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CHAPTER - VI
CFD ANALYSIS OF TWO PHASE FLOW
Background
The experimental pressure drop obtained from the present
study is compared with the correlations available in the literature in
the previous chapter and the salient points of the results that form the
motivation for the present chapter are presented as follows. At low
mass flux of 200 kg/m2s, all the correlations of pressure drop used in
the comparison exhibited larger deviations of more than 30-40% from
the experimental data. It is observed that Lockhart and Martinelli
correlation which is widely used in the analytical modeling of
condensing flows exhibits more than 100% deviation depending on the
mass flux. In addition, comparatively larger deviations, in the range of
20-45% are observed for low pressure refrigerant, R134a. These
results give scope for the modeling of two phase flow using CFD
analysis.
The objective of the chapter is to perform CFD analysis for
simulating flow regimes and to obtain pressure drop of two phase flow
of refrigerants at high pressures. The scope of the present chapter is
to simulate the flow regimes predicted by Thome et al. [2003a] flow
regime map for refrigerants, R22, R134a and R407C using existing
VOF model in the commercial CFD software, FLUENT under adiabatic
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conditions. Secondly, to obtain the pressure drop from the VOF model
and compare with the experimental data and correlations.
Schepper et al. [2008] modeled air – water and gas – oil flows
inside a channel at atmospheric pressure using CFD analysis and
simulated flow regimes. These simulated flow regimes are compared
with Baker [1954] flow regime map. Except slug flow regime, they
could reproduce all other flow regimes given by Baker map. The
present study extends their work by simulating the vapor-liquid flow
of refrigerants at high pressures.
6.1 Modeling Multi Phase Flows
There are two approaches in the modeling of multiphase flows:
the Euler-Lagrange approach and the Euler-Euler approach [2005].
In Euler-Lagrange approach, the fluid phase is treated as a
continuum by solving the time-averaged Navier-Stokes equations,
while the dispersed phase is solved by tracking a large number of
particles, bubbles, or droplets through the calculated flow field. A
fundamental assumption made in this model is that the dispersed
phase occupies a low volume fraction, though high mass loading is
acceptable making the model inappropriate for applications where the
volume fraction of the dispersed phase is not negligible.
In the Euler-Euler approach, different phases are treated
mathematically as interpenetrating continua. Since the volume of a
phase cannot be occupied by the other phases, the concept of phase
volume fraction is introduced. These volume fractions are assumed to
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be continuous functions of space and time and their sum is equal to
unity.
In the commercial CFD software, FLUENT, three different Euler-
Euler multiphase models are available: the volume of fluid (VOF)
model, the mixture model, and the Eulerian model. In the present
study, Volume of Fluids model is used, which is a surface is tracking
technique applied to a fixed Eulerian mesh. The model is apt for the
present study as the position of the interface between the vapor and
liquid phases is of interest to predict the flow regimes for vapor-liquid
flow of refrigerants, R22, R134a and R407C.
6.1.1 The Volume of Fluids (VOF) Model
In the volume of fluid (VOF) model [2005], a single set of
conservation equations is shared by the phases and the volume
fraction of each of the phases is tracked in each computational cell
throughout the domain. The values for all variables and properties are
shared by the phases and calculated as volume-averaged values,
provided the volume fraction of each of the phases is known at a given
location.
6.1.1.a Governing Equations
The governing equations for each of the phase are written as follows.
Conservation of Mass:
(6.1)
Conservation of Momentum:
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(6.2)
The term on the right-hand side of the continuity equation
represents the sum of volumetric sources of all ‘n’ phases which is
zero in the present case as only flow is considered here. Similarly, the
first term on the right-hand side of the momentum equation
represents molecular contributions, which include pressure and
viscous force per unit volume. The last two terms on the right-hand
side represent the gravitational force per unit volume and any other
external force. The numerical solution of the set of Eqs. (6.1) and (6.2)
is extremely difficult and computationally intensive. The main
difficulty arises from the interaction between the moving interface and
the fixed Eulerian grid that is employed to solve the flow field.
The motion of the interface is deduced indirectly from the motion
of different phases separated by an interface. Motion of the different
phases is tracked by solving a continuity equation for the volume
fraction of each phase. Thus, when a control volume is not entirely
occupied by one phase, mixture properties are used while solving Eqs.
(6.1) and (6.2). This approach avoids abrupt changes in properties
across a very thin interface. The mixture properties like mixture
density and dynamic viscosity are related to the volume fraction of all
phases as given by Eq. (6.3).
