Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence (in EN)
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.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility (ALCF)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC02-06CH11357
- OSTI ID:
- 2581374
- Journal Information:
- Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 981; ISSN 0022-1120
- Publisher:
- Cambridge University PressCopyright Statement
- Country of Publication:
- United States
- Language:
- EN
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