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State of the art in pool boiling heat transfer of new refrigerants
International Journal of Refrigeration 24 (2001) 6±14
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State of the art in pool boiling heat transfer of new refrigerants Dieter Goren¯o * WaÈrme- und KaÈltetechnik, UniversitaÈt Paderborn, Germany Dedicated to Professor Dr.-Ing. Dr. h.c. mult. Karl Stephan on the occasion of his 70th birthday Received 31 May 2000; received in revised form 8 June 2000; accepted 8 June 2000
Abstract The predictive methods for the calculation of the heat transfer coecient with pool boiling are important tools for the optimum design of the evaporator and for the successful operation of refrigeration units. The method given in the VDI Heat Atlas is discussed as an example of the currently available methods/ and results of recent experimental investigations on nucleate boiling of partly ¯uorinated hydrocarbons (HFCs) and of hydrocarbons (HCs) are added covering those parts where the predictive methods should be improved, namely boiling of mixtures, in¯uence of surface structure and material of the heating wall, and in¯uence of additional ¯ow of bubbles and liquid in tube bundles. # 2000 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Heat transfer; Pool boiling; Refrigerants; Replacement; HFC; Hydrocarbon; Heat transfer coecient; Survey
Etat du calcul pour le transfert de chaleur en eÂbullition libre de nouveaux frigorigeÁnes ReÂsume Les meÂthodes preÂvisionnelles permettant le calcul du coecient de transfert de chaleur a en eÂbullition libre sont des outils importants dans le domaine de la conception optimale de l'eÂvaporateur et le bon fonctionnement des groupes frigori®ques. La meÂthode donneÂe dans le VDI Heat Atlas est examineÂe en tant qu'exemple d'une meÂthode disponible actuellement ; l'auteur couvre eÂgalement les eÂtudes expeÂrimentales reÂcentes sur l'eÂbullition nucleÂeÂe des hydrocarbures partiellement ¯uoreÂs (HFC) et les hydrocarbures (HC), donnant des aspects des meÂthodes preÂvisionnelles qui devraient eÃtre ameÂlioreÂs, c'est-aÁ-dire l'eÂbullition des meÂlanges, l'in¯uence de la structure super®cielle et le mateÂriau de la paroi chauante, et l'in¯uence d'un eÂcoulement suppleÂmentaire de bulles et de ¯uide dans les faisceaux de tubes. # 2000 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : Transfert de chaleur ; Ebullition libre ; FrigorigeÁnes ; Substitut ; HFC ; Hydrocarbure ; Coecient de chaleur ; EnqueÃte
1. Introduction One of the important features for the successful operation of a refrigeration unit is the heat transfer * Tel.: +49-5251-60-2393; fax: +49-5251-60-3522. E-mail address: [email protected] (D. Goren¯o).
performance of the refrigerant within the evaporator. The optimum design of the evaporator depends on the correct evaluation of the nucleate boiling and the convective contributions to heat transfer. This is particularly important when new refrigerants and refrigerant mixtures are being introduced to replace the former working ¯uids with their negative eects on the atmosphere.
0140-7007/01/$20.00 # 2000 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00046-3
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
In the following, heat transfer within shell-and-tube evaporators used in medium or big refrigeration units will be discussed, and the prediction method given in the VDI Heat Atlas will be taken as an example for the methods available in literature. For plain tubes and pure ¯uids, the in¯uence of heat ¯ux, saturation pressure and thermophysical properties of the boiling liquid are predicted already quite well with various calculation methods. In the case of mixtures, prediction is worse because heat and mass transfer near the heated wall are more complex and because less experimental data exist in the literature. For the comparatively low saturation pressures used in refrigeration applications, however, and for the moderate temperature glides occuring with the mixtures to replace R22, R502 and R13B1, the situation is not so bad, as will be shown by new measurements with binary and ternary mixtures of partly ¯uorinated hydrocarbons (HFCs). The parts of the predictive methods which should be improved are the in¯uence of the surface structure and material of the heating wall and the in¯uence of additional ¯ow of bubbles and liquid in tube bundles. Also for these domains experimental results in pool boiling will be discussed which should be incorporated in the prediction methods in the future.
FWR Pa =Rao 2=15 and FWM lc=lo o co 1=4
4
The in¯uence of the thermophysical properties of the boiling liquid is contained in the reference value 0 under the reference conditions: qo 20 kW/m2, po 0:1, lo , o , co thermal conductivity, density, or speci®c heat respectively of copper, and Pao 0:4 mm=mean roughness height of the heating surface [according to the new international standard DIN EN ISO 4287 (10.98)]. This implies that o must be determined by experiment or calculated independently of Eq. (1). In the latter case, the correlation of Stephan and Preusser [7] is recommended for pure ¯uids, and the approach of SchluÈnder [8] for mixtures of new refrigerants: ÿ id = 0 1 Tph ÿ Ts =Tid
5
with id q=Tid and Tid Sxj Tj
6
7
x, y molar fraction of liquid or vapour, mass transfer coecient, , hv density or heat of vaporization of the liquid, B ®tting parameter [because of the poor knowledge of , also (B= ) may be taken for ®tting]. The mean heat transfer coecient ev of the evaporator is calculated from a1 for a single plain tube by ev = 1 f geometry of single heater and whole apparatus; effects of impurities operating conditions
8
3. Discussion of new experimental results In the following, new results on mixture boiling, roughness and material of the heating wall, and on convective eects in tube bundles will be highlighted.
