THEORETICAL AND EXPERIMENTAL STUDIES IN SHELL-SIDE CONDENSATION

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1 HEFAT8 6 th International Conerence on Heat Transer, Fluid Mechanics and Thermodynamics 3 June to July 8 Pretoria, South Arica Paper number: K THEORETICAL AND EXPERIMENTAL STUDIES IN SHELL-SIDE CONDENSATION Briggs A. School o Engineering and Materials Science Queen Mary, Uniersity o London London, E 4NS United Kingdom a.briggs@qmul.ac.uk ABSTRACT The undamental phenomena behind condensation on simple banks o plain tubes and ree and orced conection condensation on single integral-in tubes are examined. This is ollowed by a detailed ealuation o aailable theoretical models and empirical correlations. Throughout the paper, a strong emphasis is placed on quantitatie ealuation o predictie methods. For example, in the case o condensation on banks o plain tubes a data base o nearly ie thousand points, coering 6 test luids and 3 tube bank geometries is compared to theoretical models aailable in the literature. Finally, gaps in the aailable knowledge are highlighted and it is hoped that this will help stimulate urther work on these areas. INTRODUCTION The condenser is a major component o process, rerigeration and power plant. Major reductions in capital cost can be achieed by improements to design leading to smaller units. Increased condenser perormance can also lead to signiicant increases in cycle eiciency o power plants by reducing turbine exhaust pressure. A program o condenser research has been in progress at Queen Mary, Uniersity o London or some time and the author has been inoled in many aspects o this work or nearly twenty years. The work includes experimental and theoretical work on both shell-side and tube-side condensation. This paper will concentrate on two areas o this work; namely condensation on banks o plain tubes and condensation on integral-in tubes. NOMENCLATURE A Empirical constant in equations (35) and (36) A, A Parameters in equation (3) a Empirical constant in equations (35) and (36) a, a Empirical constants in equation (3) B, B Empirical constants in equation (5) b Fin spacing at in tip C Parameter in equation (3) C, C Constants in equation (9) c P Speciic heat capacity d Diameter o smooth tube or in-root diameter o inned tube d o Diameter at in tip F Dimensionless parameter, (μgdh g /ku m ΔT) raction o in lank "blanked" by condensate "wedge" s raction o interin tube surace "blanked" by condensate "wedge" G Mass elocity, U ρ g Speciic orce o graity h Radial in height h g Speciic enthalpy o eaporation h Mean ertical in height (see equations (6) and (7)) J Dimensionless parameter (see equation (5)) j Constant in equation (6) k Thermal conductiity k w Thermal conductiity o tube M Empirical constant in equation (36) m Empirical constant in equation (3) N Empirical constant in equation (3) N tot Number o data points Nu Nusselt number, αd/k Nu l Nusselt number based on liquid lowing alone in bank n Empirical constant in equation (3), (4) and (5) P Pressure P t, P l Transerse and longitudinal tube pitchs Pr Prandtl number, μc P /k p Fin pitch q Heat lux based on area o plain tube with in root diameter Re eq Equialent Reynolds number, deined by equation (3) Re,gr Film Reynolds number based on graity drained low Re,u Film Reynolds number based on uniormly distributed low Re l,max Reynolds number or liquid lowing alone through bundle and based on maximum elocity (i.e. through minimum cross-sectional area between the tubes) Re,max Vapour Reynolds number based on maximum elocity ρ U max d/μ Re tp,max Two-phase Reynolds number based on maximum elocity, ρu max d/μ Re tp,min Two-phase Reynolds number based on minimum elocity, ρu d/μ Re tp,m Two-phase Reynolds number based on means oid elocity, ρu m d/μ r Local radius o curature o condensate surace s Fin spacing at in root t Fin thickness at in tip U max Vapour elocity based on apour olume low rate and minimum cross sectional area o test section (i.e. between adjacent tubes in a row or between single tube and test section wall) U m Vapour elocity based on apour olume low rate and mean-oid cross sectional area o test section (i.e. the total olume o the test

