Measurements of Pressure Distribution in a Cavity Flow by Integrating the Material Acceleration

Abstract

In turbulence research, the velocity-pressure-gradient tensor in the Reynolds stress transport equation is critical for understanding and modeling of turbulence. Pressure is also of fundamental importance in understanding and modeling of cavitation. Motivated by the lack of experimental tools to measure the instantaneous pressure distribution away from boundaries, the paper introduces a non-intrusive method for simultaneously measuring the instantaneous velocity and pressure distribution over a sample area. The technique utilizes four exposure PIV to measure the distribution of material acceleration, and integrating it to obtain the pressure distribution. If necessary, e.g., for cavitation research, a reference pressure at a single point is also required. Two cameras and perpendicularly polarized Nd:Yag lasers are used for recording four exposures on separate frames. Images 1 and 3 are used for measuring the first velocity distribution, whereas images 2 and 4 give the second velocity map. The material acceleration is calculated from the velocity difference in sample areas shifted relative to each other according to the local velocity. Averaged omni-directional integration of the material acceleration over the entire flow field, while avoiding regions dominated by viscous diffusion, provides the pressure distribution. To improve the accuracy of the acceleration measurement, cross-correlation of the corresponding image correlation maps is implemented in areas with high velocity gradient. Applications of these procedures to synthetic flows show that the standard deviation of the measured instantaneous pressure from the theoretical value is about 2%. The system has been used to measure the instantaneous pressure and velocity distributions of a 2D cavity flow field in a water tunnel. Three pressure transducers mounted at different locations on the wall are being used for comparison and calibration. Detailed measurements of acceleration, vorticity and pressure distributions within the cavity shear layer indicate that the cavity shear layer flow exhibits highly unsteady behavior due to the self-excited oscillation.