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

Abstract

In technical applications, pumping fluids through pipes often generates turbulent flows with high Reynolds numbers, where over 90% of the pumping energy is dissipated by near-wall turbulence. Relaminarization of such flows offers significant energy savings. Streamwise traveling waves of wall blowing and suction have been shown to relaminarize turbulent pipe flow at a low friction Reynolds number (Reτ = 110), reducing friction losses and energy consumption. This work extends the investigation to higher Reynolds numbers, demonstrating that traveling waves can trigger relaminarization up to Reτ = 720. A parametric study is conducted at Reτ = 180 and Reτ = 360, examining upstream traveling waves (UTWs, c < 0) and downstream traveling waves (DTWs, c > 0) while varying amplitude a, celerity c, and wavelength λ. Consistent with channel flow studies, UTWs destabilize the flow yet can generate sublaminar drag; only low-speed UTWs with large amplitudes effectively reduce energy consumption. For DTWs, a wide range of parameters reduces drag, but significant net energy savings occur only for 0.067Uc,lam < a < 0.1Uc,lam, c ≈ Uc,lam, and λ ≈ 360δν , independent of Reynolds number. During relaminarization, the turbulent kinetic energy decays exponentially nearly to zero within 3D/uτ , while the flow accelerates to its terminal velocity over 65D/uτ . The relaminarized flow exhibits half-vortical structures scaling in viscous units superimposed on a laminar profile, effectively reducing the pipe cross section. Within 180 ≤ Reτ ≤ 540, over 97% of the theoretically achievable drag reduction is realized. These scaling relations enable prediction of traveling wave-induced relaminarization at higher Reynolds numbers, offering a practical approach for energy-efficient turbulent pipe flow control.