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Geometrical Properties of the Resolved-Scale Velocity and Temperature Fields Predicted using Large-Eddy Simulation

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Abstract

In this paper, local geometrical properties of the velocity and temperature fields of combined forced and natural convection in a vertical slot are studied using large-eddy simulation based on both numerical and analytical approaches. Previous studies on turbulence geometrical statistics appearing in the literature have primarily focused on either isothermal or isotropic turbulent flows; whereas in this work, we extend the scope of research to investigation of a wall-bounded thermal flow. In particular, we focus on studying the resolved helicity, enstrophy generation, local vortex stretching, and a variety of characteristic geometrical alignment patterns between the resolved velocity, vorticity, temperature gradient, subgrid-scale heat flux and the eigenvectors of the resolved strain rate tensor. In order to quantify the effect of buoyancy on the geometrical properties of the thermal flow field, a systematic comparative analysis has been conducted based on three different flow regimes (i.e., viscous sublayer, buffer layer and logarithmic layer) in both the hot and cold wall regions. The near-wall restriction on the geometrical property of the thermal flow field has been analyzed and some interesting wall-limiting geometrical alignment patterns in the form of Dirac delta functions are also reported.

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References

  1. Vieillefosse, P.: Internal motion of a small element of fluid in an inviscid flow. Physica A 125, 150–162 (1984)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Pelz, R.B., Yakhot, V., Orszag, S.A., Shtilman, L., Levich, E.: Velocity-vorticity patterns in turbulent flows. Phys. Rev. Lett. 54, 2505–2508 (1985)

    Article  ADS  Google Scholar 

  3. Ashurst, W.T., Kerstein, A.R., Kerr, R.M., Gibson, C.H.: Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 2343–2353 (1987)

    Article  ADS  Google Scholar 

  4. Kerr, R.M.: Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett. 59, 783–786 (1987)

    Article  ADS  Google Scholar 

  5. Honkan, A., Andreopoulos, Y.: Vorticity, strain-rate and dissipation characteristics in the near-wall region of turbulent boundary layers. J. Fluid Mech. 350, 29–96 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  6. Lund, T.S., Rogers, M.M.: An improved measure of strain state probability in turbulent flows. Phys. Fluids 6, 1838–1847 (1994)

    Article  MATH  ADS  Google Scholar 

  7. Rogers, M.M., Moin, P.: Helicity fluctuations in incompressible turbulent flows. Phys. Fluids 30, 2662–2671 (1987)

    Article  ADS  Google Scholar 

  8. Tsinober, A., Kit, E., Dracos, T.: Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169–192 (1992)

    Article  ADS  Google Scholar 

  9. Nomura, K.K., Post, G.K.: The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence. J. Fluid Mech. 377, 65–97 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Blackburn, H.M., Mansour, N.N., Cantwell, B.J.: Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Tsinober, A., Eggels, J.G.M., Nieuwstadt, F.T.M.: On alignments and small scale structure in turbulent pipe flow. Fluid Dyn. Res. 16, 297–310 (1995)

    Article  Google Scholar 

  12. She, Z.-S., Jackson, E., Orszag, S.A.: Structure and dynamics of homogeneous turbulence: models and simulations. Proc. R. Soc. Lond. A 434, 101–124 (1991)

    MATH  ADS  Google Scholar 

  13. Tao, B., Katz, J., Meneveau, C.: Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech. 457, 35–78 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Horiuti, K.: Roles of non-aligned eigenvectors of strain-rate and subgrid-scale stress tensors in turbulence generation. J. Fluid Mech. 491, 65–100 (2003)

    Article  MATH  ADS  Google Scholar 

  15. Borue, V., Orszag, S.A.: Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Higgins, C.W., Parlange, M.B., Meneveau, C.: Alignment trends of velocity gradients and subgrid-scale fluxes in the turbulent atmospheric boundary layer. Boundary-Layer Meteorol. 109, 59–83 (2003)

    Article  ADS  Google Scholar 

  17. Porté-Agel, F., Pahlow, M., Meneveau, C., Parlange, M.B.: Atmospheric stability effect on subgrid-scale physics for large-eddy simulation. Adv. Water Resour. 24, 1085–1102 (2001)

