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At least 289 records · Page 16

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DOE OSTI2024

A Green's Function Wind Turbine Induction Model That Incorporates Complex Inflow Conditions

ABSTRACT In this work, we develop a new analytical turbine induction model that can incorporate complex inflow conditions including cases where the wind velocity and temperature profiles can vary as functions of height. This induction model is derived from the linearized Navier–Stokes and leads to a second‐order ODE that can be solved using a Green's function formulation. The corresponding Green's function for several configurations are found including the infinite domain, semi‐infinite domain with ground plane, and a power law velocity inflow profile. The results of this approach are then compared with simulations of the turbine induction field using the AMR‐Wind CFD solver with a uniformly loaded actuator disk model. These comparisons show that the Green's function approach captures the centerline blockage, three‐dimensional blockage flow field, and streamwise velocity slow down, with very good agreement for lower thrust conditions and at larger distances away from rotor disk. The effects of shear on the turbine blockage were also compared using a power law inflow profile, and we show that this approach matches the CFD predictions for the cases considered.

17 WIND ENERGY↗

DOE OSTI2025

A Comparison of Pre‐Construction and Operational Wake Loss Estimates for Land‐Based Wind Plants

The overall bias between pre‐construction energy yield assessment (EYA) estimates of wind plant energy production and the achieved operational production is improving in the wind industry, but uncertainty remains high for individual wind plants. Wake effects within wind plants are one of the largest sources of energy loss considered in the EYA process, and previous work shows wake loss estimates to be a major source of disagreement among wind energy consultants who perform EYAs. To better understand the accuracy of wake loss predictions, we compare overall operational wake loss estimates based on supervisory control and data acquisition data to pre‐construction estimates provided by six wind energy consultants for five land‐based wind plants in North America. By augmenting existing approaches for quantifying operational wake losses, we estimate wake losses during the period of record for which operational data are available as well as the expected long‐term wake losses, based on historical reanalysis weather data, to which the EYA estimates are compared. To account for power variations at different turbine locations caused by terrain‐induced wind resource heterogeneity, we correct the operational wake loss estimates using predicted freestream wind speed variations from the Wind Systems Engineering Reynolds‐averaged Navier–Stokes (RANS) tool. We identify long‐term corrected operational wake losses between 1.9% and 6.4% for the five plants, with a mean loss of 4%. For the project deemed most acceptable for operational wake loss assessment, which is located in the simplest terrain and isolated from neighboring plants, the mean EYA wake loss estimate is within 0.7 percentage points of the operational value of 6.4%. For most of the remaining plants, results suggest that wake losses are generally overpredicted by 2.6–6.3 percentage points. However, operational wake losses may be underestimated for many of these projects because of spatial wind resource variations not captured by the RANS model, external wake effects that are unaccounted for in the estimation process, and wind plant blockage effects. To better understand factors that contribute to the observed wake losses, we investigate operational wake losses as a function of wind direction and wind speed. As expected, wake losses are generally concentrated near wind directions that are aligned with rows of closely spaced turbines and at below‐rated wind speeds; however, for some projects, the energy produced by the wind plant exceeds the estimated potential energy of the plant without wake interactions for certain wind directions and wind speeds, suggesting inaccurate assumptions in the wake loss estimation method for those plants. Lastly, we compare predicted and operational wake losses for individual wind turbines, finding that even when overall wake losses are predicted accurately, large uncertainty exists at the turbine level.

17 WIND ENERGY↗

DOE OSTI2022

Exact WKB and the quantum Seiberg-Witten curve for 4d $N$ = 2 pure SU(3) Yang-Mills. Abelianization

We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on $\mathbb{CP}^1$ with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,$\mathbb{C}$)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S 1

We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S 1 . We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of N-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even N and global inconsistency for odd N. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗

DOE OSTI2021

Beyond Taylor’s hypothesis: a novel volumetric reconstruction of velocity and density fields for variable‑density and shear flows

Abstract This work presents a novel numerical procedure for reconstructing volumetric density and velocity fields from planar laser-induced fluorescence (PLIF) and stereoscopic particle image velocimetry (SPIV) data. This new method is theoretically and practically demonstrated to provide more accurate 3D vortical structures and density fields in high shear flows than reconstruction methods based on the mean convective velocity. While Taylor’s hypothesis of frozen turbulence is commonly applied by using the local mean streamwise velocity, the proposed algorithm uses the measured local instantaneous velocity for data convection. It consists of a step-by-step reconstruction based on a mixed Lagrangian–Eulerian solver that includes the 3D interpolation of scattered flow data and that relaxes the Taylor’s hypothesis by iterative enforcement of the incompressibility constraint on the velocity field. This methodology provides 3D fields with temporal resolution, spatial resolution, and accuracy comparable to that of real 3D snapshots, thus providing a practical alternative to tomographic measurements. The procedure is validated using numerical data of the constant-density channel flow available on the Johns Hopkins University Turbulence Database (JHTDB), showing the accurate reconstruction of the 3D velocity field. The algorithm is applied to an experimental dataset of PLIF and SPIV measurements of a variable-density jet flow, demonstrating its capability to provide 3D velocity and density fields that are more consistent with the Navier–Stokes equations compared to the mean flow convective method. Graphic abstract

