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Three-dimensional density field of a screeching under-expanded jet in helical mode using multi-view digital holographic interferometry

Published online by Cambridge University Press:  30 August 2022

O. Léon Open the ORCID record for O. Léon [Opens in a new window] ,
D. Donjat Open the ORCID record for D. Donjat [Opens in a new window] ,
F. Olchewsky ,
J.-M. Desse Open the ORCID record for J.-M. Desse [Opens in a new window] ,
F. Nicolas Open the ORCID record for F. Nicolas [Opens in a new window]  and
F. Champagnat Open the ORCID record for F. Champagnat [Opens in a new window]
O. Léon*
Affiliation:
ONERA/DMPE, Université de Toulouse, 2 avenue Edouard Belin, 31055 Toulouse, France
D. Donjat
Affiliation:
ONERA/DMPE, Université de Toulouse, 2 avenue Edouard Belin, 31055 Toulouse, France
F. Olchewsky
Affiliation:
ONERA/DAAA, Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, 59000 Lille, France
J.-M. Desse
Affiliation:
ONERA/DAAA, Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, 59000 Lille, France
F. Nicolas
Affiliation:
ONERA/DAAA, Université Paris Saclay, 92190 Meudon, France
F. Champagnat
Affiliation:
ONERA/DTIS, Université Paris Saclay, 91123 Palaiseau, France
*
†Email address for correspondence: olivier.leon@onera.fr
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Abstract

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

JFM classification

Compressible Flows: Supersonic flow Nonlinear Dynamical Systems: Low-dimensional models Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A36
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

