Three-Dimensional Modeling Shock-Wave Interaction with a Fin at Mach 5

Research Article - Mechanical Engineering
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Abstract

The three-dimensional single-fin configuration finds application in an intake geometry where the cowl-shock wave interacts with the side-wall boundary layer. Accurate numerical simulation of such three-dimensional shock/turbulent boundary-layer interaction flows, which are characterized by the appearance of strong crossflow separation, is a challenging task. Reynolds-averaged Navier–Stokes computations using the shock-unsteadiness modified Spalart–Allmaras model is carried out at Mach of 5 at large fin angle of \(23^{\circ }\). The computed results using the modified model are compared to the standard Spalart–Allmaras model and validated against the experimental data. The focus of the work is to implement the modified model and to study the flow physics in detail in the complex region of swept-shock-wave turbulent boundary-layer interaction in terms of the shock structure, expansion fan, shear layer and the surface streamlines. The flow structure is correlated with the wall pressure and skin friction in detail. It is observed that the standard model predicts an initial pressure location downstream of the experiments. The modified model reduces the eddy viscosity at the shock and predicts close to the experiments. Overall, the surface pressure using modified model has predicted accurately at all the locations. The skin friction is under-predicted by both the models in the reattachment region and is attributed to the poor performance of turbulence models due to flow laminarization.

Keywords

High-speed flows Shock wave Turbulent boundary layer Shock-unsteadiness Separation bubble Turbulence modeling Single fin Compressible flows Computational fluid dynamics 

List of symbols

\(b'_1\)

Shock-unsteadiness damping parameter

\(C_\mathrm{f}\)

Skin friction coefficient

\(c_{b_1}'\)

Shock-unsteadiness parameter

\(M_{1n}\)

Upstream Mach number normal to shock

\(z_2^+\)

Wall-normal distance to the nearest point in wall coordinates

\(\delta _0\)

Boundary-layer thickness upstream of interaction

\(\mu _T\)

Eddy viscosity

\(\nu \)

Kinematic molecular viscosity

\(\tilde{\nu }\)

Modified turbulent kinematic viscosity

Subscripts

0

Stagnation condition

n

Normal to shock wave

w

Wall condition

\(\infty \)

Freestream condition

Abbreviation

CFL

Courant-Friedrichs-Lewy

SA

Spalart–Allmaras

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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Aeronautical EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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