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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS

The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $ω$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $ω$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $τ$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.

Nek5000↗
DOE OSTI2023

Large Eddy Simulation of Gasoline Sprays in a Lagrangian–Eulerian Framework Using the High-Order Spectral Element Method

Predicting the spray evolution using simulations requires accurate modeling of the turbulent gas-phase flow field. Here, in this study, the high-order spectral-element method (SEM), implemented in the code Nek5000, was used to provide highly resolved solutions to the turbulent flow field. Spray modeling capabilities were implemented into the Nek5000 code. The spray is modeled in a Lagrangian–Eulerian (LE) framework, where the liquid is represented by discrete parcels of droplets. The method for coupling liquid and gas in the context of SEM is described, which allows for very fine meshes to be used without affecting the stability of the solution. Large-eddy simulations (LES) of the eight-hole ECN Spray G gasoline injector were conducted. Numerical results are compared against experimental data for liquid penetration, droplet size and gas velocity. The morphology of the multiplume spray is compared against experimental data. The effect of different spray injection inputs is analyzed. It was found that using a plume direction of 33 deg and an injection cone angle of 30 deg produced the best results overall. This work shows the applicability of SEM for spray modeling applications, where use of a high-order flow solver can help us understand the multiplume spray aerodynamics and how it leads to plume collapse under certain conditions. Results also highlight the need for tuning spray input parameters in the LE framework, even when high-fidelity gas flow solutions are possible.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Energy Exascale Computational Fluid Dynamics Simulations With the Spectral Element Method

Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Further, recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.

42 ENGINEERING↗
DOE OSTI2020

Toward Exascale: Overview of Large Eddy Simulations and Direct Numerical Simulations of Nuclear Reactor Flows with the Spectral Element Method in Nek5000

At the beginning of the last decade, Petascale supercomputers (i.e., computers capable of more than 1 petaFLOP) emerged. Now, at the dawn of exascale supercomputing, we provide a review of recent landmark simulations of portions of reactor components with turbulence-resolving techniques that this computational power has made possible. In fact, these simulations have provided invaluable insight into flow dynamics, which is difficult or often impossible to obtain with experiments alone. We focus on simulations performed with the spectral element method, as this method has emerged as a powerful tool to deliver massively parallel calculations at high fidelity by using large eddy simulation or direct numerical simulation. We also limit this paper to constant-property incompressible flow of a Newtonian fluid in the absence of other body or external forces, although the method is by no means limited to this class of flows. We briefly review the fundamentals of the method and the reasons it is compelling for the simulation of nuclear engineering flows. We review in detail a series of Petascale simulations, including the simulations of helical coil steam generators, fuel assemblies, and pebble beds. Even with Petascale computing, however, limitations for nuclear modeling and simulation tools remain. In particular, the size and scope of turbulence-resolving simulations are still limited by computing power and resolution requirements, which scale with the Reynolds number. In the final part of this paper, we discuss the future of the field, including recent advancements in emerging architectures such as GPUbased supercomputers, which are expected to power the next generation of high-performance computers.

computational fluid dynamics↗
DOE OSTI2021

Spectral Element Modeling of Acoustic to Seismic Coupling Over Topography

Acoustic waves in the atmosphere are commonly recorded on seismometers as they couple into the ground. These signals, here called ground coupled airwaves, are not commonly considered in numerical modeling of infrasound propagation, which often assumes a rigid unmeshed boundary. Starting from an analytically-tractable spherical wave model, we analyze how the coupling of an acoustic wave into a planar elastic halfspace changes over a wide range of scenarios. We use energy admittance to quantify acoustic to seismic coupling over both a planar elastic halfspace and meshed topography. Our spectral element and analytic calculations have different maxima as a function of incidence angle, with very high admittance values for near-vertical incidence (maximum ≈78%). Energy admittance calculations at shallow incidence angles are much smaller (less than 1%). In simulations over the complex topography of Sakurajima Volcano, we attribute the variable spatial pattern of energy admittance to changes in earth parameters between each model. The observed pressure difference over the simulated 15 km region appears to be < 2%. While this value is relatively small, the cumulative addition over 100s of km and multiple acoustic bounce points may be significant. Acoustic to seismic coupling along the propagation path may bias long distance yield estimates, particularly when infrasound propagates over regions with steep topography or particularly slow seismic velocities, such as alluvial planes.

58 GEOSCIENCES↗
DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Verification and Validation of Spectral Element Code for Supercritical CO2 Flow in Vertical Heated Tubes

