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Assessment of Five SGS Models for Low-R e m MHD Turbulence

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Abstract

Assessment of three regularization-based and two eddy-viscosity-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are carried out in the context of magnetohydrodynamic (MHD) decaying homogeneous turbulence (DHT) with a Taylor scale Reynolds number (R e λ ) of 120 and a MHD transition-to-turbulence Taylor-Green vortex (TGV) problems with a Reynolds number of 3000, through direct comparisons to direct numerical simulations (DNS). Simulations are conducted using the low-magnetic Reynolds number approximation (R e m <<1). LES predictions using the regularization-based Leray- α,LANS- α, and Clark- α SGS models, along with the eddy viscosity-based non-dynamic Smagorinsky and the dynamic Smagorinsky models are compared to in-house DNS for DHT and previous results for TGV. With regard to the regularization models, this work represents their first application to MHD turbulence. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields made between the varying magnetic field cases demonstrated that the regularization models performed poorly compared to the eddy-viscosity models for all MHD cases, but the comparisons improved with increase in magnitude of magnetic field, due to a decrease in the population of SGS eddies within the flow field.

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References

  1. Agullo, O., Muller, W., Knaepen, B., Carati, D.: Large eddy simulation of decaying magnetohydrodynamic turbulence with dynamic subgrid-modeling. Phys. Plasmas 8, 3502–3505 (2001)

    Article  Google Scholar 

  2. Bensow, R., Larson, M., Vesterlund, P.: Vorticity-strain residual-based turbulence modelling of the Taylor-Green vortex. Int. J. Numer. Meth. Fluids 54, 745–756 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Biskamp, D.: Magnetohydrodynamic Turbulence. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  4. Brachet, M.E.: Direct numerical simulation of three-dimensional turbulence in Taylor-Green vortex. Fluid Dynamics Research 8, 1–8 (1991)

    Article  Google Scholar 

  5. Brachet, M.E., Meiron, D.I., Orszag, S.A., Nickel, B.G., Morf, R.H., Frisch, U.: Small scale structure of the Taylor-Green vortex. J. Fluid Mech. 130, 411–452 (1983)

    Article  MATH  Google Scholar 

  6. Burattini, P., Kinet, M., Carati, D., Knaepen, B.: Anisotropy of velocity spectra in quasistatic magnetohydrodynamic turbulence. Phys. Fluids 20(165), 110 (2008)

    MATH  Google Scholar 

  7. Burattini, P., Zikanov, O., Knaepen, B.: Decay of magnetohydrodynamic turbulence at low magnetic Reynolds number. J. Fluid Mech 657, 502–538 (2010)

    Article  MATH  Google Scholar 

  8. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral methods in fluid dynamics. Springer-Verlag, New York (1987)

    MATH  Google Scholar 

  9. Chandy, A.J., Frankel, S.H.: Regularization-based sub-grid scale (sgs) models for large eddy simulations (les) of high-re decaying isotropic turbulence. J. Turbul. 10(10) (2009)

  10. Chandy, A.J., Frankel, S.H.: The t-model as a large eddy simulation model for Navier-Stokes equations. SIAM Multiscale Model Sim. J. 8, 445–462 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chandy, A.J., Frankel, S.H.: Leray- α les of magnetohydrodynamic turbulence at low magnetic Reynolds number. J. Turbul., N17 (2011)

  12. Chen, S., Foias, C., Holm, D., Olson, E., Titi, E.: Wynne: A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. Phys. Fluids 11, 2343–2353 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen, S., Foias, C., Holm, D., Olson, E., Titi, E., Wynne, S.: Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Let. 81, 5338–5341 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Chen, S., Holm, D., Margolin, L.G., Zhang, R.: Direct numerical simulations of the Navier-Stokes alpha model. Phys. D Nonlinear Phenom 133, 66–83 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Cheskidov, A., Holm, D., Olson, E., Edriss, S.T.: On a leray- α model of turbulence. Proc. Royal Soc. London, A 461, 629–649 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Cho, J., Lazarian, A., Vishniac, E.: MHD turbulence: Scaling laws and astrophysical applications. Springer, New York (2003)

    Google Scholar 

  17. Clark, R.A., Ferziger, J.H., Reynolds, W.C.: Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16 (1979)

    Article  MATH  Google Scholar 

  18. Davidson, P.: Magnetohydrodynamics in materials processing. Ann. Rev. Fluid. Mech. 31, 273–285 (1999)

    Article  Google Scholar 

  19. Davidson, P.: Introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  20. Drikakis, D., Fureby, C., Grinstein, F., Youngs, D.: Simulation of transition and turbulence decay in the Taylor-Green vortex. J. Turbulence 8, 20 (2007)

    Article  MATH  Google Scholar 

  21. Fox, R.O.: Computational models for turbulent reacting flows. Cambridge University Press (2003)

  22. Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A: Fluid Dynamics (1989-1993) 3, 1760–1765 (1991)

