Boiling Hot Issues—Some Resolved and Some Not-Yet-Resolved

0263±8762/98/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 76, Part A, February 1998

BOILING HOT ISSUESÐ SOME RESOLVED AND SOME NOT-YET-RESOLVED V. V. WADEKAR Heat Transfer and Fluid Flow Service (HTFS), AEA Technology plc, Harwell, Oxfordshire, UK

T

he paper presents an overview of ¯ ow boiling heat transfer in terms of various key issues, some of which have been resolved satisfactorily in the recent years and others are still waiting. Topics of ¯ ow boiling mechanisms, similarity between the convective component of ¯ ow boiling and condensation heat transfer, two-phase ¯ ow patterns and the onset of boiling are covered. Additionally, the industrially relevant topics of boiling in narrow channels of compact exchangers and boiling of multicomponent ¯ uids are also discussed. In the general context of not-yet resolved issues, areas where the current level of information is insuf® cient and new research efforts are warranted are also highlighted. Keywords: ¯ ow boiling; mechanisms; mixture effects; ¯ ow patterns

INTRODUCTION

transfer mechanisms and their interaction with each other is a single tube; vertical orientation being preferable than horizontal because it avoids the ¯ ow strati® cation effects. A number of systematic experimental studies have been carried out which report the data on boiling of single component ¯ uids in a vertical tube, for example, Kenning and Cooper1 and Robertson and Wadekar 2 . These studies con® rm the existence of two main regions of heat transfer, originally proposed by Chen3 . First is the two-phase convective heat transfer region, where the measured ¯ ow boiling coef® cient is independent of heat ¯ ux or wall superheat, increasing with mass ¯ ux and vapour quality, and decreasing with increasing pressure. Second is the nucleate boiling region where the measured heat transfer coef® cient increases with rising heat ¯ ux and pressure and is independent of mass ¯ ux and vapour quality. The two heat transfer mechanisms corresponding to these two main regions can combine and interact with each other resulting in a mixed heat transfer region.

An ever-increasing number of research papers published in boiling heat transfer, covering both fundamental as well as applied aspects, re¯ ect the growing interest as well as the advances being made in this area. In addition to this openly published research work, organizations such as HTFS conduct their own applied research, part of which is occasionally published in open literature. Whether openly published or not, the research is generally aimed at resolving some of the important fundamental and applied issues in ¯ ow boiling heat transfer. This paper attempts to provide an overview which covers the current progress in either fully or partially resolving various issues in ¯ ow boiling. The overview is presented with a backdrop of an industrial perspective. Many important issues in ¯ ow boiling arise from the mechanistic considerations. Better understanding of the mechanisms gives rise to the possibility of improved, less conservative design methods for industrial equipment. However, the inherent complexity of the mechanisms make them dif® cult to experiment with and understand. Besides identifying and understanding them, there are many questions regarding the mechanisms, such as how these mechanisms interact with each other and how they are in¯ uenced by the presence of more than one component and how they are in¯ uenced by the channel geometry and twophase vapour-liquid ¯ ow patterns. Several sections are devoted to addressing these questions. The increasing use of compact heat exchangers for twophase applications makes the issue of boiling in narrow passages very important. Therefore this topic is also discussed in some detail. Two other topics of industrial importance which are covered in this paper include the onset of boiling and the boiling of multicomponent mixtures.

Two-Phase Convective Heat Transfer Region In this region evaporation occurs at the vapour-liquid interface in the bulk ¯ ow away from the wall, so that heat must be convected across an intervening layer of superheated liquid. The normal vapour bubble activities of nucleation, bubble growth and bubble departure associated with nucleate boiling are unlikely to have any signi® cant role in transferring heat in this region. In ¯ ow boiling this is the region where the measured heat transfer data are relatively easy to analyse, interpret and correlate. There are several reasons for this but the main reason is that, unlike in the nucleate boiling region, the experimental results tend to be more reproducible here. Better reproducibility is due to little or no in¯ uence of the heating surface characteristics on the two-phase convective heat transfer. Kenning and Cooper1 state that in the convective region their data were reproducible within 6 2% while in the nucleate boiling region the range of reproducibility was worse at 6 10%.

HEAT TRANSFER MECHA NISMS IN FLOW BOILING The simplest geometry for studying the ¯ ow boiling heat 133

134

WADEKAR

Figure 2. Comparison of ¯ ow boiling data in nucleate boiling dominated region with the Stephan and Abdelsalam correlation for pool nucleate boiling9 . Figure 1. Separating measured ¯ ow boiling data into the convective heat transfer region and nucleate boiling region (Data to the left of line AA are in the convective region).

