34

void fraction expressions is also presented. A survey of correlations for

pressure drop and heat transfer developed based on these two phase

models, experimental and CFD studies reported in the literature are

presented in Chapter - III.

CHAPTER - III

LITERATURE SURVEY

3.1 Condensation inside a Horizontal Tube

Heat transfer and pressure drop studies on condensation inside

a horizontal tube can be categorized into analytical/semi empirical

studies and experimental studies. The information available in the

literature on two phase flow and in-tube condensation is presented as

follows.

i) Analytical/ Semi empirical Models

a) Pressure drop Correlations

b) Heat Transfer Correlations

ii) Experimental Analysis

iii) CFD Analysis

35

3.2 Analytical/ Semi empirical Models

In many applications where condensation occurs the dominant

flow regime is annular with gravity driven flow regimes occupying only

10 to 20% of the total quality range. Hence, most of the analytical

models to determine pressure drop and heat transfer are based on

annular flow regime.

3.2.1 Pressure drop Correlations

Pressure drop prediction is important in the thermal design of

condensers as the local condensing temperature is a function of local

pressure. Thus pressure drop affects the mean temperature difference

in the heat exchanger and hence its heat duty.

Pressure drop during condensation inside a horizontal tube of

constant cross sectional area, is sum of terms involving wall friction

and momentum transfer (flow acceleration/ deceleration), given by Eq.

(3.1).

(3.1)

During evaporation the momentum transfer term,

contributes to the overall pressure drop due to the increase of vapor

quality. However, for a condensing flow the kinetic energy of outgoing

flow is smaller than that of incoming flow. Hence the momentum

pressure head results in an increase in the pressure at the exit than

at the inlet, i.e. a pressure recovery. For condensing flows, it is

common to ignore the momentum recovery as only some of it may

36

actually be realized in the flow and ignoring it provides some

conservatism in the design. Hence, the correlations of frictional

pressure gradient, developed using the two-phase frictional

multiplier approach are presented as follows.

3.2.1.a Frictional Pressure Drop

The two phase multipliers pioneered by Lockhart and Martinelli

[1947] for adiabatic air-water mixtures are introduced in Chapter II.

Their correlations were later modified for diabatic flows by Martnelli

and Nelson [1948]. These multipliers are functions of Martinelli

parameter, which is dimensionless combination of the physical

properties. Subsequently, is being used in several convective

condensation and boiling correlations as one of the governing

parameters. The generality of Lockhart and Martinelli multipliers is

thus well acclaimed in two phase studies. Later many correlations

were developed using two phase multiplier approach. In general, the

frictional pressure gradient, in terms of two phase multiplier

is represented as,

(3.2)

where is calculated for ‘liquid only’ flow as,

37

(3.3)

The two phase multiplier, given by different correlations is

presented in Table 3.1.

Table 3.1 Frictional Pressure Drop Correlations

38

Description Correlation

GrönnerudCorrelation[1979]

(3.4)

(3.5)

If , or if ,

where (3.6)

ChisholmCorrelation[1973]

Flow Regime:Adiabatic two-phase flow-annular

Range:>1000 &G > 100 kg/m2s

(3.7)where =0.25 andFor , Chisholm’s parameter iscalculated as:

forfor

forFor , is:

for

for

For , is: (3.8)

FriedelCorrelation[1979]

Flow Regime:Adiabatic two-phase flow-annular

Range:<1000

(3.9)where and

(3.10)

(3.11)

(3.12)

The liquid Weber, ‘ ’is defined as,

Müller-Steinhagen andHeckCorrelation[1986]

(3.13)

Where the factor is, (3.14)and are the frictional pressure gradients

for all the flow liquid flow, and for all

vapor flow, .

39

Grönnerud correlation [1979] is developed for refrigerants.

Chisholm method [1973] is recommended for fluids with property

index, . Friedel [1979] developed a correlation

for two phase multiplier for vertical upward and horizontal flow in

round tubes and is recommended for fluids with . Müller-

Steinhagen and Heck [1986] proposed an empirical interpolation

between all liquid and all vapor flow.

All these correlations though developed for two phase flows at

atmospheric pressure and for evaporating flows, were used extensively

for pressure drop predictions and analytical modeling of condensing

flows also.

