Global mode-based control of laminar and turbulent high-speed jets

Mahesh Natarajan; Jonathan B. Freund; Daniel J. Bodony

doi:10.1016/j.crme.2018.07.005

Global mode-based control of laminar and turbulent high-speed jets

Mahesh Natarajan ¹; Jonathan B. Freund ²; Daniel J. Bodony ¹

¹ Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
² Department of Mechanical Science & Engineering and Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA

Comptes Rendus. Mécanique, Volume 346 (2018) no. 10, pp. 978-996.

Abstract

The emitted noise from round jets is reduced using linear feedback controllers designed using structural sensitivity analysis. Linear global modes inform the selection and placement of the controller, and Navier–Stokes simulations are used to demonstrate effectiveness in a Mach-1.5 cold axisymmetric jet and in a Mach-0.9 cold turbulent jet. In both jets, each fitted with a cylindrical nozzle, the control reduces the radiated noise and modifies the baseflow in a way that enhances the relative amplitudes of low-frequency $St \approx 0.05$ global modes that do not have significant support in the acoustic field.

Received: 2017-06-09
Accepted: 2018-05-16
Published online: 2018-08-14

DOI: 10.1016/j.crme.2018.07.005

Mots clés : Active flow control, Global modes, Jet noise

Author's affiliations:

Mahesh Natarajan ¹; Jonathan B. Freund ²; Daniel J. Bodony ¹

¹ Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
² Department of Mechanical Science & Engineering and Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA

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Mahesh Natarajan; Jonathan B. Freund; Daniel J. Bodony. Global mode-based control of laminar and turbulent high-speed jets. Comptes Rendus. Mécanique, Volume 346 (2018) no. 10, pp. 978-996. doi : 10.1016/j.crme.2018.07.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.07.005/

References
Cited by

[1] P. Jordan; T. Colonius Wave packets and turbulent jet noise, Annu. Rev. Fluid Mech., Volume 45 (2013), pp. 173-195

[2] C.K.W. Tam; P.J. Morris The radiation of sound by the instability waves of a compressible plane turbulent shear layer, J. Fluid Mech., Volume 98 (1980), pp. 349-381

[3] C.K.W. Tam; D.E. Burton Sound generated by instability waves of supersonic flows. Part 1. Two-dimensional mixing layers, J. Fluid Mech., Volume 138 (1984), pp. 249-271

[4] C.K.W. Tam; D.E. Burton Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets, J. Fluid Mech., Volume 138 (1984), pp. 273-295

[5] A. Michalke Survey on jet instability theory, Prog. Aerosp. Sci., Volume 21 (1984), pp. 159-199

[6] C.K. Tam; F.Q. Hu On the three families of instability waves of high-speed jets, J. Fluid Mech., Volume 201 (1989), pp. 447-483

[7] M.E. Goldstein; S. Leib The role of instability waves in predicting jet noise, J. Fluid Mech., Volume 525 (2005), pp. 37-72

[8] A. Samanta; J.B. Freund Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit, J. Fluid Mech., Volume 612 (2008), pp. 407-438

[9] A. Samanta; J.B. Freund A model supersonic buried-nozzle jet: instability and acoustic wave scattering and the far-field sound, J. Fluid Mech., Volume 778 (2015)

[10] T. Suzuki; T. Colonius Instability waves in a subsonic round jet detected using a near-field phased microphone array, J. Fluid Mech., Volume 565 (2006), pp. 197-226

[11] K. Gudmundsson; T. Colonius Parabolized Stability Equation Models for Turbulent Jets and Their Radiated Sound, 2009 (AIAA Paper 2009-3380)

[12] A. Sinha; D. Rodríguez; G.A. Brès; T. Colonius Wavepacket models for supersonic jet noise, J. Fluid Mech., Volume 742 (2014), pp. 71-95

[13] P. Balakumar Prediction of Supersonic Jet Noise, 1998 (AIAA Paper 98-1057)

[14] C. Yen; N. Messersmith The Use of Compressible Parabolized Stability Equations for Prediction of Jet Instabilities and Noise, 1999 (AIAA Paper 99-1859)

[15] L.C. Cheung; D.J. Bodony; S.K. Lele Noise Radiation Predictions from Jet Instability Waves Using a Hybrid Nonlinear PSE-Acoustic Analogy, 2007 (AIAA Paper 2007-3638, Presented at the 13th AIAA/CEAS Aeroacoustics Conference, Rome, Italy)

