Estimation of solid concentration in solid–liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study, an inverse-problem method was applied to estimate the solid concentration in a solid–liquid two-phase flow. An algebraic slip mixture model was introduced to solve the forward problem of solid–liquid convective heat transfer. The time-average conservation equations of mass, momentum, energy, as well as the volume fraction equation were computed in a computational fluid dynamics (CFD) simulation. The solid concentration in the CFD model was controlled using an external program that included the inversion iteration, and an optimal estimation was performed via experimental measurements. Experiments using a fly-ash–water mixture and sand–water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method. The estimated results were rectified using a method based on the relationship between the estimated results and estimation error; consequently, the accuracy of the corrected inversion results improved significantly. After a verification through experiments, the inverse-problem method was concluded to be feasible for predicting the solid concentration, as the estimation error of the corrected results was within 7% for all experimental samples for a solid concentration of less than 50%. The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid–liquid two-phase flow systems.