The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 21
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Often this correction factor has been presumed to be a function of property ratios.An example of such an approach is the correlation of Dougall and Rohsenow (1963) for which the heattransfer coefficient h is given by© 1999 by CRC Press LLC4-92Section 4éæ GD ö æöùrhDx + v (1 - x )÷ ú= 0.023 êçç÷kvrlø úûêëè m v ø è0.84Prv0,.sat(4.4.17)For further information on mechanisms of convective boiling, see the texts of Collier (1981), Stephan(1992), and Carey (1992).CondensationAs in the case of boiling, surface tension effects, surface wetting characteristics, and metastable phasestability also can play important roles in condensation processes.
As a result of interfacial tension, thepressure inside a spherical liquid droplet of radius r must exceed that in the surrounding liquid by 2s/r.A consequence of this and basic thermodynamics is that at equilibrium the surrounding vapor mustactually be slightly supersaturated. The amount of supersaturation required at equilibrium increases asthe radius of curvature of the bubble interface decreases.For a liquid droplet on a solid surface with a specified volume, the wetting contact angle dictates theradius of curvature of the droplet interface. Because of the linkage between the interface curvature andthe required equilibrium supersaturation, the wetting behavior thus determines the level above whichthe vapor supersaturation must be raised for the droplet to grow.
Steady condensation on the dropletinterface can be sustained only if the vapor is driven beyond this supersaturation level by cooling ordepressurization. For such conditions, the vapor is in the metastable supersaturated range indicated inFigure 4.4.2.Condensation on external surfaces of a body immersed in a gas phase generally falls into one or twocategories: dropwise condensation or film condensation.
In dropwise condensation, the liquid-phasecondensate collects as individual droplets which grow in size with time on the cold surface. This modeof condensation is most likely when the liquid poorly wets the solid surface. When the condensationrate is high or the liquid readily wets the surface, a film of liquid condensate covers the solid surface,and the process is referred to as film condensation.Dropwise Condensation. Dropwise condensation may occur on a solid surface cooled below the saturation temperature of a surrounding vapor when the surface is poorly wetted except at locations wherewell-wetted contaminant nuclei exist. The poorly wetted surface condition can result from contaminationor coating of the surface with a substance which is poorly wetted by the liquid phase of the surroundingvapor.
In practice, this can be achieved for steam condensation by (1) injecting a nonwetting chemicalinto the vapor which subsequently deposits on the surface, (2) introducing a substance such as a fatty(i.e., oleic) acid or wax onto the solid surface, or (3) by permanently coating the surface with a lowsurface-energy polymer or a noble metal. The effects of the first two methods are generally temporary,since the resulting surface films eventually are dissolved or eroded away.During dropwise condensation, the condensate is usually observed to appear in the form of dropletswhich grow on the surface and coalesce with adjacent droplets.
When droplets become large enough,they are generally removed from the surface by the action of gravity or drag forces resulting from themotion of the surrounding gas. As the drops roll or fall from the surface they merge with droplets intheir path, effectively sweeping the surface clean of droplets. Droplets then begin to grow anew on thefreshly-exposed solid surface. This sweeping and renewal of the droplet growth process is responsiblefor the high heat transfer coefficients associated with dropwise condensation. Theoretical aspects ofdropwise condensation are described in two publications by Tanaka (1975, 1979).
A discussion ofcorrelations for the heat transfer coefficient associated with dropwise condensation is provided in thereview article by Merte (1973).External Film Condensation. If the liquid phase fully wets a cold surface in contact with a vapor nearsaturation conditions, the conversion of vapor to liquid will take the form of film condensation. As thename implies, the condensation takes place at the interface of a liquid film covering the solid surface.Because the latent heat of vaporization must be removed at the interface to sustain the process, the rate© 1999 by CRC Press LLC4-93Heat and Mass Transferof condensation is directly linked to the rate at which heat is transported across the liquid film from theinterface to the surface.The classic integral analysis of Nusselt (1916) for laminar falling-film condensation on a verticalsurface considers the physical circumstances shown in Figure 4.4.7.
The surface exposed to a motionlessambient of saturated vapor is taken to be isothermal with a temperature below the saturation temperature.Note that although a vertical surface is considered here, the analysis is identical for an inclined surface,except that the gravitational acceleration g is replaced by g sin W, with W being the angle between thesurface and the horizontal.