3.2.2 Heat Transfer Correlations

The heat transfer correlations available in the literature

can be classified into gravity driven and annular flow correlations

based on the dominant flow regime. The correlations of gravity driven

condensation are presented in Table 3.2.

3.2.2.a Gravity Driven Condensation

At low vapor velocities, gravitational forces that tend to pull

condensate down the tube wall are much stronger than vapor shear

forces that tend to pull the condensate in the direction of the flow as

shown in Fig. 3.1. In this case, the Nusselt [1916] theory for laminar

condensation is generally valid over the top, thin film region of the

tube. The gravity-driven flow regimes include stratified, wavy, and

slug flow regions. These regimes are often lumped together as the

40

dominant heat transfer mechanism in each of the regimes is

conduction across the film at the top of the tube.

Chato [1962] developed a similarity solution to the upper

portion of the tube considering the vapor as stagnant and the

condensate flows under hydraulic gradient as shown in Fig 3.1. It was

modeled after Chen’s [1961] analysis of falling film condensation

outside a horizontal cylinder and obtained Nusselt type correlation.

Jaster and Kosky [1976] proposed a correlation similar to

Chato’s for stratified flow condensation. To account for the variation of

liquid pool depth in a manner consistent with pressure driven flow,

where the condensate at the tube outlet fills the tube cross section as

shown in Fig 3.2, they replaced the constant in Eq. (3.15) given in

Table 3.2, with a function of void fraction, , given by Eq. (3.16).

Fig 3.1 Gravity Driven Condensation in Stratified Flow Regime [1998]

Fig.3.2 Stratified Flow Regime under Pressure Gradient [1962]

41

Chato and Jaster and Kosky correlations, both neglected heat

transfer in the liquid pool at the bottom of the tube. However, it is

observed that for high mass flux and low quality situations, convective

heat transfer prevails at the bottom of the tube.

Rosson and Meyers [1965] collected experimental data for

stratified, wavy and slug flows and suggested that film condensation

occurs at the top of the tube with superimposed effects of vapor shear,

Table 3.2 Gravity Driven Condensation Correlations

Description Correlation

Chato Correlation[1962] (3.15)

Jaster and KoskyCorrelation[1976]

(3.16)

- Zivi Void fraction model (3.17)

Rosson andMeyersCorrelation[1965]

(3.18)

and (3.19)

(3.20)

(3.21)

if

if (3.22)

42

thus modifying the constant in Nusselt solution with a empirically

determined function of vapor Reynolds number, given by Eq. (3.19) in

Table 3.2. In the bottom of the tube, they postulated forced convective

heat transfer using heat and momentum transfer analogy, given by

Eq. (3.20). They defined a parameter, that represents the fraction of

tube perimeter over which film condensation occurs.

3.2.2.b Annular Flow Correlations

Generally, annular flow correlations are classified into three

categories, viz. two-phase multiplier based, shear-based and boundary

layer based as given by Dobson et al. [1998].

Two Phase Multiplier Correlations

Two-phase multiplier-based correlations were pioneered for

predicting convective evaporation data by Dengler and Addoms [1956]

and were adapted for condensation by Shah [1979]. The hypothesis is

that the heat transfer process in annular two-phase flow is similar to

that in single-phase flow of the liquid, through which all of the heat is

transferred and thus their ratio may be characterized by a two-phase

multiplier, using the same rationale as the Lockhart-Martinelli two-

phase multiplier, developed for the prediction of two-phase frictional

pressure drop. The single-phase heat transfer coefficients are typically

predicted by the Dittus - Boelter correlation [1930]. The correlations of

heat transfer using two-phase multiplier approach are presented in

Table 3.3.

The most widely cited correlation of two phase multiplier type is

that of Shah [1979] correlation. It is developed based on the similarity

43

between the mechanisms of condensation and evaporation in the

absence of nucleate boiling.

Cavallini and Zecchin [1974] used the results of a theoretical

annular flow analysis to deduce the dimensionless groups and later

performed regression analysis to develop the correlation.

Dobson [1994] developed a correlation for annular based on

their experimental data, considering the data with (Modified

Froude number given by Soliman et al. [1983]).