; (6.3)
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In the case of turbulence quantities, a single set of transport
equations is solved, and the turbulence variables are shared by the
phases throughout the field.
The volume fraction of each phase, is calculated by tracking
the interface between different phases throughout the solution
domain. Tracking of the interfaces between different phases present
in the system is accomplished by solving continuity equations of the
phase volume fraction for phases. For the th phase, this
equation has the following form.
(6.4)
The first term of the left-hand side of Eq. (6.4) represents
accumulation and the second term represents the contribution of
convection. The term on the right-hand side represents the
contribution of sum of volumetric sources of the volume fraction
which is zero in the present case.
By solving this continuity equation for phases, the value of
the volume fraction of all phases is determined throughout the
solution domain. Several specialized techniques [2005] have been
proposed to track the geometry of the interface accurately and are
described as follows.
6.1.1.b Interface Interpolation Techniques
The simplest VOF interface tracking methods are the Simple
Line Interface Calculation (SLIC) algorithms with first order accuracy.
Typically, the reconstructed interface is made up of a sequence of
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segments aligned with the grid, which makes the reconstruction
relatively rough. Fig 6.1 c) illustrates the interface reconstruction of
the actual interface shown in Fig 6.1 a) by means of a SLIC algorithm.
More accurate VOF techniques that fit the interface through piecewise
linear segments are known as the Piecewise Linear Interface
Calculation (PLIC) algorithms.
The PLIC interpolation scheme assumes that the interface
between two fluids has a linear slope within each cell and this linear
slope is used for the calculation of the advection of the fluid through
the cell interfaces. The first step in this scheme is calculating the
position of the linear interface relative to the center of each partially
filled cell, based on information about the volume fraction and its
derivatives in the cell. The second step is calculating the advecting
amount of fluid through each face using the computed linear interface
representation and information about the normal and tangential
velocity distribution on the face. The third step is calculating the
Fig 6.1 VOF interface reconstruction methods (a) Actual interface(b) PLIC/ Geo Reconstruct method (c) SLIC method [2005]
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volume fraction in each cell using the balance of fluxes calculated
during the previous step.
Fig 6.1(b) illustrates the interface reconstruction by means of a
second-order accurate PLIC algorithm. For all transient simulations in
the presented work, a PLIC interface reconstruction method known as
Geo-Reconstruct method in FLUENT has been used for interpolation
in a cell. In the existing CFD code, this scheme is the most accurate
one and it is applicable for general and unstructured meshes.
6.2 Prediction of Flow Regime: Transient Analysis
6.2.1 Tube Geometry and Operating Conditions
The simulations are carried out for the inner tube of test section
which is a horizontal tube with a diameter of 8 mm and a length of
1200 mm. To test the grid independency, the wall shear stress for
different grids is computed for R22 at different mass fluxes as shown
in Fig 6.2. The wall shear stress is considered to study grid
independency as it quantifies the boundary layer phenomenon
particularly at medium to high vapor qualities where a very thin liquid
film forms around the circumference of the tube due to the onset of
annular flow regime.
Five different grids are considered initially to evaluate the wall
shear stress and the graphs are plotted as shown in Fig. 6.2. All the
grids used the boundary layer mesh as shown in Fig. 6.3, except the
grid with 193,890 hexahedral cells.
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Fig 6.2 Variation of Wall Shear Stress with Different Grids for R22 ata) G= 200 b) G= 400 and c) G= 600 kg/m2s
a)
c)
b)
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In general, the wall shear stress increases with increasing vapor
quality. Fig 6.2 shows that the grid with 193, 890 hexahedral cells
does not represent this trend for any of the mass flux considered,
while other grids including the grid with comparatively less number of
hexahedral cells of 181,000 follow the trend, particularly for low and
medium mass flux. This behavior shows the significance of boundary
layer mesh for modeling of two phase flows considered in the present
study.
Fig 6.2 a) shows that at low mass flux, the variation of wall
shear stress with different grids is not significant. This is due to
gravity driven flow regime that prevails at this mass flux, for which
comparatively large number of hexahedral cells are patched with
liquid phase, while specifying the initial conditions. But with the
increase of mass flux, flow regime transforms into annular and thin
liquid film forms around the circumference of the tube. If less number
of cells is available at the wall, lesser number of cells will be patched
with liquid phase and the resulting wall stress will exhibit an
oscillating trend with the vapor quality. The same is represented in
Figs 6.2 b) and 6.2 c), which shows that up to medium qualities, the
wall shear stress calculated from different grids exhibit an increasing
trend with quality, but at higher qualities with the onset of annular
regime, it exhibits an oscillating trend. Figs 6.2 b) and 6.2 c) show
that the grid with 278,712 volumetric cells follows the trend of wall
shear stress variation with quality even at high mass flux with
comparatively minor deviations and is as good as the grid with
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332,196 cells. Also taking the computational time into consideration,
the grid with 278,712 hexahedral cells is judiciously selected for
further simulations.
