Phase relationship in laminar channel flow controlled by traveling-wave-like blowing or suction

Abstract

The phase relationship between the streamwise and the wall-normal velocity disturbances induced by a traveling-wave-like blowing or suction control [T. Min, J. Fluid Mech. 558, 309 (2006)] in a two-dimensional laminar Poiseuille flow is investigated. The investigation is done by solving the linearized Navier-Stokes equation and by using the identity equation between the skin-friction drag and the Reynolds shear stress [K. Fukagata, Phys. Fluids 14, L73 (2002)]. It has been known that a traveling wave creates a nonquadrature between the velocity disturbances and generates the positive phase shift of the streamwise velocity disturbance in the case of a skin-friction drag reduction. The present analysis further reveals that this nonquadrature consists of an inviscid base phase relationship and a near-wall phase shift induced by the viscosity. The analogy between the present control and Stokes' second problem is discussed. The thickness of the near-wall region in which the viscous phase shift takes place is found to be scaled similarly to the Stokes' second problem.

Drag reduction by streamwise traveling wave-like Lorenz Force in channel flow

“…Their control succeeded to sustain a sublaminar drag both in laminar and turbulent flows: the negative RSS was induced in the region near the wall when the wave travels to the upstream direction. Mamori, Fukagata, & Hoepffner (2010) reproduced Min et al 's laminar flow results and revealed by means of a linear analysis and a detailed phase analysis the mechanism to induce this negative RSS. The viscosity induces the phase lead of the streamwise velocity fluctuation from the wall-normal velocity fluctuation and the non-quadrature between them induced thereby makes the RSS negative.…”

“…According to the phase analysis by Mamori, Fukagata, & Hoepffner (2010), the RSS in a laminar flow is generated by the non-quadrature between the streamwise and wall-normal velocities fluctuations. The Fourier transform is defined as…”

“…Here, the phaseaveraged velocity is compared with the laminar flow case of the same input parameters. The controlled laminar velociy field is obtained by using the linear analysis (Mamori, Fukagata, & Hoepffner (2010)). The governing equations are two-dimensional and linearized: u = u + u, v = v, and p = p + p are substituted into the Eqs.…”

Heat transfer in fully developed turbulent channel flow with streamwise traveling wave-like wall deformation

“…The positive and negative ⟨− u v⟩ alternate while the non-quadrature between u and v appears in the region near the wall. A significant amount of ⟨− v θ⟩ also appears in the region near the wall, which creates the periodic contribution to the heat transfer similarly to that to the friction drag (Min et al, 2006;Mamori et al, 2010). The upstream wave-like wall deformation or blowing and suction is known to work to destabilize the flow as was shown by DNS (Min et al, 2006;Nakanishi et al, 2012).…”

Test Bench Simulator for Heart Valves

“…Fig. 4 shows a typical time-fluid volume curve for the left ventricle of a human heart [1]: it's easy to observe that there are discontinuities in transition from suction phase to sending phase and therefore it cannot be set directly to linear motor [29][30][31][32]. It was necessary to interpolate it through fourth order polynomials.…”