Relationship between wall pressure and velocity-field sources

Abstract

The objective of this investigation is to study the velocity-field sources for the fluctuating wall pressure, determine their locations in the boundary layer, and investigate their physics. The velocity-field sources and partial wall pressures were computed from a database generated by a direct numerical simulation of a low Reynolds number, fully developed, turbulent channel flow. Results show that the mean-shear (MS) and turbulence-turbulence (TT) partial pressures (πMS and πTT, respectively) are the same order of magnitude. The buffer region dominates most of the wave number range; the viscous shear layer is significant at the highest wavenumbers; the buffer and logarithmic regions are important at low wavenumbers. Over most of the wavenumber range, the contribution from the buffer region is the dominant TT component; in the low-wavenumber range, the viscous shear layer, buffer region, and logarithmic region are significant; in the medium and high wavenumbers the viscous shear layer and buffer region dominate. The most important TT partial pressures are π23TT, π13TT and π12TT from the buffer region. It is conjectured that π23TT and π13TT may be generated by quasi-streamwise vortices. π12TT may be due to near-wall shear layers and spanwise vortices. π23TT, π22TT and π33TT from the viscous shear layer are the dominant high-wavenumber partial pressures.

Wall effects on pressure fluctuations in turbulent channel flow

“…The last field in the superposition (2.2) is introduced to satisfy the wall boundary-conditions associated with the normal-to-the-wall (y) momentum equation because of the no-slip wall boundary-condition u i (x, y = ± 1 2 L y , z, t) = 0 ∀x, z, t. By (2.4) the field p (τ ) is obviously related to the fluctuating wall-shear-stress, and is usually called Stokes pressure (Mansour et al 1988;Kim 1989;Chang et al 1999) although Pope (2000, p. 439) suggests the alternative term harmonic pressure, because in incompressible flow…”

“…The classical solution of (2.6) by Kim (1989), using a Green's function approach, provides detailed information on the structure of the rapid and slow fields, and was extended by Chang et al (1999) to study the detailed influence of the sources, both in type (slow and rapid) and y-location in the channel. In the present work we extend this analysis by identifying and studying the wall-echo influence.…”

“…The exact solution to (2.6a) with boundary conditions (2.6b), for the xz-Fouriercomponents (2.5a) of the slow p (s) and rapid p (r) fields, is given in Kim (1989), and has been widely used (Mansour et al 1988;Chang et al 1999;Foysi et al 2004). Following the analysis in §B.2.1 for κ = 0 (B 10b) and in §B.3.1 for κ = 0 (B 28), it reads…”

“…where the rapid p (r) , slow p (s) and Stokes p (τ ) pressure fluctuations are solutions of (Kim 1989;Chang et al 1999…”

“…† The separate solution for each source-term (1.1), permits the separation of slow p (s) and rapid p (r) parts. In this way (Kim 1989;Chang et al 1999), the slow and rapid contributions to φ ij were computed (Mansour et al 1988). This procedure (Kim 1989) is now used in a standard way in incompressible plane channel flow dns, at least as far as p 2 (s) , p 2 (r) , and p 2 (τ ) are concerned, and has also been extended to compressible flow studies (Foysi et al 2004).…”