Countercurrent gas-liquid flow in plate-fin heat exchangers with plain and perforated fins

Countercurrent gas–liquid flow in narrow rectangular channels simulated by plain and perforated fins is studied. Different flow patterns dependent on flow rates are observed and visualised in the channels. Flooding velocities and pressure drops are measured. Results are compared with previous experimental data obtained in rectangular channels. The present results focus on two particular types of flooding phenomena: that occurring at the column base and linked to plugging and that at the top, linked to reentrainment. A further set of experiments using perforated fins surprisingly shows a greater tendency to flooding of the perforated fins. However, there are marked differences for the two types of fins and an explanation may be the two distinct flooding occurrences


Introduction
In vertical gas±liquid countercurrent ¯ow at constant liquid ¯ow rate increasing the gas ¯ow rate will eventually lead to a critical point at which upward ¯ow of some liquid is observed.This occurrence is referred to as ¯ooding.
More precisely, ¯ooding may be de®ned by a series of phases (Delhaye, 1981): (a) For low gas ¯ow rates, liquid (L) ¯ows downwards unaected by the upward ¯ow of the gas (G) (Fig. 1(a)).
(b) As the gas ¯ow rate increases, waves of large amplitude travelling upward appear along the ®lm (Fig. 1(b)).
(c) Raising the gas ¯ow rate more causes the ®lm to become `agitated' and droplets are torn o from the crests of the waves and entrained with the gas ¯ow (Fig. 1(c)).
(d) Gas ¯ow rates above this lead to more and more liquid being entrained (Fig. 1(d)).
(e) Eventually wall drying will occur as well as an upward liquid ®lm ¯ow (Fig. 1(e)).The third stage (c) is particularly interesting and corresponds to the so-called ¯ooding point.However, de®nition of this transition varies among authors since it seems to be greatly dependent on the experimental system.Some authors de®ne the ¯ooding point via entrainment levels and others on liquid bridging of the ¯ow channel.Flooding can either be considered as a result of the gas±liquid interface instability or as a limit condition of the countercurrent ¯ow.
Flooding limits can be determined either from visual observations or from experimental measurements: (a) Typical visual observations and dierent models associated are the occurrence of a standing wave on the liquid ®lm (Shearer and Davidson, 1965); liquid ®lm instabilities (Jameson and Cetinbudaklar, 1969;Cetinbudaklar and Jameson, 1969;Imura et al., 1977); no net ¯ow in the liquid ®lm (Grolmes et al., 1974); droplet entrainment from the liquid ®lm (Dukler and Smith, 1977).(b) Flooding limit consequences can be detected by measurement (Bachir, 1987): the occurrence of a standing wave on the liquid ®lm (®lm thickness measurement); droplet entrainment from the liquid ®lm (pressure drop or ¯ow rate measurement).However, only a quantitative de®nition of ¯ooding emerges from previous studies (Delhaye, 1981): pressure drop increases sharply above the injection zone indicating that droplets are entrained with the gas ¯ow.
Generally, it seems that there is ¯ooding when interfacial friction balances buoyancy and inertial forces.However, ¯ooding also depends on various experimental parameters such as: (i) Entrance or exit conditions for the liquid: an abrupt entry causes local perturbations and is favourable to ¯ooding (Barathan and Wallis, 1983;Mishima and Nishihara, 1984).
(ii) Channel diameter: it is well established that proximity of the walls tends to favour the onset of ¯ooding, (Bachir, 1987).
(iii) Long tube lengths: long lengths in circular geometry are favourable to the onset of ¯ooding but these eects are masked for high viscosity liquid.In rectangular channels, a study by Celata et al. (1986) showed no length eect.It may be that length eects are observed by entrance and exit conditions as ¯ooding is generated by local perturbations linked to these conditions.(iv) Physical properties of the ¯uid: high liquid viscosity seems to diminish the tendency to ¯ooding and high surface tension also has a stabilising eect especially in narrow channels (Damon, 1996).However, no clear in¯uence has been established.Flooding in countercurrent gas±liquid ¯ows is a signi®cant problem in the process industry, particularly in re¯ux condensers where vapour ¯ows upward and the condensate falls down countercurrent to it.Flooding induces an undesirable removal of liquid and this may lead to blockage of the condenser.As a consequence, ¯ooding has been the subject of several experimental investigations in circular tubes for the last ®ve decades.No adequate theories have been provided so far.Some empirical correlations have been developed but they can only be used within a limited range of validity.This range depends on geometry, gas and liquid ¯ow rates and experimental setup.The current use of compact heat exchangers as re¯ux condensers cannot neglect a phenomenon like ¯ooding.A vapour±gas mixture is introduced at the lower part of the condenser and the re¯ux liquid ¯ows downwards enriched with the less volatile components.Such a device is designed for separating these less volatile species from gas mixtures.With this geometry, it is essential that the gas ¯ow rate is not so high as to cause ¯ooding.However, the lack of reliable correlations for predicting the onset of ¯ooding in the re¯ux condensation case remains a substantial problem (Webb, 1996).
The aim of the present study is to reproduce ¯ooding conditions in a simulated re¯ux condenser.When used to compare the data, all the experiments are carried out for a ®xed gas ¯ow rate under adiabatic conditions.The test section is similar to a compact heat exchanger but air and water replace vapour and condensate, respectively.Water is injected through a porous system.The eect of high and low ¯ow rates on ¯ow con®gurations and on ¯ooding limits is examined.Perforated ®ns are also studied since they are employed in the process industry for condensation and they are considered to be more ecient in terms of heat transfer.However, their ef-®ciency in terms of ¯ooding has never been established.Pressure drop measurements at the bottom of the test section are used to characterise the ¯ooding limit accurately.Finally, comparisons with previous studies in rectangular channels are made as well as with previously published correlations.
In this study, only the hydraulic aspects are simulated in order to characterise the ¯ow in narrow rectangular channels.Compared to the study of a compact heat exchanger functioning in re¯ux condensation, there is an evident dierence in the liquid injection system.Indeed, in the case of re¯ux condensation, the condensate is formed gradually and the ®lm thickness is not constant throughout the condenser.Injecting the liquid at the top can in¯uence the ¯ooding phenomenon.The common points between the hydraulic study and the thermal study are the injection of gas at the lower end, the geometry considered, the countercurrent ¯ow obtained and the characterisation of the ¯ooding point by the in¯uence of the vapour ¯ow on the liquid ¯ow.Additionally, the adiabatic system stabilises quickly and the ¯ow rates are easily adjusted to measure the ¯ooding points.

