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Jet resonance in truncated ideally contoured nozzles

Published online by Cambridge University Press:  27 May 2021

Florian Bakulu ,
Guillaume Lehnasch Open the ORCID record for Guillaume Lehnasch [Opens in a new window] ,
Vincent Jaunet Open the ORCID record for Vincent Jaunet [Opens in a new window] ,
Eric Goncalves da Silva  and
Steve Girard
Florian Bakulu
Affiliation:
ISAE-ENSMA, Institut Pprime, Université de Poitiers, UPR-3346 CNRS 1 Avenue Clement Ader, 86360Chasseneuil-du-Poitou, France
Guillaume Lehnasch*
Affiliation:
ISAE-ENSMA, Institut Pprime, Université de Poitiers, UPR-3346 CNRS 1 Avenue Clement Ader, 86360Chasseneuil-du-Poitou, France
Vincent Jaunet
Affiliation:
ISAE-ENSMA, Institut Pprime, Université de Poitiers, UPR-3346 CNRS 1 Avenue Clement Ader, 86360Chasseneuil-du-Poitou, France
Eric Goncalves da Silva
Affiliation:
ISAE-ENSMA, Institut Pprime, Université de Poitiers, UPR-3346 CNRS 1 Avenue Clement Ader, 86360Chasseneuil-du-Poitou, France
Steve Girard
Affiliation:
ISAE-ENSMA, Institut Pprime, Université de Poitiers, UPR-3346 CNRS 1 Avenue Clement Ader, 86360Chasseneuil-du-Poitou, France
*
†Email address for correspondence: [email protected]
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Abstract

Unsteady side loads observed in supersonic nozzles operating in over-expanded regimes are most often associated with intrinsic unsteadiness of the shock system and separation line, featuring random motions with mainly broadband low-frequency contributions. A tonal flow behaviour, rather associated with energy peaks of fluctuating wall pressure in the middle frequency range, is also found to emerge for particular operating conditions in a truncated ideally contoured nozzle. The corresponding flow field is here investigated to understand its origin and show how it modifies side-load properties. The temporal and spatial organization of wall pressure and jet velocity field are first experimentally characterized based on synchronized acquisition of both wall pressure along rings of pressure probes located within the nozzle, and high-rate time-resolved particle image velocimetry velocity fields measured in a plane section crossing the jet downstream of the nozzle exit. The external jet aerodynamics and internal wall pressure field are first shown to be clearly linked, but only at this frequency peak for which a significant coherence emerges between first azimuthal mode of fluctuating wall pressure and first azimuthal mode of fluctuating external velocity field. A delayed detached eddy simulation is carried out and validated against experimental results in order to reproduce this tonal flow dynamics. The analysis of simulation data shows that the tonal flow behaviour of first azimuthal mode is indeed more globally felt within the whole flow structure where both upstream and downstream propagating waves are shown to coexist, even far downstream of the nozzle exit. The analysis shows that both waves possess support in the jet core and have a non-negligible pressure signature in the separated region. The spectral proper orthogonal decomposition of fluctuating pressure field at this tonal frequency reveals that the nature and intensity of lateral pressure forces is directed by the resonance related to the upstream- and downstream-propagating coherent structures, which imposes the shock waves network to respond and modulate the pressure levels on the nozzle internal surface.

