Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-30T23:59:21.294Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculation of boundary-layer development using the turbulent energy equation

Published online by Cambridge University Press:  28 March 2006

P. Bradshaw ,
D. H. Ferriss  and
N. P. Atwell
P. Bradshaw
Affiliation:
Aerodynamics Division, National Physical Laboratory, Teddington
D. H. Ferriss
Affiliation:
Aerodynamics Division, National Physical Laboratory, Teddington
N. P. Atwell
Affiliation:
Aerodynamics Division, National Physical Laboratory, Teddington
Get access Rights & Permissions [Opens in a new window]

Abstract

The turbulent energy equation is converted into a differential equation for the turbulent shear stress by defining three empirical functions relating the turbulent intensity, diffusion and dissipation to the shear stress profile. This equation, the mean momentum equation and the mean continuity equation form a hyperbolic system. Numerical integrations by the method of characteristics with preliminary choices of the three empirical functions compare favourably with the results of conventional calculation methods over a wide range of pressure gradients. Nearly all the empirical information required has been derived solely from the boundary layer in zero pressure gradient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 3 , 26 May 1967 , pp. 593 - 616
Copyright
© 1967 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

Batchelor, G. K. 1950 J. Aero. Sci. 17, 441.
Bradshaw, P. 1965 Nat. Phys. Lab. Aero. Rept. no. 1172.
Bradshaw, P. 1966 Nat. Phys. Lab. Aero. Rept. no. 1184, and J. Fluid Mech. (to be published).
Bradshaw, P. & Ferriss, D. H. 1965a Aero. Res. Counc. Lond, curr. pap. 899.
Bradshaw, P. & Ferriss, D. H. 1965b Nat. Phys. Lab. Aero. Rept. no. 1145.
Bradshaw, P. & Ferriss, D. H. 1966 Nat. Phys. Lab. Aero. Rept. no. 1217.
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 J. Fluid Mech. 19, 591.
Coles, D. 1962 Rand Corp. U.S.A. Rept. R-403-PR (see also Aero. Res. Counc. Lond. no. 24, 497, 1963).
Collatz, L. 1959 The Numerical Treatment of Differential Equations. Berlin: Springer.
Davies, R. W. 1952 J. Appl. Phys. 23, 941.
Dryden, H. L. 1946 Paper presented at 6th Int. Congr. Appl. Mech. (see also Nat. Adv. Comm. Aero. Wash. Tech. Note no. 1168 (1947)).
Ferriss, D. H. & Bradshaw, P. 1966 Nat. Phys. Lab. Aero. Rept. no. 1195.
Glushko, G. S. 1965 Izv. Akad. Nauk. SSSR (Mekhanika), July-August, p. 13 (see also Min. of Av. T.I.L. T/5664 (1966)).
Head, M. R. 1958 Aero. Res. Counc. Lond. R. & M., no. 3152.
Herring, H. J. & Norbury, J. F. 1963 Princeton University Rept. FLD-15.
Johnson, D. S. 1959 J. Appl. Mech. 26, 235.
Keffer, J. F. 1965 J. Fluid Mech. 22, 135.
Klebanoff, P. S. 1955 Nat. Adv. Comm. Aero. Wash. Rept. no. 1247.
Mcdonald, H. & Stoddart, J. A. P. 1965 Brit. Aircr. Corp. Warton, Rept. no. Ae 225 (see also Aero. Res. Counc. Lond. no. 27, 644).
Monin, A. S. 1959 Adv. Geophys. 6, 331.
Morkovin, M. V. 1962 Mécanique de la Turbulence, Colloques Intern. du C.N.R.S. no. 108, 367.
Newman, B. G. 1951 Adv. Comm. Aero., Australia, Rept. no. 53.
Pasquill, F. 1966 Quart. J. Roy. Met. Soc. 92, 185.
Ralston, A. & WILF, H. S. (eds.) 1960 Mathematical Methods for Digital Computers. Wiley.
Richtmyer, R. D. 1957 Difference Methods for Initial-Value Problems. Interscience.
Rose, W. G. 1966 J. Fluid Mech. 25, 97.
Sarnecki, A. J. 1958 Ph.D. Dissertation, Dissertation.
Schubauer, G. B. & Klebanoff, P. S. 1951 Nat. Adv. Comm. Aero. Wash., Rept. no. 1030.
Schubauer, G. B. & Spangenberg, W. G. 1960 J. Fluid Mech. 8, 10.
Spalding, D. B. & Chi, S. W. 1964 J. Fluid Mech. 18, 117.
STAFF OF MATHEMATICS DIVISION, 1961 Nat. Phys. Lab., Modern computing methods. Nat. Phys. Lab. Note on Appl. Sci. 16.
Thompson, B. G. J. 1964 Aero. Res. Counc. Lond. no. 26, 109.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1961 J. Fluid Mech. 11, 97.
Townsend, A. A. 1965 J. Fluid Mech. 22, 799; 23, 767.
Winter, K. G., Smith, K. G. & Gaudet, L. 1965 Agardograph, 97, 97.