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Direct numerical simulations of temporal compressible mixing layers in a Bethe–Zel'dovich–Thompson dense gas: influence of the convective Mach number

Published online by Cambridge University Press:  02 July 2021

Aurélien Vadrot Open the ORCID record for Aurélien Vadrot [Opens in a new window] ,
Alexis Giauque Open the ORCID record for Alexis Giauque [Opens in a new window]  and
Christophe Corre
Aurélien Vadrot*
Affiliation:
LMFA – Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134Ecully Cedex, France
Alexis Giauque
Affiliation:
LMFA – Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134Ecully Cedex, France
Christophe Corre
Affiliation:
LMFA – Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134Ecully Cedex, France
*
†Email address for correspondence: [email protected]
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Abstract

The present article investigates the effects of a BZT (Bethe–Zel'dovich–Thompson) dense gas (FC-70) on the development of turbulent compressible mixing layers at three different convective Mach numbers $M_c=0.1$, 1.1 and 2.2. This study extends a previous analysis conducted at $M_c=1.1$ (Vadrot et al., J. Fluid Mech., vol. 893, 2020) Several three-dimensional direct numerical simulations (DNS) of compressible mixing layers are performed with FC-70 using the fifth-order Martin–Hou thermodynamic equation of state (EoS) and air using the perfect gas EoS. After having carefully defined self-similar periods using the temporal evolution of the integrated streamwise production term, the evolutions of the mixing layer growth rate as a function of the convective Mach number are compared between perfect gas and dense gas flows. Results show major differences for the momentum thickness growth rate at $M_c=2.2$. The well-known compressibility-related decrease of the momentum thickness growth rate is reduced in the dense gas. Fluctuating thermodynamics quantities are strongly modified. In particular, temperature variations are suppressed, leading to an almost isothermal evolution. The small scales dynamics is also influenced by dense gas effects, which calls for a specific sub-grid-scale model when computing dense gas flows using large eddy simulation. Additional dense gas DNS are performed at three other initial thermodynamic operating points. DNS performed outside and inside the BZT inversion region do not show major differences. BZT effects themselves therefore only have a small impact on the mixing layer growth.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bethe, H.A. 1942 The theory of shock waves for an arbitrary equation of state. Tech. Paper 545. Office of Scientific Research and Development.Google Scholar
Cadieux, F., Domaradzki, J.A., Sayadi, T., Bose, T. & Duchaine, F. 2012 DNS and LES of separated flows at moderate Reynolds numbers. In Proceedings of the 2012 Summer Program, Center for Turbulence Research, NASA Ames/Stanford University, Stanford, CA, June, pp. 77–86.Google Scholar
Chung, T.H., Ajlan, M., Lee, L.L. & Starling, K.E. 1988 Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Ind. Engng Chem. Res. 27 (4), 671–679.CrossRefGoogle Scholar
Cinnella, P. & Congedo, P.M. 2005 Numerical solver for dense gas flows. AIAA J. 43 (11), 2458–2461.CrossRefGoogle Scholar
Cinnella, P. & Congedo, P.M. 2007 Inviscid and viscous aerodynamics of dense gases. J. Fluid Mech. 580, 179–217.CrossRefGoogle Scholar
Colin, O. & Rudgyard, M. 2000 Development of high-order Taylor–Galerkin schemes for LES. J. Comput. Phys. 162 (2), 338–371.CrossRefGoogle Scholar
Cook, A.W. & Cabot, W.H. 2004 A high-wavenumber viscosity for high-resolution numerical methods. J. Comput. Phys. 195 (2), 594–601.CrossRefGoogle Scholar
Cramer, M.S. 1989 Negative nonlinearity in selected fluorocarbons. Phys. Fluids A: Fluid Dyn. 1 (11), 1894–1897.CrossRefGoogle Scholar
Cramer, M.S. 1991 Nonclassical dynamics of classical gases. In Nonlinear Waves in Real Fluids, pp. 91–145. Springer.CrossRefGoogle Scholar
Cramer, M.S. & Kluwick, A. 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142, 9–37.CrossRefGoogle Scholar
Desoutter, G., Habchi, C., Cuenot, B. & Poinsot, T. 2009 DNS and modeling of the turbulent boundary layer over an evaporating liquid film. Intl J. Heat Mass Transfer 52 (25-26), 6028–6041.CrossRefGoogle Scholar
Durá Galiana, F.J., Wheeler, A.P.S. & Ong, J. 2016 A study of trailing-edge losses in organic rankine cycle turbines. Trans. ASME J. Turbomach. 138 (12).CrossRefGoogle Scholar
Freund, J.B., Lele, S.K. & Moin, P. 2000 Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech. 421, 229–267.CrossRefGoogle Scholar
Fu, S. & Li, Q. 2006 Numerical simulation of compressible mixing layers. Intl J. Heat Fluid Flow 27 (5), 895–901.CrossRefGoogle Scholar
Fujiwara, H., Matsuo, Y. & Arakawa, C. 2000 A turbulence model for the pressure–strain correlation term accounting for compressibility effects. Intl J. Heat Fluid Flow 21 (3), 354–358.CrossRefGoogle Scholar
Giauque, A., Corre, C. & Menghetti, M. 2017 Direct numerical simulations of homogeneous isotropic turbulence in a dense gas. J. Phys.: Conf. Ser. 821 (1), 012017.Google Scholar
Giauque, A., Corre, C. & Vadrot, A. 2020 Direct numerical simulations of forced homogeneous isotropic turbulence in a dense gas. J. Turbul. 21 (3), 186–208.CrossRefGoogle Scholar
