Scaling of pressure fluctuations in compressible turbulent plane channel flow

The purpose of the paper is to identify Mach-number effects on pressure fluctuations p ' in compressible turbulent plane channel flow. We use data from a specifically constructed (Re-tau*,(M) over bar CLx)-matrix direct numerical simulation (DNS) database, with systematic variation of the centreline streamwise Mach number 0.32 <=(M)over bar>CLx <= 2.49 and of the HCB (Huang et al., J. Fluid Mech., vol. 305, 1995, pp. 185-218) friction Reynolds number 66 <= Re tau(sic)1000. Strong (M) over bar CLx effects (enhanced by the increasingly cold-wall condition) appear for (M) over bar CLx(sic)2, for all Re-tau*, very close to the wall (y(sic)15). Compared with incompressible flow at the same Re tau*, the wall root-mean-square [p ' rms]+w (in wall-units, i.e. scaled by the average wall shear stress (tau) over barw) strongly increases with (M) over bar CLx. In contrast, the peak level across the channel, [p ' rms](+)PEAK, slightly decreases with increasing (M) over bar CLx. In order to study the near-wall coherent structures we introduce a new wall-distance-independent non-local system of units, based for all y on wall friction and the extreme values of density and dynamic viscosity, namely, for cold walls {(tau) over bar (w),min(y)(rho) over bar ,max(y)(mu) over bar}. The average spanwise distance between streaks, scaled by this length-unit, is nearly independent of -MCLx at constant Re-tau?. Using the in-plane (parallel to the wall) Laplacian del;(2)(xz)p ' we find that the (+/-)-p ' wave-packet-like structures appearing inside the low-speed streaks (y(sic)15) with increasing (M) over bar CLx(sic)2 are part of a more complex wave system with spanwise extent over several streaks, whose spatial density decreases rapidly with decreasing (M) over bar CLx or increasing y(star). These p ' wave packets appear to be collocated with strong (+/-)-v ' events and could be responsible for compensating towards 0 the negative incompressible-flow correlation coefficient cp ' v ', with increasing (M) over bar CLx very near the wall.

Automated summary

The paper investigates the effects of Mach number on pressure fluctuations in compressible turbulent plane channel flow. Using direct numerical simulation, the study finds strong Mach number effects near the wall, with increased wall root-mean-square pressure fluctuations but slightly decreased peak level across the channel. The research also reveals the existence of complex wave systems and wave-packet-like structures, which appear to be responsible for compensating the negative correlation coefficient between pressure fluctuations and velocity fluctuations.