Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T16:40:53.925Z Has data issue: false hasContentIssue false
  • English
  • Français

Second-order boundary-layer effects in hypersonic flow past axisymmetric blunt bodies

Published online by Cambridge University Press:  28 March 2006

R. T. Davis  and
I. Flügge-Lotz
R. T. Davis
Affiliation:
Division of Engineering Mechanics, Stanford University, Stanford, California Now with the Engineering Mechanics Department, Virginia Polytechnic Institute.
I. Flügge-Lotz
Affiliation:
Division of Engineering Mechanics, Stanford University, Stanford, California
Get access Rights & Permissions [Opens in a new window]

Abstract

First- and second-order boundary-layer theory are examined in detail for some specific flow cases of practical interest. These cases are for flows over blunt axisymmetric bodies in hypersonic high-altitude (or low density) flow where second-order boundary-layer quantities may become important. These cases consist of flow over a hyperboloid and a paraboloid both with free-stream Mach number infinity and flow over a sphere at free-stream Mach number 10. The method employed in finding the solutions is an implicit finite-difference scheme. It is found to exhibit both stability and accuracy in the examples computed. The method consists of starting near the stagnation-point of a blunt body and marching downstream along the body surface. Several interesting properties of the boundary layer are pointed out, such as the nature of some second-order boundary-layer quantities far downstream in the flow past a sphere and the effect of strong vorticity interaction on the second-order boundary layer in the flow past a hyperboloid. In several of the flow cases, results are compared with other theories and experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 4 , December 1964 , pp. 593 - 623
Copyright
© 1964 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

Baxter, D. C. & Flügge-Lotz, I. 1957 The solution of compressible laminar boundary layer problems by a finite-difference method, Part II. Further discussion of the method and computation of examples. Div. Engng Mech., Stanford Univ., Tech. Rep. no. 110. (Abbreviated version published in Z. angew. Math. Phys. 9b, 81-96.)Google Scholar
Chapman, S. & Cowling, T. G. 1961 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
Cheng, H. K. 1963 The blunt-body problem in hypersonic flow at low Reynolds number. Cornell Aero. Lab. Rep. no. AF-1285-A-10.Google Scholar
Davis, R. T. & Flügge-Lotz, I. 1963 Laminar compressible flow past axisymmetric blunt bodies (results of a second-order theory). Div. Engng Mech., Stanford Univ., Tech. Rep. no. 143.Google Scholar
Davis, R. T. & Flügge-Lotz, I. 1964 The laminar compressible boundary-layer in the stagnation-point region of an axisymmetric blunt body including the second-order effect of vorticity interaction. Int. J. Heat & Mass Transf. 7, 341–70.Google Scholar
Erdelyi, A. 1961 An expansion procedure for singular perturbations. Atti della Scienze de Torino, 95.Google Scholar
Flügge-Lotz, I. & Baxter, D. C. 1956 The solution of compressible laminar boundary layer problems by a finite difference method. Div. Engng Mech., Stanford Univ., Tech. Rep. no. 103.Google Scholar
Flügge-Lotz, I. & Blottner, F. G. 1962 Computation of the compressible laminar difference methods. Div. Engng Mech., Stanford Univ., Tech Rep. no. 131. (Abbreviated version published in J. Méchanique, 2, 397–423.)Google Scholar
Flügge-Lotz, I. & Yu, E. Y. 1960 Development of a finite-difference method for computing a compressible laminar boundary-layer with interaction. Div. Engng Mech., Stanford Univ., Tech. Rep. no. 127 (AFOSR TN 60-577).Google Scholar
Inouye, M. & Lomax, H. 1962 Comparison of experimental and numerical results for the flow of a perfect gas about blunt-nosed bodies. NASA Tech. Note no. D-1426.Google Scholar
Kinslow, M. & Potter, J. L. 1962 The drag of spheres in rarefied hypervelocity flow. Arnold Engng Devt. Center, Tech. Rep. no. AEDC-TDR-62-205 (also in AIAA J. 1, 2467-2473).Google Scholar
Lagerstrom, P. A. 1957 Note on the preceding two papers. J. Math. Mech. 6, 605.Google Scholar
Lenard, M. 1962 Stagnation point flow of a variable property fluid at low Reynolds numbers. Cornell University Thesis.
Maslen, S. H. 1958 On heat transfer in slip flow. J. Aero Sci. 25, 400.Google Scholar
Maslen, S. H. 1962 Second order effects in laminar boundary layers. Martin Co. Res. Rep. PR-29 (also in AIAA J. 1, 33-40).Google Scholar
Petrovsky, I. G. 1954 Lectures on Partial Differential Equations. New York: Interscience.
Probstein, R. F. 1961 Shock-wave and flow field development in hypersonic re-entry. ARS J. 31, 185.Google Scholar
Raetz, G. S. 1957 A method of calculating three-dimensional laminar boundary layers of steady compressible flows. Northrop Aircraft, Inc., Rep. no. NAI-58-73.Google Scholar
Smith, A. M. O. & Clutter, D. W. 1963a Solution of the incompressible laminar boundary-layer equations. AIAA J. 1, 2062–2071.Google Scholar
Smith, A. M. O. & Clutter, D. W. 1963b Solution of Prandtl's boundary-layer equations. Douglas Aircraft Company Engng Paper 1530.Google Scholar
Street, R. E. 1960 A study of boundary conditions in slip-flow aerodynamics. Rarefied Gas Dynamics (ed. F. M. Devienne), pp. 276–92. London: Pergamon Press.
Ting, L. 1960 Boundary layer over a flat plate in presence of shear flow. Phys. Fluids, 3, 78.Google Scholar
Van Dyke, M. 1962a Second-order compressible boundary-layer theory with application to blunt bodies in hypersonic flow. Hypersonic Flow Research (ed. F. R. Riddell), pp. 37–76. New York: Academic Press.
Van Dyke, M. 1962b Higher approximations in boundary-layer theory. Part 1. J. Fluid Mech. 14, 161.Google Scholar
Wu, J. C. 1960 The solution of laminar boundary-layer equations by the finite difference method. Douglas Aircraft Company, Inc., Rep. no. SM-37484 (see also, On the finite difference solution of laminar boundary layer problems, in Proc. 1961 Heat Trans. & Fluid Mech. Inst., Stanford Univ. Press).