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DOE OSTI2023

A reduced-order modeling of a tubular solar reactor for long duration thermochemical energy storage

The storage of solar energy in a solid form, referred to as a “solar fuel”, can be achieved through a process known as endothermic solar thermochemistry. This process transforms the absorbed solar energy into a stable and retrievable form that can be stored for extended periods of time. This paper presents a low–order heat transfer model of a counter–current tubular falling bed reactor designed to produce thermally reduced magnesium manganese oxide pellets for long duration thermochemical energy storage. The energy required for the endothermic reduction was supplied by concentrated solar energy or renewable electricity via indirect heating of the gas and solid reactants flowing in a ceramic tube. The counter-current gas flow enhances the mixing of the solid particles with the heat recuperation zone, allowing the gas and particles to enter and exit the tubular reactor close to room temperature. Further, the reactor was vertically oriented and was heated circumferentially by an adjustable level heat flux along a finite segment of its length. The temperature distribution of the reactor in response to transient changes along the tube was modeled by considering conduction, convection, and radiation heat transfer. Governing equations for the heat transfer model were solved by discretizing the reactor tube into a finite number of control volumes and using an energy balance for the heat exchange between the reactor wall, gas, and particles within the control volume. The energy absorbed during this endothermic reaction was modeled numerically by fitting the data of the chemical conversion rate with the corresponding temperature of particles in the heating zone. The numerical model has been experimentally validated using a reactor prototype made of a 121.92 cm alumina tube heated by a 7kW electric tube–furnace. The alumina tube receives magnesium manganese oxide pellets of 3.66±0.516 mm in diameter from the top, and a counter–current gas flow from the bottom. The reactor wall temperature was monitored by six thermocouples installed along the reactor tube length. The experimental procedure was numerically simulated, and the temperature variation along the reactor tube was compared with a matrix of experimental runs for a range of particles mass flowrates (0.75–1.25g/s) and corresponding gas flowrates (36–65 SLPM). The reactor system was heated gradually from room temperature to a steady state temperature of 1673K, and then cooled down to room temperature. The heating and cooling processes were simulated, and the numerical and experimental results were compared throughout processes. The numerical model showed similar trends to the experimental results, with an error of 0.69 to 7.9% for the particle inlet and 0.7 to 7.9% for the gas inlet during steady-state operation. The proposed numerical model can be implemented as a simplified physical model to design a feedback control system to regulate reactor temperature.

