COMBINING AN IMPLICIT SOLUTION WITH AN EXPLICIT CORRECTOR STEP FOR THE SOLUTION OF THE CONTINUITY EQUATIONS IN A TWO-FLUID SOLVER

Abstract

To model two-phase flows in industrial applications, for example the raceway zone in a blast furnace, an Eulerian two-fluid model is usually the method of choice. It has proven to predict the behavior of gas-solid flows well and has a justifiable computational demand. Although, it is already widely used, there are still some deficiencies which arise from the averaged equations. Especially the continuity equation needs some special care compared to single phase flows. The consistency and boundedness need to be ensured, which is not straightforward. One widely used approach to target this problem is to use the relative velocities in the continuity equation. A drawback is, that this modified equation is non-linear in the phase fraction and therefore needs to be solved iteratively if solved implicitly. We propose to solve the discretized equation by combining an implicit solution step with (an) explicit corrector step(s). This new approach was implemented in the open source software OpenFOAM® and compared with the standard implementation. The new algorithm gives good prediction results for several test cases and this implicit approach could lead to larger time steps through better stability of the solution procedure.