2 U X tt X x section not occupied by tubes diided by its length in the direction o the low) Vapour elocity based on apour olume low rate and total cross sectional area o test section (i.e. just upstream o test bank or test tube) Lockhart-Martinelli parameter Coordinate measured along condensate-apour interace Vapour quality Special Characters α Vapour-side, heat-transer coeicient, q/δt β in tip hal angle Γ Mass low rate o condensate draining rom tube γ Mass low rate o luid condensing on tube ΔT Vapour-side temperature dierence ε Enhancement ratio (heat-transer coeicient or inned tube diided by heat-transer coeicient or smooth tube, both based on smooth tube area at in root diameter and or same apour-side temperature dierence and apour elocity) μ Viscosity ν Kinematic iscosity ξ(φ ) Function approximated by equation (8) ρ ~ ρ σ φ Density ρ ρ Surace tension Retention angle measured rom top o tube Subscripts None Condensate calc Calculated alue exp Experimental alue gr Pertaining to graity controlled low Nu Calculated rom Nusselt [7] theory root Pertaining to in root sh Pertaining to or shear controlled low tip Pertaining to in tip Vapour w Ealuated at outside wall temperature CONDENSATION ON BANKS OF PLAIN TUBES For condensation on banks o tubes, the low pattern is generally three-dimensional and inoles complex interactions between apour and condensate. Heat transer is eected by condensate inundation and the reduction in apour elocity down the bank accompanying condensation. A ast amount o experimental data is aailable in the open literature and the releant ariables hae been studied systematically. Furthermore, attempt hae been made to incorporate the complex interactions outlined aboe into theoretical correlations. Experimental Data Base Table summarises an extensie experimental data base extracted rom the open literature. It includes data or 6 condensing luids and 3 tube bank conigurations extracted rom 5 sources. Figure shows schematics o the test section geometries used in the studies. The test sections can be diided into two types; those where the whole test bank is actie (with the exception o dummy hal tubes on the walls o the triangular test banks) and those where a single actie tube is positioned in a bank o dummy tubes. In both cases artiicial condensate inundation was sometimes employed to simulate conditions near the bottom o a larger tube bank. The Model o Shekriladze and Gomelauri [6] This purely theoretical model was deeloped or condensation on a single tube in an ininitely wide duct but has shown some success in predicting heat-transer coeicients or banks o tubes. It proides a useul baseline or comparison with more complex models. The authors used the assumptions o the Nusselt [7] model or ree conection on a single tube but added the asymptotic, ininite condensation rate approximation or the shear stress at the condensate-apour interace. Their result can be represented by the equation o Rose [8] as ollows Nu Re F / = () / / / 4 tp, m ( F + F) Equation () tends to Nu/Re tp,m / =.9 or small F (high apor elocity) while at large F (low apour elocity) it tends to the result o Nusselt [7], which can be written as Nu Re / tp,m / 4 =.78F () Beore comparing the whole experimental data set to equation () it is worthwhile comparing the model to data with a apour quality o upstream o the test tubes, i.e. data where no condensate, either artiicial or generated by other actie tubes, is present. This reduced data set consists mainly o data or the top row o the arious tube banks but also, in the case o the data o Nobbs [], Gogonin and Dorokho [6, 7] and Beech [3], data set 3, where a single actie tube was positioned in a dummy bank and the case o Beech [3], data set, where rows o dummy tubes were positioned upstream o the irst actie row (see Figure ). The comparison is shown in Figure, where the apour elocity used is based on the apour mass low rate just upstream o the tubes and the mean oid area o the test section, i.e. the total olume o the test section not occupied by tubes diided by its length in the direction o the low. Three sets o data stand out in Figure. Those o Kutataladze et al. [] are aboe the theoretical line and show a large degree o scatter, while the data o Briggs and Bui [5] and Shah [] are below the theoretical prediction. The rest o the data are in relatiely good agreement with the theoretical line o Sheriladze and Gomelauri [6] or low apour elocities (high alues o F) but show a distinctie upturn in the alues o Nu/Re tp.5 at alues o F below and. or steam and nonsteam data respectiely. This may suggest transition to turbulent low in the condensate ilm. When all the aailable data are compared to equation () the situation not surprisingly becomes more complex. Figures 3a and b show the steam and non-steam data respectiely. In both cases much o the data (with the marked exception o those o Kutataladze et al. []) are below the Shekriladze and Gomelauri [6] line suggesting that condensate inundation is haing a measurable and negatie eect on the heat transer. For the steam data the upturn in the data at low alues o F is een more marked. Condensate inundation rom tube rows higher up the bank onto those below produces higher ilm

3 Nobbs [] - Nobbs [] - Briggs and Briggs and Bui [5] Sabaratnam [4] Briggs et al. [5] Kutataladze [] Shah [9, ] Ramamurthy [8] Beech [3] Michael [] Beech [3] - Beech [3] - 3 Key Instrumented Tube Actie, Uninstrumented Tube Dummy Tube Artiicial Inundation Tube Honda et al. [4] - Honda et al. [4] - Caallini et al. [, 3] Gogonin and Dorokho [6, 7] Figure Schematics o Test Banks