JFM classification

Wakes/Jets: Separated flows Compressible Flows: Supersonic flow Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A32
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Aghababaie, A.A. & Theunissen, R. 2015 Modeling free shock separation induced side loads in overexpanded rocket nozzles. AIAA J. 53 (1), 93–103.CrossRefGoogle Scholar
Chauvet, N., Deck, S. & Jacquin, L. 2007 Zonal detached eddy simulation of a controlled propulsive jet. AIAA J. 45 (10), 2458–2473.CrossRefGoogle Scholar
Clemens, N.T. & Narayanaswamy, V. 2014 Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu. Rev. Fluid Mech. 46, 469–492.CrossRefGoogle Scholar
Deck, S. 2009 Delayed detached eddy simulation of the end-effect regime and side-loads in an overexpanded nozzle flow. Shock Waves 19 (3), 239–249.CrossRefGoogle Scholar
Deck, S. 2012 Recent improvements in the zonal detached eddy simulation (zdes) formulation. Theor. Comput. Fluid Dyn. 26 (6), 523–550.CrossRefGoogle Scholar
Deck, S. & Guillen, P. 2002 Numerical simulation of side loads in an ideal truncated nozzle. J. Propul. Power 18 (2), 261–269.CrossRefGoogle Scholar
Donald, B.W., Baars, W.J., Tinney, C.E. & Ruf, J.H. 2014 Sound produced by large area-ratio nozzles during fixed and transient operations. AIAA J. 52 (7), 1474–1485.CrossRefGoogle Scholar
Dumnov, G. 1996 Unsteady side-loads acting on the nozzle with developed separation zone. AIAA Paper 1995-3220.CrossRefGoogle Scholar
Edgington-Mitchell, D., Jaunet, V., Jordan, P., Towne, A., Soria, J. & Honnery, D. 2018 Upstream-travelling acoustic jet modes as a closure mechanism for screech. J. Fluid Mech. 855, R1.CrossRefGoogle Scholar
Georges-Picot, A., Hadjadj, A. & Herpe, J. 2014 Influence of downstream unsteadiness on shock pattern in separated nozzle flows. AIAA Paper 2014-4000.CrossRefGoogle Scholar
Gojon, R., Bogey, C. & Mihaescu, M. 2018 Oscillation modes in screeching jets. AIAA J. 56 (7), 2918–2924.CrossRefGoogle Scholar
Goncalves, E. & Houdeville, R. 2001 Reassessment of the wall functions approach for RANS computations. Aerosp. Sci. Technol. 5, 1–14.CrossRefGoogle Scholar
Goncalves, E. & Houdeville, R. 2004 Turbulence model and numerical scheme assessment for buffet computations. Intl J. Numer. Meth. Fluids 46, 1127–1152.CrossRefGoogle Scholar
Goncalves, E., Lehnasch, G. & Herpe, J. 2017 Hybrid RANS/LES simulation of shock-induced separated flow in truncated ideal contour nozzle. In 31st International Symposium on Shock Waves (ed. A. Sasoh, T. Aoki & M. Katayama), pp. 507–513. Springer.CrossRefGoogle Scholar
Hadjadj, A., Perrot, Y. & Verma, S. 2015 Numerical study of shock/boundary layer interaction in supersonic overexpanded nozzles. Aerosp. Sci. Technol. 42, 158–168.CrossRefGoogle Scholar
Jameson, A. 1991 Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. AIAA Paper 91-1596.Google Scholar
Jameson, A., Schmidt, W. & Turkel, E. 1981 Numerical solution of the euler equations by finite volume methods using Runge Kutta time stepping schemes. AIAA Paper 1981-1259.CrossRefGoogle Scholar
Jaunet, V., Arbos, S., Lehnasch, G. & Girard, S. 2017 Wall pressure and external velocity field relation in overexpanded supersonic jets. AIAA J. 55, 4245–4257.CrossRefGoogle Scholar
Jordan, P., Jaunet, V., Towne, A., Cavalieri, A.V.G., Colonius, T., Schmidt, O. & Agarwal, A. 2018 Jet-flap interaction tones. J. Fluid Mech. 853, 333–358.CrossRefGoogle Scholar
Lammari, M.R. 1996 Mesures par vélocimétrie laser doppler dans une couche de mélange turbulente supersonique : quelques aspects du processus de mesure. PhD thesis, Université de Poitiers.Google Scholar
Lárusson, R., Andersson, N. & Östlund, J. 2017 Dynamic mode decomposition of a separated nozzle flow with transonic resonance. AIAA J. 55, 1295–1306.CrossRefGoogle Scholar