The 3D-computational domain is divided into 278,712
hexahedral cells. Near the tube wall, four layers of cells are positioned
to capture the boundary layer phenomenon as shown in Fig. 6.3.
Vapor phase of the refrigerant is considered as primary phase and
liquid phase as secondary phase, as this phase is patched based on
volume fraction while specifying the initial conditions in VOF model.
For all simulations, a no-slip condition is imposed at the tube wall.
The influence of the gravitational force on the flow has been taken into
account as the main feature of two phase flow inside horizontal tube
is stratification of liquid phase. At the inlet of the tube, mass flow rate
of each phase is specified. At outlet, outflow boundary is imposed to
model the experimental conditions where the refrigerant flow is in
Fig 6.3 Mesh Model of Tube Cross Section
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closed circuit. The surface tension effects are not considered as the
values of Weber number for the finite cell of the mesh used are greater
than unity for all refrigerants and at all flow rates considered.
6.2.2 Solution Strategy and Convergence Criteria
The calculations are performed by combination of the PISO
algorithm [2005] for pressure–velocity coupling, PRESTO algorithm for
pressure interpolation [2005] and a second order upwind calculation
scheme [2005] for the determination of momentum and volume
fraction. PRESTO algorithm is selected as it uses the discrete
continuity balance for a staggered control volume about the face to
compute the staggered pressure. PISO algorithm is similar to SIMPLE
algorithm with a higher degree of approximate relation between
corrections for pressure and velocity. Though it takes higher
computational time, the number of iterations is less as it does
momentum correction and skewness correction.
A time step of 0.001s is considered for transient simulation
based on the flow velocities and the minimum volume considered in
the present study. The numerical computation is considered
converged when the scaled residuals of the different variables are
lowered by three orders of magnitude.
The liquid and vapor properties of refrigerants, R134a, R22 and
R407C at the saturation temperature of 400C are obtained from
refrigerant property data base, REFPROP version. 6.01. Firstly, the
analysis is performed at steady state for a given vapor quality to
determine the flow field of one of the phases so that the starting point
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for the transient simulation is fully converged flow field of one phase.
For the steady state simulations, implicit interface interpolation
scheme is used. The phase, initially filling the tube as a result of
steady state simulation, is pushed out of the tube during transient
simulation. The simulations are stopped when the entire length of the
tube is supplied with both the phases, and there is no further change
in the established flow regime except for more diffusion of both the
phases.
6.2.3 Simulation Results
Table 6.1 gives the flow conditions selected for simulations
based on the predictions of Thome et al. [2003a] flow regime maps for
R22, R134a and R407C as shown in Fig 6.4 Flow conditions for
simulations are carefully selected such that they represent all the flow
regimes and the transition zones of stratified wavy to annular and
slug to annular as shown in Fig 6.4.
For a mass flux of 400 or 600 kg/m2s and at a vapor quality of
0.5, R22 and R407C represent transition regime where as R134a
represent an annular flow regime, due to its low reduced pressure as
shown in Fig 6.4. These operating conditions are also selected for
simulations as given in the Table 6.1 to test whether CFD analysis can
predict the transition regime for R22 and R407C and annular flow
regime for R134a.
The results of transient simulations are taken at different time
steps. The flow regimes are obtained by plotting the contours of
mixture density. As mixture density is proportional to its phase
137
composition, the distribution of vapor and liquid phases of refrigerant
is clearly seen in these contours.
Fig 6.4 Flow Conditions and Flow Regimes Predicted by Thome et alFlow Regime Maps for a) R22 b) R134a and c) R407C
c)
a)
b)
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6.2.3.a Mixture Density Contours of R22
The flow conditions mentioned in Table 6.1 for R22 are
simulated and the flow regimes are obtained by plotting the contours
of mixture density as shown in Figs 6.5 to 6.9. The red color
represents the pure liquid and blue color represents pure vapor of
refrigerant. The scale in the left hand side of Fig. 6.5 represents the
density variation of mixture from liquid density of 1129 kg/m3 to
vapor density of 66.2 kg/m3 of R22.
