Predictions of canonical wall-bounded turbulent flows via a modified k–ω equation

ABSTRACT

A major challenge in computation of engineering flows is to derive and improve turbulence models built on turbulence physics. Here, we present a physics-based modified k–ω equation for canonical wall-bounded turbulent flows (boundary layer, channel and pipe), predicting both mean velocity profile (MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy over a wide range of Reynolds number (Re). The result builds on a multi-layer quantification of wall flows, which allows a significant modification of the k–ω equation. Three innovations are introduced: first, an adjustment of the Karman constant to 0.45 is set for the overlap region with a logarithmic MVP; second, a wake parameter models the turbulent transport near the centreline; third, an anomalous dissipation factor represents the effect of a meso-layer in the overlap region. Then, a highly accurate (above 99%) prediction of MVPs is obtained in Princeton pipes, improving the original model prediction by up to 10%. Moreover, the entire SMKP, including the newly observed outer peak, is predicted. With a slight change of the wake parameter, the model also yields accurate predictions for channels and boundary layers.

Keywords:

• Turbulent boundary layers
• turbulence modelling
• Reynolds-averaged Navier–Stokes

PACS numbers:

• 47.27.eb
• 47.27.nb
• 47.27.nd
• 47.27.nf

Acknowledgment

We thank B. B. Wei who has contributed significantly during the initial stage of the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Nature Science Fund [11221062], [11452002] and by MOST 973 project [2009CB724100].