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Eddy Viscosity and Mixing Length from Measured Boundary Layer Developments

Published online by Cambridge University Press:  07 June 2016

R A McD Galbraith  and
M R Head
R A McD Galbraith
Affiliation:
Cambridge UniversityEngineering Department
M R Head
Affiliation:
Cambridge UniversityEngineering Department
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Summary

To obtain profiles of shear stress and eddy viscosity, the boundary-layer equations in finite-difference form have been applied to published turbulent-boundary-layer developments measured in nominally two-dimensional conditions. In applying this procedure, measured velocity profiles have been represented by members of Thompson’s profile family. Except close to separation, these representations are very satisfactory, and derived shear-stress profiles are generally in good agreement with direct measurements. Various eddy-viscosity and mixing-length models are compared with the results of the analysis and are found in general to differ widely among themselves and from the present results. The widely used assumption, l = ky in the wall region, appears to be invalid.

Type
Research Article
Information
Aeronautical Quarterly , Volume 26 , Issue 2 , May 1975 , pp. 133 - 154
Copyright
Copyright © Royal Aeronautical Society. 1975

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References

1 Cebeci, T Behaviour of turbulent flow near a porous wall with pressure gradient. AIAA Journal, Vol 8, No 12, pp 2152–2156, 1970.CrossRefGoogle Scholar
2 Cebeci, T Calculation of compressible turbulent boundary layers with heat and mass transfer. AIAA Journal, Vol 6, No 9, pp 1091–1097, 1971.Google Scholar
3 Cebeci, T A general method for calculating three-dimensional incompressible laminar and turbulent boundary layers. II, Three-dimensional flows in cartesian coordinates. McDonnell Douglas Report MDC J6517, 1974.Google Scholar
4 Mellor, G L Incompressible turbulent boundary layers with arbitrary pressure gradients and divergent or convergent flows. AIAA Journal, Vol 5, No 9, pp 1570–1579, 1967.CrossRefGoogle Scholar
5 Thompson, B G J A new two-parameter family of mean velocity profiles for incompressible boundary layers on smooth walls. ARC R & M 3463, 1965.Google Scholar
6 Sarnecki, A J The turbulent boundary layer on a permeable surface. PhD dissertation, Cambridge University, 1959.Google Scholar
7 Dvorak, F A Head, M R Heat transfer calculations for the constant-property turbulent boundary layer and comparisons with experiment. ARC R & M 3592, 1969.Google Scholar
8 Patel, V C Calibration of the Preston tube and limitations on its use in pressure gradients. Journal of Fluid Mechanics, Vol 26, pp 481–506, 1965.Google Scholar
9 Coles, D E Hurst, E A (Editors) Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction. Vol 2, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
10 Patel, V C Head, M R A simplified version of Bradshaw’s method for calculating two-dimensional turbulent boundary layers. Aeronautical Quarterly, Vol XXI, pp 243–262, August 1970.Google Scholar
11 McQuaid, J Incompressible turbulent boundary layers with distributed injection. ARC R & M 3542, 1968.Google Scholar
12 Head, M R Prahlad, T S The boundary layer on a plane of symmetry. Aeronautical Quarterly Vol XXV, pp 293–304, November 1974.CrossRefGoogle Scholar
13 Thwaites, B (Editor) Incompressible Aerodynamics. Clarendon Press, Oxford, p 73, 1960.Google Scholar
14 Bradshaw, P The turbulent structure of equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol 29, pp 625–645, 1967.CrossRefGoogle Scholar
15 Schubauer, G B Spangenberg, W B Forced mixing in boundary layers. Journal of Fluid Mechanics, Vol 8, pp 10–38, 1958.CrossRefGoogle Scholar
16 Klebanoff, P S Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Report 1247, 1955.Google Scholar
17 Bradshaw, P Ferriss, D H The response of a retarded equilibrium turbulent boundary layer to the sudden removal of pressure gradient. NPL Aero Report 1145, 1965.Google Scholar
18 Spalding, D B As referenced by M P Escudier. The distribution of mixing length in turbulent flows near walls. Imperial College Report TWF/TN/1, 1965.Google Scholar
19 Patankar, S V Spalding, D B Heat and Mass Transfer in Boundary Layers. Second Edition, Intertext, London, 1970.Google Scholar
20 Mellor, G L Herring, H J Two methods of calculating turbulent boundary layer behaviour based on numerical solution of the equations of motion. Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction. Vol 1, pp 331–395, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
21 Cebeci, T Smith, A M O A finite difference solution of the incompressible turbulent boundary layer by eddy-viscosity concept. Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction. Vol 1, pp 346–355, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
22 Anyiwo, J C Meroney, R N Effective viscosity model for turbulent wall boundary layers. Aeronautical Quarterly, Vol XXV, pp 92–102, 1973.Google Scholar
23 Szablewski, W New approach to the calculation of incompressible turbulent boundary layers. Fluid Dynamics, Vol 5, No 2, pp 277–288, 1970.CrossRefGoogle Scholar
24 Driest, E R van On turbulent flow near a wall. Journal of the Aeronautical Sciences, Vol 23, pp 1007–1011, November 1956.Google Scholar
25 Landweber, L Poreh, M To be published. Referenced by V C Patel. A unified view of the law of the wall using mixing length theory. Aeronautical Quarterly, Vol XXIV, pp 55–70, February 1973.Google Scholar
26 Launder, B E Priddin, C H The near wall mixing length profile. A comparison of some variants of van Driest. Imperial College Report TM/TN/A/15, 1971.Google Scholar
27 Cebeci, T Mosinskis, G J Computation of incompressible boundary layers at low Reynolds numbers. AIAA Journal, Vol 9, No 8, pp 1632–1634, 1971.CrossRefGoogle Scholar
28 Simpson, R L Characteristics of the turbulent boundary layer at low Reynolds number. Journal of Fluid Mechanics, Vol 42, pp 45–60, 1970.Google Scholar
29 Reeves, B L Two layer model of turbulent boundary layers. AIAA Journal, Vol 12, No 7, pp 932–939, 1974.CrossRefGoogle Scholar
30 Mellor, G L Gibson, D M Equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol 24, pp 225–253, 1966.Google Scholar
31 Glowacki, W Chi, S Effect of pressure gradient on mixing length for equilibrium turbulent boundary layers. AIAA Paper 72-213, 1972.Google Scholar