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Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers

Published online by Cambridge University Press:  26 April 2006

Shawn D. Anderson  and
John K. Eaton
Shawn D. Anderson
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Present address: Shell Development Corporation, Houston, Texas.
John K. Eaton
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

The development of the Reynolds stress field was studied for flows in which an initially two-dimensional boundary layer was skewed sideways by a spanwise pressure gradient ahead of an upstream-facing wedge. Two different wedges were used, providing a variation in the boundary-layer skewing. Measurements of all components of the Reynolds stress tensor and all ten triple products were measured using a rotatable cross-wire anemometer. The results show the expected lag of the shear stress vector behind the strain rate. Comparison of the two present experiments with previous data suggests that the lag can be estimated if the radius of curvature of the free-stream streamline is known. The magnitude of the shear stress vector in the plane of the wall is seen to decrease rapidly as the boundary-layer skewing increases. The amount of decrease is apparently related to the skewing angle between the wall and the free stream. The triple products evolve rapidly and profiles in the three-dimensional boundary layer are considerably different than two-dimensional profiles, leaving little hope for gradient transport models for the Reynolds stresses. The simplified model presented by Rotta (1979) performs reasonably well providing that an appropriate value of the T-parameter is chosen.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 263 - 294
Copyright
© 1989 Cambridge University Press

