title: Simulation of 3-D Viscous Flow Around a Nozzle-Afterbody at High Speeds
Creators: name: Hoffman, Wendy B.
Publisher: name: Old Dominion University
publisherIdentifier: https://ror.org/04zjtrb98
publisherIdentifierScheme: ROR
Year: 1991

description: Turbulent shear flows at supersonic and hypersonic speeds around a nozzle-afterbody are numerically simulated and investigated. The specific application is for the flow around the nozzle-afterbody of a generic hypersonic vehicle. Accurate simulation of viscous, separating flows is not an easy task, and it is complicated by turbulence modeling concerns. A main objective of this study is to numerically simulate the afterbody flowfield while addressing the turbulence modeling problem. The viscous flow considered i~ this study is characterized by three-dimensional corner flows, shock boundary layer interactions, plume flow, shear layers, and cross-flow separations. Accurate simulation of this flow requires solution of the three-dimensional compressible Navier-Stokes equations, which are Reynolds-averaged and used in conjunction with a turbulence model to account for turbulent flow effects. The governing equations are integrated over a control volume and ensure conservation of mass, momentum and energy across cell interfaces. An implicit, upwind method is used to solve the governing equations. The convective and pressure terms are upwind differenced using either the Van Leer flux-vector splitting method or the Roe flux difference splitting method. Convergence is accelerated by a mesh-sequencing technique. The effect of turbulence is incorporated by a modified Baldwin-Lomax eddy viscosity model. This algebraic model is chosen as a compromise for the large computational time and memory required by the flow being simulated. The modifications to the model reflect the effects of high compressibility, multiple walls, and turbulent memory effects (wake relaxation), in addition to the local equilibrium effects.

The nozzle-afterbody configuration requires upstream boundary layer profiles for initial boundary conditions. The supersonic duct flow solution depicts boundary layer growths on the side walls and corner regions. The external double-corner flow solution computationally captures the interaction between the two adjacent hypersonic streams. A detailed investigation of the nozzle-afterbody flowfield reveals a three-dimensional expanding nozzle flow which forms a shear layer as it mixes with the hypersonic flow. The flow is further complicated by crossflow separations which result from shock boundary layer interactions. The computed pressure distributions compare favorably with the experimentally obtained surface and off-surface flow surveys. These results show the suitability of the numerical method to these types of flows.

The success of the standard Baldwin-Lomax model in simulating turbulence for this flow type is shown by comparing it to a laminar case. The modifications made to the model are also shown to improve flow prediction when compared to the standard Baldwin-Lomax model.

A better flow prediction may be achieved with a more sophisticated turbulence model, though this would be costly, if not infeasible for this case. Implementation of three-dimensional adaptative gridding and multispecies mixing to simulate the jet exhaust would most likely improve the solution accuracy.