Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T22:15:47.817Z Has data issue: false hasContentIssue false
  • English
  • Français

Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer

Published online by Cambridge University Press:  20 April 2006

Udo R. Müller
Udo R. Müller
Affiliation:
Aerodynamisches Institut, Technische Hochschule Aachen, West Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental study of a steady, incompressible, three-dimensional turbulent boundary layer approaching separation is reported. The flow field external to the boundary layer was deflected laterally by turning vanes so that streamwise flow deceleration occurred simultaneous with cross-flow acceleration. At 21 stations profiles of the mean-velocity components and of the six Reynolds stresses were measured with single- and X-hot-wire probes, which were rotatable around their longitudinal axes. The calibration of the hot wires with respect to magnitude and direction of the velocity vector as well as the method of evaluating the Reynolds stresses from the measured data are described in a separate paper (Müller 1982, hereinafter referred to as II). At each measuring station the wall shear stress was inferred from a Preston-tube measurement as well as from a Clauser chart. With the measured profiles of the mean velocities and of the Reynolds stresses several assumptions used for turbulence modelling were checked for their validity in this flow. For example, eddy viscosities for both tangential directions and the corresponding mixing lengths as well as the ratio of resultant turbulent shear stress to turbulent kinetic energy were derived from the data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 121 - 153
Copyright
© 1982 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

