
for which the specific energy consumption is minimum. They have used the integral flow
model for predicting pressure drop and solid particle concentration. They have proved
that there can be an optimum size of particles for which the energy required for
transportation of slurry having that particle size will be lesser than the energy required for
slurry having even smaller particle size. They have also concluded that modified
Karabela’s model is able to predict the solid concentration with good accuracy.
Ling et al. (2001) have used a horizontal pipeline having a fully developed solid
liquid flow in order to perform the numerical investigations. They have employed an
12
algebraic slip model (ASM) in order to model two phase flow and RNG K-ε model for
accurately modeling the turbulence effects. They have used an unstructured grid in order
to discretize the flow domain. Finite volume method is used for the determining the
solution of the governing equations. The pipeline used in the study has a length of 1.4 m
with a diameter of 0.0221 m. They have used silica sand and Zirconia sand particles with
densities of 2380 Kg per cubic meter and 4223 Kg per cubic meter respectively. They
have displayed various slurry characteristics which include slurry density, volume
fraction variations, slip velocity magnitude, slurry mean velocity variations and skin
friction variation. Their results vary significantly for silica and zirconia sand particles as
they have different densities. Their results have been found in good agreement with the
experimental data when the slurry mean velocity has a magnitude higher than the critical
deposition velocity. Their results are also found to match the results obtained in current
research which are presented in Results and Discussion section. The effects of density of
particles are clearly visible in the results obtained.
Lin et al (2007) have studied the developing slurry flow in the entrance region of
a horizontal pipe. They have also used algebraic slip model (ASM) in order to model two
phase flow and RNG K-ε model for modeling the turbulence effects. They have used an
unstructured grid with 67200 cells. The turbulence intensity level used in their
computations as a boundary condition is 4%. They have plotted the profiles for
comparison of volume fraction, density distribution, mean velocity profiles and mean
skin friction coefficients. They have also shown the variation of volume fraction in the
vertical central plane of the pipe’s cross section for volume fractions 0.172414 and
0.20689. This is shown in Fig. 2.2. The results obtained in the current research for
13
velocity profiles along the vertical axis in the entrance region of the pipe slurry flow are
compared with those obtained by Lin et al in chapter 4. The results of Lin et al. for
velocity profiles of slurry are shown in Fig. 2.3. They have concluded that volume
fraction and mean density will be lower in the upper part compared to lower part of the
pipe in the entrance region. In the fully developed region, in the upper part of pipe, the
solid liquid density will be almost equal to primary fluid density and the volume fraction
will be almost zero.
Fig. 2.2 Evolution of volume fraction of silica sand at the vertical central plane of
the pipe’s cross section (Source: Lin et al (2007))
Hossain et al (2003) have used the multiphase mixture model available in Fluent
in order to study the particle deposition and suspension in a horizontal pipe flow. They
have considered the diameter of particle, density of fluid and velocity of fluid as the
decisive factors for the deposition of particles in the pipe flow. Similar to the current
research, they have also considered the gravitational forces as well as hydrodynamic drag
forces on the particles. They have quantified the gravitational settling velocities and free
flight velocities. It has been concluded on the basis of same that those larger particles that
have gravitational settling velocity more than twice their free flight velocities will be
more likely to settle. Similarly, smaller particles with gravitational settling velocities less
than half of their free flight velocities will be have dominance of turbulent diffusion and
14
hence are dispersed along the cross section of the pipe. The results obtained in the current
research are compared with findings expressed by Hossain et al. in chapter 4.
Fig. 2.3 Velocity profiles of single and double species slurry flow along the vertical
centerline from the entrance region to fully developed slurry flow region (volume
fraction=20%, particle diameter =100 microns, pipe diameter = 0.0221m (Source:
Lin et al (2007))
Eesa et al. (2008) have conducted similar studies and have used a Eulerian-
Eulerian Computational fluid dynamics approach for investigating the flow of coarse
particles in a horizontal or vertical pipe. They also conducted experimental measurements
in order to validate the results predicted through modeling. The positron emission particle
technique (PEPT) has been utilized for the experimental verification. The results of the
previous studies have been used in the validation of the pressure drop computations. The
particles employed in the study can be considered neutrally buoyant. The solid and liquid
phase velocities, pressure drop and particle concentration profiles are found to be
15
dependent upon the particle diameter and their concentration, mean flow velocity and the
rheological properties that the carrier fluid possesses. Due to large particle diameters,
asymmetry is found to arise in the solid as well as liquid velocity profiles. Pseudo-homogeneous
flow takes place for smaller particles while the concentration profiles are
distorted for particles with larger diameters as larger particles are more likely to settle
during the flow. Higher solid concentrations result in increase in pressure drop along with
more uniform radial distribution of particles. The non-dimensional solid and liquid phase
velocities and particle concentration profiles were not dependent on the particle diameter
and their concentrations.
Kaushal et al. (2002) have studied the concentration profiles along with the
pressure drop through a pipe of diameter 105 mm for a zinc tailings slurry flow
consisting of more than one size particle. The particle size in the slurry ranges from 38
μ m to 739 μ m. It has been observed that many researchers have made attempts in the
direction of prediction of pressure drop along with Wasp et al. (1977), Doron et al.,
(1987), Gillies et al. (1991), Sundqvist et al (1996), Mishra et al. (1998), Ghanta and
Purohit, (1999), Wilson et al. (2002), to name some of them. Out of these, the
approaches and models proposed by Wasp et al. (1977) and Gillies et al. (1991) are more
accurate. Kaushal et al. (2002) have made an attempt to modify Wasp et al.’s two layer
model. They have also modified the Karabelas (1977) empirical model for solid
concentration profiles. They have conducted the experiments with three different flow
velocity magnitudes of 2m/s, 2.75m/s and 3.5m/s. The efflux concentration for each
velocity magnitude ranges from 4% to 26 % by volume. Like other researchers, they also
observed that the solid concentration profiles were functions of particle size, flow
16
velocity and particle efflux concentration of slurry. In case of pressure drop
measurements flow velocities ranged between 1.2m/s to 4m/s. with the efflux
concentration ranging between 4% to 26% by volume.
Kaushal et al. (2002) have compared the results obtained for solid particles
concentration profiles with those predicted by the Karebelas (1977) model. It has been
observed that the model predicts accurately for the finest particle size but as the particle
size increase the results predicted vary such that it overestimates the concentration at the
bottom of pipe while underestimating the same at the top of the pipe. On the other hand,
comparison of the experimental data for pressure drop with those predicted by the Wasp
model shows good agreement when the efflux concentration is low at all values of flow
velocities. Exceptions are found when the efflux concentration was high along with high
flow velocities. The predictions made by Gillies et al’ s (1991) two layer model were
found to be in good agreement with the experimental results. Kaushal et al. (2002) have
made changes by modifying some of the limiting assumptions used in the Karebelas and
Wasp models. It has been observed that the modified Karebelas and Wasp models are
capable enough to predict accurate results which established fair consensus with
experiments.
2.4 Other studies focusing on two phase: This portion will discuss some other studies
in which flow is taking place through any other geometry except the pipe.
Wei et al. (2002) have developed a K-ε -T model in order to predict the flow
characteristics of dense liquid –solid flows. They have used fluid turbulent kinetic energy
and turbulent dissipation rate to describe the turbulent flow of fluid. On the other hand
they used turbulent kinetic energy, dissipation rate and pseudo thermal temperature to
17
describe the random motion of particles. They have explained that random velocity
associated with collection of particles is characterized by the turbulent kinetic energy of
the particles. In case of an individual particle the random velocity magnitude is defined
by the pseudo thermal temperature. They have designed the iterative procedure required
to solve the equations involved in the modeling. Their simulation results were found to be
in good agreement with the literature. They have concluded that anisotropy dominates in
two phase flows.
As discussed in the above paragraphs, Xu et al’s (2004) research is inspired from
the working of atomic hydrogen propellant feed systems in which the solid hydrogen
particles may be transported to engines by using the carrier fluid in the form of liquid
helium. They have made use of three dimensional two phase mixture model in order to
simulate the flow of the solid hydrogen particles and liquid helium. They utilized the K-
ε mixture turbulence model which plays a crucial role in the turbulent mixing of the
solid particles and liquid fluid. They indicated that the slurry flow of hydrogen-helium
has a high Reynolds number. The Stokes number which is defined as the ratio of the
particle response time to the fluid response time also plays an important role. When its
value is less than one the particle motion will be tightly coupled with fluid motion. It has
been observed that the Stokes number for this two phase flow system is less than or equal
to one which is mandatory in order for the hydrogen particles to attain the near
equilibrium velocities so that the particles can remain in suspension with the liquid.
Different test cases have been discussed on the basis of the governing factors and their
influences on the dispersion of hydrogen particles in liquid helium. The governing factors
18
include the hydrogen particle size, inlet velocities and the inlet particle volume fraction.
Table 2.2 shows the cases as identified by Xu et al. (2004),
Test Case # Inlet velocity
(m/s)
Inlet particle volume
fraction (%)
Particle diameter (mm)
1 1.0 19.0 1.00
2 1.0 19.0 0.10
3 1.0 19.0 0.01
4 3.0 19.0 0.01
5 3.0 30.0 0.01
6 3.0 10.0 0.01
7 5.0 19.0 0.01
Table 2.1 Cases as identified by Xu et al. (2004)
Effect of particle size: Considering the case 1, 2 and 3 in the above table, contours of
particle volume fraction have been obtained as shown in Fig. 2.4 for case 3, which have
the smallest particle diameter of 0.01 mm, show the best results of all the three cases for
the dispersion of hydrogen particles with a very small amount of particles accumulating
at the top which is less than the cases 1 and 2.
