Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-01T02:31:44.979Z Has data issue: false hasContentIssue false

The effect of a low-viscosity near-wall film on bypass transition in boundary layers

Published online by Cambridge University Press:  05 May 2015

Seo Yoon Jung
Affiliation:
Department of Mechanical Engineering, Imperial College, London SW7 2AZ, UK
Tamer A. Zaki
Affiliation:
Department of Mechanical Engineering, Imperial College, London SW7 2AZ, UK

Abstract

Bypass transition in a two-fluid boundary layer is examined using direct numerical simulations (DNSs). A less-viscous wall film is considered and the impact on transition location is evaluated at two different viscosity ratios and free-stream turbulence intensities. The less-viscous wall film absorbs the mean shear from the outer stream, weakens the lift-up mechanism, and alters the disturbance field inside the boundary layer. These effects all favour a delay in the onset of bypass transition. However, the viscosity and mean-shear discontinuities across the two-fluid interface introduce a new mechanism for the generation of wall-normal vorticity in the boundary layer, and can therefore promote transition to turbulence. Conditionally averaged statistics and streak tracking techniques are adopted in order to examine the impact of the wall film on the bypass transition process. It is shown that the weaker amplification of the streaks in the outer fluid can delay breakdown to turbulence, despite the additional disturbance generation at the two-fluid interface. The efficacy of the wall film in delaying transition is demonstrated at moderate level of free-stream turbulence intensity, but is reduced as the turbulence intensity is increased.

Type
Papers
Copyright
© 2015 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

Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 2960.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167198.CrossRefGoogle Scholar
Brodkey, R. S., Wallace, J. M. & Eckelmann, H. 1974 Some properties of truncated turbulence signals in bounded shear flows. J. Fluid Mech. 63, 209224.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 16371650.Google Scholar
Charru, F. & Hinch, E. J. 2000 Phase diagram of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability. J. Fluid Mech. 414, 195223.Google Scholar
Cheung, L. C. & Zaki, T. A. 2010 Linear and nonlinear instability waves in spatially developing two-phase mixing layers. Phys. Fluids 22, 052103.Google Scholar
Cheung, L. C. & Zaki, T. A. 2011 A nonlinear PSE method for two-fluid shear flows with complex interfacial topology. J. Comput. Phys. 230, 67566777.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75110.CrossRefGoogle Scholar
Desjardins, O., Moureau, V. & Pitsch, H. 2008 An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J. Comput. Phys. 227, 83958416.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73L76.Google Scholar
Gueyffier, D., Li, J., Nadim, A., Scardovelli, R. & Zaleski, S. 1999 Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys. 152, 423456.Google Scholar
Hack, M. J. P. & Zaki, T. A. 2014 Streak instabilities in boundary layers beneath free-stream turbulence. J. Fluid Mech. 741, 280315.Google Scholar
Hedley, T. B. & Keffer, J. F. 1974 Turbulent/non-turbulent decisions in an intermittent flow. J. Fluid Mech. 64, 625644.Google Scholar
Hernon, D., Walsh, E. J. & McEligot, D. M. 2007 Experimental investigation into the routes to bypass transition and the shear-sheltering phenomenon. J. Fluid Mech. 591, 461479.Google Scholar
Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463465.CrossRefGoogle Scholar
Hooper, A. P. & Boyd, W. G. C. 1987 Shear-flow instability due to a wall and a viscosity discontinuity at the interface. J. Fluid Mech. 179, 201225.Google Scholar
Hunt, J. C. R. & Durbin, P. A. 1999 Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24 (6), 375404.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of Summer Program, pp. 914. Centre for Turbulence Research, Stanford University.Google Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and the continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10, 20062011.Google Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185212.Google Scholar
Kang, H. S., Choi, H. & Yoo, J. Y. 1998 On the modification of the near-wall coherent structure in a three-dimensional turbulent boundary layer on a free rotating disk. Phys. Fluids 10, 23152322.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.Google Scholar
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23, 495537.Google Scholar
Kravchenko, G., Choi, H. & Moin, P. 1993 On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5, 33073309.Google Scholar
Kurian, T. & Fransson, J. H. M. 2009 Grid-generated turbulence revisited. Fluid Dyn. Res. 41, 021403.CrossRefGoogle Scholar
Le, A. T., Coleman, G. N. & Kim, J. 2000 Near-wall turbulence structures in three-dimensional boundary layers. Intl J. Heat Fluid Flow 21, 480488.Google Scholar
Lee, J., Jung, S. Y., Sung, H. J. & Zaki, T. A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196225.Google Scholar
Littell, H. S. & Eaton, J. K. 1994 Turbulence characteristics of the boundary layer on a rotating disk. J. Fluid Mech. 266, 175207.Google Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289309.CrossRefGoogle Scholar
Malik, S. V. & Hooper, A. P. 2007 Three-dimensional disturbances in channel flows. Phys. Fluids 19, 052102.CrossRefGoogle Scholar
Mandal, A. C., Venkatakrishnan, L. & Dey, J. 2010 A study on boundary-layer transition induced by free-stream turbulence. J. Fluid Mech. 660, 114146.Google Scholar
Matsubara, M. & Alfredsson, P. H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.Google Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471504.Google Scholar
Nelson, J. J., Alving, A. E. & Joseph, D. D. 1995 Boundary layer flow of air over water on a flat plate. J. Fluid Mech. 284, 159169.Google Scholar
Nolan, K. P. & Walsh, E. J. 2012 Particle image velocimetry measurements of a transitional boundary layer under free stream turbulence. J. Fluid Mech. 702, 215238.Google Scholar
Nolan, K. P. & Zaki, T. A. 2013 Conditional sampling of transitional boundary layers in pressure gradients. J. Fluid Mech. 728, 306339.Google Scholar
Nourgaliev, R. R. & Theofanous, T. G. 2007 High-fidelity interface tracking in compressible flows: unlimited anchored adaptive level set. J. Comput. Phys. 224, 836866.Google Scholar
Ó Náraigh, L., Spelt, P. D. M., Matar, O. K. & Zaki, T. A. 2011a Interfacial instability in turbulent flow over a liquid film in a channel. Intl J. Multiphase Flow 37, 812830.CrossRefGoogle Scholar
Ó Náraigh, L., Spelt, P. D. M. & Zaki, T. A. 2011b Turbulent flow over a liquid layer revisited: multi-equation turbulence modelling. J. Fluid Mech. 683, 357394.Google Scholar
Osher, S. & Sethian, J. A. 1988 Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79, 1249.CrossRefGoogle Scholar
Otsu, N. 1979 A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9 (1), 6266.Google Scholar
Peng, D., Merriman, B., Osher, S., Zhao, H. & Kang, M. 1999 A PDE-based fast local level set method. J. Comput. Phys. 155, 410438.CrossRefGoogle Scholar
Renardy, Y. 1987 The thin-layer effect and interfacial stability in a two-layer Couette flow with similar liquids. Phys. Fluids 30, 16271637.CrossRefGoogle Scholar
Roach, P. E. & Brierley, D. H. 1990 The influence of a turbulent freestream on zero pressure gradient transitional boundary layer development, part I: test cases T3A and T3b. In ERCOFTAC Workshop: Numerical Simulation of Unsteady Flows and Transition to Turbulence, Lausanne, Switzerland, pp. 319347. Cambridge University Press.Google Scholar
Rosenfeld, M., Kwak, D. & Vinokur, M. 1991 A fractional step solution method for the unsteady incompressible Navier–Stokes equations in generalized coordinate systems. J. Comput. Phys. 94, 102137.Google Scholar
Saha, S., Jung, S. Y. & Zaki, T. A.2010 Stabilization of wall shear beneath vortical disturbances using a thin film. In The 7th International Conference on Multiphase Flow, Tampa, USA.Google Scholar
Schlatter, P., Brandt, L., de Lange, H. C. & Henningson, D. S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20, 101505.Google Scholar
Sethian, J. A. & Smereka, P. 2003 Level set methods for fluid interfaces. Annu. Rev. Fluid Mech. 35, 341372.CrossRefGoogle Scholar
Shu, C.-W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439471.Google Scholar
Vaughan, N. J. & Zaki, T. A. 2011 Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks. J. Fluid Mech. 681, 116153.Google Scholar
van der Vorst, H. A. 1992 Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631644.Google Scholar
van der Vorst, H. A. 2003 Iterative Krylov Methods for Large Linear Systems, 1st edn. Cambridge University Press.Google Scholar
Westin, K. J. A., Boiko, A. V., Klingmann, B. G. B., Kozlov, V. V. & Alfredsson, P. H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 1. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193218.Google Scholar
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 6592.Google Scholar
Yang, J. & Stern, F. 2009 Sharp interface immersed-boundary/level-set method for wave-body interactions. J. Comput. Phys. 228, 65906616.Google Scholar
Yecko, P. & Zaleski, S. 2005 Transient growth in two-phase mixing layers. J. Fluid Mech. 528, 4352.Google Scholar
Yih, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337352.Google Scholar
Zaki, T. A. 2013 From Streaks to spots and on to turbulence: exploring the dynamics of boundary layer transition. Flow Turbul. Combust. 91, 451473.Google Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85111.Google Scholar
Zaki, T. A. & Durbin, P. A. 2006 Continuous mode transition and the effects of pressure gradient. J. Fluid Mech. 563, 357388.Google Scholar
Zaki, T. A. & Saha, S. 2009 On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers. J. Fluid Mech. 626, 111147.Google Scholar
Zalesak, S. T. 1979 Fully multi-dimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31, 335362.Google Scholar