A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part One: Zero-Dimensional Analysis

Abstract

A two-temperature CFD (computational fluid dynamics) solver is a prerequisite to any spacecraft re-entry numerical study that aims at producing results with a satisfactory level of accuracy within realistic timescales. In this respect, a new two-temperature CFD solver, hy2Foam, has been developed within the framework of the open-source CFD platform OpenFOAM for the prediction of hypersonic reacting flows. This solver makes the distinct juncture between the trans-rotational and multiple vibrational-electronic temperatures. hy2Foam has the capability to model vibrational-translational and vibrational-vibrational energy exchanges in an eleven-species air mixture. It makes use of either the Park TTv model or the coupled vibration-dissociation-vibration (CVDV) model to handle chemistry-vibration coupling and it can simulate flows with or without electronic energy. Verification of the code for various zero-dimensional adiabatic heat baths of progressive complexity has been carried out. hy2Foam has been shown to produce results in good agreement with those given by the CFD code LeMANS (The Michigan Aerothermodynamic Navier-Stokes solver) and previously published data. A comparison is also performed with the open-source DSMC (direct simulation Monte Carlo) code dsmcFoam. It has been demonstrated that the use of the CVDV model and rates derived from Quantum-Kinetic theory promote a satisfactory consistency between the CFD and DSMC chemistry modules.

Numerical Modeling and Simulation of Supersonic Flows in Propulsion Systems by Open-Source Solvers

“…In hyFoam the species heat capacities are obtained by adding the contributions of the different energy modes [21]. The same is applied for the total energy.…”

“…Unfortunately the latter OpenFOAM implementations are not yet fully open-source. The OpenFOAM-based hyFoam 1 and its variant with a two-temperature model hy2Foam [21,22], are solvers developed at the University of Strathclyde with the purpose of studying external aerodynamics in re-entry flows around vehicles characterized by high-temperatures effects.…”

A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis

“…(27) For a given colliding pair (m, s), the tabulated values of A m,s and B m,s used in this paper can be found in [4]. The collision-limited relaxation time introduced by Park [2] is a function of the average molecular speed,c m , the limited collision cross-section, σ v,m , and the number density of the colliding pair, n m,s .…”

“…Vibrational-vibrational (V-V) energy transfer is denoted by Q m, V−V and modelled according to the formulation given by Knab et al [26,27], as described in [4]. In Equation (14), Q h−e , Q m, e−V , and Q e−i stand for the energy exchange between free-electrons and heavy-particles, free-electrons and the vibrational mode, and the vibrational energy removal due to electron impact ionisation, respectively.…”

“…The term in U · ∇p e represents an approximation to the work done on the electrons by the electric field induced by the electron pressure gradient [28]. Finally, the vibro-electronic energy added or removed by chemical reactions to species m, and represented by Q m, C−V , is modelled either with the Park TTv model [2] or the coupled vibration-dissociation-vibration (CVDV) model in hy2Foam [4].…”