Skip to main content Accessibility help
×
×
Home

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

  • TAMER A. ZAKI (a1), JAN G. WISSINK (a2), WOLFGANG RODI (a3) and PAUL A. DURBIN (a4)
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.

Copyright
Corresponding author
Email address for correspondence: t.zaki@imperial.ac.uk
References
Hide All
Abdessemed, N., Sherwin, S. J. & Theofilis, V. 2009 Linear instability analysis of low-pressure turbine flows. J. Fluid Mech. 628, 5783.
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, 213228.
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of short laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 128.
Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134150.
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167198.
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous flow. Phys. Fluids 4 (8), 16371650.
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, 211233.
Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14 (8), L57L60.
Fasel, H. F. 2002 Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave. J. Fluid Mech. 450, 133.
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, 115.
Goldstein, M. E. & Lee, S. S. 1992 Fully coupled resonant–triad interaction in an adverse-pressure-gradient boundary layer. J. Fluid Mech. 245, 523551.
Goldstein, M. E. & Sescu, S. 2008 Boundary-layer transition at high free-stream disturbance levels: beyond Klebanoff modes. J. Fluid Mech. 613, 95124.
Görtler, H. 1940 Über eine Dreidimensionale Instabilität Laminarer Grenzschichten an Konkaven Wänden, Nachr. Wiss. Ges. Göttingen Math. Phys. Kl. 2, 126.
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, 392404.
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487526.
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.
Hilgenfeld, L. & Pfitzner, M. 2004 Unsteady boundary layer development due to wake-passing effects on a highly loaded linear compressor cascade. J. Turbomach. 126, 493500.
Hodson, H. P. & Howell, R. J. 2005 Bladerow interactions, transition, and high-lift aerofoils in low-pressure turbines. Annu. Rev. Fluid Mech. 37, 7198.
Hughes, J. D. & Walker, G. J. 2001 Natural transition phenomena on an axial flow compressor blade. J. Turbomach. 123, 392401.
Jacobs, R. G. & Durbin, P. A. 2000 Simulations of bypass transition. J. Fluid Mech. 428, 185212.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
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, 175207.
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. 2330. ASME.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 124.
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23, 495537.
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, 169203.
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008 a Boundary layer transition by interaction of discrete and continuous modes. J. Fluid Mech. 604, 199233.
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.
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289309.
Matsubara, M. & Alfredsson, P. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.
Morkovin, M. V. 1969 The many faces of transition. In Viscous Drag Reduction (ed. Wells, C. S.), pp. 131. Plenum Press.
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2007 Leading edge effects in bypass transition. J. Fluid Mech. 572, 471504.
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, 135169.
Phillips, O. M. 1969 Shear-flow turbulence. Annu. Rev. Fluid Mech. 1, 245264.
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.
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379409.
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291319.
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), 482492.
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), 350359.
Spalart, P. R. & Strelets, M. K. H. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329349.
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, 193218.
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), 626635.
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, 209347.
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, 721729.
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, 91133.
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, 249286.
Wu, X. & Durbin, P. A. 2001 Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage. J. Fluid Mech. 446, 199228.
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, 109153.
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85111.
Zaki, T. A. & Durbin, P. A. 2006 Continuous mode transition and the effects of pressure gradient. J. Fluid Mech. 563, 357388.
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.
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, 307322.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed