Parabolized stability analysis of jets from serrated nozzles

Abstract

We study the viscous spatial linear stability characteristics of the time-averaged flow in turbulent subsonic jets issuing from serrated (chevroned) nozzles, and compare them to analogous round jet results. Linear parabolized stability equations (PSE) are used in the calculations to account for the non-parallel base flow. By exploiting the symmetries of the mean flow due to the regular arrangement of serrations, we obtain a series of coupled two-dimensional PSE problems from the original three-dimensional problem. This reduces the solution cost and manifests the symmetries of the stability modes. In the parallel-flow linear stability theory (LST) calculations that are performed near the nozzle to initiate the PSE, we find that the serrated nozzle reduces the growth rates of the most unstable eigenmodes of the jet, but their phase speeds are approximately similar. We obtain encouraging validation of our linear PSE instability wave results vis-à-vis near-field hydrodynamic pressure data acquired on a phased microphone array in experiments, after filtering the latter with proper orthogonal decomposition (POD) to extract the energetically dominant coherent part. Additionally, a large-eddy simulation database of the same serrated jet is investigated, and its POD-filtered pressure field is found to compare favourably with the corresponding PSE solution within the jet plume. We conclude that the coherent hydrodynamic pressure fluctuations of jets from both round and serrated nozzles are reasonably consistent with the linear instability modes of the turbulent mean flow.

Instability waves and low-frequency noise radiation in the subsonic chevron jet

“…Nevertheless, the present results match well with RANS solutions of Engel et al [15]. Also, the profiles of axial velocities with respect to z at the lip-line match well with those of Sinha et al [13] and Bridges and Brown [1], as illustrated in Fig. 2.…”

“…Compared with LES and experimental data, the present simulation shows a longer potential core length and faster decay rate beyond the poten- Table 1 The flow conditions of the round and chevron jet [15], filled triangle from Xia et al [16]. The small figure shows the iso-contours ofū z at z = r 0 [13], open circle from Bridges and Brown [1] tial core. Similar deviations are also found in round jet case SMC000.…”

“…A simplified method was proposed in Refs. [9,13], and here we briefly introduce this method. In the current chevron configuration, the chevron jet is periodic in the azimuthal direction, thus the energy is lumarized in azimuthal wavenumbers that are integral multiples of the chevron count (C).…”

“…Very recently, Uzun et al [10] and Sinha et al [11,12] further analyzed the spatial stability of chevron jets at the low frequency and investigated the influence of the chevron parameters. Additionally, Sinha et al [13] studied the instability waves in the downstream region and found a good match between the instability waves and the hydrodynamic fluctuations in the near field. Therefore, there is no doubt that instability waves play an important role in flow mixing and noise radiation in the chevron jet.…”

Temporal stability analysis of jets of lobed geometry

“…In the study of Sinha et al (2016), a viscous spatial linear stability analysis was performed numerically using the PSE (Parabolized Stability Equation) approach. The solutions to the parallel-flow stability equations were obtained first to initiate the PSE.…”