19
Fig. 2.4.Contour of particle volume fraction in the channels for different particle
sizes at elapsed time t=2 s. (Influx particle volume fraction αp,0=19.0%, flow
velocity ) (Source : Xu et al. (2004))
Also, they have plotted the normalized particle volume fraction curves along a channel
parallel to the axis at the intersection of y=0.01m and z=0 planes in Fig. 2.5 It has been
realized that the closer the normalized particle volume fraction is to 1 that much better
will be the dispersion of hydrogen particles. Fig. 2.5 also supports the fact that small
particle size is a better choice for better degree of particle dispersion.
Fig. 2.5 Particle volume fraction at intersection of surfaces y=0.01 m and z=0 m for
different particle sizes at elapsed time t=2 s. (Influx particle volume fraction
αp,0=19.0%, flow velocity m/s.) (Source: Xu et al. (2004))
Effect of Inlet velocities: In Table 2.1, consider the cases 3, 4 and 7 where all the
parameters are constant except the influx velocities. The case 7 with inlet velocity as
20
5m/s. which is the highest of the three cases is found to have better dispersion. Thus,
higher the inlet velocity better the particle dispersion achieved.
Effect of inlet particle volume fraction: Here case 4, 5 and 6 from Table 2.1 with
respectively 19%, 30% and 10% volume fraction have been discussed. It has been found
that higher the influx volume fraction the better the particle distribution in the flow.
Logos et al. (1995) have made an attempt to study the coal water slurries in terms
of their rheological behavior. The rheological properties were established to be the
functions of solid coal particle size, concentration, and the particle size distribution.
These slurries have been formed by mixing water with coal particles with size of the
order of 45μ m. For lower concentration of coal particles, slurries exhibit Newtonian
fluid properties while for higher concentration they have viscoplastic and shear thinning
effects. Their methods involved the mixing of coarser coal particles in the already
existing fine coal particles slurry. In the first step they have used the size of coarser coal
particles of the order of 208-279 μ m for mixing with the fine coal slurry keeping the
solid particle concentration constant. This has resulted in a decrease in the slurry
viscosity. Furthermore with a ratio of 40% -60% of coarse to fine coal particles in the
slurry , slurry viscosity becomes almost five times smaller than that of the slurry with just
fine particles with the same solid concentration. Another loss of slurry viscosity by 50%
has been observed on adding the coarse coal particles with size ranging between 279-325
μ m. They have explained this behavior owing to the effect of spatial rearrangement of
the solid particles and an apparent dilution effect. Their results have proved that a coal-water
slurry can be formed with a high solid concentration but with a lower slurry
viscosity.
21
Fan et al. (2005) have used an improved inner outer iterative method in order to
simulate the two phase solid liquid turbulent flows making use of slender particles
instead of the regular spherical one. The inner outer approach mentioned here has been
proposed by Brucato et al. (1998) and was later modified by Wang et al. (2002). The
improved inner outer approach has been explained later in the discussion of Wang et al.
(2002). The set up used in their modeling process consists of a tank which has the stirrer
in the form of a Rushton turbine. They have employed the standard K-ε turbulence
model. Since the slender particles differ with the spherical particles in the fact that they
are dependent on the orientation hence a comparison has been made between the results
obtained using the slender particles with those obtained using spherical particles. They
have also conducted solid liquid two phase flow experiments in the baffled tank using the
digital particle image velocimetry technique. This has been a useful step in order to
validate the results obtained from simulation. They have compared the velocity profiles
in the experimental and the simulation results following the cylindrical coordinate
system. Fig. 2.6 shows the velocity profile of the two results.
Fig. 2.6 (a) Experimental velocity profile (b) Simulation velocity profile. Both are in
r-z plane. (Source: Fan et al. (2005))
22
They have studied the orientation of slender particles and the effect of impeller speed on
the orientation. They used three different speeds i.e. at 200, 300 and 400 rpm of the
impeller. It has been observed that the radial and axial velocities as well as the fluctuation
velocities are increased due to increase in impeller speed while there is a decrease in the
solid concentration in the center of the tank owing to the fact that high impeller speeds
result in better and uniform dispersion of particles in the tank. As there is increase in the
impeller speed the orientation of the slender particles in the far region from the impeller
is not affected. In the near region the orientation decreases with increase in impeller
speed due to the particles following the direction of the impeller with large speed.
Comparison has been made on the basis of three different velocity components of the
flow in case of slender particles and spherical particles of equal volume. Fig. 2.7 shows
the comparison curve obtained.
Fig. 2.7 Comparison of simulated velocity between spherical and slender
particles. (Source: Fan et al. (2005))
It can be inferred that the velocity components for two types of particles are
similar. This can be explained using the fact that due to the high impeller speed,
turbulence effects dominate over the particle shape characteristics.
23
Wang et al. (2003) have also studied the dispersion of solid particles in a solid-liquid
baffled stirred vessel with a Rushton impeller. They have also utilized the
improved inner outer iterative procedure. They have made an attempt to determine the
recirculation below the impeller. They have also used K-ε turbulence model for
simulations. According to Wang et al. the main problems encountered in simulation of
flow field in stirred vessels involving multiphase flow are the exact representation of the
impeller action, the interactions between the participating phases and the turbulent
quantities. They have intended to extend this work as a base for the design and
modification of solid liquid mixing vessels by numerical simulation. The modified inner
outer approach as mentioned earlier subdivides the whole computational domain into two
zones which are partially overlapping. Fig. 2.8 shows the two zones of the modified inner
outer iterative method.
Fig. 2.8.Inner and outer zones in modified inner outer iterative method.
(Source: Wang et al. (2003))
The inner zone has the impeller while the outer zone consists of the wall baffles. In the
computational process, first the inner domain is simulated in the reference frame that
24
rotates with the impeller using the arbitrary boundary conditions that are imposed on
surface Σ 2. This will result in the first trial flow field to be obtained in the impeller
region inclusive of the flow parameters distribution on surface Σ 1. The flow parameters
distribution obtained on the surface Σ 1 is used in the form of the boundary conditions to
simulate the flow on the outer domain. The flow parameters have not been averaged and
hence the information available represents the whole of the computational domain which
fortunately also includes flow parameters on the boundary surface Σ 2. Further the
parameters on the surface Σ 2 are used for the second inner simulation as the boundary
condition. This will continue until a satisfactory numerical solution is obtained by
convergence. Fig. 2.9 shows the computational grid used. It has 36 x 36 x 90 nodes in all.
Wang et al. have compared their grid with those used in the previous similar studies by
Gosman et al. (1992) with 20 x 15 x 27 nodes and Altway et al. (2001) with 21 x 64 x 45
nodes. They have used a better and denser grid comparatively.
Fig. 2.9 Computational grid of ‘inner’ and ‘outer’ domains. (Source: Wang et
al. (2003))
25
The study conducted by Wang et al. (2003) can be used for the systems of solid-liquid
flows where the solid loading can be as high as 20%. They have modified the inner-outer
approach which can be applied to other systems also where there is an unavailability of
the experimental data for the initial boundary conditions.
2.5 Fourier Transformed Infrared (FTIR) spectroscopy: Fourier transform
spectroscopy can be defined as a technique used for measurement in which the time
dependent coherence of a radiative source is measured in order to collect the spectra.
These spectra are required for the study of the material or mixture characteristics.
Infrared spectroscopy is the spectroscopy technique that deals with the infrared region of
the electromagnetic spectrum. The Fourier transform spectroscopy when combined with
infrared spectroscopy brings the Fourier Transformed Infrared (FTIR) spectroscopy into
existence. An FTIR method consists of collecting an interferogram with the help of
interferometer and then it is Fourier transformed to get the spectra. The FTIR
spectrometer is used to digitize the interferogram and does the Fourier transformation to
yield the spectrum. Either near infrared or far infrared spectra can be obtained by a FTIR
spectrometer. The FTIR spectrometer offers advantages of high spectral resolution, the
capability of working with weak signals, high spectral accuracy, quick acquisition of
spectra with high signal to noise ratio (S/N ratio) and the capability to work with infrared.
FTIR spectroscopy has a wide range of applications. In the current study, FTIR/NIR
probes are considered for applications to a turbulent slurry flow. In this section an
attempt has been made to review some of the applications of FTIR/NIR methods.
26
2.5.1 Studies related to FTIR/NIR spectroscopy:
Abebe et al. (2007) have conducted experiments that indicate that Near Infrared
spectroscopy is a very good tool while dealing with slurries. According to them the
manufacturing processes that involve solid particulates pose a higher degree of
difficulties in various chemical, nuclear and pharmaceutical industries as compared to
single phase liquids and gases. Lack of effective measurement techniques contributes a
lot to the difficulties resulting in optimization and precision manufacturing of particulate
solid products. Their experiments demonstrate that NIR spectra can reveal rich and
important information about the concentration of solution, solid concentration, particle
size and the crystal structure. They have stated that NIR technique has a wide potential
for simultaneous measurements of multiple number of solids as well as liquid properties.
