Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T12:55:03.978Z Has data issue: false hasContentIssue false
  • English
  • Français

Investigation of passive control of the wake past a thick plate by stability and sensitivity analysis of experimental data

Published online by Cambridge University Press:  12 September 2017

S. Camarri Open the ORCID record for S. Camarri [Opens in a new window] ,
R. Trip  and
J. H. M. Fransson
S. Camarri*
Affiliation:
Dipartimento di Ingegneria Civile ed Industriale, Università di Pisa, 56126 Pisa, Italy
R. Trip
Affiliation:
Linné Flow Centre, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden
J. H. M. Fransson
Affiliation:
Linné Flow Centre, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we propose a strategy, entirely relying on available experimental data, to estimate the effect of a small control rod on the frequency of vortex shedding in the wake past a thick perforated plate. The considered values of the flow Reynolds number range between $Re\simeq 6.6\times 10^{3}$ and $Re=5.3\times 10^{4}$. By means of particle image velocimetry, an experimental database consisting of instantaneous flow fields is collected for different values of suction through the body surface. The strategy proposed here is based on classical stability and sensitivity analysis applied to mean flow fields and on the formulation of an original ad hoc model for the mean flow. The mean flow model is obtained by calibrating the closure of the Reynolds averaged Navier–Stokes equations on the basis of the available experimental data through an optimisation algorithm. As a result, it is shown that the predicted control map agrees reasonably well with the equivalent one measured experimentally. Moreover, it is shown that even when turbulence effects are neglected, the stability analysis applied to the mean flow fields provides a reasonable estimation of the vortex shedding frequency, confirming what is known in the literature and extending it up to $Re=5.3\times 10^{4}$. It is also shown that, when turbulence is taken into account in the stability analysis using the same closure that is calibrated for the corresponding mean flow model, the prediction of the vortex shedding frequency is systematically improved.

JFM classification

Instability: Instability Flow Control: Instability control Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 753 - 778
Check for updates
Copyright
© 2017 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

Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Eur. Lett. 75 (5), 750–756.Google Scholar
Camarri, S. 2015 Flow control design inspired by linear stability analysis. Acta Mechanica 226 (4), 979–1010.Google Scholar
Camarri, S., Fallenius, B. E. G. & Fransson, J. H. M. 2013 Stability analysis of experimental flow fields behind a porous cylinder for the investigation of the large-scale wake vortices. J. Fluid Mech. 715, 499–536.CrossRefGoogle Scholar
Emerson, B., Lieuwen, T. & Juniper, M. P. 2008 Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes. J. Fluid Mech. 788, 549–575.Google Scholar
ESDU1986 Mean forces, pressures and flow field velocities for circular cylindrical structures: single cylinder with two-dimensional flow. ESDU Tech. Rep. 80025.Google Scholar
Fallenius, B. E. G., Trip, R. & Fransson, J. H. M.2014 A new test section for wind tunnel studies on wake instability and its control. Tech. Rep. Royal Inst. of Technology, Dep. of Mechanics, TRITA-MEK 2014:08.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.Google Scholar
Hammond, D. A. & Redekopp, L. G. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231–260.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Khor, M., Sheridan, J., Thompson, M. C. & Hourigan, K. 2008 Global frequency selection in the observed time-mean wakes of circular cylinders. J. Fluid Mech. 601, 425–441.CrossRefGoogle Scholar
Leontini, J. S., Thompson, M. C. & Hourigan, K. 2010 A numerical study of global frequency selection in the time-mean wake of a circular cylinder. J. Fluid Mech. 645, 435–446.Google Scholar
Luchini, P., Giannetti, F. & Pralits, J. 2009 Structural sensitivity of the finite-amplitude vortex shedding behind a circular cylinder. In IUTAM Symp. on Unsteady Separated Flows and their Control (ed. Braza, M. & Hourigan, K.), IUTAM Bookseries, vol. 14, pp. 151–160. Springer.CrossRefGoogle Scholar
Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow. J. Fluid Mech. 1 (05), 521–539.Google Scholar
Mantič-Lugo, V., Arratia, C. & Gallaire, F. 2014 Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake. Phys. Rev. Lett. 113, 084501.Google Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.Google Scholar
Meliga, P., Pujals, G. & Serre, É. 2012 Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability. Phys. Fluids 24, 061701.CrossRefGoogle Scholar
Mittal, S. 2008 Global linear stability analysis of time-averaged flows. Intl J. Numer. Meth. Fluids 58 (1), 111–118.CrossRefGoogle Scholar
Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.CrossRefGoogle Scholar
Noack, B. R., Afanasiev, K., Morzynski, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.Google Scholar
Parezanović, V. & Cadot, O. 2009 The impact of a local perturbation on global properties of a turbulent wake. Phys. Fluids 21 (7), 071701.CrossRefGoogle Scholar
Parezanović, V. & Cadot, O. 2012 Experimental sensitivity analysis of the global properties of a two-dimensional turbulent wake. J. Fluid Mech. 1 (1), 1–35.Google Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.CrossRefGoogle Scholar
Reau, N. & Tumin, A. 2002 On harmonic perturbations in a turbulent mixing layer. Eur. J. Mech. (B/Fluids) 21 (2), 143–155.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (02), 263–288.Google Scholar
Rukes, L., Paschereit, C. O. & Oberleithner, K. 2016 Turbulence models for linear hydrodynamic stability analysis of strongly swirling jets. Eur. J. Mech. (B/Fluids) 59, 205–218.Google Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.CrossRefGoogle Scholar
Spalart, P. R. & Allmaras, S. R. 1994 One-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1, 5–21.Google Scholar
Tammisola, O. & Juniper, M. P. 2016 Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes. J. Fluid Mech. 792, 620–657.CrossRefGoogle Scholar
Trip, R. & Fransson, J. H. M. 2014 Boundary layer modification by means of wall suction and the effect on the wake behind a rectangular forebody. Phys. Fluids 26 (12), 125105.CrossRefGoogle Scholar
Trip, R. & Fransson, J. H. M.2016 On the effect of boundary layer modification on the near-wake topology of a rectangular forebody. PhD thesis, Royal Institute of Technology, Stockholm, Paper no. 6.Google Scholar
Turton, S. E., Tuckerman, L. S. & Barkley, D. 2015 Prediction of frequencies in thermosolutal convection from mean flows. Phys. Rev. E 91, 043009.Google ScholarPubMed
Viola, F., Iungo, G. V., Camarri, S., Porté-Agel, F. & Gallaire, F. 2014 Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data. J. Fluid Mech. 750, R1.Google Scholar
Wang, D., Kirby, R. M. & Johnson, C. R. 2011 Finite-element-based discretization and regularization strategies for 3D inverse electrocardiography. IEEE Trans Biomed Engng 58 (6), 1827–1838.Google Scholar