Pressure and Acceleration Determination Methods Using PIV Velocity Data

Simultaneous knowledge of the entire pressure, acceleration and velocity fields in a region of a flow is a major factor in understanding and modeling a case under study, especially for fluid dynamic and engineering applications. At present, the accuracy of the velocity map coming from particle image velocimetry (PIV) using higher order cross-correlation algorithms with advanced post processing including filters, removing and replacing the odd data, and smoothing functions is in an acceptable range. Using PIV velocity data to determine the acceleration and pressure distribution causes a kind of error accumulation; thus, the inaccuracy of the acceleration and pressure data is several times greater than that of the velocity data; therefore, the need for accurate algorithms cannot be ignored. In this paper, a synthetic image generation code is used to create benchmark images for an unsteady forced vortex flow with known velocity, acceleration and pressure data. These known data are necessary to investigate the accuracy of the results. Different acceleration methods including pseudo-tracing, regression and central finite difference are introduced and compared. In addition, the influence of some involved parameters, the time interval between the velocity fields (Δt), cell size and overlapping is studied synthetically. The results show that the methods strongly depend on the time interval Δt, and increasing it improves the accuracy until a critical Δt is reached. In steady flows, the methods are time independent, but for the tracing method, a time step is introduced. The tracing method among all methods represents the most accurate acceleration results for both steady and unsteady flows. Navier-Stokes equations are used as the pressure-estimation method since they show more details of the flow field. Pressure gradients are integrated by using a numerical integration method that shows high accuracy for images with no bluff body inside them.