The photographs of flow regimes given by Ewing et al. [1999] for
air water mixture are shown below the corresponding contours. The
photographs show very unstable interface compared to the vapor –
liquid interface of refrigerant obtained in the simulations. This is due
to the low of values of liquid to vapor density ratio of refrigerants at
Table 6.1 Flow Conditions and Flow Regimes Predicted using Thome et alFlow Regime Maps for R134a, R22 and R407C
MassFlux
Qual-ity
Flow RegimeR22
Flow RegimeR134a
Flow RegimeR407C
100 0.3 SW SW SW
100 0.8 SW SW SW
200 0.3 SW SW SW
200 0.5 Wavy-Annular Wavy-Annular Wavy-Annular
400 0.3 Intermediate Intermediate Intermediate
400 0.5 Slug-annular Annular Slug-annular
400 0.6 Annular Annular Annular
600 0.3 Intermediate Intermediate Intermediate
600 0.5 Slug-annular Annular Slug-annular
600 0.6 Annular Annular Annular
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high pressures considered in the simulations compared to that of air –
water mixture at atmospheric pressure.
Fig 6.5 Contours of Mixture Density for R22 at a) G = 100 kg/m2s and x=0.3b) G = 100 kg/m2s and x=0.8 c) G = 200 kg/m2s and x=0.3 andd) Cross sectional view at G = 100 kg/m2s and x=0.3e) Stratified Wavy regime obtained by Ewing et al. [1999] for air –
water mixture
a)
b)
c)
d)
e)
140
Fig 6.5 shows that the contours of mixture density represent a
stratified wavy flow regime for the flow conditions mentioned for low
mass flux at low qualities, thus reproducing the flow regime given by
Thome et al. flow regime map in Fig 6.4 a). The flow regime obtained is
similar to stratified wavy regime given by Ewing et al. [1999] in Fig 6.5
e) for air – water mixture.
The stratified wavy flow regime is similar to stratified flow with
heavy liquid phase flowing at the bottom of the tube and lighter vapor
phase flowing in the upper portion, but the vapor-liquid interface
becoming unstable giving rise to surface waves as shown in Fig 6.5.
The increase of wave amplitude can be clearly seen from Figs 6.5 a) to
Fig. 6.5 c) as the mass flux increases from 100 to 200 kg/m2s. Fig 6.5
d) represents the typical cross sectional view of stratified wavy flow
regime at a mass flux of 100 kg/m2s.
The contours of mixture density at a mass flux of 200 kg/m2s
and a vapor quality of 0.5 are shown in Fig 6.6 at different time
intervals of 0.1, 0.2 and 0.5s corresponding to the time steps of 100,
200 and 500. The interface becoming more unstable at a vapor quality
of 0.5 compared to that at 0.3 for the same mass flux of 200 kg/m2s
can be clearly seen from Figs 6.5 c) and 6.6 a). Waves trapping liquid
slugs can also be seen in Fig 6.6 a). Figs 6.6 a) to 6.6 c) show the
progressive rising of waves from the bottom pool of liquid and
touching the upper portion of tube to form a wavy annular flow regime
with a discontinuous liquid film around the circumference. The
transition regime obtained from the simulations as shown in Fig 6.6 c)
141
is similar to the wavy-annular regime given by Ewing et al [1999] in
Fig 6.6 d). Thome et al. map in Fig. 6.4 a) shows that at a mass flux of
200 kg/m2s and a vapor quality of 0.5, the flow regime falls on the
borderline of stratified wavy regime and into annular regime, thus
matching with the contours of mixture density obtained in CFD
analysis.
Fig 6.6 Contours of Mixture Density for R22 at G = 200 kg/m2s and x=0.5a) Time step = 100 b) Time step = 200 and c) Time step = 500d) Wavy Annular regime obtained by Ewing et al. [1999]
a)
b)
c)
d)
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Fig 6.7 shows the contours of mixture density of R22 at a
quality of 0.3 for mass fluxes, 400 and 600 kg/m2s. A very unstable
interface with large liquid slugs is clearly visible in the cross section
view represented in Fig 6.7 c). Figs 6.7 a) and 6.7 b) show the
increased slug formation with the increase of mass flux. These
contours match with the slug flow given by Ewing et al. [1999] in Fig
6.7 d). The flow regime corresponding to these conditions is
intermediate which includes slug flow, as predicted by Thome et al.
flow regime map shown in Fig 6.4 a), thus matching with the contours
of mixture density.
