Linear response analysis of supersonic turbulent channel flows with a large parameter space

Abstract

In this work, the linear responses of turbulent mean flow to both harmonic and stochastic forcing are investigated for supersonic channel flow. Well-established universal relations are utilized to obtain efficiently the mean profiles with a large parameter space, with the bulk Mach number up to 5 and the friction Reynolds number up to $10^4$ , so a systematic parameter study is feasible. The most amplified structure takes the form of streamwise velocity and temperature streaks forced optimally by the streamwise vortices. The outer peak of the pre-multiplied energy amplification corresponds to the large-scale motion, whose spanwise wavelength ( $\lambda _z^+$ ) is very insensitive to compressibility effects. In contrast, the classic inner peak representing small-scale near-wall motions disappears for the stochastic response with increasing Mach number. Meanwhile, the small-scale motions become much less coherent. A decomposition of the forcing identifies different effects of the incompressible counterpart and the thermodynamic components. Wall-cooling effects, arising with high Mach number, increase the spacing of the most amplified near-wall streaks; the spacing becomes nearly invariant with Mach number if expressed in semi-local units. Meanwhile, the coherence of stochastic response with $\lambda _z^+>90$ is enhanced, but on the other hand, with $\lambda _z^+<90$ it is decreased. The geometrical self-similarity of the response in the mid- $\lambda _z$ range is still roughly satisfied, insensitive to Mach number. Finally, theoretical analyses of the perturbation equations are presented to help with understanding the scaling of energy amplification.

Study of the vortex structure in compressible wall-bounded turbulence

“…Through the comparison of Figs. 6(b) and 6(c), most vortices populate around low-speed streaks since low-speed streaks are recognized to be induced by the moving hairpin leg [50]. This close connection is also reported by Jiménez and Pinelli [51] and Ringuette et al [52] in incompressible flows, and Pirozzoli et al [19] in a compressible turbulent boundary layer at Ma = 2.…”

On the streamwise velocity, temperature and passive scalar fields in compressible turbulent channel flows: a viewpoint from multiphysics couplings

“…This treatment is not arbitrary. On the one hand, T is typically considered as a passive scalar in incompressible wall turbulence Antonia, Abe & Kawamura 2009) and compressible wall turbulence at low Mach number (Chen et al 2023a;, just like g . On the other hand, T can strikingly influence the u field through the interactions between the momentum and energy equations in compressible wall turbulence, whereas g cannot.…”

Progress in physical modeling of compressible wall-bounded turbulent flows

“…Such a scaling was proposed by Song et al [137] through deducing the GRA with fitted coefficients. Subsequently, closed ODEs were established by Song et al [138] and Chen et al [139], whose predictions of the mean velocity and temperature (and density) attain high accuracy. Notably, the Trettel-Larsson and total-stress-based transformations are used throughout, although they are not designed to work in the outer region.…”

“…The statistical characteristics of some decomposed modes satisfy the predictions of the attached-eddy model. Chen et al [139] investigated the linear responses of turbulent mean flow to both harmonic and stochastic forcings for supersonic channel flow, and found that the scale features of the most amplified streamwise velocity structures are in tune with those of incompressible wall turbulence; see Fig. 19(a) and (c).…”

“…Cheng and Fu [162] further revealed that T ′ motions in the logarithmic region are organized as hierarchical structures, and their footprints on the near-wall region can be treated as a Gaussian variable. Chen et al [139] compared the optimal harmonic response for the modes of the velocity and temperature in a high-Reynolds-number compressible channel flow; see Fig. 19.…”