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The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer

Published online by Cambridge University Press:  28 March 2006

D. B. Spalding  and
S. W. Chi
D. B. Spalding
Affiliation:
Mechanical Engineering Department, Imperial College of Science and Technology, London, S.W. 7
S. W. Chi
Affiliation:
Mechanical Engineering Department, Imperial College of Science and Technology, London, S.W. 7
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Abstract

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).

A new calculation procedure is developed from the postulate that a unique relation exists between cfFc and RFR where cf is the drag coefficient, R is the Reynolds number, and Fc and FR are functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for both Fc and FR to be deduced empirically, so Fc is calculated by means of mixing-length theory and FR is found semi-empirically. Tables and charts of values of Fc and FR are presented for a wide range of MG and TS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 1 , January 1964 , pp. 117 - 143
Copyright
© 1964 Cambridge University Press

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References

Abbot, I. H. 1953 AGARD Memo. AG/8M4.
Brevoort, M. J. & Arabian, B. D. 1958 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 4248.
Brinich, P. F. 1961 Nat. Aero. Space Admin., Tech. Note, no. D-1047.
Brinich, P. F. & Diaconis, N. S. 1952 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2742.
Burgraff, O. R. 1962 J. Aero. Sci. 29, 434.
Chapman, D. R. & Kester, R. H. 1953 J. Aero. Sci. 20, 441.
Chapman, D. R. & Kester, R. M. 1954 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3097.
Chi, S. W. 1962 Unpublished work at Imperial College.
Clemmow, D. M. 1950 Aero. Res. Counc., London, no. 14051, F.M. 1568, DGWRD Rep. 50/6.
Coles, D. 1954 J. Aero. Sci. 21, 433.
Coles, D. E. 1962 Rand Corporation, Rep. no. R-403-PR.
Cope, W. F. 1943 Aero. Res. Counc., London, Rep. & Mem., no. 2840.
Cope, W. F. 1952 Proc. Roy. Soc. A, 215, 84.
Dahwan, S. 1952 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2567.
Deissler, R. G. & Loeffler, A. L. 1959 Nat. Aero. Space Admin., Tech. Rep., no. R-17.
Donaldson, C. dup 1952 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2962.
Dorrance, W. H. 1960 Convair Sci. Res. Lab. Res. Rep. no. 6.
Dutton, R. A. 1957 Aero. Res. Counc., London, Rep. & Mem., no. 3058.
Eckert, E. R. G. 1955 J. Aero. Sci. 22, 585.
Falkner, V. M. 1943 Aircraft Engng, 15, 65.
Ferrari, C. 1950 Quart. Appl. Math. 18, 33.
Frankl, F. & Voishel, V. 1937 Translation Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 1052 (1943).
Goddard, F. E. 1959 J. Aero./Sp. Sci. 26, 1.
Hakkinen, R. J. 1955 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3486.
Hama, F. R. 1947 Rep. Inst. Sci. and Tech., Tokyo, Japan, 1, 13 and 19.
Hill, F. K. 1956 J. Aero. Sci. 23, 35.
Hill, F. K. 1959 Phys. Fluids, 2, 668.
Hilton, W. F. 1951 J. Aero. Sci. 18, 97.
Hughes, G. 1952 Trans. Inst. Nav. Arch. 94, 287.
Kalikman, L. E. 1959 Dokl. Akad. Nauk, SSSR, 106, 123.
Kaye, J. 1954 J. Aero. Sci. 21, 117.
Kempf, G. 1929 Werft, Reed., Hafen. 11, 234.
Klebanoff, P. S. & Diehl, Z. W. 1951 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2475.
Korkegi, R. H. 1956 J. Aero. Sci. 23, 97.
Kosterin, S. I. & Koshmarov, Y. A. 1960 Soviet Phys. 4, 819.
Kutateladze, S. S. & Leont'ev, A. I. 1961 Discussion of Heat and Mass Transfer, Akad. Nauk BSSR, Minsk, 1, Translation TIL T5258.
Landweber, L. & Siao, T. T. 1958 J. Ship Res. 1, 21.
Li, T. Y. & Nagamatsu, H. T. 1951 J. Aero. Sci. 18, 696.
Lin, C. C. & Shen, S. F. 1951 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2542.
Ludwig, H. & Tillmann, W. 1949 Translation Nat. Adv. Comm. Aero., Wash., Tech. Mem., no. 1285.
Matting, F. M., Chapman, D. R., Nyholm, J. R. & Thomas, A. G. 1951 Nat. Aero. Space Admin., Tech. Rep., no. R-82.
Mickley, H. S. & Davis, R. S. 1957 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 4017.
Monaghan, R. J. 1950 Aero. Res. Counc., London, no. CP 45.
Monaghan, R. J. & Cooke, J. R. 1953a Aero. Res. Counc., London, no. CP 139.
Monaghan, R. J. & Cooke, J. R. 1953b Aero. Res. Counc., London, no. CP 140.
Monaghan, R. J. & Johnson, J. E. 1952 Aero. Res. Counc., London, no. CP 64.
O'Donell, R. M. 1954 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3122.
Pappas, C. C. 1954 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3222.
Peterson, J. B. 1963 Nat. Aero. Space Admin., Tech. Note, no. D-1795.
Rubesin, M. W., Maydew, R. C. & Varga, S. A. 1951 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2305.
Schlichting, H. 1960 Boundary Layer Theory, 2nd ed. Translated by J. Kestin. London: McGraw-Hill.
Schoenherr, K. E. 1932 Trans. Soc. Nav. Arch. Mar. Engrs, 40, 279.
Schultz-Grunow, F. 1940 Translation Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 986.
Shen, S. F. 1951 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2543.
Slaok, E. G. 1952 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2686.
Smith, D. W. & Walker, J. H. 1958 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 423.
Smith, F. & Harrop, R. 1946 Roy. Aircraft Estmt, Tech. Note, Aero. 1759.
Sommer, S. C. & Short, B. J. 1955 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3391.
Spalding, D. B. 1962a Int. J. Heat Mass Transfer, 5, 1133.
Spalding, D. B. 1962b Northern Research and Engineering Corporation, Camb., Mass. Rep. no. 1058-1.
Spence, D. A. 1959 Roy. Aircraft Estmt, Rep. Aero. 2631.
Spivak, H. M. 1950 Aero. Phys. Lab., Nor. Am. Aviation, Inc., Rep. no. CM-615, CAL-1052.
Stalder, J. R., Rubesin, M. W. & Tendeland, T. 1950 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2077.
Tucker, M. 1951 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2337.
Van Driest, E. R. 1951 J. Aero. Sci. 18, 145.
Van Driest, E. R. 1955 50 Years of Boundary Layer Theory (Ed. H. Görtler and W. Tollmien), p. 257. Braunschweig: F. Vieweg u. Sohn.
Von Kármán, Th. 1935 Proc. 5th Volta Congress, Rome, p. 255.
Wieghart, K. 1944 Translation Nat. Adv. Comm. Aero., Wash., Tech. Mem., no. 1314 (1951).
Wilson, R. E. 1950 J. Aero. Sci. 17, 585.
Winkler, E. M. 1961 J. Appl. Mech., Trans A.S.M.E. 28, Ser. E, 323.
Young, C. B. M. & Janssen, E. 1952 J. Aero. Sci. 19, 229.
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