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Data-Driven Turbulence Modeling: Summary and Outcomes of the 2022 NASA Symposium

A three-day symposium sponsored by NASA was held in July 2022 in Suffolk, Virginia on the subject of Turbulence Modeling: Roadblocks, and the Potential for Machine Learning. This meeting brought together over 80 experts from academia, government, and industry to discuss critical issues for Reynolds-averaged Navier-Stokes (RANS) turbulence and transition models, as well as to evaluate the results from a collaborative testing challenge based on data-driven methods and machine learning (ML) technology. The symposium represents a continuation of an earlier symposium sponsored by the University of Michigan and NASA, held in Ann Arbor, MI in 2017. The 2022 symposium included a wide variety of talks on the subjects of RANS and ML, five invited talks, and three panel discussions. This talk summarizes the main outcomes of the symposium, and includes suggested recommendations and future directions.

machine learning↗

On Generalizably Improving RANS Predictions of Flow Separation and Reattachment

This work presents progress in an ongoing data-driven turbulence modeling effort at NASA Langley Research Center to improve predictions for separated flows. Two augmentation strategies are presented – one to improve predictions for the point of reattachment after smooth-body separation, and another to improve predictions for flow separation due to prolonged adverse pressure gradients. The reattachment augmentation was inspired from lessons learned during attempts at using field inversion and machine learning (FIML); however, it is prescribed as a conventional analytic closed-form expression. Results show that, when introduced into the SST k-w model, it shortens the otherwise overpredicted separation bubble length for three cases characterized by different Reynolds numbers and flow geometries. The second augmentation, which addresses flow separation under prolonged adverse pressure gradients, is inferred via FIML and applied as a neural network within the Spalart-Allmaras model. It uses features that are chosen such that the presented results show an improved predictive accuracy for the training case without affecting other cases where the augmentation is not needed. Further testing is required to establish the generalizability of this augmentation. The rationale behind the chosen features that serve as inputs to both these augmentations is also presented for the benefit of the reader.

machine learning↗

In Search of Data-Driven Improvements to RANS Models Applied to Separated Flows

The goal of this work is to improve the capability of Reynolds-averaged Navier-Stokes turbulence models for separated flows using data-driven enhancements. The resulting model should be “universal” in the sense that it can be used by anyone and applied to as many flows as possible without concern for unusual or detrimental behavior. At worst, the data-driven corrections should not degrade the accuracy of the baseline model (in this case the Spalart-Allmaras one-equation model), while preserving the Galilean invariance and similar theoretical qualities of the original model. In the literature, most current data-driven improvements to turbulence models are only applicable to very similar types of cases as those used to train the model for a specific class of flows. In this work, the impact of using a wide array of cases in the machine-learning training is described. Unwanted behaviors from trained neural networks are examined, and possible mitigation strategies are proposed. However, to date, consistent and broadly applicable data-driven improvements for separated flows have not been achieved.

turbulence modeling↗

Exploring data-driven modeling of boundary layer transition

Prediction of laminar-turbulent transition in boundary layer flows is an important component of predicting the aerodynamic performance of a number of aerospace configurations. According to the CFD Vision 2030 [1], transition modeling represents acriticalarea in CFD simulation capability that will remain a pacing item for the foreseeable future. The fact thattransition can take placevia either one of a myriad possible paths adds to the challenges inreliable transition predictions, despite a limited knowledge of the relevant input parameters. In the low disturbance environments typical of flight applications, transition is often initiated by small amplitude disturbances in the form of linear instability waves of the laminar boundary layer. These disturbances amplify linearly at first and eventually undergo a sequence of nonlinear interactions that result in transition to turbulence. Because the nonlinear phase is rather rapid, the amplification of boundary layer instabilities is governed by the linearstability theory over a majority of the distance leading up to the onset of transition. Semi-empirical transition correlations based on the linear stability theory have been successful in explaining the observed trends in transition location within a broad class of flows. However, the application of stability theory is highly non-robust and often requires a significant domain expertise. Recent work at the NASA Langley Research Center has beenaimed at bridging the gap between physics based transition analyses such as those based on linear stability theory and practical applications that require transition prediction by users that may not be well versed in transition physics. The applications of deep learning have been at the center of these efforts. This presentation will focus on the progress achieved thus far, highlighting the applications of neural networks to selectedtransition scenarios across a range of Mach numbers and flow configuration, as well as the lessons learnedand remaining challengeswithrespect to the selection of training data and neural networks architectures, hyperparameter tuning, and the physical insights distilled from the otherwise black-box models.