    Article  Google Scholar 

  18. Fureby, C., Grinstein, F.F.: Large eddy simulation of high-Reynolds-number free and wall-bounded flows. J. Comp. Phys. 181, 68–97 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. Wang, B.-C., Yee, E., Bergstrom, D.J.: Geometrical description of the subgrid-scale stress tensor based on Euler axis/angle. AIAA J. 44, 1106–1110 (2006)

    Article  ADS  Google Scholar 

  20. Wang, B.-C., Bergstrom, D.J., Yin, J., Yee, E.: Turbulence topologies predicted using large eddy simulation. J. Turbul. 7(34) (2006)

  21. Wang, B.-C., Yee, E., Bergstrom, D.J.: Geometrical properties of the vorticity vector derived using large-eddy simulation. Fluid Dyn. Res. 40, 123–154 (2008)

    Article  MATH  ADS  Google Scholar 

  22. Pullin, D.I.: A vortex-based model for the subgrid flux of a passive scalar. Phys. Fluids 12, 2311–2319 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  23. Misra, A., Pullin, D.I.: A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 2443–2454 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. Voelkl, T., Pullin, D.I., Chan, D.C.: A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 12, 1810–1825 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  25. Nomura, K.K., Elghobashi, S.E.: Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence. Phys. Fluids A 4, 606–625 (1992)

    Article  MATH  ADS  Google Scholar 

  26. Martín, J., Dopazo, C., Valiño, L.: Joint statistics of the scalar gradient and the velocity gradient in turbulence using linear diffusion models. Phys. Fluids 17(028101) (2005)

  27. Boratav, O.N., Elghobashi, S.E., Zhong, R.: On the alignment of strain, vorticity and scalar gradient in turbulent, buoyant, nonpremixed flames. Phys. Fluids 10, 2260–2267 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. Higgins, C.W., Parlange, M.B., Meneveau, C.: The heat flux and the temperature gradient in the lower atmosphere. Geophys. Res. Lett. 31(L22105) (2004)

  29. Soria, J., Sondergaard, R., Cantwell, B.J., Chong, M.S., Perry, A.E.: A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6, 871–884 (1994)

    Article  MATH  ADS  Google Scholar 

  30. Pope, S.B.: Turbulent Flows. Cambridge University, Cambridge, UK (2000)

    MATH  Google Scholar 

  31. Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT, Cambridge, MA (1972)

    Google Scholar 

  32. Taylor, G.I.: Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. Lond. A 164, 15–23 (1938)

    MATH  ADS  Google Scholar 

  33. Tsinober, A., Shtilman, L., Vaisburd, H.: A study of properties of vortex stretching and enstrophy generation in numerical and laboratory turbulence. Fluid Dyn. Res. 21, 477–494 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  34. Ruetsch, G.R., Maxey, M.R.: Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids A 3, 1587–1597 (1991)

    Article  ADS  Google Scholar 

  35. Andreotti, B.: Studying Burgers’ models to investigate the physical meaning of the alignments statistically observed in turbulence. Phys. Fluids 9, 735–742 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. Lesieur, M.: Turbulence in Fluids, 2nd Edition. Kluwer Academic, Dordrecht (1990)

    MATH  Google Scholar 

  37. Pelz, R.B., Shtilman, L., Tsinober, A.: The helical nature of unforced turbulent flows. Phys. Fluids 29, 3506–3508 (1986)

    Article  ADS  Google Scholar 

  38. Kasagi, N., Nishimura, M.: Direct numerical simulation of combined forced and natural turbulent convection in a vertical plane channel. Int. J. Heat Fluid Flow 18, 88–99 (1997). (DNS data available from www.thtlab.t.u-tokyo.ac.jp)

    Article  Google Scholar 

  39. Davidson, L., Čuturić, D., Peng, S.-H.: DNS in a plane vertical channel with and without buoyancy. In: Hanjalić, K., Nagano, Y., Tummers, M.J. (eds.) Proc. Turbulence Heat and Mass Transfer 4, pp. 401–408. Begell House (2003)

  40. Yin, J., Wang, B.-C., Bergstrom, D.J.: Large-eddy simulation of combined forced and natural convection in a vertical plane channel. Int. J. Heat Mass Trans. 50, 3848–3861 (2007)

