空間率関数とレイノルズ数

抄録

The sedimentation rate of multiparticle suspension in a stationary fluid, u_m, decreases with increasing particle concentrations. The voidage function F(ε) is defined as F(ε)=v_∞/u_m, where v_∞ is the terminal velocity of single particle in the infinite stationary fluid.
In order to generalize the voidage function to cover the entire ranges of flow, namely, laminar (St), intermediate (Al), and turbulent (N) flow regions, the following equation is given.
F_St(ε)=[F_Al(ε)]^m=[F_N(ε)]²
where m varies from 1 to 1.63 continuously with Reynolds number in the intermediate flow region, when calculated from the drag coefficient correlation of a single sphere motion according to Schiller. Previously, Richardson-Zaki has pointed out that m varies from 1 to 2 in the same intermediate flow region and some other investigators reported m to be 1.4 or constant.
The voidage function in each flow region, obtained from the correlations of Kozeny-Carman or Ergun, has been found in good agreement with the voidage function of Richardson-Zaki in a certain range of voidage.