Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence

• Published in: Journal of fluid mechanics Vol. 981
• Main Authors: Baars, Woutijn J., Dacome, Giulio, Lee, Myoungkyu
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 21.02.2024
• Subjects: Accuracy; Acoustic noise; Channel flow; Coherence; Control systems; Control systems design; Controllers; Correlation coefficient; Correlation coefficients; Direct numerical simulation; Fluctuations; Fluid flow; Fourier transforms; Friction; JFM Papers; Mechanics; Physics; Pressure; Real time; Reynolds number; Robust control; Scaling; Sensors; Spectral analysis; Spectrum analysis; State estimation; Systems analysis; Turbulence; Turbulent flow; Velocity; Velocity coupling; Wall pressure; turbulent boundary layers; boundary layer structure; turbulence control
• DOI: 10.1017/jfm.2024.46
• ISSN: 0022-1120

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range $Re_\tau \approx 550\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of $\lambda _x/y \approx 14$ (and $\lambda _x/y \approx 8$ for the wall-normal velocity). When extending the analysis to both homogeneous directions in $x$ and $y$, the peak coherence is centred at $\lambda _x/\lambda _z \approx 2$ and $\lambda _x/\lambda _z \approx 1$ for $p_w$ and $u$, and $p_w$ and $v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of $Re_\tau \approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of $\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.