Sarma et al. [2002] solved forced convective condensation of

vapors treating it as homogeneous model. In the estimation of two

phase multiplier, , they employed several models that satisfy the

relevant boundary conditions.

Description Correlation

Shah Correlation[1979] (3.23)

Cavallini andZecchin Correlation[1974]

(3.24)

DobsonCorrelation[1994] (3.25)

Sarma et al.Correlation [2002] (3.26)

Shear Based Correlations

Carpenter and Colburn [1951] pioneered the development of

shear-based correlations for annular flow condensation. These

Table 3.3 Two Phase Multiplier Correlations for Heat Transfer Coefficient

44

correlations presented in Table 3.4 assume that the dominant thermal

resistance to heat transfer occurs in the laminar sub-layer of the

liquid film and that the vapor core causes the film to become

turbulent at much lower Reynolds numbers than for single-phase

flow.

Soliman et al. [1968] proposed an equation utilizing the frame

work of Carpenter and Colburn to predict local condensation heat

transfer coefficient. The index 0.65 to liquid Prandtl number was

chosen to satisfy the correlation for wide range of organic liquids.

Chen et al. [1987] developed a generalized correlation for

vertical flow using the pressure drop model of Dukler [1960] and

neglecting acceleration head. They stated that the correlation was also

appropriate for horizontal flows, though they made no comparison

with horizontal flow data.

Description Correlation

Soliman et al.Correlation[1968]

(3.27)

Chen et al.Correlation[1987]

(3.28)

Boundary Layer Based Correlations

Boundary layer-based correlations are similar to shear-based

correlations, except that the thermal resistance throughout the entire

liquid film thickness is considered, instead of only in the laminar sub-

Table 3.4 Shear-Based Correlations for Heat Transfer Coefficient

45

layer. These correlations, presented in Table 3.5 are all similar in

approach that they apply the momentum and heat transfer analogy to

an annular flow model using the Von Karman [1939] universal velocity

distribution to describe the liquid film.

Kosky and Staub [1971] applied this analogy, assuming uniform

thickness of annular film to develop an expression for heat transfer

coefficient in terms of non dimensional temperature and non

dimensional film thickness, . The Traviss et al. [1973] correlation is

another most widely quoted correlation in this class. Traviss et al.

[1973] stated that their expression agree well with experimental data

for low vapor qualities or high values of Martinelli parameter, , but

significantly under-predicted the data at high qualities or low values

of .

The above mentioned correlations of heat transfer coefficient are

generally applicable to pure refrigerants. In case of refrigerant

mixtures, mass transfer correction should be incorporated given by,

Silver [1947] and Bell-Ghaly method [1973]. Accordingly, the effective

heat transfer coefficient, of mixture refrigerants is,

(3.29)

where, condensation heat transfer coefficient, can be obtained from

any of the two phase heat transfer correlations for pure fluids and

vapor heat transfer coefficient, is obtained using Dittus-Boelter

46

equation. The parameter, is the ratio of the sensible cooling of the

vapor to the total cooling rate given by Eq. (3.30).

(3.30)

3.2.2.c Flow Regime Based Correlations

Flow regime based correlations are the improvement over

analytical correlations and recent flow regime based correlations were

Table 3.5 Boundary Layer-Based Correlations for Heat Transfer Coefficient

Description Correlation

Kosky andStaubCorrelation[1971]

(3.31)

Where , and frictional pressure drop is

obtained using Wallis [1969] separate cylinders model.

for

for

for (3.32)

for

for(3.33)

Traviss et al.Correlation[1973]

(3.34)

for

for

for (3.35)

47

developed by Thome et al. [2003a, 2003b] and Cavallini et al. [2002].

The detailed description of Cavallini et al. correlation is presented as

follows.

Cavallini et al. [2002] correlation is developed for all flow

regimes using a large data base of halogenated refrigerants. Their

predictive procedure is given in Table 3.6. They reported that their

computational method can be used for condensation of halogenated

refrigerants inside tubes of diameter greater than 3 mm, at reduced

pressure, <0.75 and density ratio, >4. The flow regime

parameters are dimensionless vapor velocity, and Martinelli

parameter, . The model is based on the flow regime map developed

by Cavallini et al. [2002] as shown in Fig 3.3.