M. R. Malik↗

Augmenting RANS Turbulence Models Guided by Field Inversion and Machine Learning

This report investigates the use of a data-driven approach, viz., Field Inversion and Machine Learning (FIML), to improve conventional RANS turbulence models like the Spalart-Allmaras model and the Menter SST k-ω model. One of the crucial aspects of using an ML-based approach with limited training data to produce corrections that are generalizable to a large range of flow configurations is to design appropriate “features” (inputs to the ML model). A model, based on guidance from the FIML methodology, is presented in analytical form. An additional list of potential features is provided. Although these were not used in the present correction, they were considered in the course of its development, and are included to fully document the complete process employed in the present work.

turbulence modeling↗

A Data-Driven Reduced Order Model of an Isolated Rotor

There are numerous conceptual design stage rotorcraft analysis tasks which demand a high-fidelity and low cost method for rotor load distribution predictions. Considering Urban Air Mobility (UAM) vehicles aim to operate in close proximity to buildings and with unique rotor configurations, there is a significant challenge in quickly and accurately modeling rotors operating in complex, turbulent flow fields. One potential path for deriving a high-fidelity, low cost rotor model is with data-driven surrogate modeling. In this study, an initial investigation is taken to apply a proper orthogonal decomposition (POD) based reduced order model (ROM) for the purpose of pressure distribution prediction. In this study, a POD ROM was derived to produce distributed pressure predictions on rotor blades subjected to topology change due to variation in twist and taper ratio. Rotor twist was varied between 0◦, 10◦, 20◦, and 30◦ while taper ratio was varied between 1.0, 0.9, 0.8, and 0.7. All rotors consisted of a single blade. The POD ROM was validated for three demonstration cases; a high thrust rotor in hover, a low thrust rotor in hover, and a rotor in forward flight with a flight speed of M = 0.1. Results showed highly accurate distributed load predictions could be achieved at minimal computational cost. Computational cost for hovering blade surface pressure modeling was reduced from 12 hours on 440 cores to 10−5 seconds on a single core. For blade in forward flight cost was reduced from 20 hours on 440 cores to 0.6 seconds on a single core. For cases of high thrust and low thrust rotors, POD ROM was used to undergo a design optimization of the rotor such that figure of merit was maximized. Total optimization time for each case was 1 minute.

Data-Driven↗

NASA Symposium on Turbulence Modeling: Roadblocks, and the Potential for Machine Learning

A three-day symposium sponsored by NASA was held in July 2022 in Suffolk, Virginia on the subject of Turbulence Modeling: Roadblocks, and the Potential for Machine Learning. This meeting brought together over 80 experts from academia, government, and industry to discuss critical issues for Reynolds-averaged Navier-Stokes turbulence and transition models, as well as to evaluate the results from a collaborative testing challenge based on data-driven methods and machine learning technology. This report puts this symposium in context with an earlier similar meeting and summarizes many of the questions, discussions, and conclusions that arose from it. Next steps are suggested.

machine learning↗

Intermittency Model for Coupled CFD-Stability Transition Analysis in Hypersonic Flow

