A Green's Function Approach to PIV Pressure Estimates with an Application to Micro Energy Harvesters in Turbulent and Vortical Flows

In the present work we demonstrate the feasibility to harness energy from fluid flows by using piezoelectric generators. These ac-coupled devices convert fluid kinetic energy, which otherwise would be wasted, into electrical energy. The available power density in a flowing fluid is proportional to the cube of its velocity and if it is properly harvested can be used for continuously powering very small electronic devices or can be rectified and stored for intermittent use. A key quantity in these applications which affects the performance is the forcing which the fluid exerts on the harvesters. An analytical solution is presented for the Pressure Poisson Equation (PPE) that uses Particle Image Velocimetry (PIV) field data to find the pressure in a flow domain and to calculate the pressure and therefore the force exerted by the fluid on the solid surface. The solution provides a favorable method of calculating pressure field from PIV data as it eliminates the need to compute higher order derivatives of velocity on the domain that are present in viscous terms as well as eliminates the need to integrate Navier-Stokes equations to find the pressure along the boundaries of interest. The solution is validated against a theoretical solution for a pressure distribution inside a tornado-like vortex; pressure solutions obtained by derivative momentum transform method for a vortex flow and some experimental results for the pressure distribution inside a turbulent boundary layer. Several experiments were carried out in which pressure was calculated using PPE: i) a discrete vortex passing over a simple cantilever beam harvester ii) a simple cantilever harvester placed in the boundary layer iii) a self-excited harvester placed in the free stream flow. In a discrete vortex experiment, the self-propelled vortex is passed over the cantilever beam. The pressure distribution and the net force of the beam are calculated by solving PPE as the vortex passes over the beam. In a boundary layer flow, PPE solution was used to estimate pressure fluctuations that are present in the turbulent boundary layer. A simple cantilever harvester is then placed inside the boundary layer. The beam is placed inside the boundary layer at various distances from the wall (y/delta~0-1.5) and at various orientations with respect to the free stream flow angle of attack beta=0o°- -- 180°) for free stream flows 2--11 m/s. Power maps are presented showing the power harvested for various heights and orientations of the harvester. In a self-excited harvester experiment, a harvester with a cylindrical tip mass attached is placed in a uniform cross flow. The PPE solution is used to estimate the strength of pressure inside vortices that are shed off the cylinder forcing it into oscillation. In another experiment to characterize the performance of harvesters inside turbulent flows several simple-cantilever harvesters were placed downstream of passive, semi-passive or an active grid. Passive grid consists of square rods spanning the width and the height of the wind tunnel, semi passive grid is similar to passive but has threaded balls attached to the grid in order to increase turbulence intensity. Active grid has flaps attached to the rods that actively control the closing and opening of sections of the flow thus dramatically increasing turbulence intensity. It is shown that as long as the motion of the harvester actuator does not affect the flow field locally, the power produced to the harvester is proportional to the turbulent kinetic energy of the flow locally.