For annular flow regime, when as shown in Fig 3.3,

Kosky and Staub model is used. When and , the flow

enters annular-stratified flow transition and stratified flow region. The

heat transfer coefficient, is calculated from a linear interpolation

between the heat transfer coefficient at the boundary of the annular

flow region and that for fully stratified flow, .

In stratified flow, at very low , heat is transferred in the upper

part of the tube through a thin gravity driven film and, in the lower

part of the tube, through a thick liquid film. Accordingly, the heat

transfer coefficient is expressed as the sum of film condensation

48

on the upper part of tube and convective term that refers to the lower

part of the tube.

Cavallini et al. [2002] Correlation

For annular flow with :

(3.36)

for

for

for (3.37)

for & for (3.38)

and (3.39)

;

; &

and for

Fig 3.3 Cavallini et al. [2002] Flow Regime Map

Table 3.6 Cavallini et al. [2002] Flow Regime Based Correlation

49

and for (3.40)

For annular-stratified flow when and :

(3.41)

Where is obtained from annular flow equations, Eqs. (3.36)-(3.40)

at a given and . (3.42)

(3.43)

; ; (3.44)

and (3.45)

For stratified and slug flow when and :(3.46)

Where (3.47)

is calculated from Eqs. (3.41) – (3.45).

3.3 Experimental work

Two types of experimental methods are generally used in analyzing

heat transfer coefficients

Local heat transfer method, where heat transfer information is

obtained with associated small changes in vapor quality and is

reported for the average vapor quality. Thus the heat transfer

coefficients obtained are quasi local values for the average vapor

quality of test section. The method presents an insight into the

condensation process by relating heat transfer coefficient and

pressure drop with the prevailing flow regime.

50

Average heat transfer method, where observations are made over

a broad range of vapor quality change, viz. from vapor (x = 1.0)

to nearly liquid (x = 0.0).

The second method is widely used as it requires less time for

setting up of experiment and is more cost-effective, but provides

limited insight into mechanisms of the flow condensation process.

The first method is more desirable, although the resulting test

matrix would be time consuming due to the large number of test

combinations that need to be covered. A detailed review of recent

quasi local condensation studies of refrigerants is presented as follows

and a summary is presented in Table 3.7.

Dobson and Chato [1994] conducted an experimental study of

heat transfer and flow regimes for refrigerants, R12, R22, R134a and

near-azeotropic blends of R32 and R125 inside horizontal tubes of

diameter ranging from 3.14 mm to 7.04 mm for a mass flux ranging

from 25 to 800 kg/m2s. Their technical paper [1998] gives a very good

insight of in-tube condensation and a comprehensive classification of

flow regimes. They proposed new correlations for annular and wavy

flow regimes, based on two broad flow regime categories of gravity

dominated and shear dominated. They reported that their correlations

predicted the experimental data with a mean deviation of 4.4 - 13.7 %.

They stated that the correlations apply reasonably well for larger

diameter tubes, higher mass fluxes and can also accommodate

51

refrigerant mixtures. Later, Sweeny and Chato [1996] extended the

Dobson correlations to zeotropic refrigerant blends, by using a Sweeny

multiplier based on the experimental data of zeotrope, R407C. Dobson

et al. also performed extensive review of existing flow regime maps.

Accordingly, they stated that Taitel-Dukler [1976] map and Soliman

[1983] flow regime predictors matched their experimental observations

very well.

Experiments on flow condensation of pure R32, R134a and their

mixtures was performed by Shao and Granryd [1998] for a range of

mass flux, 130 – 400 kg/m2s inside a tube of diameter, 6mm and

length, 10 m divided into subsections to study the behavior of NARMs

(Non-Azeotropic Refrigerant Mixtures or Zeotropes) on heat transfer

performance. They observed that the potential causes of heat transfer

degradation associated with NARMs are due to the combined effects of

non-ideal properties of NARMs, temperature glide and concentration

difference between liquid and vapor phases during phase change.

Granryd [1991] proposed a theoretical approach to evaluate two phase

heat transfer coefficient of refrigerant mixtures for evaporation and

condensation using the similar assumptions implemented by Silver

[1947] and Bell-Ghaly [1973] method.