14 SOLAR ENERGY↗

DOE OSTI2015

Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT

Purpose: In x-ray computed tomography (CT), a violation of the Tuy data sufficiency condition leads to limited-view artifacts. In some applications, it is desirable to use data corresponding to a narrow temporal window to reconstruct images with reduced temporal-average artifacts. However, the need to reduce temporal-average artifacts in practice may result in a violation of the Tuy condition and thus undesirable limited-view artifacts. In this paper, the authors present a new iterative reconstruction method, synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON), to eliminate limited-view artifacts using data acquired within an ultranarrow temporal window that severely violates the Tuy condition. Methods: In time-resolved contrast enhanced CT acquisitions, image contrast dynamically changes during data acquisition. Each image reconstructed from data acquired in a given temporal window represents one time frame and can be denoted as an image vector. Conventionally, each individual time frame is reconstructed independently. In this paper, all image frames are grouped into a spatial–temporal image matrix and are reconstructed together. Rather than the spatial and/or temporal smoothing regularizers commonly used in iterative image reconstruction, the nuclear norm of the spatial–temporal image matrix is used in SMART-RECON to regularize the reconstruction of all image time frames. This regularizer exploits the low-dimensional structure of the spatial–temporal image matrix to mitigate limited-view artifacts when an ultranarrow temporal window is desired in some applications to reduce temporal-average artifacts. Both numerical simulations in two dimensional image slices with known ground truth and in vivo human subject data acquired in a contrast enhanced cone beam CT exam have been used to validate the proposed SMART-RECON algorithm and to demonstrate the initial performance of the algorithm. Reconstruction errors and temporal fidelity of the reconstructed images were quantified using the relative root mean square error (rRMSE) and the universal quality index (UQI) in numerical simulations. The performance of the SMART-RECON algorithm was compared with that of the prior image constrained compressed sensing (PICCS) reconstruction quantitatively in simulations and qualitatively in human subject exam. Results: In numerical simulations, the 240{sup ∘} short scan angular span was divided into four consecutive 60{sup ∘} angular subsectors. SMART-RECON enables four high temporal fidelity images without limited-view artifacts. The average rRMSE is 16% and UQIs are 0.96 and 0.95 for the two local regions of interest, respectively. In contrast, the corresponding average rRMSE and UQIs are 25%, 0.78, and 0.81, respectively, for the PICCS reconstruction. Note that only one filtered backprojection image can be reconstructed from the same data set with an average rRMSE and UQIs are 45%, 0.71, and 0.79, respectively, to benchmark reconstruction accuracies. For in vivo contrast enhanced cone beam CT data acquired from a short scan angular span of 200{sup ∘}, three 66{sup ∘} angular subsectors were used in SMART-RECON. The results demonstrated clear contrast difference in three SMART-RECON reconstructed image volumes without limited-view artifacts. In contrast, for the same angular sectors, PICCS cannot reconstruct images without limited-view artifacts and with clear contrast difference in three reconstructed image volumes. Conclusions: In time-resolved CT, the proposed SMART-RECON method provides a new method to eliminate limited-view artifacts using data acquired in an ultranarrow temporal window, which corresponds to approximately 60{sup ∘} angular subsectors.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Dependence of the bit error rate on the signal power and length of a single-channel coherent single-span communication line (100 Gbit s{sup -1}) with polarisation division multiplexing

We have studied experimentally and using numerical simulations and a phenomenological analytical model the dependences of the bit error rate (BER) on the signal power and length of a coherent single-span communication line with transponders employing polarisation division multiplexing and four-level phase modulation (100 Gbit s{sup -1} DP-QPSK format). In comparing the data of the experiment, numerical simulations and theoretical analysis, we have found two optimal powers: the power at which the BER is minimal and the power at which the fade margin in the line is maximal. We have derived and analysed the dependences of the BER on the optical signal power at the fibre line input and the dependence of the admissible input signal power range for implementation of the communication lines with a length from 30 – 50 km up to a maximum length of 250 km. (optical transmission of information)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1993

On the measurement of lateral velocity derivatives in turbulent flows

Direct numerical simulation data for the lateral velocity derivative delta(u)/delta(y) at the centerline of a fully developed turbulent channel flow provide reasonable support for Wyngaard's analysis of the error involved in measuring this quantity using parallel hot wires. Numerical data in the wall region of the channel flow also provide a useful indication of how to select the separation between the wires. Justification for this choice is obtained by comparing several measured statistics of delta(u)/delta(y) with the corresponding numerical data.

Antonia, R. A.↗

DOE OSTI2016

SU-F-T-273: Using a Diode Array to Explore the Weakness of TPS DoseCalculation Algorithm for VMAT and Sliding Window Techniques

Purpose: To identify the weakness of dose calculation algorithm in a treatment planning system for volumetric modulated arc therapy (VMAT) and sliding window (SW) techniques using a two-dimensional diode array. Methods: The VMAT quality assurance(QA) was implemented with a diode array using multiple partial arcs that divided from a VMAT plan; each partial arc has the same segments and the original monitor units. Arc angles were less than ± 30°. Multiple arcs delivered through consecutive and repetitive gantry operating clockwise and counterclockwise. The source-toaxis distance setup with the effective depths of 10 and 20 cm were used for a diode array. To figure out dose errors caused in delivery of VMAT fields, the numerous fields having the same segments with the VMAT field irradiated using different delivery techniques of static and step-and-shoot. The dose distributions of the SW technique were evaluated by creating split fields having fine moving steps of multi-leaf collimator leaves. Calculated doses using the adaptive convolution algorithm were analyzed with measured ones with distance-to-agreement and dose difference of 3 mm and 3%.. Results: While the beam delivery through static and step-and-shoot techniques showed the passing rate of 97 ± 2%, partial arc delivery of the VMAT fields brought out passing rate of 85%. However, when leaf motion was restricted less than 4.6 mm/°, passing rate was improved up to 95 ± 2%. Similar passing rate were obtained for both 10 and 20 cm effective depth setup. The calculated doses using the SW technique showed the dose difference over 7% at the final arrival point of moving leaves. Conclusion: Error components in dynamic delivery of modulated beams were distinguished by using the suggested QA method. This partial arc method can be used for routine VMAT QA. Improved SW calculation algorithm is required to provide accurate estimated doses.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ 2 -norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Partitioned Quantum Subspace Expansion

