(401b) Numerical Simulation of Scalar Transport in Flows over Complex Surfaces

The solution of the Reynolds-averaged Navier-Stokes equations is, up to the moment, almost the only possibility for the simulation of complex engineering flow situations. Other ? more accurate ? techniques like large-eddy simulations require high computational efforts which are not affordable for actual design purposes now and in the near future. One of the main problems of commonly used k-ε-models in RANS simulations is their failure to accurately predict the flow behavior in regions with low Reynolds numbers, for example in the vicinity of walls. This is of particular interest for heat transfer calculations where the heat transfer takes place at the wall and for the calculations of the surface drag. In the past, the near-wall behavior of the models was altered by introducing artificial and non-physical damping factors. An attempt to overcome these problems was given by Durbin (1993). The recently presented k-ε-ζ-f-model of Hanjalic et al. (2004) overcomes the severe numerical stability problems of Durbin's model.

We present results from the numerical computation of the heat and mass transfer in flows over complex surfaces by means of the k-ε-ζ-f-model. For the numerical computations we use an unstructured parallel algorithm developed by B. Niceno and K. Hanjalic of the Department of Multiscale Physics, Delft University of Technology. The computational domain consists of a complex bottom surface and a flat top wall. As complex bottom surface we choose at first a sinusoidal wavy bottom wall where the wave propagates in the streamwise direction of the flow. At second, we use the superposition of two waves with the same wavelength and amplitude, one again propagating in the streamwise direction and the second wave propagating in the spanwise direction. This leads to a surface with periodic bumps in the streamwise and spanwise direction. The flow is fully inhomogeneous in all co-ordinate directions. The wavelengths and amplitude-to-wavelength ratios are equal for both geometries.

For the heat transfer calculations we use a distributed source located at the complex bottom wall which releases a constant heat flux into the mean flow. Periodic boundary conditions are used in the streamwise direction and the spanwise direction whereas a no-slip boundary condition is used at the bottom and top wall. For the mass transfer calculation we assessed a different kind of source. A point source is located at the crest of either the wavy surface or the bumpy surface. A low momentum turbulent plume is released from the point source. For this configuration, the computational domain is divided into two sub-domains. The first sub-domain is similar to the domain for the heat transfer calculations and is used to produce accurate inflow conditions for the second sub-domain. For the second sub-domain, an inflow boundary condition and a convective boundary condition is used in the streamwise direction. In the spanwise direction periodic boundary conditions are applied.

The results show generally good agreement with results from well-resolved large-eddy simulations and experiments. The used RANS model is able to produce accurate values of the pressure drop and the heat transfer characterized by the Nusselt number. The heat transfer from the wavy wall is increased by a factor of 3 compared to a plane channel flow. The Nusselt number for the bumpy surface is somewhat higher than for the wavy surface. Preliminary results show an increased pressure drop (30%) for the bumpy surface compared to a wavy wall. The RANS computations show satisfactory results for the spreading rate of the turbulent scalar plume and the values of the mean scalar concentration. The turbulent scalar fluxes are in fairly good agreement with results from large-eddy simulations.

References

Durbin PA (1993) A Reynolds stress model for near-wall turbulence. J Fluid Mech 249: 465-498

Hanjalic K; Popovac M; Hadziabdic M (2004) A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD. Int J Heat Fluid Fl 25: 1047-1051