Gloerfelt, X., Robinet, J.C., Sciacovelli, L., Cinnella, P. & Grasso, F. 2020 Dense-gas effects on compressible boundary-layer stability. J. Fluid Mech. 893.CrossRefGoogle Scholar
Guardone, A., Vigevano, L. & Argrow, B.M. 2004 Assessment of thermodynamic models for dense gas dynamics. Phys. Fluids 16 (11), 3878–3887.CrossRefGoogle Scholar
Hamba, F. 1999 Effects of pressure fluctuations on turbulence growth in compressible homogeneous shear flow. Phys. Fluids 11 (6), 1623–1635.CrossRefGoogle Scholar
Huang, S. & Fu, S. 2008 Modelling of pressure–strain correlation in compressible turbulent flow. Acta Mechanica Sin. 24 (1), 37–43.CrossRefGoogle Scholar
Kourta, A. & Sauvage, R. 2002 Computation of supersonic mixing layers. Phys. Fluids 14 (11), 3790–3797.CrossRefGoogle Scholar
Lee, S., Lele, S.K. & Moin, P. 1991 Eddy shocklets in decaying compressible turbulence. Phys. Fluids A: Fluid Dyn. 3 (4), 657–664.CrossRefGoogle Scholar
Luo, K.H. & Sandham, N.D. 1994 On the formation of small scales in a compressible mixing layer. In Direct and Large-Eddy Simulation I, pp. 335–346. Springer.CrossRefGoogle Scholar
Martin, J.J. & Hou, Y. 1955 Development of an equation of state for gases. AIChE J. 2 (4), 142–151.CrossRefGoogle Scholar
Martin, J.J., Kapoor, R.M. & De Nevers, N. 1959 An improved equation of state for gases. AIChE J. 5 (2), 159–160.CrossRefGoogle Scholar
Martínez Ferrer, P.J., Lehnasch, G. & Mura, A. 2017 Compressibility and heat release effects in high-speed reactive mixing layers I. Growth rates and turbulence characteristics. Combust. Flame 180, 284–303.CrossRefGoogle Scholar
Matsuno, K. & Lele, S.K. 2020 Compressibility effects in high speed turbulent shear layers – revisited. In AIAA Scitech 2020 Forum, p. 0573.Google Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30 (1), 539–578.CrossRefGoogle Scholar
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329–371.CrossRefGoogle Scholar
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477.CrossRefGoogle Scholar
Park, C.H. & Park, S.O. 2005 A compressible turbulence model for the pressure–strain correlation. J. Turbul. 6, N2.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M., Marié, S. & Grasso, F. 2015 Early evolution of the compressible mixing layer issued from two turbulent streams. J. Fluid Mech. 777, 196–218.CrossRefGoogle Scholar
Poinsot, T.J. & Lele, S.K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.CrossRefGoogle Scholar
Rossmann, T., Mungal, M.G. & Hanson, R.K. 2001 Evolution and growth of large scale structures in high compressibility mixing layers. In TSFP Digital Library Online. Begel House Inc.CrossRefGoogle Scholar
Sandham, N.D. & Reynolds, W.C. 1990 Compressible mixing layer: linear theory and direct simulation. AIAA J. 28 (4), 618–624.CrossRefGoogle Scholar
Sarkar, S. 1995 The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282, 163–186.CrossRefGoogle Scholar
Sarkar, S., Erlebacher, G., Hussaini, M.Y. & Kreiss, H.O. 1991 The analysis and modelling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493.CrossRefGoogle Scholar
Sarkar, S. & Lakshmanan, B. 1991 Application of a Reynolds stress turbulence model to the compressible shear layer. AIAA J. 29 (5), 743–749.CrossRefGoogle Scholar
Sciacovelli, L., Cinnella, P. & Gloerfelt, X. 2017 a Direct numerical simulations of supersonic turbulent channel flows of dense gases. J. Fluid Mech. 821, 153–199.CrossRefGoogle Scholar
Sciacovelli, L., Cinnella, P. & Grasso, F. 2017 b Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. 825, 515–549.CrossRefGoogle Scholar
Shuely, W.J. 1996 Model liquid selection based on extreme values of liquid state properties in a factor analysis. Tech. Rep. Edgewood Research Development and Engineering Center, MD.Google Scholar
Stephan, K. & Laesecke, A. 1985 The thermal conductivity of fluid air. J. Phys. Chem. Ref. Data 14 (1), 227–234.CrossRefGoogle Scholar
Thompson, P.A. 1971 A fundamental derivative in gasdynamics. Phys. Fluids 14 (9), 1843–1849.CrossRefGoogle Scholar
Vadrot, A., Giauque, A. & Corre, C. 2020 Analysis of turbulence characteristics in a temporal dense gas compressible mixing layer using direct numerical simulation. J. Fluid Mech. 893.CrossRefGoogle Scholar
Vreman, A.W., Sandham, N.D. & Luo, K.H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S., Xie, C., Zheng, Q., Wang, L.-P. & Chen, S. 2020 Effect of flow topology on the kinetic energy flux in compressible isotropic turbulence. J. Fluid Mech. 883.CrossRefGoogle Scholar
Wheeler, A.P.S. & Ong, J. 2014 A study of the three-dimensional unsteady real-gas flows within a transonic ORC turbine. In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers.CrossRefGoogle Scholar
White, F.M. 1998 Fluid Mechanics. McGraw-Hill.Google Scholar
Zel'dovich, J. 1946 On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 16 (4), 363–364.Google Scholar
Zeman, O. 1990 Dilatation dissipation: the concept and application in modeling compressible mixing layers. Phys. Fluids A: Fluid Dyn. 2 (2), 178–188.CrossRefGoogle Scholar
Zhou, Q., He, F. & Shen, M.Y. 2012 Direct numerical simulation of a spatially developing compressible plane mixing layer: flow structures and mean flow properties. J. Fluid Mech. 711, 1–32.CrossRefGoogle Scholar