DRAG COEFFICIENT OF A SOLID SPHERE UNDER NON-ISOTHERMAL CONDITIONS

Abstract

The results of an experimental study of gravitational settling of a cooled (T = 82 K, 250 K) and a heated (T = 373 K, 473 K, 573 K) steel ball in glycerin and polymethylsiloxane liquids (PDMS-10000, PDMS-30000) in the range of the Reynolds numbers Re = 10−3–1 are presented. It is shown that the stationary velocity of gravitational settling of a particle decreases with its cooling and, conversely, it increases with heating of the particle. A time dependence of the distance traveled by the particle is found to be linear for both heated, cooled, and etalon (T = Tl) solid spheres. The effect of the difference in the particle and carrier medium temperatures on the drag coefficient of the solid sphere is analyzed. For the considered Reynolds numbers, it is revealed that the drag coefficient of a single solid sphere is determined by CD = a /Re , where a is the empirical coefficient depending on the ratio of the particle and liquid temperatures T = T /Tl . Using the regression analysis method, the expression for a drag coefficient of a solid particle under non-isothermal conditions at T >> 1 is found to be similar to the Hadamard –Rybczynski expression CD = 16/Re, which is obtained for a spherical bubble (or a drop). The empirical dependences of the drag coefficient for a cooled and a heated solid sphere on the difference in the particle and liquid temperatures δТ = 1− T are obtained.