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3.1. Pool boiling of new refrigerant mixtures
2
Heat transfer with pool boiling of the new refrigerants R134a(CH2F.CF3), R143a(CH3.CF3), R125(CHF2.CF3), R32(CH2F2), and their mixtures has been investigated
with n n p 0:9 ÿ 0:3p0:3
3
ÿ Tph ÿ Ts STsj xj ÿ yj 1 ÿ exp ÿBq= hv
A theoretically consistent calculation method for the heat transfer coecient in nucleate boiling, which should be based on the physical phenomena connected with vapour bubbles growing, departing and sliding on the wall and with the interactions of bubbles and of neighbouring nucleation sites within the microstructure of the heating surface does not yet exist, despite the increasing number of papers on the subject in the recent past (cf. the literature reviews by Dhir [1], Lienhard [2], Goren¯o et al. [3], and Auracher and Kenning [4]). Instead, the predictive methods for available in the literature at present are empirical or semiempirical, especially for heat transfer conditions relevant in practice. In the VDI Heat Atlas method [5,6], a relationship for a reduced heat transfer coecient 1 = 0 on a single plain tube is established in which the relative in¯uences of the main groups of variables on are treated separately by: Fq for the heat ¯ux, Fp for the saturation pressure ps (in terms of p ps =pc , pc pressure in the critical state), FWR and FWM for the microstructure or material, respectively, of the heating surface,
Fq q=qo n ;
Fp 1:2p0:27 2:5p p = 1 ÿ p
and
2. Prediction of nucleate boiling heat transfer
1 = 0 Fq Fp FWR FWM
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D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
over wide ranges of heat ¯ux and saturation pressure, together with the vapour liquid equilibrium (VLE) and densities (cf. e.g. KoÈster [9]). In Fig. 1, the saturation temperatures Ts (dot±dashed lines in the triangle diagram) and the temperature glide Tbp of Ts for total evaporation (solid lines) are shown for the ternary system R125, R143a, R134a at atmospheric pressure, as an example. It can be seen that there is indeed no temperature glide with the commercial azeotrope R507 at p=1bar (p*=0.027) and that this holds fairly well throughout the pressure range (cf. the table in Fig. 1). The ternary mixture R404A also displays nearly azeotropic behaviour (Tbp < 1 K, cf. triangle diagram and table), while the maximum temperature glides at p=1 bar, Tbp 5:4 or 4.9 K, are found for the two binaries with the high boiling R134a, near the equimolar compositions. In the so called standard apparatus for pool boiling heat transfer measurements developed some years ago [10,11], we investigated the (approximately) equimolar binary of R125 and R134a (and gave it the internal abbreviation R407*) at pool boiling on a horizontal copper tube with emeried surface (Pa 0:34 mm),
. because it is the mixture with the maximum temperature glide of the whole ternary system (approx.), . because its vapour pressure curve is almost the same as for R22 throughout the temperature range important for refrigeration (cf. Fig. 2, top), and . because the temperature glide is only slightly smaller than for the commercial ternary R407C (cf. the table in Fig. 1). The results in Fig. 3 agree with the well known behaviour of mixtures (and pure liquids) in nucleate boiling on horizontal copper tubes with emeried surface (cf. e.g. Goren¯o and KoÈster [12]): . marked increase of with rising heat ¯ux q and saturation pressure ps (in terms of p ps =pc ), . straight interpolation lines for constant pressure in double logarithmic plots of over q and . diminishing increase of with q at p=const with rising pressure. In Fig. 4, the relative dependence of on the heat ¯ux q Ð in terms of the exponent n from qn Ð and on the pressure p* according to Eq. (2) or (3), resp., is compared with measurements for (a) pure refrigerants and (b) mixtures. As is known from comparisons with
Fig. 1. Saturation temperatures Ts and glide Tbp of Ts for total evaporation of the ternary system R125/R143a/R134a. Fig. 1. TempeÂratures de saturation Ts et glissement de tempeÂrature Tbp de Ts pour l'eÂvaporation totale du systeÁme ternaire R125/R143a/R134a.
Fig. 2. Vapour pressure curves of refrigerants. Fig. 2. Courbes des pressions de vapeur de frigorigeÁnes.
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
Fig. 3. Heat transfer coecient over the heat ¯ux q for pool boiling of a R125/R134a-mixture on a horizontal copper tube at various saturation pressures. Fig. 3. Coecient de transfert de chaleur a pour le ¯ux thermique lors de l'eÂbullition libre d'un meÂlange de R125 et de R134a sur un tube en cuivre horizontal, pour diverses pressions de saturation.
other new measurements in recent years (cf. e.g. KoÈster et al. [13]), Eqs. (2) and (3) are a somewhat conservative approach for pure substances at intermediate and high heat ¯uxes and pressures (q > 10 kW/m2 and ps > 0:1pc ). The results for the azeotrope R507 (squares in Fig. 4b) agree with the data for the pure refrigerants as can be seen from analogous deviations of the squares in Fig. 4b as of all symbols in Fig. 4a from the Heat Atlas lines for pure substances. This was to be expected for azeotropic mixtures without shift of the composition between vapour and liquid. The relative increase of with q and p for the nearly azeotropic mixture R404A is already somewhat smaller, particularly at higher pressures (circles in Fig. 4b). For the zeotropic mixtures R407C and R407*, however, the relative increase of a with q and p is signi®cantly smaller than for the pure refrigerants (cf. the triangles in Fig. 4b). This is due to the depletion of the lower boiling component(s) and subsequent increase of the local saturation temperature in the liquid layer near the heating wall. At low pressures p 40:1, important for evaporators of refrigerants, the eect gets smaller despite the increasing temperature glide Tbp and shift of composition xy, see Fig. 4b and the table and small diagram in Fig. 1. It seems that the more pronounced separation of the components at low pressures is less than predicted by the phase equilibrium [14] and that it is compensated to a large extent by the liquid turbulence in the boundary layer due to the vigorous motion of the rising bubbles after detachment from the tube surface.
9
Calculations of the a-values according to Eqs. (5)±(7) agree well with the measurements for these comparatively narrow boiling refrigerant mixtures, especially at intermediate heat ¯uxes and not too high pressures. In general, however, some of the simplifying assumptions in these correlations have to be revisited (for a more detailed discussion, cf. [12,14]). The application of the principle of corresponding states by comparing the heat transfer data of dierent ¯uids at constant normalized pressure p ps =pc is a valuable tool in describing the results in a generalized way, as follows from Fig. 4. In practice, however, the heat transfer performance of dierent refrigerants should be known at constant saturation temperature Ts , in order to decide which one should be applied. The outcome will be dierent in both cases for most of the refrigerants, compare the lines for p 0:1 const and for Ts 0 C=const in the lower diagram of Fig. 2. In Fig. 5, the comparison is demonstrated with R143a, R134a and the equimolar R125/R134a-mixture (R407*). At constant normalized pressure p 0:07, the experimental results nearly coincide for moderate heat ¯uxes q410 kW/m2 (cf. the symbols in the left hand diagram). These measurements belonging to the temperature range ÿ 204Ts 40 C, the second comparison is made at Ts 0 or ÿ20 C, respectively, by interpolation from the diagrams in Fig. 4 (Fig. 5, middle, right). Now it is seen that the a-values are better for R143a than for R134a by approx. 67 or 100% at Ts ÿ20 or 0 C, resp., while the dierences for p 0:07 are smaller than 10% (symbols at q 5 kW/m2, on the left). In contrast to this, the two kinds of comparisons will yield the same result for refrigerants with small dierences between the vapour pressure curves in the normalized p , Ts -plot of Fig. 2, bottom, like R404A, R507 and R143a on the one hand, or R407C and R407* on the other. 3.2. Roughness and material of the heating wall In the predictive methods for the heat transfer coecient in nucleate boiling applied in practice, the in¯uence of the surface roughness of the heating wall is modelled by a single roughness parameter like Pa in Eq. (4) which originates from Stephan [15] (cf. also [16,17]). Various systematic investigations devoted to the in¯uence of roughness on bubble formation have come to the conclusion that the eect of roughness should be interpreted by further parameters of the micro-topography of the heating surface, which are characteristic for bubble formation (cf. e.g. [18±20]). Valuable tools for ®nding such parameters are a new stylus instrument and an evaluation procedure developed recently. By these means the topography of the emeried surface of a copper tube (D 4 mm) has been investigated, see Fig. 6. It was produced by 1000 parallel runs (0.5 mm long and 0.5 mm separated from each other) of the slim diamond
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Fig. 4. Relative dependence of the exponent n of qn and of the heat transfer coecient at an intermediate heat ¯ux q 20 kW/ m2 on the reduced saturation pressure p ps =pc (a) for various pure refrigerants, according to Bednar [28], Caplanis [29], KoÈster [9], (b) for two (nearly) azeotropic and two zeotropic mixtures [9]). Fig. 4. Relation entre l'exposant n d'a qn et le coecient de transfert de chaleur a pour un ¯ux thermique q = 20 kW/m2 pour la pression de saturation reÂduite p* = ps/pc (a) pour divers frigorigeÁnes purs, selon Bednar [28], Caplanis [29], KoÈster [9], (b) pour deux meÂlanges quasi azeÂotropiques et deux meÂlanges zeÂotropiques [9].