Accurate prediction of aerothermodynamic loads on hypersonic vehicles requires precise modeling of surface quantities across the boundary layer transition zone. The peak heating loads and total heat transfer are determined by parameters such as the transition zone length and the magnitude of potential overshoots in heat flux and skin friction beyond their respective values in fully turbulent flows. While previous studies on CFD integrated transition modeling using linear stability correlations have shown promise in modeling these features, they did not develop an intermittency model for hypersonic flows. This paper presents a data-driven approach to develop a model of this type by correlating experimental transition data with the relevant flow parameters. The resulting model demonstrates significant improvements over previous low-speed models in terms of predicting heat transfer distributions during the transition process associated with first and second mode instabilities in axisymmetric high-speed flows. Separate correlations for flight and ground test conditions are developed, and the potential to combine these correlations is discussed.

Transition↗

Enhancements to Linear Stability-Based, CFD-integrated Transition Prediction for High-Speed Flows

Combining linear stability calculations with computational fluid dynamics (CFD) simulations has great potential for the automated modeling of high-speed flows, especially when adequate information about the configuration and the disturbance environment is available. However, a significant impediment to the applicability of this technique is the lack of an efficient method to calculate the crucial amplification ratio corresponding to the onset of transition in hypersonic flows. This ratio, also known as the "transition N-factor," is dependent upon the freestream disturbance environment as well as the surface properties of the test article. In response to the need for an engineering solution to predict the transition N-factor within conventional hypersonic wind tunnels, this paper presents a data-driven correlation that expands the existing correlations from straight circular cones with a narrow range of half angles to a broader array of axisymmetric configurations. Furthermore, when tested against a chosen dataset that was not used in its calibration, the suggested correlation shows good predictive accuracy with an RMS error of only 6.9%. Although similar accuracy may also be achieved via existing correlations based on similar datasets, predictions based on the proposed correlation have the advantage of not requiring an extensive amount of configuration-specific data. Practical applications often have access to the input parameters needed for this correlation, such as the freestream disturbance intensity, Mach number, and body-based slenderness Reynolds number. Additionally, this correlation outperforms the traditional assumption of a constant N-factor, particularly for configurations with blunted nose geometries. The development of this correlation is grounded in an extensive dataset encompassing conical models with body half-angles varying between 5 degrees and 16 degrees, Mach numbers ranging from 5 to 14, and nosetip-based Reynolds numbers approaching the transition reversal limit for blunt-nosed cones.

CFD↗

Enhancements to Linear Stability-Based, CFD-integrated Transition Prediction for High-Speed Flows

Combining linear stability calculations with computational fluid dynamics (CFD) simulations has great potential for the automated modeling of high-speed flows, especially when adequate information about the configuration and the disturbance environment is available. However, a significant impediment to the applicability of this technique is the lack of an efficient method to calculate the crucial amplification ratio corresponding to the onset of transition in hypersonic flows. This ratio, also known as the "transition N-factor," is dependent upon the freestream disturbance environment as well as the surface properties of the test article. In response to the need for an engineering solution to predict the transition N-factor within conventional hypersonic wind tunnels, this paper presents a data-driven correlation that expands the existing correlations from straight circular cones with a narrow range of half angles to a broader array of axisymmetric configurations. Furthermore, when tested against a chosen dataset that was not used in its calibration, the suggested correlation shows good predictive accuracy with an RMS error of only 6.9%. Although similar accuracy may also be achieved via existing correlations based on similar datasets, predictions based on the proposed correlation have the advantage of not requiring an extensive amount of configuration-specific data. Practical applications often have access to the input parameters needed for this correlation, such as the freestream disturbance intensity, Mach number, and body-based slenderness Reynolds number. Additionally, this correlation outperforms the traditional assumption of a constant N-factor, particularly for configurations with blunted nose geometries. The development of this correlation is grounded in an extensive dataset encompassing conical models with body half-angles varying between 5 degrees and 16 degrees, Mach numbers ranging from 5 to 14, and nosetip-based Reynolds numbers approaching the transition reversal limit for blunt-nosed cones.

CFD↗