Experiment
Fig. 2 is a schematic view of the air±water experimental facility.Such an equipment is designed to visualise the ¯ow and to measure gas and liquid ¯ow rates.Additionally, the experimental setup allows pressure drop measurements.
The water is injected through a porous system in the upper part of the test section.The porous system evenly distributes the water into every channel.Liquid ¯ows down due to gravity and it is collected at the bottom of the experiment to be reinjected in the system.No additional device is used to collect liquid ¯ow except gravity.The liquid ¯ow rate is measured by two calibrated ¯owmeters for two dierent ranges 10±50 or 31.5±300l/h.Ambient air is blown at the lower part of the test section and enters the test section at 70°C.A convergent system supplies the air ¯ow to the channels.The ¯ow rate is regulated by Kutateladze number (Eq. ( 5) two valves and measured by a calibrated ¯owmeter in the range 0.2±6 m 3 /h.

Estimation of the uncertainty on the mass ¯owmeter
The uncertainty on the mass ¯owmeter data by the calibration certi®cate of the manufacturer is of AE1% of the maximum ¯ow which is 6 m 3 =h.We thus have a 0:06 m 3 =h absolute error.

Estimation of the uncertainties on the rotameters
For the range of ¯ow [10±50 l/h], the misreading is estimated at AE 0.5 l/h.For the range of ¯ow [31.5±300 l/h], the misreading is estimated at AE2:5l =h.

