Comparison of energy-, pressure- and enthalpy-based approaches for modeling supercritical flows

Abstract

At supercritical conditions, thermodynamics may become strongly nonlinear which is reflected by large thermodynamic Jacobian values. This means that small variations in density, momentum or energy can result in large pressure perturbations. Because of such nonlinearities, simulations of high-pressure flows are subject to stability issues when the conservative form of the Navier-Stokes system is employed. In high-Reynolds number simulations, transported quantities

Large-Eddy Simulations of the Mascotte Test Cases Operating at Supercritical Pressure

“…One major issue is the capability of numerical methods to remain stable and accurate in regions of large density gradients. The strong non-linearity of thermodynamic properties renders the system highly sensitive to small variations of density or energy, that may generate high amplitude, unphysical, pressure oscillations [26,31,[38][39][40]. These unphysical phenomena, produced in underresolved gradients or during numerical dissipation, may artificially perturb the flow and affect the prediction of combustion instabilities.…”

On the Consideration of Diffusive Fluxes Within High-Pressure Injections

“…For example, an adiabatic mixing is generally defined as a thermodynamic process where mixing is controlled solely by convective transport and is not influenced by any diffusive transport of heat or mass from the surrounding. Investigations in the context of super-and transcritical jet injections were performed by Lacaze et al, Ma and Matheis [23,25,27]. For a given pressure and adiabatic conditions, the specific molar enthalpy is a linear function in the molar composition space with…”

“…Adiabatic mixing was observed with a fully-conservative approximation of the Navier-Stokes equations in [23,27] with insufficient grid resolution. For a given pressure and isochoric conditions the specific molar volume is a linear function in the molar composition space with…”

“…Isochoric mixing was observed with quasi-conservative approximations of the Navier-Stokes equations in [23,27] with insufficient grid resolution. Here we use the double flux method presented by Föll et al [14][15][16] and literature therein.…”

“…However diffusive or non-equilibrium thermodynamic effects related to, e.g. Fourier, Fickian, Dufour or Soret contributions are not considered in plots presented in [23,25,27] and Fig. 4.…”