The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 20
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Other geometries are treated by Lienhard et al. (1973) and Lienhard and Dhir (1973b). Analternative model has been proposed by Haramura and Katto (1983).Lienhard and Witte (1985) discuss the development and limitations of hydrodynamic CHF theories.As shown in the Figure 4.4.3, the boundary between the transition boiling regime and the film boilingregime corresponds to a minimum in the heat flux vs. superheat curve.
This condition is referred to asthe minimum heat flux condition, referred to as the Leidenfront point. The minimum heat flux corresponds approximately to the lowest heat flux which will sustain stable film boiling.For an infinite flat (upward-facing) heated surface, vapor generated at the interface during stable filmboiling is released as bubbles at the nodes of a standing two-dimensional Taylor wave pattern.
The¢¢ derived by Zuber (1959) and Berenson (1961).following relation for the minimum heat flux qminé s (r - r ) ùglvúqmin¢¢ = 0.09rv h fg ê2ê (rl + rv ) úëû14(4.4.6)qmin¢¢ correlations have been developed by Lienhard and Wong (1964) for horizontal cylinders andGunnerson and Cronenberg (1980) for spheres.In film boiling, transport of heat across the vapor film from the wall to the interface may occur byconvection, conduction, and radiation. The radiation contribution depends on the nature of the solidsurface, but when the radiation effect is small, the heat transfer for film boiling is independent of thematerial properties and finish of the surface. For buoyancy-driven laminar film boiling over a verticalflat isothermal surface in a pool of saturated liquid, the local heat transfer coefficient from the surfacecan be obtained from the following relation:é kv3 grv (rl - r v ) h fg ùh=êúêë 4m v (Tw - Tsat ) x úû14(4.4.7)At low surface temperatures, radiation effects are negligible and consideration of convective transportalone is sufficient to predict the heat transfer.
At higher temperatures radiation effects must also beincluded. If the vapor in the film absorbs and emits radiation at infrared wavelengths, a detailed treatmentof the radiation interaction with the vapor may be necessary to accurately predict the film boiling heattransfer.Additional information mechanisms such as interfacial waves, turbulence, and variable properties issummarized in Carey (1992).Transition pool boiling has traditionally been interpreted as a combination of nucleate and film boilingalternately occurring over the heated surface, and a model of transition boiling that accounts for contactangle effects has been proposed by Ramilison and Lienhard (1987).Internal Convective BoilingFlow boiling in tubes is perhaps the most complex convective process encountered in applications.
Inmost evaporator and boiler applications, the flow is either horizontal or vertically upward. Figure 4.4.5schematically depicts a typical low-flux vaporization process in a horizontal round tube. In this exampleliquid enters as subcooled liquid and leaves as superheated vapor. As indicated in Figure 4.4.5, the flowundergoes transitions in the boiling regime and the two-phase flow regime as it proceeds down the tubes.The regimes encountered depend on the entrance conditions and the thermal boundary conditions at the© 1999 by CRC Press LLCHeat and Mass Transfer4-89FIGURE 4.4.5 Qualitative variation of the heat transfer coefficient h and flow regime with quality for internalconvective boiling in a horizontal tube at moderate wall superheat.tube wall. At low quality the vaporization process is dominated by nucleate boiling, with convectiveeffects being relatively weak. As the quality increases, the flow quickly enters the annular film flowregime in which convective evaporation of the annular liquid film is the dominant heat transfer mechanism.
Often the conditions are such that liquid droplets are often entrained in the core vapor flow duringannular flow evaporation. Eventually, the annular film evaporates away, leaving the wall dry. Mist-flowevaporation of entrained liquid droplets continues in the post-dryout regime until only vapor remains.Similar, sequences of flow and boiling regimes occurring in vertical upward flow, as indicated in Figure4.4.6.The boiling regime trends shown in Figures 4.4.5 and 4.4.6 are typical for low heat flux vaporizationprocesses. At high wall superheat levels, transition boiling or film boiling can also occur.