They have carried out their experiments using a 500 ml jacketed glass reactor. They have
used distilled water as the liquid while the chemicals they have employed are L-glutamic
acid (L-GA). They have used two different forms of L-glutamic acid namely α and β
forms. The experimental set up is shown in Fig. 2.10. The glass reactor consist of a
retreat curve impeller, a temperature control bath, a Platinum resistance thermometer (PT
100), a glass condenser and the NIR transflectance probe having 12 mm optical path
length. A 2m silica fiber optics cable is used to transmit signal to the FT-NIR
spectrometer.
27
Fig. 2.10.Experimental set up. 1 Personal computer, 2 NIR instrument, 3 Fiber
optics cable, 4 Transflectance probe, 5 Stirrer motor, 6, Temperature probe, 7
Reactor temperature control, 8 Stirrer, 9 glass jacketed reactor (500 ml), 10
Condenser.
The slurries were made for both α and β crystals and at different solid concentrations, and
over the six particle size ranges for each polymorph. The effect of crystal size on
absorbance was explained using the raw spectra plots of the slurries as shown in Fig.
2.11. On the other hand, they have explained the effect of solid concentration using Fig.
2.12. It has been observed that higher the solid concentration the larger will be the
baseline shift. The greater solid concentration results in more scattering of radiation and
hence less light reaching the detector ultimately resulting in baseline shift at all
wavelengths. They have concluded that near infrared radiations are very much effective
in predicting the slurry characteristics like particle size, and concentration unlike mid
infrareds. NIR spectroscopy can be used as an effective technique in chemical,
agricultural and environmental applications owing to the properties such as ability to use
fiber-optics for rapid data transmission, good accuracy in measuring both low and high
concentrations of solutions, and simple in operation.
28
Fig. 2.11. Raw NIR spectra of slurries of α-form L-GA crystals of different particle
sizes, under fixed temperature and solid concentration.
Fig. 2.12. α-form spectra at varied solid concentrations but fixed particle size
(70 μm) and temperature (40 °C)
It has been observed that the indoor concentrations of substances like
formaldehyde (HCHO) and nitrogen dioxide (NO2) have increased compared to that
outside and these concentrations obviously are capable of producing adverse results. The
quantitative measurement for such substances is a must to ensure better quality of
ambience though it is not possible to do this accurately with conventional methods. In
29
such a circumstance FTIR spectroscopy techniques prove to be advantageous. Chen et al.
(1999) have studied the quality of the indoor air in a simulated kitchen ambience. They
have measured concentrations of major combustion products like carbon dioxide, carbon
monoxide and nitric oxide in a room where a conventional natural gas appliance is
operated. They have employed FTIR extractive technique in order to measure the
combustion products. A comparison has been made further with the results obtained by
FTIR technique and those which were obtained from conventional techniques. The FTIR
technique was proven to be better. On the other hand they have also furnished the CFD
simulations which helped in designing the experimental set up along with interpreting the
experimental data. The experimental set up is shown below in Fig. 2.13. It has a room
with a conventional four burner stove gas cook top system. The cook top produces a blue
flame during the experiments. Air has been taken out using an exhaust fan while fresh air
is made to enter using a meshed vent. Three different experiment cases were considered
on the basis of different ventilation rates of 2.4, 4.3 and 6.6 air changes per hour (ACH).
The total heat generating rate was 3.92kW meter per hour. Similarly while in the CFD
simulations three different cases were considered. The grid used for modeling has same
Fig. 2.13.Experimental set up with the measurement locations and cook ups at S1,
S2, S3 and S4. (Source: Chen et al. (1999))
30
dimensions as that of the testing room. It has 29 x 32 x 34 cells in the direction
coordinates. The combustion source is modeled on the box shaped obstacle. CFX4 has
been used as the CFD package which uses the finite volume methods for solving the
conservation equations that govern the problem. A K-ε model with buoyancy correction
has been utilized. The simulation results can be depicted as shown in the Fig. 2.14. The
results obtained using CFD simulations were able to predict similar qualitative results as
obtained by the experiments. The confirmation of stratification of temperature and
combustion products concentration has been made. High flow rates were better predicted
quantitatively than lower flow rates. This may be due to the use of a less sophisticated
turbulence model. Hence, Reynolds flux model can be used. It has been proved that a
high flow rate system needs to be positioned above the source to extract the major part of
pollutants.
Fig. 2.14. Predicted velocity vectors and CO2 mass fraction contours at the
centre y plane for an air flow rate of 2.4 ACH. (Source: Chen et al. (1999))
FTIR spectroscopy can be combined with other techniques to obtain desired
solutions. Fabbri et al. (2000) have combined the mid infrared fiber optics (wavelength
31
ranging between 1100 nm to 2500 nm) technique with FTIR in order to devise a method
with the help of which a non-invasive reflectance measurements can be performed. It has
a wider area of application in the field of non-invasive analysis of aesthetic works. With
this technique measurements can be done with paintings and polychrome sculptures with
the view to analyze the composition of painted layers without sampling. This technique
uses portable FTIR spectrophotometer using mid infrared fiber optics which enables it to
be used on site, i.e., without even moving objects from their places. They have introduced
two terms: Surface reflection (Rs) and volume reflection (Rv). Surface reflections are the
radiations that have not entered the sample and have suffered single or multiple
reflections on the upper surface of the particles of the sample while volume reflections
are those radiations that enter the sample and are reflected back after suffering internal
partial refractions getting transmitted by the particles.
Friesen (1996) have used an online fiber optic probe in order to collect the spectra
of a slurry flowing through a pipe. An attempt has been made to verify the feasibility of
the NIR spectroscopy method for developing a reliable method for processing of oil sand
slurries in oil sand extraction plants. They have gathered data for a continuous period of
nine hours for which there has been a regular variation of the type of ore and the slurry
water content. They have utilized a near infrared reflectance analysis (NIRA) technique.
They have used an NIR spectrometer installed at a point downstream from the tumbler
which is used to mix hot water and sodium hydroxide with oil sand in the first step of hot
water extraction. The spectrometer with a protective cover has been mounted on a
vibration isolation platform placed on steel table close to the measurement point. A probe
with 1m long fiber optic bundle has been inserted into the pipeline having the probe
32
diameter of 25mm such the window was flush with inside surface of the pipe. The
window material is made of sapphire due to high resistance required against abrasion due
to sand. This method is used as an efficient method for characterizing the appropriate
samples owing to its advantages of being prompt and non destructive technique.
Following this method, if there is any need for sample preparation in a specific case, it
requires very small amount of sample preparation. This method can be used to analyze
large samples.
Switalski et al. (1998) have also tried to investigate the near infrared (NIR)
diffuse reflectance spectroscopy as a processing method. Diffuse reflectance carries the
merit of analyzing powders having as high as 40% volatility, slurries consisting of as
much as 40% solid concentration and emulsions as well. Diffuse reflectance spectroscopy
has the capability to examine both the solid and liquid phases on the substance. In this
study efforts have been made by researchers to monitor the dryer simulator that is used
for the simulation of production rotary dryer in the laboratory. They have mentioned the
examples from the industry using NIR diffuse reflectance spectroscopy in monitoring the
chemical industry processes of mixing, drying and polymorphism. These are indicative of
the fact that many of the other processes can be monitored using this technique.
3 Conclusions:
Thus, from the above discussion some of the points that are eligible to attract our
attention include the dependence of multiphase solid-liquid flows on the solid particle
inlet concentrations, inlet velocities of the solid and liquid phases and the particle shape
and size. It has been observed that smaller the particle diameter better will be the particle
dispersion. Spherical particle shapes are likely to disperse more than the slender ones.
33
Higher inlet velocity and high inlet volume fraction contributes to better dispersion of
solid particles. It was also observed that in order for the flow of solid particles with the
liquid fluids the velocity of the solid particles should be just above the deposition critical
velocity. In order to achieve such a velocity or more precisely to maintain the particles in
suspension in the flow the phenomenon of turbulence is a must. Turbulent mixing plays a
vital role for the particle dispersion. In order to simulate the turbulent flows K-ε
turbulence model is most preferred. Turbulent K-ε model has been found to be the
widely used turbulence model. It can be used efficiently in both dilute as well as dense
solid liquid flows.
FTIR methods have also been used as efficient technique for non-invasive
measurements as well as in the analysis of liquid slurry characteristics. Being a non-destructive
technique, it requires little or no sample preparation. An optical probe can be
employed which can be used for the detection of the substances. Thus in the present study
all these considerations have been taken in to account in order to optimize the quality of
obtained results.
34
CHAPTER III
NUMERICAL APPROACH
3.1 Introduction
Computational Fluid Dynamics (CFD) is classified as a branch of fluid mechanics
which deals with the numerical solution of flow of fluids by employing the computational
power of modern computers. Computational Fluid Dynamics solves the governing
differential equations that are characteristic to the flow. These governing equations
consist of the equations of continuity, conservation of momentum also known as Navier
Stokes equations and equation of conservation of energy. On the other hand, in case of
inviscid flow the Euler equations are momentum equations which govern the flow. In the
present study we are dealing with the viscous flow. So the prime concern will be the
solution of Continuity and Navier Stokes equation. Some of the advantages of using
CFD methods are considered to be the accuracy and reliability of the end results, lower
cost of application of CFD compared to the expensive experimental methods, availability
of software and graphical tools to visualize the flow without actually making the fluid to
flow which results in accurate predictions. In addition, the study of dangerous species can
be performed without any risk.