Fig 6.7 Contours of Mixture Density for R22 at a) G = 400 kg/m2s, x=0.3b) G = 600 kg/m2s, x=0.3 and c) Cross section view for slug flow atG = 400 kg/m2s, x=0.3d) Slug flow regime obtained by Ewing et al. [1999]
a)
b)
c)
d)
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Fig 6.8 shows the contour plots for R22 for a vapor quality of
0.5 at mass fluxes, 400 and 600 kg/m2s. At medium and high mass
fluxes, the slugs formed at low qualities rise to the upper portion of
tube with increasing vapor quality owing to the large wave amplitudes
at the interface and wet the upper portion as shown in Figs 6.8 a) and
6.8 b). These contours represent the transition of slug to annular flow
regime which agree well with the transition regime given by Ewing et
Fig 6.8 Contours of Mixture Density for R22 a) at G = 400 kg/m2s, x=0.5b) at G = 600 kg/m2s, x=0.5 andc) Cross section view for transition/annular flow at
G = 400 kg/m2s, x=0.5d) Transition regime obtained by Ewing et al. [1999]
a)
c)
b)
d)
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al. [1999] in Fig. 6.8 d). The cross sectional view in Fig. 6.8 c) shows
the partial formation of circumferential liquid film.
The contours of mixture density obtained at a vapor quality of
0.6 for mass fluxes, 400 and 600 kg/m2s are shown in Fig 6.9. A thin
annular film with vapor flowing in the core can be seen in cross
sectional view given in Fig 6.9 c). As shown in Fig 6.9, the thickness of
the liquid film at the bottom of the tube is more compared to the top
Fig 6.9 Contours of Mixture Density for R22 a) at G = 400 kg/m2s, x=0.6b) at G = 600 kg/m2s, x=0.6 andc) Cross section view for annular flow at G = 400 kg/m2s, x=0.6d) Annular regime obtained by Ewing et al. [1999]
a)
b)
c)
d)
145
owing to high density of liquid. This result is in agreement with
annular regime with almost uniform circumferential liquid film
obtained by Ewing et al. [1999] for air-water mixture as shown in Fig
6.9 d). Thus all the flow regimes predicted by Thome et al. map are
simulated for R22.
6.2.3.b Mixture Density Contours of R134a
Fig 6.10 Contours of Mixture Density for R134a at a) G = 100 kg/m2s and x=0.3b) G = 100 kg/m2s and x=0.8 c) G = 200 kg/m2s and x=0.3 andd) Cross sectional view at G = 100 kg/m2s and x=0.3
a)
b)
c)
d)
146
Transient simulations performed for refrigerant, R134a are
presented in Figs 6.10 to 6.12. The contours of mixture density
obtained for R134a at low mass fluxes as shown in Fig 6.10
represents a stratified wavy flow regime. The scale in the left hand
side of figure represents the variation of mixture density from liquid
density of 1147 kg/m3 to vapor density, 50.09 kg/m3.
Contours of R134a show a comparatively smooth interface of
liquid and vapor phases compared to that of R22 at the same
operating conditions as represented in Figs 6.5 and 6.10. This is due
to high liquid density and high liquid viscosity of R134a compared to
that of R22 as given in Appendix III, which tend to flatten the waves.
Fig 6.11 represents the contours of mixture density at different
time steps. Unlike R22, the liquid slugs formed as shown in Fig 6.11
a)
b)
c)
Fig 6.11 Contours of Mixture Density for R134a at G = 200 kg/m2s and x=0.5a) Time step = 100 b) Time step = 200 and c) Time step = 500
147
a) rise from the bottom pool as shown in Figs 6.11 b) and 6.11 c) with
increasing time interval, but comparatively less wetting of the upper
portion of the tube is observed even at further time steps. Hence the
flow regime is characterized as stratified wavy. The predicted flow
regime is on the border line of stratified wavy regime as shown in flow
regime map in Fig 6.4 b). The interface is observed to be unstable
compared to R22 at for the same operating conditions as shown in Fig
6.6. This is due to higher value of liquid to vapor density ratio as given
in Appendix III. But, possibly the gravity and viscous forces are
dominant compared to the inertia forces of vapor for R134a due its to
high liquid density and viscosity, which limited the wetting of upper
portion of the tube at the flow conditions considered.
Fig 6.12 shows the formation of slug flow regime at a quality of
0.3 for mass fluxes 400 and 600 kg/m2s which match with predicted
flow regime. The formation of slugs from the liquid flowing at the
bottom of the tube can be clearly seen in Fig 6.12 a). The cross
sectional view of slug flow regime in Fig 6.12 c) shows the liquid at
bottom of tube and detached slugs. The entrapment of liquid from the
stratified pool of liquid due to increase in mass flux from 200 to 600
kg/m2s can be clearly seen in Figs 6.11, 6.12 a) and 6.12 b).