Uncertainty on the determination of the ¯ooding air ¯ow rate
The ¯ooding point is evaluated according to the measurement of the pressure together with visual observations.However, while the measurements were taken, it was that there is an uncertainty on the determination of the ¯ooding air ¯ow rate, uncertainty estimated at AE0:1m 3 =h, which gives a total uncertainty of 0:16 m 3 =h.
The test section consists of an aluminium corrugated plate 0.4 mm thick sandwiched between two parallel plane plates resulting in 56 rectangular channels, see Fig. 3.The channel dimensions are 2:14 Â 5:10 mm 2 ; a Â b cross-section.Plain and perforated ®ns are used.The front plate is made of Plexiglas to visualise the ¯ow patterns in the channels.
Pressure measurements are located at the top, the middle and the bottom of the test section and the pressure drop between the inside test section and atmospheric pressure is measured.The top test section is opened to the atmosphere.As a consequence, pressure measurement located at the top gives the atmospheric pressure and the one located at the middle does not present a signi®cative dierence of pressure.The pressure drop between the bottom of the test section and atmospheric pressure is measured by using a manometer graduated from 0 to 120 mm.The overall system is adiabatic at atmospheric pressure.The liquid Reynolds numbers vary from 6 to 350.The Reynolds numbers in terms of super®cial velocities for both phases are: Since the test section is made of transparent walls, observation of 28 channels and photography of ¯ow patterns during measurement are possible (Fig. 4).

Visual observations and pressure drop measurement of plain ®ns
In a vertical countercurrent ¯ow, the ¯ow patterns observed depend on gas and liquid ¯ow rates, dimensions of the channel and physical properties of the gas±liquid system such as viscosity or surface tension.Typical ¯ow patterns of countercurrent ¯ow observed in the test section are shown in Fig. 5: ®lm ¯ow, plug and churn ¯ows.All these patterns are observed simultaneously in dierent channels.However, some con®gurations preferentially appear for a speci®c range of liquid ¯ow rates: churn and ®lm ¯ow occur at high liquid ¯ow rates (100± 300 l/h) with thick ®lm ¯ow predominating.Thin ®lm, churn and plug ¯ow appear for low liquid ¯ow rates (10±100 l/h) with plug ¯ow predominating in this case.
The classi®cation of these ¯ows was based on: ®lm ¯ow where downward ¯owing liquid ®lls a signi®cant part of the channel (Fig. 5(a)); plug ¯ow where liquid plugs ¯ow down and gas goes through passages separating the liquid plugs (Fig. 5(b)); and churn ¯ow where liquid plugs tend to increase in size and proximity (Fig. 5(c)).Again, well-de®ned transition between these ¯ow patterns is dicult to ®x over such a large number of channels.A resulting diculty is to determine the onset of ¯ooding in the test section since some channels quickly reach a ¯ooded state whereas others retain a countercurrent ¯ow con®guration.
A measurable characteristic of ¯ooding is a sharp increase in pressure drop above the injection zone.Since the pressure measurement above the injection zone was not measurable the ¯ooding limit was determined by measuring the pressure drop between the inlet and the outlet of the test section.For four liquid ¯ow rates [10, 50, 100, 200 l/h], see Fig. 6, an increase of pressure drop at the ¯ooding point is observed.Then, the pressure increases more or less irregularly with the liquid ¯ow rate.It is necessary to identify two causes of pressure drop augmentation at ¯ooding: surface friction forces and droplets in the gas core.Below the injection liquid zone the pressure drop increase is caused by surface friction forces since the liquid ®lm is thicker there.Above this zone, pressure drop alteration is caused by droplet entrainment by the gas phase.This second zone is more inclined to ¯ooding.However, pressure drops measured in the present study are de®ned as the dierence between pressure at the bottom of the test section and atmospheric pressure outside.Thus, pressure drop measurements were only possible at the lower part of the test rig since measurements taken higher do not present a sucient dierence with external pressure.
Therefore, the two methods, visual observations and pressure drop measurement, allow the determination of the ¯ooding limit.

