Condensation gravity-controlled

In compact geometries the heat transfer coefficient depends on the two-phase flow pattern (51-67). For low condensation rates, the heat transfer is gravity controlled, and the heat transfer coefficient depends on the liquid film thickness. For higher condensation rates, the heat transfer coefficient depends on the vapor shear effect, and for small passages the liquid-vapor interaction leads to high heat transfer coefficients. 

Vapor Shear Controlling For vertical in-tube condensation with vapor and liquid flowing concurrently downward, if gravity controls, Figs. 5-7 and 5-8 may be used, if vapor shear controls, the Carpenter-Colburn correlation (General Discussion on Heat Transfer, London, 1951, ASME, New York, p. 20) is applicable ... 

R. Hashimoto, K. Yanagi, and T. Fujii, Effects of Condensate Flow Patterns upon Gravity-Controlled Condensation of Ethanol and Water Mixtures on a Vertical Surface, Heat Transfer-Japanese Research, 23, pp. 330-348,1994. 

Heat transfer coefficients for condensation processes depend on the condensation models involved, condensation rate, flow pattern, heat transfer surface geometry, and surface orientation. The behavior of condensate is controlled by inertia, gravity, vapor-liquid film interfacial shear, and surface tension forces. Two major condensation mechanisms in film condensation are gravity-controlled and shear-controlled (forced convective) condensation in passages where the surface tension effect is negligible. At high vapor shear, the condensate film may became turbulent. 

Heat Transfer Correlations for External Condensation. Although the complexity of condensation heat transfer phenomena prevents a rigorous theoretical analysis, an external condensation for some simple situations and geometric configurations has been the subject of a mathematical modeling. The famous pioneering Nusselt theory of film condensation had led to a simple correlation for the determination of a heat transfer coefficient under conditions of gravity-controlled, laminar, wave-free condensation of a pure vapor on a vertical surface (either flat or tube). Modified versions of Nusselt s theory and further empirical studies have produced a list of many correlations, some of which are compiled in Table 17.23. 

Film condensation in tube bundles (more commonly used in shell-and-tube heat exchangers) characterize more complex physical conditions compared to condensation on a single tube. The gravity-controlled and surface-shear-stress-influenced condensate films must be modeled in different ways to accommodate combined influences of condensate drain to lower tubes (i.e., condensate inundation) and shear effects. Such a correlation, the fourth correlation from the top of Table 17.24, was proposed by Kern and modified by Butterworth [81]. 

Vertical Surfaces. If the laminar flow direction is downward and gravity-controlled, heat transfer coefficient for internal condensation inside vertical tubes can be predicted using the correlations for external film condensation—see Table 17.23. The condensation conditions usually occur under annular flow conditions. Discussion of modeling of the downward internal convective condensation is provided in Ref. 76. 

Reactor pressure is normally controlled with turbine throttle and bypass valves. When the reactor vessel is isolated from the turbine condenser, an isolation condenser controls pressure. This device was selected because of its simplicity and because it provides high-pressure reactor water inventory control. A failure of the isolation condenser to control reactor pressure, is not expected during the plant live. If such a failure occurs, safety and depressurization valves provide a backup depressurization to the suppression pool which is positioned above the reactor vessel. When the reactor pressure is sufficiently low, check valves open in the suppression pool-to-vessel fill lines and water flows by gravity into the reactor vessel to keep the core covered. The response to a loss-of-coolant accident and transient with failure to scram is similar. 

Since acrylic polymerizations liberate considerable heat, violent or mnaway reactions are avoided by gradual addition of the reactants to the kettie. Usually the monomers are added by a gravity feed from weighing or measuring tanks situated close to the kettie. The rate of monomer addition is adjusted to permit removal of heat with full flow of water in the condenser and a partial flow in the cooling jacket. Flow in the jacket can be increased to control the polymerization in cases of erroneous feed rates or other unexpected circumstances. A supply of inhibitor is kept on hand to stop the polymerization if the cooling becomes inadequate. 

These designs have provisions for the removal of noncondensable vapors and air, for the prevention of freezing during cold weather. Excessive buildup of noncondensable vapors in the main condenser would prevent effective condensation. Protection against ice formation is usually accomplished by warm air recirculation and/or fan control. Condensed steam from cooling coils flows by gravity to condensate receivers and is pumped back to the feedwater circuit by a condensate pump. 

The rate of condensation on a vertical surface is controlled by the force of gravity acting on the condensed liquid film. A consideration of Eq. (11.20) shows for example that for a vertical plate the mean heat transfer rate from the plate with laminar flow in the film is proportional to gw. Attempts have therefore been made to increase condensation rates by using centrifugal forces instead of the gravitational force to drain the condensed liquid film from the cold surface [55], The simplest example of this would be condensation on the upper surface of a cooled circular plate rotating in a horizontal plane. This situation is shown in Fig. 11.23. A Nusselt-type analysis of this situation will be considered in the present section. 

The vapor leaving the exhausting column to pass to the heater is substantially in equilibrium with the liquid on the top plate of the column. It is partially condensed in the heater, enriched in its alcohol content, and then passes to the condenser where it is completely condensed. The portion of the vapor condensed in the heater is returned to the top plate of the column together with a controlled portion of the vapor condensed in the condenser, from the regulating bottle E. The distillate flows, through the tester F where its quantity and specific gravity may be measured, to the storage tank G. The water supply for the condenser is obtained from the constant level feed tank N. ... 

The plant shown in Fig. 18.7 is often simplified for small installations. In place of the reboiler, a heating coil may be placed in the bottom of the column and generate vapor from the pool of liquid there. The condenser is sometimes placed above the top of the column and the reflux pump and accumulator are omitted. Reflux then returns to the top plate by gravity. A special valve, called a reflux splitter, may be used to control the rate of reflux return. The remainder of the condensate forms the overhead product. 

Condensation in vertical tubes depends on the vapor flow direction and its magnitude. During downflow of vapor, if the vapor velocity is very low, then the condensate flow is controlled by gravity, and the Nusselt results for a vertical flat plate are applicable (unless the tube inside diameter is very small and tube wall curvature effects become important [36]). 

An interfacial shear may be very important in so-called shear-controlled condensation because downward interfacial shear reduces the critical Re number for onset of turbulence. In such situations, the correlations must include interfacial shear stress, and the determination of the heat transfer coefficient follows the Nusselt-type analysis for zero interfacial shear [76], According to Butterworth [81], data and analyses involving interfacial shear stress are scarce and not comprehensive enough to cover all important circumstances. The calculations should be performed for the local heat transfer coefficient, thus involving step-by-step procedures in any condenser design. The correlations for local heat transfer coefficients are presented in [81] for cases where interfacial shear swamps any gravitational forces in the film or where both vapor shear and gravity are important. 

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