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A Reference-Plane Method for the Solution of Three-Dimensional Supersonic Flows

Published online by Cambridge University Press:  07 June 2016

R Camarero
R Camarero*
Affiliation:
University of Sherbrooke, Quebec
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Summary

A numerical method for the solution of three-dimensional supersonic flows and the associated computer programme have been devised. The present algorithm is based on a reference-plane characteristic network. The physical region between the shock wave and the body surface is replaced by a computational mesh facilitating the incorporation of different boundary conditions and arbitrary body shapes. For reasons of stability and computing time a Hartree-type grid was used where the characteristic segments are projected upstream. The base points do not coincide with nodal points and interpolation by means of Tchebycheff polynomials is required to obtain the flow properties. Numerical differentiation is carried out by means of spline functions. The programme has been used and verified under a wide variety of flows past circular and elliptic cones, tangent ogives and a delta wing body. After a series of numerical experiments it was found that accurate solutions could be found using a 7 × 7 grid, and that the essence of the solution is preserved using a very coarse mesh of 4 × 4. Furthermore, the good agreement obtained with experimental results indicates that it could be applied successfully to problems of practical interest.

Type
Research Article
Information
Aeronautical Quarterly , Volume 27 , Issue 1 , February 1976 , pp. 75 - 86
Copyright
Copyright © Royal Aeronautical Society. 1976

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References

1 Moretti, G Inviscid flow field about a pointed cone at an angle of attack. AIA A Journal, Vol 5, pp 789–791, 1967.Google Scholar
2 Thornhill, C K The numerical method of characteristics for hyperbolic problems in three independent variables. ARC R&M 2615, 1948.Google Scholar
3 Ferrari, C On the application of the method of characteristics to the study of irrotational three-dimensional supersonic flow. Cornell Aeronautical Laboratory Report CAL-53, 1953.Google Scholar
4 Holt, M The method of characteristics for steady supersonic rotational flow in three dimensions. Journal of Fluid Mechanics, Vol 1, pp 409–423, 1956.Google Scholar
5 Camarero, R Numerical solutions of internal and external hypersonic flows at high incidence. McGill University, MERL Report 73-5, August 1973.Google Scholar
6 Sauerwein, H The calculation of two- and three-dimensional inviscid unsteady flows by the method of characteristics. MIT Fluid Dynamic Research Laboratory Report 64-4, June 1964.Google Scholar
7 Butler, D S The numerical solution of hyperbolic systems of partial differential equations in three independent variables. Proc Roy Soc A, Vol 255, pp 232–252, 1960.Google Scholar
8 Sauer, R The method of finite differences for the initial value problem. Numerische Mathematik, Vol 5, pp 55–67, 1963. (Translated by Trirogoff, K N, Literature Research Group, Aerospace Library Services, LRG-65-7-28.Google Scholar
9 Jones, D J Tables of inviscid supersonic flow about circular cones at incidence, γ = 1.4. AGARDograph 137, 1969.Google Scholar
10 Jones, D J Numerical solutions of the flow field for conical bodies in a supersonic stream. NRC Aero Report LR-507, 1968.Google Scholar
11 Rainbird, W J The external flow field about yawed circular cones. In Hypersonic Boundary Layers and Flow Fields, AGARD Conference Proceedings 30, 1968.Google Scholar
12 Rainbird, W J Errors in measurement of mean static pressure of a moving fluid due to pressure holes. NRC (Canada) Report DME/NAE (3), pp 55–89, 1967.Google Scholar
13 Zakkay, V Visich, M Jr Experimental pressure distribution on conical elliptical bodies at M∞ = 3.09 and 6.0. Polytechnic Institute of Brooklyn, PIBAL Report 467, 1959.Google Scholar
14 Savin, R C Application of the generalized shock-expansion method to inclined bodies of revolution travelling at high-supersonic airspeeds. NACA TN-3349, 1955.Google Scholar
15 Camarero, R A numerical method for the solution of three-dimensional internal flows. Proceedings of the 2nd International Symposium on Air Breathing Engines, 24-29 March 1974, Sheffield, England.Google Scholar
16 Camarero, R A numerical method for the solution of three-dimensional supersonic flows. CASI Transactions, Vol 8, No 2, September 1975.Google Scholar