Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

Supersonic jets, particularly shock-containing jets, often exhibit high-intensity, discrete-frequency acoustic tones. These tones are the signature of an aeroacoustic resonance loop established by ...

https://journals.sagepub.com/doi/pdf/10.1177/1475472X19834521

Aeroacoustic resonance and self-excitation in screeching and impinging supersonic jets – A review:

The aeroacoustic feedback loop establishing in a supersonic round jet impinging on a flat plate normally has been investigated by combining compressible large-eddy simulations and modelling of that loop. At the exit of a straight pipe nozzle of radius r0, the jet is ideally expanded, and has a Mach number of 1.5 and a Reynolds number of 60000. Four distances between the nozzle exit and the flat plate, equal to 6r0, 8r0, 10r0 and 12r0, have been considered. In this way, the variations of the convection velocity of the shear-layer turbulent structures according to the nozzle-to-plate distance are shown. In the spectra obtained inside and outside of the flow near the nozzle, several tones emerge at Strouhal numbers in agreement with measurements in the literature. At these frequencies, by applying Fourier decomposition to the pressure fields, hydrodynamic-acoustic standing waves containing a whole number of cells between the nozzle and the plate and axisymmetric or helical jet oscillations are found. The tone frequencies and the mode numbers inferred from the standing-wave patterns are in line with the classical feedback-loop model, in which the loop is closed by acoustic waves outside the jet. The axisymmetric or helical nature of the jet oscillations at the tone frequencies is also consistent with a wave analysis using a jet vortex-sheet model, providing the allowable frequency ranges for the upstream-propagating acoustic wave modes of the jet. In particular, the tones are located on the part of the dispersion relations of the modes where these waves have phase and group velocities close to the ambient speed of sound. Based on the observation of the pressure fields and on frequency–wavenumber spectra on the jet axis and in the shear layers, such waves are identified inside the present jets, for the first time to the best of our knowledge, for a supersonic jet flow. This study thus suggests that the feedback loop in ideally expanded impinging jets is completed by these waves.

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Feedback loop and upwind-propagating waves in ideally expanded supersonic impinging round jets

Noise generation mechanisms for a perfectly expanded supersonic Mach number turbulent jet impinging on a inclined plate are investigated for a Reynolds number of employing a large-eddy simulation. Excellent comparisons with experimental acoustic far-field measurements and pressure measurements on the impingement plate are obtained. Two local maxima are identified in the far-field overall sound pressure levels in the and observer directions, which are associated with different noise generation mechanisms. The peak frequencies in the spectra with Strouhal numbers of for and for match the experimental measurements. The jet-impingement region generates pressure waves that propagate predominantly in the observer direction. The noise generation in this region is attributed to vortex stretching and tearing during shear-layer impingement, and shock oscillations that are induced by the motion of downstream convected vortical flow structures. The second peak in the overall sound pressure distribution at is associated with noise sources located in the wall jet. The noise generation in the wall jet is associated with supersonically convecting large-scale coherent flow structures that also interact with tail shocks in the wall jet causing large localized pressure fluctuations. Strongly coherent flow structures are identified by applying proper orthogonal decomposition (POD) to the unsteady flow field. The frequency characteristics of the most energetic POD modes are distinctly different based on which energy norm is chosen. The most energetic entropy-based POD modes contain a peak frequency of approximately , while the most energetic turbulent kinetic-energy-based POD modes appear to be dominated by lower-frequency content. The causality method, based on Lighthill’s acoustic analogy, is used to link the acoustic noise signature to the relevant physical mechanisms in the source region. A differentiation is made between the application of normalized and non-normalized cross-correlation functions for noise source identification and characterization.

Noise generation mechanisms for a supersonic jet impinging on an inclined plate

Large-eddy simulations are performed using high-fidelity numerical schemes developed for turbulence simulations and computational aeroacoustics to study near-ideally expanded and tone-producing supersonic jets vertically impinging on a large flat plate. The simulations compute the complex interaction of the supersonic jet with the flat impingement plane and directly provide the noise generated by this interaction. Two jet-operating temperatures, which correspond to isothermal and heated conditions, are considered in the simulations. The simulation results from both cases are examined to investigate the intense tonal noise generation arising from the jet impingement. The comparisons between the simulation results and the corresponding experimental measurements generally show a reasonable agreement and provide credibility to the quality of the simulation predictions. The simulations reveal important details about the problem of interest, which are not observable from the experiments. A dynamic mode decompos...

Simulation of Tonal Noise Generation by Supersonic Impinging Jets

This paper presents a computational study of the flow and flow-induced acoustic fields of a supersonic jet impinging on an inclined flat plate. For the numerical simulations, we solved three-dimensional compressible Navier-Stokes equations with a modified weighted compact nonlinear scheme. We analyzed the simulation results mainly from the viewpoint of the acoustic emission and propagation mechanism, and we investigated the acoustic field characteristics such as directivity, their spectra, and acoustic wave source positions. The acoustic fields indicate that there are at least three types of acoustic waves in all the cases considered in the study: (i) Mach waves generated from the shear layer of the main jet, (ii) acoustic waves generated from the impingement region, and (iii) Mach waves generated from the shear layer of the supersonic flow downstream of the jet impingement. The indication of the second type of wave (ii) is important because the commonly used empirical method for the estimation of the aco...