35
In CFD, a continuous fluid is discretized by considering the flow domain to be
constituted of very small units called cells. This cell structure in the flow volume is
known as mesh or grid. These cells are used for the analysis of the flow problem. When
proceeding with the cell-based analysis approach, a preprocessing is required. For
preprocessing, the geometry of the problem should be understood. Mesh has to be
constructed in the region where the fluid is going to flow. Further, one should be aware of
the governing equations on which the flow properties are dependent. These governing
equations may also include some equations which are specific to the problem or type of
fluid. Furthermore, the boundary conditions of the flow problem play a major role in
determining the accuracy of the simulation process and have to be given attention during
the preprocessing of the flow problem. Boundary conditions specify the fluid
characteristics at the flow boundaries and the specific properties of viscosity, surface
tension that the fluid has.
Computational Fluid Dynamics can be used to model flow with low Reynolds
number as well as those with high Reynolds number. Various turbulent modeling and
simulation techniques like Direct Numerical Simulation (DNS), Large Eddy Simulation
(LES), Reynolds stress model, K-Epsilon model, K-Omega model, Spalart-Allmaras
model are available and each one of them can be efficiently used in their specific areas of
applications. These will be covered in some detail later in this chapter. In the present
study wall bounded turbulent flows have been modeled and the K-Epsilon model with
near wall treatment has been employed.
CFD techniques are suitable for the areas of single phase flow as well as
multiphase flow. A multiphase phase flow will have the flow consisting of gas-solid,
36
solid-liquid, gas-liquid phases, liquid-liquid phases or even more than two phases. The
point to be considered is that the phases must be non-reacting during the flow. The
complexity in the flow arises due to the mutual interaction of different phases.
Experimental methods are not capable in every case to completely analyze the flow.
Currently, our area of consideration is the flow of solid (particles) and liquid phases
where even the clustering of suspended particles depends upon the small scales of
turbulence to be resolved. This is very difficult using experimental techniques. Hence
numerical simulation plays an important role for the analysis of multiphase turbulent flow
problems. Using the computational techniques the role of some crucial physical factors
including the effect of gravity and surface tension can be also evaluated in the flow
problems.
As it has been mentioned earlier that CFD requires computational power of
modern computers in order to give useful results, hence it requires software application
codes in order to do the computational work. Many CFD software applications are
available that can be used on the basis of the advantages they offer in different fields of
applications. In the current research, Fluent has been used as the simulation software
package and Gambit has been utilized as the preprocessor. As we mentioned that meshing
of flow geometry needs to be done before simulating the flow, Gambit is used for the
construction and meshing of the flow geometry. In this case, flow geometry is a pipe with
a Fourier Transformed Infrared Reflectance (FTIR) probe placed at half of the length of
the pipe inserted through the upper wall of the pipe. The construction and meshing of the
probe and pipe geometry are considered later in this chapter.
37
3.2 Governing Equations
The governing equations are nothing but the mathematical representations of
the principles that controls the flow behavior in a particular fluid problem. These
principles are the conservation of mass, momentum, and energy. For the present study,
one has to deal with the equations of continuity which represents the conservation of
mass principle and Navier Stokes equations in three different coordinate axes which
respectively represent the momentum conservation principles in the directions of X, Y
and Z. Following are the equations as discussed in the preceding lines. The equation of
continuity or conservation of mass in three dimensional coordinate systems is expressed.
(3.1)
Where u, v, w are the velocity components in X, Y and Z directions. This is
the continuity equation for incompressible flow. The Navier stokes equation is expressed.
(3.2)
This is the basic form of Navier Stokes equations where each term has its
own meaning which is explained as
38
(3.3)
Thus, the terms on the left represents the acceleration of the fluid while the
terms on the right hand side stand for the forces acting on the fluid. The above equation
holds good when talking about incompressible constant viscosity flow. The Navier
Stokes equation is a form of conservation of momentum which is explained from
Newton’s second law of motion and the equation
F = ma (3.4)
is justified as the Navier Stokes equation has acceleration terms on one side
and all the existing forces on the other side. The Navier Stokes equation in the Cartesian
form for three different coordinate axes for incompressible and constant viscosity flow
yields,
(3.5)
(3.6)
(3.7)
39
3.3 Numerical methods in CFD
In the old days when CFD was discovered, experimental techniques were
considered to be advantageous. Nowadays, due to the promptness and accuracy of the
computational power, CFD is widely used. The solution of flow problems are obtained by
discretizing and then solving the differential equations governing the flow. There is
availability of several types of numerical methods for the solution of governing equations
such as finite difference, finite volume, and finite element methods. For our area of
concern all these three are of interest.
Finite difference method: This method uses the Taylor series approximation at any
general point xi. Thus any term of the PDE can be expressed as,
( ) Σ =
=
+
≅
2
1
1 j J
j J
n i n j i j
n
C f
x
f x
dx
d
(3.8)
Where x represents the mesh size in the grid under consideration and is
taken constant. fk represents the value of the function f(x) at xk. Taylor’s expansion gives
the value of coefficients CJ. J1 and J2 are the integers which are related with the order n
and the desired degree of accuracy. Thus following the above scheme the first and second
order derivatives can be represented as follows.
( )
x
f f
dx
df x i i i
−
≅ + −
2
1 1 (3.9)
(Here n=1 and J1 =1 and J2 =1 i.e. first order derivative with first order
accurate scheme). And
( )
xx i
i i i i f
x
f f f
dx
d f x
≡
− +
≅ + −
2
1 1 1
2
2 2
…….. (3.10)
40
(Here n=2 and J1 =1 and J2 =1 i.e. second order derivative with first order
accurate scheme).
For higher order derivatives the value of n will increase and for higher
degree of accuracy the difference between J1 and J2 goes on increasing. Similar equations
are used while discretizing the time derivatives having the time interval t. In finite
difference method systems of governing differential equations is converted to a system of
algebraic equations in terms of the value of function f at different nodes of the mesh.
Finite element method: In this method the flow domain is discretized by dividing it into
smaller divisions or elements and each element is considered while developing the
solution using the basis functions. Thus the solution is obtained element wise in terms of
the basis functions. As the solution is constructed in terms of the specific basis functions,
it explains better about the solution as compared to the finite difference and finite volume
methods. But there are always complications in choosing the basis functions which also
brings ambiguity in determining the boundary conditions. This method is widely used for
structural mechanics problems. It is also applied in areas of fluid studies. One more area
of concern is that it requires more memory for computation comparatively. In this method
a weighted residual equation is obtained which is represented as
(3.11)
41
Where Ri is the equation residual at an element vertex i, Q represents
conservation equation expressed on an element basis, Wi is the weight factor and Ve is
the element volume.
Finite volume method: In this method the flow volume is constituted of a number of
small volumes and the discretization is based upon the integral form of the partial
differential equations (governing equations). The governing equations are discretized
such that they can be solved for every volume. The resulting equations obtained consist
of fluxes of conserved variables. This method uses the conservative form of governing
equations for discretization which ensures that the fluxes through each volume remain
conserved. This method is useful for the fact that there is no limitation of using only a
structured grid.
Comparison of the three methods: All the three methods have found wide applications
in their respective areas on the basis of the ease of applicability. Finite element method
provides an end to end continuous solution but it requires lots of programming skills.
Similarly finite volume methods are known to provide conservative solutions. Thus on
the basis of the qualities and limitations of the three methods they can be chosen to be
applied to a given problem. In the current work, Fluent is used as the analysis and
simulation software package which is based upon the finite volume method. The
discretization in Fluent/Gambit takes place by dividing the flow volume into a number of
cells and each has their own volume. Thus the finite volume method comes into picture.
Since the finite volume approach uses the integral form of conservation equations, the
42
equation of continuity expressed in the integral form for a steady and incompressible
flow will be,
……… (3.12)
Where S and nˆ are the surface of the cell or control volume and the normal to
the surface respectively. The above equation represents the net flow in and out of the
control volume will be zero. For better interpretation it will be a good idea to look at the
following figure.
Fig. 3.1 Rectangular cell control volume (Source: CFD Introduction,
Bhaskaran and Collins)
The velocity on any face can be expressed as
(3.13)
Applying the conservation of mass on the cell control volume will result in
another equation expressed as,
43
(3.14)
This equation is the equation of continuity applied to a single cell. It
explains that the net mass flow in the cell adds to zero. The values at the cell centers are
obtained by inverting the discrete system. The values of u1, v1, u2, v2 are obtained by using
the interpolation technique on the cell center values at the adjacent cells. In this way the
discrete equations for momentum and energy conservation can also be written. This is
how Fluent incorporates finite volume analysis.
3.4 Selection of turbulence model:
A model is defined as a mathematical formulation of the physical and
chemical aspects which define the process or product. This does not include the solution
of these mathematical formulations. Simulations on the other hand are one of the
activities that can be performed with the models. It involves solving a problem using an
appropriate model. The observation of turbulent flows is a common phenomenon in
various scientific processes that involve fluid motion. Turbulent flows have characteristic
velocities that do not have stable behavior rather they are fluctuating in nature. These
fluctuating velocities have a vital role to play in the continuity, momentum and energy
transport equations. These quantities depict fluctuating characteristics which may vary in
magnitude and frequency of fluctuations. Due to the variable nature of the quantities it
demands a lot of computational power for calculation of these quantities. By calculating
fluctuating quantities shorter length scales of turbulence can be resolved but it becomes
extremely expensive in practical problems due to the amount of computational power
needed. Such models are the Direct Numerical Simulation (DNS) and Large Eddy
Simulation (LES) models. On the other hand, Reynolds averaged Navier Stokes models
44
(RANS) calculate average quantities. RANS models do not resolve all the turbulence
scales. Fig. 3.2 shows the extent of modeling and resolving the turbulence scales in case
of different modeling approaches.