148
Fig 6.13 shows the contours of mixture density at a quality of
0.5 for mass fluxes, 400 and 600 kg/m2s. For both the mass fluxes, at
a quality of 0.5, entire tube is filled with very small slugs rising to the
upper portion and wetting the surface as shown in Figs 6.13. The
reduction in the size of the slugs with the increase of mass flux from
400 to 600 kg/m2s is clearly seen from Figs 6.13 a) and 6.13 b). The
size of the slugs is smaller for R134a compared to that of R22 at the
same conditions as shown in Fig 6.8. This is due to comparatively
Fig 6.12 Contours of Mixture Density for R134a a)G = 400 kg/m2s, x=0.3b) G = 600 kg/m2s, x=0.3 and c) Cross section view for slug flow
atG = 400 kg/m2s, x=0.3
b)
c)
a)
149
high value of liquid to vapor density ratio of R134a resulting into
higher vapor velocity that breaks the larger slugs.
A very thin liquid film is formed along the circumference with
almost negligible liquid slugs as shown in Fig 6.13 c), representing the
annular flow regime. This result matches very well with predicted flow
regime as shown in Fig 6.4 b), where the flow regime representing
Fig 6.13 Contours of Mixture Density for R134a a)G = 400 kg/m2s, x=0.5b)G = 600 kg/m2s, x=0.5 andc) Cross section view of annular flow at G = 400 kg/m2s, x=0.5
c)
b)
a)
150
operating conditions falls in the annular region away from the
transition border.
Fig 6.14 shows that contours of mixture density represent
annular flow regime with continuous annular film around the
circumference for mass fluxes of 400 and 600 kg/m2s at a quality of
0.6 which matches with the predicted flow regime as given in Table
6.1 and Fig 6.4 b). Thus for the low pressure refrigerant, R134a also,
all the flow regimes predicted by Thome et al. map are reproduced
using transient simulations of VOF model.
Fig 6.14 Contours of Mixture Density for R134a a) at G = 400 kg/m2s, x=0.6b) at G = 600 kg/m2s, x=0.6 andc) Cross section view for annular flow at G = 400 kg/m2s, x=0.6
b)
a)
c)
151
6.2.3.c Mixture Density Contours of R407C
Fig 6.15 shows the contours of mixture density for R407C at low
mass fluxes. The contours represent stratified wavy flow.
The contours for a mass flux of 200 kg/m2s at a quality of 0.5
are shown in Fig. 6.16 at different time steps. Figs 6.16 a) to 6.16 c)
show the waves detaching from the bottom liquid pool and forming
c)
d)
b)
a)
Fig 6.15 Contours of Mixture Density for R407C at a) G = 100 kg/m2s and x=0.3b) G = 100 kg/m2s and x=0.8 c) G = 200 kg/m2s and x=0.3 andd) Cross sectional view at G = 100 kg/m2s and x=0.3
152
small slugs that raise to the upper portion and wet the surface with
increasing time interval forming a wavy annular flow. The cross
sectional view in Fig 6.16 d) shows the partial formation of thin
annular film around the circumference.
Fig 6.16 Contours of Mixture Density for R407C at G = 200 kg/m2s and x=0.5a) Time step = 100 b) Time step = 200 and c) Time step = 500 andd) Cross sectional view of wavy annular flow at G = 200 kg/m2s, x=0.5
b)
d)
a)
c)
153
Fig 6.17 shows the formation of slug flow regime at mass fluxes
400 and 600 kg/m2s and vapor quality of 0.3. Increased number of
slug formation with the increase of mass flux is clearly seen from Figs
6.17 a) and 6.17 b). Due to low liquid density and viscosity, more
diffusion can also be observed as shown in Figs 6.17 a) and 6.16 c).
Fig 6.18 shows the transition flow regime between slug and
annular regimes for mass fluxes, 400 and 600 kg/m2s at a vapor
quality of 0.5. The cross sectional view as shown in Fig 6.18 c)
Fig 6.17 Contours of Mixture Density for R407C a)G = 400 kg/m2s, x=0.3b)G = 600 kg/m2s, x=0.3 and c) Cross section view for slug flow
at G = 400 kg/m2s, x=0.3
b)
c)
a)
154
represents the slugs and a thin liquid film formation along the
circumference of the tube.
Similarly, Fig 6.19 shows the formation of annular flow regime
at a vapor quality of 0.6, for mass fluxes, 400 and 600 kg/m2s. Thus
the transient simulations performed using VOF model under adiabatic
conditions reproduced all the flow regimes predicted by Thome et al.
