Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T18:47:17.332Z Has data issue: false hasContentIssue false
  • English
  • Français

Characteristics of acoustic and hydrodynamic waves in under-expanded supersonic impinging jets

Published online by Cambridge University Press:  04 November 2020

Shahram Karami Open the ORCID record for Shahram Karami [Opens in a new window] ,
Daniel Edgington-Mitchell Open the ORCID record for Daniel Edgington-Mitchell [Opens in a new window] ,
Vassilis Theofilis Open the ORCID record for Vassilis Theofilis [Opens in a new window]  and
Julio Soria Open the ORCID record for Julio Soria [Opens in a new window]
Shahram Karami*
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne3800, Australia
Daniel Edgington-Mitchell
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne3800, Australia
Vassilis Theofilis
Affiliation:
School of Engineering, University of Liverpool, LiverpoolL69 7ZX, UK
Julio Soria
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne3800, Australia
*
†Email address for correspondence: shahram.karami@monash.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In this study large-eddy simulations of under-expanded supersonic impinging jets are performed to develop a better understanding of the characteristics of the acoustic and hydrodynamic waves. Time history, dispersion relation and autocorrelation of the velocity and pressure fluctuations are used to investigate the propagation velocity, time and length scales of the dominant flow structures in the shear layer and near field. The mechanism by which the initial high-frequency instabilities change to low-frequency coherent structures within a short distance is investigated utilising Mach energy norm and linear spatial instability analysis with streamwise varying mean flow profiles. It is shown that the hydrodynamic and acoustic wavepackets have different propagation velocities and length scales while having a similar dominant frequency. It is also observed that the hydrodynamic wavepackets form approximately one jet diameter downstream of the nozzle lip. No evidence has been found to support the ‘collective interactive’ mechanism proposed by Ho & Nosseir (J. Fluid Mech., vol. 105, 1981, pp. 119–142). The ‘vortex pairing’ proposed by Winant & Browand (J. Fluid Mech., vol. 63, 1974, pp. 237–255) is observed near the nozzle; however, it has an insignificant role in the sharp reduction of the most unstable frequency of disturbances. Nonetheless, both Mach energy norm and linear spatial instability analyses show that the most unstable frequency of disturbances decreases rapidly in a very short distance from the nozzle lip in the near-nozzle region through the spatial growth of instabilities where the linear instability analysis overpredicts the frequency of the most unstable instabilities downstream of the nozzle.

JFM classification

Aerodynamics: High-speed flow Turbulent Flows: Shear layer turbulence Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A34
Check for updates
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Alvi, F. S., Shih, C., Elavarasan, R., Garg, G. & Krothapalli, A. 2003 Control of supersonic impinging jet flows using supersonic microjets. AIAA J. 41 (7), 1347–1355.CrossRefGoogle Scholar
Amili, O., Edgington-Mitchell, D., Honnery, D. & Soria, J. 2015 a High resolution PIV measurements of an impinging underexpanded supersonic jet. In Turbulence and Shear Flow Phenomena. June 30–July 3, Melbourne, Australia. University of Melbourne.Google Scholar
Amili, O., Edgington-Mitchell, D., Honnery, D. & Soria, J. 2016 Interaction of a supersonic underexpanded jet with a flat plate. In Fluid-Structure-Sound Interactions and Control, pp. 247–251. Springer.CrossRefGoogle Scholar