Flooding characteristics
It is dicult to de®ne precisely the ¯ooding point in a multichannel exchanger as one can do for a single channel since the phenomenon is unstable and it does not occur simultaneously in all the channels.It occurs also dierently for the two ¯ow rate ranges considered here.
At high liquid ¯ow rates in the range 100±300 l/h, the liquid cannot ¯ow down the channels and some droplets are entrained up to the top of the test section.Then, as the gas ¯ow rate increases, more and more liquid is entrained and tends to remain at the upper end of the test section (Fig. 7).In this range, we consider the test section to be ¯ooded when some droplets are carried out of the test section.
At lower liquid ¯ow rates (10±100 l/h), ¯ooding is caused by the instability of the liquid in the lower part of the test section.The liquid is removed from the lower part to the top of the test section and the gas±liquid ¯ow becomes cocurrent for a few seconds.The liquid ¯ow tends to oscillate between co-and countercurrent regimes.This type of ¯ooding will occur in a small number of channels.The instability of the liquid ®lm tends to spread to other channels and then to every channel of the test section particularly when the gas ¯ow rate increases.So, we consider the test section to be ¯ooded when the liquid ¯ow oscillates in a sucient number of channels (20% of the test section is ¯ooded).
To summarise, ¯ooding occurs near the injection point for high ¯ow rates whereas it occurs at the lower part of the test section for lower ¯ow rates.The ¯ooding limit in plain ®n geometry is considered to be at the point where the ¯ow goes upward in at least three channels (5±100 l/h), or when liquid is removed above the liquid injection system (100±300 l/h).The ¯ooding point characteristics cover a large range of air ¯ow rates.As a consequence, the ¯ooding limit reached is assumed to be when no return to a non-¯ooded state is possible.Fig. 8 is a schematic view of the ¯ow patterns and ¯ooding occurring in the two liquid ¯ow rate ranges.Dukler and Smith (1977) report ®ve ¯ooding mechanisms depending on liquid ¯ow rates and ¯ow patterns and two of them are observed in the present study.For a thin ®lm thickness, at a given gas velocity, the liquid ®lm is hanging on and the transition leads to cocurrent liquid ¯ow.This phenomenon is called a `hanging ®lm', which is similar to the two above-described liquid ¯ow rates.Droplets are extracted from the liquid ®lm, which becomes agitated near the injection zone.This is a consequence of the ¯ow pattern (churn ¯ow) predominating for high ¯ow rates.

Flooding velocities
Wallis (1961) de®nes the following dimensionless super®cial velocities, where J i is the super®cial velocity of the ith phase given by: J i _ M i =q i S, _ M i is the corresponding mass ¯ow rate, S the channel cross-section area and l the characteristic length.In this study, the latter is assumed to be the hydraulic diameter.q G is determined at the entrance of the test section.Note that J Ã G and J Ã L are analogous to Froude numbers and represent the ratio of inertial and gravitational forces.
The ¯ooding velocities are often correlated in terms of the dimensionless super®cial velocities J Ã1=2 G and J Ã1=2 L and the experimental data are plotted in this way, Fig. 9.The ¯ooding points tend to spread out over a relatively large range of the dimensionless super®cial air velocity (DJ Ã1=2 G 0:1) for a de-®ned liquid ¯ow rate (J Ã1=2 L 0:3).This is a consequence of the dierent measurement procedures (increasing or decreasing the air ¯ow rate) and of the de®nition of the ¯ooding limit (number of ¯ooded channels).Mishima and Nishihara (1984) and Osakabe and Kawasaki (1989) measured the ¯ooding velocities in rectangular channels.Here, we brie¯y review their data for narrow rectangular channels.These types of studies have been carried out for nuclear research.Mishima and Nishihara (1984) used three dierent single channels with dimensions 5 Â 40; 2:4 Â 40 and 1:5 Â 40 mm 2 .The channel height was 470 mm.The results and the corresponding correlations are reported in Figs.11 and 12.The top of the test section has a sharp-edged ¯ange, which is connected to the upper plenum and serves as a water reservoir.Air is introduced by an entrance region, which is 130 mm long, and a tapered rectangular duct is connected to the bottom of the test section.The test procedure is to ®x a gas ¯ow rate and to increase the liquid ¯ow rate until ¯ooding occurs.In this study, ¯ooding is determined by visual observations.It is controlled by the growth of large disturbance waves at the top of the test section.Roll waves grow until their crest touches that on the opposite side of channel and forms a liquid bridge.Flooding occurs only at the top of the test section.Osakabe and Kawasaki (1989) tested simultaneously three rectangular channels with a cross-section of 10 Â 100; 5 Â 100 and 2 Â 100 mm 2 .Air was supplied to the test section from a lower plenum and discharged through a separator.Water was supplied to an upper plenum and collected at the lower one through the test section.Flooding is determined by measuring the downward water ¯ow rate, but it is not clearly expressed.The data are indicated by stars in Fig. 10.The ¯ooding tendency decreases in the present experimental data indicating that decreasing the number of channels is favourable to the onset of ¯ooding.
Furthermore, the present range of liquid ¯ow rates is larger than in previous investigations cited in the literature since a liquid super®cial velocity 0.9 is reached.This is very important since the in¯uence of the liquid ¯ow rate cannot be neglected, especially in narrow channels.

