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Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer

Published online by Cambridge University Press:  28 March 2006

H. Thomann
H. Thomann
Affiliation:
Aeronautical Research Institute of Sweden, Bromma 11, Sweden Now at the Institut für Aerodynamik, Eidg. Technische Hochschule, Zürich, Switzerland.
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Abstract

Experiments described here show that the rate of heat transfer in a supersonic, turbulent, boundary layer on a concave wall is increased by the streamwise curvature of the wall. For the arrangement investigated, the pressure is kept constant along the wall, and the increase of about 20% is therefore only due to the wall curvature. For a convex wall, a comparable decrease was found, also with constant pressure along the wall.

It is likely that this change in heat-transfer rate is mainly due to an increase or decrease of turbulent mixing by the effect of the curvature. The increase on a concave wall can in principle also be explained by large-scale vortices with axes in the flow direction (Görtler vortices). However, disturbances of this type cannot explain the decrease observed on the convex wall. They cannot therefore be the only cause.

A simple criterion indicating the effect of curvature on the turbulent motion normal to the wall is given. It is derived from an inviscid-flow analysis. The criterion shows that, for most Mach numbers and wall temperatures of practical interest, the change in mixing depends mainly on the velocity gradient normal to the wall. For high supersonic and hypersonic Mach numbers, however, there is a layer near the outer edge of the boundary layer where the change depends mainly on the temperature (density) gradient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 2 , 12 August 1968 , pp. 283 - 292
Copyright
© 1968 Cambridge University Press

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References

Eckert, E. R. G. 1955 Engineering relations for friction and heat transfer to surfaces in high velocity flow J. Aero. Sci. 22, 585–587.Google Scholar
GöRTLER, H. 1959 Ueber eine Analogie zwischen den Instabilitäten laminarer Grenzschichtströmungen an konkaven Wänden und an erwärmten Wänden Ingenieur-Archiv, 28, 71–78.Google Scholar
Margolis, D. P. & Lumley, J. L. 1965 Curved turbulent mixing layers Phys. Fluids, 8, 1775–1784.Google Scholar
Michel, R. 1960 Résultats sur la couche limite turbulente aux grandes vitesses. 10th Int. Congress Appl. Mech. Stresa.
Rotta, J. C. 1966 On the effects of streamwise wall curvature on compressible turbulent boundary layers. Aerodynamische Versuchsanstalt Göttingen Rep. no. 66 A 44. And International Symposium on Boundary Layers and Turbulence, Kyoto, Japan (September 1966).Google Scholar
Sandmayr, G. 1966 Ueber das Auftreten von Längswirbeln in turbulenten Grenzschichten an konkaven Wänden. Deutsche Luft-und Raumfahrt, Forschungsbericht 66–41.Google Scholar
Tani, I. 1962 Production of longitudinal vortices in the boundary layer along a concave wall J. Geophys. Res. 67, 3075–3080.Google Scholar
Thomann, H. 1967 Heat transfer in a turbulent boundary layer with a pressure gradient normal to the flow. Aeronaut. Res. Inst. of Sweden Rep. no. 113.Google Scholar
Walz, A. 1966 Strömungs- und Temperaturgrenzschichten. Karlsruhe: G. Braun.