Velocity profiles and wall shear stress values in the wall jet region of planar underexpanded impinging jets are parameterized based on nozzle parameters (stand-off height, jet hydraulic diameter, and nozzle pressure ratio). Computational fluid dynamics is used to calculate the velocity fields of impinging jets with height-to-diameter ratios in the range of 15 to 30 and nozzle pressure ratio in the range of 1.2 to 3.0. The wall jet has an incomplete self-similar profile with a typical triple-layer structure as in traditional wall jets. The effects of compressibility are found to be insignificant for wall jets with Ma<0.8. Wall jet analysis yielded power-law relationships with source dependent coefficients describing maximum velocity, friction velocity, and wall distances for maximum and half-maximum velocities. Source dependency is determined using the conjugate gradient method. These power-law relationships can be used for the mapping of wall shear stress as a function of nozzle parameters.

中文翻译：

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撞击平面欠膨胀射流的壁射流相似性

平面欠膨胀冲击射流壁射流区域的速度剖面和壁面剪切应力值基于喷嘴参数（间隔高度、射流水力直径和喷嘴压力比）进行参数化。计算流体动力学用于计算高径比在 15 到 30 范围内和喷嘴压力比在 1.2 到 3.0 范围内的撞击射流的速度场。壁射流具有不完整的自相似轮廓，具有与传统壁射流一样的典型三层结构。发现对于 Ma<0.8 的壁面射流，可压缩性的影响是微不足道的。壁射流分析产生了与源相关系数的幂律关系，这些系数描述了最大速度和半最大速度的最大速度、摩擦速度和壁距。使用共轭梯度法确定源依赖性。这些幂律关系可用于将壁剪切应力映射为喷嘴参数的函数。