Comparison with correlations proposed in literature
To compare the experimental data with existing correlations, it is wise to recall that empirical relations are usually established in particular experimental con®gurations.Flooding correlations are simple expressions of entire experimental data sets obtained in speci®c conditions.Considering the several ¯ooding mechanisms observed, the eect of physical ¯uid properties, like dynamic viscosity and surface tension and experimental conditions a ¯ooding correlation can be used only within its range of validity.
Essentially two types of ¯ooding correlations have been used throughout the literature.One group correlates the dimensionless gas and liquid velocity under ¯ooding conditions and the other represents the ratio of the gas inertial forces and forces due to gravity acting on capillary waves.The ®rst one, e.g., Wallis (1961), gives the ¯ooding conditions prediction by with m in the range from 0.8 to 1.0 and C in the range from 0.7 to 1.0, the latter is given by the Kutateladze number and reads with r= q L À q G g 1=2 the characteristic length of the capillary wave.The Kutateladze number can be expressed using the dimensionless super®cial velocity and the Bond number This study deals either with correlations including physical properties as dynamic viscosity and surface tension or with correlations established for rectangular channels.We select and compute the correlations ( 7) and ( 12) for the present data.
The ®ve following correlations (7)±( 10) are either the more accurate for the present study, i.e., the nearest to the range of validity or the more used in the process industry to predict ¯ooding in re¯ux condensers or the more used to predict ¯ooding in rectangular channels.
For rectangular channels Wallis (1961) proposed m 1 and C 0:725 for Eq. ( 4) Ku G 0:286Bo 0:26 Fr À0:22 1 l L 10 À3 À0:18 : 10 The authors analyse a compilation of a data bank containing 2762 experimental ¯ooding points.As a result, a modi®ed form of the correlation presented by Alekseev et al. (1972) is recommended for the most accurate prediction of ¯ooding conditions.Fr is the speci®c Froude number as de®ned by Mc Quillan and Whalley (1985): In the process industry, correlation (12) below is used to predict ¯ooding in re¯ux condensers particularly in re¯ux condensers with tapered tubes, English et al. (1963) J G 0:286 D 0:322 h q 0:419 L r 0:097 q 0:462 l 0:15 L J 0:075 However, the Wallis correlation with m 1 and C 0:725, L 0:725, seems to be a good approximation for low ¯ow rates (Fig. 11).This result emphasises that gravity forces are far more important than viscous forces in this range.Dierently, the English modi®ed correlation, which underlines viscous forces and super®cial tension, is more convenient for high ¯ow rates.Moreover, the ¯ow patterns in plain ®n channels are not the same in all the channels because they depend on the ¯ow rate studied as we have seen in Section 3.3.Two types of ¯ooding were observed and the results expressing ¯ooding limit in Fig. 11 showed two slopes, so one relationship cannot correlate all the data.The two correlations ( 7) and ( 12) modi®ed seem to approximate the present data well.Each correlation corresponds to a speci®c range of ¯ow rate, the Wallis correlation correlates the data for low ¯ow rates, whereas the modi®ed English correlation is well adapted for higher liquid ¯ow rates.

Flooding characteristics
The usage of re¯ux condensers with perforated ®ns is common in the process industry nowadays, because it is supposed that they are more ecient in terms of heat transfer.Otherwise, the eciency in terms of ¯ooding has not yet been a subject of study to the authors' knowledge.The procedure to obtain the ¯ooding point is dierent compared to the nonperforated ®ns.If this procedure has been used to increase the air volume ¯ow rate at ®xed liquid volume ¯ow rate the following events were observed: • no discontinuity in pressure drop, even if the air ¯ow rate is increased to the highest value, • small oscillations and instability of the liquid ¯ow but no transition to upward ¯ow, • no liquid removal or ¯ooding point is observed.The liquid ¯ow rate is ®xed at its lowest value of 10 l/h and the air ¯ow rate is directly increased to its maximum value of 10 m 3 =h.The test section is fully ¯ooded in this situation.At this time, the air ¯ow rate is decreased until the ¯ooding limit is reached; this is the procedure to characterise ¯ow reversal so the reversibility of the phenomenon is uncertain.When the air volume ¯ow rate decreases, three con®gurations are observed (Fig. 12).
The ®rst type occurs when the air volume ¯ow rate is decreased to the lowest value corresponding to the ¯ooding limit.The ¯ooding is partial, one third of the test section height is ¯ooded, and according to the air volume ¯ow rate, a few channels are ¯ooded (situation (a)).The second type occurs when gas volume ¯ow rate is increased from the former value.All the height of the test section is ¯ooded, but only in some channels (situation (b)).The last type corresponds to a fully ¯ooded test section since all the channels are ¯ooded and the liquid is removed at the top of the test section (situation (c)).
Whereas the ®rst type visually seems to be the onset of ¯ooding, we do not assume this point to be the proper limit.Pressure drop measurements showed no discontinuity at this point.Moreover, if one waits a moment, this ¯ow con®guration returns to a typical countercurrent ¯ow.The third type seems to occur after the ¯ooding limit since the liquid is removed in the whole test section.In the second type, some channels are ¯ooded and the pressure drop measurements have a discontinuity at this point.So, the second pattern is assumed to be the de®nition of ¯ooding in perforated ®ns.

