Scaling of wall-pressure–velocity correlations in high-Reynolds-number turbulent pipe flow

Abstract

An experimental study was conducted in the CICLoPE long-pipe facility to investigate the correlation between wall-pressure and turbulent velocity fluctuations in the logarithmic region, at high friction Reynolds numbers ( $4794 \lesssim Re_\tau \lesssim 47\,015$ ). Hereby, we explore the scalability of employing wall-pressure to effectively estimate off-the-wall velocity states (e.g. to be of use in real-time control of wall-turbulence). Coherence spectra for wall-pressure and streamwise (or wall-normal) velocity fluctuations collapse when plotted against $\lambda _x/y$ and thus reveals a Reynolds-number-independent scaling with distance-from-the-wall. When the squared wall-pressure fluctuations are considered instead of the linear wall-pressure term, the coherence spectra for the wall-pressure-squared and velocity are higher in amplitude at wavelengths corresponding to large-scale streamwise velocity fluctuations (e.g. at $\lambda _x/y = 60$ , the coherence value increases from roughly 0.1 up to 0.3). This higher coherence typifies a modulation effect, because low-frequency content is introduced when squaring the wall-pressure time series. Finally, quadratic stochastic estimation is employed to estimate turbulent velocity fluctuations from the wall-pressure time series only. For each $Re_\tau$ investigated, the estimated time series and a true temporal measurement of velocity inside the turbulent pipe flow yield a normalised correlation coefficient of $\rho \approx 0.6$ for all cases. This suggests that wall-pressure sensing can be employed for meaningful estimation of off-the-wall velocity fluctuations and thus for real-time control of energetic turbulent velocity fluctuations at high- $Re_\tau$ applications.

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