Universality in small scale structures in pressure fluctuation in turbulence

本文报道了在雷诺数R_λ = 200 ~ 1200范围内自由射流压力统计的实验结果。以及传统的压力统计标度性理论。在一些重要方面尚未得到证实。流场压力脉动的测量分别用标准的四分之一英寸电容传声器和小型传感器完成。它们装有一个管道作为压力管道，并插入到流域中，这样的方式，麦克风（或换能器）主体的轴与平均流对齐。静电管直径为1 mm，长度为15 mm，表面有四个直径为0.4mm的静电孔。麦克风的频率响应与必要的辅助设备是平坦的高达15 kHz。但较低的频率可以测量到20赫兹。这对于高雷诺数流动或包含大尺度运动的流动是不够的。因此，在R_λ小于等于300的情况下，我们采用了小探头。与能谱的情况相比，压力谱的标度似乎没有达成一致。实验结果表明，当R_λ小于等于650时，能满足明显的-7/3幂律。这比速度统计中惯性标度所需的雷诺数高得多。小于此雷诺数，但R_λ [大于或等于] 350，谱指数偏离-7/3。系数C_p不是普适的，而是依赖于雷诺数。若在双对数坐标系下用线性拟合近似，则为C_p &lt;$R_λ^<1.3>。我们认为这些结果是全新的实验结果。

In this study we report on the experimental result of pressure statistics measured in the free jet in the range of Reynolds number ; 200 【less than or equal】 R_λ 【less than or equal】 1200. And the traditional theories for the scaling properties of pressure statistics. Which are not yet confirmed in a number of important aspect, are checked. The measurement of pressure fluctuation in the flow field was accomplished with standard quarter-inch condenser microphone and the small transducer, respectively. They were fitted with a tubing as a pressure duct and were inserted into the flow domain in such a way that the axis of the microphone (or the transducer) body was aligned with the mean stream. The static tube is 1mm in diameter and 15mm in length which has four static holes (0.4mm in diameter) on the surface. The frequency response of the microphone with the necessary ancillary equipment is flat up to 15kHz. But the lower frequency can be measured down to 20Hz. This is not enough for high Reynolds number flow or the flow in which the large scale motions are contained. So we adopted the small transducer in the case of 300 【less than or equal】 R_λ. There seems to be no agreement about the scaling of pressure spectrum when compared to the case of energy spectrum. The present experiment shows that the clear -7/3 power-law was confirmed for 650 【less than or equal】 R_λ. This is significantly higher Reynolds number than those needed for inertial scaling in velocity statistics. Smaller than this Reynolds number, but R_λ 【greater than or equal】 350, the spectral exponent departs from -7/3. The coefficient C_p is not universal but depends on the Reynolds number. If we approximate the relation by the linear fit in log-log coordinate, it is C_p ∝ R_λ^<1.3>. We think these results are rally new experimental results.