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Direct numerical simulations of transition in a compressor cascade: the influence of free-stream turbulence

Published online by Cambridge University Press:  27 October 2010

TAMER A. ZAKI ,
JAN G. WISSINK ,
WOLFGANG RODI  and
PAUL A. DURBIN
TAMER A. ZAKI*
Affiliation:
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK
JAN G. WISSINK
Affiliation:
School of Engineering and Design, Brunel University, Uxbridge, UB8 3PH, UK
WOLFGANG RODI
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76128 Karlsruhe, Germany
PAUL A. DURBIN
Affiliation:
Aerospace Engineering, Iowa State University, Ames, IA 50011, USA
*
†Email address for correspondence: [email protected]
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Abstract

The flow through a compressor passage without and with incoming free-stream grid turbulence is simulated. At moderate Reynolds number, laminar-to-turbulence transition can take place on both sides of the aerofoil, but proceeds in distinctly different manners. The direct numerical simulations (DNS) of this flow reveal the mechanics of breakdown to turbulence on both surfaces of the blade. The pressure surface boundary layer undergoes laminar separation in the absence of free-stream disturbances. When exposed to free-stream forcing, the boundary layer remains attached due to transition to turbulence upstream of the laminar separation point. Three types of breakdowns are observed; they combine characteristics of natural and bypass transition. In particular, instability waves, which trace back to discrete modes of the base flow, can be observed, but their development is not independent of the Klebanoff distortions that are caused by free-stream turbulent forcing. At a higher turbulence intensity, the transition mechanism shifts to a purely bypass scenario. Unlike the pressure side, the suction surface boundary layer separates independent of the free-stream condition, be it laminar or a moderate free-stream turbulence of intensity Tu ~ 3%. Upstream of the separation, the amplification of the Klebanoff distortions is suppressed in the favourable pressure gradient (FPG) region. This suppression is in agreement with simulations of constant pressure gradient boundary layers. FPG is normally stabilizing with respect to bypass transition to turbulence, but is, thereby, unfavourable with respect to separation. Downstream of the FPG section, a strong adverse pressure gradient (APG) on the suction surface of the blade causes the laminar boundary layer to separate. The separation surface is modulated in the instantaneous fields of the Klebanoff distortion inside the shear layer, which consists of forward and backward jet-like perturbations. Separation is followed by breakdown to turbulence and reattachment. As the free-stream turbulence intensity is increased, Tu ~ 6.5%, transitional turbulent patches are initiated, and interact with the downstream separated flow, causing local attachment. The calming effect, or delayed re-establishment of the boundary layer separation, is observed in the wake of the turbulent events.

