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Shock-Turbulence Interaction in Variable Density Flows

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Modeling and Simulation of Turbulent Mixing and Reaction

Part of the book series: Heat and Mass Transfer ((HMT))

Abstract

Accurate numerical simulations of shock-turbulence interaction (STI) are conducted by a hybrid monotonicity preserving-compact finite difference scheme for a detailed study of STI in variable density flows. Numerical accuracy of the simulations has been established using a series of grid, particle, and linear interaction approximation (LIA) convergence tests. The results show that for current parameter ranges, turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist in STI. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions with different densities. The correlation between rotation and strain is weaker in the multi-fluid case, which is shown to be the result of complex role density plays when the flow passes through the shock wave. Furthermore, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic velocity gradient tensor (VGT) is observed in the multi-fluid case. Lagrangian dynamics of the VGT and its invariants are studied and the pressure Hessian contributions are shown to be strongly affected by the shock wave and local density, making them important to the flow dynamics and turbulence structure.

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References

  1. H.S. Ribner, Convection of a pattern of vorticity through a shock wave. NACA TR-1164 (1954)

    Google Scholar 

  2. L.S.G. Kovasznay, Turbulence in supersonic flow. J. Aeronaut. Sci. 20, 657–674 (1953)

    Article  Google Scholar 

  3. S. Lee, S.K. Lele, P. Moin, Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533–562 (1993)

    Article  Google Scholar 

  4. R. Hannappel, R. Friedrich, Direct numerical simulation of a Mach 2 shock interacting with isotropic turbulence. Appl. Sci. Res. 54(3), 205–221 (1995)

    Article  Google Scholar 

  5. K. Mahesh, S. Lee, S.K. Lele, P. Moin, The interaction of an isotropic field of acoustic waves with a shock wave. J. Fluid Mech. 300, 383–407 (1995)

    Article  MathSciNet  Google Scholar 

  6. S. Lee, S.K. Lele, P. Moin, Interaction of isotropic turbulence with shock waves: effect of shock strength. J. Fluid Mech. 340, 225–247 (1997)

    Article  MathSciNet  Google Scholar 

  7. K. Mahesh, S.K. Lele, P. Moin, The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334, 353–379 (1997)

    Article  MathSciNet  Google Scholar 

  8. S. Jamme, J.-B. Cazalbou, F. Torres, P. Chassaing, Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence. Flow Turbul. Combust. 68(3), 227–268 (2002)

    Article  Google Scholar 

  9. J. Larsson, S.K. Lele, Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21(12), 126101 (2009)

    Article  Google Scholar 

  10. J. Larsson, I. Bermejo-Moreno, S.K. Lele, Reynolds- and Mach-number effects in canonical shock-turbulence interaction. J. Fluid Mech. 717, 293–321 (2013)

    Article  MathSciNet  Google Scholar 

  11. J. Ryu, D. Livescu, Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756, R1 (2014)

    Article  Google Scholar 

  12. D. Livescu, J. Ryu, Vorticity dynamics after the shock-turbulence interaction. Shock Waves 26(3), 241–251 (2016)

    Article  Google Scholar 

  13. R. Quadros, K. Sinha, J. Larsson, Turbulent energy flux generated by shock/homogeneous-turbulence interaction. J. Fluid Mech. 796, 113–157 (2016)

    Article  MathSciNet  Google Scholar 

  14. Y.P.M. Sethuraman, K. Sinha, J. Larsson, Thermodynamic fluctuations in canonical shock-turbulence interaction: effect of shock strength. Theor. Comp. Fluid Dyn. 32(5), 629–654 (2018)

    Article  MathSciNet  Google Scholar 

  15. Y. Tian, F. Jaberi, Z. Li, D. Livescu, Numerical study of variable density turbulence interaction with a normal shock wave. J. Fluid Mech. 829, 551–588 (2017)

    Article  MathSciNet  Google Scholar 

  16. Y. Tian, F.A. Jaberi, D. Livescu, Z. Li, Numerical simulation of multi-fluid shock-turbulence interaction, in AIP Conference Proceedings, vol. 1793, p. 150010 (AIP Publishing, 2017)

    Google Scholar 

  17. T. Jin, K. Luo, Q. Dai, J. Fan, Simulations of cellular detonation interaction with turbulent flows. AIAA J. 54(2), 419–433 (2015)

    Article  Google Scholar 

  18. C. Huete, T. Jin, D. Martínez-Ruiz, K. Luo, Interaction of a planar reacting shock wave with an isotropic turbulent vorticity field. Phys. Rev. E 96(5), 053104 (2017)

    Article  Google Scholar 

  19. M.S. Chong, A.E. Perry, B.J. Cantwell, A general classification of three-dimensional flow fields. Phys. Fluids A-Fluid 2(5), 765–777 (1990)

    Article  MathSciNet  Google Scholar 

  20. C. Meneveau, Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245 (2011)

    Article  MathSciNet  Google Scholar 

  21. M.S. Chong, J. Soria, A.E. Perry, J. Chacin, B.J. Cantwell, Y. Na, Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247 (1998)

    Article  MathSciNet  Google Scholar 

  22. A. Ooi, J. Martin, J. Soria, M.S. Chong, A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174 (1999)

    Article  MathSciNet  Google Scholar 

  23. L. Wang, X.Y. Lu, Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255–278 (2012)

    Article  MathSciNet  Google Scholar 

  24. Y. Tian, F. Jaberi, D. Livescu, Z. Li, Numerical study of shock–turbulence interactions in variable density flows, in Proceedings of TSFP-10 (2017) Chicago, vol. 3 of International Symposium on Turbulence and Shear Flow Phenomena, pp. 8C–3 (2017)

