The primary parameter of a standard $k\text{-}ϵ$ model, $C_{\mu }$, 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 $C_{\mu }$. Considerable spatial variation was observed in $C_{\mu }$, 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 $C_{\mu }$ in modeling may lead to poor Reynolds stress predictions at mixing interfaces. A data-driven modeling approach that can predict this spatial variation of $C_{\mu }$ based on known state variables may lead to improved simulation results without the need for calibration.

标准的主要参数 $ķ\text{--}ϵ$ 模型， $C_{\mu }$从立体粒子图像测速（PIV）数据计算出超音速射流排入跨音速错流的速度。这需要确定湍动能，湍流涡流粘度和湍流能量耗散率。优化了图像查询，使用了不同的平均应变率和雷诺应力程序，以产生有用的湍流涡流粘度场。通过对PIV数据中可获得的三维应变率张量的所有分量进行最小二乘拟合，计算出涡流粘度。这样消除了使用单个应变分量时观察到的伪影和噪声。通过Kolmogorov的相似性假设和二阶结构函数确定局部耗散率。然后将涡流粘度和耗散率合并确定$C_{\mu }$。观察到相当大的空间变化$C_{\mu }$在湍动能相对较低但湍流混合很重要的区域（例如沿高应变射流边缘和尾流区域）具有最高值。这表明使用常数$C_{\mu }$建模中的模型可能会导致混合界面的雷诺应力预测不佳。一种数据驱动的建模方法，可以预测$C_{\mu }$ 基于已知状态变量的结果可能会导致改进的仿真结果，而无需进行校准。