Comparison of the two types of ®ns
Fig. 13 shows the super®cial velocities at the ¯ooding point for plain and perforated ®ns.Various types of ¯ooding are represented, particularly the three types presented in the last section.
In the second type of ¯ooding (situation (b) in Fig. 12) the whole plate is not ¯ooded.In the perforated plate, when liquid is removed at the top, liquid tends to go through the perforations.Liquid ¯ows down again in some channels since the liquid is not removed enough by the constant gas volume ¯ow rate.So, this modi®cation in liquid ¯ow distribution has changed the ¯ow patterns and particularly the liquid ¯ow rates in all the channels.Some channels have lower liquid volume ¯ow rates than others at constant gas volume ¯ow rate.This eect can explain the earlier onset of ¯ooding in these channels.So, ¯ooding occurrence in perforated ®ns is caused by dierences in ¯ow distribution in the channels due to lateral perforations.
It seems that the plain ®ns have a better eciency than the perforated ®ns in terms of ¯ooding.However, one can only partially conclude like this since the de®nitions of the ¯ooding point are dierent in these two types of geometry.Also the procedure to get ¯ooding is dierent.

Conclusion
The present study aims to analyse ¯ooding limit in order to design a compact re¯ux condenser with a special type of ®nning de®ning narrow rectangular channels.Flooding behaviour is studied and the relation between ¯ow patterns and ¯ooding arising is considered.Experimental data are compared with previous results of the literature and with empirical correlations.
Visualisation shows that two or three types of ¯ow patterns predominate in the two ranges of ¯ow rate studied, ®lm ¯ow, plug ¯ow and churn ¯ow.So, ¯ooding limit occurs dierently according to this range of ¯ow rates.More precisely, the present study shows two types of ¯ooding depending on the two ranges of ¯ow rates, 10±100 and 100±300 l/h.The ®rst ¯ooding type is characterised by ¯owing up and down of the liquid and the second type presents entrainment of liquid droplets near the liquid injection point.In terms of super®cial velocities, the Wallis relationship, Eq. ( 1), with m 1 and C 0:725, correlates well (2±13%) with the results for low ¯ow rates.
Perforated ®ns are studied in the same way to estimate ¯ooding occurrence in such a geometry often used in the process industry.As ¯ooding occurs dierently in perforated ®ns, the procedure to get the ¯ooding limit is dierent and perforated ®ns appear to be less ecient in terms of ¯ooding.
The present study tries to determine the ¯ooding limit in a real industrial geometry.Moreover a single channel study is necessary in order to de®ne precisely the ¯ow patterns and transitions in a narrow rectangular channel and to compare with other studies in rectangular channel.A theoretical study will be undertaken to obtain a better understanding of the physical phenomena.Physical properties' in¯uence on viscosity or surface tension has to be studied too.
With the results obtained in adiabatic contercurrent air± water ¯ow, some conclusions for re¯ux condensation emerge.The present results focus on two particular types of ¯ooding phenomena: the ®rst linked to plugging instability and the second linked to reentrainment.The two types of ¯ooding depend on ¯ow con®gurations, gas and liquid ¯ow rates.So, we can conclude that ¯ooding at the column base for low condensate ¯ow rate and ¯ooding at the top for high condensation rate will appear in a re¯ux condenser with similar dimensions.With this assumption, we can design the re¯ux condenser in terms of dimensions and ¯ow rates.

Fig. 12 .
Fig. 11.Comparison of the present study with correlations.