Pressure statistics and fine vortex structure in Turbulence

用电容式传声器和压阻式传感器测量了湍流射流中的压力波动。从Kolmogorov普适标度的角度讨论了归一化压力谱的幂律指数和比例常数。在600<R_λ范围内，确定了清晰的幂律，标度指数接近于-7/3。这些雷诺数要比速度波动中的雷诺数大得多，以达到柯尔莫哥罗夫标度。谱常数不是普遍的，而是依赖于雷诺数。将实测压力pdf与直接数值模拟结果进行了比较。因此，人们寻求新的方法和改进的测量技术。本研究采用小型传感器和传声器同时测量湍流边界层的静压和壁面压力。所得结果可总结如下。(1)利用平均压力分布求出垂直速度分量的均方根，得到的剖面与直接v分量测速的结果更吻合。v^+的峰值位置按雷诺数的函数进行缩放；y_p^+=0.00135乘以R_θ^1.42。(2)壁压均方根经内变量归一化后，R_θ呈递增函数；p_rms ^ +∝R_θ^ 0.28。这一趋势与DNS的结果相似。(3)边界层静压r.m.s.， p_rms^+的分布不存在雷诺数标度。如果p_rms^+在对数区域内取平均值，则其雷诺数依赖关系近似为幂律；p_rms ^ +∝R_θ^ 0.32。这种雷诺数依赖性比流向速度或垂直速度分量强得多。(4)壁面与边界层静压的相关关系为正值。如果R_θ>7000与壁面的距离归一化为Δ，相关系数的分布与雷诺数无关。(5)相对于流向流速u，静压的均方根按ρu_rms^2缩放。内部区域的比值p_rms/ρu_rms^2为1的数量级。压力与流速的相关性表明，局部最小值在y/Δ=0.05处，局部最大值在y/Δ=0.2处。在外围区域，0.25<y/Δ，相关性变为负相关。这些趋势可以在DNS中观察到。少

Pressure fluctuation was measured in a turbulent jet using a condenser microphone and piezoresistive transducer. The power-law exponent and proportional constant of normalized pressure spectrum are discussed from the standpoint of Kolmogorov universal scaling. The clear power-law with scaling exponent close to -7/3 was confirmed in the range of 600<R_λ. These Reynolds numbers are much larger than those in velocity fluctuation to achieve Kolmogorov scaling. The spectral constant is not universal but depends on Reynolds numbers. Measured pressure PDFs are compared with direct numerical simulation.New methods and improved measurement techniques are thus sought for. In this study, both static pressure and wall pressure in turbulent boundary layers have been measured simultaneously by using small transducer and microphone. Obtained results may be summarized as follows.(1)The root mean square of vertical velocity component is evaluated by means of mean pressure distribution The profile is su … More fficiently agree with the result obtained by direct v-component velocity measurement.The peak location of v^+ is scaled as a function of Reynolds number ; y_p^+=0.00135 times R_θ^1.42.(2)Root mean square of wall pressure, normalized by inner variable, indicates an increasing function of R_θ ; p_rms^+∝R_θ^0.28. This trend is similar with the result by DNS.(3)The distribution of static pressure r.m.s., p_rms^+, across the boundary layer does not show the Reynolds number scaling. If p_rms^+ is averaged within the log-region, its Reynolds number dependence is approximated by the power-law ; p_rms^+∝R_θ^0.32. This Reynolds number dependence is much stronger than that of stream-wise velocity or vertical velocity component.(4)The correlation between wall and static pressure across the boundary layer indicates the positive value. The distribution of correlation coefficient does not show the Reynolds number dependence if the distance from the wall is normalized by Δ for R_θ>7000.(5)In relation to streamwise velocity u, the root mean square of static pressure is scaled by ρu_rms^2. The ratio p_rms/ρu_rms^2 is the order of 1 in the inner region. The correlation between the pressure and streamwise velocity indicates the local minimum and maximum value at y/Δ=0.05 and y/Δ=0.2,respectively. In the outer region, 0.25<y/Δ, the correlation becomes negative. These trends are observed in DNS. Less