A computational study of inviscid hypersonic flows using energy relaxation method

Abstract

Reasonable analysis of hypersonic flows requires a thermodynamic non-equilibrium model to properly simulate strong shock waves or high pressure and temperature states in the flow field. The energy relaxation method (ERM) has been used to model such a non-equilibrium effect which is generally expressed as a hyperbolic system of equations with a stiff relaxation source term. Relaxation time that is multiplied with source terms is responsible for nonequilibrium in the system. In the present study, a numerical analysis has been carried out with varying values of relaxation time for several hypersonic flows with AUSM (advection upstream splitting method) as a numerical scheme. Vibration modes of thermodynamic nonequilibrium effects are considered. The results obtained showed that, as the relaxation time reduces to zero, the solution marches toward equilibrium, while it shows non-equilibrium effects, as the relaxation time increases. The present computations predicted the experiment results of hypersonic flows with good accuracy. The work carried out suggests that the present energy relaxation method can be robust for analysis of hypersonic flows.

Thrust augmentation optimization through supersonic after-burning in scramjet engine nozzles via surrogate-assisted evolutionary algorithms

“…The Navier-Stokes equations for steady flowfields are solved via an implicit algorithm with second order spatial accuracy, higher order term relaxation with a relaxation factor of 0.25 is used to accelerate convergence. Flux vectors are computed according to the Advection Upstream Splitting Method (AUSM), which accurately captures shock discontinuities and has been used in a wide range of problems concerning hypersonic aerodynamics [23,24]. Combustion within the nozzle is represented by the Evans and Schexnayder supersonic hydrogen flame model which considers 12 species and 25 chemical reactions as presented in Table 3 [25].…”