An Equation of State Tabulation Approach for Injectors with Non-Condensable Gases: Development and Analysis

In this work, a general equation of state (EOS) tabulation method is presented, which allows arbitrary combinations of EOSs in different phases and can be used with single-phase flow solvers by adding one additional transport equation for the total partial density of all noncondensable gases. The new tabulation method assumes instantaneous equilibrium for all phase change processes and uses Legendre transformation to construct the convex hull of the energy surface. Newton iterations are applied to improve the accuracy within the tabulation step as well as of the data retrieved at runtime. A high-order 5-equation multiphase solver with stiffened-gas equations as EOS for all phases and with the ability to use different time scales for the relaxation processes between liquid and vapor phase is used to discuss the full equilibrium assumption of the tabulation approach. Furthermore, results using different EOSs for the tabulation are compared. The implication of choosing a stiffened-gas equation or a cubic EOS, such as the Peng-Robinson equation for the vapor phase, on the saturation quantities is discussed. A nozzle simulation performed under typical gasoline direct injection (GDI) conditions is finally used to demonstrate the advantages of the new tabulation method and to evaluate additional computational cost.