    Google Scholar 

  25. Y. Tian, F. Jaberi, D. Livescu, Density effects on the flow structure in multi-fluid shock-turbulence interaction, in 2018 AIAA Aerospace Sciences Meeting, p. 0374 (2018)

    Google Scholar 

  26. R. Boukharfane, Z. Bouali, A. Mura, Evolution of scalar and velocity dynamics in planar shock-turbulence interaction. Shock Waves 28(6), 1117–1141 (2018)

    Article  Google Scholar 

  27. A. Suresh, H.T. Huynh, Accurate monotonicity-preserving schemes with Runge-Kutta time stepping. J. Comput. Phys. 136, 83–99 (1997)

    Article  MathSciNet  Google Scholar 

  28. Z. Li, F.A. Jaberi, A high-order finite difference method for numerical simulations of supersonic turbulent flows. Int. J. Numer. Meth. Fl. 68, 740–766 (2012)

    Article  MathSciNet  Google Scholar 

  29. S.K. Lele, Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42 (1992)

    Article  MathSciNet  Google Scholar 

  30. S. Lee, S.K. Lele, P. Moin, Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow. Phys. Fluids A-Fluid 4(7), 1521–1530 (1992)

    Article  Google Scholar 

  31. D. Livescu, J.R. Ristorcelli, Buoyancy-driven variable-density turbulence. J. Fluid Mech. 591, 43–71 (2007)

    Article  Google Scholar 

  32. D. Livescu, Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh-Taylor instability. Phil. Trans. R. Soc. A 371, 20120185 (2013)

    Article  MathSciNet  Google Scholar 

  33. P.K. Yeung, S.B. Pope, An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79(2), 373–416 (1988)

    Article  Google Scholar 

  34. M. Lombardini, D.J. Hill, D.I. Pullin, D.I. Meiron, Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech. 670, 439–480 (2011)

    Article  Google Scholar 

  35. D. Livescu, J.R. Ristorcelli, Mixing asymmetry in variable density turbulence, in Advances in Turbulence XII, ed. by B. Eckhardt, vol. 132 of Springer Proceedings in Physics, pp. 545–548 (Springer, 2009)

    Google Scholar 

  36. D. Livescu, J.R. Ristorcelli, M.R. Petersen, R.A. Gore, New phenomena in variable-density Rayleigh-Taylor turbulence. Phys. Scripta T142, 014015 (2010)

    Article  Google Scholar 

  37. F.A. Jaberi, D. Livescu, C.K. Madnia, Characteristics of chemically reacting compressible homogeneous turbulence. Phys. Fluids 12(5), 1189–1209 (2000)

    Article  Google Scholar 

  38. S. Pirozzoli, F. Grasso, Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16(12), 4386–4407 (2004)

    Article  Google Scholar 

  39. S. Suman, S.S. Girimaji, Velocity gradient invariants and local flow-field topology in compressible turbulence. J. Turbul. 11(2), 1–24 (2010)

    Article  Google Scholar 

  40. Y.B. Chu, X.Y. Lu, Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438 (2013)

    Article  MathSciNet  Google Scholar 

  41. N.S. Vaghefi, C.K. Madnia, Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 67–94 (2015)

    Article  MathSciNet  Google Scholar 

  42. J. Wang, Y. Shi, L.P. Wang, Z. Xiao, X.T. He, S. Chen, Effect of compressibility on the small-scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631 (2012)

    Article  MathSciNet  Google Scholar 

  43. Y. Tian, F. Jaberi, D. Livescu, Shock propagation in media with non-uniform density, in International Symposium on Shock Waves, pp. 1167–1175 (Springer, 2017)

    Google Scholar 

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Acknowledgements

This work was performed under the auspices of DOE. YT and FJ were supported by Los Alamos National Laboratory, under Grant No. 319838. Los Alamos National Laboratory is managed by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract 89233218CNA000001. Computational resources were provided by the High Performance Computing Center at Michigan State University and Texas Advanced Computing Center (TACC) at The University of Texas at Austin.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Yifeng Tian & Farhad Jaberi

  2. Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Daniel Livescu

Authors
  1. Yifeng Tian
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  2. Farhad Jaberi
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  3. Daniel Livescu
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Correspondence to Daniel Livescu .

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Editors and Affiliations

  1. CCS-2, Computational Physics and Methods, Los Alamos National Laboratory, Los Alamos, NM, USA

    Daniel Livescu

  2. School of Engineering, University of Pittsburgh, Pittsburgh, USA

    Arash G. Nouri

  3. Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA

    Francine Battaglia

  4. School of Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Peyman Givi

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Tian, Y., Jaberi, F., Livescu, D. (2020). Shock-Turbulence Interaction in Variable Density Flows. In: Livescu, D., Nouri, A., Battaglia, F., Givi, P. (eds) Modeling and Simulation of Turbulent Mixing and Reaction. Heat and Mass Transfer. Springer, Singapore. https://doi.org/10.1007/978-981-15-2643-5_4

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  • DOI: https://doi.org/10.1007/978-981-15-2643-5_4

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  • Online ISBN: 978-981-15-2643-5

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