An Oscillation-Free Real Fluid Quasi-Conservative Finite Volume Method for Transcritical and Phase-Change Flows

TL;DR

The paper tackles spurious pressure oscillations in real-fluid simulations containing transcritical and phase-change phenomena by generalizing the quasi-conservative five-equation framework. It introduces Real Fluid Quasi-Conservative (RFQC) methodology that locally freezes two thermodynamic coefficients, $ξ=\frac{1}{Γ}$ and $E_0$, evolves them by advection, reconstructs an oscillation-free pressure with $p=\frac{ρ e - E_0}{ξ}$, and enforces consistency through a thermodynamic re-projection. Theoretical analysis shows the re-projection error grows with entropy production, yielding high-order accuracy in smooth regions and remaining aligned with shock-capturing errors in discontinuous regions; numerical tests with n-dodecane under Peng–Robinson EoS demonstrate robust performance across transcritical, flash evaporation, and shock–interface problems, outperforming both pressure-based and double-flux methods in stability and accuracy. The work offers a practical, generalizable toolkit for accurate, oscillation-free real-fluid simulations in propulsion-relevant regimes, with future directions including higher-order schemes and 3D extensions.

Abstract

A new Real Fluid Quasi-Conservative (RFQC) finite volume method is developed to address the numerical simulation of real fluids involving shock waves in transcritical and phase-change flows. To eliminate the spurious pressure oscillations inherent in fully conservative schemes, we extend the classic five-equation quasi-conservative model, originally designed for two-phase flows, to real fluids governed by arbitrary equations of state (EoS). The RFQC method locally linearizes the real fluid EoS at each grid point and time step, constructing and evolving the frozen Grüneisen coefficient $Γ$ and the linearization remainder $E_0$ via two advection equations. At the end of each time step, the evolved $Γ$ and $E_0$ are utilized to reconstruct the oscillation-free pressure field, followed by a thermodynamic re-projection applied to the conserved variables. Theoretical analysis demonstrates that, in smooth regions, the energy conservation error of the RFQC method is a high-order term relative to the spatial reconstruction truncation error. In discontinuous regions, this error is determined by the entropy increase rate, thereby maintaining consistency with the inherent truncation error of shock-capturing methods. A series of numerical tests verifies that the method can robustly simulate complex flow processes with only minor energy conservation errors, including transcritical flows, phase transitions, and shock-interface interactions. The RFQC method is proven to be both accurate and robust in capturing shock waves and phase transitions.

Figures (8)

• Figure 1: Fuel spray and phase diagram
• Figure 2: Comparison of frozen thermodynamic coefficients between the two methods
• Figure 3: Verification of Energy Conservation Error in Smooth Advection
• Figure 4: Results of the Transcritical RP Calculation
• Figure 5: Results of the Completely Evaporated FeRP Calculation