Fig. 3.2 Extent of resolution of turbulence scales and modeling in different
turbulence models. (Source: BELL, B. Turbulent flow cases, Fluent Inc. 2003)
The selection of a turbulence model for a specific flow problem is based on
dynamics involved in the problem, the computational power available, the time available
for simulations, the particular practices prevalent for the kind of problem, and also the
level of accuracy required. Fluent offers a wide variety of turbulence models and
depending on the suitability of the model to the type of flow being considered, it can be
45
chosen to obtain the solution of the flow problem. The RANS models that Fluent offers
consist of Spalart-Allmaras, K- and its variations, K-omega and its variations and
Reynolds stress models (RSM). Fluent also offers the LES and DNS models but the
current study does not necessitate talking about those models at length. In the current
study we have used K- model and its variations which is a two equation model (K and
equations) which ensures that turbulent velocities and length scales can be determined
independently. The assumptions used behind the model are that the flow should be fully
turbulent and the molecular viscosity does not play a significant role in the flow. There
are two other variations of this model namely RNG K- model and realizable K- . The
RNG K- and realizable K- models have some modifications compared to standard
K- . To name a few, the RNG K- model accounts for swirling effects on turbulence
and has an extra term for rapidly strained flows in the equation. Similarly the
Realizable K- model has an improved formulation for turbulent viscosity and a new
equation for dissipation rate .
3.5 Modeling the multiphase flow: A phase can be defined as a particular
distinguishable class of material that exhibits unique inertial behavior when interacting
with the flow. A multiphase flow has more than one phase in the flow domain. In the
present study liquid–solid flow is a concern. Some examples of liquid-solid are slurry
flow, hydrotransport, sedimentation etc. The concentration in this study is on the slurry
flows. There are two approaches with the help of which multiphase flow can be modeled.
They are Euler-Lagrangian approach and Euler-Euler approach. Euler-Euler approach is
of relevance in the present issue.
46
Euler-Euler approach: It is a fact that a phase cannot occupy the volume or content of
another phase. Owing to this fact, in this approach the concept of volume fractions of
different phases has been introduced. The phases are considered to be interpenetrating
mathematically. Each phase has a volume fraction and the outcome of the addition of all
volume fractions is unity. These volume fractions are considered continuous functions of
space and time and are spatially and temporally dependent. Conservation equations for
each phase are obtained to form a set of equations which is solved using constitutive
relations. There are three different models under Euler-Euler approach. They are Volume
of fluid (VOF) model, Mixture model and Eulerian model. They are described in more
detail in the following paragraphs.
Volume of fluid (VOF) model: VOF model is generally used for two fluids that rarely
mix with each other or rather are immiscible. The VOF model formulates a common set
of momentum equations for all the fluids while each fluid has a different volume fraction
equation and the volume fraction is calculated at each cell. The major applications of this
model are involved in motion of large bubbles, steady or unsteady tracking of the liquid-gas
interface, prediction of jet break up, etc.
Mixture model: The mixture model is an Eulerian multiphase model which is suitable
for the modeling of mainly solid particles and liquid fluids flowing together. The solid
and liquid should be in strong coupling with each other. The mixture model aims at
solving the momentum equations for the mixture. This model can model the phases
which are moving with different velocities and hence slip velocity comes into existence.
It uses the relative velocities to describe the secondary or dispersed phases. Mixture
47
model has an advantage that it is independent of the number of phases participating in the
flow i.e. it can model any number of phases present in the flow. In this model one can
select granular phases also and it enables us to find the properties of granular phases.
Since in the current study particles are being dealt with therefore it makes the mixture
model most suitable to be used as a multiphase model for the present work. All the
related equations and concepts of the mixture multiphase model will be discussed in the
next section.
Eulerian model: This model aims at solving different set of continuity and momentum
equations for each phase involved in the flow. The coupling between the phases is
obtained by using the pressure and interphase exchange coefficients. This induces higher
degrees of complexities in this model. The granular and non-granular phases are treated
differently and in case of granular phases kinetic theory is used to determine the granular
properties. For handling the momentum exchange between the phases, user defined
functions are employed. Using the Eulerian model any number of phases can be modeled
but one thing to be considered is the availability of sufficient memory. Applications of
this model include fluidized bed, particle suspension to name a few.
3.5.1 Modeling with Mixture multiphase model: As has already been mentioned the
mixture model uses only one set of continuity and momentum equations for the mixture
as a whole and hence it uses less memory. Along with the merits of the mixture model
there have been some limitations also. Just for example, while using mixture model one
cannot use the density solvers in Fluent. Before moving to the governing equations used
48
in the mixture model it should be realized that apart from using common set of
continuity, momentum and energy equations for the mixture, it solves the volume fraction
equation for the secondary phases and algebraic expressions which pertains to the relative
velocities if the phases are moving with different velocities.
3.5.2 Equations used in mixture model: The equations that are solved in the mixture
model are the following.
Continuity equation-
( ) + ∇.( )= 0
∂
∂
m m
m v
t
ρ
ρ
(3.15)
Where m v and m ρ represent the mass averaged velocity mixture density such that,
m
k k
n
k
k
m
v
v
ρ
ρ α Σ=
= 1 (3.16)
And k
n
k
m kρ α ρ Σ=
=
1
. (3.17)
For k α being the volume fraction of kth phase.
Momentum equations: The set of momentum equations solved in the mixture model are
written as,
( ) ( ) [ ]
∇ + + + ∇ + ∇ ∇ + −∇ =
+∇
∂
∂ Σ=
dr k
n
k
m k k dr k
T
m m m m m m
m m v v p v v g F v v
t
v
,
1
, . ρ .μ ρ . α ρ
ρ
(3.18)
Here n, F and m μ are the number of phases, total body force and the viscosity of
mixture respectively and dr k v , is the drift velocity such that,
49
Σ=
=
n
k
m k k
1
μ α μ (3.19)
And d k k m v = v − v , (3.20)
Energy equation: The energy equation is given as,
(3.21)
Where first and the second terms on the right hand side account for heat transfer owing to
conduction and miscellaneous volumetric heat sources respectively.
And
= (Σ ( + )) eff k k t k α k k (3.22)
is the effective conductivity. Subscript t in the conductivity t k stands for the turbulence
and it is the turbulent conductivity and its value depends on the turbulence model.
Slip velocity: In the mixture model the phases participating may have different
velocities hence an algebraic slip formulation is employed in Fluent. So the expression
for the relative velocity is given as,
pq p q v = v − v (3.23)
50
Where p v and q v are velocities of primary and secondary phase respectively.
The expression for drift velocity is stated as,
(3.24)
Where k c is the mass fraction of any phase k expressed as,
(3.25)
Studies reveal that slip velocity is a function of drag function, relaxation time, and
acceleration of the particles of secondary phase ( a ). When the flow is turbulent, slip
velocity will also depend upon the dispersion due to the dispersed phase. Hence Fluent
accounts for this by adding a diffusion term in the expression for slip velocity as shown,
(3.26)
Where,
= m v Turbulent viscosity of mixture.
= drag f Drag function.
= D σ Prandlt dispersion coefficient.
In Fluent, there are several choices available for the drag functions.
51
Volume fraction equation for the secondary phase: Volume fraction equations have
been obtained from the continuity equation for the secondary phase. It is expressed as
follows,
(3.27)
3.5.3 Limitations and assumptions of Mixture model: Along with the simplicity
and ease of using the mixture model it has certain limitations also. Some of these
limitations include the use of only the pressure based solver but not the density based
one, inability for modeling inviscid flows and the flows involving solidification and
melting. Mixture model cannot be used with some other models available in Fluent which
include LES Turbulence model, shell conduction model, multiple reference frame (MRF)
model (for relative velocity formulation) and Discrete Phase Model (when particles are
tracked simultaneously). The mixture model is incapable for modeling streamwise
periodic flows with constant mass flow rate and flows consisting of more than one
compressible ideal gases. The mixture model uses the assumption of a local equilibrium
between the participating phases in order to calculate the relative velocity between the
participating phases. This local equilibrium is assumed to be limited to short length scales
only.
Apart from the mixture model being used in the current study, Eulerian model can
also be a good simulation model. It can also be applied to the current problem. Eulerian
model is the most complex multiphase flow model among all the three multiphase flow
models. Eulerian model employs as many sets of momentum and continuity equations as
the number of phases participating in the flow. In the current case there has been a wide
52
distribution of particles in the slurry. Owing to this fact, mixture model becomes more
feasible over the Eulerian model. The disadvantage that Eulerian model carries is that it
demands a lot of computational power. This is also one of the reasons for preferring the
mixture model over the Eulerian model.
3.5.4 K-ε Equations used in mixture model: K-ε turbulence mixture model has been
used which is by default employed in Fluent when multiphase flow is combined with
turbulence. It is suitable for stratified flows. Following are the K andε equations used in
capturing the relevant characteristics,
(3.28)
And
(3.29)
Where,
, (3.30)
(3.31)
Turbulent viscosity,
(3.32)
53
And turbulent kinetic energy production is given by,
(3.33)
3.6 Incorporation of sensor and pipe geometry using Gambit meshing and
formulation:
FTIR probe description: The Fourier Transformed Infrared Reflectance (FTIR) probe
consists of a cylindrical section with a gap or slot through its curved surface. The sensing
is performed across this slot. The sketch of the probe is shown in the Fig. 3.3. All the
dimensions are shown in the figure except one which shows the variable part of the probe
whose dimension can be varied in order to vary the slot dimensions.