The large body of research that exists in ¯ ow boiling heat transfer indicates that the best way of dealing with this region is to express the ¯ ow boiling coef® cient as a product of the two-phase enhancement factor and the liquid phase heat transfer coef® cient. Whether the liquid coef® cient used is for the liquid fraction3,4 or for the total ¯ ow as liquid5 is a matter of convenience. Both correlation schemes tend to work equally well. Figure 1 shows how the data corresponding to the convective heat transfer region could be separated from the measured data in order to derive a correlation for the two-phase enhancement factor. There are some important implications of better reproducibility and, therefore, of better predictability of ¯ ow boiling heat transfer in the convective region for industrial practice. Firstly, the performance of all types of industrial reboilers and vaporizers can be better predicted if they operate in this region and therefore they can be designed in a less conservative manner. The second implication pertains to the advantage of compact heat exchangers over their not-so-compact counterparts. Due to their high thermal effectiveness, compact exchangers generally tend to operate with a close temperature approach, resulting into boiling at low wall superheat. Therefore, as a default, they will operate in the convective region. Thus compact heat exchangers may offer this added advantage over other not-so-compact exchangers when used for boiling duties. Nucleate Boiling Heat Transfer Region The vapour bubble activities of nucleation, bubble growth and bubble departure associated with pool nucleate boiling are responsible for transferring heat here. The key question in this region is to what extent nucleate boiling under ¯ ow conditions is similar to pool nucleate boiling. Theories range from the well-known Chen’ s hypothesis3 of suppression of nucleate boiling due to ¯ ow to Mesler’ s hypothesis of enhancement of nucleation (for example, Mesler and Mailen6 ) when nucleate boiling occurs in thin liquid ® lms. As thin liquid ® lms can be created by two phase annular ¯ ow, Mesler’ s hypothesis is equivalent to the enhancement

of nucleate boiling due to ¯ ow. More discussion on Mesler’ s hypothesis is given in the next section. No direct experimental evidence from ¯ ow boiling studies has yet been reported which could support Mesler’ s hypothesis of the enhanced form of nucleate boiling. Aounallah and Kenning7 have reported that Chen’ s suppression factor for nucleate boiling could be excessive. There is some evidence to suggest that in the limit of high wall superheat ¯ ow boiling heat transfer approaches pool nucleate boiling heat transfer. For example, Figure 2 shows a good agreement between the Stephan and Abdelsalam8 correlation for nucleate pool boiling and the measured ¯ ow boiling data of Wadekar9 . The use of the nucleate pool boiling coef® cient in the correlation by Steiner and Taborek5 is also based on the assumption that ¯ ow nucleate boiling approaches the limit of pool nucleate boiling at high heat ¯ ux. Interaction of Heat Transfer Mechanisms The question of how the two mechanisms of ¯ ow boiling heat transfer interact with each other becomes much more important in the mixed region where both the convective and nucleate boiling heat transfer mechanisms are present. It appears that the asymptotic model expressed mathematically by equation (1) provides the most practical answer. a

T

= (a + a n c

n 1/ n nb

)

(1)

Steiner and Taborek have used equation (1) in their recent correlation. For a value of n between 3 to 4, equation (1) gives a good prediction of data as long as correct correlations are chosen for the convective and nucleate boiling coef® cients, a c and a n b , respectively. This approach does not provide an insight into the underlying physics of the interaction but addresses the practical need of correlating the data. Wadekar4 demonstrated that it is possible to correlate ¯ ow boiling data using a non-conventional concept of the suppression of the convective rather than the nucleate boiling component. It was argued that the heating surface area over which nucleate boiling is active is not available for the convective heat transfer to act upon. The general success of equation (1) in correlating ¯ ow boiling data also suggests that suppression of both the nucleate boiling component as Trans IChemE, Vol 76, Part A, February 1998

BOILING HOT ISSUES Ð SOME RESOLVED AND SOME NOT-YET-RESOLVED

Figure 3. Typical graph of the measured heat transfer coef® cient against vapour quality for boiling and condensation duties (Sun and Hewitt 11 ).

well as the convective component should occur at either extremes of wall superheat or heat ¯ ux. BOILING AND CONDENSATION As discussed in the previous section, measured boiling data can be separated into the convective and nucleate boiling dominated regions. A fundamental issue regarding ¯ ow boiling has been about the nature of the heat transfer mechanism in the convective region. The conventional view has been that in this region the vapour bubble-related mechanisms, which drive nucleate boiling heat transfer are not present. According to Mesler’ s hypothesis, however, a special form of boiling may occur in the apparently convective region because of the presence of thin liquid ® lms. He argued that a vapour bubble bursting from a thin liquid ® lm generates very small droplets some of which can strike the vapour-liquid interface entraining a small amount of vapour. The tiny vapour bubbles thus generated, serve as effective nucleation centres for subsequent bubble growth. Mesler referred to this as the secondary nucleation to distinguish it from wall nucleation, and claimed that this provides a very ef® cient mode of heat transfer requiring very low wall superheats. The linearity between the measured `convective’ heat transfer coef® cient and the applied heat ¯ ux alone is not suf® cient to disprove the theory of secondary nucleation because the secondary nucleation may also show the same behaviour. As secondary nucleation is expected to play very little or no role in condensation heat transfer, an effective method of resolving the issue of secondary nucleation is to compare ¯ ow boiling and condensation heat transfer under identical thermal hydraulic conditions. If the boiling heat transfer coef® cient in the absence of conventional nucleate boiling is higher than the condensation coef® cient, then secondary nucleation is present, and is making a contribution to boiling heat transfer. If, on the other hand, boiling and condensation heat transfer coef® cients are nearly identical, then the secondary nucleation is not playing any role in boiling heat transfer. With the above logic, Hewitt and his co-workers10,11 set out to compare boiling and condensation heat transfer under similar thermalhydraulic conditions. By installing an adiabatic calming zone between the prevaporizer and the test-section, they made sure that the effect of hydrodynamic Trans IChemE, Vol 76, Part A, February 1998

