Sanjiva K. Lele

In flows of engineering interest, Large Eddy Simulation (LES) subgrid stress modeling directly impacts the integrated quantities of interest such as coefficient of lift and drag. A novel graph neural network (GNN) architecture is further explored for complex geometry simulations of an airfoil and cylinder. A priori, the neural network is trained on four different canonical flows, forced homogeneous isotropic turbulence (HIT), channel flow, zero pressure gradient boundary layer, and adverse pressure gradient boundary layer. The graph neural network model does not suffer performance degradation when trained on all four canonical flows as compared to just one canonical flow, and can extend to non-cartesian meshes even though the training set only consists of cartesian meshes. A posteriori results show that the neural network model is able to extrapolate to a cylinder flow. In addition, the training dataset is augmented with a converging-diverging channel and cylinder flow configurations. A GNN model trained on this augmented training dataset is also evaluated on a NACA 4412 airfoil, where it predicts the coefficient of lift more accurately than traditional models.

Large Eddy Simulation (LES) subgrid stress modeling directly impacts the quality of the LES solution, and should be improved to help advance the accuracy of higher Reynolds number simulations of engineering interest. A novel graph neural network architecture is introduced that can scale to complex simulations, and is able to outperform existing neural network models and traditional models. A priori, the newly proposed graph neural network model is also able to extrapolate to various grid sizes not in the training set, and to non-cartesian meshes even though the training set only consists of cartesian meshes. A posteriori, the graph neural network architecture outperforms existing neural network and traditional subgrid stress models when evaluated on flows and grid resolutions in the training set, while avoiding catastrophic failure during extrapolation to grid resolutions coarser than the training set. Furthermore, the graph neural network is evaluated on flow over a cylinder, even though it is never trained on curvilinear meshes or a cylinder flow, and provides surface pressure measurements and coefficient of drag predictions that match experimental studies.

To understand the reliability of successful ignition through use of laser energy deposition for a liquid-oxygen gaseous-methane rocket combustor, we conduct large-eddy simulations (LESs). We first ensure that pre-ignition flow statistics accurately reproduce companion experimental measurements conducted at Purdue University. With satisfactory agreement observed in pre-ignition, we vary physical input parameters to construct an ensemble of LES ignition trials. The majority of the computations are coarse LES but a small set of enhanced refinement calculations with an order of magnitude more grid points verify that the ignition mechanism is the same across fidelities. Subsequently, alignment between experiments and simulations is enabled by a parameter estimation framework, whereby unmeasurable quantities associated with the laser operation are inferred by the uncertainty in underlying successful ignition likelihoods that arises from a limited number of experimental trials. With confidence established in the LES, we subsequently report the ignition pathways contrasting the critical instances that lead to ignition failure or success.

Neural network subgrid stress models often have a priori performance that is far better than the a posteriori performance, leading to neural network models that look very promising a priori completely failing in a posteriori Large Eddy Simulations (LES). This performance gap can be decreased by combining two different methods, training data augmentation and reducing input complexity to the neural network. Augmenting the training data with two different filters before training the neural networks has no performance degradation a priori as compared to a neural network trained with one filter. A posteriori, neural networks trained with two different filters are far more robust across two different LES codes with different numerical schemes. In addition, by ablating away the higher order terms input into the neural network, the a priori versus a posteriori performance changes become less apparent. When combined, neural networks that use both training data augmentation and a less complex set of inputs have a posteriori performance far more reflective of their a priori evaluation.

Large Eddy Simulations (LES) are becoming increasingly viable due to the growth in computational power the last few decades, and subgrid stress modelling plays a large role in the accuracy of LES. A new class of neural network models, S4 and S4ND models, allow for learning a continuous representation of the discrete dataset, which facilitates a principled approach to incorporating grid dependence in neural network subgrid stress modelling. A S4ND Unet neural network architecture is proposed and trained on both forced Homogeneous Isotropic Turbulence (HIT) and channel flow, where a priori, it is shown to generalize to grid spacings that are coarser than the training set grid spacings, while simpler artificial neural network (ANN) models fail. A posteriori tests on both forced HIT and channel flow indicate that the S4ND model is more accurate than traditional models and ANN-based models on grid sizes that are in the training set. The S4ND model is also able to generalize to grid sizes that are coarser than the training set a posteriori, and is more accurate than many traditional and neural network subgrid stress models. Finally, the proposed model is also evaluated on flows at increasing Reynolds numbers, where it is seen that the proposed neural network remains stable even at a Reynolds number that is 500,000 times that seen in the training set.

