Turbulence Modelling for Aerodynamic Heating in Hypersonic Flows

Abstract

The current study aims to validate and extend RANS approaches, using linear and non-linear eddy viscosity models, by considering the modelling of hypersonic flows, especially those with SWBLIs. The main objective is to assess the performance of three EVMs, widely used in industrial applications, in predicting flow separation and aerodynamic heating in hypersonic flows, and to explore adaptations that can improve their performance, by accounting for influences such as strong compressibility and discontinuity in flow variables. The turbulence models employed are the linear k-ε model of Launder and Sharma (1974) (LSY model), the linear k-ω shear stress transport model of Menter et al. (2003) (SST model) and the non-linear k-ε model of Craft et al. (2000) (CLS model). To give an objective, uniform and reliable evaluation of the performance of the turbulence models selected, the formulation of RANS equations for high-speed flows has first been investigated. A new density-based compressible solver, with various options of including, or excluding, several terms that were typically omitted in low speed (and sometimes high speed) flow simulations has developed within the framework of OpenFOAM. The influence of partially, or fully, ignoring these terms in the RANS equations has been analysed with comparisons of spatial quantities and wall quantities in supersonic and hypersonic cases. The numerical results show that while omitting these terms is typically fine for low-speed applications, they can have a significant effect on predictions of SWBLI cases in the hypersonic regime. There-fore, the form of RANS equations with all these terms fully included is selected to run all the simulations in this research. The non-linear CLS model has been implemented in the OpenFOAM framework in a similar way as the linear models tested in the current study and then examined, together with the other two linear models, by comparing results over a range of typical hypersonic SWBLIs benchmark cases, 2D, axisymmetric or 3D, over a wide range of Mach numbers and Reynolds numbers. The three models tested do generally return reasonable predictions of wall pressure in most cases, while the non-linear CLS model presented the best capability among the three in predicting the flow separations. Nevertheless, the wall heat flux in the interaction region is overpredicted in most cases by all three models (sometimes showing quite a dramatic overprediction). To improve the accuracy of predictions of wall heat flux, a new source term in the modelled dissipation rate equation, aimed at restricting the turbulent length scale in the shock wave boundary layer interaction region, is proposed. This term will cause no impact on incompressible flows and only has a limited influence on the predic-tions of wall pressure in hypersonic flows. The introduction of this new source term to the LSY and CLS models is shown to largely eliminate their over predictions of the peaks of wall heat flux in the interaction region (in some test cases, the peak value was reduced by around 80%), while the extra cost of the numerical simulation is less than 2%.

Date of Award	31 Dec 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Hector Iacovides (Supervisor) & Timothy Craft (Supervisor)