135

non-equilibrium on the two-phase ¯ ow in the test-section was minimal. Chan10 conducted his experiments in a double pipe heat exchanger with up-¯ ow of a steam-water mixture in the central 9.5 mm diameter tube, and heating or cooling ¯ uid ¯ owing downwards in the annular space. He used glycerol as a heating medium for boiling experiments and water as a cooling medium for condensation experiments. Chan’ s experiments indicated that the boiling heat transfer coef® cients were up to 80% higher than the condensation coef® cients. In view of the experimental dif® culties of measuring small differences in the bulk ¯ uid temperatures of heating or cooling ¯ uids to provide the local heat ¯ ux, Hewitt and his co-workers decided to repeat the experiments using only water as a heating or cooling medium. Some other changes were made to the experimental apparatus to improve the distribution of the heating/cooling water in the annular space. The improved second set of experiments reported by Sun and Hewitt11 show that essentially there is no difference between boiling and condensation cases, disproving the hypothesis of secondary nucleation. Figure 3 shows a graph of the measured heat transfer coef® cient against vapour quality for boiling and condensation duties. It can be seen from this graph that the coef® cients for both the duties are nearly identical. To a large extent, the issue of secondary nucleation thus appears to be resolved. There are other pieces of work which however point to differences between condensation and boiling heat transfer. Cornwell et al.12 studied boiling and condensation heat transfer in a test-section simulating shellside geometry of a shell and tube exchanger. They observed that the boiling coef® cients in the absence of nucleate boiling were up to two times higher than the corresponding condensation coef® cients under similar thermalhydraulic conditions. Cornwell et al. hypothesized that the heat transfer coef® cient associated with the thin liquid ® lm underneath a vapour bubble sliding along the tube circumference, is likely to be higher for evaporation due to the thinning of the liquid ® lm by evaporation. Wadekar and Kenning13 have theoretically investigated possible differences in boiling and condensation heat transfer. They hypothesized that vapour bubbles attached to the wall may act as heat pipes between the wall and the turbulent core of the saturated liquid, bypassing the thermal resistance of the laminar sublayer. With this mechanism they concluded that the boiling coef® cient in the absence of nucleate boiling could be 10 to 15% higher than the corresponding condensation coef® cient. Further experimental evidence with different ¯ uids and different geometries is thus required to con® rm the conclusion of Sun and Hewitt 11 . FLOW BOILING AND TWO PHASE FLOW PATTERNS In theory all the main two phase ¯ ow patterns such as bubble ¯ ow, slug ¯ ow, churn ¯ ow and annular ¯ ow occurring from zero vapour quality up to dryout are likely to exhibit different ¯ ow boiling heat transfer characteristics. However, practically all correlations (3±5) that exist correlate ¯ ow boiling data using a single equation covering all the different ¯ ow patterns. Some correlations such as those by Shah14 and Kandlikar15 , contain multiple equations,

136

WADEKAR

Figure 5 A graph of heat transfer coef® cient against vapour quality showing measured and predicted data for top and bottom positions in a horizontal test-section 19 . Figure 4. A graph of the ratio of two-phase convective heat transfer coef® cient to the single phase heat transfer coef® cient against the reciprocal of the Martinelli parameter 16 .

but these are used to cover nucleate boiling and convective heat transfer regions rather than different ¯ ow patterns. It is generally recognized that a more accurate prediction of ¯ ow boiling can be obtained by adopting a ¯ ow pattern speci® c method for each individual ¯ ow regime. However, progress has been slow in this area. Various important issues as well as the reasons for the slow progress in this area are described here. Flow Patterns and Axial Thermal Measurements Flow boiling experiments, involving local measurements of wall temperatures and bulk ¯ uid temperatures along the length of a test-section, can provide detailed information on the axial variation of the local heat transfer coef® cient. Such information should be useful in identifying the effect of different ¯ ow patterns on ¯ ow boiling heat transfer. However, the relative magnitudes of the convective heat transfer and nucleate boiling can change as vapour quality changes along the length of a test-section, thereby swamping any effect arising from the changes in the local ¯ ow pattern. This may be a reason for the relative lack of experimental data in this area. Interference of nucleate boiling heat transfer with the thermal characteristics of an individual ¯ ow regime can be avoided if the data could be selected from purely convective region. Such data are available from the work of Kenning and Cooper1 and some of these data do show the effect of the local ¯ ow patterns. While analysing these data, Wadekar and Kenning16 made the following observations: (i) the thermal measurements obtained from a 14.4 mm diameter tube show two distinct regions of heat transfer characteristics (ii) the differences in these characteristics can be related to a broad classi® cation of ¯ ow patterns into only two categories, namely, intermittent two-phase ¯ ow and non-intermittent two-phase ¯ ow. Wadekar and Kenning included slug and churn ¯ ow into the intermittent category and annular ¯ ow into the non-intermittent category. They showed that it was possible to predict the boiling data in the intermittent region by a slug ¯ ow heat transfer model. Later, Wadekar17 extended the work to include the effect of nucleate boiling on slug ¯ ow heat transfer. Figure 4 obtained from reference16 shows a graph of the

