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At least 145 records · Page 8

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DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Pore-Scale Modeling of Electrokinetics in Geomaterials

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials developed on the application of an external voltage and pressure difference, respectively. Here, this model is used to predict the macroscale permeabilities of geomaterials via the widely used Carmen–Kozeny equation and through the electrokinetic coupling coefficients. The permeability results for a two-dimensional X-ray tomography-derived sand microstructure are within the same order of magnitude as the experimentally calculated values. The effect of the particle aspect ratio and orientation on the electrokinetic coupling coefficients and subsequently the electrical and hydraulic tortuosity of the porous media has been determined. These calculations suggest a highly tortuous geomaterial can be efficient for applications like decontamination and desalination.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Toward Predictive RANS and SRS Computations of Turbulent External Flows of Practical Interest

In this work, we investigate the main challenges to prediction of turbulent external flows of practical interest with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) models. This represents a crucial step toward further developing and establishing these formulations so they can be confidently utilized in engineering problems without reference data. The study initiates by identifying the major challenges to prediction. A literature review is performed to illustrate their effects in RANS and SRS computations. Afterward, we evaluate the impact of the challenges to prediction by analyzing representative statistically steady and unsteady flows with prominent RANS and SRS methods. These include multiple turbulent viscosity and second-moment RANS closures, and hybrid and bridging SRS models. The results demonstrate the potential of the selected SRS models to predict engineering flows. Yet, they also show the importance of considering the challenges to prediction during the setup and conduction of numerical experiments. These can suppress the advantages of using SRS formulations. The data also indicate that only SRS models can confidently predict statistically unsteady flows. In contrast, the results demonstrate that mean-flow quantities of statistically steady flows can be efficiently calculated with RANS closures, especially second-moment closures. Among the selected SRS methods, bridging models reveal better suited for prediction due to their ability to prevent commutation errors and enable the robust evaluation of numerical and modeling errors. This last property allows the use of a new validation technique that does not require reference data.

42 ENGINEERING↗

DOE OSTI2024

Three-step LES-C models for flows at high Reynolds numbers

Here, we investigate the need for the second correction step in the recently proposed LES-C models for fluid flows at high Reynolds numbers. These models use a predictor-corrector idea to enhance the efficiency of the existing Large Eddy Simulation models. Different three-step(one defect step, two corrections) LES-C models, based on the Leray-α, ADM and NS-ω LES models, are tested in three different situations. The new Leray-α-C2 model (C2 stands for two correction steps) is applied to the Navier–Stokes equations; the ADC2 is applied to the MagnetoHydroDynamic flow; and the NS-ω-C2 is used in the fluid-fluid interaction problem. We evaluate the effectiveness of the second correction step in all these settings, using qualitative and quantitative numerical tests.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Benchmark study of the DTU OWC chamber with both two-way and one-way absorption

This paper reports on a benchmark study based on small-scale (1:50) measurements of a single, oscillating water column chamber mounted sideways in a long flume. The geometry of the OWC chamber is extracted from a barge-like, attenuator-type floating concept “KNSwing” with 40 chambers targeted for deployment in the Danish part of the North Sea. In addition to traditional two-way energy extraction we also consider one-way energy extraction with passive venting and compare chamber response, pressures and total absorbed energy between the two methods. A blind study was established for the numerical modeling, with participants applying several implementations of weakly nonlinear potential flow theory and commercial Navier–Stokes solvers (CFD). Both compressible and incompressible models were used for the air phase. Potential flow calculations predict more energy absorption near the chamber resonance for one-way absorption than for two-way absorption, but the opposite is found from the experimental measurements. This outcome is mainly attributed to energy losses in the experimental passive valve system, but this conclusion must be confirmed by better experimental measurements. Modeling the one-way valve in CFD proved to be very challenging and only one team was able to provide results which were generally closer to the experiments. The study illustrates the challenges associated with both numerical and experimental analysis of OWC chambers. Air compressibility effects were not found to be important at this scale, even with the large volume of additional air used for the one-way case.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

A Geometric Volume of Fluid-Based Multiphase Flow Solver Extension to the Reacting Flow Solver, PeleLM

A new algorithm is presented to simulate multiphase flows with surface tension in a pathway for spray combustion simulation. The algorithm combines capabilities from two open-source packages, including the interface reconstruction library (IRL), a library of computational geometry routines to enable the volume of fluid (VOF) method, and PeleLM, a solver for the reacting Navier-Stokes equations. Additionally, surface tension is implemented using the continuum surface force (CSF) model with an improved height function technique in the volume fraction field. Spurious errors in volume fraction arising from our combined strategy are corrected through a topology-based method that improves both numerical stability and accuracy. Multiple validation simulations are conducted, including (i) translations and rotations of Zalesak's disk, (ii) a stationary circular droplet with surface tension, (iii) an oscillating elliptical droplet, and (iv) three-dimensional deformation of a spherical droplet. Results indicate that the combined scheme retains the favorable properties of each of the component algorithms.