Fig 6.18 Contours of Mixture Density for R407C a)G = 400 kg/m2s, x=0.5b)G = 600 kg/m2s, x=0.5 andc) Cross section view of transition/ annular flow at
G = 400 kg/m2s, x=0.5
c)
b)
a)
155
map for the refrigerants considered in the present study, including the
mixture refrigerant, R407C. The CFD simulations also predicted the
transition of flow regimes excellently for the refrigerants. These results
have led to the evaluation of the wall shear stress and pressure drop,
under steady state conditions.
Fig 6.19 Contours of Mixture Density for R407C a) G = 400 kg/m2s, x=0.6b) G = 600 kg/m2s, x=0.6 andc) Cross section view for annular flow at G = 400 kg/m2s, x=0.6
a)
c)
b)
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6.3 Prediction of Pressure drop: Steady Simulations
The contours of mixture density obtained from the transient
simulations perfectly match with the predicted flow regime using
Thome et al. [2003a] flow regime map, though the simulations are
performed under adiabatic conditions. This shows that the phase
volume fractions and mixture density are unaffected by the slight
variations in temperature that occur during condensation. Hence the
wall shear stress and pressure drop across the tube is evaluated
under adiabatic conditions. Most of the correlations used for
comparison of experimental data were also developed for adiabatic two
phase flows.
The operating conditions and solver controls are as explained
for transient simulations, except a few changes in the solution
controls that are to be adopted for steady state simulations. The
amount of liquid as per the vapor quality at the given mass flux is
patched while initializing the solution. The liquid amount is calculated
using Zivi void fraction formula [1964] and . is the angle
subtended by the vapor region at the centre of the tube as shown in
Fig 6.20. The expression of Biberg [1999] based on void fraction is
used to calculate the stratified angle given by Eq. (6.5).
(6.5)
157
From the converged solution, the wall shear stress is evaluated
at each quality for a given mass flux. Pressure gradient can be directly
taken from the volume integral for the control volume of the tube. The
pressure drop obtained from the CFD simulations is compared with
correlations and experimental data.
6.4 Comparison of CFD Model with Experiment
The pressure gradient obtained from CFD simulations is
compared with that of experimental data and is presented in Figs 6.21
and 6.22 for refrigerants, R22, R134a and R407C.
In general, CFD data over predicts the experimental data as
shown in Fig 6.21. For R134a and R407C at medium and high
qualities for a high mass flux of 600 kg/m2s, the model under
predicts the experimental data as shown in Figs 6.21 b) and 6.21 c).
Fig 6.20 Schematic Representation of Stratified flow [2003a]
158
a)
c)
b)
159
The deviation and parity graphs presented in Fig 6.22 show that
that most of the data falls within the deviation of ±20%, except the
points representing low mass flux that fall outside the ±20% deviation
lines.
Fig 6.22 Comparison of CFD Data of Pressure Gradient with that ofExperiment for a) Deviation Graph b) Parity Graph
Fig 6.21 Comparison of CFD Data of Pressure Gradient with that ofExperiment for a) R22 b) R134a and c) R407C
a)
b)
160
Fig 6.22 a) shows that at a low mass flux of 200 kg/m2s, the
deviation of CFD result from the experiment is 34% for R22 and
exhibits comparatively larger deviations in the range of 43 – 45% for
R134a.
At a medium mass flux of 400 kg/m2s, the deviation of CFD
data from experiment is 5% for R22, 16% for R134a and 7% for
R407C while at a high mass flux of 600 kg/m2s, the deviation the
deviation is in the range of 12% for R22, 4% for R134a and 8% for
R407C. These results show an excellent agreement with the
experimental data particularly at medium and high mass fluxes for
the refrigerants considered in the present study.
The CFD results are also compared with correlations to observe
their relative performance in predicting the experimental data.
6.5 Comparison of CFD Data with Correlations
6.5.1 Comparisons for R22
Fig 6.23 shows the comparison of pressure drop data obtained
from CFD simulations using VOF model and from the correlations in
predicting the experimental data of R22 obtained in the present study.
At low mass flux, only CFD model and Müller - Steinhagen and
Heck correlation predicted the experimental data within 20 – 40%
161
deviation as shown in Figs 6.23 a) and 6.23 d). All other correlations
exhibited further larger deviations.
