Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-21T18:40:28.286Z Has data issue: false hasContentIssue false

Nonlinear effects in steady supersonic dissipative gasdynamics. Part 2. Three-dimensional axisymmetric flow

Published online by Cambridge University Press:  29 March 2006

T. H. Chong
Affiliation:
Division of Applied Mathematics and Centre for Fluid Meohanics, Brown University, Providence, R.I.
L. Sirovich
Affiliation:
Division of Applied Mathematics and Centre for Fluid Meohanics, Brown University, Providence, R.I.

Abstract

Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is divided into zones based on the presence or absence of nonlinearity and dissipation. Estimates and criteria which describe the extent of these zones are given.

Type
Research Article
Copyright
© 1973 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171.Google Scholar
Chong, T.H. & Sirovich, L. 1970 On the structure of three-dimensional linearized supersonic and hypersonic flows. Phys. Fluids, 13, 1990.Google Scholar
Chong, T. H. & Sirovich, L. 1971 Non-linear effects in steady supersonic dissipative gasdynamics. Part 1. Two-dimensional flow. J. Fluid Mech. 50, 161.Google Scholar
Cole, J. D. 1968 Perturbatim Methods in Applied Mathematics. Waltham, Mass. : Blaisdell.
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. Survep in Mechanics (ed. G. K. Batchelor & R. M. Davies). Cambridge University Press.
Ryzhov, O. S. 1965 Asymptotic pattern of flow past bodies of revolution in a sonic stream of viscous and heat-conducting gas. Prikl. Math. Mech. 29, 1004.Google Scholar
Ryzhov, O. S. & Shefter, G. M. 1964 On the effect of viscosity and thermal conductivity on the structure of compressible flows. Prikl. Math. Mech. 28, 996.Google Scholar
Salathé, E. P. 1969 The fundamental matrix in three-dimensional dissipative gasdynamics. J. Fluid Mech. 39, 209.Google Scholar
Sirovich, L. 1968 Steady gasdynamic flows. Phys. Fluids, 11, 1424.Google Scholar
Szaniawski, A. 1968 The asymptotic structure of weak shock waves in flows over symmetrical bodies at Maoh number unity. Acta Mechunica, 5, 189.Google Scholar
Van Dyke, M. 1952 A study of second-order supersonic flow theory. N.A.C.A. Rep. no. 1081.Google Scholar
Ward, G. N. 1955 Linearized Theory of Steady High-speed Plow. Cambridge University Press.
Whitham, G. B. 1950 The behaviour of supersonic flow past a body of revolution, far from the axis. Proc. Roy. SOC. A 201, 89.Google Scholar
Whitham, G. B. 1952 The flow pattern of a supersonic projectile. Comm. Pure Appl. Math. 5, 301.Google Scholar
Whitham, G. B. 1966 On the propagation of weak shock waves. J. Fluid Mech. 1, 290.Google Scholar