42 ENGINEERING↗

DOE OSTI2021

Improved natural convection heat transfer correlations for reactor cavity cooling systems of high-temperature gas-cooled reactors: From computational fluid dynamics to Pronghorn

The Reactor Cavity Cooling System (RCCS) is a common reactor safety system in High Temperature Gas Cooled Reactors (HTGR) that removes heat from the Reactor Pressure Vessel (RPV) by radiation ($\sim 80\%$) and natural convection ($\sim 20\%$). For simulation of accident scenarios of HTGRs, intermediate fidelity and system codes models must be employed for limiting the models' execution time. While accurate quantification of the radiative heat transfer is available in these models, quantification of natural convection must rely on correlations of questionable accuracy for the Nusselt number. Commonly used correlations are based in experiments performed at low Rayleigh numbers and/or using isothermal walls in simplified geometries. Here, this work improves on the accuracy of natural convection heat transfer correlations in support for HTGR designs. These correlations include both local and average Nusselt numbers as a function of the global Rayleigh number, the local Rayleigh number, and the temperature profile at the hot wall of the RCCS. In the absence of dedicated experiments and the difficulty of performing high-fidelity simulations at realistic Rayleigh numbers, the data to fit the correlations are generated with Computational Fluid Dynamics (CFD) using Reynolds Averaged Navier-Stokes (RANS) models. First, a careful selection of the RANS turbulence model is performed by comparing the results obtained with different RANS turbulence models against high fidelity simulations of natural convection at $Ra \ 1 \times 10^{11}$ in a rectangular cavity. Next, the selected model is used to perform simulations of an HTGR cavity at different high Rayleigh numbers $\in [6.1 \times 10^{11},2.9 \times 10^{13}]$ to encompass several HTGR designs, assuming an isothermal RPV wall. The results obtained are used to fit a correlation for the average and space-varying Nusselt number as a function of the global and local Rayleigh numbers via a sparsity-promoting least-squares method. The selected RANS model is then used to perform simulations of a PBMR 400 HTGR cavity with the temperature profiles at the RPV wall obtained during a PLOFC transient. We use the results obtained to fit a temperature-dependent correction to the space-varying Nusselt number with the sparsity-promoting least-squares method. The results obtained in this work, enable system-level codes, such as Pronghorn, to perform higher-fidelity simulations of the heat exchange process in the RCCS while still maintaining a low computational cost.

42 ENGINEERING↗

DOE OSTI2024

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM +. For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed. The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. In conclusion, given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

DNS↗

DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗

DOE OSTI2021

Modeling of thermal and kinetic processes in non-equilibrium plasma ignition applied to a lean combustion engine

In recent years novel ignition systems have been developed to enable stable and efficient engine operations with lean mixtures. Among them, radio-frequency corona ignition systems create discharges that involve a much wider region compared to traditional spark, and produce non equilibrium plasma with high levels of active radicals and excited species. These devices considerably increase the early flame growth speed and extend stable operating limits. With the aim of expanding the knowledge on high efficiency lean-burn SI engines, this paper investigates and compares the combustion development generated by spark and corona ignitions through computational fluid dynamics, within the Reynolds-Averaged Navier-Stokes framework for turbulence modeling. In order to simultaneously take thermal and chemical effects into account, the Perfectly Stirred Reactor combustion model is used. Experimental data are also collected for validation in an optical access engine, for different mixture levels, from stoichiometric to very lean. Furthermore, the faster burn rate generated by the corona system in the initial stage of the combustion is well predicted by the simulations, in all the relative air-fuel ratio conditions. Remarkably, as the mixture becomes lean, simulations are able to capture the non-linear transition from fast to slow kernel growth, before a self-sustainable flame propagation is established. This correlates very well with the measured engine cyclic variability and the corresponding steep change in the duration of the flame kernel formation. Ultimately, this study highlights the important role of the atomic oxygen, as active radical, in promoting and enhancing the combustion initiated by a corona discharge, in addition to the volumetric ignition effect. By contrast, the validated simulations allow to explain that the high-temperature thermal plasma generated in a traditional spark discharge is insensitive to kinetic aspects.

