Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T09:27:50.554Z Has data issue: false hasContentIssue false
  • English
  • Français

Assessment of two-equation models of turbulent passive-scalar diffusion in channel flow

Published online by Cambridge University Press:  26 April 2006

Kiyosi Horiuti
Kiyosi Horiuti
Affiliation:
Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi. Minato-ku, Tokyo 106, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

Models for the transport of passive scalar in turbulent flow were investigated using databases derived from numerical solutions of the Navier—Stokes equations for fully developed plane channel flow, these databases being generated using large-eddy and direct numerical simulation techniques. Their reliability has been established by comparison with the experimental measurements of Hishida. Nagano & Tagawa (1986). The present paper compares these simulations and calculations using the Nagano & Kim (1988) ‘two-equation’ model for the scalar variance (kθ) and scalar variance dissipation (εθ). This model accounts for the dependence of flow quantities on the Prandtl number by expressing eddy diffusivity in terms of the ratio of the timescales of velocity and scalar fluctuations. However, the statistical analysis by Yoshizawa (1988) showed that there was an inconsistency in the definition of the isotropic eddy diffusivity in the Nagano—Kim model, the implications of which are clearly demonstrated by the results of this paper where large-eddy simulation and direct numerical simulation (LES/DNS) databases are used to compute the quantities contained in both models. An extension of the Nagano-Kim model is proposed which resolves these inconsistencies, and a further development of this model is given in which the anisotropic scalar fluxes are calculated. Near a rigid surface, a third-order ‘anisotropic representation’ of scalar fluxes may be used as an alternative model for reducing the eddy diffusivity, instead of the conventional ‘damping functions’. This model is similar but distinct from the algebraic scalar flux model of Rogers, Mansour & Reynolds (1989). A third aspect of this paper is the use of the LES/DNS databases to evaluate certain coefficients (those for modelling the pressure-scalar gradient terms) of another model of a similar type, namely the algebraic scalar flux model of Launder (1975).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 405 - 433
Copyright
© 1992 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