ratio of two-phase convective heat transfer coef® cient to the single phase heat transfer coef® cient against the reciprocal of the Martinelli parameter. The measured data, which are free from nucleate boiling, are shown by various symbols corresponding to different mass ¯ uxes. The dashed line is the best ® t curve for the annular ¯ ow data of Kenning and Cooper1 and is not too different from the convective part of the Chen correlation3 . Various solid lines correspond to the prediction of the slug ¯ ow model at different mass ¯ uxes. It can be seen that at least at low mass ¯ uxes the trends in the data are closer to the slug ¯ ow model rather than the best ® t curve for the annular ¯ ow data. The measured data shown in Figure 4 satis® ed the following simple criterion, which separates the slug/churn ¯ ow data from the annular ¯ ow data, Çmx j *G = (2) 05 < 1 gDq g (q 1 - q g ) . Kenning and Cooper1 also reported data from a 9.6 mm internal diameter tube. However, those data, which satisfy the above criterion for slug/churn ¯ ow, exhibit the trends of annular ¯ ow. The reason for this behaviour is unclear and it constitutes another issue yet to be resolved. Jung18 has reported very detailed local thermal measurements for a horizontal test-section using refrigerant ¯ uids. At a given measurement station, he measured wall temperatures at the top, bottom and middle positions of the tube. But in his analysis he used only the average wall temperatures based on these detailed measurements. Sun et al.19 showed that it is possible to relate Jung’ s detailed measurements to a slug ¯ ow pattern prevailing at lower vapour qualities. Figure 5 obtained from Sun et al.19 shows a graph of the heat transfer coef® cient against the vapour quality showing measured and predicted data for top and bottom positions in the horizontal test-section. The prediction method uses a slug ¯ ow model for a horizontal tube. It can be seen that the model is reasonably successful in predicting the observed trends. ONSET OF BOILING In a heated channel, the onset of boiling marks a boundary between the single phase and two-phase ¯ ow regions. As these two regions have markedly different thermal hydraulic characteristics, the understanding and Trans IChemE, Vol 76, Part A, February 1998

BOILING HOT ISSUES Ð SOME RESOLVED AND SOME NOT-YET-RESOLVED

137

Figures 7. (a) Onset of boiling with superheated bulk liquid for a constant wall temperature boundary condition25 . (b) Onset of boiling with subcooled bulk liquid for a constant wall temperature boundary condition25 .

Figure 6. Axial temperature pro® les for the onset of boiling with (a) superheated bulk liquid (b) subcooled bulk liquid22 .

prediction of boiling onset is important to the design and operation of vaporizing equipment. Sato and Matsumura20 proposed the following equation for predicting the wall superheat at the onset of boiling. 8r Tsat qÇ 1/ 2 (3) k l q v D hv Davis and Anderson21 extended this work to non-circular vapour bubble shapes. To date equation (3) still remains the most commonly used expression in the open literature, although it is recognized that it tends to predict very low wall superheats for initiation of boiling. Wadekar22 demonstrated that for organic ¯ uids the onset of boiling can occur under superheated, saturated or

D Tsat,onset

=

Trans IChemE, Vol 76, Part A, February 1998

subcooled bulk liquid conditions, depending upon the chosen thermalhydraulic conditions. This work reconciles the standard picture of onset of boiling occurring under subcooled bulk ¯ uid conditions in the textbooks (for example, Collier and Thome23 ) and the observation by Robertson and the co-workers (for example Clarke and Robertson24 ) that they have always found that the onset in plate-® n test-section occurs under superheated bulk liquid conditions. For the tube test-section under investigation, it was reported that the conditions of high mass ¯ ux, low inlet subcooling and low heat ¯ ux tend to result in a boiling onset where bulk ¯ uid was superheated; conditions of low mass ¯ ux, high inlet subcooling and high heat ¯ ux favoured a subcooled onset22 . The most likely reason for the observations of Robertson and co-workers could be the low heat ¯ ux and low inlet subcooling conditions employed by them to simulate typical operating conditions of industrial plate® n reboilers. Figure 6 from reference22 shows typical temperature pro® les for the onset of boiling under superheated and subcooled bulk liquid conditions. In both cases a wall superheat of over 20 K was required to initiate the boiling; a value considerably higher than that predicted by equation (3). Practically all the reported work on the onset of boiling is using heat ¯ ux controlled experiments. To the author’ s knowledge, the only reported work close to a constant wall temperature boundary condition is by Clarke and Robertson24 . In a plate-® n geometry, they heated the boiling liquid nitrogen stream in the central passage with a nitrogen stream, condensing at a higher pressure in two adjacent passages. The condensing stream was at a nearly constant condensing temperature. Figures 7a and 7b show possible temperature pro® les that can be obtained for a constant wall temperature boundary

138

WADEKAR

Figure 8. Convective and nucleate boiling regions for ¯ ow boiling of R114 in a plain plate-® n passage 29 . Figure 9. Flow regimes in narrow channels30 . 25

condition . In both ® gures letter `A’ marks the position of the onset. Clark and Robertson24 observed the temperature pro® les similar to that shown in Figure 7a, when the onset of boiling occurs under a superheated bulk liquid condition. Figure 7b, on the other hand, is a speculative diagram showing what the temperature pro® les would be like, if the onset were to occur under a subcooled bulk liquid condition. In spite of the work done by a number of researchers, an accurate prediction of the onset of boiling remains elusive. One of the primary reasons for the lack of progress in this area is that the wall superheat at onset is very sensitive to the pressure and temperature history of the boiling surface22 . BOILING IN COMPACT PASSAGES Compact heat exchangers have established themselves as cost effective alternatives to shell and tube heat exchangers for single phase applications up to moderately high temperatures and pressures. Now they are receiving increasing attention for two-phase applications including boiling duties. Compact heat exchangers tend to use narrow, non-circular and often tortuous ¯ ow passages. In order to understand boiling in these passages, it is important to understand different issues related to boiling in small circular passages and non-circular passages such as rectangular channels. Small Circular Passages This is an area where the present state of our understanding of boiling phenomena is far from complete. Even the effect of tube diameter on the boiling phenomena remains unclear because of the lack of systematic studies. Lazarek and Black26 and Wambsganss and co-workers27,28 have carried out studies on tubes with diameters of 3.1 and 2.46 mm, respectively with various refrigerants. Their studies show that for these smaller diameter tubes the ¯ ow boiling coef® cients are higher than those predicted by the standard correlations developed for larger diameter tubes. Generally, nucleate boiling heat transfer was found to prevail down to small values of wall superheats. Small Non-Circular Passages As mentioned earlier, most of the compact heat exchangers contain non-circular ¯ ow passages, some more complex than others. The simplest and most commonly

