Theoretical models of flow control in near-wall areas
Abstract
We present a non-linear near-wall flows control algorithm. This algorithm uses captured vortices in the cross grooves and fluid ejection. The controller is based on a model of point vortices with one degree of freedom and consists of the equation of vortex equilibrium and the Kutta condition in the groove edges. Parameters of a control system for grooves of different depths in a stationary stream are calculated. We determined that in shallow grooves, the region of stability of vortices is wider, than in deep grooves, so they are more promising for control. These results are used to estimate the parameters of the active control scheme with a feedback in a nonstationary flow when the system is responsive to external perturbations. Examples of an implementation of such a scheme are presented for the case when the flow velocity changes periodically or linearly.References
Gad-el-Hak M., Bushnell D.M. Separation control: rewiew // Journal of Fluids Engineering. — 1991. — 113, № 1. — P. 5–30.
Protas B., Wesfreid J.E. Drag force in the open-loop control of the cylinder wake in the Laminar Regime // Physics of Fluids. — 2002. — 14, № 2. — P. 810–826.
Wu J.Z., Vakili A.D., Wu J.M. Review of the physics of enhancing vortex lift by unsteady excitation // Progress in Aerospace Sciences. — 1991. — 28, № 2. — P. 73–131.
Roos F.W., Kegelman J.T. Control of coherent structures in reattaching laminar and turbulent shear layers // AIAA Journal. — 1980. — 24, №12. — P. 1956–1963.
Gorban V., Gorban I. Dynamics of vortices in near-wall flows: eigenfrequencies, resonant properties, algorithms of control // AGARD Report. — 1998. — 827. — P. 15–11.
Protas B. Vortex dynamics models in flow control problems // Nonlinearity. — 2008. — 21, № 9. — P. 1-54.
Betchelor Dzh. Vvedeniye v dinamiku zhidkosti. — M.: Mir. — 1973. — 757 c.
Chorin A.J. Vorticity and Turbulence. — Berlin: Springer. —1994. — 330 p.
Aref H., Kadtke J.B., Zawadski I. Point vortex dynamics: recent results and open problems // J. Fluid Dyn. Res. — 1988. — 3. — P. 63–64.
Meleshko V.V., van Heijst G.J.F. Interacting two-dimensional vortex structures: point vortices, contour kinematics and stirring properties // Chaos, Solutions and Fractals. — 1994. — 4. — P. 977–1010.
Ringleb F.O. Two-Dimensional Flow with Standing Vortex in Ducts and Diffusers // ASME J. Basic Eng. — 1960. — 82, № 4. — P. 921–927.
Bunyakin A.V., Chernyshenko S.I., Stepanov G.Yu. High-Reynolds-number Bftchelor-model asymptotics of a flow past an aerofoil with a vortex trapped in a cavity // J. Fluid Mech. — 1998. — 358. — P. 283–297.
Gorban I.M., Homenko O.V. Dynamics of vortices in near-wall flows with irregular boundaries // Continuous and Distributed Systems: Theory and Applications. Solid Mechanics and Its Applications / M.Z. Zgurovsky, V.A. Sadovnichiy (Eds.). — 2014. — 211. — P. 115–128.
Cortelezzi L., Leonard A., Doyle J. An example of active circulation control of the unsteady separated flow past a semi-infinite plate // J. Fluid Mech. — 1994. — 260. — P. 127–154.
Chernyshenko S.I. Stabilization of trapped vortices by alternating blowing suction // J. Phys. Fluids. — 1995. — 7, № 4. — P. 802–807.
Iollo A., Zanetti L. Trapped vortex optimal control by suction and blowing at the wall // European Journal of Mechanics B-fluids. — 2001. — 20, № 1. — P. 7–24.
Fil’chakov P.F. Priblizhennyye metody konformnykh otobrazheniy. — K.: Naukova dumka. — C. 531.
Clements R.R. An inviscid model of two-dimensional vortex shedding // Journal of Fluid Mechanics. — 1973. — 57. — P. 321–336.
Cortelezzi L. Nonlinear feedback control of the wake past a plate with a suction point on the downstream wall // Journal of Fluid Mechanics. — 1996. — 327. — P. 303–324.