Fig. 5. ; q-Plots of three refrigerants at constant normalized saturation pressures p (left) and at constant saturation temperature Ts (middle, right). Fig. 5. a, Courbes q de trois frigorigeÁnes aÁ des pressions de saturation constantes normaliseÂes p* (en haut) et aÁ une tempeÂrature de saturation constante Ts (au milieu et en bas).
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
cone (radius: 1 mm; angle: 60 ) of the new stylus instrument without touching the surface. Various standardized roughness parameters evaluated from the measurements are listed in the table within Fig. 6. The new local analysis is demonstrated by the two diagrams for the same selected run. They show the pro®le of the surface together with envelope curves produced by virtual balls of dierent radii RK (2.5 or 0.25 mm) gliding over the pro®le (note the great dierence in the scales of the run for the pro®le departure and the gauge length). The regions between two neighbouring contacts of the pro®le and the envelope are classi®ed as cavities to produce potential active nucleation sites. From this, not only size distributions of characteristic features of the cavities can be derived, but also their relative distances. Furthermore, more and smaller cavities can be de®ned within the same region by diminishing the size of the balls which produce the envelope, thus taking into account that more and smaller cavities will get activated within a big cavity at higher saturation pressures and/or heat ¯uxes. (Example of Fig. 6: RK 2:5 mm: four cavities within shaded area; RK 0:25 mm: 14 cavities). Very recently, the new local analysis has been extended and applied to topographies, and envelope areas have been formed instead of the envelope curves of the diagrams in Fig. 6. This allows the de®nition of three dimensional features of the cavities and
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their two dimensional distribution on the heated surface [21]. The in¯uence of the wall material, entering Eq. (1) by the factor FWM , is another domain with poor quantitative knowledge, particularly with reference to local heat transfer. This may be highlighted by an example of twodimensional ®nite element calculations (FEM) in Fig. 7 for the heating wall of a (horizontal) mild steel tube with D 88:4 mm at pool boiling of n-hexane on the tube surface under low pressure (ps =pc 0:01; from [22]). The vigorous motion of the big bubbles produced at this low pressure and sliding along the tube surface enhances heat transfer near the ¯anks of the tube and diminishes the superheat TTE ÿ Ts by approx. 5 or 10%, compared with the bottom or top of the tube, respectively, cf. the experimental data (circles) and the calculation (FEM) in the upper diagram. With the commonly used assumption that the heat is ¯owing exclusively in the radial direction, the amount of the relative extent of this eect on the heat transfer coecient will be the same as on T (q qradial const T, symbols in the intermediate and the straight line in the lower diagram). In reality, however, the relative increase of near the ¯anks is much more pronounced (up to more than 50% over the top of the tube, cf. the solid line in the middle), because the favourable heat transfer conditions near the ¯anks cause the heat to ¯ow partially in the azimuthal
Fig. 6. Topography, standardized parameters and new local analysis of the roughness structure of an emeried copper tube with 4 mm diameter. Fig. 6. Topographie, parameÁtres harmoniseÂs et nouvelle analyse locale de la rugosite d'un tube en cuivre eÂmeÂrise avec un diameÁtre de 4 mm.
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direction through the tube wall and increase the radial heat ¯ux qrad near the ¯anks, as the two-dimensional FEM-calculation reveals (curve in the lower diagram). The slight inhomogeneity in the curve at ' 90 is the result of a stainless steel barrier soldered in the tube wall (closed bar) in order to reduce azimuthal heat ¯ow (particularly for measurements with the tube being heated only on the upper or lower half, respectively). Altogether, the in¯uence of the heat conduction in the wall Ð and hence the wall material Ð on the local heat transfer can be very pronounced and will be important for improvements of the performance of the evaporator, e.g. in eorts to enhance heat transfer. The in¯uence on the average heat transfer coecient, however, is comparatively small and amounts to not more than 1.3% in the example of Fig. 7 ( dashed and dot-dashed lines in the intermediate diagram).
3.3. Convective eects in tube bundles Within shell-and-tube evaporators, the additional convective ¯ow induced by bubbles and liquid streaming upward from the lower tubes of the tube bundle will enhance the heat transfer in comparison with single tubes, especially at small heat ¯uxes and low pressures, as is well known for pure substances. For binary mixtures, the enhancement will be even more pronounced and extended to higher heat ¯uxes because of the deterioration of heat transfer compared to pure liquids at nucleate boiling without additional convection. The eect of the additional convection within tube bundles has been simulated by bubble production on a heater below a horizontal test tube with big diameter (88.4 mm). The big tube was chosen in order to get a pronounced eect of the superimposed convective ¯ow along the tube surface [23]. The double logarithmic plot of the heat transfer coecient a2 on the upper tube (No. 2) in Fig. 8 demonstrates the eect of the additional ¯ow of bubbles on 2 at constant heat ¯ux q1 on the (simulated) lower tube (No. 1). It is seen that in the convective domain at small heat ¯uxes q2 the 2 -values with additional ¯ow of bubbles . are signi®cantly increased and are (nearly) independent of the heat ¯ux q2 , and . are only (very) slightly smaller for the mixture than for the pure component.
Fig. 7. n-Hexane boiling on a horizontal steel tube (D 88:4 mm) at p 0:011: local superheat TTE ÿ Ts of the wall, heat transfer coecient , and radial heat ¯ux qrad from FEM-calculations (qazi heat ¯ux in azimuthal direction). Fig. 7. Ebullition de n-hexane sur un tube en acier horizontal (D = 88,4 mm) ouÁ p* = 0,011 : surchaue locale TTE ± Ts de la paroi, coecient de transfert (de chaleur, et le ¯ux thermique radial qrad des calculs FEM (qazi = ¯ux thermique dans la direction azimutale).