Amili, O., Edgington-Mitchell, D., Weightman, J., Stegeman, P., Ooi, A., Honnery, D. & Soria, J. 2015 b PIV measurement of an impinging underexpanded supersonic jet and comparison with LES. In 11th International Symposium on Particle Image Velocimetry. September 14–16, Santa Barbara, California, USA.Google Scholar
Amjad, S., Karami, S., Soria, J. & Atkinson, C. H. 2020 Assessment of three-dimensional density measurements from tomographic background-oriented schlieren (BOS). Meas. Sci. Technol. 31 (11), 114002.CrossRefGoogle Scholar
Baars, W. J. & Tinney, C. E. 2014 Shock-structures in the acoustic field of a mach 3 jet with crackle. J. Sound Vib. 333 (12), 2539–2553.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750–756.CrossRefGoogle Scholar
Bell, G., Soria, J., Honnery, D. & Edgington-Mitchell, D. 2018 An experimental investigation of coupled underexpanded supersonic twin-jets. Exp. Fluids 59 (9), 139.CrossRefGoogle Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.CrossRefGoogle Scholar
Bodony, D. J. & Lele, S. K. 2005 On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets. Phys. Fluids 17 (8), 085103.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2006 Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering. Comput. Fluids 35 (10), 1344–1358.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2010 Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets. J. Fluid Mech. 663, 507–538.CrossRefGoogle Scholar
Bogey, C. & Gojon, R. 2017 Feedback loop and upwind-propagating waves in ideally expanded supersonic impinging round jets. J. Fluid Mech. 823, 562–591.CrossRefGoogle Scholar
Bogey, C., Marsden, O. & Bailly, C. 2011 Large-eddy simulation of the flow and acoustic fields of a Reynolds number $10^5$ subsonic jet with tripped exit boundary layers. Phys. Fluids 23 (3), 035104.CrossRefGoogle Scholar
Brehm, C., Housman, J. A. & Kiris, C. C. 2016 Noise generation mechanisms for a supersonic jet impinging on an inclined plate. J. Fluid Mech. 797, 802–850.CrossRefGoogle Scholar
Brès, G. A., Ham, F. E., Nichols, J. W. & Lele, S. K. 2017 Unstructured large-eddy simulations of supersonic jets. AIAA J. 55 (4), 1164–1184.CrossRefGoogle Scholar
Brès, G. A., Jaunet, V., Le Rallic, M., Jordan, P., Towne, A., Schmidt, O., Colonius, T., Cavalieri, A. V. & Lele, S. K. 2015 Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound. AIAA Paper 2016-3050.CrossRefGoogle Scholar
Bridges, T. J. & Morris, P. J. 1984 Differential eigenvalue problems in which the parameter appears nonlinearly. J. Comput. Phys. 55 (3), 437–460.CrossRefGoogle Scholar
Brouzet, D., Haghiri, A., Talei, M, Brear, M. J., Schmidt, O. T., Rigas, G. & Colonius, T. 2020 Role of coherent structures in turbulent premixed flame acoustics. AIAA J. 58 (6), 2635–2642.CrossRefGoogle Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.CrossRefGoogle Scholar
Brunton, S. L & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67 (5), 050801.CrossRefGoogle Scholar
Carling, J. C. & Hunt, B. L. 1974 The near wall jet of a normally impinging, uniform, axisymmetric, supersonic jet. J. Fluid Mech. 66 (1), 159–176.CrossRefGoogle Scholar
Cierpka, C., Soria, J. & Kahler, C. J. 2014 Ultra-high-speed 3D astigmatic PTV in supersonic underexpanded impinging jets. In 17th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 7–10 July. Lisbon Symposia.Google Scholar
Colonius, T. & Lele, S. K. 2004 Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog. Aerosp. Sci. 40 (6), 345–416.CrossRefGoogle Scholar
Diebold, J. M. & Elliott, G. S. 2014 High-speed schlieren imaging of a high-speed jet impinging on a flat plate. AIAA Paper 2014-3094.CrossRefGoogle Scholar
Edgington-Mitchell, D. 2019 Aeroacoustic resonance and self-excitation in screeching and impinging supersonic jets – a review. Intl J. Aeroacoust. 18 (2–3), 118–188.CrossRefGoogle Scholar
Edgington-Mitchell, D., Honnery, D. R. & Soria, J. 2012 The visualization of the acoustic feedback loop in impinging underexpanded supersonic jet flows using ultra-high frame rate Schlieren. J. Vis. (Tokyo) 15 (4), 333–341.Google Scholar
