Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T11:50:25.414Z Has data issue: false hasContentIssue false
  • English
  • Français

The rough favourable pressure gradient turbulent boundary layer

Published online by Cambridge University Press:  25 November 2009

RAÚL BAYOÁN CAL ,
BRIAN BRZEK ,
T. GUNNAR JOHANSSON  and
LUCIANO CASTILLO
RAÚL BAYOÁN CAL*
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97207-0751, USA
BRIAN BRZEK
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
T. GUNNAR JOHANSSON
Affiliation:
Department of Applied Mechanics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
LUCIANO CASTILLO
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Laser Doppler anemometry measurements of the mean velocity and Reynolds stresses are carried out for a rough-surface favourable pressure gradient turbulent boundary layer. The experimental data is compared with smooth favourable pressure gradient and rough zero-pressure gradient data. The velocity and Reynolds stress profiles are normalized using various scalings such as the friction velocity and free stream velocity. In the velocity profiles, the effects of roughness are removed when using the friction velocity. The effects of pressure gradient are not absorbed. When using the free stream velocity, the scaling is more effective absorbing the pressure gradient effects. However, the effects of roughness are almost removed, while the effects of pressure gradient are still observed on the outer flow, when the mean deficit velocity profiles are normalized by the U∞ δ∗/δ scaling. Furthermore, when scaled with U2∞, the 〈u2〉 component of the Reynolds stress augments due to the rough surface despite the imposed favourable pressure gradient; when using the friction velocity scaling u∗2, it is dampened. It becomes ‘flatter’ in the inner region mainly due to the rough surface, which destroys the coherent structures of the flow and promotes isotropy. Similarly, the pressure gradient imposed on the flow decreases the magnitude of the Reynolds stress profiles especially on the 〈v2〉 and -〈uv〉 components for the u∗2 or U∞2 scaling. These effects are reflected in the boundary layer parameter δ∗/δ, which increase due to roughness, but decrease due to the favourable pressure gradient. Additionally, the pressure parameter Λ found not to be in equilibrium, describes the development of the turbulent boundary layer, with no influence of the roughness linked to this parameter. These measurements are the first with an extensive number of downstream locations (11). This makes it possible to compute the required x-dependence for the production term and the wall shear stress from the full integrated boundary layer equation. The finding indicates that the skin friction coefficient depends on the favourable pressure gradient condition and surface roughness.

