Supersonic and Hypersonic Flows

Renewed interest in hypersonic air vehicles such as the Boeing X-51 has focused research on topics critical to hypersonic flight. The design of hypersonic air vehicles involves numerous engineering disciplines including aerothermodynamic analysis. Indicative examples from our work on supersonic and hypersonic flows are presented below:

In particular, the interaction of shock waves with the vehicle boundary layers can lead to regions of enhanced aerothermody- namic loading, and therefore accurate modelling of shock wave boundary layer interactions(‘‘shock interactions’’)is essential. During the past decade two NATO Research Technology Organiza- tion (RTO) Working Groups (WGs) have assessed the capabilities for prediction of aerothermodynamic loads in high speed flight. AGARD Working Group 18 (WG18) examined the Computational Fluid Dynamics (CFD) capability for prediction of 2-D and 3-D shock wave laminar and turbulent boundary layer interactions for generic configurations such as single fin, double fin and hollow cylinder flare (Fig. 1).

Hypersonic flow around a double cone geometry (see [1] for more details)

We have also employed a Finite Volume Godunov-type implicit large eddy simulation method to study fuel injection into the combustion chamber of HyShot-II scramjet engine without chemical reaction/combustion in order to understand the fuel injection and air-fuel (hydrogen) mixing [2]. The study is carried out in two parts; part one presents analysis of 2D HyShot-II geometry (without fuel injection) incorporating high temperature gas formulation which is validated against the NASA Thermally-Perfect-Gas code in order to obtain the combustion chamber inlet conditions. These combustor initial conditions are then utilized in part two for 3D combustion chamber simulations with hydrogen injection but cold flow where a digital filter based turbulent inflow boundary condition has been utilized. The purpose of our study is to understand the flow physics, hydrogen jet penetration and air & fuel mixing inside the HyShot-II combustor which is vital at the design stages. Various flow features are investigated such as the Mach number, velocity, pressure distributions, temperature, turbulent kinetic energy, Reynolds stresses and the effect of counter rotating vortices on mixing. The results of full geometry simulations are compared with computational results from the German Aerospace Centre, DLR, whereas due to unavailability of any data for hydrogen cold flow the validity of the results is based upon a similar validation case [3]

Internal and external shock formations around the HyShot-II scramjet engine: (a) Two dimensional full geometry analysis; (b) Close-up view of shock formations at bleed section and combustion chamber entrance showing a shock generated by bottom wall and entering into combustion chamber; (c) Mach number contours at combustion chamber entrance; and (d) Shock train travelling inside combustion chamber.

Jet injection into a supersonic cross-flow is a challenging fluid dynamics problem in the field of aerospace engineering which has applications as part of a rocket thrust vector control system for noise control in cavities and fuel injection in scramjet combustion chambers. Several experimental and theoretical/numerical works have been conducted to explore this flow; however, there is a dearth of literature detailing the instantaneous flow which is vital to improve the efficiency of the mixing of fluids. We have studied a sonic jet in a Mach 1.6 free-stream using a finite volume Godunov type implicit large eddy simulations technique, which employs fifth-order accurate MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) scheme with modified variable extrapolation and a three-stage second-order strong-stability-preserving Runge–Kutta scheme for temporal advancement. A digital filter based turbulent inflow data generation method is implemented in order to capture the physics of the supersonic turbulent boundary layer. This paper details the averaged and instantaneous flow features including vortex structures downstream of the jet injection, along with the jet penetration, jet mixing, pressure distributions, turbulent kinetic energy, and Reynolds stresses in the downstream flow. It demonstrates that Kelvin–Helmholtz type instabilities in the upper jet shear layer are primarily responsible for mixing of the two fluids. The results are compared to experimental data and recently performed classical large eddy simulations (LES) with the same initial conditions in order to demonstrate the accuracy of the numerical methods and utility of the inflow generation method. Results show equivalent accuracy for 1/ 45th of the computational resources used in the classical LES study.

Instantaneous snapshot of incoming shock turbulent boundary layer (STBL) using digital filter based turbulent inflow data generator and the injection of a sonic jet creating a complex flow structure downstream the jet plume; density gradient contours (vertical plane) and velocity contours (horizontal plane). The line indicates the Mach 1.5 position to demonstrate the location of lambda shock just upstream of the jet plume.
Typical shocks and flow features are identified as the sonic jet mixes with transverse Mach 1.6 flow; Two-dimensional jet injection into a supersonic cross-flow (JISC) structures at the midline transverse plane (Z/D =0, top figure) and three-dimensional iso-surfaces (bottom figure)

Other studies we have performed

The hypersonic flow around a blunted-cone– cylinder–flare (HB-2). See below flow around the HB-2 and comparisons between CFD and experiments [4, 5].
Shock diffraction around a cylinder
Nozzle flows, space propulsion


  • D. Knight, J. Longo, D. Drikakis, D. Gaitonde, A. Lani, I. Nompelis, B. Reimann, L. Walpot, Assessment of CFD capability for prediction of hypersonic shock interactions, Progress in Aerospace Sciences, Vol 48-49, 8-26, 2012.
  • Z.A. Rana, B. Thornber, D. Drikakis, Dynamics of Sonic Hydrogen Jet Injection and Mixing Inside Scramjet Combustor, Journal of Engineering Application in Computational Fluid Mechanics, Vol 7, 1, 13-39, 2013.
  • Z.A. Rana, B. Thornber, D. Drikakis, Transverse jet injection into a supersonic turbulent cross-flow, Physics of Fluids, Vol. 23, 4, 046103, 2011.
  • S. Tissera, D. Drikakis, T. Birch, Computational Fluid Dynamics Methods for Hypersonic Flow Around Blunted-Cone-Cylinder-Flare, Journal of Spacecraft and Rockets, Vol. 47, 4, 563-570, 2010.
  • P. Tsoutsanis, V.A. Titarev, D. Drikakis. WENO schemes on arbitrary mixed element unstructured meshes in three space dimensions, Journal of Computational Physics, Vol. 230, 4(20), 1585-1601, 2011.
  • Z.A. Rana, B. Thornber, D. Drikakis, On the importance of generating accurate turbulent boundary condition for unsteady simulations, Journal of Turbulence, Vol. 12, 2011.
  • A. Panaras, D. Drikakis, Physical and numerical aspects of the high-speed unsteady flow around concave axisymmetricbodies, CEAS Space Journal, 1(1-4), 23-32, 2011.
  • A. Panaras, D. Drikakis, High-speed unsteady flows around spiked-blunt bodies, Journal of Fluid Mechanics, Vol. 632, 69-96, 2009.
  • D. Drikakis, D. Ofengeim, E. Timofeev, P. Voinovich, Computation of non-stationary shock-wave/cylinder interaction using adaptive grid methods, Journal of Fluids and Structures, 11, 7, 665-691, 1997.
  • D. Ofengeim, D. Drikakis, Simulation of blast wave propagation over a cylinder, Shock Waves Journal, 7, 305-317, 1997.
  • D. Drikakis, S. Tsangaris, Real Gas effects for Compressible Nozzle Flows, ASME Journal of Fluids Engineering, Vol. 115, 115-120, 1993.
  • D. Drikakis, S. Tsangaris, On the Accuracy and Efficiency of CFD Methods in Real Gas Hypersonics, International Journal for Numerical Methods in Fluids, Vol. 16, 759-775, 1993.