Correlation for Volume Fraction of Solid-phase in Liquid-solid Upward Two-phase Flows in Vertical Pipes

Abstract

A correlation based on the drift-flux model is proposed to estimate volume fraction of solid-phase in developed steady liquid-solid upward two-phase flows in vertical pipes. The distribution parameter and the drift velocity in the model are expressed by the six non-dimensional groups composed of input physical quantities and others. Their fundamental frames are given as follows:
   V_S = J_S/α_S = Co(J_L+J_S) − {1-(d_S/D)²}α_L^s V_ST
       C_o=A₁(d_S/D)^a{J_L/(J_L+J_S)}^b{J_S/(J_L+J_S)}^e(ρ_S/ρ_L)^f{(J_L+J_S)/(gD)^0.5}^h
          {ρ_LD(J_L+J_S)/μ_L}^j + B₁
       α_L=A₂(d_S/D)^k{J_L/(J_L+J_S)}^m{J_S/(J_L+J_S)}ⁿ(ρ_S/ρ_L)^p{(J_L+J_S)/(gD)^0.5}^q
          {ρ_LD(J_L+J_S)/μ_L}^r + B₂
By using these new expressions, the volume fraction of solid-phase can be estimated with higher precisions than the author's previous correlation and Bankoff-type correlation.