Because the liquid film flows down the surface because of gravity, thissituation is sometimes referred to as falling-film condensation.FIGURE 4.4.7 System model for the Nusselt analysis of falling-film condensation.In its simplest form, the classic Nusselt analysis incorporates the following idealizations: (1) laminarflow, (2) constant properties, (3) that subcooling of liquid is negligible in the energy balance, (4) thatinertia effects are negligible in the momentum balance, (5) that the vapor is stationary and exerts nodrag, (6) that the liquid-vapor interface is smooth, and (7) that heat transfer across film is only byconduction (convection is neglected).
With these idealizations, the following relation for the local heattransfer coefficient h can be obtained3hz é rl (rl - r v ) gh fg z ù=êúkl ëê 4kl m l (Tsat - Tw ) úû14(4.4.18)Modified versions of this analysis have been subsequently developed which relax many of these assumptions. Laminar film condensation on a vertical surface can also be analyzed with a full boundary layerformulation.
An example of this type of approach is the analysis presented by Sparrow and Gregg (1959).The analyses described above do not include two physical mechanisms which can significantly affectthe transport: (1) the effects of waves on the liquid-vapor interface and (2) interfacial vapor shear dragon the interface. The effects of interfacial shear have been studied analytically by numerous investigators.The effects of surface waves on laminar film condensation are more difficult to incorporate into theoreticalanalyses. In general, interfacial waves are expected to enhance convective heat transport in the film sinceit intermittently thins the film, increases the interfacial area, and induces mixing. Because of these effects,laminar film condensation heat transfer data are often significantly higher than the values predicted bysimple boundary layer models.As for any boundary layer flow, when the film Reynolds number becomes large enough, it is expectedthat a transition to turbulent flow will occur.
Eddy diffusivity models of the resulting turbulent transporthave been developed by Seban (1954), Dukler (1960), and others. This methodology was later extendedto evaporation of a falling liquid film (see, for example, Mills and Chung, 1973).© 1999 by CRC Press LLC4-94Section 4Subsequent studies (see, for example, Mills and Chung, 1973) have suggested that the presence ofthe interface tends to damp larger turbulent eddies near the interface in the liquid film. This implies thata viscous sublayer exists at the interface as well as at the wall.
Recent efforts to model turbulent fallingfilm evaporation and condensation processes have therefore included a variation of the eddy viscosityin which it goes to zero at both the wall and the interface. The analysis tools and correlations describedabove work reasonably well for values of liquid Prandtl number above 1. However, deviation of thepredictions using these methods from heat transfer data for liquid metals can be quite significant.Because of its importance to the design of tube-and-shell condensers, condensation on the outside ofhorizontal tubes has been the subject of numerous studies.
The length of the tube perimeter over whichthe condensate flows is usually small for commonly used tubes. Consequently, the film Reynolds numberis usually low and the flow in the liquid film is laminar.With slight modification, the Nusselt (1916) analysis of laminar falling-film condensation over a flatplate can be adapted to film condensation on an isothermal horizontal cylinder. Doing so yields thefollowing relation for the mean heat transfer coefficient:é (rl - r v ) gh fg D3 Prl ùhD= 0.728 êú2klêë rl vl c pl (Tsat - Tw ) úû14(4.4.19)Selin (1961) found that better agreement with film condensation data for horizontal tubes was obtainedby replacing the constant factor in Equation (4.4.19) by 0.61.
Correlations similar to the single-tuberelation above have also been developed for the average condensation heat transfer coefficient for banksof round tubes.Analytical treatment of laminar film condensation on a sphere is virtually the same as that for ahorizontal cylinder. The only differences result from the angular variation of the body perimeter becauseof the spherical geometry. A general analytical prediction of the local heat transfer coefficient for laminarfilm condensation on arbitrary axisymmetric bodies has been developed by Dhir and Lienhard (1971).Condensation in the Presence of a Noncondensable Gas. In nature and in a number of technologicalapplications, condensation of one component vapor in a mixture may occur in the presence of othernoncondensable components. The most common example is the condensation of water vapor in the airon a cold solid surface. If the component gases are considered to be a mixture of independent substances,condensation of one component vapor will occur if the temperature of the surface is below the saturationtemperature of the pure vapor at its partial pressure in the mixture.
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