Fig. 8. Heat transfer coecient 2m as function of the heat ¯ux q2 for n-butane or a mixture, resp., boiling on a horizontal steel tube (D 88:4 mm) with and without bubbles produced by the heat ¯ux q1 10:7 kW/m2 on a (simulated) tube below. Fig. 8. Coecient de transfert de chaleur a2m en fonction du ¯ux thermique q2 pour le n-butane ou un meÂlange respectivement, en eÂbullition sur un tube en acier horizontal (D = 88,4 mm) avec ou sans bulles produites par le ¯ux thermique q1 = 10,7 kW/m2 sur un tube (simuleÂ) dessous.
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
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Fig. 9. Deviation of calculated and measured heat transfer coecients 2;m with additional ¯ow of bubbles in the convective domain for pure hydrocarbons and mixtures [26]. Fig. 9. Ecart des coecients de transfert de chaleur a2m calculeÂs et mesureÂs avec un eÂcoulement suppleÂmentaire de bulles dans le domaine convectif pour les hydrocarbures purs et les meÂlanges [26].
In fully developed nucleate boiling, however, the additional bubbles are no longer favourable to heat transfer, and the deterioration of the heat transfer coef®cient of mixtures compared to the pure components remains unchanged. The experimental results for various hydrocarbons and mixtures at dierent pressures in the convective domain with small heat ¯uxes were compared with a calculation method developed by Fujita et al. [24] based on measurements with the former refrigerant R113 (C2F3Cl3) at comparatively low normalized saturation pressures and already successfully applied to our experiments with propane and n-hexane at pressures p 40:12, (cf. e.g. [25]). For higher pressures, however, increasing deviations occur between the calculation and the measurements. A new modi®cation of the calculation procedure has been developed for pure substances [26] replacing the one proposed by Goren¯o et al. [23], which represents all the measurements of pure hydrocarbons within 10% (Fig. 9, on the left), but somewhat too high heat transfer coecients are predicted for the mixtures (middle). This is caused by the fact that the vapour production with mixture boiling is smaller than for the pure components. Taking this into account by means of a model of SchoÈmann [27] and experiments of Bednar [28] and Bier, Schmidt [14], the errors are not higher than for the pure substances (diagram on the right), without any ®tting to the 2 -values of the mixtures. 4. Conclusions Some of the new results discussed above can be incorporated in the existing prediction methods in the near future, others are needed for the long term aim to develop a calculation procedure for the heat transfer coecient in nucleate boiling based on the heat and
mass transfer processes connected with bubble formation and motion. Acknowledgements The author thanks Dr.-Ing. Andrea Luke, Dr. Gerhard Herres, Dipl.-Ing. Martin Buschmeier, Dipl.-Ing. Ralf KoÈster, Dipl.-Ing. Paul Kaupmann for valuable contributions to the chapter about the new experimental results, and Dipl.-Ing. Elisabeth Danger, Dipl.-Ing. Untung Chandra for their assistance in the preparation of the manuscript.
References [1] Dhir VK. Nucleate and transition boiling heat transfer under pool and external ¯ow conditions. In: Proc. 9th Int. Heat Transfer Conf. vol. 1, Jerusalem, 1990. p. 129±55. [2] Lienhard JH. Snares of pool boiling research: putting our history to use, In: Proc. 10th Int. Heat Transfer Conf., vol. 1, Brighton, 1994. p. 333±48. [3] Goren¯o D, Luke A, Danger E. Interactions between heat transfer and bubble formation in nucleate boiling. In: Proc. 11th Int. Heat Transfer Conf., vol. 1, Kyongju, 1998. p. 149±74. [4] Auracher H, Kenning DBR. Special issue on new developments in pool boiling. Int J Refrig 1997;20:533±622. [5] Goren¯o D. BehaÈltersieden (Sieden bei freier Konvektion). 8th ed. Abschn. Hab VDI-WaÈrmeatlas. Berlin, Springer 1997. [6] Goren¯o D. Pool boiling. In: VDI Heat Atlas, 1993 (chapter Ha). [7] Stephan K, Preusser P. Heat transfer and critical heat ¯ux in pool boiling of binary and ternary mixtures. Ger Chem Engng 1979;2:161±9. [8] SchluÈnder EU. UÈber den WaÈrmeuÈbergang bei der Blasenverdampfung von Gemischen. vt Verfahrenstechnik 1982;16:692±98.
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[9] KoÈster, R., Phasengleichgewicht und WaÈrmeuÈbergang beim Sieden von GemischkaÈltemitteln. Diss. UniversitaÈt Paderborn 2000, in preparation. [10] Goren¯o D, Goetz J, Bier K. Vorschlag fuÈr eine Standardapparatur zur Messung des WaÈrmeuÈbergangs beim Blasensieden. WaÈrme-und StouÈbertragung 1982;16:69±78. [11] Goren¯o D, Fath W. Heat transfer in pool boiling on the outside of ®nned tubes at high saturation pressures. In: Proc. 17th Int. Congr. Refrig., vol. B, Wien, 1987. p. 955±60. [12] Goren¯o D, KoÈster R. Pool boiling heat transfer from horizontal tubes to mixtures. In: Convective ¯ow and pool boiling. Philadelphia: Taylor & Francis, 1999. p. 3±22. [13] KoÈster R, Herres G, Kaupmann P, HuÈbner P. In¯uence of the heat ¯ux in mixture boiling: experiments and correlations. Int J Refrig 1997;20:598±605. [14] Bier K, Schmidt J. Bubble formation with pool boiling of pure liquids and binary ¯uid mixtures. In: 2nd Europ. Therm. Sciences Conf., vol. 1, Rome, 1996. 1661±8. [15] Stephan K. Beitrag zur Termodynamik des WaÈrmeuÈbergangs beim Sieden. Abh. d. Deutsch. KaÈltetechn. Ver., no. 18, 1963. [16] Nishikawa K, Fujita Y, Ohta H, Hidaka S. Eect of the surface roughness on the nucleate boiling heat transfer over the wide range of pressure. In: Proc. 7th Int. Heat Transfer Conf., vol. 4, MuÈnchen, 1982. p. 61±6. [17] Luke A, Goren¯o D. Pool boiling heat transfer from horizontal tubes with dierent surface roughness. In: Proc. EUROTHERM Seminar No. 48, Pool Boiling 2, Paderborn, 1996. p. 55±64. [18] Tanes MY. Zum Ein¯uû der Ober¯aÈchenbeschaenheit der Heiz¯aÈche auf den WaÈrmeuÈbergang beim Blasensieden. Diss. UniversitaÈt Karlsruhe (TH), 1976. [19] Knabe V. Zum Ein¯uû der Heiz¯aÈchenrauhigkeit auf den WaÈrmeuÈbergang und die maximale WaÈrmestromdichte beim Blasensieden; DKV-Forschungsbericht No. 10. Diss. UniversitaÈt Paderborn, 1984.
