Relaminarization of turbulent pipe flow induced by streamwise traveling wave wall transpiration and its scaling

Abstract: In technical applications, more than 90\% of the energy required to pump the fluids through pipes is dissipated by turbulence near the wall. In this respect, streamwise traveling waves of wall blowing and suction have been used to relaminarize turbulent pipe flow at a low friction Reynolds number of $\mathrm{Re}\tau=110$, considerably reducing friction losses and energy consumption. Here, we demonstrate that streamwise traveling waves of wall blowing and suction applied to initially turbulent pipe flow can trigger relaminarization up to friction Reynolds numbers of $\mathrm{Re}\tau=720$. Furthermore, we perform a parametric study comprising both upstream traveling waves (UTWs, $c<0$) and downstream traveling waves (DTWs, $c>0$) by varying the traveling wave amplitude $a$, celerity $c$, and wavelength $\lambda$ at $\mathrm{Re}\tau=180$ and $\mathrm{Re}\tau=360$ in order to investigate the scaling of the maximum drag reduction and of the net energy saving rate in direct numerical simulations. Consistent with channel flow studies in the literature, we found that UTWs destabilize the flow, while generating sublaminar drag due to the pumping effect. However, only low-speed UTWs with large amplitudes were discovered to decisively reduce energy consumption. For DTWs, a large range of wave parameters lead to a conspicuous drag reduction. Nevertheless, only a subgroup of these wave parameters are associated with siginificant net energy savings, i.e. $0.067U_{c,lam} \lesssim a \lesssim0.1U_{c,lam}$, $c \approx U_{c,lam}$, and $\lambda\approx 360\delta_\nu$, independent of the Reynolds number. Here, $U_{c,lam}=1/2\mathrm{Re}\tau u\tau$ is the centerline velocity of the corresponding laminar flow, and $\delta_\nu = \nu/u_\tau$ is the viscous length scale.