11 chapter 3
TRANSCRIPT
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
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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
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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.
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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.