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DOE OSTI2022

Updates to Nek5000: RANS wall functions, NRC support, and documentation

As a key part of the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program (NEAMS), the next generation of tools for nuclear reactor design are being developed. A primary metric for success of this program is the adoption of those tools by industry stakeholders. To help meet this metric for Nek5000, development efforts this year have focused on the expansion of the available Reynolds-averaged Navier-Stokes (RANS) turbulence models to include wall function models, continued support of the U.S. Nuclear Regulatory Commission in simulating a hydrogen mitigation benchmark experiment, and expansion of the Nek5000 documentation to enhance the code’s usability. The implementation of wall functions is intended to significantly decrease time to-solution for a wide range of problems and it has been identified as an important feature by stakeholders across the nuclear community. The initial implementation of standard and pressure corrected wall functions has been tested in Nek5000 on the classical problems of channel flow and a backward facing step. It has also been tested on a 2D molten salt fast reactor core and a T-junction. The recommended formulation of choosing y + = 30 as a boundary value combined with a Neumann-Neumann formulation of the boundary condition for k and τ produces the most consistent results compared to a wall resolved approach. The collaboration with the NRC is a continuing exercise that has been ongoing for multiple years. This year we have concluded investigations into appropriate inlet conditions, showing that fully developed turbulent conditions are adequate for the full PANDA domain. We have also concluded simulations for an unobstructed jet and are now refocusing to the original obstructed jet case. The expansion of the code documentation has also been an ongoing effort over the past few years to address feedback from the various stakeholders. The documentation now more fully covers many of the available features and closes identified SQA gaps. Finally we report on three training sessions that were offered over the past year in an effort to expand the Nek5000 user base.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Computational fluid dynamic modeling to determine the indoor environment of an electron-ion collider service building

The design for the Electron-Ion Collider (EIC) calls for several service buildings that house various power supplies and control electronics for the collider ring itself. In order to operate within specified conditions, the ambient air entering the power supplies needs to be within a certain temperature range while dissipating the heat from losses. Proper cooling is therefore a necessity in the service buildings to ensure that every aspect of the EIC works as intended. Since the EIC is in the design stage, we are evaluating the indoor environment of the service building using the current design specifications. We have researched multiple forms of literature and performed the necessary calculations to compile a list of boundary conditions that accurately represent the situation at hand. We are using computational fluid dynamics modeling to solve the conservation equations for mass, momentum, and energy (Navier-Stokes). This allows us to perform a finite element analysis which will give us the flow distribution in the room as well as temperature profiles throughout the building. We have obtained a simulation result giving us the temperature profiles for the building and it shows that the placement of the racks and supply vents are essential to obtaining an even temperature distribution. This model will provide a basis for design decisions which will affect the overall cooling of the service building without extending the schedule and avoiding a costly reworking of the cooling system.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Design and Testing of the Vortex Ring Facility

This document summarizes the efforts of building an experimental test facility to study the evolution of the cloud following a nuclear detonation above ground level and support the development of numerical models to describe it. The experimental facility allows nonintrusive flow visualization and measurements of buoyant vortex ring formation and evolution using background-oriented Schlieren and particle image velocimetry techniques. In addition, 3D unsteady computational fluid dynamics simulations using unsteady Reynolds-averaged Navier–Stokes and volume-of-fluid numerical methods were performed to support the experimental design as well as to provide insight about the formation and evolution of the vortex ring.

42 ENGINEERING↗

DOE OSTI2023

Simulation of Molecular Hydrogen Jets and Visualization of Associated Hydrodynamic Features [Slides]

A numerical method is presented for solving the Navier-Stokes equations to represent a steady-state hydrogen jet expanding into a vacuum chamber. This numerical method has been evaluated using three test problems with promising results. Simulations of the hydrogen jet indicate the presence of a low temperature region (less than 15 K) within the jet for the high flow rate case. The high flow rate case also gives rise to a large recirculation region within the jet. The conditions at the minimum temperature point within the jet approach the hydrogen sublimation line when the mass flow rate exceeds 2 g/s, which may allow for the formation of hydrogen ice crystals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Passive Ultrasonic Deterrents to Reduce Bat Mortality in Wind Farms (Final Report)