encountered non-circular geometry is a rectangular passage in plate-® n exchangers. In a rectangular passage, the liquid ® lm will tend to be thicker in the corners, leaving it thinner on the side walls. Therefore the rectangular passages are likely to have different boiling characteristics than the circular passages of the same hydraulic radius. Until recently the information in the open literature suggested domination of either the convective or the nucleate boiling heat transfer mechanism for the rectangular passages. It has now been demonstrated that under the appropriate conditions both regimes of heat transfer can be realized with these passages (for example, Tran et al.28 ). Figure 8 shows both convective and nucleate boiling regions for ¯ ow boiling of R114 in a plain plate-® n passage29 . Cornwell et al.’ s approach30 of dividing boiling in narrow passages into three regions, namely, isolated bubble, con® ned bubble and annular-slug ¯ ow regions appears very promising (see Figure 9). Although some validation of this approach is presented by these workers, further validation against more experimental data covering a wider variation of parameters is required. MULTICOMPONENT FLUIDS As the most extensively used vapour generating equipment in the process industry is a reboiler attached to a distillation column, boiling of multicomponent ¯ uids is a norm rather than an exception in the process industry. More recently multicomponent boiling has become important to refrigeration industry too. This is because new ozone friendly refrigerants are used in refrigeration cycles as mixtures rather than single component ¯ uids. It is well known that the ¯ ow boiling heat transfer coef® cient is generally less for mixtures than for the individual components. These mixture effects essentially arise from the composition differences between the bulk liquid phase and the vapour-liquid interface. An increasing amount of evidence suggests that even if the nucleate boiling coef® cient is signi® cantly reduced, there is very little or no reduction in the two-phase convective coef® cient31,32 . This is in sharp contrast to falling ® lm evaporation where a signi® cant reduction in the heat transfer coef® cient is observed even for the convective region33 . The issue of this difference between falling ® lm evaporation and ¯ ow boiling needs to be resolved. The following is a possible explanation. Trans IChemE, Vol 76, Part A, February 1998

BOILING HOT ISSUES Ð SOME RESOLVED AND SOME NOT-YET-RESOLVED

139

Figure 10. Comparison of correlations for gas-liquid and vapour-liquid heat transfer.

In falling ® lm evaporation the liquid and vapour phase velocities are relatively low and the vapour-liquid interface is also relatively quiescent. In contrast with this, in ¯ ow boiling where the convective heat transfer region prevails, the vapour quality and therefore vapour velocity tend to be high. A high vapour velocity increases the liquid velocity and also the interfacial area by enhancing the liquid entrainment in the vapour phase and creating disturbance waves along the interface. This increase in the interfacial area can be very signi® cant. Increased interfacial area, coupled with increased interfacial turbulence, can effectively increase the rate of mass transfer; thus minimizing, and in some case even eliminating, the composition differences between the bulk liquid phase and the interface. This in turn can minimize or eliminate the mixture effects. In a very comprehensive review of pool boiling heat transfer to mixtures with boiling on the outside of horizontal tubes, Goren¯ o and Koster34 have raised a number of new and interesting issues about mixture effects. Heat Transfer to Gas-Liquid Two-phase Flow Heat transfer to gas-liquid two-phase ¯ ow may not constitute actual boiling. However, even when there is no boiling involved, the process has some similarities with the convective heat transfer component of ¯ ow boiling. Moreover, the subject area is of direct relevance to the oil and gas industry. Data exist in the literature on heat transfer to gas-liquid ¯ ows, for example Rezkallah and Sims35 ; although most of the available data are with air-water mixtures. Correlations of the following general form are developed by various researchers,

= Fa a

(4)

l

The single phase liquid fraction coef® cient, a l , is obtained from a Dittus-Boelter type equation with a viscosity ratio correction. The two-phase ¯ ow multiplier, F, is expressed as a function of void fraction35 or the ratio of gas and liquid phase super® cial velocities36 or the Lockhart-Martinelli parameter37 . Figure 10 shows a graph comparing two typical correlations for the gas-liquid heat transfer data with the Chen convective component correlation for ¯ ow boiling. The Chen convective component correlation is obtained from the following equation given by Kenning and Cooper1 . F

= 1.8(1/ X ) + 1 tt

0 .87

(5)

The graph of F factor, which is the ratio of two-phase to Trans IChemE, Vol 76, Part A, February 1998

Figures 11. (a, b) Typical comparisons of gas-liquid data with various predictive methods38 .