[16] V. Theofilis Global linear instability, Annu. Rev. Fluid Mech., Volume 43 (2011), pp. 319-352

[17] V. Theofilis; T. Colonius Special issue on global flow instability and control, Theor. Comput. Fluid Dyn., Volume 25 (2011), pp. 1-6

[18] J.W. Nichols; S.K. Lele Global modes and transient response of a cold supersonic jet, J. Fluid Mech., Volume 669 (2011), pp. 225-241

[19] X. Garnaud; L. Lesshafft; P. Schmid; P. Huerre Modal and transient dynamics of jet flows, Phys. Fluids (1994–present), Volume 25 (2013)

[20] W. Coenen; L. Lesshafft; X. Garnaud; A. Sevilla Global instability of low-density jets, J. Fluid Mech., Volume 820 (2017), pp. 187-207

[21] O. Semeraro; L. Lesshafft; V. Jaunet; P. Jordan Modeling of coherent structures in a turbulent jet as global linear instability wavepackets: theory and experiment, Int. J. Heat Fluid Flow, Volume 62 (2016), pp. 24-32 (Part A)

[22] J. Chomaz Global instabilities in spatially developing flows: non-normality and nonlinearity, Annu. Rev. Fluid Mech., Volume 37 (2005), pp. 357-392

[23] F. Giannetti; P. Luchini Structural sensitivity of the first instability of the cylinder wake, J. Fluid Mech., Volume 581 (2007), pp. 167-197

[24] D.J. Bodony; M. Natarajan Controller selection and placement in compressible turbulent flows, Proceedings of the Summer Program, Center for Turbulence Research, 2012, pp. 35-42

[25] M. Natarajan; J.B. Freund; D.J. Bodony Actuator selection and placement for localized feedback flow control, J. Fluid Mech., Volume 809 (2016), pp. 775-792

[26] A.V. Cavalieri; D. Rodríguez; P. Jordan; T. Colonius; Y. Gervais Wavepackets in the velocity field of turbulent jets, J. Fluid Mech., Volume 730 (2013), pp. 559-592

[27] M.R. Visbal; D.V. Gaitonde On the use of higher-order finite-difference schemes on curvilinear and deforming meshes, J. Comput. Phys., Volume 181 (2002), pp. 155-185

[28] J. Freund Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound, AIAA J., Volume 35 (1997), pp. 740-742

[29] D.J. Bodony Analysis of sponge zones for computational fluid mechanics, J. Comput. Phys., Volume 212 (2006), pp. 681-702

[30] H.R. Lewis; P.M. Bellan Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates, J. Math. Phys., Volume 31 (1990), pp. 2592-2596

[31] M. Natarajan Actuator Selection and Placement for Linear Feedback Control of Compressible Flows, University of Illinois at Urbana–Champaign, IL, USA, 2017 (Ph.D. thesis)

[32] B. Strand Summation by parts for finite difference approximations for d/dx, J. Comput. Phys., Volume 110 (1994), pp. 47-67

[33] P. Moin; K. Squires; W. Cabot; S. Lee A dynamic subgrid-scale model for compressible turbulence and scalar transport, Phys. Fluids A, Fluid Dyn. (1989–1993), Volume 3 (1991), pp. 2746-2757

[34] D.K. Lilly A proposed modification of the Germano subgrid-scale closure method, Phys. Fluids A, Fluid Dyn., Volume 4 (1992), pp. 633-635

[35] E.T. Spyropoulos; G.A. Blaisdell Evaluation of the dynamic model for simulations of compressible decaying isotropic turbulence, AIAA J., Volume 34 (1996), pp. 990-998

[36] S.K. Lele Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., Volume 103 (1992), pp. 16-42

[37] S. Kawai; S.K. Shankar; S.K. Lele Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows, J. Comput. Phys., Volume 229 (2010), pp. 1739-1762

[38] M. Svärd; M. Carpenter; J. Nordström A stable high-order finite difference scheme for the compressible Navier–Stokes equations, far-field boundary conditions, J. Comput. Phys., Volume 225 (2007), pp. 1020-1038

[39] M. Svärd; J. Nordström A stable high-order finite difference scheme for the compressible Navier–Stokes equations: no-slip wall boundary conditions, J. Comput. Phys., Volume 227 (2008), pp. 4805-4824

