Computational Methods for Homogeneous Multi-phase Real Fluid Flows at All Speeds

Abstract

Computations of all-speed multi-phase real fluid flows are known to be very demanding owing to several issues that include robust capturing of two-phase shock/phase discontinuity and proper scaling of numerical flux at steady/unsteady all-speed flows. This paper contributes several solutions for addressing difficulties arising from these issues. It consists of two part: development of accurate and efficient numerical schemes for multi-phase real fluid flows at all-speeds and high fidelity computation of a cryogenic cavitating flows around turbopump inducer. In first part, the baseline numerical schemes, RoeM and AUSMPW+ schemes for multi-phase flows, are extended for real fluid flow and improved for unsteady low Mach number flows. The shock-discontinuity-sensing term used in the two-phase RoeM and AUSMPW+ schemes is modified, as the existing shock-discontinuity-sensing term is not suitable for complex equation of state of real fluids. The accuracy of the two-phase RoeM and AUSMPW+ schemes for unsteady low Mach number flows is then improved through separate scaling of the velocity- and pressure-difference terms. it is shown that the proposed schemes, called RoeM N and AUSMPW+ N schemes, are capable of robustly and accurately capturing phenomena involving phase and shock discontinuities and interactions between them for numerous two-phase problems. Signifi- cant improvements in accuracy are observed for the unsteady convection- and acoustic-dominated problems over the previous two-phase RoeM and AUSMPW+ schemes. Finally, steam condensing and cryogenic cavitation problems are presented to demonstrate the accurate and robust behavior of the proposed schemes in simulating two-phase real fluid flows at all speeds. Based on the newly developed numerical methods, the second part deal with the numerical computations of cryogenic cavitating flows around turbopump inducer in liquid rocket. Quantifying thermal effect of cavitation is very important to understand and predict inducer performance. To better understand their impact on inducer performance, extensive numerical simulations of three-dimensional KARI turbopump inducer are carried out under various flow conditions with water and cryogenic fluids, and the difference in inducer flow physics depending on the working fluid are examined.