Analysis of Coherent Structures in an Under-Expanded Supersonic Impinging Jet Using Spectral Proper Orthogonal Decomposition (SPOD)

Abstract

The spatiotemporal dynamics of the coherent structures in an under-expanded supersonic impinging jet are studied using a spectral proper orthogonal decomposition technique. For this analysis, a large eddy simulation of an under-expanded supersonic impinging jet at a pressure ratio of 3.4 and a stand-off distance of 2 jet diameters at a Reynolds number of 50,000 is performed. The mean flow fields illustrate some striking features of this flow, such as an oblique shock, a stand-off shock, a Mach disk, and a recirculation bubble. The spectral proper orthogonal decomposition method is applied to time-resolved three-dimensional flow fields. The accumulative energy of modes within each azimuthal mode number reveals that the first three azimuthal modes contain most of the energy of the flow. The spectra of these azimuthal modes show that the flow exhibits a low-ranked behaviour with discrete frequencies at the optimal symmetric azimuthal mode while other two azimuthal modes have negligible contributions in this behaviour. Three peaks are observed in the spectra of the optimal symmetric azimuthal mode. The spatial fields of the streamwise velocity and pressure of these peaks show that the complex structures are consequences of the under-expansion, Mach disk, and the impingement. Strong hydrodynamic instabilities exist in the shear layer of the jet in the optimal azimuthal mode at each of these dominant frequencies. High-amplitude acoustic waves are also present in the near-field of the jet. These acoustic waves are strong at the nozzle lip, suggesting that a feedback loop linking these two processes exists for dominant frequencies in the optimal mode. High cross-spectrum density of near-field pressure fluctuations and streamwise velocity fluctuations near the nozzle lip at these frequencies confirms the hydro-acoustic coupling, which is necessary to close the feedback loop.

Linear modelling of self-similar jet turbulence

“…This method has been used extensively to identify coherent structures in the near field (e.g. Gudmundsson & Colonius 2011;Schmidt et al 2018) and the far field (Gamard et al 2002(Gamard et al , 2004) of turbulent jets, as well as supersonic impinging jets (Karami & Soria 2018). Due to its clear frequency separation, it allows for a consistent comparison with linear stability models.…”

“…2018) and the far field (Gamard et al. 2002, 2004) of turbulent jets, as well as supersonic impinging jets (Karami & Soria 2018). Due to its clear frequency separation, it allows for a consistent comparison with linear stability models.…”

Effects of Nozzle Pressure Ratio and Nozzle-to-Plate Distance to Flowfield Characteristics of an Under-Expanded Jet Impinging on a Flat Surface

“…With the recent improvement in digital imaging cameras, high-speed schlieren is enable to acquire large datasets of time-resolved flowfield information (Berry et al [56]), although the measured quantities are scalars derived from density gradients (Berry et al [54]). The statistical dominant flow structures and dynamical evolution of large-scale flow structures can be extracted from the time-resolved schlieren images or from the time-resolved velocity fields obtained from large-eddy simulations using POD (Weightman et al [10], Berry et al [54], Nair et al [57], Berry et al [58], Weightman et al [59]), spectral POD (Karami and Soria [60]), and dynamic mode decomposition (DMD) (Berry et al [56]) techniques.…”

Акустические Характеристики Автоколебательного Процесса, Возникающего При Взаимодействии Сверхзвуковой Недорасширенной Струи С Цилиндрической Полостью

“…Экспериментальные и численные результаты для различных каверн приводятся в работах [13][14][15]. Генерация тонального шума, возникающего при взимодействии сверхзвуковых струй с преградами, обсуждается в работах [16,17].…”