Supersonic jet noise is known to cause negative health effects on personnel and on aircraft structures. Experiment results have demonstrated that fluidic injection is effective at mitigating supersonic jet noise, but the mechanism for noise mitigation for rectangular jet is not well established. This paper presents the initial steps towards determining the mechanism. We explored the grid sensitivity of the acoustic prediction by comparing two baseline Large Eddy Simulation (LES) case. We find that it is critical to fully resolved relevant turbulence scale in order to get an accurate prediction for far-field acoustics. We further explored how the fluidic injection modifies the supersonic jet flow with a port injection configuration. It is found that the fluidic injection reduces the shock cell strength in potential core, most likely caused by the weakening of the shocks emanating from the nozzle lip and the increased level of turbulence in the initial shear layers near the nozzle outlet. Further iterations on the simulations for both baseline and fluidic injection will be conducted to further establish the mechanisms involved and allow more detailed comparison with the experiments.

A detailed study of the guided jet mode involved in screech tone generation for an aspect ratio 4:1 rectangular jet is performed using large-eddy simulation (LES) data generated by Wu et al. (2022). 2D linear stability analysis is performed using cross-sectional mean flow profiles obtained from LES. The dominant flapping Kelvin-Helmholtz wave and guided jet mode are identified through linear theory. The properties of the guided jet modes and the duct modes supported by the jet are analyzed as functions of the downstream location. The flapping guided jet mode is found to be propagative in a narrow region downstream that aligns well with the peak guided jet mode amplitude in LES. Downstream of this region, the flapping guided jet mode and duct mode are evanescent. A velocity variance budget equation is formulated for the guided jet mode and evaluated using LES data. The dynamics of the guided jet mode are found to be well-explained by triadic interactions involving the Kelvin-Helmholtz wave, the shock-cell structure, and the slowly-varying mean jet flow. Source terms are evaluated in physical space, revealing where the guided jet mode gains kinetic energy and where it loses kinetic energy to specific triadic interactions.

Neural networks applied to turbulence modeling often do not learn locality or generalize to very high Reynolds number reasonably. Here, a two neural network architecture is introduced that learns the relevant neighborhood needed for sub-filter stress modeling through convolutions and the U-net architecture while generalizing reasonably to Reynolds numbers far larger than the training set on forced homogeneous isotropic turbulence and channel flow.

Sub-filter stress (SFS) modelling is crucial for accuracy in Large-eddy simulations (LES). Data driven state space models, such as S4 and S4ND models, encode a continuous representation of the data, which is more closely aligned to the physics of the problem while allowing for a principled approach to incorporating grid dependence into SFS modelling. A data driven state space model is designed utilizing the Unet architecture with a tensor basis neural network backend. Training on various filter widths with data from both forced homogeneous isotropic turbulence and channel flow suggests that the model will be amenable to training on more conditions in the future. A physics-informed loss function that enforces sub-filter dissipation directly ensures that simulations can accurately predict the SFS and the dissipation field in an a priori setting. A posteriori tests on both forced homogeneous isotropic turbulence and channel flow show that the neural network is able to extrapolate to grid sizes unseen during training, and the extrapolative simulations provide more accurate results of spectra and correlations for HIT as well as more accurate Reynolds stresses for channel flow as compared to existing data driven and non data driven models.

