Publications

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This work was conducted as part of a Harry S. Truman Fellowship Laboratory Directed Research and Development project. The goal was to use machine learning methods to provide uncertainty quantification and model improvements for Reynolds Averaged Navier Stokes (RANS) turbulence models. For applications of interest in energy, safety, and security, it is critical to be able to model turbulence accurately. Current RANS models are unreliable for many flows of engineering relevance. Machine learning provides an avenue for developing improved models based on the data generated by high fidelity simulations. In this project, machine learning methods were used to predict when current RANS models would fail. They were also used to develop improved RANS closure models. A key aim was developing a tight feedback loop between scientific domain knowledge and data driven methods. To this end, a methodology for incorporating known invariance constraints into the machine learning models was proposed and evaluated. This work demonstrated that incorporating known constraints into the data driven models provided improved performance and reduced computational cost. This research represents one of the first applications of deep learning to turbulence modeling.

Abstract not provided.

Abstract not provided.

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, "Flow Topologies and Turbulence Scales in a Jet-in-Cross-Flow," Phys. Fluids, 27(4), p. 045101), as well as RANS k-ε 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.

Abstract not provided.

In many aerospace applications, it is critical to be able to model fluid-structure interactions. In particular, correctly predicting the power spectral density of pressure fluctuations at surfaces can be important for assessing potential resonances and failure modes. Current turbulence modeling methods, such as wall-modeled Large Eddy Simulation and Detached Eddy Simulation, cannot reliably predict these pressure fluctuations for many applications of interest. The focus of this paper is on efforts to use data-driven machine learning methods to learn correction terms for the wall pressure fluctuation spectrum. In particular, the non-locality of the wall pressure fluctuations in a compressible boundary layer is investigated using random forests and neural networks trained and evaluated on Direct Numerical Simulation data.

Abstract not provided.

Computational mechanics simulations often output large, high dimensional data sets. Analyzing and understanding these data sets can prove challenging because of the difficulty associated with visualizing data in more than two dimensions. In this paper, the t-Distributed Stochastic Neighbor Embedding (t-SNE) methodology is used to reduce the dimensions of computational fluid dynamics data sets for improved visualization. This visualization technique enables easy comparisons between data sets. These comparisons are particularly useful in assessing the applicability of data-driven turbulence models, which are most accurate on flows that have similar characteristics to the flows on which the data-driven model was calibrated. The t-SNE technique is applied to a range of different flow configurations and the results and modeling implications are discussed.

Abstract not provided.

The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. Here we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. The close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.

In film cooling flows, it is important to know the temperature distribution resulting from the interaction between a hot main flow and a cooler jet. However, current Reynolds-averaged Navier-Stokes (RANS) models yield poor temperature predictions. A novel approach for RANS modeling of the turbulent heat flux is proposed, in which the simple gradient diffusion hypothesis (GDH) is assumed and a machine learning algorithm is used to infer an improved turbulent diffusivity field. This approach is implemented using three distinct data sets: two are used to train the model and the third is used for validation. The results show that the proposed method produces significant improvement compared to the common RANS closure, especially in the prediction of film cooling effectiveness.

We investigate a novel application of deep neural networks to modeling of errors in prediction of surface pressure fluctuations beneath a compressible, turbulent flow. In this context, the truth solution is given by Direct Numerical Simulation (DNS) data, while the predictive model is a wall-modeled Large Eddy Simulation (LES). The neural network provides a means to map relevant statistical flow-features within the LES solution to errors in prediction of wall pressure spectra. We simulate a number of flat plate turbulent boundary layers using both DNS and wall-modeled LES to build up a database with which to train the neural network. We then apply machine learning techniques to develop an optimized neural network model for the error in terms of relevant flow features.

For many aerospace applications, there exists significant demand for more accurate tur- bulence models. Data-driven machine learning algorithms have the capability to accurately predict when Reynolds Averaged Navier Stokes (RANS) models will have increased model form uncertainty due to the breakdown of underlying model assumptions. These machine learning models can be used to adaptively trigger relevant model corrections in the regions they are needed. This paper presents a framework for data-driven adaptive physics model- ing that leverages known RANS model corrections and proven machine learning methods. This adaptive physics modeling framework is evaluated for two case studies: fully developed turbulent square duct flow and flow over a wavy wall. It is demonstrated that implement- ing model corrections zonally based on machine learning classification of where underlying RANS model assumptions are violated can achieve the same accuracy as implementing those corrections globally.

Classical RANS turbulence models have known deficiencies when applied to jets in crossflow. Identifying the linear Boussinesq stress-strain hypothesis as a major contribution to erroneous prediction, we consider and contrast two machine learning frameworks for turbulence model development. Gene Expression Programming, an evolutionary algorithm that employs a survival of the fittest analogy, and a Deep Neural Network, based on neurological processing, add non-linear terms to the stress-strain relationship. The results are Explicit Algebraic Stress Model-like closures. High fidelity data from an inline jet in crossflow study is used to regress new closures. These models are then tested on a skewed jet to ascertain their predictive efficacy. For both methodologies, a vast improvement over the linear relationship is observed.

Abstract not provided.

Abstract not provided.

There exists significant demand for improved Reynolds-Averaged Navier-Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

Abstract not provided.