The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 22
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This temperature threshold is referredto as the dew point of the mixture.Because only the vapor is condensed, the concentration of the noncondensable gas at the interface ishigher than its value in the far ambient. This, in turn, decreases the partial pressure of the vapor at theinterface below its ambient value. The corresponding saturation temperature at the interface is thereforelower than the bulk temperature.
The resulting depression of the interface temperature generally reducesthe condensation heat transfer rate below that which would result for pure vapor alone under the sameconditions. Space limitations here preclude a detailed discussion of the effects of noncondensable gases.The interested reader may find more-extensive discussions of this topic in the references by Collier(1981) and Carey (1992).Internal Convective Condensation. In most power and refrigeration systems, the flow in the condenseris either horizontal or vertically downward. Figure 4.4.8 schematically depicts a typical condensationprocess in a horizontal round tube. Superheated vapor enters the tube and at the exit end the liquid issubcooled.
At a point some distance downstream of the entrance, vapor begins to condense on the wallsof the tube. The location at which this occurs is at or slightly before the bulk flow reaches the equilibriumsaturation condition. In most condensers, the liquid readily wets the interior of the tube and at highvapor volume fractions the liquid forms a thin liquid film on the interior wall of the tube.© 1999 by CRC Press LLC4-95Heat and Mass TransferFIGURE 4.4.8 Flow regimes during horizontal cocurrent flow with condensation.The vapor velocity is generally high at the inlet end of the condenser tube, and the liquid film isdriven along the tube by strong vapor shear on the film.
At low vapor flow rates, some stratification mayoccur and the film may be thicker on the bottom of the horizontal tube. At high vapor flow rates, turbulentstresses acting on the liquid may tend to keep the thickness of the liquid film nominally uniform overthe perimeter of the tube.In most condenser applications, shear-dominated annular flow persists to very low qualities and theoverwhelming majority of the heat transfer occurs in this regime. The very last stage of the condensationprocess, corresponding to qualities less than a few percent, may occur in slug, plug, or bubbly two-phaseflow. Generally these regimes represent such a small portion of the overall heat transfer in the condenserthat some inaccuracy in estimating the heat transfer coefficient for them is tolerated.
As a first estimate,the heat transfer coefficient may be predicted using a correlation for pure single-phase liquid flow inthe tube at the same total flow rate, or a correlation for annular flow condensation may simply beextrapolated to zero quality.Because most of the heat duty occurs in the annular flow regime, accurate prediction of the overallheat transfer performance of the condenser requires a predictive methodology that accurately treats thetransport in this regime.
For this reason, the form of most correlation methods for predicting localconvective condensation heat transfer coefficients are optimized to match data in the annular flow regime.One example of such a correlation is the following relation for the local heat transfer coefficient forannular flow condensation proposed by Traviss et al. (1973):0.92.85 ùhD 0.15Prl Re l é 1=+ 0.476 úêklFTë Xtt Xtt û(4.4.20)whereRe l =and FT is given by© 1999 by CRC Press LLCG(1 - x ) D,ml1- xöXtt = æè x ø0.9æ rv öçr ÷è lø0.5æ ml öçm ÷è vø0.14-96Section 4{FT = 5Prl + 5 ln{1 + 5Prl } + 2.5 ln 0.0031Re l0.812{()}= 5Prl + 5 ln 1 + Prl 0.0964 Re l0.585 - 1= 0.707Prl Re l0.5}for Re l > 1125for 50 < Re l < 1125for Re l < 50Carey (1992) has shown that the generic form of this correlation can be derived from a theoretical modelof annular flow condensation in a round tube.
Several correlations of this general type have beendeveloped as fits to experimental data; see Carey (1992) for a summary. The predictions of thesecorrelations may vary significantly for a given set of conditions. When possible, a correlation should beselected which has been tested against data for conditions close to those for the application of interest.A correlation methodology that can be used to predict internal convective condensation heat transferfor slug, plug, or wavy stratified flow has also been proposed by Rossen and Meyers (1965). To predictthe overall heat transfer performance of a condenser, methods to predict the local heat transfer coefficientmust be combined with a scheme to numerically integrate finite-difference forms of the energy, mass,and momentum balances in the tube.
