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Supersonic scattering of a wing-induced incident shock by a slender body of revolution

Published online by Cambridge University Press:  07 August 2007

A. V. FEDOROV ,
N. D. MALMUTH  and
V. G. SOUDAKOV
A. V. FEDOROV
Affiliation:
Department of Aeromechanics and Flight Engineering, Moscow Institute of Physics and Technology, Zhukovski, 140180, Russia
N. D. MALMUTH
Affiliation:
Teledyne Scientific and Imaging Company, Thousand Oaks, CA 91360, USA
V. G. SOUDAKOV
Affiliation:
Department of Aeromechanics and Flight Engineering, Moscow Institute of Physics and Technology, Zhukovski, 140180, Russia
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Abstract

The lift force acting on a slender body of revolution that separates from a thin wing in supersonic flow is analysed using Prandtl–Glauert linearized theory, scattering theory and asymptotic methods. It is shown that this lift is associated with multi-scattering of the wing-induced shock wave by the body surface. The local and global lift coefficients are obtained in simple analytical forms. It is shown that the total lift is mainly induced by the first scattering. Contributions from second, third and higher scatterings are zero in the leading-order approximation. This greatly simplifies calculations of the lift force. The theoretical solution for the flow field is compared with numerical solutions of three-dimensional Euler equations and experimental data at free-stream Mach number 2. There is agreement between the theory and the computations for a wide range of shock-wave strength, demonstrating high elasticity of the leading-order asymptotic approximation. Theoretical and experimental distributions of the cross-sectional normal force coefficient agree satisfactorily, showing robustness of the analytical solution. This solution can be applied to the moderate supersonic (Mach numbers from 1.2 to 3) multi-body interaction problem for crosschecking with other computational or engineering methods.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 305 - 322
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards, Applied Mathematics Series 55.Google Scholar
Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies. Addison–Wesley.Google Scholar
Belk, D. M., Janus, J. M. & Whitfield, D. L. 1987 Three-dimensional unsteady Euler equations solution on dynamic grids. AIAA J. 25, 1160–1161.CrossRefGoogle Scholar
Bowman, J. J., Senior, T. B. A. & Uslenghi, P. L. E. 1969 Electromagnetic and Acoustic Scattering by Simple Shapes. North-Holland.Google Scholar
Chakravarthy, S. R. & Osher, S. 1985 A new class of high accuracy TVD schemes for hyperbolic conservation laws. AIAA Paper 85-0363.CrossRefGoogle Scholar
Cole, J. D. & Cook, L. P. 1986 Transonic Aerodynamics. Elsevier, North-Holland.Google Scholar
Gapcynski, J. P. & Carlson, H. W. 1957 The aerodynamic characteristics of a body in the two-dimensional flow field of a circular-arc wing at a Mach number 2.01. NACA Res. Mem. L57E14.Google Scholar
Jordan, J. K. 1992 Computational investigation of predicted store loads in mutual interference flow fields. AIAA Paper 92-4570.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1986 Theoretical Physics, vol. 6: Hydrodynamics. Nauka Moscow (in Russian).Google Scholar
Lependin, L. F. 1978 Acoustics. Vysshaya Shkola, Moscow(in Russian).Google Scholar
Loitsyansky, L. G. 1970 Fluid and Gas Mechanics. Nauka, Moscow (in Russian).Google Scholar
Malmuth, N. D. 2005 Theoretical aerodynamics in today's real world, opportunities and challenges. Julian D. Cole Lecture. AIAA Paper 2005-5059.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, pp. 1376–1382, McGraw–Hill.Google Scholar
Prewitt, N. C., Belk, D. M. & Maple, R. C. 1999 Multiple-body trajectory calculations using the Beggar code. J. Aircraft 36, 802–808.Google Scholar
Roe, P. L. 1986 Characteristic based schemes for the Euler equations. Annu. Rev. Fluid Mech. 18, 337–365.Google Scholar
Shalaev, V. I., Fedorov, A. V. & Malmuth, N. D. 2004 Theoretical modeling of interaction of multiple slender bodies in supersonic flows. AIAA Paper 2004-1127.Google Scholar
Thoms, R. D. & Jordan, J. K. 1995 Investigation of multiple body trajectory prediction using time accurate computational fluid dynamics. AIAA Paper 95-870.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.Google Scholar
Weiss, J. M., Maruszewski, J. P. & Smith, W. A. 1997 Implicit solution of the Navier–Stokes equations on unstructured meshes. AIAA Paper 97-2103.CrossRefGoogle Scholar