Supercritical carbon dioxide (sCO2) plays an important role in improving the sustainability of technologies such as power and refrigeration systems. However, heat transfer effects within sCO2 boundary layers are still being studied. This study investigates heat transfer effects in six direct numerical simulations of zero-pressure-gradient compressible turbulent boundary layers with carbon dioxide as the fluid under transcritical and supercritical conditions. The simulations are run using high-order compact finite-difference methods and real-gas equation-of-state and transport models. In addition, the wall and freestream temperatures are chosen to straddle or lie to one side of the Widom line, which marks the location of the pseudo-phase change, to study the effects of the pseudo-phase change on heat transfer, and three of the cases are run at a constant wall-to-freestream density ratio. The results show large gradients in mean properties near the wall that influence the collapse of turbulence statistics and wall-normal profiles. Semi-local scalings from the literature greatly improve the collapse of streamwise velocity profiles along the wall-normal direction, and semi-local defect law scalings perform well in collapsing velocity and temperature defect profiles. In addition, classical friction correlations from the literature are influenced by large wall-to-freestream density ratios, and profiles of the friction temperature provide insight into the effectiveness of heat transfer in sCO2 near the wall under different temperature conditions.

High-fidelity large-eddy simulation (LES) data combined with Ffowcs Williams-Hawkings far-field propagation is used to study noise generated by a dual-stream jet with the NASA Plug20 lobed mixer and internal plug (configuration 122Am5pInt). Far-field acoustic predictions at set point 1183, which is subcritical and has a Mach 0.3 flight-stream, are compared to experimental measurements. LES data inside the nozzle is used to study the mixing of core and bypass streams, which is responsible for the reduction in low-frequency noise and increase in high-frequency noise associated with forced internal mixers. Spectral Proper Orthogonal Decomposition is used to extract the dominant spatial-temporal coherent structures shed from the lobed mixer in the form of entropy, vorticity, and pressure perturbations. These coherent structures couple with the near-wall pressure inside the nozzle, which is believed to contribute to the external acoustics through scattering at the sharp nozzle lip. The sensitivity of the far-field acoustics to the mesh resolution inside the nozzle and the boundary layer on the nozzle exterior are also investigated in order to guide future LES of internally-mixed dual-stream jets in flight-stream.

Atomization occurs when a liquid jet from a nozzle is discharged into a stagnant or moving gas causing the gas-liquid interface to become unstable and break up into a collection of droplets. The objective of this work is to simulate a simplified problem of a 2D, planar two-phase mixing layer between a co-flowing liquid and high-speed gas stream in a compressible regime, relevant to rocket propulsion. Discontinuities like shocks and material interfaces with high density ratios are prone to oscillations and numerical errors which makes numerical simulation of compressible multiphase flow challenging. To address this challenge, the performance of 6th order staggered, compact finite difference method with a 5-equation model, 2nd order interface sharpening, localized artificial diffusivity (LAD), and continuum surface force (CSF) method for surface tension modeling is evaluated for basic flows related to the two-phase mixing layer. The use of a high order scheme is motivated by the high accuracy necessary to resolve the wide range of instabilities present in the break-up of a liquid jet. Different pressure equilibrium preservation (PEP) methods are compared. Ensuring PEP allows for filtering to be removed, minimizing numerical dissipation, for high density, surface tension driven flows when it is combined with staggered numerics and LAD. The suitability of the numerical method is evaluated by comparison to linear stability theory of a two-phase shear layer where good agreement is found. The nonlinear regime of the two phase shear layer problem is explored for varying Mach numbers.

A further scrutiny of flow features present in transonic laminar shock buffet is conducted towards an improved understanding of potential feedback mechanisms that have been proposed and observed. The analysis is based on high-resolution data from a wall-resolved large-eddy simulation conducted for the flow over the OALT25 laminar supercritical airfoil at a free-stream Mach number of 0.735 and angle of attack of 4 degrees, with a Reynolds number of 1 million based on the chord length reported by Song el. al AIAA-2024-2141. Cross-correlation analysis of this data is used to characterize the convection velocity of disturbances in different regions and their spatial distribution. To further investigate the significance of various elements of potential feedback cycles, spectral proper orthogonal decomposition is applied to a cyclic probe set that includes the near-wall dynamics. A wavenumber decomposition of the SPOD eigenvectors corresponding to the dominant dynamics is conducted, allowing for the eduction of the spatial distributions of the energetics of upstream and downstream-directed waves. An analysis using geometrical acoustics is also presented to analyze upstream signal propagation and facilitate interpretation of the feedback cycle.