    Article  MATH  Google Scholar 

  23. Geurts, B.J.: Holm: Leray and LANS- α modelling of turbulent mixing. J. Turbulence 7, 1–33 (2006)

    Article  MathSciNet  Google Scholar 

  24. Geurts, B.J., Holm, D.: Regularization modelling for large-eddy simulation. Phys. Fluids 15, L13—L16 (2003)

    Article  MathSciNet  Google Scholar 

  25. Geurts, B.J., Kuczaj, A., Titi, E.: Regularization modelling for large-eddy simulation of homogeneous isotropic decaying turbulence. J. Phys. A: Math. Theor. 41 (344), 008 (2008)

    MathSciNet  MATH  Google Scholar 

  26. Graham, J., Holm, D., Mininni, P., Pouquet, A.: Three regularization models of the Navier-Stokes equations. Phys. Fluids 20(035), 107 (2008)

    MATH  Google Scholar 

  27. Grinstein, F.F., Margolin, L.G., Rider, W.J.: Implicit large eddy simulation: computing turbulent fluid dynamics. Cambridge University Press (2007)

  28. Highes, T.: Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods. Comput. Meth. Appl. Mech. Engg. 127, 387–401 (1995)

    Article  Google Scholar 

  29. Kang, H., Chester, S., Meneveau, C.: Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy-simulation. J. Fluid Mech. 480, 129–160 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kassinos, S., Knaepen, B., Carati, D.: The transport of a passive scalar in magnetohydrodynamic turbulence subjected to mean shear and frame rotation. Phys. Fluids 19(015), 105 (2007)

    MATH  Google Scholar 

  31. KC, A.: Numerical simulations of magnetohydrodynamic flow and heat transfer. University of Akron, Master’s thesis (2014)

    Google Scholar 

  32. Knaepen, B., Kassinos, S., Carati, D.: Magnetohydrodynamic turbulence at moderate magnetic Reynolds number. J. Fluid Mech. 513, 199–220 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  33. Knaepen, B., Moin, P.: Large eddy simulation of conductive flows at low magnetic Reynolds number. Phys. Fluids 16, 1255–1261 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  34. Lilly, D.: The representation of small-scale turbulence in numerical simulation experiments. 320-1951, 195–210. Scientific Computing Symposium Environmental Sciences (1967)

  35. Moffatt, H.: On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571–592 (1967)

    Article  Google Scholar 

  36. Mohseni, K., Kosovic, B., Shkoller, S., Marsden, J.E.: Numerical simulations of the lagrangian averaged Navier-Stokes equations for homogenous isotropic turbulence. Phys. Fluids 15, 524–544 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  37. Orszag, S.A.: Numerical simulation of the Taylor-Green vortex. Lect. Notes Comput. Sci. 11, 50–64 (1973)

    Article  Google Scholar 

  38. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  39. Reeuwijk, M.V., Jonker, H.J.J., Hanjali, K.: Incompressibility of the leray- α model for wall-bounded flows. Phys. Fluids 18(018), 103 (2006)

    MathSciNet  Google Scholar 

  40. Roberts, P.: An Introduction to Magnetohydrodynamics. Elsevier, New York (1967)

    Google Scholar 

  41. Rogallo, R.S.: Numerical experiments in homogeneous turbulence. NASA TM 81315, NASA (1981)

  42. Sagaut, P.: Large eddy simulation for incompressible flows: An introduction, Third Edition. Springer, New York (2006)

    MATH  Google Scholar 

  43. Schumann, U.: Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field. J. Fluid Mech. 74, 31–58 (1976)

    Article  MATH  Google Scholar 

  44. Smagorinsky, J.: General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weather Rev. 91(3), 99–164 (1963)

    Article  Google Scholar 

  45. Su, M., Chen, Q., Chiang, C.M.: Comparison of different subgrid-scale models of large eddy simulation for indoor airflow modeling. J. Fluids Eng. 123, 628–639 (2001)

    Article  Google Scholar 

  46. Vorobev, A., Zikanov, O., Davidson, P., Knaepen, B.: Anisotropy of magnetohydrodynamic turbulence and low magnetic Reynolds number. Phys. Fluids 16(125), 105 (2005)

    MathSciNet  MATH  Google Scholar 

  47. Zikanov, O., Thess, A.: Direct numerical simulation of forces mhd turbulence at low magnetic Reynolds number. J. Fluid Mech. 358, 299–333 (1998)

    Article  MATH  Google Scholar 

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  1. Department of Mechanical Engineering, University of Akron, Akron, OH, 44325-3903, USA

    Amar KC & Abhilash J. Chandy

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  1. Amar KC
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  2. Abhilash J. Chandy
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Correspondence to Abhilash J. Chandy.

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KC, A., Chandy, A.J. Assessment of Five SGS Models for Low-R e m MHD Turbulence. Flow Turbulence Combust 96, 693–716 (2016). https://doi.org/10.1007/s10494-015-9657-6

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