Edgington-Mitchell, D., Honnery, D. R. & Soria, J. 2014 a The underexpanded jet mach disk and its associated shear layer. Phys. Fluids 26 (9), 1578.CrossRefGoogle Scholar
Edgington-Mitchell, D., Jaunet, V., Jordan, P., Towne, A., Soria, J. & Honnery, D. 2018 a Upstream-travelling acoustic jet modes as a closure mechanism for screech. J. Fluid Mech. 855, R1.CrossRefGoogle Scholar
Edgington-Mitchell, D., Oberleithner, K., Honnery, D. R. & Soria, J. 2014 b Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748, 822–847.CrossRefGoogle Scholar
Edgington-Mitchell, D., Weightman, J. L., Honnery, D. R. & Soria, J. 2018 b Sound production by shock leakage in supersonic jet screech. AIAA Paper 2018-3147.CrossRefGoogle Scholar
Elavarasan, R., Krothapalli, A., Venkatakrishnan, L. & Lourenco, L. 2001 Suppression of self-sustained oscillations in a supersonic impinging jet. AIAA J. 39 (12), 2366–2373.CrossRefGoogle Scholar
Freund, J. & Colonius, T. 2002 POD analysis of sound generation by a turbulent jet. In 40th AIAA Aerospace Sciences Meeting and Exhibit 2002. AIAA.CrossRefGoogle Scholar
Fukagata, K. & Kasagi, N. 2002 Highly energy-conservative finite difference method for the cylindrical coordinate system. J. Comput. Phys. 181 (2), 478–498.CrossRefGoogle Scholar
Gad-El-Hak, M. 2019 Coherent structures and flow control: genesis and prospect. Bull. Pol. Acad. Sci.-TE 67 (3), 411–444.Google Scholar
Gaitonde, D. V. & Samimy, M. 2011 Coherent structures in plasma-actuator controlled supersonic jets: axisymmetric and mixed azimuthal modes. Phys. Fluids 23 (9), 095104.CrossRefGoogle Scholar
Gojon, R. & Bogey, C. 2017 Flow structure oscillations and tone production in underexpanded impinging round jets. AIAA J. 55 (6), 1792–1805.CrossRefGoogle Scholar
Gojon, R., Bogey, C. & Marsden, O. 2015 Large-eddy simulation of underexpanded round jets impinging on a flat plate 4 to 9 radii downstream from the nozzle. AIAA Paper 2015-2210.CrossRefGoogle Scholar
Gudmundsson, K. 2010 Instability wave models of turbulent jets from round and serrated nozzles. PhD thesis, California Institute of Technology.Google Scholar
Gudmundsson, K. & Colonius, T. 2007 Spatial stability analysis of chevron jet profiles. AIAA Paper 2007-3599.CrossRefGoogle Scholar
Hammond, D. A. & Redekopp, L. G. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231–260.CrossRefGoogle Scholar
Hamzehloo, A. & Aleiferis, P. G. 2014 Large eddy simulation of highly turbulent under-expanded hydrogen and methane jets for gaseous-fuelled internal combustion engines. Intl J. Hydrogen Energ. 39 (36), 21275–21296.CrossRefGoogle Scholar
Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids 8 (3), 826–837.CrossRefGoogle Scholar
Henderson, B., Bridges, J. & Wernet, M. 2005 An experimental study of the oscillatory flow structure of tone-producing supersonic impinging jets. J. Fluid Mech. 542, 115–137.CrossRefGoogle Scholar
Henderson, B. & Powell, A. 1993 Experiments concerning tones produced by an axisymmetric choked jet impinging on flat plates. J. Sound Vib. 168 (2), 307–326.CrossRefGoogle Scholar
Henderson, L. F. 1966 Experiments on the impingement of a supersonic jet on a flat plate. Z. Angew. Math. Phys. 17 (5), 553–569.CrossRefGoogle Scholar
Ho, C.-M. & Nosseir, N. S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119–142.CrossRefGoogle Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41 (2), 241–258.CrossRefGoogle Scholar
Illingworth, S. J., Monty, J. P. & Marusic, I. 2018 Estimating large-scale structures in wall turbulence using linear models. J. Fluid Mech. 842, 146–162.CrossRefGoogle Scholar
Jaunet, V., Mancinelli, M., Jordan, P., Towne, A., Edgington-Mitchell, D. M, Lehnasch, G. & Girard, S. 2019 Dynamics of round jet impingement. AIAA Paper 2019-2769.CrossRefGoogle Scholar
