Predictions of canonical wall bounded turbulent flows via a modified $k-\omega$ equation

摘要

A major challenge in computation of engineering flows is to derive andimprove turbulence models built on turbulence physics. Here, we present aphysics-based modified $k-\omega$ equation for canonical wall bounded turbulentflows (boundary layer, channel and pipe), predicting both mean velocity profile(MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy overa wide range of Reynolds number ($Re$). The result builds on a multi-layerquantification of wall flows, which allows a significant modification of the$k-\omega$ equation. Three innovations are introduced: First, an adjustment ofthe Karman constant to 0.45 is set for the overlap region with a logarithmicMVP. Second, a wake parameter models the turbulent transport near thecenterline. Third, an anomalous dissipation factor represents the effect of ameso layer in the overlap region. Then, a highly accurate (above 99\%)prediction of MVPs is obtained in Princeton pipes, improving the original modelprediction by up to 10\%. Moreover, the entire SMKP, including the newlyobserved outer peak, is predicted. With a slight change of the wake parameter,the model also yields accurate predictions for channels and boundary layers.