Particle tracking velocimetry applied to estimate the pressure field around a Savonius turbine

Abstract

Particle tracking velocimetry (PTV) is applied to flows around a Savonius turbine. The velocity vector field measured with PTV is utilized to estimate the pressure field around the turbine, as well as to evaluate the torque performance. The main objective of the work is the establishment of the pressure estimation scheme required to discuss the turbine performance. First, the PTV data are interpolated on a regular grid with a fourth-order ellipsoidal differential equation to generate velocity vectors satisfying the third-order spatio-temporal continuity both in time and space. Second, the phase-averaged velocity vector information with respect to the turbine angle is substituted into three different types of pressure-estimating equations, i.e. the Poisson equation, the Navier–Stokes equation and the sub-grid scale model of turbulence. The results obtained based on the Navier–Stokes equation are compared with those based on the Poisson equation, and have shown several merits in employing the Navier–Stokes-based method for the PTV measurement. The method is applied to a rotating turbine with the tip-speed ratio of 0.5 to find the relationship between torque behaviour and flow structure in a phase-averaged sense. We have found that a flow attached to the convex surface of the blades induces low-pressure regions to drive the turbine, namely, the lift force helps the turbine blades to rotate even when the drag force is insufficient. Secondary mechanisms of torque generation are also discussed.