single phase liquid fraction coef® cient, against the reciprocal of the Lockhart-Martinelli parameter, 1/Xt t , is prepared using the physical properties of air-water mixtures. Two distinct trends can be observed from the graph depending upon the value of 1/Xtt which in turn is related to vapour quality. Firstly, at low values of 1/ Xtt the F factors for gasliquid two-phase ¯ ow are higher than that for the convective component for ¯ ow boiling. Secondly, this trend is reversed at higher values of 1/Xt t . One important difference between heat transfer to gasliquid ¯ ow and vapour-liquid ¯ ow is likely to be responsible for the above mentioned trends. During heat transfer to gasliquid ¯ ow, sensible heat needs to be transferred to the gas phase whereas for vapour-liquid heat transfer (i.e. boiling) sensible heat transfer to vapour phase is not required (for single component ¯ uids). The additional gas phase heat transfer resistance, associated with the sensible heat transfer to the gas phase, tends to reduce the two-phase heat transfer coef® cient based on the measured mixed bulk ¯ uid temperature for gas-liquid ¯ ow, reducing the F factor. The higher values of gas-liquid heat transfer coef® cient, which lead to higher F factors at the lower values of 1/Xt t is likely to be a result of intermittent ¯ ow patterns such as slug ¯ ow, and may be explained on the basis of a ¯ ow pattern speci® c model. Wadekar et al.38 have reported air-water heat transfer data obtained speci® cally in the slug/churn ¯ ow region. Typical comparisons of these data with various predictive methods are shown in Figures 11a and 11b. The comparisons are made using the graphs of heat transfer coef® cient against vapour quality and the F factor against the reciprocal of the Lockhart-Martinelli parameter. In both graphs, the solid curve represents predictions of the convective component of

140

WADEKAR For a salt solution exhibiting an inverse solubility behaviour, i.e. decreasing solubility with increasing temperature, deposition or precipitation of the salt can occur as boiling proceeds. Deterioration in heat transfer rate is to be expected in this case, resulting from the fouling of the heating surface. However, the published studies (for example, Najibi et al.40 ) indicate that even for those solutions, where the salt solubility increases with temperature, there is a noticeable reduction in the boiling heat transfer coef® cient. In a recent study, Wadekar et al.41 argue that at least a part of this reduction is due to the mixture effect similar to that observed for a multicomponent mixture containing miscible liquids. They modi® ed the theory for boiling of mixtures by taking into account the fact that when a salt solution is vaporized, the vapour contains only the solvent. Some typical results from their work are shown in Figures 12a and 12b. GENERAL REMARKS AND SCOPE FOR FURTHER WORK Some general remarks and suggestions for further work are given in the following discussion. It should be noted that these items for discussion are not presented in any particular order.

Figures 12. (a, b) Typical comparison of boiling of salt solutions with predictions41 .

¯ ow boiling heat transfer according to the Chen correlation (equation (5)). It can be seen that the data are underpredicted at lower qualities and overpredicted at higher qualities by the convective component of the Chen correlation. The dashed curves in both graphs show the predictions of the slug ¯ ow model developed by Wadekar and Kenning16 and Wadekar17 . It can be seen, especially from the F factor against 1/Xtt graph, that the trends in the data are probably better represented by the slug ¯ ow model. However, there is a signi® cant amount of overprediction of the data. Finally, the heavy solid lines, marked as the present method in Figures 11a and 11b appear to predict the data reasonably well. These lines are based on the slug ¯ ow predictions corrected for sensible heating of the gas phase. More details of this method are given by Wadekar et al.38 . Flow Boiling of Salt Solutions Evaporative heat transfer to aqueous salt solutions is a common industrial operation in manufacturing a variety of inorganic salts. In order to produce fresh water, desalination plants also need to evaporate sea water, an aqueous salt solution. Subcooled as well as saturated boiling occurs in the evaporators used for transferring heat to salt solutions. The amount of information that exists for salt solutions is very limited. However, due to its practical signi® cance, this hitherto neglected subject area is now gaining increasing attention in the literature. Boiling characteristics of aqueous salt solutions are likely to be different from those of pure water because of the differences in surface tension, wetting characteristics and bubble coalescence behaviour. Fundamental studies related to vapour bubble dynamics in nucleate pool boiling of a salt solution highlight these differences (for example, Jamialahmadi et al.39 ).

1. Non-Newtonian FluidsÐ there is a lot of interest in boiling of non-Newtonian ¯ uids in plate heat exchangers. For example, in the manufacturing of health care products water vapour needs to be removed from non-Newtonian ¯ uids. Plate heat exchangers are often used for these duties. It is desirable to study boiling of these ¯ uids in a simple tubular geometry to provide a base line case for comparison with any subsequent work in the complex channels of plate heat exchangers. 2. Gas-liquid systemsÐ these represent a limiting case of boiling of mixtures where a large portion of the added heat goes into sensible heating of the phases. It will therefore be interesting to see to what extent tube insert devices can enhance the sensible heat transfer to the gas phase, thereby improving the overall two-phase heat transfer for this limiting case of mixture boiling. 3. Salt solutionsÐ when other complicating effects such as inverse solubility, salt deposition etc are absent, salt solutions can provide another limit for the boiling of multicomponent ¯ uids. The reason for this is as follows. As only solvent rather than solute is boiled off, diffusional mass transfer processes only occur in the liquid phase and not in vapour phase. Therefore this provides an ideal opportunity to concentrate on the liquid phase mass transfer. Similar opportunities are also provided by mixtures of two miscible liquids where one of them has a very high boiling point, e.g. ethylene glycol and water mixture. 4. Diameter effectÐ systematic studies are required for effect of tube diameter on in-tube boiling heat transfer. Experiments with smaller diameter tubes tend to generate the data in the convective region because it is easier to obtain high mass ¯ uxes. Also, as the high mass ¯ uxes are obtained at low ¯ ow rates, higher vapour qualities can easily be obtained within a test-section. Conversely, the data obtained from larger diameter tubes tend to fall in the nucleate boiling region. This needs to be taken into account when designing test rigs for tubes with varying diameters. Trans IChemE, Vol 76, Part A, February 1998