The overall objective of this project was to develop active and passive ultrasonic deterrent concepts to mitigate bat mortality at wind turbines. The research was supported by the US Department of Energy under the contract DE-EE0008731. Novel ultrasonic bat deterrents are investigated in this study. The deterrents are based on the idea of aerodynamic whistles wherein flow-acoustic resonance is used to produce high-amplitude tonal sound at desired ultrasonic frequencies. The deterrents can be grouped into active and passive. The active deterrents/whistles are driven by pressurized air supplied by an external source (e.g., an air compressor). The passive deterrents/whistles are designed to be mounted on wind turbine blades and are “powered” by the energy in the air moving past the rotor blades. Multiple active and passive deterrent ideas are proposed and investigated numerically and experimentally. The computational analysis involves solving the compressible unsteady Reynolds-averaged Navier-Stokes (URANS) equations and coupling the near-field aerodynamic solution with an integral method based on the Ffowcs Williams-Hawkings acoustic analogy to predict ultrasound in the farfield. Experiments are performed in the anechoic chamber at ISU (for the active whistles) and in the Stability wind tunnel at Virginia Tech (for the passive whistles).

17 WIND ENERGY↗

DOE OSTI2021

Deployment of the Finite Volume Method in Pronghorn for Gas and Salt cooled Pebble Bed Reactors

This report summarizes the activities related to ”Complete FHR and HTGR pebble bed simulator, including initial validation” funded by the NEAMS thermal-hydraulics focus area. The activity revolves around the coarse-mesh thermal-hydraulics code Pronghorn and its application to gas and salt cooled Pebble bed reactor (PBR). The main difference between gas and salt cooled PBR from a thermal-hydraulics perspective is the fluid. To address the difference in fluid behavior, two separate approaches are implemented in the MOOSE Navier Stokes module: 1) a Boussinesq approximation and 2) a fully compressible formulation. The developed finite volume method capabilities are used for improving pre-existing gas-cooled and salt-cooled pebble-bed reactor models. A steady-state, multiphysics gas-cooled pebble-bed reactor model is created that couples the equilibrium core depletion capability developed in previous work, and the finite volume method capability developed for this report. The salt-cooled pebble-bed reactor model is upgraded to use the incompressible finite volume method capability and then extended to three spatial dimensions. Finally, several verification-and-validation exercises performed with Pronghorn are documented using the verification-and-validation report of the MooseDoc system. The goal of this effort to document the verification-and-validation level of Pronghorn and improve stakeholder confidence in the results obtained with Pronghorn.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Improvement of Numerical Methods in Pronghorn

During the fiscal year of 2021, the finite-volume method (FVM) was deployed in Pronghorn to provide improved efficiency, stability, and accuracy for coarse-mesh, thermal-hydraulics problems. While the main goals of fiscal year 2021 were met, several issues emerged from the early deployment of the finite-volume method in Pronghorn. These issues were: The compressible and incompressible formulations that were implemented are inadequate for many nuclear reactor flow problems; Omission of terms accounting for the porosity and Darcy-Forchheimer body force discontinuities in the Rhie-Chow interpolation lead to oscillations in pressure and velocity at these discontinuities; The FVM lacks a correction for non-orthogonal grids for computing accurate pressure gradient leading to loss of accuracy in regions with skewed elements; The FVM currently uses a monolithic solver. Monolithic solvers have issues dealing with the saddle-point nature of the discretized fluid equations. The result are bad convergence if direct factorization is not used and large memory consumption when direct factorization is used. These four issues are addressed in this report. In particular, we report the completion of the following task: Implementation of a weakly compressible formulation in the MOOSE Navier-Stokes module; Implementation of Moukalled’s method for including body forces in the RCI. Additionally, we identified the need to smooth the porosity using Moukalled’s face-cell smoothing operator; Implementation of a non-orthogonal correction for the Green-Gauss gradient computation; Preliminary implementation of a SIMPLE segregated solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Turbulence Modeling with Nek5000/RS, SOD2D and Alya

