Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-31T23:11:30.024Z Has data issue: false hasContentIssue false
  • English
  • Français

Laterally strained turbulent boundary layers near a plane of symmetry

Published online by Cambridge University Press:  26 April 2006

Lucio Pompeo ,
Marco S. G. Bettelini  and
Hans Thomann
Lucio Pompeo
Affiliation:
Institut für Fluiddynamik, Swiss Federal Institute of Technology (ETH), CH-8092 Zürich, Switzerland Present address: McKinsey & Company. Inc, CH-8703 Erlenbach, Switzerland.
Marco S. G. Bettelini
Affiliation:
Institut für Fluiddynamik, Swiss Federal Institute of Technology (ETH), CH-8092 Zürich, Switzerland Present address: ABB/Asea Brown Boveri AG, CH-5400 Baden, Switzerland.
Hans Thomann
Affiliation:
Institut für Fluiddynamik, Swiss Federal Institute of Technology (ETH), CH-8092 Zürich, Switzerland
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments are presented for three turbulent boundary layers generated by laterally converging, laterally diverging and parallel flow on a flat plate. A converging potential flow field outside the boundary layer was generated by superposing a parallel flow in the x-direction, a row of equally spaced line sources in the wall-normal (y) direction and an analogous row of sinks in the transversal (z) direction. This arrangement resulted in a velocity that was constant far upstream, far downstream and along the x-axis. The convergence – ∂W/∂z has its maximum in the plane of the source and sink rows. This flow field was realized with the test section shown in figure 1, based on streamlines intersecting a rectangular cross-section far upstream. The diverging flow was generated by reversing the flow direction through the test section.

The tests were conducted at about 42 m/s leading to a unit Reynolds number of 2.5 × 106/m and to a Reynolds number based on the momentum thickness of 4000 to 4700 at the inlet of the test sections, increasing up to 25000 at the outlet. In all three cases the velocity distribution near the wall agreed very well with the logarithmic law of the wall. The wake contribution in the outer layer was considerably increased by convergence and decreased by divergence. The Reynolds stresses, measured with crossed hot-wire probes, and the wall shear stress, measured with a floating-element balance, were generally increased by divergence and decreased by convergence and the same holds true for the mixing length and the turbulent viscosity.

A finite-difference boundary-layer code using a simple turbulence model was used to predict the experimental results. The comparison showed good agreement for the two-dimensional flow, reasonable agreement for the diverging flow and poor agreement for the converging one. Use of the experimentally determined turbulent viscosity as input into the computation did not systematically improve the agreement but excellent agreement was found if it was combined with anisotropy of the turbulent viscosity. It was much more difficult to predict the converging flow as small errors in the crossflow had a large effect on the flow in the plane of symmetry (z = 0).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 507 - 532
Copyright
© 1993 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

Anderson, S. D. & Eaton, J. K. 1987 An experimental investigation of pressure-driven three-dimensional turbulent boundary layers. Stanford University, Thermosci. Div. Rep. MD-49.
Anderson, S. D. & Eaton, J. K. 1989 Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers. J. Fluid Mech. 202, 263–294.Google Scholar
Bradshaw, P. 1988 Effects of extra rates of strain — review. Zoran Zaric Memorial Sem., Dubrovnik. Hemisphere.
Bradshaw, P., Ferris, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 593–616.Google Scholar
Bettelini, M. S. G. 1990 Numerical study of some engineering turbulence models for three-dimensional boundary layers. Dissertation, ETH No. 9182.
Bettelini, M. S. G. & Fanneløp, T. K. 1993 A systematic comparison of mathematically simple turbulence models for three-dimensional boundary layers. AIAA J. 31, 999–1006.Google Scholar
Cebeci, T. & Smith, A. M. O. 1968 A finite-difference solution of the incompressible turbulent boundary-layer equations by an eddy-viscosity model. In 1968 AFOSR-IFP-Stanford Conf. on Computation of Turbulent Boundary Layers (ed. S. J. Klein et al.) Stanford University.
Crawford, M. E. & Kays, W. M. 1976 STAN5–A program for numerical computation of two-dimensional internal and external boundary layer flows. NASA CR 2742.
Degani, A. T., Smith, F. T. & Walker, J. D. A. 1992 The three-dimensional turbulent boundary layer near a plane of symmetry. J. Fluid Mech. 234, 329–360.Google Scholar
Hirota, M., Fujita, H. & Yokosawa, H. 1988 Influences of velocity gradient on hot-wire anemometry with an X-wire probe. J. Phys. E: Sci. Instrum. 21, 107–1084.Google Scholar
Hirt, F., Zurfluh, U. & Thomann, H. 1986 Skin friction balances for large pressure gradients. Exps Fluids 4, 296–300.Google Scholar
Humphreys, D. A., van den Berg, B. 1981 Three-dimensional turbulent boundary layers. In 1980-81 AFOSR-HTTM-Stanford Conf. on Turbulent Flows (ed. S. J. Kline, B. J. Cantwell & G. M. Lilley). Stanford University.
Kline, S. J., Cantwell, B. J., Lilley, G. M. (Ed.) 1981 Complex turbulent flows. 1980-81 AFOSR-HTTM-Stanford Conference on Turbulent Flows. Stanford University.
Kline, S. J., Morkovin, M. V., Sovran, G., Cockrell, D. J., Coles, D. E., Hirst, E. A. (Ed) 1968 Proc. Computation of Turbulent Boundary Layers. 1968 AFOSR-IFP-Stanford Conference, Stanford University.
Lamb, H. 1945 Hydrodynamics, 6th edn. Dover.
Moore, F. K. 1956 Three-dimensional boundary layer theory. Adv. Appl. Mech. IV, 159–228.
Patel, V. C. & Baek, J. H. 1987a Boundary layers in planes of symmetry. Part I: Experiments in turbulent flow. AIAA J. 25, 550–559.Google Scholar
Patel, V. C. & Baek, J. H. 1987b Boundary layers in planes of symmetry. Part II: Calculations for laminar and turbulent flows. AIAA J. 25, 812–814.Google Scholar
Pauley, W., Eaton, J. & Cutler, A. 1989 Diverging boundary layers with zero streamwise pressure gradient. AIAA Paper 89-0134.
Pompeo, L. 1992 An experimental study of three-dimensional turbulent boundary layers. Dissertation, ETH No 9780.
Pompeo, L. & Thomann, H. 1993 Quadruple hot-wire probes in a simulated wall flow. Exps Fluids 14, 145–152.Google Scholar
Saddoughi, S. G. & Joubert, P. N. 1991 Lateral straining of turbulent boundary layers. Part 1. Streamline divergence. J. Fluid Mech. 229, 173–204.Google Scholar
Schlichting, H. 1982 Grenzschicht-Theorie. G. Braun.
Scholtysik, M., Bettelini, M. S. G. & Fanneløp, T. K. 1993 A note on problems in 3D boundary layer computations in streamline coordinates. Z. Angew. Math. Phys. (to appear.)Google Scholar
Smits, A. J., Eaton, J. A. & Bradshaw, P. 1979 The response of a turbulent boundary layer to lateral divergence. J. Fluid Mech. 94, 243–268.Google Scholar
Zurfluh, U. E. 1984 Experimentelle Bestimmung der Wandschubspannung in turbulenten Grenzschichten. Dissertation, ETH No 7528.