BOILING HOT ISSUES Ð SOME RESOLVED AND SOME NOT-YET-RESOLVED 5. Variation of pressureÐ pressure is a key variable in ¯ ow boiling, regardless of the geometry in which boiling occurs. As it affects the convective and nucleate boiling components in exactly opposite manners, it is an important tool in deciphering ¯ ow boiling mechanisms. This has been well proven by studies at HTFS as well as by other researchers such as Goren¯ o et al.42 . CONCLU DING REMARKS Although a number of contentious issues in ¯ ow boiling have been resolved in recent years, many others are still waiting to be resolved. New industrial applications, such as those involving boiling in narrow channels, are creating new sets of issues which also need to be addressed. This combination of not-yet-resolved and new emerging issues together represent fresh challenges to researchers in the ¯ ow boiling area. NOMENCLATUR E D F g m Ç qÇ T x

v

a tt

D T l k q r D hv

channel diameter, m ratio of two phase to single phase transfer coef® cient gravitational acceleration, m/s ±2 mass ¯ ux, kg m ±2 s- 1 heat ¯ ux, W m- 2 temperature, K vapour quality heat transfer coef® cient, W m- 2 K Lockhart-Martinelli parameter = (1 - x/ x)0.9 (q g / q 1 )0.5 (l 1 / l g )0.1 wall superheat, Tw-Tsat (K) viscosity, Pa s thermal conductivity, W m- 1 K- 1 density, kg m ±3 surface tension, N m- 1 latent heat of vaporization, J kg- 1

Subscripts c convective nb nucleate boiling sat saturation T total

REFERENCES 1. Kenning, D. B. R. and Cooper, M. G., 1989, Saturated ¯ ow boiling of water in vertical tubes, Int J Heat Mass Transfer, 32: 445±458. 2. Robertson, J. M. and Wadekar, V. V., 1988, Vertical up¯ ow boiling of ethanol in a 10 mm diameter tube, Proc 2nd UK National Heat Transfer Conference, Glasgow, 1: 67±77. 3. Chen, J. C., 1966, Correlation for boiling heat transfer to saturated liquids in convective ¯ ow, Ind Eng Chem Process Design and Develop, 5: 322±329. 4. Wadekar, V. V., 1995, An alternative model for ¯ ow boiling heat transfer, paper no IV-11, Int Conference on Convective Flow Boiling, Banff, Canada. 5. Steiner, D. and Taborek, J.,1992, Flow boiling heat transfer in vertical tubes correlated by an asymptotic model, Heat Transfer Engineering, 13: 43±69. 6. Mesler, R. and Mailen, G., 1977, Nucleate boiling in thin liquid ® lms, AIChE Journal, 23(6): 954±957. 7. Aounallah, Y. and Kenning, D. B. R., 1987, Nucleate boiling and the Chen correlation for ¯ ow boiling heat transfer, Experimental Heat Transfer, 1(2): 87±92. 8. Stephan, K. and Abdelsalam, M., 1980, Heat transfer correlations for natural convection boiling, Int J Heat Mass Transfer, 23: 73±80. 9. Wadekar, V. V., 1996, A comparative study of in-tube boiling on plain and high ¯ ux coated surfaces, 2nd European Thermal Sciences/14th Italian National Heat Transfer Conference, 1: 195±201. 10. Chan, W. H. G. T., 1990, Evaporation and condensation in annular vertical upward ¯ ow of water-seam, PhD Thesis (Imperial College, University of London).

