Turbulent-viscosity modeling applicable to swirling flows, based on a composite time scale with mean flow helicity partially incorporated

Abstract

Helical motion contributes to the stabilization of turbulent flows, as is recognized through their mean velocity profiles. This feature indicates that swirl is capable of suppressing momentum transport. In the current Reynolds-averaged modeling, the flow is regarded as beyond the scope of the explicit algebraic modeling with the turbulent-viscosity representation as a key ingredient, and the second-order modeling is utilized as the sole approach at the cost of the increase in mathematical and computational complexity. The present work aims at reproducing primary features of swirling flows within the framework of an isotropic turbulent-viscosity model and extending the ability of the explicit algebraic modeling. Its cornerstone is the introduction of a composite time scale with the mean flow helicity partially incorporated without violating the Galilean invariance. The time scale is synthesized with the single ones familiar in the current modeling, on the basis of which the turbulent viscosity is modeled and incorporated into the two-equation modeling. The model is tested in a swirling pipe flow and is confirmed to reproduce its primary features, showing that the momentum transport is suppressed by the partial mean flow helicity due to the circumferential flow and the vorticity resulting from the retarded axial flow.

Keywords:

• Reynolds-averaged modeling
• turbulent viscosity
• helicity
• swirling flow
• turbulence time scale

Acknowledgments

Parts of this work were done while one of the authors (A.Y.) was in Japan Aerospace Exploration Agency as a visiting scientist. The author (A.Y.) is grateful to Mr. Shoiti Nisizima and Dr. Nobumitsu Yokoi for their long-term (1990∼2004) cooperation in the research of swirling flows at Institute of Industrial Science, University of Tokyo.