Mechanisms For Drag Reduction In Turbulent Wall Flows Utilizing Spanwise Motions

The surface of most mobile devices is inwrapped by turbulent bundary layer. The coherent structures of wall turbulence, charactered by the streaks and longitudinal vortex structures, are responsible for the generation of high turbulent skin-friction drag. When spanwise motions imposed by external forcing excitation are applied to modify the near-wall turbulent flow, the coherent structure of wall turbulence can be disrupted effectively, thereby suppressing the production of turbulence near the wall, leading to significant turbulent skin-friction drag reduction. Several different ways of introducing spanwise flow modifications in turbulent channel flow are investigated by direct numerical simulation (DNS) based on standard Fourier-Chebyshev spectral method. The database of turbulent channel flow is produced by DNS. Control strategies can be classified into two categories. The first class uses wall motions, including spanwise wall oscillation, and streamwise travelling wave induced by spanwise wall oscillation; the second class adopts Lorentz forcing exitation, including spanwise and streamwise travelling waves induced by spanwise oscillating Lorentz force. In the simulations, the incompressible Navier-Stokes (N-S) equations are used as the basic control equations to describe the turbulent channel flow. Different boundary conditions or body-force terms are added to the N-S equations according to the adopted control strategies.1) Flow control and drag reduction due to spanwise wall oscillation in turbulent channel flow are investigated numerically. The skin-friction drag can be reduced significantly by changing the amplitude and the period of the spanwise wall oscillation. Along with the increase of the mean drag reduction rate, time evolution of skin-friction drag becomes steadier and shows longer periodicity. A type drag reduction periodicity is divided to three typical phases to investigate the energy spectra of turbulent fluctuation kinetic energy and flow physics of turbulent channel flow subject to spanwise wall oscillation. It is found that the suppressions of total vorticity energy for these three phases are different. The distribution of the two-dimensional energy spectra of velocity fluctuation show that turbulent fluctuation kinetic energy decrease significantly, and there seems a trend that energy concentrates to a certain wave vector at low-wave number end. Combining these observations with the different states of the near-wall turbulent structures in the three typical phases, the mechanisms of turbulence suppression and drag reduction via spanwise wall oscillation are further analysed. The results suggest that two kinds of mechanisms of turbulence suppression and drag reduction due to spanwise wall oscillation work by turns, one of which is the incline of streamwise vorticity and the streaks induced by oscillation of the wall, leading to creation of a negative spanwise vorticity in the near-wall region, which is in favor of drag reduction, and the other is the relative displacement of the streamwise vorticity and the streaks over the oscillating wall, which can induce the streaks broad and the streamwise vorticity weak.2) The control and drag reduction in turbulent channel flow via streamwise travelling wave induced by spanwise-wall oscillation are investigated by DNS. The effects of streamwise wave number on the the associated statistics and the skin-friction drag are discussed. The induced Stokes layer, the near-wall flow structure, as well as the turbulent burst events are analysed. In addition, the mechanisms of turbulence suppression and drag reduction via streamwise traveling wave induced by spanwise-wall oscillation are also discussed. The results suggest that the intrinsic and induced flows are modified each other when the travelling wavy wall is utilized to modulate the near-wall turbulent flow. Only the low-frequency waves have the significant influence on the near-wall turbulent structures which induces the great variations of the the turbulent bursting events which can be detected by VITA detective technique. The variations of the frequency and the intensity of the burst are unsynchronized with wave number, and there exists an optimal wave number, in which the influence of the intrinsic flow on the induced flow is weakest, and on the contrary, the intrinsic turbulent flow is modified strongly by the induced flow, and the largest amount of drag reduction is obtained. Otherwise, the effects of the oscillation parameters on the maximum drag reduction rate are presented, further confirming the existence of the optimal wave number for drag reduction.3) Mechanism for turbulent control and drag reduction in a channel flow subject to a spanwise travelling wave (STW) via Lorentz forcing is investigated numerically. The results show that the intrinsic flow structures are modified by the induced flow on application of STW control to the turbulent bundary layer. The induced flow is consisted by a distinct set of longitudinal vortices, moving along the spanwisae direction with same spanwise spacing, and paralleling with each other. As travelling with the spanwise Lorentz force, these generated longitudinal vortices can suppress positive random longitudinal vortices and merge negative random longitudinal vortices in the near-wall region of the intrinsic turbulent flow. Then, the intrinsic longitudinal vortex structures and the near-wall pairs of streaks are reduced over time. The induced flow finally dominates the near-wall flow and consequently relaminarizes the flow, leading to a reduction in turbulent drag of more than30%. Otherwise, the influences of the spanwise wavelength in the control were discussed. As the wavelength large enough, the influence of the intrinsic flow on the induced flow is weaker, and on the contrary, the streaks and vortex structures in the intrinsic turbulent flow can be reduced remarkably by the induced flow, and correspondingly, the turbulent bursting events are suppressed efficiently. Consequently, larger amount of drag reduction is obtained. If the wavelength is too short, ejection and sweeping activities of the fluid will be enhanced significantly by the induced flow, which will result in notable drag increase.4) The control and drag reduction in turbulent channel flow via streamwise travelling wave induced by spanwise oscillatory Lorentz force are investigated numerically by DNS. The effects of streamwise control parameter on the skin-friction drag and associated statistics are discussed. The induced spanwise velocity, near-wall flow structures, as well as the frequency and intensity of the turbulent bursting events are analysed to disclose the mechanisms of turbulence suppression and drag reduction via such wavy Lorentz force. The results are very similar with what have been obtained by the streamwise travelling wave induced by spanwise-wall oscillation. Only the low-frequency waves have the significant influence on the near-wall turbulent structures which induces the great variations of the the turbulent bursting events. The results show that the frequency and intensity vary with wave number in the contradictious tendencies. There is an optimal wave number in flow control, in which the maximum is obtained. The optimal wave number and the maximum drag reduction are also affected by the oscillation parameters of the wavy Lorentz forces. In addition, the results show that there is an efficiency improvement for the proposed method compared with the spanwise oscillating Lorentz force method.(The reviewers of Physics of Fluids appraise that the work is well motivated and the results are interesting. They provide new and relevant information on the effect of an oscillating spanwise Lorentz force on a turbulent channel flow. In particular, the effect of a streamwise wavenumber in the force distribution is studied. Overall, I think the manuscript will merit publication in Phyiscs of Fluids.)...