Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T05:52:44.630Z Has data issue: false hasContentIssue false

On a Convergent Multi-Moment Method for the Laminar Boundary Layer Equations

Published online by Cambridge University Press:  07 June 2016

Howard E. Bethel*
Affiliation:
Wright-Patterson Air Force Base, Ohio
Get access

Summary

This paper presents a summary of a multi-moment method for solving the laminar boundary layer equations. Results obtained with the method tend to converge to the exact values as higher moments are used. Both similar and non-similar external flow fields are considered. The present results are compared with those obtained by another multi-moment method, a finite-difference method and a refined Pohlhausen-type method.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1967

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.)

Footnotes

*

Captain, USAF; Research Engineer, Hypersonic Research Laboratory, Aerospace Research Laboratories.

References

1. Galerkin, B. G. Series solutions of some problems of elastic equilibrium of rods and plates. (In Russian.) Vestnik Inzhenerov, Vol. 1, p. 879, 1915.Google Scholar
2. Kantorovich, L. V. Method of reduction to ordinary equations. (In Russian.) Doklady Akadamii Nauk SSSR, Vol. 2, p. 534, 1934.Google Scholar
3. Kantorovich, L. V. Use of the idea of the Galerkin method in the method of reduction to ordinary differential equations. (In Russian.) Prikladnaya Matematika i Mekhanika, Vol. VI, p. 31, 1942.Google Scholar
4. Dorodnitsyn, A. A. On a method of solving the laminar boundary layer equations. (In Russian.) Prikladnaya Matematika i Tekh-Fiz., Vol. 1, p. 111, 1960.Google Scholar
See also Dorodnitsyn, A. A. General method of integral relations and its application to boundary layer theory. Advances in Aeronautical Sciences, Vol. 3. Pergamon Press, London, 1962.Google Scholar
5. Dorodnitsyn, A. A. Numerical methods of solution of equations of the laminar boundary layer. Archiwum Mechaniki Stosowanej, Vol. 14, p. 343, 1962.Google Scholar
(Translation available as Foreign Technology Division, Technical Translation, FTD-TT-65-67.) See also Dorodnitsyn, A. A. Exact numerical methods in the boundary layer theory. (Fiszdon, W., editor.) Fluid Dynamic Transactions, Vol. 1. Pergamon Press, London, 1964.Google Scholar
6. Bethel, H. E. On the convergence and exactness of solutions of the laminar boundary-layer equations using the N-parameter formulation of Galerkin-Kantorovich-Dorodnitsyn. PhD Thesis, Purdue University, 1966.Google Scholar
7. Goertler, H. A new series for the calculation of steady laminar boundary layer flows. Journal of Mathematics and Mechanics, Vol. 6, p. 1, 1957.Google Scholar
8. Sun, E. Y. CH. A compilation of coordinate transformations applied to the boundary-layer equations for laminar flows. Deutsche Versuchsanstalt für Luftfahrt, Report DVL 121, 1960.Google Scholar
9. Kantorovich, L. V. and Krylov, V. I. Approximate methods of higher analysis. Inter-science Publishers, New York, 1958.Google Scholar
10. Collatz, L. Numerical treatment of differential equations (Third Edition). Springer-Verlag, Berlin, 1960.Google Scholar
11. Schlichting, H. Boundary layer theory (Fourth Edition). McGraw-Hill, New York, 1960.Google Scholar
12. Truckenbrodt, E. A quadrature method for calculation of laminar and turbulent boundary layers in plane and rotationally symmetric flow. (In German.) Ingenieur Archiv, Vol. XX, p. 211, 1952.CrossRefGoogle Scholar
13. Walz, A. Advances in approximation theory and calculation practice for compressible laminar and turbulent boundary layers with heat transfer. (In German.) Zeitschrift für Flugwissenschaften, Vol. XIII, p. 89, 1965.Google Scholar
14. Hanson, F. B. and Richardson, P. D. Use of a transcendental approximation in laminar boundary layer analysis. Journal of Mechanical Engineering Sciences, Vol. 7, p. 131, 1965.CrossRefGoogle Scholar
15. Leadon, B. M., Rosciszewski, J., Gallaher, W. H., Holst, W. R. and Carter, W. V. The effects of active cooling on the aero-thermodynamic characteristics of slender bodies of revolution. Air Force Flight Dynamics Laboratory Technical Report AFFDL-TR-64-187, 1964.Google Scholar
16. Schetz, J. A. On the approximate solution of viscous-flow problems. Journal of Applied Mechanics, Vol. 30, p. 263, 1963.CrossRefGoogle Scholar
17. Bethel, H. E. Comments on “Approximate solution of second-order boundary-layer equations.” AIAA Journal, Vol. 4, p. 1882, 1966.CrossRefGoogle Scholar
18. Smith, A. M. O. Improved solutions of the Falkner and Skan boundary-layer equations. Institute of Aeronautical Sciences, Sherman M. Fairchild Fund Paper FF-10, 1964.Google Scholar
19. Schoenauer, W. A differencing method for solving the boundary layer equations for stationary, laminar, incompressible flow. (In German.) Ingenieur Archiv, Vol. 33, p. 173, 1964.Google Scholar
20. Terrill, R. M. Laminar boundary-layer flow near separation with and without suction. Philosophical Transactions, Vol. A253, p. 55, 1960.Google Scholar
21. Van Inoen, J. L. Theoretical and experimental investigations of incompressible laminar boundary layers with and without suction. PhD Thesis, Technische Hogeschool Te Delft, 1965.Google Scholar
22. Geropp, D. Contribution to computation of compressible laminar boundary layers with heat transfer with two-parameter solving arrangement for the velocity profile. (In German.) Deutsche Versuchsanstalt für Luft- und Raumfahrt Report DVL 288, 1963.Google Scholar
23. Walz, A. Stromungs- und temperaturgrenzschichten. Braun, G., Karlsruhe, 1966.Google Scholar
24. Howarth, L. On the solution of the laminar boundary layer equations. Proceedings of the Royal Society, Series A, Vol. 164, p. 547, 1938.Google Scholar
25. Tani, I. On the solution of the laminar boundary-layer equations. Journal of the Physics Society of Japan, Vol. 4, p. 149, 1949.CrossRefGoogle Scholar