Fig. 3.3 Fourier Transformed Infrared Reflectance probe
The pipe that has been considered for different cases is 7.112 m in length and
0.1016 m in diameter. The probe is placed at distance of 4.064m from the inlet and is
3.048m before the outlet. The Reynolds number of the flow is of the order of 240,000.
54
In order to design the probe and pipe assembly in Gambit, coordinates of vertices
have to be entered using Operation->Geometry->Vertices. After entering the vertices,
edges have to be constructed through Operation->Geometry->Edge by using two or more
vertices. These edges can be linear, circular or arc. Further edges created will be used for
making faces of the assembly design through Operation->Geometry-> Face. And at last
by using Operation-> Geometry->Volume, faces are either stitched or swept to obtain
three dimensional geometries. It should be pointed that Stitch and Swept are two
command options in Gambit used to make a volume by stitching multiple faces or
sweeping one single face in a direction perpendicular to it and the swept region is
converted to volume. For the current case the pipe has been designed in three volumes in
inlet, outlet and probe regions.
The next step which is the most important step of the design is the mesh
generation or grid formation in the constructed geometry. For the current design
Operation-> Mesh-> Mesh volumes have been used. The volume in the probe region has
been meshed using the tetrahedral grid meshing with the interval count of the grid points
on the faces being 10. The inlet and outlet volume regions have been meshed using
hexagonal cooper meshing scheme available in Gambit with an interval count of 40. The
total number of cell volumes formed after meshing are 0.68 million. A plain pipe is also
designed in order to determine the results of fully developed flow. It has been meshed
using the hexagonal cooper scheme and interval count of 50.
The last step of the design process is the specification of boundary conditions.
Following Operation->Zones->Specify Boundary Types, desired boundary conditions
55
can be specified in Gambit. The boundary types specified in the current case are Velocity
inlet, Pressure outlet, Wall. Figure shows the boundaries specified.
Fig. 3.4 Boundary types shown in Gambit
After when all the above steps are successfully implemented we can expect a meshed
geometry similar to as shown in the Fig. 3.5
Fig. 3.5 The meshed pipe and probe assembly in Gambit.
56
The meshed geometry is then saved using File--> Save. Further, the meshed
geometry will have to be exported using File-> Export-> Mesh to Fluent where the actual
analysis will take place. This will save a .msh file in the Gambit working folder.
3.7 Simulations in Fluent: Proceeding with the next stage of the work done in Gambit,
click on the Fluent icon to open Fluent. While opening Fluent, 3ddp (Three dimensional
double precision) version has to be selected in Full simulation mode. First, the .msh file
exported in Gambit is imported in Fluent using File-> Read-> Case. Next the Grid has to
be checked for discrepancies, if any. This is done using Grid-> Check. Further the
problem is set in Fluent by defining the models and input values of the relevant variables.
Using the Define panel solver being used, the multiphase model employed and the
turbulence model are specified as Define-> Models-> Solver, Define-> Models->
Multiphase and Define-> Models-> Viscous respectively. For the present study, pressure
based solver, multiphase mixture model and turbulence K-ε models have been utilized.
When mixture model is selected, the user has to specify the number of phases involved in
the flow, slip velocity computation if required and any implicit body forces if acting
during the flow. The current study makes use of both slip velocity as well as implicit
body force which is gravity in this case. Moving ahead the solid and liquid phase
materials which are being used in simulation process are selected using Define panel as
Define-> Materials. Generally all the materials are available in Fluent database but user
can input the materials by adding the name of material along with the required properties.
In this case the Table 3.1 shows the input values of the liquids and solid particles. There
are two different cases for which two different sets of materials are used.
57
MATERIAL DENSITY
(in kg per cubic
meter)
VISCOSITY (in Kg per
second meter)
CASE I
2-Amino-4,6-
dimethylpyrimidine (ADP)
particles.
1480 -
Xylene (Liquid) 870 6.2e-04
CASE II
Calcium carbonate particles. 2800 1.72e-05
Water 998.2 1.003e-03
Table 3.1 Input materials in Fluent
MATERIAL PHASE
CASE I
2-Amino-4,6-dimethylpyrimidine
(ADP) particles
Secondary
Xylene Primary
CASE II
Calcium carbonate particles. Secondary
Water Primary
Table 3.2 Input materials phase in Fluent
58
Using Define-> Phase, one has to define the primary and secondary phases along
with their state. Table 3.2 above indicates the phase of the materials used.
For the secondary phase, granular characteristics have been chosen in all the
present cases. Further through the Define panel one can choose to select the interactions
between the phases which include specifying the drag functions, slip velocities etc. Using
the Define panel, Operating conditions and Boundary conditions are provided using
Define-> Models-> Operating conditions and Define-> Boundary conditions respectively.
In the Operating conditions panel the gravity check box has to be selected and its value is
given in Y direction as -9.81m/sec2. In the Boundary conditions panel different input
values have to be provided at different boundaries. Table 3.3 gives a better explanation of
the input variables and their values in the current case. The turbulent intensity of the flow
is calculated using the following formula which depends upon Reynolds number
(3.34)
The backflow turbulent intensity is one of the parameters that need to be input.
Backflow turbulent intensity refers to the intensity of turbulence if there is any flow
taking place in the reverse direction. Backflow parameters are used by Fluent if
any backflow occurs during the iterations, otherwise they are not used. A good guess of
these parameters will help the solution to run stable if backflow occurs, a bad guess can
cause divergence also.
59
Boundary
types
Primary phase
input values.
Secondary phase
input values.
Mixture input
values
Inlet (Velocity
inlet)
Flow velocity of
liquid phase
=2m/sec.
Flow velocity of
particle phase
=1.5m/sec. and
volume fraction
=0.4
Specification
method
(Turbulent
intensity= 3.5%.
and hydraulic
diameter
=0.1016m)
Outlet (Pressure
outlet)
None.
Backflow volume
fraction =0.4
Specification
method (Back
flow Turbulent
intensity=
0.001%. and
hydraulic
diameter
=0.1016m)
Wall None None. Default values
Fluid None None
Rotation axis
direction Z=1.
Table 3.3 Input variables and their magnitudes.
60
Further the solution parameters are provided using the Solve panel. Solve-> Controls-
>Solution controls is used to open the Solution controls panel where the under-relaxation
factors, pressure-velocity coupling types and discretization laws are specified. For the
current problem as the geometry is complex due to presence of the probe in the flow,
hence first order upwind discretization is preferred for all the quantities. One can play
with the underrelaxation factors in order to govern the convergence of the residuals. The
next step involves the solution initialization using Solve -> Initialize-> Solution
initialization. In the current case solution is initialized from inlet. In the next step,
convergence criteria are mentioned for all the variables using Solve -> Monitors->
Residuals. Generally it is set at 1e-5 or smaller. Also one has to activate the plot option to
enable Fluent to plot residuals. Next step is the one in which iteration parameters like
time step size, numbers of time steps, numbers of iterations per time step are specified for
a transient flow problem. This is done using Solve -> Iterate-> Iterate. For the present
work the time step size has been taken of the order of 0.1. Then iterations are performed
to achieve convergence of residuals.
Fluent follows an iterative scheme to find the solution of the flow problem. All
the governing equations are solved for each and every time step. This is done until the
convergence is achieved in every time step. Once the convergence is obtained in a time
step the solution is increased by one time step. This can be expressed as shown in Fig.
3.6. This scheme also considers the non-linear nature of the governing equations as well
as the inter-relation between the equations.
61
Fig. 3.6 Solution strategy in Fluent (Source: Fluent 6.3 user guide)
Fluent offers versatile post processing tools to visualize and analyze the flow.
These tools include XY plots, contour plots, vectors displays etc which can be found
under the Display and Plot panels. Post processing has been done and fairly good results
have been obtained which have been dealt with in the next chapter.
62
CHAPTER IV
Results and Discussion
4.1 Brief recapitulation:
It has been discussed in the preceding chapters that Computational Fluid
Dynamics is playing an important role in predicting the characteristics of the multiphase
flow involving liquid and solid particles. In the current study CFD has been applied to the
flow of a chemical slurry in which 2-Amino-4, 6-dimethylpyrimidine (ADP) is used as
particles and Xylene is the liquid. In a different case, calcium carbonate particles were
made to flow through water forming calcium carbonate-water slurry. The flow has taken
place through pipes with the ratio of length to diameter being 70. The modeled Fourier
Transform Infrared reflectance probe is placed such that its distance from the inlet is
more than that from the outlet of the pipe vertically on the upper surface. The probe is at
a distance 40 times the diameter from the inlet and 30 times the diameter from the outlet.
This chapter aims at presenting the important findings of the current research. It
has been mentioned that the current research focuses on the application of CFD to
visualize the flow over and through the sensing gap of the FTIR/NIR probe. It also aims
to determine the profiles of solid particle concentration and velocity through the sensing
gap of the probe. The post processing tools of Fluent have been utilized in order to ensure
self explanatory and descriptive visualization of the flow. In addition,
63
Tecplot 260 has been employed for plotting the concentration profiles and velocity
profiles of slurry flowing through the sensing gap of the probe. The results obtained by
using ADP particles and Xylene are compared with those with the calcium carbonate
particles and water. In all the plots shown all distances are in meters and negative sign
on Z velocities represents direction as the slurry is flowing in the negative Z
direction.
