Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-01T01:49:46.582Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence measurements in an adverse-pressure-gradient three-dimensional turbulent boundary layer along a circular cylinder

Published online by Cambridge University Press:  20 April 2006

H. H. Fernholz  and
J.-D. Vagt
H. H. Fernholz
Affiliation:
Hermann-Föttinger-Institut für Thermo- und Fluidynamik, Technische Universität Berlin
J.-D. Vagt
Affiliation:
Hermann-Föttinger-Institut für Thermo- und Fluidynamik, Technische Universität Berlin
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements, including the six components of the Reynolds-stress tensor, have been made along three generators of a centre-mounted circular cylinder with an elliptical nose cone. The pressure distribution was axisymmetric upstream and asymmetric downstream. The streamwise adverse pressure gradient led to almost zero skin friction in the direction of the limiting streamline, and the circumferential pressure gradient led to skew angles up to 30° in the vicinity of the wall. Special emphasis was laid on measurements in the wall region (y+ > 4), on the repeatability of these measurements and on an estimate of error bounds. The turbulence level encountered (up to 60% close to the wall) was much higher than in other threedimensional boundary-layer measurements. It has been shown that available measuring techniques have to be improved considerably or even abandoned if used under these conditions. Previous measurements of collateral velocity profiles in three-dimensional boundary layers will probably now have to be corrected for severe aerodynamic interference effects.

It has been shown that the normal stresses $\overline{u^{\prime 2}_i}$ and the shear stress component $\overline{u^{\prime}v^{\prime}}$ behave qualitatively much as those in a two-dimensional adverse pressuregradient boundary layer. The other components, $\overline{v^{\prime}w^{\prime}}$ and $\overline{u^{\prime}w^{\prime}}$, both characteristic of three-dimensional flow and caused by the circumferential pressure gradient, are influenced in different ways by the streamwise and circumferential pressure gradients. Spectra of u′-fluctuations are again similar to those obtained from two-dimensional boundary layers.

Mean velocity profiles obey the linear and logarithmic law of the wall known from two-dimensional boundary layers both along a line of symmetry and in the threedimensional boundary layer. This may be because the streamwise pressure gradient dominates over the circumferential pressure gradient in this experiment.

Finally it has been found that the skew angle γ of the Reynolds shear stress vector leads the skew angle ζ of the resultant velocity gradient or ‘mean shear’, both having the opposite sign of the skew angle β of the mean velocity vector except close to the wall. The ratio of Reynolds shear stress and turbulent kinetic energy is no longer ‘approximately’ constant as is assumed for two-dimensional boundary layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 233 - 269
Copyright
© 1981 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

