Forced convection boiling, calculation

Whalley, P. B., P. Hutchinson, and G. F. Hewitt, 1973, The Calculation of Critical Heat Flux in Forced Convective Boiling, Rep. AERE-R-7520, European Two Phase Flow Group Meeting, Brussels. (5) Whalley, P. B., P. Hutchinson, and G. F. Hewitt, 1974, The Calculation of Critical Heat Flux in Forced Convection Boiling, Heat Transfer 1974, vol. IV, pp. 290-294, Int. Heat Transfer Conf., Tokyo. (5) Wichner, R. P, and H. W. Hoffman, 1965, Pressure Drop with Forced Convection Boiling of Potassium, Proc. Conf. on Applications of Heat Transfer Instrumentation to Liquid Metals Experiments, ANL-7100, p. 535, Argonne National Lab., Argonne, IL. (3)... 

Both the bubble departure frequency / and the number of nucleation centers n are difficult to evaluate. These quantities are known to be dependent on the magnitude of the heat flux, material of construction of the tube, roughness of the inside wall, liquid velocity, and degree of superheat in the liquid elements closest to the tube wall. Koumoutsos et al. (K2) have studied bubble departure in forced-convection boiling, and have formulated an equation for calculating bubble departure size as a function of liquid velocity. 

The normal practice in the design of forced-convection reboilers is to calculate the heat-transfer coefficient assuming that the heat is transferred by forced convection only. This will give conservative (safe) values, as any boiling that occurs will invariably increase the rate of heat transfer. In many designs the pressure is controlled to prevent any appreciable vaporisation in the exchanger. A throttle value is installed in the exchanger outlet line, and the liquid flashes as the pressure is let down into the vapour-liquid separation vessel. 

The other parameters in Eqs. (67) and (68) are evaluated in the same manner as in Section II,B,3, with the single exception of qwn. The evaluation of the wall heat flux for nucleate boiling in flowing systems has been described briefly in the reviews by Westwater (W4, W5) and Leppert and Pitts (L2). Less quantitative information is available for this case than for pool boiling. According to these authors, the heat flux in forced-convection nucleation is independent of the fluid velocity. Westwater (W5) and Roh-senow (R1) have presented a number of correlations for calculating the total heat flux in forced-convection nucleation the general form of these correlations is... 

Our development in this chapter is primarily analytical in character and is concerned only with forced-convection flow systems. Subsequent chapters will present empirical relations for calculating forced-convection heat transfer and will also treat the subjects of natural convection and boiling and condensation heat transfer. 

Here hNB is the nucleate boiling coefficient (calculated from equations analogous to those given previously) and hFC is the forced convective component, which is related to the heat transfer coefficient h, for the liquid phase flowing alone across the tube bundle by the expression... 

Suppression correlations. Here, an attempt is made to correlate the suppression of either the nucleate boiling or the forced convective component and to correct for this suppression in calculating the total heat transfer coefficient. 

At high enough qualities and mass fluxes, however, it would be expected that the nucleate boiling would be suppressed and the heat transfer would be by forced convection, analogous to that for the evaporation for pure fluids. Shock [282] considered heat and mass transfer in annular flow evaporation of ethanol water mixtures in a vertical tube. He obtained numerical solutions of the turbulent transport equations and carried out calculations with mass transfer resistance calculated in both phases and with mass transfer resistance omitted in one or both phases. The results for interfacial concentration as a function of distance are illustrated in Fig. 15.112. These results show that the liquid phase mass transfer resistance is likely to be small and that the main resistance is in the vapor phase. A similar conclusion was reached in recent work by Zhang et al. [283] these latter authors show that mass transfer effects would not have a large effect on forced convective evaporation, particularly if account is taken of the enhancement of the gas mass transfer coefficient as a result of interfacial waves. 

In the bottom of Fig. 4.3-8 the heat transfer coefficient is indicated depending on the temperature difference. In the range of convective boiling the heat flux and the heat transfer coefficient rise with the temperature difference. The heat transfer coefficient can be calculated with the correlations for natural or forced convection. 

The steady-state simulation showed that the average reactor core channel operates in sub-cooled forced convection, with the hot core channel is in sub-cooled nucleate boiling. A minimum critical heat flux (CHF) ratio of 7.2 was calculated for the hottest location, indicating a large margin of safety during normal operation. The initial conditions obtained from the analysis of normal operation were used as the initial condition in the accident studies. 

All modules use the 2-fluid model to describe steam-water flows and four non-condensable gases may be transported. The thermal and mechanical non-equilibrium are described. All kinds of two-phase flow patterns are modelled co-current and counter-current flows are modelled with prediction of the counter-current flow limitation. Heat transfer with wall structures and with fuel rods are calculated taking into account all heat transfer processes ( natural and forced convection with liquid, with gas, sub-cooled and saturated nucleate boiling, critical heat flux, film boiling, film condensation). The interfacial heat and mass transfers describe not only the vaporization due to superheated steam and the direct condensation due to sub-cooled liquid, but also the steam condensation or liquid flashing due to meta-stable subcooled steam or superheated liquid. 

In the calculation of the heat transfer in saturated boiling it is presumed that the heat transfer is predominantly determined by the bubble formation. In addition, convection also has some influence on the heat transfer, although this may only be small. Models and empirical equations start from the heat transfer in boiling in free flow. The influence of forced flow is taken into account with an extra term. This is based on the concept that the growth of the bubbles is only slightly influenced by the flow, as long as the bubbles are smaller than the superheated boundary layer. The heat transfer coefficient is a combination of two parts... 

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