Limitations of the near-wall k-epsilon turbulence model

Comparisons are given at two different Reynolds numbers between the measured turbulent kinetic energy in channel flow and the predictions of several near-wall variants of the k-e closure. Included among these are new calculations based on a form of the e equation that is consistent with the physically correct boundary condition. It is observed that all of the approaches fail to account for the large peak k value in the wall region that is evident in the experimental data. By contrasting the computed energy budget with its measured values it is shown that this defect may be attributed to a fundamental inconsistency in the commonly used model for the pressure diffu- sion term in the k equation near the boundary. HE k-e closure is widely utilized today in the prediction of the mean properties of turbulent flowfields. In recent years, extensions of its basic form have been developed to permit treatment of complex fluid motions, such as those found in curved pipes,1 compressible boundary layers,2 com- bustion chambers,3 etc. A strong incentive for the continued development and application of the k-e model has been the remarkable success it has achieved in the prediction of mean velocity fields in wall-bounded shear flows, such as occur in channels, pipes, and boundary layers.4"6 The success of the k-e closure in these relatively simple flows is not complete, however, since the high accuracy obtained for mean velocity is not duplicated in the case of the turbulent kinetic energy, k. A notable defect4'7"9 is the 25% or more underprediction of the large peak k value shown by Clark 10 and Kreplin and Eckelmann11 to occur at y+ «15 in a channel flow. For ap- plications where predictions of turbulence levels are impor- tant, such as in internal combustion engine simulations,12 this failure can be of great practical significance. It may be expected that major errors in the prediction of k stem from deficiencies in the low turbulent Reynolds number forms of the k-e equations which have been developed for the region adjacent to boundaries. Jones and Launder4 for- mulated the first such model that permitted k and e to be calculated down to a solid wall without the use of wall func- tions. Several more recent studies, including those of Lam and Bremhorst,7 Hassid and Poreh,8 and Chien,9 have at- tempted to improve upon the Jones and Launder approach, but these authors report only modest gains in the accuracy of k. The object of the present study is to elucidate the cause of this discrepancy by making direct comparisons between the terms in the exact and modeled energy equations. To ac- complish this, a set of new calculations was performed in which e was required to satisfy the physically correct bound- ary condition at the wall. It was revealed that the failure of the k-e model to predict the correct peak k value is most likely due to reliance on a flawed model for the pressure- velocity correlation in the k equation. This relation will be shown to be inconsistent with the experimentally measured values of the exact term as found by Kreplin and Eckelmann,11 and may be directly implicated in suppressing the peak k value. Removal of this limitation should allow for better predictions of k near solid boundaries.