We present Validation and Verification (V & V) study of two high-order spectral element method (SEM) based Computational Fluid Dyanimcs (CFD) codes that we will utilize for work on turbulence modeling: Nek5000 and SOD2D. While the former solves the incompressible form of Navier-Stokes equation, the latter works with compressible set of equations and uses an entropy-viscosity formulation to account for the discontinuities for high Mach number flows. We demonstrate the accuracy of these codes for two benchmark sub-sonic turbulent flows: periodic channel and pipe flow, by carrying out first and second order statistical analysis, grid convergence and turbulent structure analysis using wall-resolved large eddy simulations (WRLES). Later, we report on the implementation and testing of various wall-modeling strategies for large eddy simulation of turbulent flows in Nek5000. These include both classical log-law based and decision-tree based machine-learning models. Accuracy of these closure strategies are analyzed and necessary future work is outlined.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Expanded verification and validation studies of hypersonic aerodynamics with multiple physics-fidelity models

Hypersonic aerothermodynamics is an important domain of modern multiphysics simulation. The Multi-Fidelity Toolkit is a simulation tool being developed at Sandia National Laboratories to predict aerodynamic properties for compressible flows from a range of physics fidelities and computational speeds. These models include the Reynolds-averaged Navier–Stokes (RANS) equations, the Euler equations with momentum-energy integral technique (MEIT), and modified Newtonian aerodynamics with flat-plate boundary layer (MNA+FPBL) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities, as well as model validation with uncertainty considerations. Code verification activities on the MNA+FPBL model build on previous work by focusing on the viscous portion of the model. Viscous quantities of interest are compared against those from an analytical solution for flat-plate, inclined-plate, and cone geometries. The code verification methodology for the MEIT model is also presented. Test setup and results of code verification tests on the laminar and turbulent models within MEIT are shown. Solution-verification activities include grid-refinement studies on simulations that model the HIFiRE-1 wind tunnel experiments. These experiments are used for validation of all model fidelities. A thorough validation comparison with prediction error and uncertainty is also presented. Three additional HIFiRE-1 experimental runs are simulated in this study, and the solution verification and validation work examines the effects of the associated parameter changes on model performance. Finally, a study is presented that compares the computational costs and fidelities from each of the different models.

42 ENGINEERING↗

DOE OSTI2021

Shear thinning rheology in a concentrated suspension of fibers: the role of attractive interactions

Fiber-reinforced composites are ubiquitously encountered in the engineering, automobile, and aerospace industries. Fabrication of these composites requires the mixing of fibers dispersed in a liquid, and the final structure is affected by fiber properties, interactions, and flow fields. A good understanding of the rheology of fiber suspensions can aid in the design and optimization of the fabrication processes. To this end, we simulate the simple shear flow of fiber suspensions by accounting for short range lubrication, van der Waals attractive, electrostatic repulsion interactions, as well as friction between fibers. Direct numerical simulations are performed using the Immersed Boundary Method where the fibers are modeled as flexible slender bodies governed by the Euler-Bernoulli beam theory and the fluid flow is resolved using the Navier-Stokes equations. The simulation results for the suspension viscosity and yield stress are consistent with the experimental data from the literature for polyamide fiber suspensions. The shear-thinning behavior becomes stronger as we increase the magnitude of attractive interactions. Furthermore, we perform a parametric study varying fiber flexibility, volume fraction, aspect ratio, inertia and examine suspension viscosity and yield stress.

Khan, Monsurul↗

DOE OSTI2021

Multi-fidelity modeling to predict the rheological properties of fiber suspensions

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications like biofuel production. The 3D numerical simulations of the suspension of fibers are often computationally expensive and time-consuming. Machine learning methods such as neural networks can simplify the prediction of rheological behavior; however, they require a relatively large training data set. Multi -fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified physical equations, can lead to optimized predictions. Here, we focus on a neural network with two levels of fidelity, i.e., high and low fidelity networks. To produce high-fidelity data, we perform direct numerical simulations to model the fibers as one-dimensional inextensible slender bodies that obey the Euler- Bernoulli beam equation. The Navier-Stokes equations govern the suspended fluid, and an immersed boundary method is used to couple the fluid and solid motion. The low-fidelity data is produced by using constitutive equations. Noticeable improvements have been observed in the accuracy of predicting the rheological behavior when a multi-fidelity network is used compared to the single-fidelity network.

