Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-07-01T07:17:22.466Z Has data issue: false hasContentIssue false

Comparison of smooth- and rough-wall non-equilibrium boundary layers with favourable and adverse pressure gradients

Published online by Cambridge University Press:  23 March 2023

Ralph J. Volino*
Affiliation:
Mechanical Engineering Department, United States Naval Academy, Annapolis, MD 21401, USA
Michael P. Schultz
Affiliation:
Naval Architecture and Ocean Engineering Department, United States Naval Academy, Annapolis, MD 21402, USA
*
 Email address for correspondence: volino@usna.edu

Abstract

Measurements were made in rough-wall boundary layers subject to favourable, zero and adverse pressure gradients. Profiles of mean velocity and turbulence quantities were acquired and velocity fields were measured in multiple planes to document flow structure. Comparisons were made to equivalent smooth-wall cases with the same free stream velocity distributions. Outer layer similarity was observed between the rough- and smooth-wall cases in all quantities in the favourable and zero pressure gradient regions, but large differences were observed with adverse pressure gradients. In both the smooth- and rough-wall cases, the favourable pressure gradient reduced the turbulence in the boundary layer, and increased the size of turbulence structures relative to the boundary layer thickness in both the streamwise and spanwise directions, while lowering their inclination angle with respect to the wall. When the boundary layer was returned to a zero pressure gradient following the favourable pressure gradient region, the turbulence level and the size and inclination of the structures returned to their canonical zero pressure gradient condition. The response of the boundary layer was somewhat faster in the rough-wall case, causing it to reach equilibrium in a shorter streamwise distance after the changes in pressure gradient than in the smooth-wall case. The adverse pressure gradient increased turbulence levels relative to the wall friction velocity, reduced the size of turbulence structures relative to the boundary layer thickness and increased their inclination angle. The changes with the adverse pressure gradient were significantly larger with the rough wall than the smooth. The results suggest that similarity might be achieved with adverse pressure gradients if smooth- and rough-wall cases with the same Clauser pressure gradient parameter history are compared.

Type
JFM Papers
Creative Commons
This is a work of the US Government and is not subject to copyright protection within the United States.
Copyright
© United States Naval Academy, 2023. Published by 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

