The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 18
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Ozisik, M.N. 1973. Radiative Transfer and Interactions with Conduction and Convection, JohnWiley & Sons, New York.9. Siegel, R. and Howell, J.R. 1992. Thermal Radiation Heat Transfer, 3rd ed., Hemisphere Publishing, New York.10. Sparrow, E.M. and Cess, R.D. 1978. Radiation Heat Transfer, Hemisphere, New York.© 1999 by CRC Press LLC4-82Section 44.4 Phase-ChangeBoiling and CondensationVan P. CareyIntroductionLiquid-vapor phase-change processes play an important role in many technological applications. Thevirtually isothermal heat transfer associated with boiling and condensation processes makes their inclusion in power and refrigeration processes highly advantageous from a thermodynamic efficiency standpoint. In addition, the high heat transfer coefficients associated with boiling and condensation have madethe use of these processes increasingly attractive in the thermal control of compact devices that havehigh heat dissipation rates.
Applications of this type include the use of boiling heat transfer to coolelectronic components in computers and the use of compact evaporators and condensers for thermalcontrol of aircraft avionics and spacecraft environments. Liquid-vapor phase-change processes are alsoof critical importance to nuclear power plant design, both because they are important in normal operatingcircumstances and because they dominate many of the accident scenarios that are studied as part ofdesign evaluation.The heat transfer and fluid flow associated with liquid-vapor phase-change processes are typicallyamong the more complex transport circumstances encountered in engineering applications.
These processes have all the complexity of single-phase convective transport, plus additional elements resultingfrom motion of the interface, nonequilibrium effects, and dynamic interactions between the phases. Dueto the highly complex nature of these processes, development of methods to accurately predict theassociated heat and mass transfer is often a formidable task.In this section, commonly used variables not defined in the nomenclature are as follows: q² = surfaceheat flux, ml = liquid viscosity, mn = vapor viscosity, Prl = liquid Prandtl number, Tw = wall surfacetemperature, Tsat = saturation temperature, cpl = liquid specific heat, kn = vapor thermal conductivity, g= gravitational acceleration, and x = mass quality.BoilingThree mechanisms that play important roles in boiling processes are (1) surface tension effects, (2)surface wetting characteristics of the liquid, and (3) metastable phase stability.Anyone who has watched small bubbles rise in a carbonated beverage or a pot of boiling water hasundoubtedly noticed that the bubbles are almost perfectly spherical, as if an elastic membrane werepresent at the interface to pull the vapor into a spherical shape.
This apparent interfacial tension orsurface tension s is equivalent to an energy stored in the interface region per unit area. The energyexcess in this region is due to the slightly larger separation of the liquid phase molecules adjacent tothe gas phase.The magnitude of the surface tension for a substance is directly linked to the strength of intermolecularforces in the material. Nonpolar liquids typically have the lowest surface tension.
Water and other polarmolecules have somewhat higher surface tension, and liquid metals, which exhibit metallic bond attraction, have very high surface tension. The surface tension of water at 20°C is 0.0728 N/m, whereas liquidmercury has a surface tension of 0.484 N/m at the same temperature. The surface tension for any pureliquid varies with temperature. It decreases almost linearly with increasing temperature, vanishingaltogether at the critical point where the distinction between the phases disappears.As a result of the surface tension at the interface, the pressure inside a spherical bubble of radius rmust exceed that in the surrounding liquid by 2s/r:Pv = Pl +© 1999 by CRC Press LLC2sr(4.4.1)4-83Heat and Mass TransferBy using the relation (1) between the pressure in the two phases it can be shown that for the bubble tobe in equilibrium with the surrounding liquid, the liquid must actually be superheated above the saturationtemperature for the ambient liquid pressure.
The amount of required superheating increases as the radiusof curvature of the bubble interface decreases.The wetting characteristics of the liquid are generally quantified in terms of a contact angle betweenthe solid surface and the tangent to the interface at the point where it contacts the solid. This angle ismeasured through the liquid phase, as shown in Figure 4.4.1. In some systems, the wetting angleestablished at equilibrium may depend on the fluid motion history. For some systems the contact angleestablished by liquid advancing over a solid surface is larger than that established when a liquid frontrecedes over the surface. This behavior is referred to as contact angle hysteresis. Contact angle hysteresiscan have an important effect on boiling and condensation processes, particularly those involving water.FIGURE 4.4.1 Definition of the contact angle q.For a bubble with a specified vapor volume, the contact angle will dictate the radius of curvature ofthe bubble interface.