The investigation of heat transfer in supercritical CO2 (sCO2) has garnered considerable attention in recent decades, given sCO2's potential as a promising working fluid for advanced power conversion cycles. Despite previous research efforts, there are still gaps in our understanding of sCO2 heat transfer, particularly in conditions associated with heat transfer deterioration. To delve into sCO2 heat transfer more comprehensively, we propose employing the high-fidelity computational fluid dynamics code NekRS to simulate sCO2 flow using the large eddy simulation technique. Through graphics processing unit acceleration, NekRS achieves a higher computational speed than traditional CPU-based systems. However, before using NekRS in practical applications involving sCO2, it is imperative to perform verification and validation. Here, this paper presents our efforts to verify and validate the NekRS code's capability for simulating sCO2 using heated vertical tubes, where heat transfer deterioration usually happens. To accommodate the unique properties of sCO2, we have modified the NekRS code by integrating third-party property modules, such as REFPROP and PROPATH. Our simulations are compared with experimental and numerical data from the literature, instilling confidence in leveraging NekRS for future engineering applications. Our simulations also reveal that the accuracy of the property module significantly impacts the results, with REFPROP outperforming PROPATH for sCO2 properties. Additionally, we observed that, depending on the flow direction, buoyancy can either enhance or suppress turbulence in sCO2 flow. In upward flow, under certain conditions, the suppressed turbulence leads to heat transfer deterioration, resulting in elevated wall temperatures.

NekRS↗
DOE OSTI2023

Large Eddy Simulation of Convective Heat Transfer in a Random Pebble Bed Using the Spectral Element Method

The development of fluoride-cooled high-temperature reactors has drastically increased the demand for an in-depth understanding of the heat transfer (HT) in packed beds cooled by liquid salts. The complex flow fields and space-dependent porosity found in a pebble bed require a detailed understanding to ensure the proper cooling of the reactor core during normal and accident conditions. As detailed experimental data are complicated to obtain for these configurations, high-fidelity simulation such as large eddy simulation and direct numerical simulation (DNS) can be employed to create a high-resolution heat transfer numerical database that can assist in addressing industrial-driven issues associated with the heat transfer behavior of fluoride-cooled high-temperature reactors. In this paper, we performed a series of large eddy simulation using computational fluid dynamics (CFD) code NekRS to investigate the heat transfer for a bed of 1741 pebbles. Further, the characteristics of the flow, such as average, rms, and time series of velocity and temperature, have been analyzed. Porous media averages have also been performed. The simulation results show a good agreement between non-conjugate heat transfer and conjugate heat transfer. The generated data will be used to benchmark heat transfer modeling methods and local maxima/minima of heat transfer parameters. It will also be used for supporting convective heat transfer quantification for Kairos Power and benchmarking lower fidelity models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Direct Numerical Simulation of Flow Over a Wall-Mounted Cube with the Nek5000 Spectral Element Code: DNS at Re h = 3900

The direct numerical simulation (DNS) of the canonical wall-mounted unit cube subjected to two distinct incident velocity profiles is performed at a Reynolds number where the bulk flow characteristics are known to become relatively Reynolds number insensitive. The aim of this work is to highlight the sensitivity of such bluff-body flows to mean shear and to provide a representative set of data for such flow scenarios where common turbulence modeling techniques often fail. Simple boundary conditions and a small domain are selected to allow for cost-effective and easy comparisons for model development purposes. In addition to mean velocity profiles, select turbulence statistics are presented in detail. Further, the basic efficacy of eddy viscosity models is evaluated and found to be adequate only for the shear stress components for the bluff-body flows examined here. Other failure mechanisms for RANS are proposed.

42 ENGINEERING↗
DOE OSTI2022

Large Eddy Simulation of Random Pebble Bed Using the Spectral Element Method

The high-fidelity simulations are performed with Nek5000/NekRS to show the importance of various phenomena associated with fluid flow and heat transfer through pebble beds. As a result of this work, Kairos Power and NEAMS have a better understanding of the behavior of pebble bed geometries. Kairos Power will leverage the data generated and conclusions reached as part of this investigation to help accelerate the deployment of their reactor design.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on finite element method--spectral element method (FEM-SEM) equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order (p = 1) finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in the polynomial degree of the high-order operator, requiring specialized solvers to treat the anisotropy. We make use of an element-structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in h and p. The method is extended to interior penalty and Bassi and Rebay (BR2) discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Finally, numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries

We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The Flux-Differencing Discontinuous Galerkin Method Applied to an Idealized Fully Compressible Nonhydrostatic Dry Atmosphere

Dynamical cores used to study the circulation of the atmosphere employ various numerical methods ranging from finite-volume, spectral element, global spectral, and hybrid methods. In this work, we explore the use of Flux-Differencing Discontinuous Galerkin (FDDG) methods to simulate a fully compressible dry atmosphere at various resolutions. We show that the method offers a judicious compromise between high-order accuracy and stability for large-eddy simulations and simulations of the atmospheric general circulation. In particular, filters, divergence damping, diffusion, hyperdiffusion, or sponge-layers are not required to ensure stability; only the numerical dissipation naturally afforded by FDDG is necessary. We apply the method to the simulation of dry convection in an atmospheric boundary layer and in a global atmospheric dynamical core in the standard benchmark of Held and Suarez

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Scalable Interpolation on GPUs for Thermal Fluids Applications

The need for efficient interpolation arises in many use cases for spectral element simulations. Towards this end, we present a fast and robust GPU-enable interpolation utility for NekRS, a spectral-element, Navier-Stokes solver. This utility is based on the findpts and findpts eval routines from the gslib library. To demonstrate the functionality, we added support for particle tracking. The GPU implementation of the interpolation allows for tracking 100 times more particles for the same computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