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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

126

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]

131

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

135

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

136

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

139

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)

142

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)

143

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)

144

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)

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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)

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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)

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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.

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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.