A prediction method for spatially decaying freestream turbulence

Abstract

A simple set of equations, capable of quantifying and predicting the spatial decay of freestream turbulence (FST) is derived in the current study. The prediction equations are based on the inviscid estimate of the turbulent kinetic energy (TKE) dissipation rate. The new set of model equations includes the integral length scale and the turbulent kinetic energy as variables and is superior to the previous set of decay equations because, unlike those, they are not dependent on any physical grid parameters (b or M). This new set of equations, when compared and validated against 17 sets (2 active grids, 2 multi-scale grids, 9 square-cross-sectioned grids and 4 circular cross-sectioned grids) of previous, well-accepted, experimental data, including those relating to grid-generated turbulence and covering a wide range of turbulent Reynolds number (Re_Lu0) (7.5 × 10¹ to 6.9 × 10⁴), where L_u0 is the initial integral length scale, showed very good agreement (within ±15%). This set of correlation equations can be used to estimate the local and/or initial turbulent kinetic energy and integral length scale (L_u) in an FST flow and to locate the region within a flow domain where nearly-constant turbulence conditions are expected to prevail.

KEYWORDS:

• Prediction
• freestream turbulence
• inviscid
• turbulent kinetic energy
• integral length scale

Acknowledgements

The authors should like to thank Md. Mahbub Hossain and Greg Kopp for providing their grid turbulence data from the wind-tunnel experiments performed at the Boundary Layer Wind Tunnel Laboratory (BLWTL) at the University of Western Ontario. The authors also wish to acknowledge Laurent Perret (Ecole Centrale de Nantes) for his constructive comments and suggestions for improving this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The financial support of the Natural Sciences and Engineering Research Council (NSERC) of Canada (grant number: RGPIN/06251-2018) is gratefully acknowledged.