Turbulent Couette–Poiseuille flow with zero wall shear

Abstract

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (uτ,S) and half the channel height (h) is Reτ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Reτ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from to the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

“…1, as well as the results from the Re = 6000 and 12 000 runs. Also included are the recent Re = 1800 CP0 DNS data of Yang et al [14]. The code-C profiles for Re = 6000 and 12 000 are dU/dy APG = 0 approximations obtained from linear combinations of, respectively, Cases C6000a & C6000b and Cases C12000a & C12000b, with weighting coefficients defined such that the resultant satisfies U = U w and dU/dy = 0 at y = +h.…”

“…Mean-velocity profiles in Stratford units. For Re = 1800 (Yang et al[14]), 3000, 6000 and 12 000, respectively, u p /U w = 0.01405, 0.01136 (A3000,B3000,C3000a), 0.00858 (A6000), 0.00867 (C6000) and 0.00664 (C12000), such that h − = 25.3, 34.1 (A3000,B3000,C3000a), 51.45 (A6000), 52.0 (C6000) and 79.6 (C12000). C6000 and C12000 profiles are linear combination of C6000a & C6000b, and C12000a & C12000b results, respectively.…”

Preferential particle concentration in wall-bounded turbulence with zero skin friction

“…∆t + : normalized time step. Characteristics of the background turbulent CP flow were discussed comprehensively by Yang et al 23,42 The key features relevant to our present discussions are the distinguishing near-wall structures and the co-existing coherent structures of different scales, i.e., the quasi-coherent turbulent structures near the stationary wall and the LSSs which span across the channel. The flow structures near the stationary wall are similar to those in a P flow, where strong turbulent regeneration events occur and streamwise-streaky turbulent structures are formed.…”

“…2,11,19 Dimensional characteristics such as the spanwise spacing between the streaks can be obtained by the spanwise two-point correlation coefficient of particle concentration fluctuations, 10,20 similar to that used in determining the fluid near-wall low-speed streaks. [21][22][23] The overall particle wall-normal segregation can be measured by a global Shannon entropy method, 24 which reflects the spatio-temporal evolution of the particle phase (definition given in Sec. II C).…”

“…The LSSs in a CP flow are large-scale longitudinal circulations which are not observed in an open-channel flow at a similar Re τ . 23,42 Differences in the underlying flow will lead to variations in the corresponding particle preferential concentration near the walls. Particle distributions in open channel flows were studied by van Haarlem et al 16 and Narayanan et al, 17 with the focus on particle wall-normal segregation.…”