ASTM - Intensive Quenching Systems - Engineering and Design 2010 - N I Kobasko, M A Aronov, J A Powell, G E Totten

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CHAPTER 2 n TRANSIENT NUCLEATE BOILING AND SELF-REGULATED THERMAL PROCESSES 29TABLE 7—Physical properties of waterT(°C) PÆ10 - 5 (Pa) q (kg/m 3 ) c p (kJ/kgK) k(W/mK)aÆ10 8(m 2 /s)lÆ10 6(PaÆs)mÆ10 6(m 2 /s)b 0 Æ10 4(1/K)rÆ10 4(N/m)Pr0 1.013 999.9 4.212 0.560 13.2 1,788 1.789 –0.63 756.4 13.510 1.013 999.7 4.191 0.580 13.8 1,306 1.306 þ 0.70 741.6 9.4520 1.013 998.2 4.183 0.597 14.3 1,004 1.996 1.82 726.9 7.0330 1.013 995.7 4.174 0.612 14.7 801.5 0.805 3.21 712.2 5.4540 1.013 992.2 4.174 0.627 15.1 653.3 0.659 3.87 696.5 4.3650 1.013 988.1 4.174 0.640 15.5 549.4 0.556 4.49 676.9 3.5960 1.013 983.1 4.179 0.650 15.8 469.9 0.478 5.11 662.2 3.0370 1.013 977.8 4.187 0.662 16.1 406.1 0.415 5.70 643.5 2.5880 1.013 971.8 4.195 0.669 16.3 355.1 0.365 6.32 625.9 2.2390 1.013 965.3 4.208 0.676 16.5 314.9 0.326 6.95 607.2 1.97100 1.013 958.4 4.220 0.684 16.8 282.5 0.295 7.52 588.6 11.75110 1.43 951.0 4.233 0.685 17.0 259.0 0.272 8.08 569.0 1.60120 1.98 943.1 4.250 0.686 17.1 237.4 0.252 8.64 548.4 1.47130 2.70 934.8 4.266 0.686 17.2 217.8 0.233 9.19 528.8 1.35140 3.61 926.1 4.287 0.685 17.2 201.1 0.217 9.72 507.2 1.26150 4.76 917.0 4.313 0.684 17.3 186.4 0.203 10.3 486.6 1.17160 6.18 907.4 4.346 0.681 17.3 173.6 0.191 10.7 466.0 1.10170 7.92 897.3 4.380 0.676 17.2 162.8 0.181 11.3 443.4 1.05180 10.03 886.9 4.417 0.672 17.2 153.0 0.173 11.9 422.8 1.03190 12.55 876.0 4.459 0.664 17.2 144.2 0.165 12.6 400.2 0.965200 15.55 863.0 4.505 0.658 17.0 136.4 0.158 13.3 376.7 0.932Note: P is pressure in Pa; q is liquid density in kg/m 3 ;c p is specific heat capacity of liquid in kJ/(kgK); k is heat conductivity of the liquid in W/mK; Pr ¼ m/ais the Prandtl number; m is kinematic viscosity in m 2 /s; a is thermal diffusivity of liquid in m 2 /s; l is dynamic viscosity in PaÆs; and b 0 is the coefficient of volumeexpansion.TABLE 8—Properties of water vapor at the saturation temperatureT(°C) PÆ10 - 5 (Pa) q 00 (kg/m 3 ) r * (kJ/kg) c p (kJ/kgK) kÆ10 2 (W/mK) aÆ10 8 (m 2 /s) lÆ10 6 (PaÆs) mÆ10 6 (m 2 /s) Pr100 1.013 0.598 2,256.8 2.135 2.372 18.58 11.97 20.02 1.08110 1.43 0.826 2,230.0 2.177 2.489 13.83 12.46 15.07 1.09120 1.98 1.121 2,202.8 2.206 2.593 10.50 12.85 11.46 1.09130 2.70 1.496 2,174.3 2.257 2.686 7.072 13.24 8.85 1.11140 3.61 1.966 2,145.0 2.315 2.791 6.130 13.54 6.89 1.12150 4.76 2.547 2,114.3 2.395 2.884 4.728 13.93 5.47 1.16160 6.18 3.258 2,082.6 2.479 3.012 3.722 14.32 4.39 1.18170 7.92 4.122 2,049.5 2.583 3.128 2.939 14.72 3.57 1.21180 10.03 5.157 2,015.2 2.709 3.268 2.339 15.11 2.93 1.25190 12.55 6.397 1,978.8 2.856 3.419 1.872 15.60 2.44 1.30200 15.55 7.862 1,940.7 3.023 3.547 1.492 15.99 2.03 1.36Note: q 00 is density of vapor in kg/m 3 ; r * is latent heat of evaporation in kJ/kg; other units defined in notes for Table 7.
