Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-22T21:58:06.226Z Has data issue: false hasContentIssue false
  • English
  • Français

An algebraic model for the turbulent flux of a passive scalar

Published online by Cambridge University Press:  26 April 2006

Michael M. Rogers ,
Nagi N. Mansour  and
William C. Reynolds
Michael M. Rogers
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Nagi N. Mansour
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
William C. Reynolds
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The behaviour of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow has been studied using direct numerical simulations of the unsteady incompressible Navier-Stokes equations with 128 × 128 × 128 grid points. It is found that, for all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are approximately aligned with the scalar flux vector itself. In addition, the time derivative of the scalar flux is also approximately aligned with the flux vector for the developed fields (corresponding to roughly constant correlation coefficients). These alignments lead directly to a gradient transport model with a tensor turbulent diffusivity. The simulation results are used to fit a dimensionless model coefficient as a function of the turbulence Reynolds and Péclet numbers. The model is tested against two different passive-scalar fields in fully developed turbulent channel flow (also generated by direct numerical simulation) and is found to predict the scalar flux quite well throughout the entire channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 203 , June 1989 , pp. 77 - 101
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K.: 1949 Diffusion in a field of homogeneous turbulence. Austral. J. Sci. Res. A2, 437–450.Google Scholar
Boussinesq, J.: 1877 Essai sur la théorie des eaux courantes. Mem. Pres. Div. Savants Acad. Sci. Paris 23, 46.Google Scholar
Corrsin, S.: 1974 Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys. 18A, 25–60.Google Scholar
Gibson, M. M. & Launder, B. E., 1976 On the calculation of horizontal, turbulent, free shear flows under gravitational influence. Trans. ASME C J. Heat Transfer 98, 81–87.Google Scholar
Kays, W. M. & Crawford, M. E., 1980 Convective Heat and Mass Transfer, 2nd edn. McGraw-Hill.
Kim, J. & Moin, P., 1987 Transport of passive scalars in a turbulent channel flow. Proc. 6th Symp. on Turbulent Shear Flows, Toulouse, France, September 7–9, 1987, pp. 5-2-1–5-2-6.Google Scholar
Kim, J., Moin, P. & Moser, R. D., 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Launder, B. E.: 1978 Heat and mass transport. In Turbulence (ed. P. Bradshaw). Topics in Applied Physics, vol. 12, pp. 231–287. Springer.
Lee, M. J. & Reynolds, W. C., 1985 Numerical experiments on the structure of homogeneous turbulence. Dept. Mech. Engng. Rep. TF-24. Stanford University, Stanford, California.
Lumley, J. L.: 1978 Computational modelling of turbulent flows. Adv. Appl. Mech. 18, 123–176.Google Scholar
Newman, G. R., Launder, B. E. & Lumley, J. L., 1981 Modelling the behaviour of homogeneous scalar turbulence. J. Fluid Mech. 111, 217–232.Google Scholar
Orszag, S. A. & Patterson, G. S., 1972 Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28, 76–79.Google Scholar
Pope, S. B.: 1983 Consistent modeling of scalars in turbulent flows. Phys. Fluids 26, 404–408.Google Scholar
Richardson, L. F.: 1920 The supply of energy from and to atmospheric eddies. Proc. R. Soc. Lond. A 97, 354–373.Google Scholar
Rogallo, R. S.: 1977 An ILLIAC program for the numerical simulation of homogeneous incompressible turbulence. NASA Tech. Mem. 73203.Google Scholar
Rogallo, R. S.: 1981 Numerical experiments in homogeneous turbulence. NASA Tech. Mem. 81315.Google Scholar
Rogers, M. M. & Moin, P., 1987 The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66.Google Scholar
Rogers, M. M., Moin, P. & Reynolds, W. C., 1986 The structure and modeling of the hydrodynamic and passive scalar fields in homogeneous turbulent shear flow. Dept. Mech. Engng Rep. TF-25. Stanford University, Stanford, California.
Shih, T.-H. & Lumley, J. L. 1986 Influence of timescale ratio on scalar flux relaxation: modelling Sirivat & Warhafts homogeneous passive scalar fluctuations. J. Fluid Mech. 162, 211–222.Google Scholar
Shirani, E., Ferziger, J. H. & Reynolds, W. C., 1981 Mixing of a passive scalar in isotropic and sheared homogeneous turbulence. Dept. Mech. Engng Rep. TF-15. Stanford University, Stanford, California.
Sirivat, A. & Warhaft, Z., 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323–346.Google Scholar
Sreenivasan, K. R., Tavoularis, S. & Corrsin, S., 1981 A test of gradient transport and its generalizations. In Turbulent Shear Flows 3 (ed. L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 96–112. Springer.
Tavoularis, S. & Corrsin, S., 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311–347.Google Scholar
Tavoularis, S. & Corrsin, S., 1985 Effects of shear on the turbulent diffusivity tensor. Intl J. Heat Mass Transfer 28, 265–276.Google Scholar
Zeman, O. & Lumley, J. L., 1979 Buoyancy effects in entraining turbulent boundary layers: a second-order closure study. In Turbulent Shear Flows 1 (ed. F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 295–305. Springer.