Robust Spectral Solver for High-Fidelity Investigations of Aerospike Nozzle Flow Dynamics

Abstract

A spectral element solver is developed for the high-fidelity simulation of the unsteady flow over an aerospike nozzle. The Navier-Stokes solver is a kinetic-energy-preserving, discontinuous Galerkin spectral element method (DGSEM) combined with a hybridization of an entropy viscosity (EV) and a finite-volume subcell element (FVSE) shock-capturing scheme. The diffusive FVSE method is locally called only at locations where the EV method cannot sufficiently smooth the sharp solution gradients that suddenly appear in the supersonic, vortex-dominated jet generated by the aerospike nozzle. Two-dimensional tests of a perfectly expanded and an underexpanded nozzle flow demonstrate that the method is high-order accurate and captures unsteady flow phenomena at supersonic and hypersonic conditions. A resolved three-dimensional simulation at a Reynolds number of 95,000 shows that the solver implicitly models turbulent dissipation at the subgrid scales. To the authors' knowledge, these simulations represent the first DGSEM computations of the resolved, unsteady flow over an aerospike nozzle.