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We propose a variance-based criterion for determining a good iterative sequence and provide numerical evidence that these good sequences display improved numerical stability over a single step in the presence of finite sampling noise. Implementing the generalisation requires additional classical processing with a polynomial overhead in the subspace dimension. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware. Our work suggests that the numerical instability limiting the accuracy of this approach can be substantially alleviated in a parameter-free way.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

The role of global cloud climatologies in validating numerical models

The purpose of this work is to estimate sampling errors of area-time averaged rain rate due to temporal samplings by satellites. In particular, the sampling errors of the proposed low inclination orbit satellite of the Tropical Rainfall Measuring Mission (TRMM) (35 deg inclination and 350 km altitude), one of the sun synchronous polar orbiting satellites of NOAA series (98.89 deg inclination and 833 km altitude), and two simultaneous sun synchronous polar orbiting satellites--assumed to carry a perfect passive microwave sensor for direct rainfall measurements--will be estimated. This estimate is done by performing a study of the satellite orbits and the autocovariance function of the area-averaged rain rate time series. A model based on an exponential fit of the autocovariance function is used for actual calculations. Varying visiting intervals and total coverage of averaging area on each visit by the satellites are taken into account in the model. The data are generated by a General Circulation Model (GCM). The model has a diurnal cycle and parameterized convective processes. A special run of the GCM was made at NASA/GSFC in which the rainfall and precipitable water fields were retained globally for every hour of the run for the whole year.

HARSHVARDHAN↗

DOE OSTI2013

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Numerical study of the effect of normalised window size, sampling frequency, and noise level on short time Fourier transform analysis

Photonic Doppler velocimetry, also known as heterodyne velocimetry, is a widely used optical technique that requires the analysis of frequency modulated signals. This paper describes an investigation into the errors of short time Fourier transform analysis. The number of variables requiring investigation was reduced by means of an equivalence principle. Error predictions, as the number of cycles, samples per cycle, noise level, and window type were varied, are presented. The results were found to be in good agreement with analytical models.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Discretization Error Estimation and Control for Farfield Acoustic Signatures

We investigate the utility of adjoint-based error estimates for sonic boom farfield simulations governed by solutions of the augmented Burgers’ equation. Solution of this nonlinear system uses operator splitting with a second-order finite volume discretization in space and second-order Runge-Kutta time marching, while the absorption and molecular relaxation are solved using second-order central differencing. The discretization error in selected ground sonic boom cost functionals is estimated using the method of adjoint-weighted residuals. Key elements of the implementation process are emphasized with details provided on the practical aspects as appliedto the sonic boom farfield propagation. We establish the accuracy of the adjoint solutions usingcomplex step and finite difference approaches, and examine the accuracy of the error estimates using analytical N-wave solutions. We then apply it to a pressure waveform corresponding to the X-59 research aircraft. The investigations demonstrate that the method of adjoint-weighted residuals accurately predicts the level of discretization error present in sonic boom farfield simulations while offering insight into which features of the near field signal are the primary drivers of ground noise metrics. The numerical results indicate that at sampling frequencies as low as50kHz, discretization error in the propagation is under 0.01 dB[A] for realistically complex examples.