4 Table Condensation on Banks o Plain Tubes - Experimental Data Base Reerence Fluid Bank layout Tube outside diameter / mm Vapour elocity* / (m/s) Nobbs [] - Steam Triangular (SAT, ACI) Nobbs [] - Steam Square (SAT, AI) Michael et al. [] Steam Triangular * Symbols used in Figures Beech [3] - Steam Triangular Beech [3] - Steam Triangular (ACI) _ Beech [3] - 3 Steam Triangular (SAT, ACI) Briggs and Sabaratnam [4] Steam Triangular Briggs and Bui [5] Steam Triangular x Gogonin and Dorokho [6] R- Triangular (SAT) Gogonin and Dorokho [7] R- Triangular (SAT) Ramamurthy [8] Iso-propanol Triangular.7.4 Shah [9] Iso-propanol Triangular * Shah [] Methanol Triangular x Kutataladze et al. [] R- Triangular (SAT) Caallini et al. [] R- Triangular Caallini et al. [3] R-3 Triangular Honda et al. [4] - R-3 Square o Honda et al. [4] - R-3 Triangular Briggs et al. [5] R-3 Triangular * At Approach to Test Bank SAT - Single Actie Tube ACI - Artiicial Inundation _ Reynolds numbers which may urther promote the onset o turbulence in the condensate ilm. Nu /Re tp,m.5. Vapour elocity based on mass low rate upstream o row and mean oid area.. F Figure Comparison o Model o Shekriladze and Gomelauri [6] to Experimental Data with No Inundation (For key see Table ) The Model o Caallini et al. [9] Caallini added a correction to the Shekriladze and Gomelauri [6] model to account or the eect o condensate inundation as ollows, Re / tp,m Nu Γ γ.6 / F = / ( F + F) / 4 The correction was based on work by Cipollone et a. [] or condensation o low elocity apour on staggered tube banks. Figures 4a and b show the data plotted on the basis o equation (3). The correction or condensate inundation shits the (3)

5 Nu /Re tp,m.5 (Nu /Re tp,m.5 ) / (Γ /γ ) -.6 a) Steam Data Vapour elocity based on mass low rate upstream o row and mean oid area... F a) Steam Data Vapour elocity based on mass low rate upstream o row and mean oid area... F Nu /Re tp,m.5 (Nu /Re tp,m.5 ) / (Γ /γ ) -.6 b) Non-Steam Data Vapour elocity based on mass low rate upstream o row and mean oid area... F Figure 3 Comparison o Model o Shekriladze And Gomelauri [6] to Experimental Data (For key see Table ) b) Non-Steam Data Vapour elocity based on mass low rate upstream o row and mean oid area... F Figure 4 Comparison o Model o Caallini [9] to Experimental Data (For key see Table ) data upwards and moes them, in most cases, aboe the theoretical line. The data o Nobbs [] are particularly eected. The exceptions are the data o Briggs and Bui [5] and Shah [] which are characterised by low inundation rates and thereore are hardly eected by the correction. There is suspicion here that the data may be eected by air in the test section, particularly at low apour elocities and towards the bottom o the banks The Model o M c Naught [] M c Naught [] examined the interaction between apour shear and graity and suggested the ollowing equation to calculate their combined eect. ( Nu ) / gr Nu Nu = + (4) The orm o equation (4), where two extreme alues o Nusselt number are combined on a power basis, has no real physical basis but is oten used to great eect in heat-transer correlations. A dimensionless parameter, J, was suggested to indicate the relatie importance o apour shear and graity eects sh x G J = (5) dg ρ ( ρ ρ ) Based on data o Nobbs [] were J <.5, M c Naught [] suggested the ollowing approximate expression or the graitycontrolled region. j Γ Nugr = Nu Nu (6) γ where j =. or square banks and.3 or triangular banks. For the shear-controlled region an empirical equation based on data o Nobbs [] were J >.5 was proposed, as ollows,.78 Nu sh =.6Nul (7) X tt where X tt is the the Lockhart-Martinelli parameter.

6 .9.5. x ρ μ X tt = (8) x ρ μ 4 a) Steam Data and Nu l is the Nusselt number calculated as i the liquid was lowing alone through the bundle, rom [] as ollows, Nu = C l ( Re ) l,max C Pr.34 μc Pkw μwcp wk Re l,max is based on the maximum elocity (i.e. through the minimum low area between the tubes),.6 (9) Nu exp C =.39 and C =.36 when Re l,max 3 C =.73 and C =.635 when 3 < Re l,max x 5 C =.4 and C =.7 when Re l,max > x 5 Figures 5a and b compare the M c Naught [] model with the data or steam and other luids respectiely. Agreement is not good. For steam the model oer predicts the data o Briggs and Bui [5] by as much as %, although this may be due to problems with the experimental data mentioned earlier. The signiicant under prediction o the data o Beech [3] and Michael [] is perhaps more serious. It should be noted that the correlation was based on only the data o Nobbs (which it agrees with quite well) while much o the other data is or higher apour approach elocities. This highlights the danger o extrapolating a correlation beyond the range o physical parameters used in its deelopment. For the non-steam data the correlation oer predicts much o the data; the exception being that o Kutataladze et al. []. The Model o Honda et al. [4] Honda et al. [4] studied condensate low characteristics within tube bundles and introduced graity drained and uniormly dispersed low models to estimate the condensate inundation rate at low and high apour elocities respectiely. In the ormer, which might be expected when apour shear is low, all condensate is assumed to all onto the tube directly below (i.e. in the next row or inline bundles and two rows down the bank or staggered bundles) while in the latter (at higher apour shear) the condensate is assumed to be uniormly distributed across the test section normal to the low and hence only a raction o the condensate impinges on the tubes below. Semi-empirical equations or determining the heat-transer coeicient o tube bundles were obtained by combining correlations or graitycontrolled and shear controlled regimes. For in-line bundles, the heat-transer coeicient was determined using and or staggered bundles using 4 4 ( Nu ) / 4 gr Nu Nu = + () 4 4 ( Nu + Nu Nu Nu ) / 4 Nu = + () gr gr sh sh sh Nu exp b) Non-Steam Data Nu cal Figure 5 Comparison o Model o M c Naught [] to Experimental Data (For key see Table ) where Nu gr is the Nusselt number or the graity-controlled regime gien by Nu Nu cal /3 g gr = d,gr ν. 5.8 (.Re +.7x Re ) / 4,gr () Re,gr is the ilm Reynolds number calculated under the assumption o graity-controlled low. Equation () was based on the low apour elocity data o Kutateladze and Gogonin [3] and Kutateladze et al. [4], or R- and or R-. Nu sh is the Nusselt number or shear controlled low gien by

