Characterization of non-equilibrium hypersonic flows using maximum entropy linear model

Abstract

This work proposes a general framework for developing reduced-order models (including both kinetics and transport) for hypersonic flows in thermo-chemical non-equilibrium. Reduced-order modeling is achieved by lumping energy states in groups and by prescribing withing each group a local representation which maximizes the entropy under constraints of mass and energy conservation (Maximum Entropy Linear model; MEL). The governing equations for the group parameters are obtained by taking energy moments of the master equations. Applications consider the complexity reduction of the O2 molecule vibrational kinetics. The accuracy of the MEL model is assessed via comparison with State-to-State predictions in two cases: (i) isothermal chemical reactor (dissociating case) and (ii) Lagrangian nozzle flow (recombining case). In both circumstances results show an excellent agreement with the master equation solution. The MEL is then applied to simulate the steady axi-symmetric viscous flow within a nozzle. Results underline the importance of a proper characterization of non-equilibrium re-combination within nozzles in high-enthalpy wind tunnels. To the author’s best knowledge, this case marks the first attempt of integration of a self-consistent reduced-order model (i.e., MEL model) in a CFD solver for non-equilibrium flows.