Using Particle Image Velocimetry to Determine Turbulence Model Parameters

Abstract

The primary parameter of a standard k-ϵ model, C μ , was calculated from stereoscopic particle image velocimetry (PIV) data for a supersonic jet exhausting into a transonic crossflow. This required the determination of turbulent kinetic energy, turbulent eddy viscosity, and turbulent energy dissipation rate. Image interrogation was optimized, with different procedures used for mean strain rates and Reynolds stresses, to produce useful turbulent eddy viscosity fields. The eddy viscosity was calculated by a least-squares fit to all components of the three-dimensional strain-rate tensor that were available from the PIV data. This eliminated artifacts and noise observed when using a single strain component. Local dissipation rates were determined via Kolmogorov’s similarity hypotheses and the second-order structure function. The eddy viscosity and dissipation rates were then combined to determine C μ . Considerable spatial variation was observed in C μ , with the highest values found in regions where turbulent kinetic energy was relatively low but where turbulent mixing was important, e.g., along the high-strain jet edges and in the wake region. This suggests that use of a constant C μ in modeling may lead to poor Reynolds stress predictions at mixing interfaces. A data-driven modeling approach that can predict this spatial variation of C μ based on known state variables may lead to improved simulation results without the need for calibration.