A more robust wall model for use with the two-equation turbulence model

Abstract

The applicability of computational fluid dynamics (CFD) modelling schemes to turbulent wall-bounded flows is a matter of concern. In the near-wall region of bounded flows, the standard high Reynolds number k-e model is not valid and requires the use of empirical wall models to mimic the behaviour of this region. A theoretical study of the physics of prevalent wall modelling techniques showed that the velocity distribution took no account of the pressure gradient. To determine the effect of this shortcoming, a typical transient three-dimensional flow was analysed using current CFD methods and the results compared with experimental flow measurements. Consideration of these results showed that the 'traditional' wall model was unable to replicate observed flow features in the near-wall region: further analysis of the computational results confirmed that these poor flow predictions arose from the inability of the model to consider local pressure gradient effects. Consequently, a strong case was made for a more robust wall model for use in conjunction with the standard high Reynolds number k-e model. A number of boundary layer analyses were reviewed and Coles' law of the wake (1956) presented as a viable candidate for the development of a new wall modelling scheme. In theory, Coles' law (1956) provides a description of bounded flows under arbitrary pressure gradients up to the point of near-separation and may be extended to the study of reversed flows. A generic algorithm for Coles' law was prepared and used to study the fundamental test cases of U-bend and backward facing step flows. In a comparison between documented experimentation, 'conventional' CFD modelling and Coles' law models of these flows, the Coles' law model was shown to provide a viable alternative to 'traditional' schemes. Consequently, the Coles' law model of the near-wall region, being valid for pressure-driven flows, offers an extension to the range of flows for which the standard high Reynolds number k-e model may be used.