van Aarle, W., Palenstijn, W.J., Beenhouwer, J.D., Altantzis, T., Bals, S., Batenburg, K.J. & Sijbers, J. 2015 The ASTRA toolbox: a platform for advanced algorithm development in electron tomography. Ultramicroscopy 157, 35–47.CrossRefGoogle ScholarPubMed
Addy, A.L. 1981 Effects of axisymmetric sonic nozzle geometry on Mach disk characteristics. AIAA J. 19 (1), 121–122.CrossRefGoogle Scholar
André, B., Castelain, T. & Bailly, C. 2011 Shock-tracking procedure for studying screech-induced oscillations. AIAA J. 49 (7), 1563–1566.CrossRefGoogle Scholar
Atcheson, B., Ihrke, I., Heidrich, W., Tevs, A., Bradley, D., Magnor, M. & Seidel, H.-P. 2008 Time-resolved 3D capture of non-stationary gas flows. ACM Trans. Graph. 27 (5), 132.CrossRefGoogle Scholar
Beck, A. & Teboulle, M. 2009 A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2 (1), 183–202.CrossRefGoogle Scholar
Bredies, K., Kunisch, K. & Pock, T. 2010 Total generalized variation. SIAM J. Imag. Sci. 3 (3), 492–526.Google Scholar
Chambolle, A. & Pock, T. 2010 A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imag. Vis. 40 (1), 120–145.CrossRefGoogle Scholar
Chambolle, A. & Pock, T. 2016 An introduction to continuous optimization for imaging. Acta Numerica 25, 161–319.CrossRefGoogle Scholar
Champagnat, F., Nicolas, F., Olchewsky, F., Donjat, D., Essaïdi, Z. & Desse, J.-M. 2018 Comparison of BOS and digital holography on an underexpanded jet. In Proceedings 18th International Symposium on Flow Visualization (ed. T. Rösgen). ETH Zurich.Google Scholar
Davies, M.G. & Oldfield, D.E.S. 1962 Tones from a choked axisymmetric jet. I. Cell structure, eddy velocity and source locations. Acta Acust. 12 (4), 257–267.Google Scholar
Desse, J.-M. & Olchewsky, F. 2017 Digital holographic interferometry for analysing high density gradients in Fluid Mechanics. In Holographic Materials and Optical Systems (ed. I. Naydenova, D. Nazarova & T. Babeva), pp. 291–317. IntechOpen.CrossRefGoogle Scholar
Dillmann, A., Wetzel, T. & Soeller, C. 1998 Interferometric measurement and tomography of the density field of supersonic jets. Exp. Fluids 25 (5–6), 375–387.CrossRefGoogle Scholar
Doleček, R., Psota, P., Lédl, V., Vít, T., Václavík, J. & Kopecký, V. 2013 General temperature field measurement by digital holography. Appl. Opt. 52 (1), A319–A325.CrossRefGoogle ScholarPubMed
Doleček, R., Psota, P., Lédl, V. & Vít, T. 2016 Heat and mass transfer measurement using method of digital holographic tomography. In Optics and Measurement International Conference 2016 (ed. J. Kovacicinova), vol. 10151, p. 1015119. International Society for Optics and Photonics. SPIE.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. 2014 a The underexpanded jet Mach disk and its associated shear layer. Phys. Fluids 26 (9), 096101.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
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., Wang, T., Nogueira, P., Schmidt, O., Jaunet, V., Duke, D., Jordan, P. & Towne, A. 2021 Waves in screeching jets. J. Fluid Mech. 913, A7.CrossRefGoogle Scholar
Epstein, C.L. 2008 Introduction to the mathematics of medical imaging. Other Titles in Applied Mathematics. SIAM Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Franquet, E., Perrier, V., Gibout, S. & Bruel, P. 2015 Free underexpanded jets in a quiescent medium: a review. Prog. Aerosp. Sci. 77, 25–53.CrossRefGoogle Scholar
Ghiglia, D.C. & Pritt, M.D. 1998 Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, vol. 4. Wiley.Google Scholar
Gilton, D., Ongie, G. & Willett, R. 2020 Neumann networks for linear inverse problems in imaging. IEEE Trans. Comput. Imag. 6, 328–343.CrossRefGoogle Scholar
Gojon, R., Bogey, C. & Mihaescu, M. 2018 Oscillation modes in screeching jets. AIAA J. 56 (7), 2918–2924.CrossRefGoogle Scholar
Grauer, S.J., Unterberger, A., Rittler, A., Daun, K.J., Kempf, A.M. & Mohri, K. 2018 Instantaneous 3D flame imaging by background-oriented schlieren tomography. Combust. Flame 196, 284–299.Google Scholar