Fig 6.23 Comparison of CFD Data of Pressure Gradient with that ofExperiment and Correlations for R22 at a) G= 200 b) 400 andc) 600 kg/m2s d) Deviation Graph e) Parity Graph
a)
c)
b)
d)
e)
f)
162
Fig 6.23 b) shows that at a medium mass flux of 400 kg/m2s,
CFD data closely follows the trend of experimental data with a
tendency of over prediction compared to the correlations and its
predictions are the best with a deviation of 5% from the experimental
data as shown in Fig 6.23 e).
At a higher mass flux of 600 kg/m2s also, the CFD data closely
follows the experimental data up to medium qualities but exhibits
fluctuations at higher qualities as shown in Fig 6.23 c). This is due to
large values of void fractions at high vapor qualities in the range of
98% result into less amount of liquid at those operating conditions.
This small amount of liquid may not be properly captured by the cells
available at the boundary of the mesh model. Hence, considering the
CFD data only upto medium qualities, the predictions show an
excellent agreement with the experimental data with a deviation of
12%, as represented in Fig 6.23 f).
6.5.2 Comparisons for R134a
Figs 6.24 a) and 6.24 d) show that the experimental data at a
low mass flux of 200 kg/m2s is predicted with a deviation of 40 – 43%
by the CFD model. Müller - Steinhagen and Heck and Friedel
correlations exhibited better deviations in the range of 20-40%.
At mass fluxes of 400 and 600 kg/m2s, CFD predictions closely
follow the experimental data as shown in Figs 6.24 b) and 6.24 c). At a
medium mass flux of 400 kg/m2s, only the points representing the
CFD model are within ±20% deviation line as shown in Fig 6.24 d),
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with a deviation of 16%. At high mass flux also, CFD model predicts
the experimental data better than correlations with a deviation of 4%
as shown in Fig 6.24 f).
Fig 6.24 Comparison of CFD Data of Pressure Gradient with that ofExperiment and Correlations for R134a a) G= 200 b) 400 andc) 600 kg/m2s d) Deviation Graph e) Parity Graph
a)
b)
c)
e)
f)
d)
164
6.5.3 Comparisons for R407C
At the medium mass flux, the CFD results show an excellent
agreement with the experimental data up to medium vapor quality
and the deviation increases at higher quality as shown in Fig 6.25 a).
Fig 6.25 c) shows that only CFD data and the predictions of Friedel
correlation fall within a deviation band of ±20%. CFD model over
predicts the experimental data with deviation of 7%, while Friedel
correlation under predicts with a deviation of 10%. All other
Fig 6.25 Comparison of CFD Data of Pressure Gradient with that ofExperiment and Correlations for R407C at a) G= 400b) 600 kg/m2s d) Deviation Graph e) Parity Graph
a) c)
d)b)
165
correlations exhibit further larger deviations from the experimental
data.
For high mass flux of 600 kg/m2s also, pressure drop evaluated
using CFD simulations scatters close to the experimental data as
shown in Figs 6.25 b) and 6.25 d) with a deviation of 8%, which is
better than the predictions of correlations as shown in Fig 6.25 d).
Thus the pressure drop data obtained from CFD simulations
using VOF model is in good agreement with the experimental pressure
drop data, compared to the correlations of pressure drop for the
refrigerants considered in the present study.
6.6 Conclusions
Liquid – vapor flow of low and high pressure refrigerants, viz.,
R134a, R22 and R407C is modeled using VOF model from existing
CFD software, FLUENT. Initially, transient simulations are performed
to track the geometry of the interface and hence obtain flow regimes at
different operating conditions for low, medium and high mass fluxes.
The flow regimes obtained by plotting the contours of mixture density,
showed that the VOF model reproduced all the flow regimes including
the flow regime transitions given by Thome et al. [2003a] map
accurately.
For a low mass flux, CFD model exhibits higher deviations in
the range of 30-45% from the experimental data obtained in the
present study. However, its predictions are better than most of the
pressure drop correlations.
166
At mass fluxes of 400 and 600 kg/m2s, the predictions of CFD
model are in excellent agreement with the experimental data with a
maximum deviation of 16% exhibited for R134a at a medium mass
flux and a minimum deviation of 4% for R134a at high mass flux. The
predictions are observed to be better than that of pressure drop
correlations for the refrigerants considered in the present study.
The CFD results of pressure drop are observed to represent
higher deviations for low pressure refrigerant, R134a at very low
qualities in case of a low mass flux of 200 kg/m2s considered in the
simulations and at medium qualities for a mass flux of 400kg/m2s,
where the flow regime is bubbly and plug/slug (Intermittent)
respectively. These regimes represent mixing type flow without a clear
interface between vapor and liquid. Since the VOF model used in the
CFD analysis is based on interface flows, larger deviations are
observed at these flow conditions.
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