Karami, S., Edgington-Mitchell, D. & Soria, J. 2018 a Large eddy simulation of supersonic under-expanded jets impinging on a flat plate. In Proceedings of the 11th Australasian Heat and Mass Transfer Conference, p. 12. AFTES.Google Scholar
Karami, S., Stegeman, P. C., Ooi, A. & Soria, J. 2019 High-order accurate large-eddy simulations of compressible viscous flow in cylindrical coordinates. Comput. Fluids 191, 104241.CrossRefGoogle Scholar
Karami, S., Stegeman, P. C., Ooi, A., Theofilis, V. & Soria, J. 2020 Receptivity characteristics of under-expanded supersonic impinging jets. J. Fluid Mech. 889, A27.CrossRefGoogle Scholar
Karami, S., Stegeman, P. C., Theofilis, V., Schmid, P. J. & Soria, J. 2018 b Linearised dynamics and non-modal instability analysis of an impinging under-expanded supersonic jet. J. Phys.: Conf. Ser. 1001, 012019.Google Scholar
Kawai, S. & Lele, S. K. 2010 Large-eddy simulation of jet mixing in supersonic crossflows. AIAA J. 48 (9), 2063–2083.CrossRefGoogle Scholar
Kennedy, C. A. & Carpenter, M. H. 1994 Several new numerical methods for compressible shear-layer simulations. Appl. Numer. Maths 14 (4), 397–433.CrossRefGoogle Scholar
Kennedy, C. A., Carpenter, M. H. & Lewis, R. M. 2000 Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Appl. Numer. Maths 35 (3), 177–219.CrossRefGoogle Scholar
Kim, M., Lim, J., Kim, S., Jee, S., Park, J. & Park, D. 2019 Large-eddy simulation with parabolized stability equations for turbulent transition using OpenFOAM. Comput. Fluids 189, 108–117.CrossRefGoogle Scholar
Koshigoe, S., Gutmark, E., Schadow, K. C. & Tubis, A. 1988 Wave structures in jets of arbitrary shape. III. Triangular jets. Phys. Fluids 31 (6), 1410–1419.CrossRefGoogle Scholar
Krothapalli, A., Rajkuperan, E., Alvi, F. & Lourenco, L. 1999 Flow field and noise characteristics of a supersonic impinging jet. AIAA Paper 1999-2239.CrossRefGoogle Scholar
Lajús, F. C., Sinha, A., Cavalieri, A. V. G., Deschamps, C. J. & Colonius, T. 2019 Spatial stability analysis of subsonic corrugated jets. J. Fluid Mech. 876, 766–791.CrossRefGoogle Scholar
Le, Q. P., Johnstone, A. D., Kosasih, B. & Renshaw, W. 2020 Vortex dynamics and fluctuations of impinging planar jet. ISIJ Int. 60 (5), 1030–1039.Google Scholar
Lesshafft, L., Semeraro, O., Jaunet, V., Cavalieri, A. V. G. & Jordan, P. 2019 Resolvent-based modeling of coherent wave packets in a turbulent jet. Phys. Rev. Fluids 4 (6), 063901.CrossRefGoogle Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A: Fluid Dyn. 4 (3), 633–635.CrossRefGoogle Scholar
Livermore, P. W., Jones, C. A. & Worland, S. J. 2007 Spectral radial basis functions for full sphere computations. J. Comput. Phys. 227 (2), 1209–1224.CrossRefGoogle Scholar
Mack, L. M. 1984 Boundary-layer linear stability theory. AGARD Rep. 709. JPL, California Institute of Technology.Google Scholar
Mercier, B., Castelain, T. & Bailly, C. 2017 Experimental characterisation of the screech feedback loop in underexpanded round jets. J. Fluid Mech. 824, 202–229.CrossRefGoogle Scholar
Michalke, A. 1977 Instability of a Compressible Circular Free Jet with Consideration of the Influence of the Jet Boundary Layer Thickness. National Aeronautics and Space Administration.Google Scholar
Mittal, S. 2008 Global linear stability analysis of time-averaged flows. Intl J. Numer. Meth. Fluids 58 (1), 111–118.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787–795.CrossRefGoogle Scholar
Morinishi, Y., Vasilyev, O. V. & Ogi, T. 2004 Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations. J. Comput. Phys. 197 (2), 686–710.CrossRefGoogle Scholar
Nguyen, T., Maher, B. & Hassan, Y. 2019 Flow field characteristics of a supersonic jet impinging on an inclined surface. AIAA J. 58 (3), 1240–1254.CrossRefGoogle Scholar