Hansen, P.C. 1998 Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM.CrossRefGoogle Scholar
Hansen, P.C. 2001 The L-curve and its use in the numerical treatment of inverse problems. In Computational Inverse Problems in Electrocardiology (ed. P. Johnston), pp. 119–142. WIT Press.Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29 (1), 245–283.CrossRefGoogle Scholar
Herraez, M.A., Burton, D.R., Lalor, M.J. & Gdeisat, M.A. 2002 Fast two-dimensional phase unwrapping algorithm based on sorting by reliability following a noncontinuous path. Appl. Opt. 41 (35), 7437–7444.Google ScholarPubMed
Holmes, P., Lumley, J.L., Berkooz, G. & Rowley, C.W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Idier, J. 2010 Bayesian Approach to Inverse Problems, vol. 35. John Wiley & Sons.Google Scholar
Ishino, Y., Hayashi, N., Razak, I.F.B.A., Kato, T., Kurimoto, Y. & Saiki, Y. 2015 3D-CT (computer tomography) measurement of an instantaneous density distribution of turbulent flames with a multi-directional quantitative schlieren camera (reconstructions of high-speed premixed burner flames with different flow velocities). Flow Turbul. Combust. 96 (3), 819–835.CrossRefGoogle Scholar
Kazantsev, D. 2019 TOmographic MOdel-BAsed Reconstruction Software. Software available at https://github.com/dkazanc/ToMoBAR.Google Scholar
Lanen, T.A.W.M., Bakker, P.G. & Bryanston-Cross, P.J. 1992 Digital holographic interferometry in high-speed flow research. Exp. Fluids 13 (1), 56–62.CrossRefGoogle Scholar
Lang, H.M., Oberleithner, K., Paschereit, C.O. & Sieber, M. 2017 Measurement of the fluctuating temperature field in a heated swirling jet with BOS tomography. Exp. Fluids 58 (7), 88.CrossRefGoogle Scholar
Lanzillotta, L., Léon, O., Donjat, D. & Le Besnerais, G. 2019 3D density reconstruction of a screeching supersonic jet by synchronized multi-camera background oriented schlieren. In Proceedings of 8th EUCASS, Madrid. EUCASS.Google Scholar
Matulka, R.D. & Collins, D.J. 1971 Determination of three-dimensional density fields from holographic interferograms. J. Appl. Phys. 42 (3), 1109–1119.CrossRefGoogle Scholar
Nicolas, F., Donjat, D., Léon, O., Besnerais, G.L., Champagnat, F. & Micheli, F. 2017 3D reconstruction of a compressible flow by synchronized multi-camera BOS. Exp. Fluids 58 (5), 46.CrossRefGoogle Scholar
Nicolas, F., Todoroff, V., Plyer, A., Le Besnerais, G., Donjat, D., Micheli, F., Champagnat, F., Cornic, P. & Le Sant, Y. 2016 A direct approach for instantaneous 3D density field reconstruction from background-oriented schlieren (BOS) measurements. Exp. Fluids 57 (1), 13.CrossRefGoogle Scholar
Nogueira, P.A.S., Jaunet, V., Mancinelli, M., Jordan, P. & Edgington-Mitchell, D. 2022 Closure mechanism of the A1 and A2 modes in jet screech. J. Fluid Mech. 936, A10.CrossRefGoogle Scholar
Nogueira, P.A.S., Jordan, P., Jaunet, V., Cavalieri, A.V.G., Towne, A. & Edgington-Mitchell, D. 2021 Absolute instability in shock-containing jets. J. Fluid Mech. 930, A10.Google Scholar
Oberleithner, K., Sieber, M., Nayeri, C.N., Paschereit, C.O., Petz, C., Hege, H.-C., Noack, B.R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.CrossRefGoogle Scholar
Olchewsky, F., Essaidi, Z., Desse, J.M. & Champagnat, F. 2018 3D reconstrcutions of jets by multidirectional digital holographic tomography. In ISFV 2018, Zurich (ed. T. Rösgen). ETH Zurich.Google Scholar
Paleo, P. 2017 Iterative Methods in regularized tomographic reconstruction. Thesis, Université Grenoble Alpes.Google Scholar
Panda, J. 1998 Shock oscillation in underexpanded screeching jets. J. Fluid Mech. 363, 173–198.CrossRefGoogle Scholar
Panda, J. & Seasholtz, R.G. 1999 Measurement of shock structure and shock–vortex interaction in underexpanded jets using Rayleigh scattering. Phys. Fluids 11 (12), 3761–3777.CrossRefGoogle Scholar
