Modelling of two-phase flow with second-order accurate scheme
The authors simulate numerically two-phase flows of liquid and vapor by using a second-order accurate computational scheme. They derive six differential equations from basic principles of continuity, momentum and energy for each phase, in a simplified one-dimensional formulation, but with proper attention to the mutual interactions between the phases. Two additional equations of state for each phase are needed to close the system of equations. Since mutual interactions between the phases cannot be precisely described, they rely on an extensive modeling with the best available knowledge. Furthermore, the Jacobian matrix of these equations possesses complex eigenvalues. The authors modify extensively the virtual-mass term, so that the equations become hyperbolic. As applications, the authors examine the Toumi's two-phase shock tube problem, the Riemann problem for the two-fluid-model, and Edwards transient pipe flow problem. In the two-phase shock tube problem, the authors illustrate the effects of the stiff source term, and show that the total energy profiles obtained from the first-order and second-order schemes are essentially the same. In the transient pipe flow problem, some comparisons of the obtained results on pressure variation against time at a certain location are made with the experimental data. There is practically no difference between the first-order and second-order calculations. However, both the first-order and second-order results on void-fraction at 1.5 m from the end of the pipe cannot follow the fast variation from the experimental data. The authors recognize significant uncertainties in the modeling of the general two-phase flows, although they claim the importance of the second-order schemes for fast transient events. The reviewer is torn between the inexactness of many approximations introduced in the study with higher-order computations, and the importance of simulating events when accident occurs in nuclear reactors.
scientific article; zbMATH DE number 1084045