Boissieux et al. [2000] conducted experiments using zeotropic

refrigerants, Isceon 59, R407C and R 404A inside horizontal tube of

52

3/8” diameter and 4 m length for range of mass flux, 150 – 400

kg/m2s and compared their experimental results with Shah [1979],

and Dobson et al. [1998] correlations. In general, they observed the

Shah correlation to satisfactorily predict their experimental data with

a overall standard deviation of 9.1%. They reported that although

Dobson et al. correlation with Sweeny multiplier was initially based on

R407C data, it also predicted the experimental data of Isceon 59 and

R 404A well with a tendency to over predict below vapor quality of 0.5.

Li et al [2000] performed experiments for R12 and R134a inside

a horizontal tube of diameter, 11 mm and length, 1300 mm for a mass

flux ranging from 200 to 510 kg/m2s. They also presented a numerical

model for predicting the local heat transfer coefficient using Von

Karman law of universal velocity distribution for the annular liquid

film in a circular tube and Lockhart-Martinelli method for determining

two phase flow pressure drop. They reported a good agreement

between the predicted and measured heat transfer coefficients in the

range of vapor quality, 0.4 to 1.0. They observed that the predicted

heat transfer coefficient was not very sensitive to the vapor quality

distribution along the flow direction and a uniform vapor quality

gradient can be considered as a good approximation. They reported

that the largest deviations of their numerical model with the

experimental data were within ±31% and ±35% for R12 and R134a

respectively.

53

Cavallini et al. [2001] had conducted experimental

investigations of HFCs, R134a, R125, R32, R410A and R236ea inside

a horizontal tube of diameter, 8mm and length, 1m for a mass flux

ranging from 100 to 750 kg/m2s. They observed that for low mass

flux, condensation heat transfer coefficients increase with the

decrease of difference between saturation temperature and wall

temperature and at high mass flux, there is no dependence of heat

transfer coefficient on temperature difference with forced convection

as the sole driving heat transfer mechanism due to fully developed

annular flow. They also measured pressure drop data for HFCs and

observed that low pressure fluids show higher pressure drop. They

plotted their experimental data at different saturation temperatures

on Breber et al. [1980] and Tandon et al. [1982] flow regime maps and

observed that while saturation temperature strongly affects the heat

transfer coefficient, it does not show similar effect on flow pattern.

They reported that their experimental data is well predicted by Kosky

and Staub [1971] and Jaster and Kosky [1976] models valid for

annular and stratified flow regime respectively. They suggested the

use of Friedel model [1979] of frictional pressure drop in conjunction

with Kosky and Staub model for prediction of heat transfer coefficient.

When the flow is not fully annular, Cavallini et al. suggested to apply

both Kosky and Staub [1971] and Jaster and Kosky [1976] models

and higher of the two to be taken as predicted heat transfer

coefficient.

54

Smit et al. [2002a] performed experimental studies using HCFC

zeotropic mixtures of R22 and R142b inside a horizontal tube of 3/8”

diameter divided into eight subsections, each of length, 1.603 m for

mass flux ranging 40 to 350 kg/m2s at a condensing temperature of

600C. They observed that at low mass flux with predominantly wavy

flow regime, the average heat transfer coefficient is decreased by 33%

from pure R22 to 50% of R22 in a mixture of R22 and R142b while at

high mass flux where the flow regime is annular, the heat transfer

coefficients were not strongly influenced by refrigerant mass fraction,

with only 7% decrease of average heat transfer coefficient. Smit et al.

[2002b] in another paper compared their experimental results with

Shah [1979], Cavallini and Zecchin [1974] and Dobson et al. [1998]

correlations and for mixtures, they applied Silver-Bell-Ghaly method

for mass correction. They concluded that for predominantly annular

flow regime, Shah correlation predicts the heat transfer coefficients

very well. They observed that in general, Dobson et al. [1998]

correlations for annular and stratified wavy regimes predicted the heat

transfer coefficients well with a maximum deviation of 8%.