[20] Luke A. Beitrag zum Ein¯uû der Mikrostruktur von Heiz¯aÈchen auf den WaÈrmeuÈbergang beim Blasensieden. Diss. UniversitaÈt Paderborn, 1996. [21] Luke A, BaumhoÈgger E, Scheunemann P. 3-dimensional description of the microstructure of heated surfaces in nucleate pool boiling. In: Proc. Boiling 2000 Conf., vol. 1, Anchorage, 2000. New York: Begell House. p. 136±51. [22] Kaupmann P. Durchmesserein¯uû und oÈrtlicher WaÈrmeuÈbergang beim Blasensieden an horizontalen Stahlrohren. Diss. UniversitaÈt Paderborn, 1999. [23] Goren¯o D, Buschmeier M, Kaupmann P. Heat transfer from a horizontal tube to boiling binary mixtures with superimposed convective ¯ow. In: Convective ¯ow boiling, Washington (DC): Taylor & Francis, 1996, p. 265±70. [24] Fujita Y, Ohta H, Hidaka S, Nishikawa K, Nucleate boiling heat transfer on horizontal tubes in bundles. In: Proc. 8th Int. Heat Transfer Conf., vol. 5, San Francisco, 1986. p. 2131±6. [25] Buschmeier M, Sokol P, Pinto AD, Goren¯o D. Pool boiling heat transfer of propane/n-butane mixtures on a single tube with superimposed convective ¯ow of bubbles or liquid. In: Proc. 10th Int. Heat Transfer Conf., vol. 5, Brighton, 1994. p. 69±74. [26] Buschmeier M. Zum WaÈrmeuÈbergang beim Blasensieden von Propan/n-Butan-Gemischen an einem horizontalen Verdampferrohr mit QueranstroÈmung. Diss. UniversitaÈt Paderborn, 1999. [27] SchoÈmann H. Beitrag zum Ein¯uû der Heiz¯aÈchenrauhigkeit auf den WaÈrmeuÈbergang beim Blasensieden. Diss. UniversitaÈt Paderborn, 1994. [28] Bednar WH. WaÈrmeuÈbertragung beim Blasensieden von binaÈren Kohlenwasserstogemischen. Diss. UniversitaÈt Karlsruhe (TH), 1993. [29] Caplanis S. WaÈrmeuÈbertragung und Blasenbildung an Hochleistungs-Verdampferrohren. Diss. UniversitaÈt Paderborn, 1997.
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State of the art in pool boiling heat transfer of new refrigerants Dieter Goren¯o * WaÈrme- und KaÈltetechnik, UniversitaÈt Paderborn, Germany Dedicated to Professor Dr.-Ing. Dr. h.c. mult. Karl Stephan on the occasion of his 70th birthday Received 31 May 2000; received in revised form 8 June 2000; accepted 8 June 2000
Abstract The predictive methods for the calculation of the heat transfer coecient with pool boiling are important tools for the optimum design of the evaporator and for the successful operation of refrigeration units. The method given in the VDI Heat Atlas is discussed as an example of the currently available methods/ and results of recent experimental investigations on nucleate boiling of partly ¯uorinated hydrocarbons (HFCs) and of hydrocarbons (HCs) are added covering those parts where the predictive methods should be improved, namely boiling of mixtures, in¯uence of surface structure and material of the heating wall, and in¯uence of additional ¯ow of bubbles and liquid in tube bundles. # 2000 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Heat transfer; Pool boiling; Refrigerants; Replacement; HFC; Hydrocarbon; Heat transfer coecient; Survey
Etat du calcul pour le transfert de chaleur en eÂbullition libre de nouveaux frigorigeÁnes ReÂsume Les meÂthodes preÂvisionnelles permettant le calcul du coecient de transfert de chaleur a en eÂbullition libre sont des outils importants dans le domaine de la conception optimale de l'eÂvaporateur et le bon fonctionnement des groupes frigori®ques. La meÂthode donneÂe dans le VDI Heat Atlas est examineÂe en tant qu'exemple d'une meÂthode disponible actuellement ; l'auteur couvre eÂgalement les eÂtudes expeÂrimentales reÂcentes sur l'eÂbullition nucleÂeÂe des hydrocarbures partiellement ¯uoreÂs (HFC) et les hydrocarbures (HC), donnant des aspects des meÂthodes preÂvisionnelles qui devraient eÃtre ameÂlioreÂs, c'est-aÁ-dire l'eÂbullition des meÂlanges, l'in¯uence de la structure super®cielle et le mateÂriau de la paroi chauante, et l'in¯uence d'un eÂcoulement suppleÂmentaire de bulles et de ¯uide dans les faisceaux de tubes. # 2000 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : Transfert de chaleur ; Ebullition libre ; FrigorigeÁnes ; Substitut ; HFC ; Hydrocarbure ; Coecient de chaleur ; EnqueÃte
1. Introduction One of the important features for the successful operation of a refrigeration unit is the heat transfer * Tel.: +49-5251-60-2393; fax: +49-5251-60-3522. E-mail address: [email protected] (D. Goren¯o).
performance of the refrigerant within the evaporator. The optimum design of the evaporator depends on the correct evaluation of the nucleate boiling and the convective contributions to heat transfer. This is particularly important when new refrigerants and refrigerant mixtures are being introduced to replace the former working ¯uids with their negative eects on the atmosphere.
0140-7007/01/$20.00 # 2000 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00046-3
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
In the following, heat transfer within shell-and-tube evaporators used in medium or big refrigeration units will be discussed, and the prediction method given in the VDI Heat Atlas will be taken as an example for the methods available in literature. For plain tubes and pure ¯uids, the in¯uence of heat ¯ux, saturation pressure and thermophysical properties of the boiling liquid are predicted already quite well with various calculation methods. In the case of mixtures, prediction is worse because heat and mass transfer near the heated wall are more complex and because less experimental data exist in the literature. For the comparatively low saturation pressures used in refrigeration applications, however, and for the moderate temperature glides occuring with the mixtures to replace R22, R502 and R13B1, the situation is not so bad, as will be shown by new measurements with binary and ternary mixtures of partly ¯uorinated hydrocarbons (HFCs). The parts of the predictive methods which should be improved are the in¯uence of the surface structure and material of the heating wall and the in¯uence of additional ¯ow of bubbles and liquid in tube bundles. Also for these domains experimental results in pool boiling will be discussed which should be incorporated in the prediction methods in the future.
