A novel approach for reconstructing pressure from PIV velocity measurements

Abstract

The purpose of this work is to develop an innovative procedure for reconstructing the pressure field from PIV velocity measurements of unsteady, incompressible flows. The proposed technique is based on a generalization of the Glowinski–Pironneau method for the uncoupled solution of the incompressible Navier–Stokes equations written in primitive variables and exploits a finite element discretization of the measurement grid. By virtue of the underlying mathematical formulation, the method is stable and more accurate than the other techniques proposed so far in the literature. The method is first applied to an exact solution of the Navier–Stokes equations, showing second-order convergence of the L∞ error for the pressure variable. The robustness of the method with respect to stochastic perturbations in the velocity field is then tested and the results compared with other techniques proposed in the literature. Finally, the proposed technique is applied to both phase-averaged and time-resolved PIV velocity measurements of the flow around a pitching airfoil employed to investigate the dynamic stall. The reconstructed pressure is compared with direct pressure measurements, showing very encouraging results

Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes

“…The utility of spatio-temporally resolved fluid pressure estimations from time-resolved particle image velocimetry (TR-PIV) measurements (van Oudheusden 2013) has been demonstrated in turbulent boundary layers (Ghaemi et al 2012;Pröbsting et al 2013;Laskari et al 2016;Schneiders et al 2016), jets (de Kat et al 2013), bluff-body wakes (de Kat and van Oudheusden 2012; Dabiri et al 2014;Fujisawa et al 2005;van Oudheusden et al 2007;McClure and Yarusevych 2016), subsonic (Auteri et al 2015;van Oudheusden et al 2006van Oudheusden et al , 2007Violato et al 2011) and supersonic aerofoils (van Oudheusden et al 2007), aircraft propellers , pulsatile diffusers (Charonko et al 2010), the region surrounding a rising bubble (Hosokawa et al 2003), cavity flows (Liu and Katz 2006), and other flow configurations (Murai et al 2007). Estimated pressure fields can be used in conjunction with measured velocity fields to extract time-resolved loadings on immersed structures (van Oudheusden et al 2007;Tronchin et al 2015), establishing a minimally intrusive methodology for the measurement of both fluid pressure and structural loading.…”

Stall Control by Plasma Actuators: Characterization along the Airfoil Span

“…Through this simplified procedure, only an approximation of the coefficient was obtained: for the PIV field of Figure 8, it is reported in Figure 9b, where a significant off-to-on growth of the C P peaks in the order of 35% is observed. Unfortunately, this estimation can hardly be compared with experimental or numerical reference data since it is known that narrow C P peaks are difficult to obtain from PIV data because of resolution limits that easily lead to underestimate the desired value [32]. In fact, the peak is related to the maximum over-speed of the flow, of which the values are usually found in a small region very close to the airfoil that would require a locally very fine grid of PIV data to be properly resolved.…”

“…This displacement may seem mild, but the involved area is quite wide and affects a region where the pressure changes on the model surface can lead to a significant lift variation. Further studies could be done investigating possible enhancements of the control authority: after optimizing the actuator for a given airspeed (Section 2) and setting the same supply to avoid an increase of power consumption, there is the chance to change the DBD location, keeping in mind that the actuation must always take place upstream of the separation, as proven in Reference [33,34]. This would lead to placing the actuator upstream around the airfoil nose, affecting the flow also in the accelerated zone between the stagnation and the nose itself, and could give rise to further developments.…”

PIV-Based Acoustic Pressure Measurements of a Single Bubble near the Elastic Boundary

“…In the past years, the availability of PIV technologies to acquire high-resolution measurements has motivated its application for the multiphase flow dynamics to obtain the measurements of fluid pressure distribution [ 29 , 30 , 31 ]. Auteri et al [ 32 ] proposed a method to calculate the pressure distribution using PIV. This methodology consists of two steps: (i) the first step generates the Neumann boundary conditions by solving inversely the Naiver-Stokes equation; (ii) the second one involves a numerical solution of the pressure Poisson equation.…”