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References

Abid, R. & Schmitt, R., 1985 An examination of turbulence models for a separating three-dimensional turbulent boundary layer. In Numerical Methods in Laminar and Turbulent Flows, Swansea, July 9–12, 1985. Office National D'Etudes et de Recherches Aerospatiales, Chatillon.
Anderson, S. D. & Eaton, J. K., 1987 An experimental investigation of pressure driven three-dimensional turbulent boundary layers. Rep. MD 49. Thermosciences Div., Dept. of Mech. Engng, Stanford University.
Baskaran, V. & Bradshaw, P., 1987a Experimental investigation of a three-dimensional turbulent shear layer over an ‘infinite’ swept concave surface. Proc. 6th Symp. of Turbulent Shear Flows, Toulouse, France.Google Scholar
Baskaran, V. & Bradshaw, P., 1987b Experimental investigation of a three-dimensional boundary layer on an ‘infinite’ swept concave wing. Imperial College of Science and Tech., Aeronautics Dept., Final Report.
Bawirzanski, E., Randolph, M. & Eckelmann, H., 1987 Direct measurement of streamwise vorticity fluctuations with a cylinder probe. Proc. 2nd Intl Symp. on Transport Phenomena in Turbulent Flows, Tokyo, pp. 605–612.Google Scholar
Bearman, P. W.: 1971 Corrections for the effect of ambient temperature drift on hot-wire measurements in incompressible flow. DISA Rep., 11, May 1971, pp. 25–30.Google Scholar
van den Berg, B.: 1982 Some notes on three-dimensional turbulent boundary layer data and turbulence modelling. In Three-Dimensional Turbulent Boundary Layers, IUTAM Symp. (ed. Fernholz, H. H. & Krause, E.). Springer.
van den Berg, B. Elsenaar, A. & Lindhout, J. P. F. 1975 Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept wing conditions and comparison with theory. J. Fluid Mech. 70, 127–148.Google Scholar
Blackwelder, R. F.: 1983 Analogies between transitional and turbulent boundary layers. Phys. Fluids 26, 2807.Google Scholar
Bradshaw, P.: 1971 Calculation of three-dimensional turbulent boundary layers. J. Fluid Mech. 46, 417–445.Google Scholar
Bradshaw, P. & Pontikos, N. S., 1985 Measurements in the turbulent boundary layer on an ‘infinite’ swept wing. J. Fluid Mech. 159, 105–130.Google Scholar
Bryer, D. W. & Pankhurst, R. C., 1971 Pressure-Probe Methods for Determining Wind Speed and Flow Direction. Her Majesty's Stationary Office, London.
Castro, I. P. & Cheun, B. S., 1982 The measurement of Reynolds stresses with a pulsed-wire anenometer. J. Fluid Mech. 118, 41–58.Google Scholar
Dechow, R. & Felsch, K. O., 1977 Measurements of the mean velocity and of the Reynolds stress tensor in a three-dimensinal turbulent boundary layer induced by a cylinder standing on a wall. Proc. Symp. on Turbulent Shear Flows, April 1977, University Park, Pennsylvania, vol. I.Google Scholar
Driver, D. M. & Hebbar, S. K., 1985 Experimental study of a three-dimensional, shear-driven turbulent boundary layer using a three-dimensional laser Doppler velocimeter. AIAA 85–1610.Google Scholar
East, L. F. & Sawyer, W. G., 1979 Measurements of the turbulence ahead of a 45 degree swept step using a double split-film probe. Royal Aircraft Establishment TR 79136.Google Scholar
Eibeck, P. A. & Eaton, J. K., 1985 An experimental investigation of the heat-transfer effects of a longitudinal vortex embedded in a turbulent boundary layer, Rep. MD-48. Thermosciences Div., Stanford University.
Elsenaar, A. & Boelsma, S. H., 1974 Measurements of the Reynolds stress tensor in a three-dimensional turbulent boundary layer under infinite swept wing conditions. NLR TR 74095 U.Google Scholar
Ezekwe, C. I., Pierce, F. J. & McAllister, J. E., 1978 Measured Reynolds stress tensors in a three-dimensional turbulent boundary layer. AIAA J. 16, 645–646.Google Scholar
Fernholz, H. H. & Vagt, J. D., 1981 Turbulence measurements in an adverse-pressure-gradient three-dimensional turbulent boundary layer along a circular cylinder. J. Fluid Mech. 111, 233–269.Google Scholar
Gregory, N., Stuart, J. T. & Walker, W. S., 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. 248, 155–199.Google Scholar
Higuchi, H.: 1983 A miniature, directional surface-fence gage for three-dimensional turbulent boundary layer measurements. AIAA 83–1722.Google Scholar
Johansson, A. V. & Alfredsson, P. H., 1983 Effects of imperfect spatial resolution on measurements of wall-bounded turbulent shear flows. J. Fluid Mech. 137, 409–421.Google Scholar
Johnston, J. P.: 1970 Measurements in a three-dimensional turbulent boundary layer induced by a swept, forward-facing step. J. Fluid Mech. 42, 823–844.Google Scholar
Johnston, J. P.: 1976 Experimental studies in three-dimensional boundary layer, Rep. MD-34. Thermosciences Div., Stanford University.
Kim, H. T., Kline, S. J. & Reynolds, W. C., 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–160.Google Scholar
Klebanoff, P. S.: 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN-3178.Google Scholar
Moffat, R. J., Yavuzkurt, S. & Crawford, M. D., 1979 Real time measurements of turbulence quantities with a triple wire system. Flow Dynamics Conf., Marseille, France.Google Scholar
Moser, R. D. & Moin, P., 1987 The effects of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479–510.Google Scholar
Muller, U. R.: 1982 Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer. J. Fluid Mech. 119, 121–153.Google Scholar
Muller, U. R.: 1987 Developments in measuring Reynolds stresses. Perspectives in Turbulence Studies (ed. H. Meier & P. Bradshaw). Springer.
Murlis, J., Tsai, H. M. & Bradshaw, P., 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.Google Scholar
Nakayama, A. & Westphal, R. V., 1986 The effects of sensor length and spacing on X-wire measurements in a boundary layer. NASA TM 88352.Google Scholar
Pauley, W. R. & Eaton, J. K., 1988 The fluid dynamics and heat transfer effects of streamwise vortices embedded in a turbulent boundary layer. Stanford Univ. Thermosci. Div. Rep. MD-51. Thermosciences Div., Stanford University.
Pierce, F. J. & Ezekewe, C. I., 1976 Measured uw stress gradients in a three-dimensional turbulent boundary layer. Trans. ASME I: J. Fluids Engng 98, 768–770.Google Scholar
Pontikos, N. S.: 1982 The structure of three-dimensional turbulent boundary layers. Ph.D. thesis, Imperial College, London. (Available on microfiche from Aeronautics Dept.)
Purtell, L. P., Klebanoff, P. S. & Buckley, F. S., 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802–811.Google Scholar
Rotta, J. C.: 1979 A family of turbulence models for three-dimensional boundary layers. In Turbulent Shear Flows I (ed. F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw). Springer.
Savill, A. M.: 1987 Recent developments in rapid distortion theory. Ann. Rev. of Fluid Mech. 19, 531–575.Google Scholar
Townsend, A. A.: 1980 The response of sheared turbulence to additional distortion. J. Fluid Mech. 98, 171–191.Google Scholar
Westphal, R. V. & Mehta, R. D., 1984 Crossed hot-wire data acquisition and reduction system. NASA TM 85871.Google Scholar
Young, A. D. & Maas, J. N., 1936 The behavior of a Pitot tube in a transverse total pressure gradient. Aero. Res. Counc. Rep. 1770.Google Scholar