Numerical effects of the semi-conservative form of momentum equations for multi-dimensional two-phase flows

Some of the thermal hydraulics codes for multi-dimensional two-phase flow analysis use the non-conservative form of momentum equations for numerical convenience. From a mathematical point of view, these equations are equal to those in the conservative form. But, numerical integration of the non-conservative momentum equations over a control volume results in different solution characteristics, which may cause inaccurate solutions under some two-phase flow conditions. In this paper, a semi-conservative form of the momentum equations is suggested which is close to the conservative form but still maintains the feature of the non-conservative form. The numerical results of the semi-conservative and the non-conservative forms are compared against analytical solutions and the solutions of the FLUENT code that uses the conservative form. The results clearly showed that the semi-conservative form of the momentum equations provides better solutions than the non-conservative form, especially for heterogeneous two-phase flows.