Water faucet problem by mixture two phase flow equations

Abstract

A set of mixture equations is used for the simulation of a two phase flow system using Lax-Friedrichs method. The governing equations are used to obtain numerical solutions of the gas volume fraction and the liquid phase velocity for the water faucet problem. It is observed that the liquid phase velocity is in excellent agreement with the analytical trends. The only deviations that are found are near the regions of discontinuity. The gas volume fraction at different time instants shows significant deviations from the analytical values. The peak values as well as the location of the peak values of gas volume fraction are far from the analytical values. This may be attributed to the highly dissipative and dispersive nature of the Lax-Friedrichs method. Another possible reason for this behavior is the oscillations in gas phase velocity. The present set of equations is able to describe a two phase system with reasonable accuracy and much simpler mathematics.A set of mixture equations is used for the simulation of a two phase flow system using Lax-Friedrichs method. The governing equations are used to obtain numerical solutions of the gas volume fraction and the liquid phase velocity for the water faucet problem. It is observed that the liquid phase velocity is in excellent agreement with the analytical trends. The only deviations that are found are near the regions of discontinuity. The gas volume fraction at different time instants shows significant deviations from the analytical values. The peak values as well as the location of the peak values of gas volume fraction are far from the analytical values. This may be attributed to the highly dissipative and dispersive nature of the Lax-Friedrichs method. Another possible reason for this behavior is the oscillations in gas phase velocity. The present set of equations is able to describe a two phase system with reasonable accuracy and much simpler mathematics.