4.2 Flow of Xylene (WITHOUT particles) in 7.112m length pipe: In this section, the
results obtained by the flow of xylene in a plain pipe (pipe with no probe) are presented.
The inlet velocity is 2m/sec. The profiles of Z velocity of xylene have been plotted along
different axes. The velocity profiles clearly depicts that fluid flow shows the fully
developed behavior.
-Z velocity variation along the centerline:
The pipe coordinate system is shown in Fig. 4.1(a). Fig. 4.1(b) shows the Z velocity
variation. The centerline Z-velocity increases as the fluid flow takes place further the
inlet. Then it decrease and gradually becomes constant. This shows that the flow has
become fully developed.
(a)
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(b)
Fig. 4.1 (a) Pipe coordinate system (plain pipe) (b) Z velocity of Xylene varying
along centerline of the pipe.
-Z velocity profiles along the vertical axis along Y direction:
Fig. 4.2 Pipe section showing the location of planes and the respective axes along
which Z velocity are plotted. Inlet (hown in blue) is near Z= -1 plane and oulet
(shown in red )lies near to Z= -7 plane. Flow direction shown by arrow.
65
(a) (b) (c)
(d) (e)
Fig. 4.3 Z velocity profiles along vertical axes in (a) Z= -1 (Z/D=9.84), (b) Z=- 2
(Z/D=19.685), (c) Z= -3.5 (Z/D=34.45), (d) Z= -5 (Z/D=49.2) and (e) Z= -7(Z/D=
68.89) cross sectional planes as shown.
Fig. 4.3 shows the Z velocity profiles of Xylene along the vertical axes lying in
different cross sectional planes normal to the axis of the pipe. The profiles shown in (a)
(b), (c), (d) and (e) are all symmetric with respect to the centerline which is at y/R=0.
The comparison of power law profile for a turbulent plain pipe flow with the non
dimensional velocity profiles is shown in Fig. 4.3(f). The inlet velocity is 1.5m/sec. The
profile in blue is obtained from Fluent while the one in red is the power law profile. The
power law index is 7. The agreement of the profiles is as shown in Fig. 4.3(f). The power
law index has been taken from Schlichting (1968).
66
4.3 (f) Comparison of velocity profile in radial direction with power law profile
(n=7) shown in red with the fluent profile in blue at Z/D=35.
Z velocity profile along the centerline of a plain pipe WITH particles:
Fig. 4.4 shows the particle Z velocity profile along the centerline of the plain pipe. The
particle diameter is 100 microns. Thus in the presence of particles the flow gains fully
developed characteristics at around Z/D= -35. Hence placing the probe at Z/D=-40 is
worthwhile in order to mount the probe in fully developed flow region.
Fig. 4.4 Particle Z velocity profile along centerline of the plain pipe.
67
(a1)
4.3 Flow of ADP particles with Xylene in 7.112m (L/D=70) length pipe:
In this section, the data obtained by the simulation of the flow of ADP particles and
Xylene have been presented. The data has been presented in the form of plots, contours
and vectors of different physical quantities. These quantities are Z-velocity and volume
fraction of particles. In order to study the variation of these quantities in particular
directions, different lines and planes have been drawn using Fluent post processing tools
and then the corresponding physical quantity has been plotted against that line/plane. The
pipe dimensions can be expressed in terms of cylindrical coordinates R, θ and Z where R
is the radius of pipe, θ being the angular distance and Z being the pipe axis corresponding
to the length of the pipe. In the current case R varies from -0.0508 m to 0.0508m, θ varies
from 0 to 360 degrees and Z varies from -3.048 m to 4.064 m. Hence the geometry is
asymmetrical with respect to Z coordinate. The position of origin is shown in Fig. 4.5(a)
as (0,0,0).
68
4.3.1 Plots of velocity profiles: Velocities have been plotted along the axial (Z/D) and
radial (y/R) directions and the conclusions have been drawn. The pipe length ranges from
inlet at Z/D=40 and outlet at Z/D= -30 (negative Z direction) with probe at Z/D=0. Y
coordinate varies from y/R= -1 to +1. The axes along which the velocity profiles have
been plotted are shown in the adjacent figures.
-Particle Z velocity vs. axis (centerline): The axial velocity (Z velocity) has been
plotted along the centerline or the axis of the pipe as shown in Figs 4.5. Fig. 4.5(a2)
shows the axis along which the velocity has been plotted. Fig. 4.5(b) depicts the variation
of Z velocity of particles along the centerline of the pipe. The negative sign on the
velocity is indicative of the direction of flow as the flow is in negative Z direction. The
particle Z velocity at injection is -1.5 m/sec which suddenly reaches to -1.73 m/sec when
comes in contact with the liquid Xylene which has initial velocity of -2m/sec. Thus -1.73
m/sec is the initial velocity of the slurry. The particle Z velocity increases and then comes
down to the previous magnitude of -1.73 m/sec as the flow progresses after the inlet. The
flow is smooth and the particle Z velocity remains constant till it reaches the vicinity of
probe where major fluctuations in the particle Z velocity are observed as shown in Fig.
4.5(c). The particle Z velocity in the probe region shows a zigzag variation. This is
attributed to the divergence of the flow in the presence of probe. The fluctuations in Z
velocity may be observed owing to 3D flow in y direction (increment in Y component of
velocity) as the particles will have the tendency to flow downwards as the probe is
approached. After the probe region the particles regain the same velocity magnitude. As
the flow approaches the outlet there is a very little decrease in the particle Z velocity. At
the outlet the particle Z velocity has the same magnitude of -1.73m/sec.
69
(a2)
(b)
70
(c)
Fig. 4.5 (a1) Probe and pipe assembly with the directional coordinate system (a2)
Axis of the pipe (b) Particle phase Z velocity variation along the centerline (c)Flow
along the probe vicinity shown between parallel lines.
-Particle Z velocity vs. axis parallel to the centerline and passing through the middle
of probe slot: Fig. 4.6 shows the variation of the particle Z velocity along the axis
parallel to the centerline and passing through the middle of the probe slot as shown in
Fig. 4.6(a). The negative sign on the velocity is indicative of the direction of flow as the
flow is in negative Z direction. Along this axis, a similar behavior of particles is observed
as along the centerline but as the flow progresses from inlet the particle Z velocity
undergo a little decrease in the magnitude and then becomes uniform until it reaches the
vicinity of probe slot. Again the major fluctuations in velocity of particles are observed in
the probe slot vicinity which is shown in Fig. 4.6(c). After the probe slot vicinity the
particle Z velocity starts climbing up to regain the previous velocity. Unlike the variation
along the centerline of the pipe, the particles travel more distance in the pipe to regain the
same velocity as shown in Fig. 4.6(c). As the flow approaches the outlet the particle Z
velocity decreases and ends up at a magnitude of 1.5m/sec.
71
(a)
(b)
(c)
Fig. 4.6 (a) Axis (b) Particle phase Z velocity variation along the axis parallel to the
centerline. (c)Flow along the probe vicinity shown between parallel lines.
72
-Particle Z velocity vs. axis parallel to the centerline and passing through the lower
solid part of probe: Fig. 4.7 shows the variation of particle Z velocity along an axis
parallel to the axis of the pipe but passing through the lower solid end of the probe. The
particle Z velocity before reaching the probe region behaves similar to the velocity
observed along the centerline of the pipe. When it reaches the vicinity of lower solid end
of the probe there is immediate drop in velocity to null value due to the presence of
(a)
(b)
73
(c)
Fig. 4.7(a) Axis. (b) Particle phase Z velocity variation along the axis parallel to the
centerline but passing through the lower solid end of the probe. (c)Flow along the
probe vicinity shown between parallel lines.
stagnation point as shown by the curve. Further downstream, the particles attain the usual
velocity again which is of the order of -1.73m/sec. The particle Z velocity fall gradually
and then becomes uniform as the outlet is approached as shown.
In all the three cases of variation of particle Z velocity (Figs. 4.5(b), 4.6(b),
4.7(b)) it can be noticed that the velocity profile in the region before the probe (Entrance
region of pipe) is similar to the profile in the entrance region of the plain pipe with
particles (Fig. 4.4) except in the above three cases uniform velocity is achieved earlier
Z/D value.
-Particle Z velocity along Y axis (i.e. Along the line through the center of the probe
slot circular section and the lines to the left and to the right of it as shown in the Fig.
(a)): The variation of particle Z velocity is shown in Fig. 4.8 (b) along the line through
the center of the probe slot circular section using the purple □. The negative sign just
indicates the direction of flow. The probe slot lies between y/R= 0.5 to y/R=0.75 with
74
center of slot at y/R=0.625. The points shown explain that the velocity of the particles is
zero at the upper and lower surface of the probe slot. The particle Z velocity profile
resembles a parabola along the axis through the center of the probe slot.
Fig. 4.8(b) also shows the variation of particle Z velocity along the axis parallel to
the Y axis but to the left of it. It is expressed as green triangle ►. There are small
variations in the particle Z velocity near the center of the probe slot as shown by the
points near the center. They exhibit very small velocity difference.