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Nosseir, N. S. & Ho, C.-M. 1979 On the feedback phenomenon of an impinging jet. Tech. Rep. University of Southern California.CrossRefGoogle Scholar
Oberleithner, K., Rukes, L. & Soria, J. 2014 Mean flow stability analysis of oscillating jet experiments. J. Fluid Mech. 757, 1–32.CrossRefGoogle Scholar
Pack, D. C. 1948 On the formation of shock-waves in supersonic gas jets. Q. J. Mech. Appl. Maths 1 (1), 1–17.CrossRefGoogle Scholar
Paredes, P., Gosse, R., Theofilis, V. & Kimmel, R. 2016 Linear modal instabilities of hypersonic flow over an elliptic cone. J. Fluid Mech. 804, 442–466.CrossRefGoogle Scholar
Paschereit, C. O., Gutmark, E. & Weisenstein, W. 1999 Coherent structures in swirling flows and their role in acoustic combustion control. Phys. Fluids 11 (9), 2667–2678.CrossRefGoogle 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
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. 66 (12), 1039.CrossRefGoogle Scholar
Powell, A. 1988 The sound-producing oscillations of round underexpanded jets impinging on normal plates. J. Acoust. Soc. Am. 83 (2), 515–533.CrossRefGoogle Scholar
Prandtl, L. 1904 Über die stationären wellen in einem gasstrahl. Phys. Z. 5, 599–6010.Google Scholar
Prandtl, L. 1907 Neue untersuchungen über die strömende bewegung der gase und dämpfe. Phys. Z. 8, 23–30.Google Scholar
Raman, G. & Srinivasan, K. 2009 The powered resonance tube: from Hartmann's discovery to current active flow control applications. Prog. Aerosp. Sci. 45 (4–5), 97–123.CrossRefGoogle Scholar
Ray, P. K., Cheung, L. C. & Lele, S. K. 2009 On the growth and propagation of linear instability waves in compressible turbulent jets. Phys. Fluids 21 (5), 054106.CrossRefGoogle Scholar
Risborg, A. & Soria, J. 2009 High-speed optical measurements of an underexpanded supersonic jet impinging on an inclined plate. In 28th International Congress on High-speed Imaging and Photonics, vol. 7126, p. 71261F. International Society for Optics and Photonics.CrossRefGoogle Scholar
Rossiter, J. E. 1964 Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Tech. Rep. 64037. Ministry of Aviation; Royal Aircraft Establishment.Google Scholar
Rowley, C. W., Colonius, T. & Basu, A. J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346.CrossRefGoogle Scholar
Sartor, F., Mettot, C., Bur, R. & Sipp, D. 2015 Unsteadiness in transonic shock-wave/boundary-layer interactions: experimental investigation and global stability analysis. J. Fluid Mech. 781, 550–577.CrossRefGoogle Scholar
Schadow, K. C., Gutmark, E., Parr, T. P., Parr, D. M., Wilson, K. J. & Crump, J. E. 1989 Large-scale coherent structures as drivers of combustion instability. Combust. Sci. Technol. 64 (4–6), 167–186.CrossRefGoogle Scholar
Sikroria, T., Soria, J., Karami, S., Sandberg, R. D. & Ooi, A. 2020 Measurement and analysis of the shear layer instabilities in supersonic impinging jets. AIAA Paper 2020-3070.CrossRefGoogle Scholar
Sinha, A., Gudmundsson, K., Xia, H. & Colonius, T. 2016 Parabolized stability analysis of jets from serrated nozzles. J. Fluid Mech. 789, 36–63.CrossRefGoogle Scholar
Sinibaldi, G., Marino, L. & Romano, G. P. 2015 Sound source mechanisms in under-expanded impinging jets. Exp. Fluids 56 (5), 105.CrossRefGoogle 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
Soria, J. & Amili, O. 2015 Under-expanded impinging supersonic jet flow. In 10th Pacific Symposium on Flow Visualization and Image Processing. June 15–18, Naples, Italy. PSFVIP.Google Scholar
Soria, J. & Risborg, A. 2019 High-speed optical measurements of an under-expanded supersonic jet impinging on an inclined plate. Monash University.Google Scholar
Stegeman, P. C., Pérez, J. M., Soria, J. & Theofilis, V. 2016 a Inception and evolution of coherent structures in under-expanded supersonic jets. J. Phys.: Conf. Ser. 708, 012015.Google Scholar