Flow condensation heat transfer coefficients of R12, R22, R32,

R123, R125, R134a and R142b were experimentally measured by

Dongsoo Jung et al. [2003] inside horizontal tubes of 3/8” diameter

and 1m length for mass fluxes, 100, 200 and 300 kg/m2s. At the

55

same mass flux, they found that the heat transfer coefficients of R32

and R142b were higher than R22 by 8 to 34%, while heat transfer

coefficients of R134a and R123 were similar to that of R22. They

compared their experimental data with correlations of Traviss et al.

[1973], Cavallini and Zecchin [1974], Shah [1979] and, Dobson et al.

[1998] that showed average deviations of less than 8%, while the

correlations by Akers and Rosson [1960], Soliman et al [1968] and

Tandon et al [1985] showed larger deviations with average deviations

more than 15%. They modified Dobson et al. correlation to fit their

experimental data by incorporating a non dimensional parameter,

Boiling number, which is the ratio of heat flux to the mass flux

with latent heat of condensation.

Later Dongsoo Jung et al. [2004] also conducted experiments

with R22, R134a, R407C and R410A and observed that the heat

transfer coefficients of R134a and R410A were similar to those of R22

while heat transfer coefficient of R407C were 11-15% lower than those

of R22, due to strong mass transfer resistance. They explained the

comparative performance of condensing refrigerants using liquid

property combination, given by Jung et al. [1989] for evaporating

flows.

Aprea et al. [2003] obtained quasi local heat transfer coefficients

of R22 and R407C for gravity driven flow regime inside a tube of

56

diameter, 20mm and length, 6.6 m divided into 12 subsections for

mass flux ranging from 45 – 120 kg/m2s. They reported that the heat

transfer coefficient of R22 is always greater than R407C with

percentage difference decreasing with increasing mass flux. They

compared their experimental data with correlations of gravity driven

condensation, using Silver-Bell-Ghaly correction factor for mixtures

and reported that Dobson et al. correlation is best fitting for their

experimental data.

Infante Farreira et al. [2003] obtained condensation heat

transfer coefficients of R404A inside a horizontal tube of 3/8”

diameter and 1m length for a mass flux ranging 200 – 600 kg/m2s.

They compared their experimental data with Dobson et al. [1998] and

Shah [1979] correlations and observed that Dobson correlation under

predicted the wavy flow region by about 20%. Shah correlation

predicted the experimental data well with an average error of 3%. They

compared their findings with that of Boissieux et al. [2000] for R404A.

Thome et al. [2003a, 2003b] adapted Kattan-Thome-Favrat flow

regime map [1998] for evaporation and developed a new flow pattern

map for condensation inside horizontal tubes. Based on their flow

regime map, they developed a new heat transfer model including the

effects of flow regime and interfacial roughness that predicts the heat

transfer coefficient for all flow regimes of stratified, stratified wavy,

57

intermediate, annular and mist flows. They compared their model with

experimental data of 15 different fluids for mass flux range of 24 to

1022 kg/m2s, reduced pressure ranging 0.02 to 0.8 and internal

diameters range of 3.1 to 21.4 mm. They noted that their model

predicts 85% of the data excluding hydrocarbons within ±20% and

predicts 75% of the entire data including hydrocarbons within ±20%.

Jiang et al. [2006] presented experimental results of R404A and

R410A inside horizontal tube of diameters, 6.2 mm and 9.4 mm at

high reduced pressures ( is 0.8-0.9) for a mass flux range of 200 –

800 kg/m2s using thermal amplification technique to measure heat

duty accurately. The experimental data primarily fell into annular and

stratified-wavy flow regime and they observed that none of the

available correlations in literature were able to satisfactorily predict

the heat transfer coefficients of blends used at such high pressures.

They reported that the wavy flow model of Dobson et al. [1998] under

predicted the data while their annular model over predicted the data.

They observed that the correlations of Cavallini et al. [2002] and

Thome et al. [2003b] resulted into better predictions comparatively.