Trans IChemE, Vol 76, Part A, February 1998

141

11. Sun, G. and Hewitt, G. F., 1996, Experimental studies on heat transfer in annular ¯ ow, 2nd European Thermal Sciences/14th Italian National Heat Transfer Conference, 3: 1345±1351. 12. Cornwell, K., Houston, S. D. and Alddlesee, A. J., 1992, Sliding bubble heat transfer on a tube under heating and cooling conditions, Proc of Engineering Foundation Conference on Pool and External Flow Boiling, Santa Barbara, pp. 48±54. 13. Wadekar, V. V. and Kenning, D. B. R., 1994, Flow boiling: a role for wall-attached vapour bubbles?, Proc of the 10th International Heat Transfer Conference, Brighton, 7: 563±568. 14. Shah, M. M., 1982, Chart correlation for boiling heat transfer: equations and further study, ASHRAE Trans., 88: 185±196. 15. Kandlikar, S. G., 1990, A general correlation for saturated two-phase ¯ ow boiling heat transfer inside horizontal and vertical tubes, J of Heat Transfer, 112(1): 219±228. 16. Wadekar, V. V. and Kenning, D. B. R., 1990, Flow boiling heat transfer in vertical slug and churn ¯ ow region, Proc of 9th International Heat Transfer Conference, Jerusalem, 3: 449±454. 17. Wadekar, V. V., 1991, Vertical slug ¯ ow heat transfer with nucleate boiling, ASME National Heat Transfer Conference, Minneapolis, HTD-Vol. 159, pp. 157±161. 18. Jung, D. S., 1989, Horizontal ¯ ow boiling heat transfer using refrigerant mixtures, EPRI Report No ER-6364. 19. Sun, G., Wadekar, V. V. and Hewitt, G. F., 1994, Heat transfer in horizontal slug ¯ ow, Proc of the 10th International Heat Transfer Conference, Brighton, 6: 271±276. 20. Sato, T., And Matsumura, H., 1964, On the conditions of incipient subcooled boiling with forced convection, Bulletin of JSME, 7(26): 392±398. 21. Davis, E. J. and Anderson, G. H., 1966, The incipience of nucleate boiling in forced convective ¯ ow, AIChE Journal, 12(4): 774±780. 22. Wadekar, V. V., 1993, Onset of boiling in vertical up¯ ow, Heat Transfer - Atlanta 1993, AIChE Symposium Series, 89: 293±299. 23. Collier, J. G. and Thome, J. R., 1994, Convective Boiling and Condensation (Clarendon Press, Oxford). 24. Clarke, R. H. and Robertson, J. M., 1984, AIChE Symposium Series, No 236, 80 (236): 98±103. 25. Wadekar, V. V. and Fox, T. A., 1994, Signi® cance of heat ¯ ux controlled ¯ ow boiling experiments to industrial vaporising equipment, Proc of the 10th International Heat Transfer Conference, Brighton, the industrial sessions papers, pp. 111±116. 26. Lazarek, G. M., and Black, S. H., 1982, Evaporative heat transfer, pressure drop and critical heat ¯ ux in a small vertical tube with R-113, Int J Heat Mass Transfer, 25(7): 945±960. 27. Wambsganss, M. W., France, D. M., Jendrzejczyk, J. A., and Tran, T. N., 1993, Boiling heat transfer in a horizontal small-diameter tube, ASME Journal of Heat Transfer, 115(4): 963±972. 28. Tran, T. N., Wambsganss, M. W. and France, D. M., 1995, Boiling heat transfer with three ¯ uids in small circular and rectangular channels, Argonne National Laboratory Report, ANL-95/9. 29. Feldman, A., Marvillet, C. and LeboucheÂ, M., 1996, Nucleate and convective boiling in plate ® n heat exchangers, submitted to Int J of Heat and Mass Transfer. 30. Cornwell, K. et al., 1995, Compact two-phase heat exchangers, Final CEC Report, Contract no JOU2-CT92-0045. 31. Fujita, Y. and Tsutsui M., 1995, Convective boiling of binary mixtures in a vertical tube, Paper VI-2, Int Conference on Convective Flow Boiling, Banff, Canada. 32. Murata, K. and Hashizume K., 1990, An investigation on forced convection boiling of nonazeotropic refrigerant mixtures, Heat Transfer Jap Res, 19: 95±109. 33. Palen, J. W., Wang Q. and Chen J. C., 1994, Falling ® lm evaporation of binary mixtures, AIChE Journal, 40(2): 207±215. 34. Goren¯ o, D. and Koster, R. 1997, Pool boiling heat transfer from horizontal tubes to mixtures, invited lecture at Convective Flow and Pool Boiling Conference, Irsee, Germany. 35. Rezkallah, K. S. and Sims G. E., 1987, An examination of correlations of mean heat transfer coef® cients in two-phase and two component ¯ ow in vertical tube, AIChE Symposium Series, 83: 109±114. 36. Knott, R. F., Anderson, R. N. Acrivos A. and Peterson, E. E., 1959, An experimental study of heat transfer to nitrogen-gas mixtures, Ind and Eng Chemistry, 51(11): 1369±1372. 37. Serizawa, A., Kataoka, I. and Michiyoshi, I., 1975, Turbulence structure of air-water bubbly ¯ owÐ III. Transport properties, Int J Multiphase Flow, 2: 247±259. 38. Wadekar, V. V., Tuzla, K. and Chen, J. C., 1996, Heat transfer to air-

142

39. 40. 41. 42.

WADEKAR

water two-phase ¯ ow in slug/churn region, ASME Proceedings of the 31st National Heat Transfer Conference, HTD Vol 326, pp. 219±226. Jamialahmadi, M., BloÈchl, R. and MuÈller-Steinhagen, H., 1990, Bubble dynamics and scale formation during boiling of aqueous calcium sulphate solutions, Chem Eng Process, 26(1): 15±26. Najibi, H., Jamialahmadi, M. and MuÈller-Steinhagen, H., 1996, Subcooled ¯ ow boiling of CaSO4 solutions, Proc of 2nd European Thermal Sciences Conference, 1: 439±444. Wadekar, V. V., Hills P. D. and Mattes J., 1997, Mixture effect in boiling of salt solutions, Heat TransferÐ Baltimore 1997, AIChE Symposium Series, 93: 233±238. Goren¯ ow, D., Sokol, P. and Caplanis, S, 1992, Measurements of enhanced pool boiling heat transfer, 3rd UK National Heat Transfer Conference and 1st European Conference on Thermal Sciences, IChemE, 1: 89±96.

ACKNOWLEDGEMENTS The author gratefully acknowledges the permission given by the Heat Transfer and Fluid Flow Service (HTFS) to publish this work.

ADDRESS Correspondence concerning this paper should be addressed to Dr V. V. Wadekar, Heat Transfer and Fluid Flow Service (HTFS), Building 392.7, AEA Technology plc, Harwell, Oxfordshire, OX11 0RA, UK. This paper was presented at the 5th UK National Heat Transfer Conference, held at Imperial College London 17± 18 September 1997.

Trans IChemE, Vol 76, Part A, February 1998