    Article  MATH  Google Scholar 

  41. Kim, J., Moin, P.: Application of a fractional-Step method to incompressible Navier–Stokes equations. J. Comp. Phys. 59, 308–323 (1985)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  42. Rhie, C.M., Chow, W.L.: Numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA J. 21, 1525–1532 (1983)

    Article  MATH  ADS  Google Scholar 

  43. Lilly, D.K.: A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635 (1992)

    Article  ADS  Google Scholar 

  44. Moin, P., Squires, K., Cabot, W., Lee, S.: A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757 (1991)

    Article  MATH  ADS  Google Scholar 

  45. Wang, B.-C., Bergstrom, D.J.: A dynamic nonlinear subgrid-scale stress model. Phys. Fluids 17(035109) (2005)

  46. Peng, S.-H., Davidson, L.: On a subgrid-scale heat fux model for large eddy simulation of turbulent thermal flow. Int. J. Heat Mass Trans. 45, 1393–1405 (2002)

    Article  MATH  Google Scholar 

  47. Speziale, C.G.: On nonlinear k-l and k-ε models of turbulence. J. Fluid Mech. 178, 459–475 (1987)

    Article  MATH  ADS  Google Scholar 

  48. Gatski, T.B., Speziale, C.G.: On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254, 59–78 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  49. Wang, B.-C., Yin, J., Yee, E., Bergstrom, D.J.: A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection. Int. J. Heat Fluid Flow 28, 1227–1243 (2007)

    Article  MATH  Google Scholar 

  50. Wang, B.-C., Yin, J., Yee, E., Bergstrom, D.J.: A general dynamic linear tensor-diffusivity subgrid-scale heat flux model for large-eddy simulation of turbulent thermal flows. Numer. Heat Trans. Part B 51, 205–227 (2007)

    Article  ADS  Google Scholar 

  51. Kuroda, A., Kasagi, N., Hirata, M.: Direct numerical simulation of turbulent plane Couette-Poiseuille flows: effect of mean shear rate on the near-wall turbulence structures. In: Durst, F., Kasagi, N., Launder, B.E., Schmidt, F.W., Suzuki, K., Whitelaw, J.H. (eds.) Proc. Turbul. Shear Flows 9, pp. 241–257. Berlin: Springer-Verlag (1995)

    Google Scholar 

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

  53. Shtilman, L., Spector, M., Tsinober, A.: On some kinematic versus dynamic properties of homogeneous turbulence. J. Fluid Mech. 247, 65–77 (1993)

    Article  MATH  ADS  Google Scholar 

  54. Vincent, A., Meneguzzi, M.: The dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258, 245–254 (1994)

    Article  MATH  ADS  Google Scholar 

  55. Garcia, A., Gonzalez, M.: Analysis of passive scalar gradient alignment in a simplified three-dimensional case. Phys. Fluids 18(058101) (2006)

  56. Diamessis, P.J., Nomura, K.K.: Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence. Phys. Fluids 12, 1166–1188 (2000)

    Article  ADS  MATH  Google Scholar 

  57. Tsinober, A., Galanti, B.: Exploratory numerical experiments on the differences between genuine and ‘passive’ turbulence. Phys. Fluids 15, 3514–3531 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  58. Kang, H.S., Meneveau, C.: Passive scalar anisotropy in a heated turbulent wake: new observations and implications for large-eddy simulations. J. Fluid Mech. 442, 161–170 (2001)

    Article  MATH  ADS  Google Scholar 

  59. Brun, C., Friedrich, R.: Modeling the test SGS tensor T ij : an issue in the dynamic approach. Phys. Fluid 13, 2373–2385 (2001)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, Univ. of Saskatchewan, Saskatoon, Saskatchewan, Canada, S7N 5A9

    Jing Yin & Donald J. Bergstrom

  2. Defence R&D Canada—Suffield, STN Main, P.O. Box 4000, Medicine Hat, Alberta, Canada, T1A 8K6

    Bing-Chen Wang

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  1. Jing Yin
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  2. Bing-Chen Wang
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  3. Donald J. Bergstrom
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Correspondence to Donald J. Bergstrom.

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Yin, J., Wang, BC. & Bergstrom, D.J. Geometrical Properties of the Resolved-Scale Velocity and Temperature Fields Predicted using Large-Eddy Simulation. Flow Turbulence Combust 81, 39–75 (2008). https://doi.org/10.1007/s10494-008-9135-5

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