Stegeman, P. C., Soria, J. & Ooi, A. 2016 b Interaction of shear layer coherent structures and the stand-off shock of an under-expanded circular impinging jet. In Fluid-Structure-Sound Interactions and Control, pp. 241–245. Springer.CrossRefGoogle Scholar
Tam, C. K. W. 1986 Excitation of instability waves by sound – a physical interpretation. J. Sound Vib. 105 (1), 169–172.CrossRefGoogle Scholar
Tam, C. K. W. & Ahuja, K. K. 1990 Theoretical model of discrete tone generation by impinging jets. J. Fluid Mech. 214, 67–87.CrossRefGoogle Scholar
Tam, C. K. W. & Dong, Z. 1994 Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics. Theor. Comput. Fluid Dyn. 6 (5–6), 303–322.CrossRefGoogle Scholar
Tam, C. K. W. & Hu, F. Q. 1989 On the three families of instability waves of high-speed jets. J. Fluid Mech. 201, 447–483.CrossRefGoogle Scholar
Tam, C. K. W. & Morris, P. J. 1985 Tone excited jets, Part V: a theoretical model and comparison with experiment. J. Sound Vib. 102 (1), 119–151.CrossRefGoogle Scholar
Theofilis, V. 1995 Spatial stability of incompressible attachment-line flow. Theor. Comput. Fluid Dyn. 7 (3), 159–171.CrossRefGoogle Scholar
Thethy, B., Tairych, D. & Edgington-Mitchell, D. 2019 Mechanics of the influx phase in the jet regurgitant mode of a powered resonance tube. Intl J. Aeroacoust. 18 (2–3), 279–298.CrossRefGoogle Scholar
Tissot, G., Zhang, M., Lajús, F. C., Cavalieri, A. V. G. & Jordan, P. 2017 Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer. J. Fluid Mech. 811, 95–137.CrossRefGoogle Scholar
Towne, A., Cavalieri, A. V. G., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. & Brès, G. A. 2017 Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 1113–1152.CrossRefGoogle Scholar
Towne, A., Rigas, G. & Colonius, T. 2019 A critical assessment of the parabolized stability equations. Theor. Comput. Fluid Dyn. 33 (3–4), 359–382.CrossRefGoogle Scholar
Tumin, A. & Reshotko, E. 2003 Optimal disturbances in compressible boundary layers. AIAA J. 41 (12), 2357–2363.CrossRefGoogle Scholar
Turton, S. E., Tuckerman, L. S. & Barkley, D. 2015 Prediction of frequencies in thermosolutal convection from mean flows. Phys. Rev. E 91 (4), 043009.CrossRefGoogle ScholarPubMed
Weightman, J. L., Amili, O., Honnery, D., Edgington-Mitchell, D. & Soria, J. 2017 a On the effects of nozzle lip thickness on the azimuthal mode selection of a supersonic impinging flow. AIAA Paper 2017-3031.CrossRefGoogle Scholar
Weightman, J. L., Amili, O., Honnery, D., Edgington-Mitchell, D. & Soria, J. 2019 Nozzle external geometry as a boundary condition for the azimuthal mode selection in an impinging underexpanded jet. J. Fluid Mech. 862, 421–448.CrossRefGoogle Scholar
Weightman, J. L., Amili, O., Honnery, D., Soria, J. & Edgington-Mitchell, D. 2017 b An explanation for the phase lag in supersonic jet impingement. J. Fluid Mech. 815, R1.CrossRefGoogle Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63 (2), 237–255.CrossRefGoogle Scholar
Wong, M. H., Edgington-Mitchell, D., Honnery, D., Cavalieri, A. V. & Jordan, P. 2019 A parabolised stability equation based broadband shock-associated noise model. AIAA Paper 2019-2584.CrossRefGoogle Scholar
Wu, R., Hong, T., Cheng, Q., Zou, H., Fan, Y. & Luo, X. 2019 Thermal modeling and comparative analysis of jet impingement liquid cooling for high power electronics. Intl J. Heat Mass Transfer 137, 42–51.CrossRefGoogle Scholar
Zaman, K. B. M. Q. 1996 Axis switching and spreading of an asymmetric jet: the role of coherent structure dynamics. J. Fluid Mech. 316, 1–27.CrossRefGoogle Scholar
Zhang, Z. & Wu, X. 2020 Nonlinear evolution and acoustic radiation of coherent structures in subsonic turbulent free shear layers. J. Fluid Mech. 884, A10.CrossRefGoogle Scholar
Zhou, J., Wang, X. & Li, J. 2019 Influences of effusion hole diameter on impingement/effusion cooling performance at turbine blade leading edge. Intl J. Heat Mass Transfer 134, 1101–1118.CrossRefGoogle Scholar