Turbulence and sound-field POD analysis of a turbulent jet
نویسندگان
چکیده
A Proper Orthogonal Decomposition (POD) is constructed for a Mach 0.9 turbulent jet using a well-validated direct numerical simulation database. Norms are defined based on near-field volume integrals of pressure, turbulence kinetic energy, streamwise velocity, and total enthalpy, two-dimensional integrals of streamswise velocity (to match experimental measurements), and far-field integrals of pressure over a sphere. We find substantially different POD modes for the different norms, and their efficiency at representing the full data is strongly dependent upon the norm and specifically which data we attempt to represent. To reproduce near-field turbulence statistics requires relatively few modes computed by a kinetic energy or pressure norm. However, a large number of the POD modes computed using a near-field norm are required to represent the sound field. The dominant near-field POD modes computed with either the near-field pressure norm or the sound field norm have the structure of wave packets. NOMENCLATURE a Sound speed J Number of POD modes retained Re Reynolds number M Mach number N Total number of snapshots n Azimuthal (Fourier) mode number r Radial coordinate ro Jet nozzle radius t Time υx Axial velocity υr Radial velocity υθ Azimuthal velocity x Axial coordinate ψ Directivity angle ρ Density φ POD mode θ Cylindrical polar coordinate Subscripts j Jet exit ∞ Ambient Other Ensemble (time) average ́ Acoustic perturbation (p, q) Inner product
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