Using large-eddy simulations (LES) and the Ffowcs Williams-Hawkings (FW-H) method, this extended abstract presents a computational aeroacoustic study of jet flows from coannular nozzles with internal mixing geometries at high transonic Mach numbers. This work is motivated by the need to reduce jet noise from next-generation supersonic transport aircraft during takeoff and landing. Four different nozzles are considered with increasing degree of geometric complexity, from a simple conical nozzle to a coannular nozzle that has a mixing duct, an internal plug, and a 16-lobe mixer. The jet Mach number considered is between 0.8 and 0.98. Analysis of nearfield flow turbulence highlights internal shear layers and wakes introduced by the mixing geometry, impacting the thrust performance in absence of the temperature and velocity differences between the two streams. Two coannular nozzles with an internal center plug and a mixing duct are studied: one with a 16-lobe mixer and one without. Aeroacoustic differences between the two nozzles are documented. A comparison of the coaxial jet with its fully mixed equivalent single jet condition shows that the coaxial jet is louder in the downstream direction. The equivalent single jet emits acoustic tones in the upstream direction, likely due to the excitation of instability waves in the shear layers. Overall, this study will improve the understanding of coaxial jet aeroacoustics, offering insights for quieter supersonic aircraft design in the future. The current abstract provides a summary of the preliminary findings to date. In the full manuscript, a detailed comparison between the LES and experimental results will be provided. The analysis of the acoustic sources in the coaxial jet will also be expanded with volumetric data from the LES.

The twin-jet configuration allows two different scenarios to close the screech feedback. For each jet, there is one loop involving disturbances which originate in that jet and arrive at its own receptivity point in phase (self-excitation). The other loop is associated with free-stream acoustic waves that radiate from the other jet, reinforcing the self-excited screech (cross-excitation). In this work, the role of the free-stream acoustic mode and the guided-jet mode as a closure mechanism for twin rectangular jet screech is explored by identifying eligible points of return for each path, where upstream waves propagating from such a point arrive at the receptivity location with an appropriate phase relation. Screech tones generated by these jets are found to be intermittent with an out-of-phase coupling as a dominant coupling mode. The instantaneous phase difference between the twin jets computed by the Hilbert transform suggests that a competition between out-of-phase and in-phase coupling is responsible for the intermittency. To model wave components of the screech feedback while ensuring perfect phase locking, an ensemble average of leading spectral proper orthogonal decomposition modes is obtained from several segments of large-eddy simulation data that correspond to periods of invariant phase difference between the two jets. Each mode is then extracted by retaining relevant wavenumber components produced via a streamwise Fourier transform. Spatial cross-correlation analysis of the resulting modes shows that most of the identified points of return for the cross-excitation are synchronised with the guided jet mode self-excitation, supporting that it is preferred in closing rectangular twin-jet screech coupling.

We systematically examine how heat conduction between two fluids at different temperatures, large contrasts in transport properties, and sudden changes in transport properties can affect the fully compressible Rayleigh-Taylor instability (RTI) using direct numerical simulations. These variations cause departures from the classical self-similar development of the RTI, along with misalignment between regions of mixing and regions of most intense turbulent activity. Under certain conditions, dynamical quantities such as vorticity and dissipation appear to depend only on the transport properties and not on past flow history.