Condensation heat transfer coefficients of hydrocarbons, R-

1270, R-290, R-600a and R22 were experimentally measured by Lee

et al [2006] inside tubes of diameters, 9.52 mm and 12.70 mm. They

reported that local heat transfer coefficients of hydrocarbons were

58

generally higher by at least 31% than that of R22. However, the

hydrocarbon refrigerants suffer from higher pressure drops by at least

50% than those of R22. They compared their experimental data with

Shah [1979], Traviss et al. [1973] and Cavallini-Zecchin [1974]

correlations and found the agreement consistently within ±20%,

though Shah correlation over predicted the data comparatively.

An experimental investigation of pressure drop and heat

transfer for in-tube condensation of ammonia with and without

miscible oil inside smooth aluminum tube of diameter, 8.1 mm for a

mass flux range of 20–270 kg/m2s is performed by Park and Hrnjak

[2008]. They reported that most correlations over predict measured

heat transfer coefficients of ammonia, up to 300%. The reasons are

attributed to difference in thermophysical properties of ammonia

compared to other halogenated refrigerants used in generation and

validation of the correlations. Based on their experimental data, they

developed a new correlation by modifying Thome et al. [2003b]

correlation that predicted most of the measured values within ±20%.

They also measured pressure drop of ammonia and observed that

Müller Steinhagen and Heck and Friedel correlations based on

separated flow model predict the pressure drop relatively well at

pressure drop higher than 1 kPa/m, while a homogeneous model

(McAdams Model) yielded acceptable values at pressure drop less than

1 kPa/m.

59

3.4 CFD Analysis of In-Tube Two Phase Flow

One of the major difficulties in modeling two phase flow is

determining the distribution of the liquid and the vapor phase in the

flow channel. As the performance parameters such as heat transfer

and pressure drop are closely related to this distribution, the

calculation of the two-phase flow pattern by means of computational

fluid dynamics (CFD) can be very useful. However, there is not much

work reported in the literature on the CFD analysis of multi phase

flows in general. A review of the recent literature on the

CFD/numerical analysis of two phase flow inside a horizontal tube is

presented as follows.

A detailed one-dimensional, steady and transient numerical

simulation of the thermal and fluid-dynamic behavior of double pipe

heat exchangers had been carried out by Valladares et al. [2004]. The

governing equations inside the internal tube and the annulus,

together with the energy equation in the internal tube wall, external

tube wall and insulation, were solved iteratively in a segregated

manner. The discretized governing equations in the zones with fluid

flow were coupled using an implicit step by step method. They used

empirical correlations viz., Dobson et al. correlation [1998] for the

evaluation of convective heat transfer, Friedel’s two phase multiplier

Table 3.7 Summary of Recent Experimental Work Reported

Description RefrigerantsTested

Mass Flux Correla-tionsCompared

CorrelationsDeveloped

Dobson

et al.[1994,1998]

R12, R22,R134a andblends of R32and R125

25-800 ----- For annularand wavyregimes

Shao &Granryd[1998]

R32, R134aand theirmixtures

130-400 ------ ModifiedTandon et al.correlation anddevelopedmodel forNARMS

Boissieuxet al.[2000]

Isceon 59,R407C andR404A

150-400 Shah andDobson etal.

------

Liet al.[2000]

R12, R134a 200-510 ---- AnalyticalModel isdeveloped usingVon KarmanVelocityDistributions

Cavallini etal. [2001,2002]

R134a, R125,R32, R410Aand R236ea

100-750 Jaster andKosky &

Kosky andStaub

Developed aFlow Regimebasedcorrelation

Smit et al.

[2002a,2002b]

Mixtures ofR22 andR142b

40-350 Shah,CavalliniandZecchinand Dobsonet al.

-----

DongsooJung et al.

[2003,2004]

Pure andMixtures ofHCFCs andHFCs

100-300 Traviss etal,CavalliniandZecchin,Shah,Dobson etal., AkersandRosson,Tandon andSoliman

ModifiedDobson et al.correlation

Aprea et al.

[2003]

R22, R407C 45-120 Dobson etal, Jasterand Kosky& Rossonand Myers

------

InfanteFerreira etal. [2003]

R404A 200-600 Shah andDobson etal.

------

Thome et Pure and 24-1022 ----- Developed Flow

60

[1979] for shear stress evaluation and Premoli [1971] model for the

evaluation of void fraction. An implicit central difference numerical

scheme and a line-by-line solver were used in the internal and

external tube walls and insulation. They compared their numerical

data for variation of temperature of refrigerant along the tube with the

experimental data of Boissieux et al.[2000] and Takamatsu et al.

