Wall-pressure-velocity transfer kernel in high Reynolds number turbulent channel flows

Woutijn J. Baars, Myoungkyu Lee

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Abstract

Since wall-pressure fluctuations would form a practically-robust input to a real-time active controller of wall-bounded turbulence, it is of high practical interest to study the scaling behavior of the wall-pressure-velocity coupling. This work investigates the coupling of the wall-pressure fluctuations with the streamwise and wall-normal velocity fluctuations. Both the gain (or coherence) and phase spectra of the wall-pressure-velocity transfer kernel are assessed using a comprehensive database, available from direct numerical simulations of turbulent channel flow. With data spanning a decade in friction Reynolds number Reτ ∼ 550-5200, a 1D analysis (in terms of the streamwise wavelength, λx) reveals that the streamwise velocity and wall-pressure are most strongly coupled at a self-similar wall-scaling of λx/y ≈ 14. For the wall-normal velocity component, the strongest coupling appears at approximately half this ratio (λx/y ≈ 8.5). An analysis of the kernel's phase demonstrates that both the coherent fluctuations of streamwise and wall-normal velocity obey a forward-leaning inclination angle of α ≈ 30. When extending the analysis to 2D (as a function of λx and λz), the peak-coherence for pw and u still resides close to λx/y ≈ 14 and is reasonably symmetric around λxz = 2.3. The 2D coherence for pw and v peaks around λxz = 1.0. Both the 2D coherence for pw and u, and pw and v, adhere to a wall-scaling with y. Scaling behaviours identified in this work will aid the efficacy of real-time controllers, by for instance the implementation of data-derived FIR filters to only control velocity structures that are captured through wall-pressure measurements.

Original languageEnglish
Number of pages6
Publication statusPublished - 2022
Event12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022 - Osaka, Virtual, Japan
Duration: 19 Jul 202222 Jul 2022

Conference

Conference12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022
Country/TerritoryJapan
CityOsaka, Virtual
Period19/07/2222/07/22

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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