Aeroacoustic waves generated from a supersonic jet impinging on an inclined flat plate

Flow and flow-induced acoustic fields of a supersonic jet impinging on an inclined flat plate is computationally studied. Effects of nozzle-plate distance and jet temperature are discussed as these are important parameters for the estimation of the acoustic wave strength from the engineering viewpoint such as a rocket plume. Three-dimensional compressible Navier-Stokes equations are solved with the modified weighted compact nonlinear scheme for the numerical simulations. Simulation results are analyzed from the viewpoints of acoustic emission and propagation mechanism, and acoustic field characteristics such as directivity, their spectra, and acoustic wave source positions are investigated. Time-averaged pressure contour on the plate shows two pressure peaks that are commonly observed in the jet-plate interaction; one by the jet impingement and the other by the plate shock wave. The acoustic fields indicate that there are at least three kinds of acoustic waves in all the cases considered in the study: (i) Mach waves generated from the shear layer of the main jet, (ii) acoustic waves generated from the impingement region, and (iii) Mach waves generated from the shear layer of the supersonic flow downstream of the jet impingement. Indication of the second one (ii) is important because the commonly-used empirical method for the estimation of the acoustic waves from a rocket plume does not consider such acoustic waves. Directivity and sound pressure level of the acoustic waves (ii) and the Mach waves (iii) change strongly with the temperature increase. Directivity and sound pressure level of the acoustic waves (ii) and the Mach waves (iii) change slightly with the nozzle-plate distance increase. The results show that whether the impinging point is inside or outside of potential core does not strongly affect the characteristics of the induced acoustic waves (ii).

Acoustic waves from a supersonic jet impinging on an inclined flat plate

Supersonic underexpanded jet impinging on an inclined flat plate is computationally simulated using RANS and ILES. In this paper, validations of these simulations for this flow field are conducted and the results show that simulations are qualitative agreeements with experiment. Furthermore, the factors leading to the localized pressure peaks on the plate surface and the unsteadiness of these pressure peaks are discussed in detail. In the present condition, there are 3 factors leading to the pressure peaks: strong shock waves in the upstream area, stagnation point of the main stream in the upstream area, interaction between the intermediate tail shock and the boundary layer. In addition, these pressure peaks have some unsteadiness respectively.

Detailed Analysis of Flat Plate Pressure Peaks Created by Supersonic Jet Impingements

Payload oscillation due to strong acoustics emitted from rocket plume is one of the most significant problems in rocket launch. It is known that the rocket plume produces strong acoustics when it impinges the rocket plume deflector. Therefore, it is important to understand this phenomenon, which can be modelled with a supersonic jet impinging on an included flat plate. Supersonic jet impinging on an inclined flat plate was experimentally studied by P. J. Lamont and B. L. Hunt 1 . They measured the pressure on the plate surface with pressure taps and visualized the flow fields with shadow graph method. However, the surface pressure data were limited because they are measured on discrete points. Nakai et al. 2 conducted experimental study of the jet impingement on an included flat plate using pressure sensitive paint and Schlieren method. Based on continuous surface pressure data on the plate and the Schlieren images, they classified the flow fields into three types, corresponding to the different shock wave structures (Figure. 1). This classification enables flow type prediction if pressure ratio, the inclined angle of the plate, and the nozzle-plate distance are given. These past researches, however, only steady phenomena are analyzed. Therefore, unsteady phenomena of the supersonic jet impingement, which are key mechanism of acoustics emission, are not well-known. An objective of the present research is to understand unsteady flow phenomena of the supersonic jet impingement using computational fluid dynamics. So far, steady flow structures have been clarified using RANS simulation, where unsteady flow structure will be analyzed using high resolution scheme. In this abstract, steady analysis of the jet impingement is shown. In Figure 2, pressure distributions at the pressure ratio PR=7.4 for four different plate angles and four different plate distances are shown as an example. Some cases have a single peak and some cases have a few different types of peaks. In these cases, there observed are four types of pressure peaks; (1) stagnation point of the main stream, (2) strong shock waves in the upstream area, (3) reattachment of the detached flow and (4) interaction between the intermediate tail shock and the boundary layer. Figure 3 shows

Yoshinori Goto

Papers

Aeroacoustic waves generated from a supersonic jet impinging on an inclined flat plate

Acoustic waves from a supersonic jet impinging on an inclined flat plate

Detailed Analysis of Flat Plate Pressure Peaks Created by Supersonic Jet Impingements

Unsteady Computational Analysis of Supersonic Underexpanded Jet Impinging on an Inclined Flat Plate