[1993a, 1993b] and observed that their results are in good agreement

with the experimental data.

Vaze et al. [2008] performed CFD analysis of two phase flow

through pipes and square ducts using commercial CFD package,

FLUENT for air velocity varied from 1 to 12.5 m/s and water velocity

from 0.0066 to 0.1 m/s. They used Volume of Fluid method for a tube

of diameter, 0.1 m and length, 1 m. They applied constant heat flux

boundary condition to conduct heat transfer studies and observed

that the effective heat transfer coefficient is a function of both water

and air flow rates.

Schepper et al. [2008] used Volume of Fluid (VOF) model with

piecewise linear interface (PLIC) reconstruction method in each

computational cell as implemented in a computational fluid dynamics

code and obtained the flow regimes. The flow regimes for water–air

flow and gas – oil flow were reproduced. They reported that all

simulations were in good agreement with the flow regimes predicted

from the Baker map [1954]. As reported by them, all flow regimes

61

predicted by Baker map are simulated for the first time. Their work

confirmed that CFD codes are able to simulate the two-phase flow

regimes as predicted by the Baker chart.

3.5 Scope for the Present Study

The review of quasi local experimental work presented in the

previous sections can be classified into experimental studies for

understanding the behavior of alternative refrigerants in order to

replace the existing CFCs and experimental studies for developing

better predictive procedures for the evaluation of performance

parameters as the better design practices and overall system efficiency

contribute to the reduction of carbon footprint in the atmosphere.

The recent experimental studies are of second type, performed

for different fluids, viz., HCFCs, HFCs, HCs and their mixtures and

inorganic refrigerants like ammonia etc. Based on the experimental

studies, reported by Jiang et al. [2006] and Park et al. [2008], it is

observed that the correlations including recently developed ones could

not predict the experimental data for pure and mixture refrigerants at

high reduced pressures and also for non-halogenated refrigerants.

Review of analytical models for two phase condensing flows

reveals that they have limited applications as they are developed

based on simplified models like homogeneous and separated models.

These correlations for heat transfer exhibited better predictions for

62

only a particular range of mass flux and vapor quality, thus leaving lot

of scope for the development of new models.

Very limited work is reported in the literature on the numerical

models for condensing flows or on CFD analysis for two phase flow in

general. The numerical models reported were developed by discretizing

the simplified, one dimensional governing equations which in turn use

semi empirical correlations for heat transfer and pressure drop. The

CFD analysis of two phase flow reported in the literature is scarce

with applications to adiabatic flows or diabatic flows without phase

change.

Therefore, the present study investigates the experimental

evaluation of heat transfer coefficient and pressure drop for different

flow regimes. A predictive procedure for the simulation of flow

regimes, and for the evaluation of pressure drop and heat transfer

coefficient using the combination of CFD analysis and numerical

model is developed.

3.5.1 Objectives of Present Study

The objective of the present study is primarily to design and

fabricate an experimental setup for measuring the performance

parameters of two phase flow, viz., heat transfer and pressure drop for

three different refrigerants, R22, R134a and R407C using quasi local

experimentation technique.

63

To study the two phase flow at high pressures in the range of

10–16 bar, corresponding to a condensing temperature of 400C

for three refrigerants.

To study the effect of mixture refrigerant on the performance

parameters of two phase flow in comparison with the pure

refrigerants.

Secondly, the work of Schepper et al. [2008] for air – water and

gas – oil mixtures at atmospheric pressures is extended to vapor –

liquid flow of refrigerants at high pressures to simulate flow regimes

as flow regimes could not be visualized in the experimental study and

hence to evaluate the two phase pressure drop.

Thirdly, the objective of the present study is to develop a

predictive procedure for two phase flow using a combination of CFD

analysis to predict the flow regimes and pressure drop; and numerical

model to evaluate the heat transfer coefficient for any fluid and at any

operating pressure.

To compare the resulting numerical heat transfer coefficient and

pressure drop with the experimental data from the present

study and with some of the widely used correlations of pressure

drop and heat transfer coefficient from the literature.