An analytical model of subcritical and critical vapor-liquid flow through a granular bed

This paper presents a computational and experimental justification of a theoretical model for the two-phase vapor-liquid flow through a fixed bed of solid particles. The theoretical description is based on the equations of gas dynamics of the granular bed and the homogeneous model of a single-component two-phase flow, given the difference between the velocities of liquid and vapor phases. Relationships between the phase slip ratio and polytropic coefficient of isenthalpic expansion of vapor-liquid flow were obtained using the multi-parameter nonlinear regression. We used the experimental data on the vapor-liquid flow with an inlet pressure, P₁, of 0.6-1.2 MPa and an inlet flow quality, x₁, of 0.016-0.178 through a H=50-355 mm bed consisting of steel spheres, 2 and 4 mm in diameter, d. An expression for the critical pressure ratio in the granular bed is proposed. The developed model makes it possible to predict the values of mass velocity of the mixture over the entire range of experimental data with an average error of 3%. Based on the model equations, we obtained expressions for dimensionless mass velocity depending on the pressure ratio that can be applied to two-phase flows through both granular beds and other porous media.