Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-09T07:19:36.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent boundary layers subjected to multiple curvatures and pressure gradients

Published online by Cambridge University Press:  26 April 2006

Promode R. Bandyopadhyay  and
Anwar Ahmed
Promode R. Bandyopadhyay
Affiliation:
Mail Stop 170, NASA Langley Research Center Hampton, VA 23665–5225, USA Present address: Code 8234, Naval Undersea Warfare Center Division, Newport, RI 02841–5047, USA.
Anwar Ahmed
Affiliation:
Mail Stop 170, NASA Langley Research Center Hampton, VA 23665–5225, USA On leave from: Aero. Department, Texas A. & M. University.
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompanying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Górtler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 503 - 527
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

Alving, A. E., Smits, A.J. & Watmuff, J. H. 1986 Turbulent boundary layer relaxation from convex curvature. J. Fluid Mech. 211, 529– 556.Google Scholar
Antonia, R.A. & Luxton, R. E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough, J. Fluid Mech. 48, 721– 761.Google Scholar
Bandyopadhyay, P.R. 1986 Review – Mean flow in turbulent boundary layers disturbed to alter skin friction. Trans. ASME J. Fluids Engng 108, 127– 140.Google Scholar
Bandyopadhyay, P.R. 1987 Rough-wall turbulent boundary layers in the transition regime. J. Fluid Mech. 180, 231– 266.Google Scholar
Bandyopadhyay, P. R. 1988 Resonant flow in small cavities submerged in a boundary layer. Proc. R. Soc. Lond. A 420, 219– 245.Google Scholar
Bandyopadhyay, P. R. 1989 Viscous drag reduction of a nose body. AIAA J. 27, 274– 282.Google Scholar
Bandyopadhyay, P. R. 1990 Convex curvature concept of viscous drag reduction. In Viscous Drag Reduction in Boundary Layers (ed. D. M. Bushnell & J. N. Hefner), vol. 123, pp. 285– 324. AIAA.
Barlow, R. S. & Johnston, J. P. 1988 Structure of a turbulent boundary layer on a concave surface. J. Fluid Mech. 191, 137– 176.Google Scholar
Baskaran, V., Smits, A. J. & Joubert, P. N. 1987 A turbulent flow over a curved hill. Part 1. Growth of an internal layer. J. Fluid Mech. 182, 47– 83.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent flow. J. Fluid Mech. 36, 177– 191.Google Scholar
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARD AG-169.Google Scholar
Bushnell, D. M. 1983 Turbulent drag reduction for external flows. AIAA Paper 83– 0227.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1– 51.Google Scholar
Erm, L. P., Smits, A. J. & Joubert, P. N. 1985 Low Reynolds number turbulent boundary layers on a smooth flat surface in a zero pressure gradient. In Fourth Symp. on Turbulent Shear Flows, Aug. 7–9, 1985, Cornell University, pp. 2.13– 2.18.
Gatski, T. B. & Savill, A. M. 1989 An analysis of curvature effects for the control of wall-bounded shear flows. AIAA Paper 89– 1014.
Gillis, J. C. & Johnston, J. P. 1983 Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall. J. Fluid Mech. 135, 123– 153.Google Scholar
Kármán, T. Von 1934 Some aspects of the turbulence problem. In Proc. Fourth Intl. Congr. of App. Mech., Cambridge University, p. 54.
Kim, S.-W. 1989 Numerical investigation of an internal layer in turbulent flow over a curved hill. NASA TM 102230.Google Scholar
Leontev, A. & Fomichev, V. M. 1983 Heat transfer and drag in a turbulent boundary layer with a pressure gradient. Inz. Fiz. Zh. (in Russian) 45, 5– 11.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
Muck, K. C., Hoffmann, P. H. & Bradshaw, P. 1985 The effect of convex surface curvature on turbulent boundary layers. J. Fluid Mech. 161, 347– 369.Google Scholar
Nash, J. F. 1965 Turbulent boundary-layer behavior of the auxiliary equation. AGARDOgraph 97, pp. 245– 279.Google Scholar
Nash, J. F. & Patel, V. C. 1972 Three-Dimensional Turbulent Boundary Layers. SBC Tech. Books, Sci. and Bus. Consultants, Inc., Atlanta, Ga.
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in adverse pressure gradients. J. Fluid Mech. 23, 185– 208.Google Scholar
Peabhu, A., Narasimha, R. & Rao, B. N. S. 1983 Structure and mean flow similarity in curved turbulent boundary layers. Proc. IUTAM Symp. on Structure of Complex Turbulent Shear Flows, Marseille, 1982 (ed, R. Dumas & L. Fulachier). Springer.
Prandtl, L. 1929 Sonderdruk aus Vortrage aus dem Gebiete, der Aerodynamik und Verwandter Gebiete. Aachen. (Transl. NACA TM 625).
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low-Reynolds numbers. Phys. Fluids 24, 802– 811.Google Scholar
Ramafrian, B. R. & Shivaprasad, B. G. 1977 Mean flow measurements in turbulent boundary layers along mildly curved surfaces. AIAA J. 15, 189– 196.Google Scholar
Rehman, F. & Bowyer, J. M. 1989 Turbulent incompressible air flow through S-shaped ducts with cross-sectional area change. Forum on Turbulent Flows. ASME FED-76, pp. 49– 57.Google Scholar
Richmond, M. C., Chen, H. C. & Patel, V. C. 1986 Equations of laminar and turbulent flows in general curvilinear coordinates. IIHR Rep. 300. Iowa inst. of Hyd. Res.
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.
Schmidt, M. C., Whitelaw, J. H. & Yianneskis, M. 1987 Flow in out-of-plane double S-bends. In 6th Symp. on Turbulent Shear Flows, Toulouse, Se. pt. 7–9, pp. 13.3.1– 13.3.6.
Smith, A. M. O. 1955 On the growth of Taylor-Görtler vortices along highly concave walls. Q. Appl. Maths 13, 233– 262.Google Scholar
Smits, A. J., Matheson, N, & Joubert, P. N. 1983 Low Reynolds number turbulent boundary layers in zero and favorable pressure gradients. J. Ship Res. 27, 147– 157.Google Scholar
Smits, A. J., Young, S. T. B. & Bradshaw, P. 1979 The effect of short regions of high surface curvature on turbulent boundary layers. J. Fluid Mech. 94, 209– 242.Google Scholar
So, R. M. C. 1975 A turbulence velocity scale for curved shear flows. J. Fluid Mech. 70, 37– 57.Google Scholar
So, R. M. C. & Mellor, G. L. 1972 An experimental investigation of turbulent boundary-layers along curved surfaces. NASA CR-1940.Google Scholar
So, R. M. C. & Melloe, G. L. 1973 Experiment on convex curvature effects in turbulent boundary layers. J. Fluid Mech. 60, 43– 62.Google Scholar
So, R. M. C. & Mellor, G. L. 1975 Experiment on turbulent boundary layers on a concave wall Aero. Q. 26, 25– 40.Google Scholar
Spalart, P. R. 1988 Direct numerical simulation of a turbulent boundary layer up to Reθ = 1410. J. Fluid Mech. 187, 61– 98.Google Scholar
Tani, I. 1962 Production of longitudinal vortices in the boundary layer along a concave wall J Geophys. Res. 67, 3075– 3081.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tsai, H. M. & Leslie, D. C. 1990 Large eddy simulation of a developing turbulent boundary layer at low Reynolds number. Intl J. Num. Meth. Fluids 10, 519– 555.Google Scholar