42 ENGINEERING↗

DOE OSTI2024

Optimization-Inspired Pin-Fin Array for Supercritical Carbon Dioxide Recuperator

Additively manufactured heat exchangers are one possible route to cost-effective sCO 2 power cycles. In this paper, experimental results are obtained for two helical pin fin tubes that were designed following parametric optimization of the fin array. Neither the numerical optimization nor the experimental testing have been previously reported in the literature. The two tube designs were, (1) the optimization inspired design, and (2) the optimization-inspired design with a fin diameter increased by a factor of 2. To characterize the print, the designs were scanned using X-ray computed tomography to measure feature sizes and heat transfer area. The optimization was conducted in a commercial, computational fluid dynamics code. The code solved the Reynolds Averaged Navier-Stokes (RANS) and energy equations with turbulence closure provided by the shear stress transport (SST) k-ω model. In the experiments, the Nusselt number augmentation was measured using the Wilson plot technique and the friction factor was determined with mass flow and pressure drop measurements. The experimental testing indicated that the optimization-inspired design had a friction factor that was four times less than the baseline tube design at equal Nusselt number. Additionally, the optimization-inspired design had a 14% improvement in Nusselt number, at equal friction factor, relative to the best performing computational fluid dynamics (CFD) trial points. Tube design (2), with the larger diameter pin fins, had similar performance, within experimental error, as the tube with the smaller diameter pin fins (1). Both tubes achieved overall fin array efficiencies near 1. A performance factor, V/V 0 , equal to the volume of the enhanced heat exchanger divided by the volume of the baseline (no-fins) heat exchanger, is recommended to quantify internal cooling performance. In conclusion, the experimental shell and tube heat exchanger, using the additively manufactured tube, is competitive with printed circuit heat exchangers in its pressure drop class and could be further improved by optimizing a shell-and-tube heat exchanger utilizing this heat transfer enhancement feature.

42 ENGINEERING↗

DOE OSTI2021

Reconstructing porous media using generative flow networks

One area of intense scientific interest for the study of sandstones, carbonates, and shale at the pore scale is the use of limited image and petrophysical data to generate multiple realizations of a rock’s pore structure. Such images aid efforts to quantify uncertainty in petrophysical properties, including porosity–permeability transforms. We develop and evaluate a deep learning-based method to synthesize porous media volumes using a so-called generative flow model trained on x-ray microscope images of rock texture and pore structure. These models are optimized on a log-likelihood objective and they synthesize large and realistic three-dimensional images. Further, we demonstrate the rapid generation of sandstone image volumes that display realism as gauged by quantitative comparison of topological features using Minkowski functionals of porosity, specific surface area, and the Euler–Poincaré characteristic (i.e., pore connectivity). We also evaluate the single-phase permeability using Navier–Stokes and lattice Boltzmann methods and show that transport properties of the generated samples match measured trends.

58 GEOSCIENCES↗

DOE OSTI2021

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Enhanced relaxed physical factorization preconditioner for coupled poromechanics

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form C^ = (C + βFF T ), where C is a symmetric positive definite matrix, FF T a rank-deficient term, and β a real non-negative coefficient. The inversion of C^, performed in an inexact way, can become unstable for large values of β, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with C^. This strategy can prove useful in other problems as well where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix C^. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of C^. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Furthermore, effectiveness and robustness of the proposed algorithms are demonstrated in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗

DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗

DOE OSTI2021

Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations (PDEs) for which a stochastic computational model (SCM) is available and which depend on a vector-valued random control parameter. The cost of a single numerical evaluation of this SCM is assumed to be such that only a limited number of points can be computed for constructing the training dataset (small data). Each point of the training dataset is made up of realizations from a vector-valued stochastic process (the stochastic solution) and the associated random control parameter on which it depends. The presented PLoM constrained by PDE allows for generating a large number of learned realizations of the stochastic process and its corresponding random control parameter. These learned realizations are generated so as to minimize the vector-valued random residual of the PDE in the mean-square sense. Appropriate novel methods are developed to solve this challenging problem. Three applications are presented. The first one is a simple uncertain nonlinear dynamical system with a nonstationary stochastic excitation. The second one concerns the 2D nonlinear unsteady Navier–Stokes equations for incompressible flows in which the Reynolds number is the random control parameter. Here, the last one deals with the nonlinear dynamics of a 3D elastic structure with uncertainties. The results obtained make it possible to validate the PLoM constrained by stochastic PDE but also provide further validation of the PLoM without constraint.

Machine learning↗

DOE OSTI2021

Topology optimization of additively manufactured fluidic components free of internal support structures

This report integrates projection-based approaches for implementing overhang constraints with fluid topology optimization to design additively manufactured fluidic components that do not require internal support structures. Internal support structures are challenging, potentially impossible to remove in complex fluid networks, yet would degrade fluidic performance if left within the part. This presents a major challenge in coupling topology optimization with additive manufacturing in the design of fluid components. The proposed approach leverages past work in overhang constraints for solid mechanics, including projection formulations and adjoint sensitivity analysis, and considers incompressible Navier–Stokes equations for laminar fluid flow. The approach is demonstrated on 2D and 3D fluid topology optimization problems to minimize pressure drop and constrain mass flow rates in pipes and manifolds. Resulting designs are crisp, logical, satisfy performance constraints, and satisfy overhang constraints, eliminating the need for internal support structures.

42 ENGINEERING↗