Adrian, R.J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure – homogeneous shear-flow. J. Fluid Mech. 190, 531559.CrossRefGoogle Scholar
Aubertine, C.D. & Eaton, J.K. 2005 Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. J. Fluid Mech. 532, 345364.CrossRefGoogle Scholar
Aubertine, C.D., Eaton, J.K. & Song, S. 2004 Parameters controlling roughness effects in a separating boundary layer. Intl J. Heat Fluid Flow 25, 444450.CrossRefGoogle Scholar
Bobke, A., Vinuesa, R., Orlu, R. & Schlatter, P. 2017 History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers. J. Fluid Mech. 820, 667692.CrossRefGoogle Scholar
Castro, I.P. 2007 Rough-wall boundary layers: mean flow univerality. J. Fluid Mech. 585, 469485.CrossRefGoogle Scholar
Christensen, K.T. & Adrian, R.J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.CrossRefGoogle Scholar
Christensen, K.T. & Wu, Y. 2005 Characteristics of vortex organization in the outer layer of wall turbulence. In Proceedings of the Fourth International Technical Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, VA, vol. 3, pp. 1025–1030.Google Scholar
Chung, D., Hutchins, N., Schultz, M.P. & Flack, K.A. 2021 Predicting the drag on rough surfaces. Annu. Rev. Fluid Mech. 53, 439471.CrossRefGoogle Scholar
Coleman, H.W., Moffat, R.J. & Kays, W.M. 1977 The accelerated fully rough turbulent boundary layer. J. Fluid Mech. 82, 507528.CrossRefGoogle Scholar
Devenport, W.J. & Lowe, K.T. 2022 Equilibrium and non-equilibrium turbulent boundary layers. Prog. Aerosp. Sci. 131, 100807.CrossRefGoogle Scholar
Flack, K. & Chung, D. 2022 Important parameters for a predictive model of ks for zero pressure gradient flows. AIAA J. 60, 59235931.CrossRefGoogle Scholar
Flack, K.A., Schultz, M.P. & Volino, R.J. 2020 The effect of a systematic change in roughness skewness on turbulence and drag. Intl J. Heat Fluid Flow 85, 108669.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. & Marusic, I. 2006 Experimental investigation of vortex properties in a turbulent boundary layer. Phys. Fluids 18, 055105.CrossRefGoogle Scholar
Hambleton, W.T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 5364.CrossRefGoogle Scholar
Hutchins, N., Hambleton, W.T. & Marusic, I. 2005 Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 2154.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent boundary layers over rough walls. Annu. Rev. Fluid Mech. 36, 173196.CrossRefGoogle Scholar
Kays, W.M. & Crawford, M.E. 1980 Convective Heat and Mass Transfer, 2nd edn. McGraw Hill.Google Scholar
Lee, J.-H. & Sung, H.J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101131.CrossRefGoogle Scholar
Marusic, I. & Monty, J.P. 2019 Attached Eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 4974.CrossRefGoogle Scholar
Mellor, G.L. & Gibson, D.M. 1966 Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225253.CrossRefGoogle Scholar
Nikuradse, J. 1933 Laws of flow in rough pipes. NACA Tech. Mem.1292 (1950).Google Scholar
Pailhas, G., Touvet, Y. & Aupoix, B. 2008 Effects of Reynolds number and adverse pressure gradient on a turbulent boundary layer developing on a rough surface. J. Turbul. 9, N43.CrossRefGoogle Scholar
Perry, A.E. & Joubert, P.N. 1963 Rough-wall boundary layers in adverse pressure gradients. J. Fluid Mech. 17, 193211.CrossRefGoogle Scholar
Pullin, D.I., Hutchins, N. & Chung, D. 2017 Turbulent flow over a long flat plate with uniform roughness. Phys. Rev. Fluids 2, 082601(R).CrossRefGoogle Scholar
Reynolds, W.C. 1976 Computation of turbulent flows. Annu. Rev. Fluid Mech. 8, 183208.CrossRefGoogle Scholar
Shin, J.H. & Song, S.J. 2015 a Pressure gradient effects on smooth- and rough-surface turbulent boundary layers – part I: favorable pressure gradient. Trans. ASME J. Fluids Engng 137, 011203.CrossRefGoogle Scholar
Shin, J.H. & Song, S.J. 2015 b Pressure gradient effects on smooth- and rough-surface turbulent boundary layers – part II: adverse pressure gradient. Trans. ASME J. Fluids Engng 137, 011204.CrossRefGoogle Scholar
Song, S. & Eaton, J.K. 2002 The effects of wall roughness on the separated flow over a smoothly contoured ramp. Exp. Fluids 33, 3846.CrossRefGoogle Scholar
Spalart, P.R. 1986 Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307328.CrossRefGoogle Scholar
Squire, D.T., Morrill-Winter, C., Hutchins, N., Schultz, M.P., Klewicki, J.C. & Marusic, I. 2016 Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech. 795, 210240.CrossRefGoogle Scholar
Tay, G.F.K., Kuhn, D.C.S. & Tachie, M.F. 2009 Influence of adverse pressure gradient on rough-wall turbulent flows. Intl J. Heat Fluid Flow 30, 249265.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Volino, R.J. 2020 Non-equilibrium development in turbulent boundary layers with changing pressure gradients. J. Fluid Mech. 897, A2.CrossRefGoogle Scholar
Volino, R.J., Devenport, W.J. & Piomelli, U. 2022 Questions on the effects of roughness and its analysis in non-equilibrium flows. J. Turbul. 23, 454466.CrossRefGoogle Scholar
Volino, R.J. & Schultz, M.P. 2018 Determination of wall shear stress from mean velocity and Reynolds shear stress profiles. Phys. Rev. Fluids 3, 034606.CrossRefGoogle Scholar
Volino, R.J. & Schultz, M.P. 2022 Effects of boundary layer thickness on the estimation of equivalent sandgrain roughness in zero pressure gradient boundary layers. Exp. Fluids 63, 131.CrossRefGoogle Scholar
Volino, R.J., Schultz, M.P. & Flack, K.A. 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263293.CrossRefGoogle Scholar
Volino, R.J., Schultz, M.P. & Flack, K.A. 2009 Turbulence structure in boundary layers with two-dimensional roughness. J. Fluid Mech. 635, 75101.CrossRefGoogle Scholar
Volino, R.J., Schultz, M.P. & Flack, K.A. 2011 Turbulence structure in boundary layers over periodic two- and three-dimensional roughness. J. Fluid Mech. 676, 172190.CrossRefGoogle Scholar
Willmarth, W.W. & Lu, S.S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 6592.CrossRefGoogle Scholar
Wu, Y. & Christensen, K.T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 5576.CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2014 Numerical simulations of sink-flow boundary layers over rough surfaces. Phys. Fluids 26, 015113.CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2015 Numerical simulation of a spatially developing accelerating boundary layer over roughness. J. Fluid Mech. 780, 192214.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.CrossRefGoogle Scholar