JFM classification

Boundary Layers: Boundary Layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 129 - 155
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Akinlade, O. G., Bergstrom, D. J., Tachie, M. F. & Castillo, L. 2004 Outer flow scaling of smooth and rough wall turbulent boundary layers. Exp. Fluids 37, 604–612.Google Scholar
Bakken, O. M., Krogstad, P.-Å., Ashrafian, A. & Andersson, H. 2005 Reynolds number effects in the outer layer of the turbulent flow in a channel with rough walls. Phys. Fluids 17, 065101.Google Scholar
Bergstrom, D. J., Kotey, N. A. & Tachie, M. F. 2002 The effects of surface roughness on the mean velocity profile in a turbulent boundary layer. ASME Trans. J. Fluids Engng 124, 664–670.Google Scholar
Bradshaw, P. 2000 A note on ‘critical roughness height’ and ‘transitional roughness’. Phys. Fluids 12, 1611.Google Scholar
Brzek, B., Cal, R. B., Johansson, T. G. & Castillo, L. 2007 Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers. Phys. Fluids 19, 065101.Google Scholar
Brzek, B., Cal, R. B., Johansson, T. G. & Castillo, L. 2008 Transitionally rough zero pressure gradient turbulent boundary layers. Exp. Fluids 44 (1), 115–124.Google Scholar
Cal, R. B. 2006 The favourable pressure gradient turbulent boundary layer. Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, NY.Google Scholar
Cal, R. B., Brzek, B., Johansson, T. G. & Castillo, L. 2008 Influence of external conditions on transitionally rough favourable pressure gradient turbulent boundary layers. J. Turbul. 9 (38), 1–22.Google Scholar
Cal, R. B. & Castillo, L. 2008 Similarity analysis on favourable pressure gradient turbulent boundary layers with eventual quasilaminarization. Phys. Fluids 20, 105106.Google Scholar
Cal, R. B., Johansson, T. G. & Castillo, L. 2006 The effects of upstream conditions on turbulent boundary layers subject to favourable pressure gradients. AIAA J. 44 (11), 2488–2499.Google Scholar
Castillo, L. 1997 Similarity analysis of turbulent boundary layers. Ph.D. dissertation, State University of New York, Buffalo, NY.Google Scholar
Castillo, L. & George, W. K. 2001 Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA J. 39 (1), 41–47.Google Scholar
Castillo, L. & Johansson, T. G. 2002 The effects of the upstream conditions on a low Reynolds number turbulent boundary layer with zero pressure gradient. J. Turbul. 3, 031.Google Scholar
Castillo, L., Seo, J., Hangan, H. & Johansson, T. G. 2004 a Smooth and rough turbulent boundary layers at high Reynolds number. Exp. Fluids 36, 759–774.Google Scholar
Castillo, L. & Walker, D. 2002 The effects of the upstream conditions on turbulent boundary layers. AIAA J. 40 (12), 2540–2542.CrossRefGoogle Scholar
Castro, I. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.Google Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21, 91–108.Google Scholar
Coleman, H. W., Moffat, R. J. & Kays, W. M. 1977 The accelerated fully rough turbulent boundary layer. J. Fluid Mech. 82, 507–528.Google Scholar
Coles, D. E. 1962 The turbulent boundary layers in a compressible fluid. Tech. Rep. USAF RAND Corp. Rept. R-403-PR. (See also: (1964) Phys. Fluids 7: 1403–1423).Google Scholar
Degraff, D. & Eaton, J. 2000 Reynolds-number scaling of the flat plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.Google Scholar
Fernholz, H. H. & Warnack, D. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axissymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329–356.Google Scholar
Flack, K. A., Schultz, M. P. & Connelly, J. S. 2007 Examination of a critical roughness height for boundary layer similarity. Phys. Fluids 19, 095104.Google Scholar
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsend's Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102.Google Scholar
George, W. K. 1994 Some new ideas for similarity of turbulent shear flows. In Turbulence, Heat and Mass Transfer I, (ed. Hanjalic, K. & Pereira, J. C. F.), pp. 13–24, Begell House, NY (ISBN 1-56700-040-1).Google Scholar
George, W. K. & Castillo, L. 1997 Zero-pressure gradient turbulent boundary layer. Appl. Mech. Rev. 50 (11, 1), 689–729.Google Scholar
Herring, H. J. & Norbury, J. F. 1966 Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. J. Fluid Mech. 27, 541–549.Google Scholar
Ichimiya, M., Nakamura, I. & Yamashita, S. 1998 Properties of a relaminarizing turbulent boundary layer under a favourable pressure gradient. Exp. Therm. Fluid Sci. 17, 37–48.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.Google Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 1–27.Google Scholar