A spatial 3D Unet Convolutional Neural Network is contrasted with a spatio-temporal 3D Unet Long-Short Term Memory Convolutional Neural Network, where both neural networks are based on a tensor basis expansion of the subgrid stress tensor. Both neural network structures are analyzed in an a priori setting to determine the subgrid stress tensor for large eddy simulations of Forced Homogeneous Isotropic Turbulence and Channel Flow conditions. Improvements to the spatial 3D Unet Convolutional Neural Network are made by introducing a novel two neural network architecture. By training on various filter widths, all neural networks are shown to generalize to an intermediate and larger filter width with acceptable accuracy. With a physics informed loss function that enforces dissipation directly while allowing for backscatter, it is demonstrated that all neural networks can accurately predict the subgrid stress even when aggressive filtering is employed in an a priori setting. The two neural network configuration is analyzed in an a posteriori setting for both Forced Homogeneous Isotropic Turbulence and Channel Flow conditions, where the model improves turbulent space-time correlations as compared to previous models for Forced Homogeneous Isotropic Turbulence while displaying improvements in the spatial correlations and mean profiles for Channel Flow.

A wall-resolved large-eddy simulation of a Mach 0.735 transonic flow over the OALT25 supercritical airfoil is performed using high-order compact finite difference schemes blended with a shock-capturing method to investigate the laminar shock buffet phenomenon. The airfoil is placed with an angle of attack of 4 deg., and the chord-length-based Reynolds number is one million. Data over a span of approximately 178 convective time units are used in the analysis. It is observed that the flow on the suction side remains laminar up to the separation region, and then transitions to turbulence. Large amplitude oscillation of the main shock occurs. Associated with the main shock buffet, periodic movement of the flow separation locations, formation and disappearance of a terminating shock, and turbulent vortex shedding are well captured in the simulation. The measurement shows that the shock buffet Strouhal number is approximately 0.1. The second dominant Strouhal number in the flow system is approximately 0.55, which is associated with turbulent vortex shedding. The variations of aerodynamic coefficients and signals of several flow properties measured at different probe locations are studied. Spectral proper orthogonal decomposition of different flow field variables is also conducted to further identify the correlation between the shock buffet and different flow phenomena.

Supercritical fluids are used in numerous existing and developing energy technologies. The accuracy of turbulence models used with supercritical fluids is not well established due to a lack of knowledge of the coupling between the complex thermodynamics and turbulence dynamics present in turbulent supercritical flows. This study aims to provide fundamental characterization of turbulent momentum and heat transfer in supercritical flows through two canonical flows: the free shear layer flow and the zero-pressure-gradient boundary layer. Direct numerical simulations using high-order compact finite difference methods are performed with real-gas equation-of-state and transport models. The simulation results indicate that the real-gas behavior influences the turbulent fluctuations of thermodynamic quantities. Besides the non-dimensional parameters used for characterizing the turbulent flow of an ideal gas, an extra parameter is needed to identify the thermodynamic state of the fluid. The results also indicate that the classic turbulent scalings observed in the velocity fields exhibit behaviors similar to those found in ideal-gas flows.

LiDAR wind-field and SCADA measurements were collected by VTT at the Santavuori wind farm from December 10, 2020 to October 31, 2021, providing deeper than normal visibility into turbine and farm performance. These measurements were used to characterize the operation of the wind farm and identify anomalous operating regimes. The measured data were further used to calculate empirical wake spreading parameter in the Park2 wake model and showed reasonable agreement with past studies. Depending on the time period over which the farm efficiency data was averaged, large differences in the calibrated value of the wake spreading parameter were observed. These differences began to appear at time scales or three days or shorter. After investigation, these differences were often driven by situations where the observed efficiency was lower than could possibly be predicted by the model, motivating the need to predict how often the Park2 model predictions are applicable. In the current data set, spectral average turbulence intensity and wind shear exponent did not show predictive capacity in logistic regression for the applicability of the Park2 model.

We have generated a database using high resolution large eddy simulations (LES) for a turbulent flow which is forced in a localized layer producing negligible mean transport or shear. The simulations are reminiscent of classical oscillating grid experiments but, with the LES methodology and modern computational resources, we are able to probe higher Reynolds numbers than are accessible in the laboratory. We show that global values of vertical kinetic energy and dissipation rate govern the evolution of turbulence quantities when stratification is unimportant. When the effects of stable stratification increase, the global scaling breaks down and local quantities must be used to compare results across cases. We conduct a preliminary analysis of the classical "k-epsilon" turbulence model and discuss plans for future modeling efforts.