For further information on such schemes see the references byCollier (1981) and Carey (1992) (Figure 4.4.9).FIGURE 4.4.9 Comparison of the variation of h with x predicted by four correlation methods for internal convectivecondensation. References cited in this figure are listed in chapter 11 of Carey (1992).Defining TermsCritical heat flux (CHF): A maximum heat flux condition that characterizes the transition betweennucleate boiling and transition boiling or film boiling.Dropwise condensation: Condensation of vapor into liquid in discrete droplets, usually attained whena cold surface is poorly wetted by the liquid phase.Film boiling: Generation of vapor at the interface of a vapor film which entirely covers the hot surface.Film condensation: Condensation of vapor onto the interface of a liquid film that completely covers acold surface.Minimum heat flux: A minimum heat flux condition on the classic boiling curve that characterizes thetransition between film boiling and transition boiling.
Also, sometimes referred to as the Leidenfrost point, it is a lower bound for heat flux values at which stable film boiling may occur.© 1999 by CRC Press LLCHeat and Mass Transfer4-97Nucleate boiling: Generation of vapor at a hot surface by formation of bubbles at discrete nucleationsites with full liquid wetting of the surface.Polar molecules: Molecules which have a permanent electric dipole moment. Examples include waterand ammonia.Pool boiling: Generation of vapor at the surface of a hot body immersed in an extensive liquid pool.Transition boiling: Generation of vapor at a hot surface with intermittent or partial liquid wetting ofthe surface.ReferencesBerenson, P.J. 1961.
Film boiling heat transfer from a horizontal surface. J. Heat Transfer, 83, 351–356.Carey, V.P. 1992. Liquid-Vapor Phase Change Phenomena. Taylor and Francis, Washington, D.C.Chen, J.C. 1966. Correlation for boiling heat transfer to saturated fluids in convective flow. Ind. Eng.Chem. Proc. Design and Dev.
5(3), 322–339.Collier, J.G. 1981. Convective Boiling and Condensation, 2nd ed. McGraw-Hill, New York.Dhir, V.K. and Lienhard, J. 1971. Laminar film condensation on plane and axisymmetric bodies innonuniform gravity. J. Heat Transfer 93, 97–100.Dougall, R.S. and Rohsenow, W.M. 1963.
Film boiling on the inside of vertical tubes with upward flowof the fluid at low qualities. MIT Report No. 9079-26. MIT, Cambridge, MA.Dukler, A.E. 1960. Fluid mechanics and heat transfer in vertical falling film systems. Chem. Eng. Prog.Symp. Ser. 56(30), 1–10.Gunnerson, F.S. and Cronenberg, A.W. 1980.
On the minimum film boiling conditions for sphericalgeometries. J. Heat Transfer 102,335–341.Haramura, Y. and Katto, Y. 1983. A new hydrodynamic model of the critical heat flux, applicable widelyto both pool and forced convective boiling on submerged bodies in saturated liquids. Int. J. HeatMass Transfer 26, 389–399.Kandlikar, S.G.
1989. A general correlation for saturated two-phase flow boiling heat transfer insidehorizontal and vertical tubes. J. Heat Transfer 112, 219–228.Katto, Y. and Ohno, H. 1984. An improved version of the generalized correlation of critical heat fluxfor the forced convective boiling in uniformly heated vertical tubes. Int. Heat Mass Transfer 21,1527–1542.Levitan, L.L. and Lantsman, F.P. 1975. Investigating burnout with flow of a steam-water mixture in around tube, Therm. Eng. (USSR). English trans., 22, 102–105.Lienhard, J.H. and Dhir, V.K.
1973. Extended hydrodynamic theory of the peak and minimum poolboiling heat fluxes. NASA CR-2270.Lienhard, J.H. and Witte, L.C. 1985. A historical review of the hydrodynamic theory of boiling. Rev.Chem. Eng. 3, 187–277.Lienhard, J.H. and Wong, P.T.Y. 1964. The dominant unstable wavelength and minimum heat flux duringfilm boiling on a horizontal cylinder. J. Heat Transfer 86, 220–226.Merte, H. 1973. Condensation heat transfer. Adv.
Heat Transfer 9, 181–272.Mills, A.F. and Chung, D.K. 1973. Heat transfer across turbulent falling films. Int. J. Heat Mass Transfer16, 694–696.Nukiyama, S. 1934. The maximum and minimum values of Q transmitted from metal to boiling waterunder atmospheric pressure. J. Jpn. Soc.
Mech. Eng. 37, 367–374.Nusselt, W. 1916. Die Oberflachenkondensation des Wasser dampfes. Z. Ver. Dtsch. Ininuere 60, 541–575.Ramilison, J.M. and Lienhard, J.H. 1987. Transition boiling heat transfer and the film transition regime.J. Heat Transfer 109, 746–752.Rohsenow, W.M. 1962. A method of correlating heat transfer data for surface boiling of liquids.
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