Loh, C.Y. & Zaman, K.B.M.Q. 2002 Numerical investigation of transonic resonance with a convergent-divergent nozzle. AIAA J. 40 (12), 2393–2401.CrossRefGoogle Scholar
Mancinelli, M., Jaunet, V., Jordan, P. & Towne, A. 2019 Screech-tone prediction using upstream-travelling jet modes. Exp. Fluids 60 (1), 22.CrossRefGoogle Scholar
Martelli, E., Ciottoli, P.P., Saccoccio, L., Nasuti, F., Valorani, M. & Bernardini, M. 2019 Characterization of unsteadiness in an overexpanded planar nozzle. AIAA J. 57 (1), 239–251.CrossRefGoogle Scholar
Martelli, E., Saccoccio, L., Ciottoli, P.P., Tinney, C.E., Baars, W.J. & Bernardini, M. 2020 Flow dynamics and wall-pressure signatures in a high-Reynolds-number overexpanded nozzle with free shock separation. J. Fluid Mech. 895, A29.CrossRefGoogle Scholar
Nguyen, A.T., Deniau, H., Girard, S. & Alziary de Roquefort, T. 2003 Unsteadiness of flow separation and end-effects regime in a thrust-optimized contour rocket nozzle. Intl J. Flow Turbul. Combust. 71, 161–181.CrossRefGoogle Scholar
Olson, B.J. & Lele, S.K. 2013 A mechanism for unsteady separation in over-expanded nozzle flow. Phys. Fluids 25 (11), 110809.CrossRefGoogle Scholar
Roe, P.L 1981 Approximate riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (2), 357–372.CrossRefGoogle Scholar
Scarano, F. 2001 Iterative image deformation methods in PIV. Meas. Sci. Technol. 13 (1), R1–R19.CrossRefGoogle Scholar
Schmucker, R.H. 1973 a Flow process in overexpanded chemical rocket nozzles part 1: Flow separation. NASA Tech. Memo. TM-77396.Google Scholar
Schmucker, R.H. 1973 b Flow process in overexpanded chemical rocket nozzles part 2: Side loads due to asymetric separation. NASA Tech. Memo. TM-77395.Google Scholar
Shams, A., Lehnasch, G. & Comte, P. 2011 Numerical investigation of the side-loads phenomena in overexpanded nozzles. In 4th European Conference for Aerospace Sciences, pp. 1–11. EUCASS Association.Google Scholar
Shams, A., Lehnasch, G., Comte, P., Deniau, H. & Alziary de Roquefort, T. 2013 Unsteadiness in shock-induced separated flow with subsequent reattachment of supersonic annular jet. Comput. Fluids 78, 63–74.CrossRefGoogle Scholar
Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D, Strelets, M.K. & Travin, A. 2006 A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20 (3), 181–195.CrossRefGoogle Scholar
Stark, R. & Wagner, B. 2009 Experimental study of boundary layer separation in truncated ideal contour nozzles. Shock Waves 19 (3), 185–191.CrossRefGoogle Scholar
Swanson, R.C., Radespiel, R. & Turkel, E. 1998 On some numerical dissipation schemes. J. Comput. Phys. 147 (2), 518–544.CrossRefGoogle Scholar
Tam, C.K.W., Seiner, J.M. & Yu, J.C. 1986 Proposed relationship between broadband shock associated noise and screech tones. J. Sound Vib. 110 (2), 309–321.CrossRefGoogle Scholar
Tatsumi, S., Martinelli, L. & Jameson, A. 1995 Flux-limited schemes for the compressible Navier–Stokes equations. AIAA J. 33 (2), 252–261.CrossRefGoogle Scholar
Towne, A., Schmidt, O.T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Verma, S.B., Hadjadj, A. & Haidn, O. 2017 Origin of side-loads in a subscale truncated ideal contour nozzle. Aerosp. Sci. Technol. 71, 725–732.CrossRefGoogle Scholar
Verma, S.B. & Haidn, O. 2014 Unsteady shock motions in an over-expanded parabolic rocket nozzle. Aerosp. Sci. Technol. 39, 48–71.CrossRefGoogle Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39 (6), 1096–1100.CrossRefGoogle Scholar
Zaman, K.B.M.Q., Dahl, M.D., Bencic, T.J. & Loh, C.Y. 2002 Investigation of a transonic resonance with convergent–divergent nozzles. J. Fluid Mech. 463, 313–343.CrossRefGoogle Scholar