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Turbulence kinetic energy exchanges in flows with highly variable fluid properties

Published online by Cambridge University Press:  17 November 2017

Dorian Dupuy ,
Adrien Toutant  and
Françoise Bataille Open the ORCID record for Françoise Bataille [Opens in a new window]
Dorian Dupuy
Affiliation:
PROMES-CNRS (UPR 8521), Université de Perpignan Via Domitia, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan, France
Adrien Toutant*
Affiliation:
PROMES-CNRS (UPR 8521), Université de Perpignan Via Domitia, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan, France
Françoise Bataille
Affiliation:
PROMES-CNRS (UPR 8521), Université de Perpignan Via Domitia, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan, France
*
†Email address for correspondence: adrien.toutant@univ-perp.fr
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Abstract

This paper investigates the energy exchanges associated with the half-trace of the velocity fluctuation correlation tensor in a strongly anisothermal low Mach fully developed turbulent channel flow. The study is based on direct numerical simulations of the channel within the low Mach number hypothesis and without gravity. The overall flow behaviour is governed by the variable fluid properties. The temperature of the two channel walls are imposed at 293 K and 586 K to generate the temperature gradient. The mean friction Reynolds number of the simulation is 180. The analysis is carried out in the spatial and spectral domains. The spatial and spectral studies use the same decomposition of the terms of the evolution equation of the half-trace of the velocity fluctuation correlation tensor. The importance of each term of the decomposition in the energy exchanges is assessed. This lets us identify the terms associated with variations or fluctuations of the fluid properties that are not negligible. Then, the behaviour of the terms is investigated. The spectral energy exchanges are first discussed in the incompressible case since the analysis is not present in the literature with the decomposition used in this study. The modification of the energy exchanges by the temperature gradient is then investigated in the spatial and spectral domains. The temperature gradient generates an asymmetry between the two sides of the channel. The asymmetry can in a large part be explained by the combined effect of the mean local variations of the fluid properties, combined with a Reynolds number effect.

JFM classification

Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent Flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 834 , 10 January 2018 , pp. 5 - 54
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© 2017 Cambridge University Press 