Antonopoulos-Domis, M. 1981 Large-eddy simulation of a passive scalar in isotropic turbulence. J. Fluid Mech. 104, 55–79.Google Scholar
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1980 Improved subgrid scale models for large eddy simulation. AIAA paper 80–1357.Google Scholar
Beguier, C., Dekeyser, I. & Launder, B. E. 1978 Ratio of scalar and velocity dissipation time scales in shear flow turbulence. Phys. Fluids 21, 307–310.Google Scholar
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577–594.Google Scholar
Bremhorst, K. & Bullock, K. J. 1970 Spectral measurements of temperature and longitudinal velocity fluctuations in fully developed pipe flow. Intl J. Heat Mass Transfer 13, 1313–1329.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81–139.Google Scholar
Clark, J. A. 1968 A study of incompressible turbulent boundary layers in channel flow. Trans. ASME D: J. Basic Engng 90, 455–468.Google Scholar
Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1977 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16.Google Scholar
Elgobashi, S. E. & Launder, B. E. 1983 Turbulent time scales and the dissipation rate of temperature variance in the thermal mixing layer. Phys. Fluids 26, 2415–2419.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
Gibson, M. M., Verriopoulos, C. A. & Nagano, Y. 1982 Measurements in the heated turbulent boundary layer on a mildly curved convex surface. In Turbulent Shear Flows 3 (ed. L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 80–95. Springer.
Grötzbach, G. & Schumann, U. 1979 Direct numerical simulation of turbulent velocity, pressure and temperature fields in channel flows. In Turbulent Shear Flows 1 (ed. F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 370–385. Springer.
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Hishida, M., Nagano, Y. & Tagawa, M. 1986 Transport processes of heat and momentum in the wall region of turbulent pipe flow. Proc. 8th Intl Symp. on Heat Transfer Conf. San Francisco, California, vol. 3, pp. 925–930.
Horiuti, K. 1985 Large eddy simulations of turbulent channel flow by one-equation modeling. J. Phys. Soc. Japan 54, 2855–2865.Google Scholar
Horiuti, K. 1987 Comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow. J. Comp. Phys. 71, 343–370.Google Scholar
Horiuti, K. 1988 Numerical simulation of turbulent channel flow at low and high Reynolds numbers. In Transport Phenomena in Turbulent Flows: Theory, Experiment and Numerical Simulation (ed. M. Hirata & N. Kasagi), pp. 743–755. Hemisphere.
Horiuti, K. 1989 The role of the Bardina model in large eddy simulation of turbulent channel flow. Phys. Fluids A 1, 426–428.Google Scholar
Horiuti, K. 1990 Higher order terms in anisotropic representation of the Reynolds stresses. Phys. Fluids A 2, 1708–1710.Google Scholar
Horiuti, K. 1991a A proper energy scale in the subgrid scale eddy viscosity of large eddy simulation. Submitted to Phys. Fluids A.Google Scholar
Horiuti, K. 1991b Validation of subgrid scale models for large eddy simulation of passive scalar. In preparation.
Hussain, A. K. M. F. & Reynolds, W. C. 1975 Measurements in fully developed turbulent channel flow. Trans. ASME I: J. Fluids Engng 97, 568–578.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kim, J. 1988 Investigation of heat and momentum transport in turbulent flows via numerical simulations. In Transport Phenomena in Turbulent Flows: Theory, Experiment and Numerical Simulation (ed. M. Hirata & N. Kasagi), pp. 715–729. Hemisphere.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.Google Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Tech. Note 3178.Google Scholar
Laufer, J. 1951 Investigation of turbulent flow in a two—dimensional channel. NACA Rep. 1053.Google Scholar
Launder, B. E. 1975 On the effects of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech. 67, 569–581.Google Scholar
Leslie, D. C. 1973 Developments in the Theory of Turbulence. Oxford University Press.
Mansour, N. N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.Google Scholar
Myong, H. K. 1988 Fundamental studies on a two-equation turbulence model for numerical predictions of wall-bounded shear flow and heat transfer. PhD dissertation, Dept of Mechanical Engineering, University of Tokyo.
Nagano, Y. & Hisida, M. 1985 Production and dissipation of turbulent velocity and temperature fluctuations in fully developed pipe flow. Proc. 5th Symp. on Turb. Shear Flows, Cornell University, Ithaca, pp. 1419–1424.
Nagano, Y. & Kim, C. 1988 A two-equation model for heat transport in wall turbulent shear flows. Trans. ASME C: J. Heat Transfer 110, 583–589.Google Scholar
Nagano, Y., Tagawa, M. & Niimi, M. 1988 A two equation model for heat transfer taking into account the near-wall limiting behaviour of turbulence. Proc. 25th Natl Heat Transfer Symp. of Japan, vol. 2, pp. 166–168 (in Japanese).
Nakajima, M., Fukui, K., Ueda, H. & Mizushina, T. 1980 Buoyancy effects of turbulent transport in combined free and forced convection between vertical parallel plates. Intl J. Heat Mass Transfer 23, 1325–1336.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
Nisizima, S. & Yoshizawa, A. 1987 Turbulent channel and Couette flows using an anisotropic k—e model. AIAA J. 25, 414–420.Google Scholar
Piomelli, U., Moin, P. & Ferziger, J. H. 1988 Model consistency in large eddy simulation of turbulent channel flows. Phys. Fluids 31, 1844–1891.Google Scholar
Pope, S. B. 1983 Consistent modeling of scalars in turbulent flows. Phys. Fluids 26, 404–408.Google Scholar
Rogers, M. M., Mansour, N. N. & Reynolds, W. C. 1989 An algebraic model for the turbulent flux of a passive scalar. J. Fluid Mech. 203, 77–101.Google Scholar
Rubinstein, R. & Barton, J. M. 1990 Nonlinear Reynolds stress models and the renormalization group. Phys. Fluids A 2, 1472–1476.Google Scholar
Rubinstein, R. & Barton, J. M. 1991 Renormalization group analysis of anisotropic diffusion in turbulent shear flows. Phys. Fluids A 3, 415–421.Google Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulation of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 376–404.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weather Rev. 91, 99–164.Google Scholar
Speziale, C. G. 1987 On nonlinear K-l and K-e models of turbulence. J. Fluid Mech. 178, 459–475.Google Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. J. Fluid Mech. 104, 311–367.Google Scholar
Tsai, H. M., Voke, P. R. & Leslie, D. C. 1987 Numerical investigation of a combined free and forced convection turbulent channel flow. Proc. 6th Symp. of Turb. Shear Flows, Toulouse, pp. 531–536.
Van Driest, E. R. 1956 On turbulent flow near a wall. J. Aero. Sci. 23, 1007–1011.Google Scholar
Wassel, A. T. & Catton, I. 1973 Calculation of turbulent boundary layers over flat plates with different phenomenological theories of turbulence and various turbulent Prandtl number. Intl J. Heat Mass Transfer 16, 1547–1563.Google Scholar
Webster, C. A. G. 1964 An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech. 19, 221–245.Google Scholar
Yoshizawa, A. 1978 A governing equation for the small-scale turbulence. II. Modified DIA approach and Kolmogorov's -5/3 power law. J. Phys. Soc. Japan 45, 1734–1740.Google Scholar
Yoshizawa, A. 1979 Statistical approach to inhomogeneous turbulent diffusion: general formulation and diffusion of a passive scalar in wall turbulence. J. Phys. Soc. Japan 47, 659–662.Google Scholar
Yoshizawa, A. 1985 Statistical analysis of the anisotropy of scalar diffusion in turbulent shear flows. Phys. Fluids 28, 3226–3231.Google Scholar
Yoshizawa, A. 1988 Statistical modelling of passive-scalar diffusion in turbulent shear flow. J. Fluid Mech. 195, 541–555.Google Scholar