Low-order estimation of the velocity, hydrodynamic pressure, and acoustic radiation for a three-dimensional turbulent wall jet

Abstract

A method for the experimental characterization of the velocity, hydrodynamic pressure, and acoustic generation in a subsonic (ReH=25,500), three-dimensional, turbulent wall jet is presented. An acoustic analogy formulated for the turbulent wall jet shows that the far-field acoustics relate to the Reynolds stress fluctuations of the velocity field or the product of the hydrodynamic pressure fluctuations and the rate-of-strain field. As these quantities cannot be measured directly with sufficient resolution, low-order reconstructions of the velocity field based on the use of the Proper Orthogonal Decomposition and Stochastic Estimation are developed. Reconstruction of the three-dimensional field is accomplished using spanwise-aligned, stereoscopic particle image velocimetry measurements, obtained at 16 streamwise locations synchronously with an array of 32 surface pressure transducers. The velocity field reconstruction is then used to calculate the fluctuating pressure field (via Poisson’s equation) allowing for the evaluation of coupled pressure-velocity terms in addition to an acoustic analogy for the acoustic far-field. Application of these methods show that the large-scale motion throughout the shear layer is captured by the velocity and hydrodynamic pressure field estimates and features of the acoustic far-field are recovered.