1、5.1CHAPTER 5TWO-PHASE FLOWBoiling . 5.1Condensing. 5.10Pressure Drop 5.13Enhanced Surfaces. 5.16Symbols 5.18WO-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
2、vapor filmforms at the 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 b
3、oiling (MFB) heat flux (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 f
4、rom the heated surface. 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 av
5、ailablefor correlating 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, asillustrated by Figure 2 (Berenson 1962). The equations proposed for correlating nucleate boiling da
6、ta canbe put in a form that relates heat transfer coefficient h to temperaturedifference (ts tsat):h = constant(ts tsat)a(1)Exponent a is normally about 3 for a plain, smooth surface; its valuedepends on the thermodynamic and transport properties of the vaporand liquid. Nucleating characteristics of
7、 the surface, including thesize 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 v
8、arious refrigerants are given.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/refrigerantmi
9、xtures have recently been 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
10、fluid. Cooper (1984) proposed 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 su
11、rfaces,to be reevaluated as 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
12、base heat transfer coefficientfor each fluid, and provided base heat transfer coefficients for manyfluids. However, many new refrigerants have been developed since1993, thus limiting this publications usefulness.In addition to correlations dependent on thermodynamic andtransport properties of the va
13、por and liquid, Borishansky et al.(1962), Lienhard and Schrock (1963) and Stephan (1992) docu-mented a correlating method based on the law of correspondingstates. The properties can be expressed in terms of fundamentalmolecular parameters, leading to scaling criteria based on reducedpressure pr= p/p
14、c, where pcis the critical thermodynamic pressurefor the coolant. An example of this method of correlation is shownin Figure 3. Reference 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 advant
15、ageous if the thermo-dynamic and particularly the transport properties used in severalequations in Table 1 are not accurately known. 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
16、explicit heat transfer coefficient correlations basedon the law of corresponding states for halogenated refrigerants(Danilova 1965), flooded evaporators (Starczewski 1965), andvarious other substances (Borishansky and Kosyrev 1966). Otherinvestigations examined the effects of oil on boiling heat tra
17、nsferFig. 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 5.3from diverse configurations, including boiling from a flat plate(Stephan 1963), a 0.55 in. OD horizontal tube using an
18、 oil/R-12mixture (Tschernobyiski and Ratiani 1955), inside horizontal tubesusing an oil/R-12 mixture (Breber et al. 1980; Green and 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
19、 R-11 and R-12 boilingover a flat horizontal copper surface.Maximum Heat Flux and Film BoilingMaximum, 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 boi
20、ling more tractable.Several mechanisms have been proposed for the onset of DNBsee Carey (1992) 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 ma
21、y result from Helmholtz instabilities in col-umns of vapor rising from the heated surface; another prominent the-ory supposes a macrolayer beneath the mushroom-shaped bubbles(Haramura and Katto 1983). In this case, DNB occurs when liquidbeneath the bubbles is consumed before the bubbles depart and a
22、llowsurrounding liquid to rewet the surface. Dhir and Liaw (1989) usedTable 1 Equations for Natural Convection Boiling Heat TransferDescription 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 5 107(T
23、1.13)where a = local accelerationGrg tstsatLc32-=hDdkl- 0.0546vl-0.5qDdAkltsat-0.67hfgDd2l2-0.248lvl-4.33=g lv-0.5h 55pr0.12 0.0868 ln Rp0.4343 ln pr0.55M0.5qA-0.67=qAvhfg-l2g lv-0.25KD=qA- 0 . 0 9 vhfgg lvlv+2-14=qA 0.6334B21 B 2+-0.250.09 vhfgglvlv+2-0.25=Lbg lv-0.5=tstsat0.127Lbvhfgkv-g lvlv+-2/3
24、vg lv-1/3=h 0.425kv3vhfgg lvvtstsatLb-0.25=h 0.62kv3vhfgg lvvtstsatD-0.25=hfghfg10.4cptwtbhfg-+=RaD3g lvv2v- P rvhfgcpv,tstsat- 0 . 4+ag-1/3=5.4 2013 ASHRAE HandbookFundamentalsa concept of bubble crowding proposed by Rohsenow and Griffith(1956) to produce a model that incorporates the effect of con
25、tactangle. Sefiane (2001) suggested that instabilities near the triple con-tact lines cause DNB. Fortunately, though significant disagreementremains about the mechanism of DNB, models using these differingconceptual approaches tend to lead to predictions within a factor of 2.When DNB (point a in Fig
26、ure 1) is assumed to be a hydrodynamicinstability phenomenon, a simple relation Equation (T1.7) can bederived to predict this flux for pure, wetting liquids (Kutateladze1951; Zuber et al. 1962). The dimensionless constant K varies fromapproximately 0.12 to 0.16 for a large variety of liquids. Kandli
