Compressible Flow at High Pressure with Linear Equation of State

TL;DR

This paper develops a closed-form solution for high-pressure compressible flow using a cubic equation of state, capturing real-gas effects and their impact on flow variables and shock behavior.

Contribution

It introduces a simplified, analytical approach to model real-gas effects in compressible flow using a cubic equation of state, applicable to various flow scenarios.

Findings

Real-gas effects significantly alter flow variables and shock relations.

The method provides modifications for choked flow, shock waves, and acoustic oscillations.

Real-gas effects can substantially increase pressure amplitudes and shock strengths.

Abstract

Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, A and B, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behavior, a closed-form solution is obtained that is valid over a wide range of conditions. An expansion in these molecular-interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behavior. Real-gas modifications in density, enthalpy, and sound speed for a given pressure and temperature lead to variations in many basic compressible flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear-wave propagation, and flow across a shock wave, all for the real gas. Modifications are obtained for allowable mass-flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl's shock relation, and the Rankine-Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and be applied to multicomponent flows or to more-complex flow configurations.