The proper orthogonal decomposition method is applied to the analysis of particle image velocimetry data obtained for a supersonic rectangular jet operated at underexpanded conditions. Phase-locked velocity field data were used to calculate the eigenfunctions and the eigenvalues. It was found that a large fraction of the total energy is contained within the first two modes. The essential features of the jet are thus captured with only two functions. A low-dimensional model for the dynamical behavior is then constructed using Galerkin projection of the isentropic compressible Navier-Stokes equations. The reduced model compares reasonably well with the experimental findings.

Three-dimensional position and velocity information can be extracted by direct analysis of the diffraction patterns of seeding particles in imaging velocimetry with real-time CCD cameras. The generalized Lorenz-Mie theory is shown to yield quantitatively accurate models of particle position, such that it can be deduced from typical experimental particle images with an accuracy of the order of 20 microm and an error of 11 gray levels rms, data obtained by comparison of theoretical and experimental images. Both the theory and an experimental verification of the problem presented here are discussed.

A procedure allowing for the analysis of complex acoustic networks, including three-dimensional cavities described in terms of zero-dimensional equivalent elements, is presented and validated. The procedure is based on the linearization of the finite volume method often used in gas-dynamics, which is translated into an acoustic network comprising multi-ports accounting for mass exchanges between the finite volumes, and equivalent 2-ports describing momentum exchange across the volume surfaces. The application of the concept to a one-dimensional case shows that it actually converges to the exact analytical solution when a sufficiently large number of volumes are considered. This has allowed the formulation of an objective criterion for the choice of a mesh providing results with a prefixed error up to a certain Helmholtz number, which has been generalized to three-dimensional cases. The procedure is then applied to simple but relevant three-dimensional geometries in the absence of a mean flow, showing good agreement with experimental and other computational results.

This paper describes the experimental imaging of a spherical particle diffraction pattern obtained in back, forward and side scattering configurations, using illumination from three different beam shapes. The experimental problems encountered for each of the viewing configurations and the theoretical analysis of the diffraction pattern of the particle on its image plane using the generalized Lorenz-Mie theory are discussed. The images obtained are quantitatively compared with calculated results and implications for particle position estimation are discussed.

No abstract