FWR Pa =Rao 2=15 and FWM lc=lo o co 1=4
4
The in¯uence of the thermophysical properties of the boiling liquid is contained in the reference value 0 under the reference conditions: qo 20 kW/m2, po 0:1, lo , o , co thermal conductivity, density, or speci®c heat respectively of copper, and Pao 0:4 mm=mean roughness height of the heating surface [according to the new international standard DIN EN ISO 4287 (10.98)]. This implies that o must be determined by experiment or calculated independently of Eq. (1). In the latter case, the correlation of Stephan and Preusser [7] is recommended for pure ¯uids, and the approach of SchluÈnder [8] for mixtures of new refrigerants: ÿ id = 0 1 Tph ÿ Ts =Tid
5
with id q=Tid and Tid Sxj Tj
6
7
x, y molar fraction of liquid or vapour, mass transfer coecient, , hv density or heat of vaporization of the liquid, B ®tting parameter [because of the poor knowledge of , also (B= ) may be taken for ®tting]. The mean heat transfer coecient ev of the evaporator is calculated from a1 for a single plain tube by ev = 1 f geometry of single heater and whole apparatus; effects of impurities operating conditions
8
3. Discussion of new experimental results In the following, new results on mixture boiling, roughness and material of the heating wall, and on convective eects in tube bundles will be highlighted.
1
3.1. Pool boiling of new refrigerant mixtures
2
Heat transfer with pool boiling of the new refrigerants R134a(CH2F.CF3), R143a(CH3.CF3), R125(CHF2.CF3), R32(CH2F2), and their mixtures has been investigated
with n n p 0:9 ÿ 0:3p0:3
3
ÿ Tph ÿ Ts STsj xj ÿ yj 1 ÿ exp ÿBq= hv
A theoretically consistent calculation method for the heat transfer coecient in nucleate boiling, which should be based on the physical phenomena connected with vapour bubbles growing, departing and sliding on the wall and with the interactions of bubbles and of neighbouring nucleation sites within the microstructure of the heating surface does not yet exist, despite the increasing number of papers on the subject in the recent past (cf. the literature reviews by Dhir [1], Lienhard [2], Goren¯o et al. [3], and Auracher and Kenning [4]). Instead, the predictive methods for available in the literature at present are empirical or semiempirical, especially for heat transfer conditions relevant in practice. In the VDI Heat Atlas method [5,6], a relationship for a reduced heat transfer coecient 1 = 0 on a single plain tube is established in which the relative in¯uences of the main groups of variables on are treated separately by: Fq for the heat ¯ux, Fp for the saturation pressure ps (in terms of p ps =pc , pc pressure in the critical state), FWR and FWM for the microstructure or material, respectively, of the heating surface,
Fq q=qo n ;
Fp 1:2p0:27 2:5p p = 1 ÿ p
and
2. Prediction of nucleate boiling heat transfer
1 = 0 Fq Fp FWR FWM
7
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D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
over wide ranges of heat ¯ux and saturation pressure, together with the vapour liquid equilibrium (VLE) and densities (cf. e.g. KoÈster [9]). In Fig. 1, the saturation temperatures Ts (dot±dashed lines in the triangle diagram) and the temperature glide Tbp of Ts for total evaporation (solid lines) are shown for the ternary system R125, R143a, R134a at atmospheric pressure, as an example. It can be seen that there is indeed no temperature glide with the commercial azeotrope R507 at p=1bar (p*=0.027) and that this holds fairly well throughout the pressure range (cf. the table in Fig. 1). The ternary mixture R404A also displays nearly azeotropic behaviour (Tbp < 1 K, cf. triangle diagram and table), while the maximum temperature glides at p=1 bar, Tbp 5:4 or 4.9 K, are found for the two binaries with the high boiling R134a, near the equimolar compositions. In the so called standard apparatus for pool boiling heat transfer measurements developed some years ago [10,11], we investigated the (approximately) equimolar binary of R125 and R134a (and gave it the internal abbreviation R407*) at pool boiling on a horizontal copper tube with emeried surface (Pa 0:34 mm),
. because it is the mixture with the maximum temperature glide of the whole ternary system (approx.), . because its vapour pressure curve is almost the same as for R22 throughout the temperature range important for refrigeration (cf. Fig. 2, top), and . because the temperature glide is only slightly smaller than for the commercial ternary R407C (cf. the table in Fig. 1). The results in Fig. 3 agree with the well known behaviour of mixtures (and pure liquids) in nucleate boiling on horizontal copper tubes with emeried surface (cf. e.g. Goren¯o and KoÈster [12]): . marked increase of with rising heat ¯ux q and saturation pressure ps (in terms of p ps =pc ), . straight interpolation lines for constant pressure in double logarithmic plots of over q and . diminishing increase of with q at p=const with rising pressure. In Fig. 4, the relative dependence of on the heat ¯ux q Ð in terms of the exponent n from qn Ð and on the pressure p* according to Eq. (2) or (3), resp., is compared with measurements for (a) pure refrigerants and (b) mixtures. As is known from comparisons with
Fig. 1. Saturation temperatures Ts and glide Tbp of Ts for total evaporation of the ternary system R125/R143a/R134a. Fig. 1. TempeÂratures de saturation Ts et glissement de tempeÂrature Tbp de Ts pour l'eÂvaporation totale du systeÁme ternaire R125/R143a/R134a.
Fig. 2. Vapour pressure curves of refrigerants. Fig. 2. Courbes des pressions de vapeur de frigorigeÁnes.
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
Fig. 3. Heat transfer coecient over the heat ¯ux q for pool boiling of a R125/R134a-mixture on a horizontal copper tube at various saturation pressures. Fig. 3. Coecient de transfert de chaleur a pour le ¯ux thermique lors de l'eÂbullition libre d'un meÂlange de R125 et de R134a sur un tube en cuivre horizontal, pour diverses pressions de saturation.
other new measurements in recent years (cf. e.g. KoÈster et al. [13]), Eqs. (2) and (3) are a somewhat conservative approach for pure substances at intermediate and high heat ¯uxes and pressures (q > 10 kW/m2 and ps > 0:1pc ). The results for the azeotrope R507 (squares in Fig. 4b) agree with the data for the pure refrigerants as can be seen from analogous deviations of the squares in Fig. 4b as of all symbols in Fig. 4a from the Heat Atlas lines for pure substances. This was to be expected for azeotropic mixtures without shift of the composition between vapour and liquid. The relative increase of with q and p for the nearly azeotropic mixture R404A is already somewhat smaller, particularly at higher pressures (circles in Fig. 4b). For the zeotropic mixtures R407C and R407*, however, the relative increase of a with q and p is signi®cantly smaller than for the pure refrigerants (cf. the triangles in Fig. 4b). This is due to the depletion of the lower boiling component(s) and subsequent increase of the local saturation temperature in the liquid layer near the heating wall. At low pressures p 40:1, important for evaporators of refrigerants, the eect gets smaller despite the increasing temperature glide Tbp and shift of composition xy, see Fig. 4b and the table and small diagram in Fig. 1. It seems that the more pronounced separation of the components at low pressures is less than predicted by the phase equilibrium [14] and that it is compensated to a large extent by the liquid turbulence in the boundary layer due to the vigorous motion of the rising bubbles after detachment from the tube surface.
