Estimation of the Drop Size in Dispersed Flow

The formulas for calculating the characteristic drop size for the mean Sauter diameter have been compared. The question on various forms of the size distribution of drops has been considered. To substantiate the applicability of the compared formulas for calculating the thermohydrodynamics in the circuits of nuclear power plants, experimental data on the wall temperature in a dispersed fl ow have been used. It has been shown that the Sauter diameter values calculated using the wall temperature in the supercritical region are in good agreement with sparse direct measurements of the drop size in steam-water fl ows. The drop sizes calculated using the tested formulas obtained for two-component gas-liquid fl ows or for single-component fl ows of coolants (various kinds of freons) and liquefi ed nitrogen turned out to be much lower. It has been shown that it is necessary to recalculate the numerical coeffi cients in the considered formulas in using them for steam-water fl ows. Introduction. Reliable and safe operation of nuclear power plants is substantiated at the design stage with the use of computer programs (codes) for better assessment of the heat transfer and hydrodynamics in the coolant loop. Most codes are based on the spatial one-dimensional two-liquid model of the two-phase fl ow. The differential equations of the model include terms refl ecting the interaction of the phases with the channel walls and on the interface determined by empirical formulas chosen depending on the fl ow conditions of the two-phase fl ow. These formulas form (together with the fl ow patterns) a system of closing relations, without which the equations of the two-liquid model cannot be solved. In the dispersed fl ow, important closing relations are the formulas for determining the drop size (these can be several formulas and an algorithm for choosing a formula corresponding to current conditions) and the chosen model of the heat transfer in the dispersed fl ow that permits distributing the heat input through the wall between the phases, as the equations of the two-liquid model require. At present, the deviation of the wall temperature calculated with the aid of codes from experimental values in the supercritical region is ±100 K. This is a too large value (for comparison, in the subcritical region the above deviation is ±10 K). It is necessary to increase the accuracy of determining the wall temperature in the supercritical zone when using computing codes. Attempts to take into account the contribution of drops to the heat transfer in the supercritical region (for example, (1-3)) lead to the introduction into the calculation formulas of such quantities as the characteristic size of drops, the rate of their fallout, the turbulent cooling coeffi cient, and the like, which cannot so far be reliably determined experimentally for steam-water fl ows in the range of practically important parameters. The above quantities can be calculated in describing the motion of drops by the Lagrange method that permits obtaining detailed information on the interaction of drops with the thermally nonequilibrium carrier fl ow, with the walls, and with one another; however, it requires enormous calculations. The equations of the two-liquid two-phase model usually used in codes are based on the Euler approach to the description of each phase. The Euler approach is the most economical of calculations and permits developing "fast" programs, which happens to be of fundamental importance for programs of more accurate estimation (e.g., in developing simulators).