Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-19T21:08:09.571Z Has data issue: false hasContentIssue false

Wavelet-spectral analysis of droplet-laden isotropic turbulence

Published online by Cambridge University Press:  26 July 2019

Andreas Freund
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
Antonino Ferrante*
Affiliation:
William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA 98195, USA
*
Email address for correspondence: ferrante@aa.washington.edu

Abstract

The spectrum of turbulence kinetic energy for homogeneous turbulence is generally computed using the Fourier transform of the velocity field from physical three-dimensional space to wavenumber $k$. This analysis works well for single-phase homogeneous turbulent flows. In the case of multiphase turbulent flows, instead, the velocity field is non-smooth at the interface between the carrier fluid and the dispersed phase; thus, the energy spectra computed via Fourier transform exhibit spurious oscillations at high wavenumbers. An alternative definition of the spectrum uses the wavelet transform, which can handle discontinuities locally without affecting the entire spectrum while additionally preserving spatial information about the field. In this work, we propose using the wavelet energy spectrum to study multiphase turbulent flows. Also, we propose a new decomposition of the wavelet energy spectrum into three contributions corresponding to the carrier phase, droplets and interaction between the two. Lastly, we apply the new wavelet-decomposition tools in analysing the direct numerical simulation data of droplet-laden decaying isotropic turbulence (in absence of gravity) of Dodd & Ferrante (J. Fluid Mech., vol. 806, 2016, pp. 356–412). Our results show that, in comparison to the spectrum of the single-phase case, the droplets (i) do not affect the carrier-phase energy spectrum at high wavenumbers ($k_{m}/k_{min}\geqslant 128$), (ii) increase the energy spectrum at high wavenumbers ($k_{m}/k_{min}\geqslant 256$) by increasing the interaction energy spectrum at these wavenumbers and (iii) decrease the energy at low wavenumbers ($k_{m}/k_{min}\leqslant 16$) by increasing the dissipation rate at these wavenumbers.

Type
JFM Papers
Copyright
© 2019 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

Bassenne, M., Moin, P. & Urzay, J. 2018 Wavelet multiresolution analysis of particle-laden turbulence. Phys. Rev. Fluid. 3 (8), 084304.10.1103/PhysRevFluids.3.084304Google Scholar
Dodd, M. S. & Ferrante, A. 2014 A fast pressure-correction method for incompressible two-fluid flows. J. Comput. Phys. 273, 416434.10.1016/j.jcp.2014.05.024Google Scholar
Dodd, M. S. & Ferrante, A. 2016 On the interaction of Taylor lengthscale size droplets and isotropic turbulence. J. Fluid Mech. 806, 356412.10.1017/jfm.2016.550Google Scholar
Dodd, M. S. & Jofre, L.2018 Tensor-based analysis of the flow topology in droplet-laden homogeneous isotropic turbulence, Annual research brief, Center for Turbulence Research.Google Scholar
Elghobashi, S. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51, 217244.10.1146/annurev-fluid-010518-040401Google Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the twoway interaction between homogeneous turbulence and dispersed solid particles, I: turbulence modification. Phys. Fluids 5 (7), 17901801.10.1063/1.858854Google Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315329.10.1063/1.1532731Google Scholar
Ishihara, T., Gotoh, T. & Kaneda, Y. 2009 Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165180.10.1146/annurev.fluid.010908.165203Google Scholar
Kim, J., Bassenne, M., Towery, C. A. Z., Hamlington, P. E., Poludnenko, A. Y. & Urzay, J. 2018 Spatially localized multi-scale energy transfer in turbulent premixed combustion. J. Fluid Mech. 848, 78116.10.1017/jfm.2018.371Google Scholar
Lee, G. R., Gommers, R., Waselewski, F., Wohlfahrt, K. & O’Leary, A. 2019 PyWavelets: A Python package for wavelet analysis. J. Open Source Softw. 4 (36), 1237.10.21105/joss.01237Google Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 555.10.1017/S0022112009994022Google Scholar
Maxey, M. R. 2017 Droplets in turbulence: a new perspective. J. Fluid Mech. 816, 14.10.1017/jfm.2017.96Google Scholar
Meneveau, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469520.10.1017/S0022112091003786Google Scholar
Perrier, V., Philipovitch, T. & Basevant, C. 1995 Wavelet spectra compared to Fourier spectra. J. Math. Phys. 36 (3), 15061519.10.1063/1.531340Google Scholar
PyWaveletsv.1.0.1 2018 doi:10.5281/zenodo.1434616.Google Scholar
Risso, F. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 2548.10.1146/annurev-fluid-122316-045003Google Scholar
Sadek, M. & Aluie, H. 2018 Extracting the spectrum by spatial filtering. Phys. Rev. Fluid. 3 (12), 124610.10.1103/PhysRevFluids.3.124610Google Scholar