9
Calculations of the a-values according to Eqs. (5)±(7) agree well with the measurements for these comparatively narrow boiling refrigerant mixtures, especially at intermediate heat ¯uxes and not too high pressures. In general, however, some of the simplifying assumptions in these correlations have to be revisited (for a more detailed discussion, cf. [12,14]). The application of the principle of corresponding states by comparing the heat transfer data of dierent ¯uids at constant normalized pressure p ps =pc is a valuable tool in describing the results in a generalized way, as follows from Fig. 4. In practice, however, the heat transfer performance of dierent refrigerants should be known at constant saturation temperature Ts , in order to decide which one should be applied. The outcome will be dierent in both cases for most of the refrigerants, compare the lines for p 0:1 const and for Ts 0 C=const in the lower diagram of Fig. 2. In Fig. 5, the comparison is demonstrated with R143a, R134a and the equimolar R125/R134a-mixture (R407*). At constant normalized pressure p 0:07, the experimental results nearly coincide for moderate heat ¯uxes q410 kW/m2 (cf. the symbols in the left hand diagram). These measurements belonging to the temperature range ÿ 204Ts 40 C, the second comparison is made at Ts 0 or ÿ20 C, respectively, by interpolation from the diagrams in Fig. 4 (Fig. 5, middle, right). Now it is seen that the a-values are better for R143a than for R134a by approx. 67 or 100% at Ts ÿ20 or 0 C, resp., while the dierences for p 0:07 are smaller than 10% (symbols at q 5 kW/m2, on the left). In contrast to this, the two kinds of comparisons will yield the same result for refrigerants with small dierences between the vapour pressure curves in the normalized p , Ts -plot of Fig. 2, bottom, like R404A, R507 and R143a on the one hand, or R407C and R407* on the other. 3.2. Roughness and material of the heating wall In the predictive methods for the heat transfer coecient in nucleate boiling applied in practice, the in¯uence of the surface roughness of the heating wall is modelled by a single roughness parameter like Pa in Eq. (4) which originates from Stephan [15] (cf. also [16,17]). Various systematic investigations devoted to the in¯uence of roughness on bubble formation have come to the conclusion that the eect of roughness should be interpreted by further parameters of the micro-topography of the heating surface, which are characteristic for bubble formation (cf. e.g. [18±20]). Valuable tools for ®nding such parameters are a new stylus instrument and an evaluation procedure developed recently. By these means the topography of the emeried surface of a copper tube (D 4 mm) has been investigated, see Fig. 6. It was produced by 1000 parallel runs (0.5 mm long and 0.5 mm separated from each other) of the slim diamond
10
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
Fig. 4. Relative dependence of the exponent n of qn and of the heat transfer coecient at an intermediate heat ¯ux q 20 kW/ m2 on the reduced saturation pressure p ps =pc (a) for various pure refrigerants, according to Bednar [28], Caplanis [29], KoÈster [9], (b) for two (nearly) azeotropic and two zeotropic mixtures [9]). Fig. 4. Relation entre l'exposant n d'a qn et le coecient de transfert de chaleur a pour un ¯ux thermique q = 20 kW/m2 pour la pression de saturation reÂduite p* = ps/pc (a) pour divers frigorigeÁnes purs, selon Bednar [28], Caplanis [29], KoÈster [9], (b) pour deux meÂlanges quasi azeÂotropiques et deux meÂlanges zeÂotropiques [9].
Fig. 5. ; q-Plots of three refrigerants at constant normalized saturation pressures p (left) and at constant saturation temperature Ts (middle, right). Fig. 5. a, Courbes q de trois frigorigeÁnes aÁ des pressions de saturation constantes normaliseÂes p* (en haut) et aÁ une tempeÂrature de saturation constante Ts (au milieu et en bas).
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
cone (radius: 1 mm; angle: 60 ) of the new stylus instrument without touching the surface. Various standardized roughness parameters evaluated from the measurements are listed in the table within Fig. 6. The new local analysis is demonstrated by the two diagrams for the same selected run. They show the pro®le of the surface together with envelope curves produced by virtual balls of dierent radii RK (2.5 or 0.25 mm) gliding over the pro®le (note the great dierence in the scales of the run for the pro®le departure and the gauge length). The regions between two neighbouring contacts of the pro®le and the envelope are classi®ed as cavities to produce potential active nucleation sites. From this, not only size distributions of characteristic features of the cavities can be derived, but also their relative distances. Furthermore, more and smaller cavities can be de®ned within the same region by diminishing the size of the balls which produce the envelope, thus taking into account that more and smaller cavities will get activated within a big cavity at higher saturation pressures and/or heat ¯uxes. (Example of Fig. 6: RK 2:5 mm: four cavities within shaded area; RK 0:25 mm: 14 cavities). Very recently, the new local analysis has been extended and applied to topographies, and envelope areas have been formed instead of the envelope curves of the diagrams in Fig. 6. This allows the de®nition of three dimensional features of the cavities and
11
their two dimensional distribution on the heated surface [21]. The in¯uence of the wall material, entering Eq. (1) by the factor FWM , is another domain with poor quantitative knowledge, particularly with reference to local heat transfer. This may be highlighted by an example of twodimensional ®nite element calculations (FEM) in Fig. 7 for the heating wall of a (horizontal) mild steel tube with D 88:4 mm at pool boiling of n-hexane on the tube surface under low pressure (ps =pc 0:01; from [22]). The vigorous motion of the big bubbles produced at this low pressure and sliding along the tube surface enhances heat transfer near the ¯anks of the tube and diminishes the superheat TTE ÿ Ts by approx. 5 or 10%, compared with the bottom or top of the tube, respectively, cf. the experimental data (circles) and the calculation (FEM) in the upper diagram. With the commonly used assumption that the heat is ¯owing exclusively in the radial direction, the amount of the relative extent of this eect on the heat transfer coecient will be the same as on T (q qradial const T, symbols in the intermediate and the straight line in the lower diagram). In reality, however, the relative increase of near the ¯anks is much more pronounced (up to more than 50% over the top of the tube, cf. the solid line in the middle), because the favourable heat transfer conditions near the ¯anks cause the heat to ¯ow partially in the azimuthal
Fig. 6. Topography, standardized parameters and new local analysis of the roughness structure of an emeried copper tube with 4 mm diameter. Fig. 6. Topographie, parameÁtres harmoniseÂs et nouvelle analyse locale de la rugosite d'un tube en cuivre eÂmeÂrise avec un diameÁtre de 4 mm.