Berg, B. Van Den 1975 A three-dimensional law of the wall for turbulent shear flows. J. Fluid Mech. 70, 149–160.Google Scholar
Berg, B. Van Den 1976 Investigations of three-dimensional incompressible turbulent boundary layers. NLR Tech. Rep. 76001 U.Google Scholar
Bissonnette, L. R. & Mellor, G. L. 1974 Experiments on the behaviour of an axisymmetric turbulent boundary layer with a sudden circumferential strain. J. Fluid Mech. 63, 369–413.Google Scholar
Bradshaw, P. 1967 ‘Inactive’ motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241–258.Google Scholar
Bradshaw, P. 1969 The response of a constant-pressure turbulent boundary layer to the sudden. application of an adverse pressure gradient. Aero. Res. Counc. R & M. 3575.Google Scholar
Bradshaw, P. 1971 Calculation of three-dimensional turbulent boundary layers. J. Fluid Mech. 46, 417–445.Google Scholar
Bradshaw, P. & Terrell, M. G. 1969 The response of a turbulent boundary layer on an ‘infinite’ swept wing to the sudden removal of pressure gradient. NPL Aero Rep. 1305.Google Scholar
Comte-Bellot, G., Strohl, A. & Alcaraz, E. 1971 On aerodynamic disturbances caused by single hot-wire probes. Trans. A.S.M.E. E, J. Appl. Mech. 93, 767–774.Google Scholar
Dahm, A. & Vagt, J.-D. 1977 Entwicklung und Herstellung interferenzarmer Hitzdrahtsonden. HFI INst. 01/77.
Dean, R. C. 1953 Aerodynamic Measurements. Gas Turbine Laboratory, M.I.T.
Dechow, R. 1977 Mittlere Geschwindigkeit und Reynoldsscher Spannungstensor in der dreidimensionalen turbulenten Wandgrenzschicht vor einem stehenden Zylinder. Dissertation Universität Karlsruhe. Strömungsmaschinen u. Strömungsmechanik Heft 21.
East, L. F. 1972 A prediction of the law of the wall in compressible three-dimensional turbulent boundary layers. RAE Tech. Rep. 72, 178.Google Scholar
East, L. F. 1974 Measurements of the three-dimensional incompressible turbulent boundary layer induced on the surface of a slender delta wing by the leading edge vortex. RAE Tech. Rep. 73, 141.Google Scholar
Eichelbrenner, E. A. 1973 Three-dimensional boundary layers. Ann. Rev. Fluid Mech. 5, 339–360.Google Scholar
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. 74095 U.Google Scholar
Ezekwe, C. I., Pierce, F. J. & McAllister, J. E. 1978 Measured Reynolds stress tensor in a three-dimensional turbulent boundary layer. A.I.A.A. J. 16, 645–647.Google Scholar
Fanneløp, T. K. & Krogstad, P. A. 1975 Three-dimensional turbulent boundary layers in external flows: a report on Euromech 60. J. Fluid Mech. 71, 815–826.Google Scholar
Fernholz, H. H. & Vagt, J.-D. 1977 Measurements in an axisymmetric turbulent boundary layer with weak and strong three-dimensional disturbances. In Structure and Mechanisms of Turbulence I, Lecture Notes in Physics, vol. 75, (ed. H. Fielder), pp. 222–233. Springer.
Fernholz, H. H., Vagt, J.-D., Dziomba, B. & Dengel, P. 1978 Messungen in einer dreidimensionalen turbulenten Wandgrenzschicht an einer gekrümmten Wand. HFI Institutsbericht 01/78. (2. ergänzte Auflage 1980). Technische Universität Berlin.
Froebel, E. & Vagt, J.-D. 1974 Ein automatisch abgleichendes Flüssigkeitsmanometer mit digitaler Anzeige. DLR-FB 74–40.
Froebel, E. & Vagt, J.-D. 1977 Meß- und Auswerteverfahren von Hitzdrahtsignalen mit dem Turbulenzgradmesser TGM III der DFVLR. DLR-FB 77–61.
Grande, G. De & Hirsch, Ch. 1978 Three-dimensional incompressible turbulent boundary layers. Int. Rep. Vrije Univ. Brussels STR-8.
Hebbar, K. S. & Melnik, W. L. 1976 Measurements in the near-wall region of a relaxing three-dimensional low speed turbulent air boundary layer. Univ. Maryland, Tech. Rep. AE-76–1.Google Scholar
Hebbar, K. S. & Melnik, W. L. 1978 Wall region of a relaxing three-dimensional incompressible turbulent boundary layer. J. Fluid Mech. 85, 33–56.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 turbulent boundary layers. Stanford Univ. Thermosciences Div. Rep. MD-34.Google Scholar
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Rep. 1247.Google Scholar
Krause, E. & Kordulla, W. 1975 Investigation of three-dimensional boundary layers on swept wings. Paper presented at Euromech 60, Trondheim.
Mccroskey, W. J. & Durbin, E. J. 1972 Flow angle and shear stress measurements using heated films and wires. Trans. A.S.M.E. I, J. Basic Engng. 94, 46–52.Google Scholar
Müller, U. 1979 Messung von Reynoldsschen Spannungen und zeitlich gemittelten Ge schwindigkeiten in einer drei-dimensionalen Grenzschicht mit nichtverschwindendem Druckgradienten. Dissertation RWTH Aachen.
Nash, J. F. & Patel, V. C. 1972 Three-Dimensional Turbulent Boundary Layers. SBC Technical Books.
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185–208.Google Scholar
Pierce, F. J. & East, J. L. 1972 Near-wall collateral flow in three-dimensional turbulent boundary layers. A.I.A.A. J. 10, 334–336.Google Scholar
Pierce, F. J. & Ezekwe, C. I. 1975 Turbulent stress tensors in a three-dimensional boundary layer. Virginia Polytech. Inst. Rep. E-75–1.Google Scholar
Pierce, F. J. & Krommenhoek, D. H. 1968 Wall shear stress diagnostics in three dimensional turbulent boundary layers. Virginia Polytech. Mech. Engng. Dept, Interim Tech. Rep. no. 2.Google Scholar
Pierce, F. J., Tennant, M. H. & Rule, J. A. 1976 Near-wall similarity in three-dimensional turbulent flows — Experimental system. Virginia Polytech. Inst. Rep. E-76–16.Google Scholar
Pierce, F. J. & Zimmerman, B. B. 1973 Wall shear stress interference from two- and three-dimensional turbulent boundary layer velocity profiles. Trans. A.S.M.E. I, J. Fluids Engng. 95, 61–67.Google Scholar
Prahlad, T. S. 1972 Méan velocity profiles in three-dimensional incompressible turbulent boundary layers. A.I.A.A.J. 11, 359–365.Google Scholar
Rogers, B. K. & Head, M. R. 1969 Measurements of three-dimensional boundary layers. J. Roy. Aeronaut. Soc. 73, 796–798.Google Scholar
Swamy Chandrasekhara, N. V., Gowda Lakshmana, B. H. & Lakshminath, V. R. 1978 Turbulence measurements in the three-dimensional boundary layer on a yawed flat plate at incidence. Z.F.W. 2, 15–22.Google Scholar
Vagt, J.-D. 1973 Bemerkungen zur Auslegung eines Unterschall-Freistrahl Windkanals. Z.f.W. 5, 159–162.Google Scholar
Vagt, J.-D. 1979 Hot-wire probes in low speed flow. Prog. Aerospace Sci. 18, 271–323.Google Scholar
Vagt, J.-D. & Fernholz, H. H. 1973 Use of surface fences to measure wall shear stress in three-dimensional boundary layers. Aero. Quart. 24, 87–91.Google Scholar
Vagt, J.-D. & Fernholz, H. H. 1977 Wall interference effects of static pressure probes in an incompressible turbulent boundary layer. Aero. Quart. 28, 176–184.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. AGARD Conf. Proceedings. 271.
Vermeulen, A. J. 1971 Measurements of three-dimensional turbulent boundary layers. Ph.D. thesis, University of Cambridge.