7 Nu exp a) Steam Data Re = (6), max ρu maxd / μ The empirical constants a, a, m and n were ound by Honda et al. [4] rom their data or R-3 and are gien in Table. Figure 6b shows good agreement between the Honda et al. [4] model and the non-steam experimental data. The exception again being those o Shah [] and Kutataladze et al. []. For steam data, howeer, agreement is much less impressie and the data o Briggs and Bui [5] are again particularly poorly predicted. Table - Values o Empirical Constants in Equations (3-6) Nu exp Nu cal 4 b) Non-Steam Data Bundles a a m n In-line Staggered.65(P t /P l ) Conclusions Beore summing up the perormance o the arious theoretical models and empirical correlations described aboe it is worth reappraising the experimental data base in the light o the initial comparisons with theory. In all the comparisons described aboe the data o Briggs and Bui [5] and Shah [] hae allen signiicantly out o line with other data and hae been oer predicted by all the theories tested. While it is perhaps imprudent to dismiss data simply because it disagrees with theory, in this case the eidence would seem to suggest that these data were eected by air in the test section, due to the low apour elocities inoled. (This was een suggested by Briggs and Bui [5] in their original work.) The data o Kutateladze et al. [] on the other hand were signiicantly under predicted by all theories and in addition showed signiicant scatter, although the reasons or this are less clear. Due to these anomalies, these three data sets will be excluded in what ollows. Mean deiations between the remaining experimental data and the arious theories and correlations, deined as ollows, where Nu cal Figure 6 Comparison o Model o Honda et al. [4] to all Data (For key see Table ) Nu ( + a A ) / ( m / ) n sh = a A Retp,max Re, u A = Re (3) m,max q ρu maxh g (4) N Mean Deiation = tot ( Nucalc Nuexp ) (7) N tot are listed in Table 3. Table 3 - Summary o mean deiations o experimental data (excluding [5], [] and [). Shek and Gom [6] Caallini et al. [9] McNaught [] Honda et al. [4] Steam Non-Steam All Data / m / ρ ν.4 A Pr = ρ ν (5)

8 Table 4 - Free-Conection Condensation on Integral-Fin Tubes - Experimental Data Base Reerence Tube Fluid Number o Symbols used Material Geometries In Figures Wanniarachchi et al. [3] Copper Steam 4 Yau et al. [3] Copper Steam 4 Briggs et al. [33] Copper Steam 8 Briggs et al. [33] Brass Steam 8 Briggs et al. [33] Bronze Steam 8 Masuda and Rose [34] Copper R3 5 Masuda and Rose [35] Copper Ethylene Glycol 4 Marto et al. [36] Copper R3 9 Briggs et al. [33] Copper R3 8 Briggs et al. [33] Brass R3 8 + Briggs et al. [33] Bronze R3 8 The poor results o the Shekriladze and Gomelauri [6] model are not surprising, since it was deeloped or single tubes, although the addition o the correction or condensate inundation suggested by Caallini et al. [9] signiicantly improes the perormance, particularly or the steam data where it is the most successul o the our. The model o Honda et al. [4] is the most successul when compared to the ull data base and is particularly eectie or non-steam data. FREE-CONVECTION CONDENSATION ON INTEGRAL- FIN TUBES When quiescent apour condenses on an integral-in tube two mechanisms inluence the low o condensate on, and hence the heat transer to, the tube. Condensate retention in the inter-in spaces on the lower part o the tube, as illustrated in Figure 7, leads to a thickening o the condensate ilm and a decrease in the heat transer. On parts o the tube not coered by condensate looding, howeer, on the in tips and the lanks and interin space aboe the looding zone, surace tension induced pressure gradients thin the condensate ilm and enhance the local heat transer. Experimental Data Base Early experimental data (see or example Katz and Geist, [5], Beatty and Katz, [6], Karkhu and Boroko, [7], Mills et al., [8] and Canaros, [9]) are diicult to interpret. Details o experimental procedure are oten ague and comparison o results is diicult due to the unsystematic choices o geometric ariables. Methods o ealuating the apour-side, heat-transer coeicient also aried, with some inestigators measuring the tube wall temperature and others using indirect methods such as Wilson plots [3]. The accuracy in many cases is diicult to assess. Most o the data, howeer, showed marked enhancement o heat-transer coeicients, in most cases greater than the increase in heat-transer surace area due to the ins. Due to the uncertainties outlined aboe, the earlier experimental data will not be used in the current inestigation. Table 4 summarise more recent data. While only three luids are included, namely steam, ethylene glycol and R-3, these gie a wide range o thermophysical properties. In addition data are included or oer 4 tube geometries and three tube materials. To quantiy the relatie perormance o inned tubes an enhancement ratio can be deined as ollows α q inned = inned ε = (8) q α plain plain at same ΔT at same ΔT Care is needed in the exact deinitions o the quantities in equation (8). In the present work, the heat-transer coeicient (or heat lux) o the inned tube is based on the area o a smooth tube with in-root diameter while the denominator reers to a plain tube o diameter equal to the in root diameter o the inned tube. A useul conclusion o the inestigations summarized in Table 4 is that or relatiely low apour elocities this enhancement ratio is irtually independent o apour-side temperature dierence. Other conclusions are: ) Enhancements ratios are generally higher than increases in surace area, although or condensation o steam this is not always the case. ) Optimum in spacings can be identiied, and these are dependent on luid properties. 3) Enhancement ratio increases monotonically with in height in most cases, although or steam condensing on low thermal conductiity tubes there is little adantage in increasing in height aboe about.5 mm, due to in-eiciency eects.

