Session HP: Turbulence and Instability Control II

Stabilizing and destabilizing effects of finite-amplitude traveling waves in 2D and turbulent channel flows

Our direct numerical simulations (DNS) have shown that skin-friction drag in a channel can be reduced substantially -- in some cases, below that of a laminar flow -- with blowing and suction at the wall applied in the form of an upstream traveling wave. The low skin-friction drag was due to the Reynolds shear stress associated with the periodic flow induced by the traveling wave. Floquet analysis of finite-amplitude traveling waves is used to investigate their effects on the stability of the channel flow. At both subcritical and supercritical Re, the predicted instability is consistent with DNS results when wave amplitudes are small. With larger wave amplitudes, the present Floquet analysis indicates unstable 2D disturbances, whereas DNS indicates the opposite.   

Laminar and turbulent comparisons for channel flow and flow control

A formula is derived that shows just how much the discrepancy between the volume flux of laminar and turbulent flow at the same pressure gradient increases as the pressure gradient is increased. We compare laminar and turbulent flows in channels with and without flow control. For the related problem of a fixed bulk Reynolds number flow, we seek the theoretical lowest bound for skin-friction drag for control schemes that use surface blowing and suction with zero-net volume-flux addition. For one such case, using a cross-flow approach, we show that sustained drag below that of the laminar Poiseuille flow case is not possible. For more general control strategies we derive a criterion for achieving sub-laminar drag, and use this to consider the implications for the control strategy design and the limitations at high Reynolds numbers.   

Sub-laminar drag in fully developed channel flow by stationary distributed blowing and suction.

Min {\it et al.} (2006, JFM, vol. 558, p. 309) showed that the skin-friction drag in a fully developed channel can be sustained below that corresponding to the laminar profile when blowing and suction is provided in the form of an upstream travelling wave. In the present study, we apply a stationary distributed blowing and suction (steady in time, sinusoidal along the streamwise direction, zero-net mass flux) to the same flow to see if sub-laminar drag is achieved using the stationary blowing and suction. The skin friction changes significantly depending on the blowing/suction wavelength and amplitude. Blowing and suction profiles at small wavelength and large amplitude produce sub-laminar drag. In some case, drag reduction amounts to 70\% at the optimum wavelength and amplitude. As observed in Min {\it et al.}, negative Reynolds shear stress is created in the near-wall region due to the blowing and suction when drag reduction is achieved. Although the control efficiency is low, it is still very interesting to note that one can indeed obtain sustainable drag below than that of fully developed laminar channel flow by a stationary zero-net mass-flux blowing and suction.   

Control of transition in channel flows by a streamwise traveling wave

Sensorless flow control is a promising technology for implementation, as it represents a much simpler alternative to feedback flow control with wall-mounted arrays of sensors and actuators. In this paper, we assess effectiveness of using a zero-net-mass-flux blowing and suction in the form of an upstream traveling wave for transition control in channel flows. Our study is motivated by a recent paper by Min {\em et al.} (J.\ Fluid Mech., vol.\ 558) where it was shown that this type of surface actuation yields a sustained sub-laminar drag in fully developed channel flows. We develop models that govern the dynamics of velocity perturbations in the presence of stochastic outside disturbances (such as free-stream turbulence and acoustic waves) and show how changes in control parameters affect perturbation kinetic energy density. Effectively, we establish that properly designed streamwise traveling waves can be used to weaken intensity of both streamwise streaks and Tollmien-Schlichting waves in transitional channel flows.   

Control-oriented models of linearized channel flow using balanced proper orthogonal decomposition

We obtain reduced-order models of linearized channel flow using balanced proper orthogonal decomposition (BPOD), and compare these to models obtained from the standard POD/Galerkin method. We consider three-dimensional perturbations of complex structure without modeling each wavenumber separately as has been done in previous works, and show that the BPOD models reproduce the frequency response of the original system much better than standard POD models of the same order. The BPOD models capture the effects of actuation better, especially in cases for which the perturbation generates traveling structures. Very low order models using BPOD better capture the behavior for off-design values of the Reynolds number than standard POD models. We also demonstrate that for a range of single-wavenumber perturbations, low-order BPOD models reproduce the dominant eigenvalues of the full system better than POD models of the same order. These features indicate that the simple, yet accurate BPOD models are a good candidate for developing model-based controllers for channel flow.   

Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow

The effects of polymer stresses on the near-wall turbulent structures are examined by using DNS database of fully developed turbulent channel flows ($Re_{\tau}=395$) with and without polymer stress. The stresses created by adding polymer are modelled by a finite extensible non-linear elastic, dumbbell model. Both low (18\%) and high drag reduction (61\%) cases are investigated. The conditionally averaged flow fields for Reynolds-stress- maximizing Q2 event show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses. The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag- reduced turbulence are very similar to those for the Q2 events, i.e., counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. The observations extend concept of vortex retardation by viscoelastic stress to fully turbulent wall flow, and offer an explanation of the mechanism of drag reduction by dilute polymers. Supported by ONR through contract N000140510687.