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References

Abe, H., Kawamura, H. & Matsuo, Y. 2001 Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. Trans. ASME J. Fluids Engng 123 (2), 382–393.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.Google Scholar
Aulery, F., Dupuy, D., Toutant, A., Bataille, F. & Zhou, Y. 2017 Spectral analysis of turbulence in anisothermal channel flows. Comput. Fluids 151, 115–131.Google Scholar
Aulery, F., Toutant, A., Bataille, F. & Zhou, Y. 2015 Energy transfer process of anisothermal wall-bounded flows. Phys. Lett. A 379 (24), 1520–1526.Google Scholar
Aupoix, B. 2000 Introduction to turbulence modelling for compressible flows. In VKI lecture series, vol. 4, pp. H1–H64. Von Karman Institute for Fluid Dynamics.Google Scholar
Bauer, P. T., Zumwalt, G. W. & Fila, L. J. 1968 A numerical method and an extension of the korst jet mixing theory for multispecie turbulent jet mixing. In 6th Aerospace Sciences Meeting, New York. AIAA Paper 68–112.Google Scholar
Bolotnov, I. A., Lahey, R. T., Drew, D. A., Jansen, K. E. & Oberai, A. A. 2010 Spectral analysis of turbulence based on the DNS of a channel flow. Comput. Fluids 39 (4), 640–655.Google Scholar
Brillant, G., Husson, S., Bataille, F. & Ducros, F. 2008 Study of the blowing impact on a hot turbulent boundary layer using thermal large eddy simulation. Intl J. Heat Fluid Flow 29 (6), 1670–1678.Google Scholar
Brun, C., Boiarciuc, M. P., Haberkorn, M. & Comte, P. 2008 Large eddy simulation of compressible channel flow. Theor. Comput. Fluid Dyn. 22 (3), 189–212.Google Scholar
Calvin, C., Cueto, O. & Emonot, P. 2002 An object-oriented approach to the design of fluid mechanics software. ESAIM: Math. Modelling Numer. Anal. 36 (05), 907–921.CrossRefGoogle Scholar
Chandesris, M., d’Hueppe, A., Mathieu, B., Jamet, D. & Goyeau, B. 2013 Direct numerical simulation of turbulent heat transfer in a fluid-porous domain. Phys. Fluids 25 (12), 125110.Google Scholar
Chassaing, P. 1985 Une alternative à la formulation des équations du mouvement turbulent d’un fluide à masse volumique variable. J. de mécanique théorique et appliquée 4 (3), 375–389.Google Scholar
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, L. & Sarkar, S. 2013 Variable Density Fluid Turbulence. Springer Science & Business Media.Google Scholar
Cimarelli, A. & De Angelis, E. 2014 The physics of energy transfer toward improved subgrid-scale models. Phys. Fluids 26 (5), 055103.Google Scholar
Cimarelli, A., De Angelis, E. & Casciola, C. M. 2013 Paths of energy in turbulent channel flows. J. Fluid Mech. 715, 436–451.Google Scholar
Cimarelli, A., De Angelis, E., Jiménez, J. & Casciola, C. M. 2016 Cascades and wall-normal fluxes in turbulent channel flows. J. Fluid Mech. 796, 417–436.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E., Schlatter, P., Brethouwer, G., Talamelli, A. & Casciola, C. M. 2015 Sources and fluxes of scale energy in the overlap layer of wall turbulence. J. Fluid Mech. 771, 407–423.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.Google Scholar
Cook, A. W. & Zhou, Y. 2002 Energy transfer in Rayleigh-Taylor instability. Phys. Rev. E 66, 026312.Google Scholar
Cousteix, J. & Aupoix, B. 1989 Turbulence models for compressible flows. In Special Course Three-Dimensional Supersonic and Hypersonic Flows Including Separation. AGARD/FDP-VKI Special course.Google Scholar
Domaradzki, J. A., Liu, W., Hartel, C. & Kleiser, L. 1994 Energy transfer in numerically simulated wall-bounded turbulent flows. Phys. Fluids 6 (4), 1583–1599.Google Scholar
Domaradzki, J. A. & Rogallo, R. S. 1990 Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2 (3), 413–426.Google Scholar
Favre, A.1965 The equations of compressible turbulent gases. Tech. Rep. AD0622097. DTIC Document.CrossRefGoogle Scholar
Gatski, T. B. & Bonnet, J. P. 2013 Compressibility, Turbulence and High Speed Flow. Academic.Google Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33.Google Scholar
Ha Minh, H., Launder, B. E. & MacInnes, J. 1982 The turbulence modelling of variable density flows-a mixed-weighted decomposition. In Turbulent Shear Flows 3, pp. 291–308. Springer.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.Google Scholar
Kida, S. & Orszag, S. A. 1992 Energy and spectral dynamics in decaying compressible turbulence. J. Sci. Comput. 7 (1), 1–34.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kozuka, M., Seki, Y. & Kawamura, H. 2009 DNS of turbulent heat transfer in a channel flow with a high spatial resolution. Intl J. Heat Fluid Flow 30 (3), 514–524.CrossRefGoogle Scholar