27、kar(2001) created a model for maximum heat flux explicitly incorporat-ing the effects of contact angle and orientation. Equation (T1.7) com-pares favorably to Kandlikars, and, because it is simpler, it is stillrecommended for general use. Carey (1992) provides correlations tocalculate maximum heat f
28、lux for various geometries based on thisequation. For orientations other than upward-facing, consult Brus-star and Merte (1997) and Howard and Mudawar (1999).Van Stralen (1959) found that, for liquid mixtures, DNB is a func-tion of concentration. As discussed by Stephan (1992), the maximumheat flux
29、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 putforward to explain the experimental data. For a mor
30、e 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 was adjusted to fitexperimental data; values predict
31、ed 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 heat transfer coefficient for film boiling ona flat
32、 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 horizontalsurface can be predicted by Equation (T1.11), and fr
33、om 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;Westwater 1963).Boiling/Evaporation in Tube BundlesI
34、n 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 generation thenstarts, increasing velocity and thus convec
35、tive heat transfer. Nucleateboiling also occurs if heat flux is high enough. Brisbane et al. (1980)proposed a computational model in which a liquid/vapor mixturemoves up through the bundle, and vapor leaves at the top while liquidmoves back down at the side of the bundle. Local heat transfer coef-fi
36、cients are calculated for each tube, considering local velocity, qual-ity, and heat flux. To use this model, correlations for local heattransfer coefficients during subcooled and saturated boiling with flowacross tubes are needed. Thome and Robinson (2004) presented acorrelation that showed agreemen
37、t with several data sets for saturatedboiling on plain tube bundles. Shah (2005, 2007) gave a general cor-relation for local heat transfer coefficients during subcooled boilingwith cross flow, and for saturated boiling with cross flow. These aregiven in Table 2. Both these correlations agree with ex
38、tensive data-bases that included all published data for single tubes and tubes insidebundles, including those correlated by Thome and Robinson (2004).Data and design methods for bundles of finned and enhancedtubes were reviewed in Casciaro and Thome (2001), Collier andThome (1996), and Thome (2010).
39、 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 boiling (Robinson and Thome 2004a,2004b). The res
40、ults with enhanced tubes proved more difficult toTable 2 Correlations for Local Heat Transfer Coefficients in Horizontal Tube BundlesDescription References EquationsSaturated boiling in plain tube bundles Shah (2007) For Bo Frl0.3 0.0008, hTP= hpb(T2.1)Verified range: water, pentane, halocarbons; si
41、ngle tubes and bundles, square in-line and triangularFor 0.00021 0.00021, hTP= 2.3hLT/(Z0.08 Frl0.22)D = 3.2 to 25.4 mm hLT D/kf= 0.21(GD/f)0.62 Prf0.4pr= 0.005 to 0.19 0is the larger of that given by the following two equations:G = 1.3 to 1391 kg/m2s 0= 443Bo0.65Rel= 58 to 4,949,462 0= 31Bo0.33Bo 1
42、04= 0.12 to 2632 hpbby Cooper correlation without multiplier for copper surface, G based on narrowest gap between tubes.Data from 18 sources Frl= G2/(f2gD) Z = (1/x 1)0.8pr0.4All properties at saturation temperatureSubcooled boiling Shah (2005) Low subcooling regime, hTP= 0hLT(T2.2)Verified range: w
43、ater and halocarbons; single tubes and tube bundles High subcooling regime, hTP= q/Tsat= (0+ Tsc/Tsat)hLTD = 1.2 to 26.4 mm 0 as for saturated boilingpr= 0.005 to 0.15 High subcooling regime whenSubcooling Tsc= 0 to 93 K q/(GCpf Tsc) 38(GDCpf /f) or when Bo 0.05 and for vertical tubes, E2= 1. For ho
44、rizontal tube with Frl0.0011F = 15.43 if Bo 0.04n = 1 for Frl 0.04Subcooled boiling in horizontal and vertical tubes and annuliShah (1977, 1983) Low-subcooling regime:Tubes: 2.4 to 27.1 dia. h = q/Tsat = 230 Bo0.5hf(T3.3a)Annuli: gaps 1 to 6.4 mm, internal, external, and two-sided heatingHigh-subcoo
45、ling regime:Fluids: water, ammonia, halocarbons, organics h = q/Tsat = (230 Bo0.5+ Tsc/Tsat)hf(T3.3b)Tube materials: copper, SS, glass, nickel, inconel All properties at bulk fluid temperature.Reduced pressure: 0.005 to 0.89 High-subcooling regime occurs whenTsc: 0 to 153 K (Tsc/Tsat) 2 or 0.00063 B
46、o1.25(T3.3c)G: 200 to 87,000 kg/(m2s) hfas above with x = 0. For annuli, equivalent diameter based on heated perimeter when gap 4 mmRel: 1400 to 360,000Bo 104: 0.1 to 541.12x1 x-0.75fg-0.41hf0.023 Rel0.8Prl0.4klD=RelG 1 xDl-= , BoqGhfg-=Frl0.12 FrlG2l2Dg-Co1 xx-0.8vl-0.5=5.8 2013 ASHRAE HandbookFund
47、amentalsMehendale et al. (2000), who used hydraulic diameter to classifymicro heat exchangers as follows:- Micro heat exchanger: 1 m dh 100 m- Meso heat exchanger: 100 m dh 1 mm- Compact heat exchanger: 1 mm dh 6 mm- Conventional heat exchanger: dh 6 mmKandlikar and Grande (2003), who classified single- and two-phase microchannels as follows:- Conventional channels