Aerodynamische Versuchsanstalt und Max-Planck-Institut für Strömungsforschung 1964 Strömungsmessgeräte und Hilfseinrichtungen, Göttingen.
Berg, B. V. D. & Elsenaar, A. 1972 Measurements in a three-dimensional incompressible turbulent boundary layer in an adverse pressure gradient underinfinite swept wing conditions. NLR Tech. Rep. no. 72092 U.Google Scholar
Berg, B. V. D., Elsenaar, A., Lindhout, J. P. F. & Wesseling, P. 1975 Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory. J. Fluid Mech. 70, 127.Google Scholar
Bradshaw, P. 1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625.Google Scholar
Bradshaw, P. 1971 Calculation of three-dimensional turbulent boundary layers. J. Fluid Mech. 46, 417.Google Scholar
Bradshaw, P. 1972 The understanding and prediction of turbulent flow. Jahrbuch der Deutschen Gesellschaft für Luft- und Raumfahrt, p. 51.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 593.Google Scholar
Champagne, F. H., Sleicher, C. A. & Wehrmann, O. H. 1967 Turbulence measurements with inclined hot-wires. Part 1. Heat transfer experiments with inclined hot-wire. J. Fluid Mech. 28, 153.Google Scholar
Chapman, D. R. 1980 Trends and Pacing Items in Computational Aerodynamics. In Proc. 7th Int. Conf. on Numerical Methods in Fluid Dynamics, Stanford University. Lecture Notes in Physics, vol. 141 p. 1. Springer.
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91.Google Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191.Google Scholar
Coles, D. E. & Hirst, E. A. (eds.) 1969 Proc. AFOSR-IFP Stanford Conf. on Computation of Turbulent Boundary Layers. Thermoscience Division, Stanford.
Dechow, R. 1977 Mittlere Geschwindigkeit und Reynoldsscher Spannungstensor in der dreidimensionalen turbulenten Wandgrenzschicht vor einem stehenden Zylinder. In Strömungsmechanik und Strömungsmaschinen, Heft 21. Mitteilungen des Instituts für Strömungslehre und Strömungsmaschinen, Univ. Karlsruhe.
Dechow, R. & Felsch, K. O. 1977 Measurements of the mean velocity and of the Reynolds stress tensor in a three-dimensional turbulent boundary layer induced by a cylinder standing on a flat wall. In Proc. 1st Symp. on Turbulent Shear Flows, Pennsylvania State Univ., p. 9.11.
East, L. F. 1975 Computation for three-dimensional turbulent boundary layers. FFA Tech. Note AE-1211.
East, L. F. & Hoxey, R. P. 1969 Low-speed three-dimensional turbulent boundary layer data. Part I. RAE Tech. Rep. no. 69041.Google Scholar
East, L. F. & Sawyer, W. G. 1979 An investigation of the structure of equilibrium turbulent boundary layers. In Turbulent Boundary Layers. Experiment, Theory and Modelling. AGARD Conf. Proc. no. 271, p. 6.1.
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 Tech. Rep. no. 74095 U.Google Scholar
Fanneløp, T. K. & Krogstad, P. Å. 1975 Three-dimensional turbulent boundary layers in external flows: a report on EUROMECH 60. J. Fluid Mech. 71, 815.Google Scholar
Galbraith, R. A. Mcd. & Head, M. R. 1975 Eddy viscosity and mixing length from measured boundary layer development. Aero. Quart. 26, 133.Google Scholar
Galbraith, R. A. Mcd., Sjolander, S. & Head, M. R. 1977 Mixing length in the wall region of turbulent boundary layers. Aero. Quart. 28, 97.Google Scholar
Gessner, F. B. & Moller, G. L. 1971 Response behaviour of hot-wires in shear flows. J. Fluid Mech. 47, 449.Google Scholar
Glowacki, W. J. & Chi, S. W. 1972 Effect of pressure gradient on mixing length for equilibrium boundary layers. A.I.A.A. Paper no. 72–213.Google Scholar
Hornung, H. G. & Joubert, P. N. 1963 The mean velocity profile in three-dimensional turbulent boundary layers. J. Fluid Mech. 15, 368.Google Scholar
Johnston, J. P. 1960 On the three-dimensional turbulent boundary layer generated by secondary flow. Trans. A.S.M.E. D, J. Basic Engng 82, 233.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.Google Scholar
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. no. 1247.Google Scholar
Krause, E. 1974 Analysis of viscous flow over swept wings. ICAS Paper no. 74–20.Google Scholar
Krause, E., Hirschel, E. H. & Bothmann, Th. 1969 Die numerische Integration der Bewegungsgleichungen dreidimensionaler laminarer kompressibler Grenzschichten. DGLR-Fachbuchreihe, Band 3.Google Scholar
Krause, E., Hirschel, E. H. & Kordulla, W. 1976 Fourth order ‘Mehrstellen’ – integration for three-dimensional turbulent boundary layers. Comp. & Fluids 4, 77.Google Scholar
Krogstad, P. 1979 Investigation of a three-dimensional turbulent boundary layer driven by simple two-dimensional potential flow. Div. Aero- and Gas Dyn., Norwegian Inst. Tech.Google Scholar
Ludwieg, H. & Tillmann, W. 1949 Untersuchung über die Wandschubspannung in turbulenten Reibungsschichten. Ing. Arch. 17, 288.Google Scholar
Mager, A. 1952 Generalization of boundary layer momentum integral equations to three-dimensional flows including those of rotating systems. NACA Rep. no. 1067.Google Scholar
Michel, R., Quémard, C. & Durant, R. 1969 Application d'un schéma de longeur de mélange à l’étude des couches limites turbulentes d’équilibre. ONERA Tech. Note no. 154.Google Scholar
Müller, U. R. 1979 Messung von Reynoldsschen Spannungen und zeitlich gemittelten Geschwindigkeiten in einer dreidimensionalen Grenzschicht mit nichtverschwindenden Druckgradienten. Dissertation, University of Aachen.
Müller, U. R. 1980 Mean velocities and Reynolds stresses measured in a three-dimensional boundary layer. In Proc. Viscous and Interacting Flow Field Effects, 5th U.S. Air Force and the Federal Republic of Germany Data Exchange Agreement Meeting. AFFDL Tech. Rep. no. 80–3088, p. 359.
Müller, U. R. 1982 On the accuracy of turbulence measurements with inclined hot wires. J. Fluid Mech. 118, 155.Google Scholar
Müller, U. R. & Krause, E. 1979 Measurements of mean velocities and Reynolds stresses in an incompressible three-dimensional turbulent boundary layer. In Proc. 2nd Symp. on Turbulent Shear Flows, Imperial College, London, p. 15.36.
Patel, V. C. 1965 Calibrations of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185.Google Scholar
Pierce, F. J. & Duerson, S. H. 1975 Reynolds stress tensors in an end-wall three-dimensional channel turbulent boundary layer. Trans. A.S.M.E. I, J. Fluids Engng 97, 618.Google Scholar
Pierce, F. J. & Ekzewe, S. H. 1974 Measurements of the Reynolds stress tensor in a three-dimensional turbulent boundary layer. Interim Tech. Rep., Virginia Polytechnic Institute.
Pierce, F. J. & Krommenhoek, D. 1968 Wall shear stress diagnostics in three-dimensional turbulent boundary layers. Interim Tech. Rep. no. 2, Project 6858E, U.S. Army Research Office — Durham.Google Scholar
Pierce, F. J. & Zimmermann, B. B. 1973 Wall shear stress inference from two and three-dimensional turbulent boundary layer velocity profiles. Trans. A.S.M.E. I, J. Fluids Engng 95, 61.Google Scholar
Pletcher, R. H. 1969 On a finite difference solution for the constant property turbulent boundary layer. A.I.A.A. J. 7, 305.Google Scholar
Prahlad, T. S. 1968 Wall similarity in three-dimensional turbulent boundary layers. A.I.A.A. J. 6, 1772.Google Scholar
Preston, J. H. 1954 The determination of turbulent skin friction by means of Pitot tubes. J. R. Aero. Soc. 58, 109.Google Scholar
Reinsch, C. H. 1967 Smoothing by cubic splines. Num. Math. 10, 177.Google Scholar
Rotta, J. C. 1977 A family of turbulence models for three-dimensional thin shear layers. In Proc. 1st Symp. on Turbulent Shear Flows, Pennsylvania State Univ., p. 10.27.
Rotta, J. C. 1979 Eine theoretische Untersuchung über den Einfluss der Druckscherkorrelation auf die Entwicklung dreidimensionaler turbulenter Grenzschichten. DFVLR-FB no. 79–05.Google Scholar
Sandborn, V. A. 1976 Effect of velocity gradients on measurements of turbulent shear stress. A.I.A.A. J. 14, 400.Google Scholar
Schraub, F. A. & Kline, S. J. 1965 A study of the structure of the turbulent boundary layer with and without longitudinal pressure gradients. Rep. MD-12, Thermosci. Div., Mech. Engng, Stanford Univ.
Schubauer, G. B. & Spangenberg, W. G. 1960 Forced mixing in boundary layers. J. Fluid Mech. 8, 10.Google Scholar
Simpson, R. L., Strickland, J. H. & Barr, P. W. 1977 Features of a separating turbulent boundary layer in the vicinity of separation. J. Fluid Mech. 79, 553.Google Scholar
Spalding, D. B. 1961 A single formula for the law of the wall. Trans. A.S.M.E. E, J. Appl. Mech. 83, 455.Google Scholar
Vagt, J. D. & Fernholz, H. H. 1979 A discussion of probe effects and improved measuring techniques in the near-wall region of an incompressible three-dimensional turbulent boundary layer. In Turbulent Boundary Layers. Experiment, Theory and Modelling. AGARD Conf. Proc. no. 271, p. 10.1.