The transitionfrom nucleate boiling to one of these regimes is termed a departure from nucleate boiling (DNB) or theCHF condition. However, the heat transfer performance of an evaporator under transition or film boilingconditions is so poor that equipment is not usually designed to operate under such conditions.Because low-quality or subcooled flow boiling are nucleate boiling dominated, the heat transfercoefficient in these regimes is often predicted using a nucleate boiling correlation developed as a fit topool boiling data. The usefulness of such an approach is a consequence of the fact that for most conditionsof practical interest, nucleate boiling heat transfer is only weakly affected by liquid subcooling or liquidbulk convection.For saturated convective boiling prior to dryout, relations to predict the heat transfer coefficient havetypically been formulated to impose a gradual suppression of nucleate boiling and gradual increase inliquid film evaporation heat transfer as the quality increases.
A number of correlations based on suchan approach have been developed. An early correlation of this type developed by Chen (1966) has beenwidely used. One of the better methods of this type is the recently developed correlation of Kandlikar© 1999 by CRC Press LLC4-90Section 4FIGURE 4.4.6 Flow regimes and boiling mechanisms for upflow convective boiling in a vertical tube at moderatewall superheat.(1989) which has been fit to a broad spectrum of data for both horizontal and vertical tubes.
For thismethod the heat transfer coefficient for a tube of diameter D is given by[h = hl C1Co C2 (25Frle )C5+ C3 Bo C4 FK](4.4.8)where1- xöCo = æè x ø0.8æ rv öçr ÷è lø0.5(4.4.9)Bo = q ¢¢ Gh fg(4.4.10)Frle = G 2 rl2 gD(4.4.11)and hl is the single-phase heat transfer coefficient for the liquid phase flowing alone in the tube computedas© 1999 by CRC Press LLC4-91Heat and Mass Transferæ k ö æ G(1 - x ) D öhl = 0.023ç l ÷ ç÷è Dø èmlø0.8Prl0.4(4.4.12)The constants C1 – C5 are given in Table 4.4.1. The factor FK is a fluid-dependent parameter.
For water,FK = 1. For R-12 and nitrogen, recommended values of FK are 1.50 and 4.70, respectively. Values of FKfor a variety of other fluids can be obtained from Kandlikar (1989).TABLE 4.4.1C1C2C3C4C5aaConstants for the Correlation of Kandlikar (1987)Co < 0.65 (Convective Region)Co ³ 0.65 (Nucleate Boiling Region)1.1360–0.9667.20.70.30.6683–0.21058.00.70.3C5 = 0 for vertical tubes and horizontal tubes with Frle > 0.04.Methods for predicting the conditions at which dryout or a DNB transition occurs have typically beenempirical in nature.
Based on fits to extensive data, Levitan and Lantsman (1975) recommended thefollowing relations for the DNB heat flux and the quality at which dryout occurs during flow boiling ofwater in a tube with an 8-mm diameter.21.2 {[ 0.25( P - 98 ) 98]- x }éæ P ö + 1.6æ P ö ù æ G öqcrite -1.5 x¢¢ = ê10.3 - 7.8úè 98 øè 98 ø û è 1000 øë(4.4.13)23-0.5éPPP ù G öx crit = ê0.39 + 1.57æ ö - 2.04æ ö + 0.68æ ö ú æè 98 øè 98 øè 98 ø û è 1000 øë(4.4.14)¢¢ is in MW/m2, P is the pressure in bar, and G is in kg/m2sec. To obtain valuesIn the above relations, qcrit¢¢ and xcrit for diameters other than 8 mm, Levitan and Lantsman (1975) recommended that the 8of qcritmm values from the above relations be corrected as follows:æ 8öqcrit¢¢ = (qcrit¢¢ )8mmè Dø8x crit = ( x crit )8mm æ öè Dø12(4.4.15)0.15(4.4.16)where D is the diameter in millimeters.
A good generalized empirical correlation for predicting dryoutor CHF conditions in vertical uniformly heated tubes is that recently proposed by Katto and Ohno (1984).In many cases, post-dryout mist flow evaporation is driven primarily by convective transport from thetube wall to the gas and then to the entrained droplets. In some circumstances, impingement of dropletsonto the heat surface and radiation interactions may also be important.
In cases where convection isdominant, predictions of the heat transfer coefficient have been developed by modifying a single-phasecorrelation for the entire flow as vapor with a correction factor which accounts for the presence of theentrained droplets.
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