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

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).