Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-12-03T00:46:53.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-equilibrium development in turbulent boundary layers with changing pressure gradients

Published online by Cambridge University Press:  09 June 2020

Ralph J. Volino Open the ORCID record for Ralph J. Volino [Opens in a new window]
Ralph J. Volino*
Affiliation:
Mechanical Engineering Department, United States Naval Academy, Annapolis, MD 21402, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Turbulence measurements were made in smooth-wall boundary layers subject to changing pressure gradients. Cases were documented over a range of Reynolds numbers and acceleration parameters. In all cases the boundary layer was subject to an initial zero pressure gradient (ZPG) development, followed by a favourable pressure gradient (FPG), a ZPG recovery and an adverse pressure gradient (APG). In the non-ZPG regions, the acceleration parameter, $K$, was held constant. Two component velocity profiles were acquired at multiple streamwise locations to document the response to the changing pressure gradient of the mean velocity, Reynolds stresses and triple products of the fluctuating velocity components. Velocity field measurements were made to document the turbulence structure using two point correlations. In general, turbulence was suppressed by the FPG while structures became larger in streamwise and spanwise extent relative to the boundary layer thickness, particularly near the wall. In the recovery region, the return to canonical ZPG conditions was rapid. Changes in the structure in the APG region were less pronounced. The changes in the turbulence statistics and correlations relative to the ZPG baseline were quantified and presented as functions of streamwise location. When the streamwise location is scaled using the acceleration parameter, the results from all cases (including all statistical moments, and the size and inclination angles of turbulence structures), collapse in each region of the flow, showing a common non-equilibrium response to changes in the pressure gradient. These are new results which apply to the present flows and those with similar types of pressure gradients, but are not necessarily applicable to all flows with arbitrary pressure gradients.

JFM classification

Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , A2
Copyright
© The Author(s), 2020. 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., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure – homogeneous shear-flow. J. Fluid Mech. 190, 531–559.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, 345–364.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, 667–692.CrossRefGoogle Scholar
Bradshaw, P. 1967 Inactive motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241–258.CrossRefGoogle Scholar
Castillo, L. & George, W. K. 2001 Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA J. 39, 41–47.CrossRefGoogle Scholar
Chien, K.-Y. 1982 Prediction of channel and boundary-layer flows with a low-Reynolds-number turbulence model. AIAA J. 20, 32–38.CrossRefGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.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 Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, Virginia, vol. 3, pp. 1025–1030. TSFP.Google Scholar
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.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245–311.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, 53–64.CrossRefGoogle Scholar
Harun, Z., Monty, J. P., Mathis, R. & marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477–498.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, 21–54.CrossRefGoogle Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.CrossRefGoogle Scholar
Jones, M. B.1998 Evolution and structure of sink flow turbulent boundary layers. PhD thesis, University of Melbourne.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.CrossRefGoogle Scholar
Kays, W. M. & Crawford, M. E. 1980 Convective Heat and Mass Transfer, 2nd edn. McGraw-Hill.Google Scholar
Kitsios, V., Sekimoto, A., Atkinson, C., Sillero, J. A., Borrell, G., Gungor, A. G., Jiménez, J. & Soria, J. 2017 Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation. J. Fluid Mech. 829, 392–419.CrossRefGoogle Scholar
Klewicki, J. C. 2010 Reynolds number dependence, scaling, and dynamics of turbulent boundary layers. Trans. ASME J. Fluids Engng 132, 094001.Google Scholar
Lee, J. H. 2017 Large-scale motions in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 810, 323–361.CrossRefGoogle Scholar
Lee, J.-H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101–131.CrossRefGoogle Scholar
Mellor, G. L. & Gibson, D. M. 1966 Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225–253.CrossRefGoogle Scholar
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32, 575–585.CrossRefGoogle Scholar
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755–770.CrossRefGoogle Scholar
Reynolds, W. C. 1976 Computation of turbulent flows. Annu. Rev. Fluid Mech. 8, 183–208.CrossRefGoogle Scholar
Samie, M., Marusic, I., Hutchins, N., Fu, M. K., Fan, Y., Hultmark, M. & Smites, A. J. 2018 Fully resolved measurements of turbulent boundary layer flows up to Re 𝜏 = 20 000. J. Fluid Mech. 851, 391–415.CrossRefGoogle Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25, 105105.CrossRefGoogle Scholar
Skåre, P. R. & Krogstad, P.-å. 1994 A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 532, 319–348.CrossRefGoogle Scholar
Skote, M., Henningson, D. S. & Henkes, R. A. W. M. 1998 Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients. Flow Turbul. Combust. 60, 47–85.CrossRefGoogle Scholar
Spalart, P. R. 1986 Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307–328.CrossRefGoogle Scholar
Vincenti, P., Klewicki, J., Morrill-Winter, C., White, C. M. & Wosniak, M. 2013 Streamwise velocity statistics in turbulent boundary layers that spatially develop to high Reynolds numbers. Exp. Fluids 54, 1629.CrossRefGoogle Scholar
Volino, R. J. 2020 Reynolds number dependence of zero pressure gradient turbulent boundary layers. Trans. ASME J. Fluids Engng 142, 051303.Google 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. & Flack, K. A. 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263–293.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, 75–101.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303–327.CrossRefGoogle Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65–92.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 55–76.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, 353–396.CrossRefGoogle Scholar