Picart, P., Gross, M. & Marquet, P. 2015 Basic Fundamentals of Digital Holography, chap. 1, pp. 1–66. John Wiley and Sons.Google Scholar
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. B 66 (12), 1039–1056.CrossRefGoogle Scholar
Powell, A. 2010 On Prandtl's formulas for supersonic jet cell length. Intl J. Aeroacoust. 9 (1–2), 207–236.CrossRefGoogle Scholar
Powell, A., Umeda, Y. & Ishii, R. 1992 Observations of the oscillation modes of choked circular jets. J. Acoust. Soc. Am. 92 (5), 2823–2836.CrossRefGoogle Scholar
Raman, G. 1999 Supersonic jet screech: half-century from Powell to the present. J. Sound Vib. 225 (3), 543–571.CrossRefGoogle Scholar
Rodrigues, N., Brown, A., Meyer, T. & Lucht, R. 2022 0.1–5 MHz ultrahigh-speed gas densitydistributions using digital holographic interferometry. Appl. Opt. 61, 28–34.CrossRefGoogle ScholarPubMed
Schmid, P.J., Violato, D. & Scarano, F. 2012 Decomposition of time-resolved tomographic PIV. Exp. Fluids 52 (6), 1567–1579.CrossRefGoogle Scholar
Schnars, U., Falldorf, C., Watson, J. & Jüptner, W. 2014 Digital holography. In Digital Holography and Wavefront Sensing, pp. 39–68. Springer.CrossRefGoogle Scholar
Sinha, A., Rodrıguez, D., Brès, G.A. & Colonius, T. 2014 Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 71–95.CrossRefGoogle Scholar
Sipkens, T.A., Grauer, S.J., Steinberg, A.M., Rogak, S.N. & Kirchen, P. 2021 New transform to project axisymmetric deflection fields along arbitrary rays. Meas. Sci. Technol. 33 (3), 035201.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Smits, A.J. 2012 Flow Visualization: Techniques and Examples. Imperial College Press.CrossRefGoogle Scholar
Snyder, R. & Hesselink, L. 1988 Measurement of mixing fluid flows with optical tomography. Opt. Lett. 13 (2), 87–89.CrossRefGoogle ScholarPubMed
Söller, C., Wenskus, R., Middendorf, P., Meier, G.E.A. & Obermeier, F. 1994 Interferometric tomography for flow visualization of density fields in supersonic jets and convective flow. Appl. Opt. 33 (14), 2921.CrossRefGoogle ScholarPubMed
Sugawara, S., Nakao, S., Miyazato, Y., Ishino, Y. & Miki, K. 2020 Three-dimensional reconstruction of a microjet with a Mach disk by Mach–Zehnder interferometers. J. Fluid Mech. 893, A25.CrossRefGoogle Scholar
Sweeney, D.W. & Vest, C.M. 1974 Measurement of three-dimensional temperature fields above heated surfaces by holographic interferometry. Intl J. Heat Mass Transfer 17 (12), 1443–1454.CrossRefGoogle Scholar
Takeda, M., Ina, H. & Kobayashi, S. 1982 Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am. 72 (1), 156–160.CrossRefGoogle Scholar
Tikhonov, A. & Arsenin, V. 1977 Solutions of Ill-Posed Problems. Winston.Google Scholar
Timmerman, B. & Watt, D.W. 1995 Tomographic high-speed digital holographic interferometry. Meas. Sci. Technol. 6 (9), 1270–1277.CrossRefGoogle Scholar
Timmerman, B.H., Watt, D.W. & Bryanston-Cross, P.J. 1999 Quantitative visualization of high-speed 3D turbulent flow structures using holographic interferometric tomography. Opt. Laser Technol. 31 (1), 53–65.CrossRefGoogle Scholar
Watt, D.W. & Vest, C.M. 1987 Digital interferometry for flow visualization. Exp. Fluids 5 (6), 401–406.CrossRefGoogle Scholar
Watt, D.W. & Vest, C.M. 1990 Turbulent flow visualization by interferometric integral imaging and computed tomography. Exp. Fluids 8 (6), 301–311.CrossRefGoogle Scholar
Xiong, Y., Kaufmann, T. & Noiray, N. 2020 Towards robust BOS measurements for axisymmetric flows. Exp. Fluids 61 (8), 178.CrossRefGoogle Scholar
Yip, B., Lyons, K., Long, M., Mungal, M.G., Barlow, R. & Dibble, R. 1989 Visualization of a supersonic underexpanded jet by planar Rayleigh scattering. Phys. Fluids A 1 (9), 1449–1449.CrossRefGoogle Scholar

Léon et al. supplementary movie

Animation of the 3D density fields obtained by tomographic reconstruction of the 2 identified reduced dynamical models.

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