1、5.1CHAPTER 5TWO-PHASE FLOWBoiling . 5.1Condensing 5.11Pressure Drop . 5.15Symbols . 5.20WO-phase flow is encountered extensively in the HVAC liquidalternately falls onto the surface and is repulsed by an explosiveburst of vapor.At sufficiently high surface temperatures, a stable vapor filmforms at t
2、he heater surface; this is the film boiling regime (regionsV and VI). Because heat transfer is by conduction (and some radi-ation) across the vapor film, the heater temperature is much higherthan for comparable heat flux densities in the nucleate boilingregime. The minimum film boiling (MFB) heat fl
3、ux (point b) is thelower end of the film boiling curve.Free Surface Evaporation. In region I, where surface tempera-ture exceeds liquid saturation temperature by less than a few degrees,no bubbles form. Evaporation occurs at the free surface by convec-tion of superheated liquid from the heated surfa
4、ce. Correlations ofheat transfer coefficients for this region are similar to those for fluidsunder ordinary natural convection Equations (T1.1) to (T1.4).Nucleate Boiling. Much information is available on boiling heattransfer coefficients, but no universally reliable method is availablefor correlati
5、ng the data. In the nucleate boiling regime, heat fluxdensity is not a single valued function of the temperature butdepends also on the nucleating characteristics of the surface, asshown by Figure 2 (Berenson 1962). The equations proposed for correlating nucleate boiling data canbe put in a form tha
6、t relates heat transfer coefficient h to temperaturedifference (ts tsat):h = constant(ts tsat)a(1)Exponent a is normally about 2 for a plain, smooth surface; its valuedepends on the thermodynamic and transport properties of the vaporand liquid. Nucleating characteristics of the surface, including th
7、esize distribution of surface cavities and wetting characteristics of thesurface/liquid pair, affect the value of the multiplying constant andthe value of a in Equation (1).In the following sections, correlations and nomographs for pre-dicting nucleate and flow boiling of various refrigerants are gi
8、ven.For most cases, these correlations have been tested for refrigerants(e.g., R-11, R-12, R-113, R-114) that are now identified as environ-mentally harmful and are no longer used in new equipment. Ther-mal and fluid characteristics of alternative refrigerants/refrigerantmixtures have recently been
9、extensively researched, and some cor-relations have been suggested.Stephan and Abdelsalam (1980) developed a statistical approachfor estimating heat transfer during nucleate boiling. The correlationEquation (T1.5) should be used with a fixed contact angle regardless of the fluid. Cooper (1984) propo
10、sed a dimensional cor-relation for nucleate boiling Equation (T1.6) based on analysis ofa vast amount of data covering a wide range of parameters. Thedimensions required are listed in Table 1. Based on inconclusiveevidence, Cooper suggested a multiplier of 1.7 for copper surfaces,to be reevaluated a
11、s more data came forth. Most other researcherse.g., Shah (2007) have found the correlation gives better agree-ment without this multiplier, and thus do not recommend its use.Gorenflo (1993) proposed a nucleate boiling correlation basedon a set of reference conditions and a base heat transfer coeffic
12、ientfor each fluid, and provided base heat transfer coefficients for manyfluids.In addition to correlations dependent on thermodynamic andtransport properties of the vapor and liquid, Borishansky et al.(1962), Lienhard and Schrock (1963), and Stephan (1992) docu-mented a correlating method based on
13、the law of correspondingstates. The properties can be expressed in terms of fundamentalmolecular parameters, leading to scaling criteria based on reducedpressure pr= p/pc, where pcis the critical thermodynamic pressurefor the coolant. An example of this method of correlation is shownin Figure 3. Ref
14、erence pressure p* was chosen as p* = 0.029pc. Thisis a simple method for scaling the effect of pressure if data are avail-able for one pressure level. It also is advantageous if the thermo-dynamic and particularly the transport properties used in severalequations in Table 1 are not accurately known
15、. In its present form,this correlation gives a value of a = 2.33 for the exponent in Equation(1) and consequently should apply for typical aged metal surfaces.There are explicit heat transfer coefficient correlations basedon the law of corresponding states for halogenated refrigerants(Danilova 1965)