9 pure saturated apour, proides the main resistance to heat transer. The graity drained models o Nusselt [7] or a ertical surace and a horizontal tube suggest that the heattranser coeicient or a ertical in o height h will surpass that o the bare tube o diameter d by a actor o order. Bare Tube R-3, σ /ρ =.4 μnm /kg α 4 ertical in.943 d (9) α horizontal tube =.78 h For low-in tubes used in condensation this is typically three or more. Equation (9) ormed the basis o the model o Beatty and Katz [6], who simply applied the Nusselt [7] equations or horizontal tubes and ertical plates to the arious suraces on a ined tube. The results are compared to the experimental data base in Figure 8. The model shows good agreement with the non-steam data but less good with the data or steam. This relect the act that surace tension, not included in the model, is much higher or water than organic luids. In particular these data are largely oer-predicted by the model, and this is due to the phenomena o condensate looding. 8 Ethylene Glycol, σ /ρ = 43.5 μnm /kg ε exp 6 4 Water, σ /ρ = 7.9 μnm /kg Figure 7 Liquid Retention on an Integral-Fin Tube (d =.7 mm, t =.5 mm, h =.6 mm, s =.5 mm) 4) Enhancement ratio decreases with in thickness since thicker ins (with ixed in spacing) result in reduced in density. Graity Drainage The enhancements in heat transer reported, oer and aboe the increase in heat-transer surace area are not unexpected. In single-phase lows the presence o short suraces with thin boundary layers produce high local heat-transer coeicients. The same is true in the case o condensation, where the boundary layer in question is the condensate ilm, which or a ε cal Figure 8 Comparison o Model o Beatty and Katz [6] to Experimental Data (For key see Table 4) Condensate Flooding The abrupt thickening o the condensate ilm between the ins at the so called looding or retention angle has been obsered by many inestigators. The retention angle can be predicted with good accuracy by the ollowing equations, deried independently by Rudy and Webb [37] and Honda et al. [38]. 4 σcosβ - φ = cos ρgbd o or b < h cosβ/( sinβ) ()