[40] K. Mattsson; M. Svärd; M. Shoeybi Stable and accurate schemes for the compressible Navier–Stokes equations, J. Comput. Phys., Volume 227 (2008), pp. 2293-2316

[41] D. Bodony Accuracy of the simultaneous-approximation-term boundary condition for time-dependent problems, J. Sci. Comput., Volume 43 (2010), pp. 118-133

[42] G.J. Chandler; M.P. Juniper; J.W. Nichols; P.J. Schmid Adjoint algorithms for the Navier–Stokes equations in the low Mach number limit, J. Comput. Phys., Volume 231 (2012), pp. 1900-1916

[43] S. Balay; J. Brown; K. Buschelman; W.D. Gropp; D. Kaushik; M.G. Knepley; L.C. McInnes; B.F. Smith; H. Zhang PETSc Web page, 2012 http://www.mcs.anl.gov/petsc

[44] S. Balay; J. Brown; K. Buschelman; V. Eijkhout; W.D. Gropp; D. Kaushik; M.G. Knepley; L.C. McInnes; B.F. Smith; H. Zhang PETSc Users Manual, Argonne National Laboratory, 2012 (Technical Report ANL-95/11 – Revision 3.3)

[45] S. Balay; W.D. Gropp; L.C. McInnes; B.F. Smith Efficient management of parallelism in object oriented numerical software libraries (E. Arge; A.M. Bruaset; H.P. Langtangen, eds.), Modern Software Tools in Scientific Computing, Birkhäuser Press, 1997, pp. 163-202

[46] V. Hernandez; J.E. Roman; V. Vidal SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems, ACM Trans. Math. Softw., Volume 31 (2005), pp. 351-362

[47] P. Amestoy; I. Duff; J. L'Excellent; J. Koster Mumps: a general purpose distributed memory sparse solver, Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, 2001, pp. 121-130

[48] E. Åkervik; L. Brandt; D. Henningson; J. Hœpffner; O. Marxen; P. Schlatter Steady solutions of the Navier–Stokes equations by selective frequency damping, Phys. Fluids, Volume 18 (2006)

[49] D. Hammond; L. Redekopp Global dynamics of symmetric and asymmetric wakes, J. Fluid Mech., Volume 331 (1997), pp. 231-260

[50] D. Sipp; A. Lebedev Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows, J. Fluid Mech., Volume 593 (2007), pp. 333-358

[51] P.J. Schmid; D.S. Henningson Stability and Transition in Shear Flows, vol. 142, Springer Science & Business Media, 2012

[52] J. Nichols; S. Lele; P. Moin Global mode decomposition of supersonic jet noise, Annual Research Briefs, Center for Turbulence Research, Stanford, CA, 2009, pp. 3-15

[53] S.-P. Han A globally convergent method for nonlinear programming, J. Optim. Theory Appl., Volume 22 (1977), pp. 297-309

[54] M. Wei; J.B. Freund A noise-controlled free shear flow, J. Fluid Mech., Volume 546 (2006), pp. 123-152

[55] J. Kim; D.J. Bodony; J.B. Freund Adjoint-based control of loud events in a turbulent jet, J. Fluid Mech., Volume 741 (2014), pp. 28-59

[56] D.J. Bodony; S.K. Lele On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets, Phys. Fluids (1994–present), Volume 17 (2005)

[57] J. Nichols; M. Jovanovic Input–output analysis of high-speed jet noise, Proceedings of the Summer Program, Center for Turbulence Research, 2014, p. 251

[58] O. Schmidt; A. Towne; T. Colonius; P. Jordan; V. Jaunet; A.V. Cavalieri; G.A. Brès Super- and multi-directive acoustic radiation by linear global modes of a turbulent jet, 22nd AIAA/CEAS Aeroacoustics Conference, 2016, p. 2808

[59] D.J. Bodony; S.K. Lele Current status of jet noise predictions using large-eddy simulation, AIAA J., Volume 46 (2008), pp. 364-380

[60] M. Samimy; J.-H. Kim; J. Kastner; I. Adamovich; Y. Utkin Active control of a Mach 0.9 jet for noise mitigation using plasma actuators, AIAA J., Volume 45 (2007), pp. 890-901

Cited by Sources:

^☆ Financial support from the United States Office of Naval Research (Drs. Brenda Henderson, Joseph Doychak and Knox Millsaps, technical monitors) is gratefully acknowledged (grant no. N00014-13-1-0545). This material is also based in part upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.

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