16、, flooded evaporators (Starczewski 1965), andvarious other substances (Borishansky and Kosyrev 1966). Otherinvestigations examined the effects of oil on boiling heat transferfrom diverse configurations, including boiling from a flat plate(Stephan 1963), a 0.55 in. OD horizontal tube using an oil/R-1
17、2Fig. 2 Effect of Surface Roughness on Temperature in Pool Boiling of Pentane(Berenson 1962)Fig. 3 Correlation of Pool Boiling Data in Terms of Reduced PressureTwo-Phase Flow 5.3mixture (Tschernobyiski and Ratiani 1955), inside horizontal tubesusing an oil/R-12 mixture (Breber et al. 1980; Green and
18、 Furse1963; Worsoe-Schmidt 1959), and commercial copper tubing usingR-11 and R-113 with oil content to 10% (Dougherty and Sauer1974). Additionally, Furse (1965) examined R-11 and R-12 boilingover a flat horizontal copper surface.Table 1 Equations for Natural Convection Boiling Heat TransferDescripti
19、on References EquationsFree convection Jakob (1949, 1957) Nu = C(Gr)m(Pr)n(T1.1)Free convection boiling, or boiling without bubbles for low t and Gr Pr 108. All properties based on liquid state.Characteristic length scale for vertical surfaces is vertical height of plate or cylinder. For horizontal
20、surfaces, Lc= As/P, where Asis plate surface area and P is plate perimeter, is recommended.Vertical submerged surface Nu = 0.61(Gr)0.25(Pr)0.25(T1.2)Horizontal submerged surface Nu = 0.16(Gr)1/3(Pr)1/3(T1.3)Simplified equation for water h 80(t)1/3, where h is in Btu/hft2F and t is in F (T1.4)Nucleat
21、e boiling Stephan and Abdelsalam (1980)(T1.5)where Dd= 0.0208 with = 35.Cooper (1984) (T1.6)where h is in W/(m2K), q/A is in W/m2, and Rpis surface roughness in m (if unknown, use 1 m). Multiply h by 1.7 for copper surfaces (see text).Critical heat flux Kutateladze (1951)(T1.7)Zuber et al. (1962) Fo
22、r many liquids, KDvaries from 0.12 to 0.16; an average value of 0.13 is recommended.Minimum heat flux in film boiling from horizontal plateZuber (1959) (T1.8)Minimum heat flux in film boiling from horizontal cylindersLienhard and Wong (1964)(T1.9)where B = (2Lb/D)2and Minimum temperature difference
23、for film boiling from horizontal plateBerenson (1961) (T1.10)Film boiling from horizontal plate Berenson (1961) (T1.11)Film boiling from horizontal cylindersBromley (1950) (T1.12)Effect of superheating Anderson et al. (1966)Substitute(T1.13)Effect of radiation Incropera and DeWitt (2002)Quenching sp
24、heres Frederking and Clark (1962)Nu = 0.15(Ra)1/3for Ra 5 107(T1.14)where a = local accelerationGrg tstsatLc32-=hDdkl- 0.0546vl-0.5qDdAkltsat-0.67hfgDd2l2-0.248lvl-4.33=g lv-0.5h 55pr0.12 0.0912 ln Rp0.4343 ln pr0.55M0.5qA-0.67=qAvhfg-v2g lv-0.25KD=qA- 0 . 0 9 vhfgg lvlv+2-14=qA 0.6334B21 B 2+-0.250
25、.09vhfgglvlv+2-0.25=Lbg lv-0.5=tstsat0.127Lbvhfgkv-g lvlv+-2/3vg lv-1/3=h 0.425kv3vhfgg lvvtstsatLb-0.25=h 0.62kv3vhfgg lvvtstsatD-0.25=hfghfg10.4cpv,tstsathfg-+=hth34- ts4tsat4tstsat-+=RaD3g lvv2v- P rvhfgcpv,tstsat- 0 . 4+ag-1/3=5.4 2017 ASHRAE HandbookFundamentals Maximum Heat Flux and Film Boili
26、ngMaximum, or critical, heat flux and the film boiling region arenot as strongly affected by conditions of the heating surface as heatflux in the nucleate boiling region, making analysis of DNB and offilm boiling more tractable.Several mechanisms have been proposed for the onset of DNBsee Carey (199
27、2) for a summary. Each model is based on the sce-nario that a vapor blanket exists on portions of the heat transfer sur-face, greatly increasing thermal resistance. Zuber (1959) proposedthat these blankets may result from Helmholtz instabilities in col-umns of vapor rising from the heated surface; a
28、nother prominenttheory supposes a macrolayer beneath the mushroom-shaped bub-bles (Haramura and Katto 1983). In this case, DNB occurs when liq-uid beneath the bubbles is consumed before the bubbles depart andallow surrounding liquid to rewet the surface. Dhir and Liaw (1989)used a concept of bubble
29、crowding proposed by Rohsenow andGriffith (1956) to produce a model that incorporates the effect ofcontact angle. Sefiane (2001) suggested that instabilities near thetriple contact lines cause DNB. Fortunately, though significant dis-agreement remains about the mechanism of DNB, models usingthese di
30、ffering conceptual approaches tend to lead to predictionswithin a factor of 2.When DNB (point a in Figure 1) is assumed to be a hydrody-namic instability phenomenon, a simple relation Equation (T1.7)can be derived to predict this flux for pure, wetting liquids (Kutate-ladze 1951; Zuber et al. 1962).