10 ..8 equation () φ / π 8.6 ε exp Rudy and Webb [33], R, n-pentane and water Honda et al. [38], R3 and Methanol Yau et al. [39], Water, Ethylene Glycol and R3 Briggs [4], Water, Ethylene Glycol and R σ cosθ / ρ gsr o Figure 9 Comparison o Flooding Angle Model to Experimental Data For rectangular cross-section ins this becomes 4σ - φ = cos ρgbd o or b < h () Figure 9 compares equations () with data or a wide range o tube geometries and luids. It includes measurements or the static case (i.e. without condensation) as well as during condensation. Rudy and Webb [37] adapted the Beatty and Katz [6] model by simply neglecting heat transer to the in lanks and root below the looding angle (as calculated using equations () and ()). The results are shown in Figure, with the majority o the data now aboe the theoretical prediction. This is because Rudy and Webb [37] neglected the positie eect o surace tension, in that it enhances heat transer aboe the looding zone by thinning the condensate ilm. Masuda and Rose [4] showed that liquid is also retained as wedges at the in roots aboe the retention angle. They deeloped expressions or rectangular cross-section ins or the proportion o the in lank and in root aboe the looding angle φ blanked by these wedges. These expressions were extended by Rose [4] to include trapezoidal cross-section ins as ollows ( β ) ( β ) tan / = + tan / s ( β ) ( β ) tan / = + tan / ( φ ) σcos β tan / ρgdh φ ( φ ) () 4σ tan / (3) ρgds φ Note that or rectangular cross-section ins β = and the leading term on the right hand sides o equations () and (3) are unity ε cal Figure Comparison o Model o Rudy and Webb [37] to Experimental Data (For key see Table 4) Surace Tension Enhancement This phenomena was irst pointed out by Gregorig [43]. A non-uniorm condensate surace curature leads to pressure gradients in the ilm. For one-dimensional curature the pressure in the liquid exceeds that in the apour by σ/r, where r is the radius o curature measured on the liquid side o the interace, so that the pressure gradient along the surace is dp d = σ ( r ) (4) dx dx On a low-in tube this pressure gradient dries liquid towards the centre o the tip o the in and along the in lank and on the interin tube surace towards the root o the in, causing the ilm to thin near the in tip and on the in lank and interin tube space near to the in root. The consequent reduction in aerage ilm thickness enhances heat transer to the tube. There hae been seeral attempts to sole this problem or integral-in tubes based on the Nusselt [7] assumptions and approximations while incorporating the surace tension induced pressure gradient into the momentum equation or the condensate ilm. Karkhu and Boroko [7], Riert [44] and Rudy and Webb [45] assumed linear pressure ariation along the in lank based on assumed radii o curature at the root and tip o the in, but these gross approximations yielded little or no improement oer the simple Rudy and Webb [37] model (see Briggs and Rose [46]). The approach o Honda and co-workers [47, 48] is the most complete to date but still contains signiicant simpliications in order to acilitate numerical solution o the goerning, ourth order dierential equations or the condensate ilm thickness. Despite this their approach has gien good agreement with experimental data coering a wide range o parameters, as illustrated by Figure, which

11 ξ( φ ) results rom application o the Nusselt [7] analysis or a horizontal tube aboe the leel o condensate retention, and can be closely approximated by ε exp ε cal Figure Comparison o Model o Honda et al. [47, 48] to Experimental Data (For key see Table 4) compares calculated results proided by Honda [49] to the data summarized in Table 4. Note that the model included conduction in the ins and thereore gies good agreement or the low conductiity brass and bronze tubes. Most recently Wang and Rose [5] ormulated the ull dierential equation or the condensate ilm thickness oer the whole in and tube surace. While representing an adance on earlier work, howeer, attempts by the authors to ind solutions to these equations were, by their own admission, incomplete. ξ( φ ) = x - φ -.64x - φ +.553x φ -.363x φ (8) φ being calculated rom equation () or (). and s account or additional condensate retention aboe the looding angle and are calculated rom equations () and (3). With B =.43 and B l =.96, equation (5) gies good agreement with the experimental data base as illustrated in Figure. It also gies the correct dependence on in spacing, thickness and height. The discrepancy between equation (5) and the data or steam condensing on brass and bronze tubes is due to the temperature drop through the ins when the parameter (αh /tk w ) becomes large. Briggs and Rose [5] proposed a modiication to the model which used slender in theory to account or conduction in the ins. They combined the original semi-empirical equations or heat transer through the condensate ilm with one-dimensional conduction through the ins. The resulting algebraic equations were soled iteratiely. The results are compared to the experimental data in Figure 3. It can be seen that the correction or temperature drop in the ins successully pulls the model into line with the data or steam condensing on brass and bronze tubes without signiicantly aecting the results or the other data which were already in good agreement with the model. Semi-Empirical Models Gien the complexities o the problem outlined aboe, Rose [4] proposed a relatiely simple, semi-empirical model or integral-in tubes or use in design and optimisation. Using a combination o Nusselt [7] or the graity contribution and dimensional analysis to account or surace tension drainage the ollowing equation was deeloped or the enhancement ratio o an integral-in tube. 8 ε exp 6 3 / 4 / 4 d o Bσd o φ d o d Bσh ε = t ~.79 / 4 3 / 4 3 ~ d t ρg π cosβ h d h ρg / 4 B d 3 σ B ( ) s ( ) s ξ ( φ ) +. 78( b + t) 3 s ~ ρg (5) where B and B l are dimensionless constants, h is the "mean ertical in height", gien by h φ = sin φ ( ) h π φ (6) / ε cal Figure Comparison o Model o Rose [4] to Experimental Data (For key see Table 4) h φ = < φ π sin φ ( ) h π (7)