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D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
direction through the tube wall and increase the radial heat ¯ux qrad near the ¯anks, as the two-dimensional FEM-calculation reveals (curve in the lower diagram). The slight inhomogeneity in the curve at ' 90 is the result of a stainless steel barrier soldered in the tube wall (closed bar) in order to reduce azimuthal heat ¯ow (particularly for measurements with the tube being heated only on the upper or lower half, respectively). Altogether, the in¯uence of the heat conduction in the wall Ð and hence the wall material Ð on the local heat transfer can be very pronounced and will be important for improvements of the performance of the evaporator, e.g. in eorts to enhance heat transfer. The in¯uence on the average heat transfer coecient, however, is comparatively small and amounts to not more than 1.3% in the example of Fig. 7 ( dashed and dot-dashed lines in the intermediate diagram).
3.3. Convective eects in tube bundles Within shell-and-tube evaporators, the additional convective ¯ow induced by bubbles and liquid streaming upward from the lower tubes of the tube bundle will enhance the heat transfer in comparison with single tubes, especially at small heat ¯uxes and low pressures, as is well known for pure substances. For binary mixtures, the enhancement will be even more pronounced and extended to higher heat ¯uxes because of the deterioration of heat transfer compared to pure liquids at nucleate boiling without additional convection. The eect of the additional convection within tube bundles has been simulated by bubble production on a heater below a horizontal test tube with big diameter (88.4 mm). The big tube was chosen in order to get a pronounced eect of the superimposed convective ¯ow along the tube surface [23]. The double logarithmic plot of the heat transfer coecient a2 on the upper tube (No. 2) in Fig. 8 demonstrates the eect of the additional ¯ow of bubbles on 2 at constant heat ¯ux q1 on the (simulated) lower tube (No. 1). It is seen that in the convective domain at small heat ¯uxes q2 the 2 -values with additional ¯ow of bubbles . are signi®cantly increased and are (nearly) independent of the heat ¯ux q2 , and . are only (very) slightly smaller for the mixture than for the pure component.
Fig. 7. n-Hexane boiling on a horizontal steel tube (D 88:4 mm) at p 0:011: local superheat TTE ÿ Ts of the wall, heat transfer coecient , and radial heat ¯ux qrad from FEM-calculations (qazi heat ¯ux in azimuthal direction). Fig. 7. Ebullition de n-hexane sur un tube en acier horizontal (D = 88,4 mm) ouÁ p* = 0,011 : surchaue locale TTE ± Ts de la paroi, coecient de transfert (de chaleur, et le ¯ux thermique radial qrad des calculs FEM (qazi = ¯ux thermique dans la direction azimutale).
Fig. 8. Heat transfer coecient 2m as function of the heat ¯ux q2 for n-butane or a mixture, resp., boiling on a horizontal steel tube (D 88:4 mm) with and without bubbles produced by the heat ¯ux q1 10:7 kW/m2 on a (simulated) tube below. Fig. 8. Coecient de transfert de chaleur a2m en fonction du ¯ux thermique q2 pour le n-butane ou un meÂlange respectivement, en eÂbullition sur un tube en acier horizontal (D = 88,4 mm) avec ou sans bulles produites par le ¯ux thermique q1 = 10,7 kW/m2 sur un tube (simuleÂ) dessous.
D. Goren¯o / International Journal of Refrigeration 24 (2001) 6±14
13
Fig. 9. Deviation of calculated and measured heat transfer coecients 2;m with additional ¯ow of bubbles in the convective domain for pure hydrocarbons and mixtures [26]. Fig. 9. Ecart des coecients de transfert de chaleur a2m calculeÂs et mesureÂs avec un eÂcoulement suppleÂmentaire de bulles dans le domaine convectif pour les hydrocarbures purs et les meÂlanges [26].
In fully developed nucleate boiling, however, the additional bubbles are no longer favourable to heat transfer, and the deterioration of the heat transfer coef®cient of mixtures compared to the pure components remains unchanged. The experimental results for various hydrocarbons and mixtures at dierent pressures in the convective domain with small heat ¯uxes were compared with a calculation method developed by Fujita et al. [24] based on measurements with the former refrigerant R113 (C2F3Cl3) at comparatively low normalized saturation pressures and already successfully applied to our experiments with propane and n-hexane at pressures p 40:12, (cf. e.g. [25]). For higher pressures, however, increasing deviations occur between the calculation and the measurements. A new modi®cation of the calculation procedure has been developed for pure substances [26] replacing the one proposed by Goren¯o et al. [23], which represents all the measurements of pure hydrocarbons within 10% (Fig. 9, on the left), but somewhat too high heat transfer coecients are predicted for the mixtures (middle). This is caused by the fact that the vapour production with mixture boiling is smaller than for the pure components. Taking this into account by means of a model of SchoÈmann [27] and experiments of Bednar [28] and Bier, Schmidt [14], the errors are not higher than for the pure substances (diagram on the right), without any ®tting to the 2 -values of the mixtures. 4. Conclusions Some of the new results discussed above can be incorporated in the existing prediction methods in the near future, others are needed for the long term aim to develop a calculation procedure for the heat transfer coecient in nucleate boiling based on the heat and
mass transfer processes connected with bubble formation and motion. Acknowledgements The author thanks Dr.-Ing. Andrea Luke, Dr. Gerhard Herres, Dipl.-Ing. Martin Buschmeier, Dipl.-Ing. Ralf KoÈster, Dipl.-Ing. Paul Kaupmann for valuable contributions to the chapter about the new experimental results, and Dipl.-Ing. Elisabeth Danger, Dipl.-Ing. Untung Chandra for their assistance in the preparation of the manuscript.
References [1] Dhir VK. Nucleate and transition boiling heat transfer under pool and external ¯ow conditions. In: Proc. 9th Int. Heat Transfer Conf. vol. 1, Jerusalem, 1990. p. 129±55. [2] Lienhard JH. Snares of pool boiling research: putting our history to use, In: Proc. 10th Int. Heat Transfer Conf., vol. 1, Brighton, 1994. p. 333±48. [3] Goren¯o D, Luke A, Danger E. Interactions between heat transfer and bubble formation in nucleate boiling. In: Proc. 11th Int. Heat Transfer Conf., vol. 1, Kyongju, 1998. p. 149±74. [4] Auracher H, Kenning DBR. Special issue on new developments in pool boiling. Int J Refrig 1997;20:533±622. [5] Goren¯o D. BehaÈltersieden (Sieden bei freier Konvektion). 8th ed. Abschn. Hab VDI-WaÈrmeatlas. Berlin, Springer 1997. [6] Goren¯o D. Pool boiling. In: VDI Heat Atlas, 1993 (chapter Ha). [7] Stephan K, Preusser P. Heat transfer and critical heat ¯ux in pool boiling of binary and ternary mixtures. Ger Chem Engng 1979;2:161±9. [8] SchluÈnder EU. UÈber den WaÈrmeuÈbergang bei der Blasenverdampfung von Gemischen. vt Verfahrenstechnik 1982;16:692±98.
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