The paper applies a wavelet filtering method based on the recursive denoising algorithm to airfoil noise in low-Mach number flows. The pressure field around the airfoil is decomposed into coherent contributions corresponding to denoised pressure and incoherent pressure corresponding to background noise. The pressure data are obtained from Large-Eddy Simulations. Both the flow and acoustic solvers are validated against experimental data at a zero angle of attack, Reynolds numbers, Re=3.2×105 and 4×105, and Mach numbers, M=0.093 and 0.058, respectively. The convergence trend and statistical nature of the wavelet algorithm are analyzed. Additionally, the decomposed pressures are examined by comparing the wavelet-based decomposition with the traditional wavenumber–frequency decomposition, and spectral analyses are conducted on the decomposed pressures. The results show that the denoised pressure represents physical phenomena associated with hydrodynamic wavy structures moving along the wall and sound propagation generated near the tripping region and the trailing edge. On the other hand, the incoherent pressure or background noise exhibits a small and constant amplitude closely adhering to the Gaussian distribution. Dynamic mode decomposition modes reveal that this background noise is prominent around the tripping and trailing-edge regions where flow perturbations are significant, but it either barely propagates to the far field or dissipates quickly. The far-field acoustic spectrum is predominantly influenced by the physical or denoised component. However, a cautious interpretation is necessary in the high-frequency range, where background noise still contributes to the far-field noise. The paper explores the potential applications of the wavelet algorithm in identifying and removing background noise.

View Video Presentation: https://doi.org/10.2514/6.2023-3690.vid Supercritical fluids have a number of thermodynamic and chemical properties which make them attractive for use in environmentally friendly technologies. However, though the thermodynamic properties of supercritical fluids have been studied comprehensively, the dynamics of supercritical and transcritical fluid flows are less well explored and understood. Studying the behavior of such fluid flows through high-quality computational investigations could provide crucial insights useful for designing and controlling flow systems operating in supercritical and transcritical regimes. An accurate and robust computational framework is a prerequisite to conducting high-quality computational investigations. This work extends a high-fidelity computational framework for ideal gas flows by including complex thermodynamic models and realistic transport models near the critical point of the fluid where abrupt changes in density and transport properties occur with small temperature or pressure fluctuations. The spatial discretization is based on compact finite difference methods that achieve high-order grid convergence and the high spectral resolution needed to resolve small scale flow structures. The computational approach achieves robustness by reducing the aliasing error and improving the spectral resolution of the viscous fluxes at high wavenumbers. No non-conservative correction or filtering is needed to maintain robustness for shock-free flows if physical or physics-based model dissipation is included. The framework is also compatible with applications of shock capturing schemes and approximated Riemann solvers and supports simulations on curvilinear meshes. Two problems involving compressible free-shear flows (temporal mixing layer) and wall-bounded flows (zero-pressure gradient flat plate boundary layer cold isothermal wall) are studied for dense gases to demonstrate the robustness and versatility of the proposed numerical formulation.

Screech resonance is studied with experimentally validated large-eddy simulation data for a 4:1 rectangular under-expanded jet at three nozzle pressure ratios. The analysis uses spectral proper orthogonal decomposition (SPOD) and spatial cross correlation to characterize the oppositely-traveling waves in the jet at the screech fundamental frequency. The results support recent theoretical framing of screech as absolute instability, and further reveal the spatial separation of individual processes for screech generation. From the leading-order SPOD mode, direct evidence of the guided jet mode being the screech closure mechanism, not the external acoustic feedback, is observed. A match in the spatial wavenumber suggests the guided jet mode is generated via interactions between the Kelvin-Helmholtz wave and the shock cells. The energy of the oppositely-moving waves shows spatially global and non-periodic behavior of the coherent structures in the streamwise direction. The ratio of wave energy identifies regions where distinct processes in screech generation take place by comparing the rate of energy propagation in the downstream direction to that of the upstream direction. The distinct regions correspond to initial shear layer receptivity, sound emission, guided jet mode excitation and decay of coherence. The leading-order SPOD mode also enables the approximation of Lighthill's stress tensor and allows for accurate calculation of the far-field screech tone amplitude with the acoustic analogy formulation. The current findings provide insights on building a physics-based reduced order model for screech amplitude prediction in the future.

