|M.Sc Student||Khodos Gregory|
|Subject||The Flow Generated by an Oscillating Plate|
|Department||Department of Aerospace Engineering||Supervisors||Professor Itzchak Frankel|
|Professor Gil Iosilevskii|
We study the flow generated by the periodic pitching motion of a 2D rigid plate about its fixed end in an unbounded incompressible fluid which is otherwise at rest, as a simple model of the operation of micro fans. Although it is well known that flow can be generated by flapping a plate, the generation of thrust by a flapping plate is not well understood. Recent experimental studies and numerical - simulation research have identified that an average pseudo-jet flow is formed by cyclic generation of counter-rotating vortices by an oscillating cantilever. Unlike classical unsteady aerodynamics dealing with wing oscillations in a uniform stream, the present problem is inherently non-linear even for small-amplitude oscillations. In the present research the physical mechanisms underlying the thrust generation are addressed within the framework of a semi-analytic model and two types of flow simulations.
2-D viscous incompressible flow field has been simulated by numerical solution of Navier-Stokes equations using a commercial (Fluent) flow solver. Unsteady incompressible potential flow was simulated using a Discrete - Vortex Method (DVM), which imitates viscous (rotational) flow topology by irrotational potential flow with concentrated vorticity (discrete vortices). The axial thrust produced by the plate is calculated by both methods. The results show that the thrust is time periodic with a constant non-zero mean. This behavior is observed from the first period of plate movement. This result, which is thoroughly discussed, shows that the thrust force is primarily governed by the near - plate flow field. Qualitative and quantitative agreement between the results of viscous- (Fluent) and inviscid- (DVM) simulations indicates that the viscous effects are indeed small.
Thrust investigation is then extended within the framework of a semi-analytic model of inviscid flow incorporating concentrated vortex shedding at the plate free end. The analysis is carried out using the theory of analytic functions of complex variables. Thus the problem has been transformed from physical (z) plane to the upper-half auxiliary (ζ) plane using conformal mapping. The present work applies to this problem a model of a concentrated growing vortex with a feeder sheet as presented by Edwards & Cheng. The model has been extended for the periodic plate oscillations during which the shed vorticity changes sign and counter rotating vortices are periodically released from the plate free end. It results in a system of nonlinear ordinary differential equations from which vortex strength and vortex-centre location are obtained numerically. Due to numerical instability only few periods of the plate movement may be calculated. However, the above mentioned numerical-simulation result of constant mean thrust indicates that these first periods are sufficient for the thrust calculation. It is then obtained semi-analytically by integration of the pressure distribution on the plate surface. This solution, being in good agreement with computational-simulation results, provides insight into the physical mechanisms underlying the thrust generation. In particular, the primary contribution turns out to be produced by fluid acceleration caused by the unsteadiness of the plate movement.