Karlsson, R. I. 1980 Studies of skin friction in turbulent boundary layers on smooth and rough walls. PhD thesis, Chalmers University of Technology, Göteborg, Sweden.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.Google Scholar
Krogstad, P.-Å. & Antonia, R. A. 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 1–21.Google Scholar
Krogstad, P.-Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460.Google Scholar
Krogstad, P.-Å., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617.Google Scholar
Launder, B. E. 1964 Laminarization of the turbulent boundary layer in a severe acceleration. Tech. Rep. Rep. 77. MIT Gas Turbine Lab. Cambridge, MA, USA.Google Scholar
Leonardi, S., Orlandi, P., Smalley, R. J., Djenidi, L. & Antonia, R. A. 2003 Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J. Fluid Mech. 491, 229–238.Google Scholar
Ligrani, P. M. & Moffat, R. J. 1986 Structure of transitionally rough and fully rough turbulent boundary layers. J. Fluid Mech. 162, 69–98.Google Scholar
Ludweig, H. & Tillman, W. 1950 Investigations of the wall shearing stress in turbulent boundary layers. Tech. Rep. TM 1285. NACAGoogle Scholar
Morrison, J., McKeon, B., Jiang, W. & Smits, A. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.Google Scholar
Mukund, R., Viswanath, P. R., Narasimha, R., Prabhu, A. & Crouch, J. D. 2006 Relaminarization in highly favourable pressure gradient on a convex surface. J. Fluid Mech. 566, 97–115.Google Scholar
Narasimha, R. & Sreenivasan, K. R. 1973 Relaminarization in highly accelerated turbulent boundary layers. J. Fluid Mech. 61, 417–447.Google Scholar
Newhall, K., Cal, R. B., Brzek, B., Johansson, T. G. & Castillo, L. 2006 Determination of skin friction on smooth and rough turbulent boundary layers subject to external favourable pressure gradients. In ASME Joint U.S.-European Fluids Engineering Conference, FEDSM-2006-98517, Miami, FL.Google Scholar
Nickels, T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217–239.Google Scholar
Nikuradse, J. 1933 Laws of Flows in rough pipes, NACA Technical memorandum 1292.Google Scholar
Österlund, J. 1999 Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
Patel, V. C. & Head, M. R. 1968 Reversion of turbulent to laminar flow. J. Fluid Mech. 23, 185–208.Google Scholar
Perry, A. E. & Li, J. D. 1990 Experimental support for the attached-eddy hypothesis in zero-pressure gradient turbulent boundary layers. J. Fluid Mech. 218, 405–438.Google Scholar
Piomelli, U., Balaras, E. & Pascarelli, A. 2000 Turbulent structures in accelerating boundary layers. J. Turbul. 1, 001. Mathematiker-Kongresses, Heidelberg, Germany.Google Scholar
Radhakrishnana, S., Keating, A. & Piomelli, U. 2006 Large eddy simulations of high Reynolds number flow over a contoured ramp. In AIAA-2006-0899, 44th AIAA Aerospace Science Meeting and Exhibit, Reno, NV.Google Scholar
Raupach, M. R., Antonia, R. A., & Rajagopalan, S. 1991 Rough-wall turbulent boundary layer. Appl. Mech. Rev. 44, 1–25.Google Scholar
Schultz, M. P. 2002 The relationship between frictional resistance and roughness for surfaces smoothened by sanding. ASME J. Fluids Engng 124, 492–499.Google Scholar
Schultz, M. P. & Flack, K. A. 2005 Outer layer similarity in fully rough turbulent boundary layer. Exp. Fluids 38, 324–340.Google Scholar
Seo, J. 2003 Investigation of the upstream conditions and surface roughness in turbulent boundary layers. PhD dissertation, Rensselaer Polytechnic Institute, Troy, NY.Google Scholar
Shafi, H. S. & Antonia, R. A. 1995 Anisotropy of the Reynolds stresses in a turbulent boundary layer on a rough wall. Exp. Fluids 18, 213–215.Google Scholar
Sreenivasan, K. R. 1982 Laminarescent, relaminarizing and retransitional flows. Acta Mech. 44, 1–48.Google Scholar
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2000 Rough wall turbulent boundary layers in shallow open channel flow. J. Fluids Engng 122, 533–541.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flows. Cambridge University Press.Google Scholar
Warnack, D. & Fernholz, H. H. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axissymmetric turbulent boundary layer. Part 2. The boundary layer with relaminarization. J. Fluid Mech. 359, 357–381.CrossRefGoogle Scholar
Zagarola, M. V. & Smits, A. J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79.Google Scholar