Skip to main content Accessibility help
×
Home
Hostname: page-component-684bc48f8b-ttgcf Total loading time: 28.617 Render date: 2021-04-14T06:29:14.662Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Linear instability analysis of low-pressure turbine flows

Published online by Cambridge University Press:  01 June 2009

N. ABDESSEMED
Affiliation:
Department of Aeronautics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
S. J. SHERWIN
Affiliation:
Department of Aeronautics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
V. THEOFILIS
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, E28040 Madrid, Spain
Corresponding

Abstract

Three-dimensional linear BiGlobal instability of two-dimensional states over a periodic array of T-106/300 low-pressure turbine (LPT) blades is investigated for Reynolds numbers below 5000. The analyses are based on a high-order spectral/hp element discretization using a hybrid mesh. Steady basic states are investigated by solution of the partial-derivative eigenvalue problem, while Floquet theory is used to analyse time-periodic flow set-up past the first bifurcation. The leading mode is associated with the wake and long-wavelength perturbations, while a second short-wavelength mode can be associated with the separation bubble at the trailing edge. The leading eigenvalues and Floquet multipliers of the LPT flow have been obtained in a range of spanwise wavenumbers. For the most general configuration all secondary modes were observed to be stable in the Reynolds number regime considered. When a single LPT blade with top to bottom periodicity is considered as a base flow, the imposed periodicity forces the wakes of adjacent blades to be synchronized. This enforced synchronization can produce a linear instability due to long-wavelength disturbances. However, relaxing the periodic restrictions is shown to remove this instability. A pseudo-spectrum analysis shows that the eigenvalues can become unstable due to the non-orthogonal properties of the eigenmodes. Three-dimensional direct numerical simulations confirm all perturbations identified herein. An optimum growth analysis based on singular-value decomposition identifies perturbations with energy growths O(105).

Type
Papers
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below.

References

Abdessemed, N., Sharma, A., Sherwin, S. & Theofilis, V. 2009 Transient growth analysis of the flow past a cylinder. Phys. Fluids. 21, 044103.CrossRefGoogle Scholar
Abdessemed, N., Sherwin, S. & Theofilis, V. 2004 On unstable 2D basic states in low pressure turbine flows at moderate Reynolds numbers. Paper 2004-2541. AIAA.Google Scholar
Akervik, E., Hoepffner, J., Ehrenstein, U. & Henningson, D. S. 2007 Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. J. Fluid Mech. 579, 305314.CrossRefGoogle Scholar
Albensoeder, S., Kuhlmann, H. C. & Rath, H. J. 2001 Multiplicity of steady two-dimensional flows in two-sided lid-driven cavities. Theor. Comput. Fluid. Dyn. 14, 223241.CrossRefGoogle Scholar
Barkley, D. & Henderson, R. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215241.CrossRefGoogle Scholar
Blackburn, H. M., Barkley, D. & Sherwin, S. J. 2008 a Convective instability and transient growth in flow over a backward facing step. J. Fluid Mech. 603, 271304.CrossRefGoogle Scholar
Blackburn, H. M., Sherwin, S. J. & Barkley, D. 2008 b Convective instability and transient growth in steady and pulsatile stenotic flows. J. Fluid Mech. 607, 267277.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Physics of Fluids A 4 (8), 16371650.CrossRefGoogle Scholar
Deville, M. O., Fischer, P. F. & Mund, E. H. 2002 High-Order Methods for Incompressible Fluid Flow. Cambridge University Press.CrossRefGoogle Scholar
Drazin, P. & Reid, W. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Fasel, H., Gross, A. & Postl, D. 2003 Control of separation for low pressure turbine blades: numerical simulations. In Proceedings of the Global Flow Instability and Control Symposium II (unpublished).Google Scholar
Ghia, U., Ghia, K. & Shin, C. 1982 High-resolutions for incompressible flow using the Navier–Stokes equations and a multigrid method. J. Comput. Physics 48, 387411.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural receptivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167197.CrossRefGoogle Scholar
Grek, H. R., Kozlov, V. V. & Ramazanov, M. P. 1985 Three types of disturbances from the point source in the boundary layer. In Proceedings of the LaminarTurbulent Transition Symposium II, (ed. Kozlov, V.), pp. 267–272.Google Scholar
Karniadakis, G. E. & Sherwin, S. J. 2006 Spectralhp Element Methods for CFD, 2nd ed. Oxford University Press.Google Scholar
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23, 495537.CrossRefGoogle Scholar
Morzynski, M. & Thiele, F. 1991 Numerical stability analysis of flow about a cylinder. Z. Angew. Math. Mech. 71, T424–T428.Google Scholar
Schmid, P. & Henningson, D. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Schreiber, R. & Keller, H. 1983 Driven cavity flows by efficient numerical techniques. J. Comput. Phys. 49, 310333.CrossRefGoogle Scholar
Sharma, A., Abdessemed, N., Sherwin, S. & Theofilis, V. 2008 Optimal growth modes in flows in complex geometries. In Proceedings of the IUTAM Symposium on Fluid Control and MEMS. (ed. Morrison, J. F., Birch, D. M. & Lavoie, P.), vol. 7, pp. 339343, Springer.CrossRefGoogle Scholar
Theofilis, V. 2000 Globally-unstable flows in open cavities. Paper 2000-1965. AIAA.Google Scholar
Theofilis, V. 2003 Advances in global linear instability of nonparallel and three-dimensional flows. Prog. Aero. Sci. 39 (4), 249315.CrossRefGoogle Scholar
Theofilis, V., Barkley, D. & Sherwin, S. 2002 Spectral/hp element technology for global flow instability and control. Aero. J. 106, 619625.Google Scholar
Theofilis, V., Duck, P. W. & Owen, J. 2004 Viscous linear stability analysis of rectangular duct and cavity flows. J. Fluid Mech. 505, 249286.CrossRefGoogle Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578584.CrossRefGoogle ScholarPubMed
Tuckerman, L. & Barkley, D. 2000 Bifurcation analysis for timesteppers. In Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems (ed. Doedel, E. & Tuckerman, L.), vol. 119, pp. 543–466. Springer.Google 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, 626635.CrossRefGoogle Scholar
Wissink, J. G., Rodi, W. & Hodson, H. P. 2006 The influence of disturbances carried out by periodically incoming wakes in the separating flow around a turbine blade. Intl J Heat Fluid Flow 27, 721729.CrossRefGoogle Scholar
Wu, X. & Durbin, P. A. 2001 Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage. J. Fluid Mech. 446, 199228.Google Scholar
Wu, X., Jacobs, R., Hunt, J. & Durbin, P. A. 1999 Simulation of boundary layer transition induced by periodically passing wakes. J. Fluid Mech. 398, 109153.CrossRefGoogle Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85111.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

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 179 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 14th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Linear instability analysis of low-pressure turbine flows
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Linear instability analysis of low-pressure turbine flows
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Linear instability analysis of low-pressure turbine flows
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *