Large-eddy simulation of underexpanded round jets impinging on a flat plate 4 to 9 radii downstream from the nozzle

Abstract

Supersonic round jets have been computed by compressible Large Eddy Simulation (LES) using low-dispersion and low-dissipation schemes. The jets are underexpanded, and are characterized by a Nozzle Pressure Ratio of N P R = Pr/Pamb = 4.03, where Pr is the stagnation pressure and Pamb is the ambient pressure. They have a fully expanded Mach number of Mj = 1.56, an exit Mach number of Me = 1, and a Reynolds number of Rej = ujD/ν = 5 × 10 4 , where ue and D are the jet exit velocity and the nozzle diameter, respectively. A free jet is first considered. Four jets impinging on a flat plate normally are then examined. The distance L between the nozzle lip and the flat plate varies from L = 4.16r0 up to L = 9.32r0 where r0 = D/2, for the impinging jets. The effects of the plate on the aerodynamic and acoustic properties of the jets are thus studied. For the free jet, snapshots of density, pressure and vorticity are presented. Mean velocity fields are displayed, they are in good agreement with experimental data. The near pressure field of the jet is investigated using Fourier decomposition. A screech tone component is found, at a frequency comparing well with experimental data and theoretical models. For the four impinging jets, similarly, flow snapshots and mean flow fields are shown. The results obtained are similar to the corresponding measurements. The convection velocity of large-scale structures in the jet shear layers is then evaluated and an expression giving the average convection velocity between the nozzle lips and the flat plate is proposed. The near pressure fields are then explored, and the main properties of the aeroacoustic feedback mechanism occurring between the nozzle lip and the flat plate are presented. The results are consistent with theoretical models and experimental data.

Experimental characterisation of the screech feedback loop in underexpanded round jets

“…resulting in variation of U c /U j from 0.7 at M j = 1 to 0.57 at M j = 1.56, where M j is the equivalent ideally expanded jet Mach number. A spatial dependence was also pointed out by Gojon, Bogey & Marsden (2015), who reported from a numerical simulation that the convective velocity increases with the downstream distance z from the nozzle. Equation (1.1) also requires that the shock cell length be constant, whereas it decreases with the axial distance from the nozzle exit z (Tam, Jackson & Seiner 1985;Tam et al 1986).…”

Estimation of convection speed in underexpanded jets from schlieren pictures

“…Further details on the simulation are provided in a previous paper. 16 The jet is underexpanded, and is characterized by a Nozzle Pressure Ratio of NPR = P r /P amb = 4.03, where P r is the stagnation pressure and P amb is the ambient pressure. The fully expanded Mach number is M j = 1.56, the exit Mach number M e = 1, and the Reynolds number is Re D = 5 × 10 4 .…”

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

“…In both mechanisms, the main parts of the feedback loop are the shear layer instabilities propagating downstream and pressure waves propagating upstream. The shear layer instabilities form unstable spatially growing hydrodynamic waves, and have been observed in previous experimental and numerical studies of free and impinging under-expanded supersonic jets [2,[4][5][6][7][8][9][10]. There is a common belief that the acoustic waves scattered by the nozzle lip through the receptivity process internalise as shear layer Kelvin-Helmholtz-type instabilities and form these coherent structures [2,11,12].…”

“…In recent years, there has been considerable interest in data-driven techniques to reveal the characteristics of coherent structures, especially in jet flows [13][14][15][16][17][18]. In the recent series of large eddy simulation studies of ideally expanded and under-expanded supersonic slot and round impinging jets [5,8,19], the discrete Fourier transform of the near-field pressure has been used to obtain the frequencies of the acoustic tones. The predicted acoustic tones and mean flow fields were in a good agreement with the experimental and numerical study of Krothapalli [20] for the ideally expanded jets, and with the experimental results of Henderson et al [3,12] for the under-expanded supersonic impinging case.…”