30 INTENSIVE QUENCHING SYSTEMS: ENGINEERING AND DESIGNTo determine the heat transfer coefficient during nucleateboiling, Tolubinsky’s equation (Eq 8) is substituted intoEq 15. In this case, boundary conditions of Eq 15 will be setin the following form:@T@r þ bm r¼R k ðT T SÞ m ¼ 0; ð16Þwhere m ¼ 3.33 for Tolubinsky’s equation and m ¼ 3 forthe Labuntsov equation [5]. In the boundary conditions ofEq 16, the value of b has the following form:b ¼ 75k0 ðr 0 r 00 Þ 0:5 g 0:5r 0:5 ðr 00 r w 00 Þ 0:7 Pr 0:2 :ð17Þ(Table 6 presents values of b for different equations.) Eq 17was obtained from Tolubinsky dimensionless correlation bythe replacement of q witha T Sf T S:It is possible to do this procedure using Eq 11: 2=3a ¼ c a T Sf T SorIt follows that:ac ¼ a2=3 T Sf T S 2=3:a ¼ c 3 T Sf T S 2: ð18ÞSubstituting the found value (from Eq 18) to boundaryconditions of the third kind in Eq 15:@T@r ¼ c3r¼Rk T 3¼Sf T S 0: ð19ÞThus, the boundary conditions during nucleate boilingare given by:@T@r þ bmr¼Rk T m¼Sf T S 0; ð20Þwhere 3 < m < 3.33.It is very important to determine these boundary conditions,since it is practically impossible to measure the surfacetemperature during nucleate boiling because:1. There is little change of temperature within the limits ofaccuracy of measurement results with respect to the changeof heat flux density that affects the intensity of steel cooling.2. While the accuracy of experimental measurementsincreases, there are other difficulties associated with thefluctuation of surface temperatures during nucleate boiling.In this case, it is necessary to use a statistical approach,which consumes additional expense and time.3. During transition boiling, local film boiling occurs, whichcomplicates three-dimensional problems for determinationof heat transfer coefficients.Therefore, the statement of boundary conditions basedon careful study of parameters and dynamics of bubblesduring nucleate boiling is of significant practical interest forsolving problems of transient heat conductivity. It is alsoimportant to have boundary conditions for the determinationof time transient nucleate boiling.In the boundary conditions of Eq 16, most important isvalue b, which depends on physical properties of the quenchingmedium. Tables 7 and 8 provide physical properties of aliquid and vapor, depending on temperature.The vapor bubble growth rate depends on pressure andunderheat of the liquid medium. Tolubinsky’s empirical correlationfor the determination of vapor bubble growth rateat higher pressures is:W 00 W0:100 ¼ r 0:1r 00 2:3þ0:5lg PPcr;ð21Þwhere:W 00 is bubble growth at current pressure;W0:1 00 is bubble growth rate at normal pressure;r 00 0:1 is vapor density at normal pressure (kg/m3 );r 00 is vapor density at current pressure (kg/m 3 );r cr is critical pressure; andP is the pressure at which the steam bubble growth rate isdetermined.2.3 HEAT TRANSFER DURINGSTEEL QUENCHINGTypically, steel parts are quenched in cold quenchants, and forintensive quenching it is assumed that there is no film boiling.This condition is achieved by reducing the quenchant temperature,using aqueous salt solutions at optimal concentrations,and creation of intensive jets and water flow during quenching.Consider the process of quenching when a part isimmersed into a cold quenchant. At the time of immersioninto the cold quenchant, a boundary boiling layer is formedand its formation can be divided into several stages:1. During the first stage, the cold liquid is heated to the saturationtemperature. The surface of a metal at this time is cooledsignificantly, and the surface temperature drops rapidly.2. During the second stage, the boundary layer is overheated,and nucleating centers of vapor formation arecreated. At the surface layer of the metal, a significanttemperature gradient is established.3. During this last stage, the surface of the metal becomescompletely covered by tiny vapor bubbles (shock boilingstarts). Additional cooling of the steel can proceed bydifferent pathways.If vapor bubbles have completely covered the surface ofmetal and heat flux density inside of the heater increases, thenfilm boiling begins. The maximum heat flux density at whichthere is transition of bubbles in a continuous vapor film iscalled the critical heat flux density. If the heat flux density isless than the critical value, then, after the formation of aboundary liquid boiling layer, nucleate boiling is established. Ifthe heat flux density is close to the critical value, then the transitionmode of boiling is initiated, where localized vapor filmsare formed on the surface; this is undesirable, since it is associatedwith nonuniform hardness distribution and distortion.Critical heat flux densities are considered in detail inChapter 3. There are actually two critical heat flux densities.The first is a transition from nucleate boiling to film boiling.The second is a transition from full film boiling back tonucleate boiling. Between the first and second critical heatflux densities, there is a well-known correlation [6,7]:q cr1q cr2 0:2;ð22Þ
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ASTM - Intensive Quenching Systems - Engineering and Design 2010 - N I Kobasko, M A Aronov, J A Powell, G E Totten

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