Airfoil noise is predicted and analyzed using wall-resolved large-eddy simulations and wavelet transforms for a NACA 0012 airfoil at a Mach number of 0.06 and a Reynolds number of 400,000 using a stair-strip forced transition and a natural transition. At a high angle of attack, vortex shedding and a laminar separation bubble (LSB) occur on the suction side. The LSB triggers the flow transition for both the forced and natural transition cases. The wavelet thresholding and denoising algorithm is used to decompose the pressure fields into the coherent or denoised pressure and the incoherent or background noise pressure. This denoising technique provides a clear picture of true noise generation and propagation. It also reveals the dominant noise source at specific frequencies when multiple noise sources are present. In another usage, the wavelet thresholding algorithm with down-sampling separates noise on the basis of flow structures. For example, the wavelet method separates noise between low-frequency vortex shedding noise and high-frequency LSB noise as well as trailing-edge noise. Finally, the wavelet transform is used to decompose the hydrodynamic and acoustic pressure components near the surface using the coherence between near-field pressure and far-field pressure. Overall, the wavelet-based decomposition is a valuable tool to study and reveal the mechanisms of airfoil noise generation.

In Figs. 10, 12, and 13 of the original paper, the phase-averaged fields at 270° are incorrect.

View Video Presentation: https://doi.org/10.2514/6.2023-0614.vid High-fidelity large-eddy simulation (LES) data is used to analyze the dominant coherent structures associated with screech for a supersonic rectangular jet with an aspect ratio of 4. The focus of this work is on the second harmonic frequency of screech and establishing a theoretical explanation of its generation in relation to the fundamental screech tone. Spectral proper orthogonal decomposition (SPOD) is used to analyze flow structures associated with hydrodynamic and acoustic fluctuations at the fundamental and harmonic frequencies. Spatial wavenumbers of the leading SPOD modes identify potential triadic interactions inside the jet which give rise to to external acoustics. These results, combined with amplitude and symmetry considerations, suggest that external acoustics at the second harmonic are generated by non-linear interaction between the downstream-traveling Kelvin-Helmholtz (KH) wave at the harmonic frequency and the shock-cell structure. A clear distinction between the guided jet mode and the mode associated with far-field acoustics is also observed at the harmonic frequency, which is in contrast to the fundamental frequency. Phase-averaging of the density gradient magnitude reveals anti-symmetric oscillations in the shock-cell structure at the fundamental frequency that are consistent with symmetry induced by the KH wave. At the harmonic frequency, symmetric shock-cell oscillations can also be linked to interaction with the KH wave, which gives rise to symmetric far-field acoustic patterns.

View Video Presentation: https://doi.org/10.2514/6.2023-1159.vid In order to obtain accurate aeroacoustic predictions from RANS data, it is important to be able to capture the statistical nature of the flow turbulence, and specifically the two-point velocity fluctuation correlations. A significant factor in properly modeling these correlations is the choice of length scale and time scale used to represent the various turbulent mechanisms acting in the flow field. A number of different forms for these characteristic turbulent scales have been proposed by previous authors, including those with spatial and frequency dependencies. In this work, we use data from a large eddy simulation of jet flow from a simple conical nozzle to explicitly study the form of the two point spatial and temporal correlations as they vary in space and with frequency. We then compare a number of proposed RANS-based models from the literature with the LES data in order to better understand in which regions of the flow different turbulent time scales become most relevant. We optimize a spatially varying form of this turbulent time scale, and compare acoustic results using this optimal form against results for the same jet case using both previously proposed RANS-based models and FWH analyis.