Boodaghidizaji, Miad↗

DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Data-driven closure modeling for hypersonic turbulent flows

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Aero-Thermal Characterization of Accelerating and Diffusing Passages Downstream of Rotating Detonation Combustors

Cycle benefits of rotating detonation engines show up to five percentage points of efficiency gain for low-pressure ratio engines. An optimal integration between the combustor and the turbine needs to be guaranteed to realize this potential gain. The rotating detonation combustor (RDC) exhausts transonic flow with shocks rotating at frequencies ranging from a few to tens of kilohertz depending on the number of present waves. Hence, the turbine design requires precise knowledge of the fluctuations and losses downstream of the combustor. This paper focuses on the quantification of fluctuations and losses for accelerating and diffusing passages. The analysis of the combustor is performed via reactive unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. The unsteady RANS equations are solved via CFD++ from Metacomp with a one-step reaction mechanism for an H2-air mixture. The resolving of the boundary layer is achieved with a structured mesh of around 36 million cells. Inlet pressure of 10 bar and two different back pressures are applied to the combustor to model the interconnection with downstream turbines. Finally, we present and assess a methodology to reduce the computational time to model these passages ten times.

Braun, James↗

DOE OSTI2022

Learning Optimal Aerodynamic Designs

This project created a framework for efficient, accurate, and scalable deep neural network representations of design optimization problem solutions. The inputs to these DNN representations are the vector of design requirement parameters, the outputs are the optimal design variables, and the goal is to learn the map from inputs to outputs (i.e., inverse design). The team addressed the problem of the optimal shape design of aerodynamic lifting surfaces—in particular aircraft wings—using a Reynolds-Average Navier Stokes model to govern the CFD-based aerodynamic shape optimization. The inverse design map for such problems is very complex and high-dimensional, involving inputs and outputs on the order of 1000s. To approximate this inverse design map, the team developed algorithms to construct parsimonious DNN architectures, which automatically identify low-dimensional manifolds in which design requirements affect optimal shape parameters, and trained these architectures with multifidelity optimization methods. The resulting methodology accurately and automatically designs optimal aerodynamic lifting surfaces with very high accuracy (99%) at interactive speeds, of the order of milliseconds, resulting in factors of one million or more speedup relative to CFD-based design optimization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Computationally Efficient Control Co-Design Optimization Framework with Mixed-Fidelity Fluid and Structure Analysis: OpenTurbineCoDe (OTCD) - ARPA-E ATLANTIS Phase I Project (Final Technical Report)

The goal of the Department of Energy (DOE) Advanced Research Projects Agency-Energy (ARPA-E) Aerodynamic Turbines Lighter and Afloat with Nautical Technologies and Integrated Servo-control (ATLANTIS) Program is to develop new technologies for floating offshore wind turbines, or wind farms, using the discipline of control co-design (CCD.) In this context, our goal is to develop a computationally efficient optimization framework for design of floating offshore wind turbines. Our specific aim is to utilize high-fidelity structural, aerodynamic, aero-structural tools, and to derive control-oriented reduced- or low-order models directly from the high-fidelity tools. We proposed a mixed-fidelity modeling approach which means that we are also using low- and mid-fidelity tools when necessary. This research is conducted by a multidisciplinary team consisting of Rutgers University, University of Michigan, Brigham Young University, and the National Renewable Energy Laboratory (NREL). The computational framework, called OpenTurbineCoDe, is designed to integrate, where possible, traditional structural, aerodynamic, aeroelastic models (e.g., OpenFAST) and advanced control algorithms with higher fidelity simulation tools including Reynolds-averaged Navier–Stokes (RANS) solvers, and three-dimensional structural finite element solvers. All the high-fidelity tools used in this research provide numerically exact gradients to facilitate both efficient optimization and local linearization for control implementation.

17 WIND ENERGY↗

DOE OSTI2023

Stakeholder-Driven Improvements to Nek5000 and NekRS

22 GENERAL STUDIES OF NUCLEAR REACTORS↗