Left (a) Right
75
(b)
Fig. 4.8(a) Axes in Y direction and along the lines to the left and to the right of it
(b)Particle Z velocity vs. Y axis (Along the line through the center of the probe slot
circular section, along the lines to the left and to the right of it.
The variation of particle Z velocity along the axis parallel to the Y axis but to the
right of it is also depicted in Fig. 4.8 (b) using blue Δ. The velocity at the lower and
upper walls of probe slot is zero. In this case also, the variation resembles a parabola but
this time density of velocity points is more near the center of the probe slot. Here the
profile defines more curvature near the center compared to the profile obtained for the
axis on the left.
4.3.2 Plots of particle volume fraction: This section will focus on the variation of the
volume fraction of the particle phase along different axes. This information can be used
to predict the particle concentration profiles through the probe slot.
76
- Particle volume fraction along Y direction (i.e. Along the line through the center of
the probe slot circular section and the lines to the left and to the right of it as shown
in the Fig. (a)): Fig. 4.9 (b) shows the variation of particle volume fraction along the
lines through the center of the probe slot circular section in Y direction and axes to the
left and to the right of it as shown in the Fig. (a). The Y axis shows the axis considered
with specification as non-dimensional distance y/R while the X axis has the particle
volume fraction.
Left (a) Right
77
(b)
Fig. 4.9(a) Axes in Y direction and along the lines to the left and to the right of it (b)
Particle volume fraction vs. Y axis (Along the line through the center of the probe
slot circular section, along the lines to the left and to the right of it.
The variation in volume fraction is of the order of 10-3 which can be neglected.
Hence the volume fraction of particles can be considered constant along the considered
axis. Even though the particle volume fraction is constant, of the three cases the profile
obtained for the axis considered on the ‘axis through probe slot left’ accounts for
maximum variation.
- Particle volume fraction along an axis parallel to Y direction but behind it:
The axis is shown in Fig. 4.10 (a) with a red line. Fig. 4.10(b) shows the variation of
volume fraction along the axis parallel to Y axis but behind it as shown by the red line in
Fig. 4.10(a). It can be inferred that volume fraction decreases as we move from upper
wall of the probe slot (y/R=0.75) to lower wall (y/R=0.5). But the magnitude of variation
78
is of the order of 0.001 hence it can be said that volume fraction is nearly constant along
the considered axis.
(a)
Fig. 4.10(a) Axes. (b) Particle volume fraction variation along the axis
behind the Y axis through probe.
79
- Particle volume fraction along an axis parallel to Y direction but in front of it: Fig.
4.11 shows the variation of volume fraction along the axis parallel to Y axis but in front
of it as shown by the green line in Fig. 4.10(a). It can be inferred that volume fraction
decreases more steeply in the center of slot as we move from upper wall of the probe slot
(y/R=0.75) to lower wall (y/R=0.5). But the magnitude of variation is small and is of the
order of 0.001. Hence it can be said that volume fraction is nearly constant along the
considered axis.
Fig. 4.11 Particle volume fraction variation along the axis in front of Y axis
through probe. The axis is shown in Fig. 4.10 (a).
-Comparison of particle volume fraction along the axes shown in Fig. 4.10(a):
Fig. 4.12 shows the comparison of variation of volume fraction along the three different
axes as shown by red, black and green lines in Fig. 4.10(a). Though by minute amount,
but for comparative study the volume fraction magnitude is highest for the variation
along the axis to the front of Y axis (Shown by green in Fig. 4.10(a)). The volume
80
fraction is lowest along the axis shown in red in Fig. 4.10 (a). This is because the axis
shown in red is nearest to the vertical wall and since probe slot has opening just opposite
to the wall so a three dimensional flow also takes place. Thus the axes farther from the
vertical wall of the probe slot have comparatively more volume fraction magnitude.
Fig. 4.12 Particle volume fraction variation along the axes shown in Fig. 4.10 (a).
4.3.3 Z velocity of slurry/mixture along the vertical and horizontal (axial) axes.
-Z velocity of slurry/mixture along the vertical axes in Z=3, 2, 1,-1,-2 planes:
Fig. 4.13 shows the variation of particle Z velocity along a vertical axis in Z=3 cross
sectional plane as shown by the blue circular section in the probe and pipe assembly in
the Fig. 4.13 (a). The end points of the axis lies at y/R = -1 to y/R = 1. The curvilinear
profile obtained is asymmetric with respect to the centerline of the pipe which at y/R=0.
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(a)
(b)
Fig. 4.13(a) Probe and pipe assembly with the planes Z=3, 2, 1,-1,-2 (left to right) (b)
Particle Z velocity along a vertical line in the cross sectional plane Z=3,
Z/D=29.527
82
Fig. 4.14 Particle Z velocity along a vertical line in the cross sectional plane Z=2,
Z/D=19.685.
Fig. 4.14 shows the variation of particle Z velocity along a vertical axis in Z=2
cross sectional plane as shown by the violet circular section in the probe and pipe
assembly in the Fig. 4.13(a).The end points of the axis can be shown at y/R = -1 to y/R =
1. Again the velocity distribution is asymmetric with respect to centerline of pipe which
is at point y/R=0. This may be due to the effect of gravity on particles.
Fig. 4.15 depicts the variation of particle Z velocity along a vertical axis lying in
Z=1 cross sectional plane as shown by orange circular section in Fig. 4.13 (a). The axis
lies along y/R = -1 to y/R = 1. The velocity distribution is less asymmetric with respect to
centerline of pipe (y/R=0) compared to the distributions in the planes nearer to the inlet
shown in Figures 4.14 and 4.13(b). Also notice that the velocity at centerline (y/R=0) is
about -1.75 m/sec.
83
Fig. 4.15 Particle Z velocity along a vertical line in the cross sectional plane Z=1,
Z/D=9.84.
Fig. 4.16 shows the variation of particle Z velocity along a vertical axis in Z= -1
cross sectional plane as shown by the green circular section in the probe and pipe
assembly in Fig. 4.13(a). The end points of the axis can be shown at y/R = -1 to y/R = 1.
The variation is found to be symmetric with respect to the centerline at point y/R=0. The
Z velocity is almost 1.75 m/sec. Since the velocity has become constant, hence this marks
the presence of fully developed characteristics in the flow. It can be seen that the above
results (Fig. 4.13- 4.16) are in agreement with the findings of Lin et al (2007). Here also,
the maximum velocity location is moving vertically up as we move downstream.
The variation of particle Z velocity along a vertical axis lying in Z= -2 cross
sectional plane is shown by white circular section in Fig. 4.17. It is found that little
asymmetricity with respect to the centerline at point y/R=0 has been introduced. This
may be due to the presence of gravity. Again the Z velocity at the centerline (y/R=0) is
found to be almost -1.75 m/sec which shows that now Z velocity can be considered
84
nearly constant along the centerline.
Fig. 4.16 Particle Z velocity along a vertical line in the cross sectional plane Z=-1,
Z/D= -9.84.
Fig. 4.17 Particle Z velocity along a vertical line in the cross sectional plane Z=-2,
Z/D = -19.685
85
-Z velocity profiles along the axes parallel to Z direction passing through probe slot:
Z velocity profiles along the lines through the probe slot and parallel to Z
direction are shown in Figs 4.18. Lines 1, 2, 3 4, and 5 are distributed from upper to
lower walls of the slot as shown in Fig. (a’). Hence velocity variations along lines 1 and 5
are very close to zero as they are very near the probe walls. Velocity variations along the
lines 2, 3 and 4 which are away from the walls are larger in magnitude. Among all the
variations the highest velocity is found along the line 3 (Fig. (c)) which is the centerline
of the probe slot and is farthest from the walls.
(a’)
(a)
86
(b)
(c)
(d) (e)
Fig. 4.18(a’) Axes. Particle Z velocity profiles through probe slot along the axial slot
lines (a)Slot line 1, y/R= 0.74 (b) Slot line 2, y/R= 0.69(c) Slot line 3, y/R= 0.625
(d) Slot line 4, y/R=0.56 (e) Slot line 5, y/R=0.51.
87
-Particle volume fraction profiles along the lines parallel to Z direction and passing
through probe slot: Z velocity profiles along the lines through the probe slot and parallel
to Z direction are shown in Fig. 4.19. The volume fraction variation along these lines are
of very small magnitudes and can be assumed nearly constant. However, for comparative
study it can be found that the variation of volume fraction along the lines which are
nearer to lower wall of probe slot is smaller. This may be due to the effect of gravity on
particles at higher elevation from lower wall. That is why volume fraction decreases
along the axes which are away from lower wall of probe slot.
Fig. 4.19 Volume fraction profiles along the axial lines through probe slot.
4.3.4 Visualization of the flow of ADP particles with Xylene: Post processing tools
available in Fluent have been utilized to visualize the flow of the slurry of ADP particles
88
and Xylene over the probe. Vector and contour plots concerning different quantities are
presented.
-Contours of Z velocity of slurry/mixture along the plane Y=0.02:
(a)
Fig. 4.20(a) Plane Y=0.02 (b) Contours of Z velocity of slurry along the plane
Y=0.02, Y/R=0.39.
Fig. 4.20(b) shows the contours of Z velocity along the horizontal plane that passes
through the lower solid portion of the probe as shown in Fig. 4.20(a). The contours of
89
velocity show that the velocity is maximum on the sides of the probe while it is minimum
on the front and the back of the probe solid cylindrical portion.
- Contours of Z velocity of