12 ε cal ε exp Figure 3 Comparison o Model o Briggs Rose [5] to Experimental Data (For key see Table 4) ethylene glycol at low (5 kpa) pressure. For low pressure steam, apour elocities up to 6 m/s were achieed and the heat-transer enhancement ratio was ound to be a strong unction o both apour elocity and in spacing. The interrelationship o these two parameters led to complex trends in the data, as illustrated by the sample results in Figure 4. At relatiely low elocities the enhancement ratio decreased with increasing apour elocity in line with results discussed aboe. At some critical apour elocity, howeer, which was dierent or dierent in geometry, apour shear on the condensate ilm began to reduce the extent o condensate retention between the ins on the lower part o the tube and this was accompanied in all cases by an increase in the enhancement ratio. Thus the eect o apour shear on looding appears to explain, at least qualitatiely, the trends obsered in Figure ε.5 d =.7 mm t =.5 mm h =.6 mm Steam (P = 5 kpa) s =.5 mm s =.5 mm FORCED-CONVECTION CONDENSATION ON INTEGRAL-FIN TUBES The combined eects o graity, apour shear and surace tension on condensation on integral-in tubes has recently receied some attention in the literature but as yet the interaction o these eects is ar rom ully understood. Experimental Data Base Table 5 summarises the experimental data aailable in the open literature. We can extend our deinition o enhancement ratio described aboe to include the additional constraint o equal apour elocity or inned and plain tube, i.e. α = α q inned inned ε = (9) plain q same ΔT and U plain same ΔT and U Early results indicated that or low apour elocities, the relatie increase in heat-transer coeicient due to apour elocity was smaller or inned tubes than or plain tubes, resulting in a decrease in enhancement ratio, as deined in equation (3) with increasing apour elocity. As more data hae become aailable, howeer, it is becoming apparent that apour shear can hae an eect on the heat transer in the looded section o a inned tube. Bella et al. [58] and Caallini et al. [59] condensed R-3 and R- on three integral-in tubes with apour elocities up to m/s. For the two more densely inned tubes ( ins per meter) apour shear aected plain and inned tubes to a similar degree and the enhancement ratio was independent o apour elocity. Caallini et al. [59] attributed this to turbulence in the condensate ilm and a local reduction o the liquid ilm thickness in the looded region. Namasiayam and Briggs [54-57, 6] tested nine tubes condensing steam at atmospheric and low (4 kpa) pressure and U / (m/s) Figure 4 Variation o Enhancement Ratio with Vapour Velocity (Data o Namasiayam and Briggs [56]) Semi-Empirical Models Caallini et al. [6] deeloped a semi-empirical model or orced-conection condensation on integral-in tubes. The ollowing equation was proposed or the apour-side, heattranser coeicient. N N [ ] N α α gr + α sh = (3) α gr in equation (3) denotes the apour-side, heat-transer coeicient under stationary apour conditions and was obtained rom the model o Briggs and Rose [5]. The second term, α sh, denotes the apour-side, heat-transer coeicient when orced-conection dominates and the eects o graity and surace tension become negligible. This was ound rom the ollowing correlation. where, k.8 3 sh C Reeq Pr d α = (3) o ρ U ρ max o Re eq = (3) μ ρ d.5

13 Table 5 - Forced-Conection Condensation on Integral-Fin Tubes - Experimental Data Base Reerence Test Fluid Pressure / (kpa) Vapour Velocity / (m/s) Number o Tubes + Symbols used in Figures Michael et al. [5] Steam Briggs et al. [53] Steam Namasiayam and Briggs [54, 55] Steam Namasiayam and Briggs [56, 57] Steam Michael et al. [5] R Briggs et al. [53] Ethylene Glycol o Bella et al. [58] Caallini et al. [59] R * Bella et al. [58] Caallini et al. [59] R * + All tubes were copper Namasiayam and Briggs [6] Ethylene Glycol where t h C = (33) p p The alues o the constants in equation 33, and the alue o N (= ) in Equation 3 were obtained rom a best it procedure using the data o Bella et al. [58] and Caallini et al. [59] or R- and R-3 condensing on 3 tubes. Figure 5 compares results o this model to the experimental data base. The model predicts non-steam data to within. It is less successul, howeer, at predicting data or steam. Briggs and Rose [6] also adopted an approach based on equation 3. In this case, howeer, α gr, was calculated rom the model o Rose [4] but with the obsered looding angle which in many cases was larger than that calculated using equations () or (), due to apour shear. (They pointed out that a more complete model would require an equation relating the retention angle to apour elocity, geometric parameters and condensate properties.) For α sh, the heat-transer coeicient or orced conection, it was argued, based on the theoretical results o Wang and Rose [5], that surace tension orces will dominate on the in lank leaing the in tip and root as the only areas eected by apour shear. Furthermore, the in root will be less aected by apour shear due to being shielded somewhat by the ins. These arguments led to the ollowing semi-empirical equation or the heat-transer coeicient or orced conection. t do φobs s α = α + α (34) sh tip root p d π p a k do a α tip = A Retp,min d (35) o d M k s a root exp α = ARetp,min d (36) h and Re tp,min is the two-phase Reynolds number based on the upstream apour elocity and the in root diameter. Equations (35) and (36) are based in part on the model o Shekriladze and Gomelauri [6] or orced-conection condensation, which or a smooth tube gies Nu =.9Re tp,min.5. The term (-exp(-s/h) M ) in equation (36) accounts or the reduced eect o apour shear at the in root and, or positie alues o M, tends to unity and zero or large and small alues o s/h respectiely. The empirical constants, M, n, A and a were ound itting the data summarised in Table 5. This gae the ollowing alues; M =., n = 3, A =. and a =.5. The act that M was ound to be positie gies conidence in the orm o equation (36). Figures 6 compares the model to the data base. It can be seen that the present model gies signiicantly better agreement with the steam data than the model o Caallini et al. [6]. The non-steam data was well predicted by the model o Caallini et al [6] since much o it was used in their correlation. The present model is less eectie with this data, although agreement is still acceptable.

