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 (ReLu 0) (7.5 × 101 to 6.9 × 104), where Lu 0 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 (Lu ) in an FST flow and to locate the region within a flow domain where nearly-constant turbulence conditions are expected to prevail.