Optimal Electromagnetic Control Of Wakes For Drag Reduction, Lift Amplification And Oscillatory Suppression

The flow of the weak electrolyte solution can be controlled by Lorentz forces achieved with the suitable magnetic and electric fields, and it has the advantages for the vortex street suppression, the drag reduction and oscillatory suppression for the flow over a bluff body. The experimental and numerical investigations on electro-magnetic control of cylinder wake and its vibration induced by vortex shedding have been performed in this paper. Experiments are conducted in a rotating annular tank filled with low-conducting electrolyte. A cylinder with electro-magnetic actuators mounted on the surface is placed into the electrolyte. Force measurements have been carried out by strain gages attached to a fixed beam mounted with the cylinder, and the flow fields are visualized by dye markers. Based on the Navier-Stokes equations, with the consideration of the electromagnetic body force, i.e. Lorentz force as the source term, in the exponential-polar coordinates, the numerical investigations are carried out by means of an Alternative-Direction Implicit algorithm and a Fast Fourier Transform algorithm. The cylinder motion is calculated with the Runge-Kutta method.1) With the exponential-polar coordinate attached on the moving cylinder, the stream function-vorticity equations of vortex-induced vibration, the initial and boundary conditions together with distribution of hydrodynamic force in shear flow are deduced where hydrodynamic force consists of inertial force, the vortex-induced force and viscous damping force. Similarly, the cylinder motion equation with virtual mass is induced where the virtual mass consists of the cylinder mass, the potential added mass and the apparent added mass induced by viscosity. Three factors are revealed which affect fluid-structure interactions from the fixed cylinder to the steady vibration:The first is the vortex shedding where one side shear layer of cylinder strengthens with the effect of the dominated vortex. The second is the vortexes strengthen in one side and weaken in the other side together with the shift of front stagnation point with the effect of background vortex which is generated by shear flow. The third is the vibration of cylinder which pushes the fluid on the pressure side and pumps that on the suction side. The character of vortex-induced vibration in shear flow are affected by the above three factors.(The reviewers of Physics of Fluids appraise that this control strategy seems to be enough interesting to be studied in detail. The paper is new and interesting.)2) The vortex street suppression, drag reduction, lift amplification and oscillatory suppression achieved by Lorentz force are investigated. The results show that the Lorentz force can be classified into the field Lorentz force and the wall Lorentz force based on the influences. The field Lorentz force can modify the cylinder force by the induced flow field which leads to suppression of vortex shedding periodically, the increase of drag, the decrease of lift vibration and suppression of cylinder vibration; However, the wall Lorentz force acts on the cylinder force directly which has no effect on the flow field and suppression of vibration, but it can increase thrust for drag reduction. With the Lorentz force applied on the higher flow velocity side(upside), the direction of cylinder lift points to the downside with the induced flow field, while the direction of lift points to the upside with the wall Lorentz force which dominates on the total force. Therefore, the lift can be increased by upside Lorentz force. Moreover, it is deduced mathematically and validated numerically with the results of electro-magnetic control that, for two-dimensional incompressible flow with no-slip boundary condition, the integral value of the Okubo-Weiss function in the whole flow regions is always equal to zero, which is independent of the shape of the body surface and the existence of the field force.(The reviewers of Fluid Dynamics Research appraise that the referee holds positive viewpoint on the investigation, which makes scientific sense in explaining the underlying mechanism of the drag reduction methodology by adding Lorentz force.)3) The optimal control of cylinder wake via Lorentz force is performed based on nonlinear optimal control theory. The extremum with a constraint of N-S equation is transformed to corresponding problem of the resolve adjoint flow and control sensitivity. The receding-horizon predictive control setting is employed to resolve flow equations and its adjoint equations. The variations of the optimal interaction parameters with time are obtained through numerical simulations of flow equations and its adjoint equations for nonlinear optimal control of cylinder wake. The results show that the cylinder wake can be controlled effectively by the optimal control. Moreover, the coverage location of electro-magnetic actuators is optimized. The results show that the drag is increased with flow field Lorentz force and reduced with wall Lorentz force. The thrust caused by wall Lorentz force gets its maximum value at the meridian plane θm=900of the cylinder, and the same to the drag caused by the field Lorentz force. Therefore, the total effect is not optimized. However, their sum gets the maximum value at about the center area of the flow separation coverage which is the optimal location for drag reduction.(The reviewers of Computers&fluids and European Journal of Mechanics appraise that the manuscript describes an interesting control approach to suppress the formation of vertices and their adverse effects in the wake of cylinder. The work appears of quality and the paper is recommended for publication.)...