31、 The dimensionless constant K var-ies from approximately 0.12 to 0.16 for a large variety of liquids.Kandlikar (2001) created a model for maximum heat flux explic-itly incorporating the effects of contact angle and orientation.Equation (T1.7) compares favorably to Kandlikars, and, becauseit is simpl
32、er, it is still recommended for general use. However, notethat this equation is valid when the end effects are unimportant.Carey (1992) provides correlations to calculate maximum heatflux for various geometries based on this equation. Surface wetta-bility, orientation, and roughness can affect DNB.
33、For orientationsother than upward facing, see Brusstar and Merte (1997) and How-ard and Mudawar (1999). Liquid subcooling increases maximumheat flux; see Elkessabgi and Lienhard (1998) for subcoolingseffects.Van Stralen (1959) found that, for liquid mixtures, DNB is a func-tion of concentration. As
34、discussed by Stephan (1992), the maximumheat flux always lies between the values of the pure components.Unfortunately, the relationship of DNB to concentration is not sim-ple, and several hypotheses e.g., McGillis and Carey (1996); Reddyand Lienhard (1989); Van Stralen and Cole (1979) have been putf
35、orward to explain the experimental data. For a more detailed over-view of mixture boiling, refer to Thome and Shock (1984).The minimum heat flux density (point b in Figure 1) in film boil-ing from a horizontal surface and a horizontal cylinder can be pre-dicted by Equation (T1.8). The factor 0.09 wa
36、s adjusted to fitexperimental data; values predicted by the analysis were approxi-mately 30% higher. The accuracy of Equation (T1.8) falls off rap-idly with increasing pr(Rohsenow et al. 1998). Berensons (1961)Equations (T1.10) and (T1.11) predict the temperature difference atminimum heat flux and h
37、eat transfer coefficient for film boiling ona flat plate. The minimum heat flux for film boiling on a horizontalcylinder can be predicted by Equation (T1.9). As in Equation(T1.8), the factor 0.633 was adjusted to fit experimental data.The heat transfer coefficient in film boiling from a horizontalsu
38、rface can be predicted by Equation (T1.11), and from a horizontalcylinder by Equation (T1.12) (Bromley 1950).Frederking and Clark (1962) found that, for turbulent film boil-ing, Equation (T1.13) agrees with data from experiments at reducedgravity (Jakob 1949, 1957; Kutateladze 1963; Rohsenow 1963;We
39、stwater 1963).Boiling/Evaporation in Tube BundlesIn horizontal tube bundles, flow may be gravity driven orpumped-assisted forced convection. In either case, subcooled liquidenters at the bottom. Sensible heat transfer and subcooled boilingoccur until the liquid reaches saturation. Net vapor generati
40、on thenstarts, increasing velocity and thus convective heat transfer. Nucle-ate boiling also occurs if heat flux is high enough. Brisbane et al.(1980) proposed a computational model in which a liquid/vapormixture moves up through the bundle, and vapor leaves at the topwhile liquid moves back down at
41、 the side of the bundle. Local heattransfer coefficients are calculated for each tube, considering localvelocity, quality, and heat flux. To use this model, correlations forlocal heat transfer coefficients during subcooled and saturated boilingwith flow across tubes are needed. Thome and Robinson (2
42、004) pre-sented a correlation that showed agreement with several data sets forsaturated boiling on plain tube bundles. Shah (2005, 2007) gave gen-eral correlations for local heat transfer coefficients during subcooledboiling with cross flow, and for saturated boiling with cross flow.These are given
43、in Table 2. Both these correlations agree with exten-sive databases that included all published data for single tubes andtubes inside bundles, including those correlated by Thome and Rob-inson (2004).Data and design methods for bundles of finned and enhancedtubes were reviewed in Casciaro and Thome
44、(2001), Collier andThome (1996), and Thome (2010). Thome and Robinson (2004)carried out extensive tests on bundles of plain, finned, and enhancedtubes using three halocarbon refrigerants. The plain and finned-tuberesults correlated quite well with an asymptotic model combiningconvective and nucleate
45、 boiling (Robinson and Thome 2004a,2004b). The results with enhanced tubes proved more difficult to ex-plain. The correlation presented accounts for the effects of reducedpressure and local void fraction (Robinson and Thome 2004c;Thome and Robinson 2006). This data set was also used by Con-solini et
46、 al. (2006) to develop models and correlations for localvoid fraction and pressure drop in flooded evaporator bundles.Eckels and Gorgy (2012) and Gorgy and Eckels (2013) per-formed wide-ranging tests on bundles of enhanced tubes with vari-ous pitches and two refrigerants. They collected extensive da
47、ta butdid not attempt to test or develop any predictive method. Their dataindicated that a pitch-to-diameter ratio of 1.33 was optimum.Swain and Das (2014) performed a detailed review of literatureon boiling in bundles with plain and enhanced tubes. The only well-verified correlation for plain tube bundles they identified was theShah correlation (Table 2). For bundles of enhanced tubes, no well-verified correlation was identified. Hence, the best recourse fordesign