The wetting behavior in combination with the surface tension effect, thus, determinesthe level of superheat required for the bubble to be in equilibrium with the surrounding liquid. The liquidmust be heated above this superheat level for the bubble to grow. A steady boiling process can besustained only if the liquid is heated above this threshold superheat level.It can be shown from basic thermodynamic analysis that a necessary and sufficient condition for phasestability is thatæ ¶P öç ÷ <0è ¶v ø T(4.4.2)where n is the specific volume. Below the critical temperature, extrapolation of the isotherms for theliquid and vapor phases consistent with an equation of state like the van de Waals equation results inan isotherm shape similar to that shown in Figure 4.4.2.The locus of points where (¶P/¶n)T = 0 are termed spinodal curves.
Regions of metastable vapor andliquid exist between the saturation curve and the spinodal curves. The effects of surface tension discussedabove require that fluid surrounding a vapor bubble be in the metastable superheated liquid region.Predictions of statistical thermodynamics imply that as (¶P/¶n)T approaches zero, the level of fluctuationsin a fluid system increases. This, in turn, increases the probability that an embryonic new phase willform as a result of density fluctuations. Initiation of a phase change in this manner is termed homogeneousnucleation. Generally, a pure liquid must be heated to nearly 90% of its absolute critical temperaturebefore homogeneous nucleation of vapor bubbles occurs.In most physical systems of engineering interest, the bulk phase is in contact with solid walls of thecontaining structures, or solid particulate contaminants.
These solid phases may provide nucleation siteswhere phase change may occur if the system state is driven into the metastable range. Nucleation ofvapor bubbles may preferentially occur at low liquid superheat levels in crevices in the solid surfacewhere gas is trapped.
This type of nucleation at the solid surface of a containment wall is categorizedas heterogeneous nucleation. Because solid containment walls usually contain microscopic crevice-type© 1999 by CRC Press LLC4-84Section 4FIGURE 4.4.2 Spinodal lines and metastable regions on a P–n diagram.imperfections, heterogeneous nucleation is more common than homogeneous nucleation in systemswhere boiling occurs.Vapor entrapment in crevices of the heated walls of evaporator heat exchangers usually makes it easierto initiate the vaporization process.
Vapor bubbles grow from these crevices until buoyancy or drag onthe bubbles exceeds the surface tension force holding the droplet to the solid surface. The bubble thenreleases into the bulk liquid. A small remnant of vapor remains in the crevice after a bubble releases,and this remnant grows in size as further vaporization occurs until the bubble grows out of the creviceagain. The result is a cyclic process of bubble growth and release known as the ebullition cycle. Crevicesat which the ebullition cycle is sustained are said to be active nucleation sites. When the ebullitionprocess occurs at many sites over a heated surface, the overall process is referred to as nucleate boiling,which is one possible mode of pool boiling.Pool BoilingVaporization of liquid at the surface of a body immersed in an extensive pool of motionless liquid isgenerally referred to as pool boiling.
The nature of the pool boiling process varies considerably dependingon the conditions at which boiling occurs. The level of heat flux, the thermophysical properties of theliquid and vapor, the surface material and finish, and the physical size of the heated surface all mayhave an effect on the boiling process.The regimes of pool boiling are most easily understood in terms of the so-called boiling curve: a plotof heat flux q² vs. wall superheat Tw – Tsat for the circumstances of interest.
Many of the features of theclassic pool boiling curve were determined in the early investigations of pool boiling conducted byNukiyama (1934). Strictly speaking, the classic pool boiling curve defined by the work of this investigatorand others applies to well-wetted surfaces for which the characteristic physical dimension L is largecompared to the bubble or capillary length scale Lb defined asLb =sg(rl - r v )(4.4.3)The discussion in this section is limited to pool boiling of wetting liquids on surfaces with dimensionslarge compared with Lb.
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