42 ENGINEERING↗

DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics

This work describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (Parallel time integration with multigrid. https://computation.llnl.gov/projects/parallel-timeintegration-multigrid) and Chombo (Chombo software package for AMR applications—design document, 2014). The former is a parallel time integration library using multigrid and the latter is a massively parallel structured AMR library. Employing this adaptive space-time parallel algorithm is Chord (Comput Fluids 123:202–217, 2015), a computational fluid dynamics (CFD) application code for solving compressible fluid dynamics problems. For the same solution accuracy, speedups are demonstrated from the use of space-time parallelization over the time-sequential integration on Couette flow and Stokes’ second problem. On a transient Couette flow case, at least a 1.5× speedup is achieved, and with a time periodic problem, a speedup of up to 13.7× over the time-sequential case is obtained. In both cases, the speedup is achieved by adding processors and exploring additional parallelization in time. The numerical experiments show the algorithm is promising for CFD applications that can take advantage of the time parallelism. Future work will focus on improving the parallel performance and providing more tests with complex fluid dynamics to demonstrate the full potential of the algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Physics-informed neural networks (PINNs) for fluid mechanics: a review

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). Here, we demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.

42 ENGINEERING↗

DOE OSTI2023

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗

DOE OSTI2024

Formulation, Implementation and Validation of a 1D Boundary Layer Inflow Scheme for the QUIC Modeling System

Recent studies have highlighted the importance of accurate meteorological conditions for urban transport and dispersion calculations. In this work, we present a novel scheme to compute the meteorological input in the Quick Urban & Industrial Complex () diagnostic urban wind solver to improve the characterization of upstream wind veer and shear in the Atmospheric Boundary Layer (ABL). The new formulation is based on a coupled set of Ordinary Differential Equations (ODEs) derived from the Reynolds Averaged Navier–Stokes (RANS) equations, and is fast to compute. Building upon recent progress in modeling the idealized ABL, we include effects from surface roughness, turbulent stress, Coriolis force, buoyancy and baroclinicity. We verify the performance of the new scheme with canonical Large Eddy Simulation (LES) tests with the GPU-accelerated FastEddy"Equation missing" solver in neutral, stable, unstable and baroclinic conditions with different surface roughness. Furthermore, we evaluate QUIC calculations with and without the new inflow scheme with real data from the Urban Threat Dispersion (UTD) field experiment, which includes Lidar-based wind measurements as well as concentration observations from multiple outdoor releases of a non-reactive tracer in downtown New York City. Compared to previous inflow capabilities that were limited to a constant wind direction with height, we show that the new scheme can model wind veer in the ABL and enhance the prediction of the surface cross-isobaric angle, improving evaluation statistics of simulated concentrations paired in time and space with UTD measurements.

54 ENVIRONMENTAL SCIENCES↗

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 OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( $d=2,3$ ). This method uses polynomials of degree $k+1$ for the stress and of degree k for the displacement ( $k\ge 0$ ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any $k \ge 0$ , the $H(\mathrm{div})$ -like error estimate for the stress and $L^2$ error estimate for the displacement are optimal. We further establish the optimal $L^2$ error estimate for the stress provided that the ${\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}$ Stokes pair is stable and $k \ge d$ . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

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 OSTI2023

Modeling ash deposition and shedding during oxy-combustion of coal/rice husk blends at 70% inlet O2

Abstract Co-firing rice husk (RH) and coal with carbon capture using oxy-combustion presents a net carbon negative energy production opportunity. In addition, the high fusion temperature of the non-sticky, silica rich, RH can mitigate ash deposition as well as promote shedding of deposits. To identify the optimum operating conditions, fuel particle sizes, and blend ratios that minimize ash deposition, a Computational Fluid Dynamic methodology with add-on ash deposition and shedding models were employed to predict outer ash deposition and shedding rates during co-combustion of coal/RH in AIR and O 2 /CO 2 (70/30 vol%, OXY70) oxidizer compositions. After ensuring that the fly-ash particle size distributions and particle Stokes numbers near the deposition surface were accurately represented (to model impaction), appropriate models for coal ash and RH ash viscosities that were accurate in the temperature region (1200–1300 K) of interest in this study were identified. A particle viscosity and kinetic energy (PKE) based capture criterion was enforced to model the ash capture. An erosion/shedding criterion that takes the deposit melt fraction and the energy consumed during particle impact into account was also implemented. Deposition rate predictions as well as the deposition rate enhancement (OXY70/AIR) were in good agreement with measured values. While the OXY70 scenario was associated with a significant reduction (60%–70%) in flue gas velocities, it also resulted in larger fly-ash particles. As a result, the PKE distributions of the erosive RH ash were similar in both scenarios and resulted in similar shedding rates.

Energy & Fuels↗