Laadhari, F. 2002 On the evolution of maximum turbulent kinetic energy production in a channel flow. Phys. Fluids 14 (10), L65–L68.Google Scholar
Lechner, R., Sesterhenn, J. & Friedrich, R. 2001 Turbulent supersonic channel flow. J. Turbul. 2 (1), 001–001.CrossRefGoogle Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19 (1), 59–98.Google Scholar
Lesieur, M. 2008 Turbulence in Fluids. Springer.Google Scholar
Maeder, T., Adams, N. A. & Kleiser, L. 2001 Direct simulation of turbulent supersonic boundary layers by an extended temporal approach. J. Fluid Mech. 429, 187–216.Google Scholar
Marati, N., Casciola, C. M. & Piva, R. 2004 Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521, 191–215.Google Scholar
Morinishi, Y., Lundhomas, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143 (1), 90–124.Google Scholar
Morkovin, M. V. 1964 The Mechanics of Turbulence. Gordon and Breach.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 590. Phys. Fluids 11 (4), 943–945.Google Scholar
Nicoud, F. 2000 Conservative high-order finite-difference schemes for low-Mach number flows. J. Comput. Phys. 158 (1), 71–97.CrossRefGoogle Scholar
Paolucci, S.1982 On the filtering of sound from the Navier–Stokes equations. Tech. Rep. SAND82-8257. Sandia National Labs., Livermore, CA (USA).Google Scholar
Patel, A., Peeters, J., Boersma, B. & Pecnik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27 (9), 095101.Google Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2. 25. Phys. Fluids 16 (3), 530–545.Google Scholar
Reynolds, O. 1894 On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Proc. R. Soc. Lond. 56 (336–339), 40–45.Google Scholar
Rotta, J. C. 1959 Über den Einfluß der Machschen Zahl und des Wärmeübergangs auf das Wandgesetz turbulenter Strömung. Z. Flugwiss. 7, 264–274.Google Scholar
Sarkar, S. 1992 The pressure–dilatation correlation in compressible flows. Phys. Fluids A 4 (12), 2674–2682.Google Scholar
Serra, S., Toutant, A. & Bataille, F. 2012a Thermal large eddy simulation in a very simplified geometry of a solar receiver. Heat Transfer Engng 33 (6), 505–524.Google Scholar
Serra, S., Toutant, A., Bataille, F. & Zhou, Y. 2012b High-temperature gradient effect on a turbulent channel flow using thermal large-eddy simulation in physical and spectral spaces. J. Turbul. 13, N49.Google Scholar
Shadloo, M. S., Hadjadj, A. & Hussain, F. 2015 Statistical behavior of supersonic turbulent boundary layers with heat transfer at M = 2. Intl J. Heat Fluid Flow 53, 113–134.Google Scholar
Shahab, M. F., Lehnasch, G., Gatski, T. B. & Comte, P. 2011 Statistical characteristics of an isothermal, supersonic developing boundary layer flow from DNS data. Flow Turbul. Combust. 86 (3–4), 369–397.Google Scholar
Sutherland, W. 1893 The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Phil. Mag. J. Sci. 36 (223), 507–531.Google Scholar
Toutant, A. & Bataille, F. 2013 Turbulence statistics in a fully developed channel flow submitted to a high temperature gradient. Intl J. Therm. Sci. 74, 104–118.Google Scholar
Toutant, A., Labourasse, E., Lebaigue, O. & Simonin, O. 2008 DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: a priori tests for LES two-phase flow modelling. Comput. Fluids 37 (7), 877–886.Google Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.Google Scholar
Trofimova, A. V., Tejada-Martínez, A. E., Jansen, K. E. & Lahey, R. T. Jr. 2009 Direct numerical simulation of turbulent channel flows using a stabilized finite element method. Comput. Fluids 38 (4), 924–938.Google Scholar
Tsukahara, T., Seki, T., Kawamura, H. & Tochio, D. 2005 DNS of turbulent channel flow at very low Reynolds numbers. In Proc. of the Fourth International Symposium on Turbulence and Shear Flow Phenomena, pp. 935–940. Begel House Inc.Google Scholar
Vreman, A. W. & Kuerten, J. G. M. 2014 Comparison of direct numerical simulation databases of turbulent channel flow at Re 𝜏 = 180. Phys. Fluids 26 (1), 015102.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 48–56.Google Scholar
Yih, C.-S. 1960 Exact solutions for steady two-dimensional flow of a stratified fluid. J. Fluid Mech. 9 (02), 161–174.Google Scholar
Zhou, Y. 1993a Degrees of locality of energy transfer in the inertial range. Phys. Fluids A 5 (5), 1092–1094.Google Scholar
Zhou, Y. 1993b Interacting scales and energy transfer in isotropic turbulence. Phys. Fluids A 5 (10), 2511–2524.Google Scholar