A spectral turbulent cascade model for single- and two-phase uniform shear flows

Abstract

A spectral turbulent cascade-transport model was developed and applied to single-and two-phase turbulent uniform shear flows. This model tracks the development of the turbulent kinetic energy spectrum by splitting the turbulent kinetic energy into wave number bins. A separate transport equation accounts for the spectral production, dissipation and transport terms and is solved for each wave number bin. The predicted evolution of the turbulence level, turbulent production and turbulent dissipation is shown to be consistent with experimental data for turbulent uniform shear flows. The shear rate in the various experiments ranges from 12.9 to 46.8 s^{− 1} for air flows, 0.96 to 1.23 s⁻¹ for water flows and was 2.9 s^{− 1} for bubbly two-phase air/water flow.

Keywords:

• uniform shear flow
• spectral cascade model
• two-phase flow

Acknowledgements

The authors would like to acknowledge the support given this study by the National Science Foundation (NSF) and the Office of Naval Research (ONR). In addition, we would like to acknowledge Professors Charles Meneveau and Andrea Prosperetti (Johns Hopkins University) who first made us aware of the potential of the spectral cascade-transport modeling approach for turbulent two-phase flows, and Professor Stephen Pope (Cornell University) for his many helpful suggestions.