Kinematic analyses of wave–packet structures in non-isothermal jet flows: Effects of length scales

Abstract

A kinematic wave–packet sound-source model is developed for non-isothermal jets based on large eddy simulation results of subsonic jets at temperature ratios 0.86, 1.0, and 2.7. To find the suitable variable for the sound-source model, coherent structures in these jets are extracted by leading modes of the proper orthogonal decomposition (POD), and they are classified according to spatial–temporal features. To extend the model, an approach is proposed to represent the growth and decay length scales separately by a single continuous function. Applying such function, the acoustic affections are discussed for the variable length scales of amplitude envelope, L, and coherence, Lc. The results show that the jet temperature desynchronizes the leading POD modes of radial velocity, pressure, and density, and the jet temperature changes the density mode from radial puffs into stripes or ridges. The axisymmetric component of the pressure clearly presents a train of radiant waves, as captured by its leading spectral-POD mode at the peak radiation frequency. Therefore, this pressure component is employed for modeling. In the wave-number domain, the elongation of L stretches the cross-spectral density (CSD) of the source signal, denoted by CSD(k1, k2), along the k1- and k2-axes; the decay of Lc stretches the CSD along the diagonal of the axes. Both of them tend to spread the CSD into a radiant region near the origin point, so as to enhance the radiation. The radiation seems insensitive to the variation of the L, as it only slightly distorts the CSD in the radiant region.