14 9 a) Steam Data 9 a) Steam Data 8 8 α exp / (kw/m K) α exp / (kw/m K) α cal / (kw/m K) α cal / (kw/m K) 3 b) Non-Steam Data 35 b ) Non-Steam Data 3 5 α exp / (kw/m K) 5 α exp / (kw/m K) α cal / (kw/m K) Figure 5 Comparison o Model o Caallini et al. [6] to Experimental Data (For key see Table 5) α cal / (kw/m K) Figure 6 Comparison o Model o Briggs and Rose [6] to Experimental Data (For key see Table 5) CONCLUSIONS Condensation on Banks o Plain Tubes The experimental data base or condensation on banks o plain tubes is summarized in Table. The data o [5], [] and [] showed poor agreement with the rest o the data and all o the models and correlations ealuated. When these data were excluded, the ollowing conclusions were reached: For condensation o steam, the models o Caallini et al. [9], M c Naught [] and Honda et al. [4] all perormed equally well, predicting the data with a mean deiation o about, with the model o Caallini et al. [9] giing slightly better agreement than the other two. None o the models gae good agreement with the ery high elocity data o Michael [] and Beech [3]. For condensation o apours other than steam, the correlation o Honda et al. [4] gae easily the best agreement with the data. None o the models speciically address the issue o turbulence in the condensate ilm, except in as much as the empirical element o the models include this i it were present in the experimental data used in the correlation. As expected,

15 this appears to be most prealent at high apour shear and high condensate inundation. Free-Conection Condensation on Integral-Fin Tubes The mechanisms behind condensation on integral-in tubes in the absence o signiicant apour shear appear to be well understood. These include the eects o condensate retention, surace tension induced enhancement and conduction in the ins. The two most successul models, i.e. those o Honda et al. [47, 48] and Briggs and Rose [5] include all these actors and gie ery good agreement with the experimental data base summarized in Table 4. Forced-Conection Condensation on Integral-Fin Tubes The combined eects o surace tension, graity and apour shear on condensation on integral-in tubes is only recently receiing attention. Experimental data is becoming aailable and is summarized in Table 5. At present, howeer, there are no reliable models or correlations aailable. The eect o apour shear on the degree o condensate looding appears to be a major actor in enhancing heat transer. In addition, the relatie eects o surace tension and apour shear on dierent areas o the tube surace aboe the looding point also needs to be addressed. The correlation o Briggs and Rose [6] attempted to include these actors in a ery simple way but with ery limited success. REFERENCES [] Nobbs, D. W, The eect o downward apour elocity and inundation on the condensation rate on horizontal tubes and tube banks, Ph.D. Thesis, Uniersity o Bristol, UK, 975. [] Michael, A. G., Lee, W. C. and Rose, J. W., Forced conection condensation o steam on a small bank o horizontal tubes, Trans ASME J Heat Transer, Vol. 4, 99, pp [3] Beech, P. M., Filmwise condensation o high elocity downward lowing steam on a bundle o horizontal tubes, Ph.D. These, Uniersity o London, UK, 995. [4] Briggs, A. and Sabaratnam, S., Condensation o steam in the presence o air on a single tube and a tube bank, Int. J. 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16 the perormance o horizontal integral-in condenser tubes, Trans ASME J. Heat Transer, Vol. 7, 985, pp [33] Briggs, A., Huang, X. S. and Rose, J. W., An experimental inestigation o condensation on integral-in tubes: eect o in thickness, height and thermal conductiity, Proceedings o ASME Nat. Heat Trans. Conerence, Portland, USA, HTD-Vol. 38, 995, pp. -9. [34] Masuda, H. and Rose, J.W., An experimental study o condensation o rerigerant-3 on low integral-in tubes, Proceedings o the International Symposium on Heat Transer, Beijing, China, Vol., Paper No.3, 985, and in Heat Transer Science and Technology, Hemisphere, pp , 987. [35] Masuda, H. and Rose, J.W., Condensation o ethylene glycol on horizontal inned tubes, Trans ASME J. Heat Transer, Vol. 988, pp. 9-. [36] Marto, P.J., Zebrowski, D., Wanniarachchi, A.S. and Rose, J.W., An experimental study o R-3 ilm condensation on horizontal inned tubes, Trans. ASME J. 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