Publications

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Although increased availability of computational resources has enabled high-fidelity simulations (e.g., large eddy simulations) of turbulent flows, the Reynolds-Averaged Navier–Stokes (RANS) models are still the dominant tools in industrial applications. However, the predictive capabilities of RANS models are limited by large model-form discrepancies due to the Reynolds stress closure. Recently, a Physics-Informed Machine Learning (PIML) approach has been proposed to learn the functional form of Reynolds stress discrepancy in RANS simulations based on available data. It has been demonstrated that the learned discrepancy function can be used to improve Reynolds stresses in new flows where data are not available. However, due to a number of challenges, the improvements are only demonstrated in the Reynolds stress prediction but not in corresponding propagated quantities of interest (e.g., velocity field). In this work, we investigate the prediction performance on the velocity field by propagating the corrected Reynolds stresses in PIML approach. To enrich the input features, an integrity basis of invariants is implemented. The fully developed turbulent flow in a square duct is used as the test case. The discrepancy model is trained on flow fields from several Reynolds numbers and evaluated on a duct flow at a higher Reynolds number than any of the training cases. The predicted Reynolds stresses are propagated to velocity field via RANS equations. Numerical results show excellent predictive performances in both Reynolds stresses and their propagated velocities, demonstrating the merits of the PIML approach in predictive turbulence modeling.

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In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.

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The question of how to accurately model turbulent flows is one of the most long-standing open problems in physics. Advances in high performance computing have enabled direct numerical simulations of increasingly complex flows. Nevertheless, for most flows of engineering relevance, the computational cost of these direct simulations is prohibitive, necessitating empirical model closures for the turbulent transport. These empirical models are prone to "model form uncertainty" when their underlying assumptions are violated. Understanding, quantifying, and mitigating this model form uncertainty has become a critical challenge in the turbulence modeling community. This paper will discuss strategies for using machine learning to understand the root causes of the model form error and to develop model corrections to mitigate this error. Rule extraction techniques are used to derive simple rules for when a critical model assumption is violated. The physical intuition gained from these simple rules is then used to construct a linear correction term for the turbulence model which shows improvement over naive linear fits.

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For film cooling of combustor linings and turbine blades, it is critical to be able to accurately model jets-in-crossflow. Current Reynolds Averaged Navier Stokes (RANS) models often give unsatisfactory predictions in these flows, due in large part to model form error, which cannot be resolved through calibration or tuning of model coefficients. The Boussinesq hypothesis, upon which most two-equation RANS models rely, posits the existence of a non-negative scalar eddy viscosity, which gives a linear relation between the Reynolds stresses and the mean strain rate. This model is rigorously analyzed in the context of a jet-in-crossflow using the high fidelity Large Eddy Simulation data of Ruiz et al. (2015), as well as RANS k-e results for the same flow. It is shown that the RANS models fail to accurately represent the Reynolds stress anisotropy in the injection hole, along the wall, and on the lee side of the jet. Machine learning methods are developed to provide improved predictions of the Reynolds stress anisotropy in this flow.

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The objective of this work is to investigate the efficacy of using calibration strategies from Uncertainty Quantification (UQ) to determine model coefficients for LES. As the target methods are for engineering LES, uncertainty from numerical aspects of the model must also be quantified. 15 The ultimate goal of this research thread is to generate a cost versus accuracy curve for LES such that the cost could be minimized given an accuracy prescribed by an engineering need. Realization of this goal would enable LES to serve as a predictive simulation tool within the engineering design process.