k-ε Predictions of Heat Transfer in Turbulent Recirculating Flows Using an Improved Wall Treatment

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Abstract
Different wall treatments, proposed in conjunction with the k-ε turbulence model to predict heat or mass transfer rates, are critically reviewed. Published comparisons with experimental data for recirculating flows show that, in most cases, Nusselt or Sherwood numbers are not well predicted in the reattachment and redevelopment regions by methods based on conventional wall functions. The use of low-Reynolds-number models leads to even more unreliable results. A new treatment is proposed that formally retains classic wall functions and scaling based on the near-wall turbulent kinetic energy, but allows the nondimensional thickness of the viscous sublayer to vary as a function of the local turbulence intensity. The rationale for this approach, and its physical meaning, are discussed in the context of recent near-wall turbulence data. Using the k-ε computer code FLOW3D, results are compared with those from a standard treatment, and with experimental data, for different geometries including single and double backward-facing steps. Significant improvement in heat transfer predictions is demonstrated.