Document aBL7bj9NJDYy33mqe4Q45VjOY

60 CHAPTER 4 1965 Guide And. Data Book Table, 7 .. ... Equations for Boiling Heat Transfer* L Free Convection Boiling, or boiling without*bubbles for low hi and NorNe* < 10*. (All properties based oa liquid state).' a. Vertical Submerged Surface (characteristiclength -- height) b.'`Horizontal Submerged Surface '*-! c. Simplified Equation for Refrigerant 12 (horizontal .tube) (1 <U < 4F, t.65F) . ; . *!;..v d. Simplified Equation for Refrigerant 22 (horizontal tub*e)^ (1 < At <4F, t 65F) . "i-- : i. e. Simplified Equation for Water (horizontal plate) . (0.1 < At < 3 F, P. - l.atnv),'.. * II. Nucleate Boiling,'or boiling with bubbles.'-- a. Initial-Bubble Diameter b. Maximum Bubble Diameter; 0 is the angle of contact! meas^' ured within the liquid ., ',! JiV., 14 22. _ .. A = 22 "--A1- 12 :'r " - 23..... : A -i /XH,'- 23. r /. o., - (1) (?) * (3) (4) (5) .(6) (7) , General .Correlation according to Rohseoow,, K8R*r24 ADS ti (8) d. General Correlation according to Kutateladze - c. General Correlation according to-Forster and Zuber; Ap is difference in pressure at saturation corresponding to At,. f. Simplified Equation for Refrigerant 12 (horizontal tube) (5 < A1 < 30 F, < 66 F) ' g. Simplified Equation for Refrigerant 22 (horizontal' tube) " (5 <At <20F,t 65F) Vh. Simplified Equation for Water (horizontal plate) .(13 F < At < 30 F, P - 1 atm.) * ; ' !*.1 V, HI: Forced Convection with Boiling (Based on data for Refriger ant 12 and 22 inside horizontaTtubes).. . ' ,}, . ... -,ir a. For exit vapor fractions below 85%-. 10* < Nt*K, < 2 X 10 25 ' AP, 22'., 22 A .= 16At`-' A - 6.1AP-* A - 0.17At* ;,W .. A.:-.;! a: rT cm ' ' (12) ... 03) i - (14) 05) ,2 X 10" < Ng*Kf < 1.5.X 10"' .w; k, ''"(16) b. For exit superheat up to 11F and inlet vapor fraction below 50%, * * . .;.*; * w " A. " Ecwtitmtfa tUa table ara appradmata, at beat.' nsca eaeSdestamki nltad before extrapeietiom to other eanditieoa are attempted. -, .. be influenced by many fmetore not epedfied here. Oripml referenoo (17) ^ due to surface tension, it; detaches and rises' through the liquid. The diameter at the momeot'of detachment'is given by* Equation 7, Table 7. These diameters'are'u^ed as characteris tic lengths in many of the equations which have been pro posed for correlating experimental data for.nucleate boiling.1*! No.equation has been, found .which provides a reasonably accurate correlation,of the gristing data in all .cases! Most of the difficulty originates from, the .dependence, ofi>the;heai transfer rate on the bubble population, .which in turn' figjwnHa' upon-the detailed., physical characteristics of,.the surface.' Three of .the. more commonly. ,used correlating } pgnwrinn^* developed' by Rohsenow,*4 Kutateladze, " and i Forster and Zuber," appear as Equations8,9;and KXm.Table|7. Simplified equations for Refrigerants 12 and-* 22, based on the experi ments ofanumberofinvestigatora**:*7'**'?'*9appear as Equa tions 11 and 12. Equation 13 is a siiriplifiKH equation for water at atmospheric pressure.! 1 . *(v *. Hooded Evaporators ; - i The use of the equations in -Table 7< for predicting heat transfer rates in flooded'evaporators" gives approximate re sults, atr best. One of.the reasons-(fpr this,is that.vapor entering Heat Transfer./- ^ tte evaporator, combined with vyor gnneratod withmthe 'may ..produce significant forced convection moiimpoaed on those due to nucleation. Nonunifonn two-pba*, vepor-liquid flow wittun the bundle of sbell-end-tube evaporators, or within the Uiiw3 of vertical-tube.flooded evaporators, is.also an unpor- of sapor generated by the bottom rowa of a tube bundle on the beat transfer coefficient for.the upper rows was Iowd by Myers and Kata fmprovement in coefficients for the urnier tube rows was greatest at low At where nucleation effects are lass pronounced. Other data for flooded tube bundles-' arc summarised by Hofmann. Cnrves typical of the performance of verticai tube natural circulation evaporators,'based on data for water, areBhown in Fig. 8. Low coefficients are obtained at low liquid levels due to insufficient liquid coverage of the heating surface.' The decrease in coefficient at high levels is due to an adverse eflect of hydrostatic head on the temperature difference and cireu- rate, similar effects have been noted in horizontal shefl- 61 Boiling with Forced Convection When boiling occurs'inside tubes, forced convection effects may exert considerable influence on the heat transfer rate. In general, higher coefficients are obtained, although they are accompanied by a drop in pressure which, decreases the net temperature `differenee'avaiiable for heat transfer. As evapo ration takes' place along the tube, various' two-phase' flow patterns may be encountered depending upon the fraction of vapor praent, the flow rate, and other variables.' A compre hensive review of heat transfer in twoiphase flow is given-by Collier.*7 * >' Tte variation in local-heat transfer coefficient for forced convection evaporation inside a horizontal tube is showir'm Fig/ 9. In*< these -teats; based on Anderson's: data for-R^ frigerant`22,** the outlet vapor fraction was varied while the change in vapor fraction was fired at Ax = 0.2. At low loads, the heat transfer coefficient varies very little with exit vapor fraction up to about it 0-8. At higher loads, however, the; coefficient increases with increases in vapor fraction due to the influence of higher vapor velocities and better surface wetting. The coefficient continues to-increase up to a leaving vapor fraction of about * 90* percent, at which point it decreases. sharply. It is believed that the.rapid drop-off in coefficient is \ due to insufficient liquid for wetting the tube walls. At 100 percent evaporation, the- coefficient approaches values, for single-phase gas convection. Tests by Witrig** and Seigel40 indicate a characteristic similar to that shown in Fig. 9. -Datafor forced convection .evaporation of refrigerants have been reported by Witxig,** Ashley,41 Davis,4* Pierre,4*'44 Johnston and Chaddock,41 Altman, Norris and Staub,44 and Wors0e-Schmidt.47 Ashley's tests were conducted with Re; frigerant 12 inside a 0.575 in. I.D. tube at a refrigerant tem perature of 40 F. Fig. 10 shows his results, together with an ^estimation of the performance of other tube diameters, ob tained by nggiiming that the heat transfer coefficient increases * as the mass velocity raised to the 0.8 power. These curves are meant only to indicate the trend, since the values are uncon firmed by tests. The effect of evaporating temperature on .average heat transfer coefficients is shown in Fig. ll'based on the data of Witzig with Refrigerant 12.** Similar results are reported by Davis.4* Bo* Pierre41-44 measured average coefficients with Refriger- . fig. 10.... Boiling Heat Transfer Coefficients for Refrigerant 12 Inside Horizontal Tubes*