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Drag reduction in transonic shock-wave/boundary-layer interaction using porous medium: a computational study

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Abstract

A computational study has been carried out to assess the effectiveness of a porous medium as a passive control device suitable for reducing the drag in a normal-shock-wave/boundary-layer interaction at transonic speeds with a view toward application in aircraft wings. Reduction in overall drag is achieved via recirculation inside the porous medium, which primarily weakens the shock structure and hence reduces the wave drag. The study has been carried out for a Mach 1.3 normal-shock-wave/boundary-layer interaction on a flat plate in the presence of a porous medium beneath the region of interaction. The computations are performed as steady-state RANS calculations using Menter’s SST \(k-\omega /k-\epsilon \) model for turbulence closure. A parametric study that investigates the dependency of the effectiveness of control on dimensions of the cavity (length and depth), relative position of the cavity, and porosity of the medium has been carried out. It is observed that the change in overall drag is pronounced for parameters which result in significant changes to the size of the lambda-shock structure, such as the length of the cavity upstream of the inviscid shock location. Among the parameters investigated, porosity is seen to strongly affect the boundary-layer properties, with increase in porosity resulting in higher viscous drag.

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Notes

  1. Computation time is approximately quadrupled with each level of refinement.

  2. The experimental data were provided to us by Holger Babinsky (personal communication).

  3. The value of S is kept close to 2 to match earlier configurations of porous medium.

Abbreviations

D :

Diameter of circle in porous medium, mm

P :

Pressure, Pa

\(P_0\) :

Total pressure, Pa

\({\overline{P}_0}\) :

Mass-averaged total pressure at a stream-wise location, Pa

\({\overline{P}}_{0\mathrm{saving}}\) :

Mass-averaged total pressure saving at a stream-wise location

p :

Observed order of convergence

S :

Aspect ratio

\(S_1\) :

Distance between centers of circles along x-direction, mm

\(S_2\) :

Distance between centers of circles along y-direction, mm

T :

Temperature, K

u :

Velocity of fluid, m/s

x :

Stream-wise direction

y :

Wall/flow normal direction

\(\delta \) :

Boundary-layer thickness, mm

\(\delta ^*\) :

Boundary-layer displacement thickness, mm

\(\varTheta \) :

Boundary-layer momentum thickness, mm

\(\theta \) :

Choking plate angle, \(^{\circ }\)

\(\rho \) :

Density, \(\hbox {kg/m}^3\)

\(\phi \) :

Porosity of porous medium

0:

Total/stagnation condition

1:

Parameters upstream of shock and/or control region

2:

Parameters downstream of shock and/or control region

\(\infty \) :

Free-stream condition

nc:

No-control case

wc:

With-control case

x :

Stream-wise component

y :

Wall/flow normal component

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Acknowledgements

The authors are grateful to Jack R. Edwards at North Carolina State University for letting them use his REACTMB code for this study. The authors also express their thanks to Holger Babinsky at University of Cambridge, for providing data related to the no-control experiments. Computing facilities at the VIRGO super-cluster are provided by the High Performance Computing Division, at Indian Institute of Technology Madras.

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    Present address: Department of Mechanical Engineering, University of Iowa, Iowa City, IA, USA

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  1. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India

    S. Roy, J. P. S. Sandhu & S. Ghosh

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Roy, S., Sandhu, J.P.S. & Ghosh, S. Drag reduction in transonic shock-wave/boundary-layer interaction using porous medium: a computational study. Shock Waves 31, 117–132 (2021). https://doi.org/10.1007/s00193-021-01009-7

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