Law of the wall for turbulent flows in pressure gradients

Abstract

Experiments show that pressure gradients have a strong effect on the law of the wall for temperature but have comparatively little effect on the law of the wall for velocity. This is contrary to the predictions of the mixing-length formulas, though these can be derived by apparently plausible dimensional analysis. To model this behavior, the choice of the transport equation for the turbulence-length scale, or its equivalent, becomes crucial; this is true both for two-equation models and for full second-moment transport models. This paper is a brief review of the experimental evidence, followed by a demonstration that the most popular variable, the dissipation rate e, and its temperature-field equivalent ej fail to reproduce the observed behavior. A more general length-scale variable can be defined as ^e, where k is the turbulent kinetic energy. It is shown that, overall, the u; variable (m = — 1, n = 1) seems to be the best choice, with its temperature-field equivalent UT for heat transfer, although there is no obvious physical reason for preferring it. Nomenclature A+ =