Direct numerical simulation of streamwise traveling wave induced turbulent pipe flow relaminarization

Abstract

For technically relevant flows with high Reynolds numbers, more than 90% of the energy required to pump fluids through pipes is dissipated by turbulence near the wall. However, Koganezawa et al. [1] showed for the low friction Reynolds number of Reτ = uτR/ν = 110—where uτ is the friction velocity, ν is the kinematic viscosity and R is the pipe radius—that for certain wave parameters, streamwise traveling waves of wall blowing/suction can lead to relaminarization, thereby significantly reducing drag. However, as reported in the recent review paper by Fukagata et al. [2], higher Reynolds number data are required for engineering applications. Therefore, we have adapted our fourth-order finite volume solver [3] to perform direct numerical simulations of turbulent pipe flow with streamwise traveling wave boundary conditions of the wall-normal velocity of friction Reynolds numbers up to Reτ = 720. For each Reynolds number the optimal set of the blowing/suction parameters is determined in terms of the drag reduction rate RD = (Cf0 − Cf )/Cf0, where Cf (Cf0) is the skin friction drag of the (un)controlled flow. In addition to the drag reduction rate RD, the net energy saving S is a crucial metric for evaluating the efficiency of the control method. The net energy saving is defined as S = (Wp0 − (Wp + Wa))/Wp0, where Wp(Wp0) is the driving power of the (un)controlled flow and Wa is the actuation power of the control. Figure 1 shows the net energy saving map at Reτ = 180 and a wavelength of λ+ = 360 wall units. As illustrated in Figure 1, downstream traveling waves with λ+ = 360, c = Uc,lam, and a = 0.07Uc,lam induce relaminarization and a maximum of net energy saving of approximately 80%. Here, Uc,lam = 1/2Reτuτ is the centerline velocity of the corresponding laminar flow. In addition, standing waves (c = 0) with low amplitudes (a ≤ 0.15Uc,lam) and slow upstream traveling waves (c = 0.1Uc,lam) lead to positive net energy savings. In the following, we are performing a parametric study by varying Reτ , as well as the traveling wave amplitude a, length λ, and velocity c. At the conference we will present the Reynolds number scaling of the blowing/suction parameters that lead to relaminarization, minimum drag, and maximum net energy saving, and elucidate the underlying mechanisms. Figure 2 presents the Reynolds number scaling of the turbulent kinetic energy decay rate of flow cases with relaminarization.