The Reynolds-averaged Navier–Stokes (RANS) equations remain a workhorse technology for simulating compressible fluid flows of practical interest. Due to model-form errors, however, RANS models can yield erroneous predictions that preclude their use on mission-critical problems. This report summarizes work performed from FY22-FY24 focused on improving RANS models for hypersonic flows using data-driven modeling and scientific machine learning. In this work we: 1. Investigate the current capabilities of RANS models in Sandia’s parallel aerodynamics and re-entry code (SPARC) for hypersonic flows with a focus on shock boundary layer interactions (SBLIs), 2. Assess several established corrections that exist in the literature aimed at improving predictions for SBLIs, 3. Develop improved models for the Reynolds stress tensor using tensor-basis neural networks, 4. Develop a neural-network-based variable turbulent Prandtl number model to reduce errors in wall heating in SBLIs. 5. Begin future investigations including employing the LIFE framework to improve wall heating predictions in SBLIs as well as the ensemble Kalman filter. We find that current RANS models in SPARC are deficient for complex SBLI flows. In particular, no current model jointly predicts wall heat flux, wall shear stress, and wall pressure with reasonable accuracy. Existing corrections help, but do not alleviate this issue altogether. The development of improved models for the Reynolds stress tensor via tensor-basis neural networks results in more predictive RANS models across a suite of low-speed and high-speed cases. For hypersonic boundary layers, the inclusion of the wall-normal Reynolds stress via TBNNs has an appreciable impact on the wall-normal momentum balance and wall quantities. However, we find that improvements to the Reynolds stress tensor do not address the over-prediction in wall heat flux in SBLIs. We find that a neural-network-based variable turbulent Prandtl number model systematically and substantially improves wall heating predictions for a range of SBLI cases.
The elemental equation governing heat transfer in aerodynamic flows is the internal energy equation. For a boundary layer flow, a double integration of the Reynolds-averaged form of this equation provides an expression of the wall heat flux in terms of the integrated effects, over the boundary layer, of various physical processes: turbulent dissipation, mean dissipation, turbulent heat flux, etc. Recently available direct numerical simulation data for a Mach 11 cold-wall turbulent boundary layer allows a comparison of the exact contributions of these terms in the energy equation to the wall heat flux with their counterparts modeled in the Reynolds-averaged Navier-Stokes (RANS) framework. Various approximations involved in RANS, both closure models as well as approximations involved in adapting incompressible RANS models to a compressible form, are assessed through examination of the internal energy balance. There are a number of potentially problematic assumptions and terms identified through this analysis. The effect of compressibility corrections of the dilatational dissipation type is explored, as is the role of the modeled turbulent dissipation, in the context of wall heat flux predictions. The results indicate several potential avenues for RANS model improvement for hypersonic cold-wall boundary-layer flows.
We develop methods that could be used to qualify a training dataset and a data-driven turbulence closure trained on it. By qualify, we mean identify the kind of turbulent physics that could be simulated by the data-driven closure. We limit ourselves to closures for the Reynolds-Averaged Navier Stokes (RANS) equations. We build on our previous work on assembling feature-spaces, clustering and characterizing Direct Numerical Simulation datasets that are typically pooled to constitute training datasets. In this paper, we develop an alternative way to assemble feature-spaces and thus check the correctness and completeness of our previous method. We then use the characterization of our training dataset to identify if a data-driven turbulence closure learned on it would generalize to an unseen flow configuration – an impinging jet in our case. Finally, we train a RANS closure architected as a neural network, and develop an explanation i.e., an interpretable approximation, using generalized linear mixed-effects models and check whether the explanation resembles a contemporary closure from turbulence modeling.
We develop methods that could be used to qualify a training dataset and a data-driven turbulence closure trained on it. By qualify, we mean identify the kind of turbulent physics that could be simulated by the data-driven closure. We limit ourselves to closures for the Reynolds-Averaged Navier Stokes (RANS) equations. We build on our previous work on assembling feature-spaces, clustering and characterizing Direct Numerical Simulation datasets that are typically pooled to constitute training datasets. In this paper, we develop an alternative way to assemble feature-spaces and thus check the correctness and completeness of our previous method. We then use the characterization of our training dataset to identify if a data-driven turbulence closure learned on it would generalize to an unseen flow configuration – an impinging jet in our case. Finally, we train a RANS closure architected as a neural network, and develop an explanation i.e., an interpretable approximation, using generalized linear mixed-effects models and check whether the explanation resembles a contemporary closure from turbulence modeling.
Machine-learned models, specifically neural networks, are increasingly used as “closures” or “constitutive models” in engineering simulators to represent fine-scale physical phenomena that are too computationally expensive to resolve explicitly. However, these neural net models of unresolved physical phenomena tend to fail unpredictably and are therefore not used in mission-critical simulations. In this report, we describe new methods to authenticate them, i.e., to determine the (physical) information content of their training datasets, qualify the scenarios where they may be used and to verify that the neural net, as trained, adhere to physics theory. We demonstrate these methods with neural net closure of turbulent phenomena used in Reynolds Averaged Navier-Stokes equations. We show the types of turbulent physics extant in our training datasets, and, using a test flow of an impinging jet, identify the exact locations where the neural network would be extrapolating i.e., where it would be used outside the feature-space where it was trained. Using Generalized Linear Mixed Models, we also generate explanations of the neural net (à la Local Interpretable Model agnostic Explanations) at prototypes placed in the training data and compare them with approximate analytical models from turbulence theory. Finally, we verify our findings by reproducing them using two different methods.
This paper explores unsupervised learning approaches for analysis and categorization of turbulent flow data. Single point statistics from several high-fidelity turbulent flow simulation data sets are classified using a Gaussian mixture model clustering algorithm. Candidate features are proposed, which include barycentric coordinates of the Reynolds stress anisotropy tensor, as well as scalar and angular invariants of the Reynolds stress and mean strain rate tensors. A feature selection algorithm is applied to the data in a sequential fashion, flow by flow, to identify a good feature set and an optimal number of clusters for each data set. The algorithm is first applied to Direct Numerical Simulation data for plane channel flow, and produces clusters that are consistent with turbulent flow theory and empirical results that divide the channel flow into a number of regions (viscous sub-layer, log layer, etc). Clusters are then identified for flow over a wavy-walled channel, flow over a bump in a channel, and flow past a square cylinder. Some clusters are closely identified with the anisotropy state of the turbulence, as indicated by the location within the barycentric map of the Reynolds stress tensor. Other clusters can be connected to physical phenomena, such as boundary layer separation and free shear layers. Exemplar points from the clusters, or prototypes, are then identified using a prototype selection method. These exemplars summarize the dataset by a factor of 10 to 1000. The clustering and prototype selection algorithms provide a foundation for physics-based, semi-automated classification of turbulent flow states and extraction of a subset of data points that can serve as the basis for the development of explainable machine-learned turbulence models.
The development of a next generation high-fidelity modeling code for wind plant applications is one of the central focus areas of the U.S. Department of Energy Atmosphere to Electrons (A2e) initiative. The code is based on a highly scalable framework, currently called Nalu-Wind. One key aspect of the model development is a coordinated formal validation program undertaken specifically to establish the predictive capability of Nalu-Wind for wind plant applications. The purpose of this document is to define the verification and validation (V&V) plan for the A2e high-fidelity modeling capability. It summarizes the V&V framework, identifies code capability users and use cases, describes model validation needs, and presents a timeline to meet those needs.