JFM classification

Boundary Layers: Boundary Layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 57 - 98
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Abdessemed, N., Sherwin, S. J. & Theofilis, V. 2009 Linear instability analysis of low-pressure turbine flows. J. Fluid Mech. 628, 57–83.CrossRefGoogle Scholar
Abu-Ghannam, B. J. & Shaw, R. 1980 Natural transition of boundary layers: the effects of turbulence, pressure gradient and flow history. J. Mech. Engng Sci. 22, 213–228.CrossRefGoogle Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of short laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.CrossRefGoogle Scholar
Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous flow. Phys. Fluids 4 (8), 1637–1650.CrossRefGoogle Scholar
Corke, T. C. & Gruber, S. 1996 Resonant growth of three-dimensional modes in Falkner–Skan boundary layers with adverse pressure gradients. J. Fluid Mech. 320, 211–233.CrossRefGoogle Scholar
Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14 (8), L57–L60.CrossRefGoogle Scholar
Fasel, H. F. 2002 Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave. J. Fluid Mech. 450, 1–33.CrossRefGoogle Scholar
Fransson, J., Brandt, L., Talamelli, A. & Cossu, C. 2005 Experimental study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks. Phys. Fluids 5, 1–15.Google Scholar
Goldstein, M. E. & Lee, S. S. 1992 Fully coupled resonant–triad interaction in an adverse-pressure-gradient boundary layer. J. Fluid Mech. 245, 523–551.CrossRefGoogle Scholar
Goldstein, M. E. & Sescu, S. 2008 Boundary-layer transition at high free-stream disturbance levels: beyond Klebanoff modes. J. Fluid Mech. 613, 95–124.CrossRefGoogle Scholar
Görtler, H. 1940 Über eine Dreidimensionale Instabilität Laminarer Grenzschichten an Konkaven Wänden, Nachr. Wiss. Ges. Göttingen Math. Phys. Kl. 2, 1–26.Google Scholar
Gostelow, J. P., Blunden, A. R. & Walker, G. J. 1994 Effects of free-stream turbulence and adverse pressure gradients on boundary layer transition. J. Turbomach. 116, 392–404.CrossRefGoogle Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.CrossRefGoogle 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, 461–479.CrossRefGoogle Scholar
Hilgenfeld, L. & Pfitzner, M. 2004 Unsteady boundary layer development due to wake-passing effects on a highly loaded linear compressor cascade. J. Turbomach. 126, 493–500.CrossRefGoogle Scholar
Hodson, H. P. & Howell, R. J. 2005 Bladerow interactions, transition, and high-lift aerofoils in low-pressure turbines. Annu. Rev. Fluid Mech. 37, 71–98.CrossRefGoogle Scholar
Hughes, J. D. & Walker, G. J. 2001 Natural transition phenomena on an axial flow compressor blade. J. Turbomach. 123, 392–401.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 2000 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jones, L. E., Sandberg, R. D. & Sandham, N. D. 2008 Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175–207.CrossRefGoogle Scholar
Kendall, J. M. 1991 Studies on laminar boundary layer receptivity to free stream turbulence near a leading edge. In FED (ed. Reda, et al. ), vol. 114, pp. 23–30. ASME.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–24.CrossRefGoogle Scholar
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23, 495–537.CrossRefGoogle Scholar
Leib, S. J., Wundrow, D. W. & Goldstein, M. E. 1999 Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203.CrossRefGoogle Scholar
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008 a Boundary layer transition by interaction of discrete and continuous modes. J. Fluid Mech. 604, 199–233.CrossRefGoogle Scholar
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008 b Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien–Schlichting waves. Phys. Fluids 20, 124102.CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.CrossRefGoogle Scholar
Matsubara, M. & Alfredsson, P. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.CrossRefGoogle Scholar
Morkovin, M. V. 1969 The many faces of transition. In Viscous Drag Reduction (ed. Wells, C. S.), pp. 1–31. Plenum Press.Google Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2007 Leading edge effects in bypass transition. J. Fluid Mech. 572, 471–504.CrossRefGoogle Scholar
Ovchinnikov, V., Choudhari, M. M. & Piomelli, U. 2008 Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence. J. Fluid Mech. 613, 135–169.CrossRefGoogle Scholar
Phillips, O. M. 1969 Shear-flow turbulence. Annu. Rev. Fluid Mech. 1, 245–264.CrossRefGoogle 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, 102–137.CrossRefGoogle Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291–319.CrossRefGoogle Scholar
Schreiber, H. A., Steinert, W., Sonoda, T. & Arima, T. 2004 Advanced high turning compressor airfoils for low Reynolds number condition. Part II: Experimental and numerical analysis. J. Turbomach. 126 (4), 482–492.CrossRefGoogle Scholar
Sonoda, T., Yamaguchi, Y., Arima, T., Olhofer, M., Sendhoff, B. & Schreiber, H.-A. 2004 Advanced high turning compressor airfoils for low Reynolds number condition. Part I. Design and optimization. J. Turbomach. 126 (3), 350–359.CrossRefGoogle Scholar
Spalart, P. R. & Strelets, M. K. H. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.CrossRefGoogle 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 freestream turbulence. Part 1. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193–218.CrossRefGoogle Scholar
Wissink, J. G. 2003 DNS of separating, low Reynolds number flow in a turbine cascade with incoming wakes. Intl J. Heat Fluid Flow 24 (4), 626–635.CrossRefGoogle Scholar
Wissink, J. G. & Rodi, W. 2006 Direct numerical simulation of flow and heat transfer in a turbine cascade with incoming wakes. J. Fluid Mech. 569, 209–347.CrossRefGoogle Scholar
Wissink, J. G., Rodi, W. & Hodson, H. P. 2006 The influence of disturbances carried by periodically incoming wakes on the separating flow around a turbine blade. Intl J. Heat Fluid Flow 27, 721–729.CrossRefGoogle Scholar
Wu, X. 2001 Receptivity of boundary layers with distributed roughness to vortical and acoustic disturbances: a second-order asymptotic theory and comparison with experiments. J. Fluid Mech. 431, 91–133.CrossRefGoogle Scholar
Wu, X. & Choudhari, M. 2003 Linear and nonlinear instabilities of a Blasius boundary layer perturbed by streamwise vortices. Part 2. Intermittent instability induced by long-wavelength Klebanoff modes. J. Fluid Mech. 483, 249–286.CrossRefGoogle Scholar
Wu, X. & Durbin, P. A. 2001 Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage. J. Fluid Mech. 446, 199–228.CrossRefGoogle Scholar
Wu, X., Jacobs, R. G., Durbin, P. A. & Hunt, J. 1999 Simulation of boundary layer transition induced by periodically passing wakes. J. Fluid Mech. 398, 109–153.CrossRefGoogle Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111.CrossRefGoogle Scholar
Zaki, T. A. & Durbin, P. A. 2006 Continuous mode transition and the effects of pressure gradient. J. Fluid Mech. 563, 357–388.CrossRefGoogle 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, 111–147.CrossRefGoogle Scholar
Zaki, T. A., Wissink, J. G., Durbin, P. A. & Rodi, W. 2009 Direct computations of boundary layers distorted by migrating wakes in a linear compressor cascade. Flow Turbulence Combust. 83, 307–322.CrossRefGoogle Scholar