CST↗

DOE OSTI2013

Influence of cold walls on PET image quantification and volume segmentation: A phantom study

Purpose: Commercially available fillable plastic inserts used in positron emission tomography phantoms usually have thick plastic walls, separating their content from the background activity. These “cold” walls can modify the intensity values of neighboring active regions due to the partial volume effect, resulting in errors in the estimation of standardized uptake values. Numerous papers suggest that this is an issue for phantom work simulating tumor tissue, quality control, and calibration work. This study aims to investigate the influence of the cold plastic wall thickness on the quantification of 18F-fluorodeoxyglucose on the image activity recovery and on the performance of advanced automatic segmentation algorithms for the delineation of active regions delimited by plastic walls.Methods: A commercial set of six spheres of different diameters was replicated using a manufacturing technique which achieves a reduction in plastic walls thickness of up to 90%, while keeping the same internal volume. Both sets of thin- and thick-wall inserts were imaged simultaneously in a custom phantom for six different tumor-to-background ratios. Intensity values were compared in terms of mean and maximum standardized uptake values (SUVs) in the spheres and mean SUV of the hottest 1 ml region (SUV{sub max}, SUV{sub mean}, and SUV{sub peak}). The recovery coefficient (RC) was also derived for each sphere. The results were compared against the values predicted by a theoretical model of the PET-intensity profiles for the same tumor-to-background ratios (TBRs), sphere sizes, and wall thicknesses. In addition, ten automatic segmentation methods, written in house, were applied to both thin- and thick-wall inserts. The contours obtained were compared to computed tomography derived gold standard (“ground truth”), using five different accuracy metrics.Results: The authors' results showed that thin-wall inserts achieved significantly higher SUV{sub mean}, SUV{sub max}, and RC values (up to 25%, 16%, and 25% higher, respectively) compared to thick-wall inserts, which was in agreement with the theory. This effect decreased with increasing sphere size and TBR, and resulted in substantial (>5%) differences between thin- and thick-wall inserts for spheres up to 30 mm diameter and TBR up to 4. Thinner plastic walls were also shown to significantly improve the delineation accuracy for the majority of the segmentation methods tested, by increasing the proportion of lesion voxels detected, although the errors in image quantification remained non-negligible.Conclusions: This study quantified the significant effect of a 90% reduction in the thickness of insert walls on SUV quantification and PET-based boundary detection. Mean SUVs inside the inserts and recovery coefficients were particularly affected by the presence of thick cold walls, as predicted by a theoretical approach. The accuracy of some delineation algorithms was also significantly improved by the introduction of thin wall inserts instead of thick wall inserts. This study demonstrates the risk of errors deriving from the use of cold wall inserts to assess and compare the performance of PET segmentation methods.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS1996

On the Spatial and Temporal Accuracy of Overset Grid Methods for Moving Body Problems

A study of numerical attributes peculiar to an overset grid approach to unsteady aerodynamics prediction is presented. Attention is focused on the effect of spatial error associated with interpolation of intergrid boundary conditions and temporal error associated with explicit update of intergrid boundary points on overall solution accuracy. A set of numerical experiments are used to verify whether or not the use of simple interpolation for intergrid boundary conditions degrades the formal accuracy of a conventional second-order flow solver, and to quantify the error associated with explicit updating of intergrid boundary points. Test conditions correspond to the transonic regime. The validity of the numerical results presented here are established by comparison with existing numerical results of documented accuracy, and by direct comparison with experimental results.

Meakin, Robert L.↗

NASA NTRS1995

Effect Of Transition Density On Performance Of A DTTL

One estimates minimum transition density needed to limit symbol-error rate. Theoretical calculations and accompanying computer simulations provide numerical basis for specification of minimum data-transition density needed for adequate performance of radio receiver processing noisy signal containing non-return-to-zero (NRZ) stream of data symbols (bits). By use of digital-data-transition-tracking loop (DTTL), receiver strives to synchronize operation with data symbols. Performance of receiver in terms of ability to keep symbol-error rate (SER) in output of receiver below specified level depends on symbol signal-to-noise ratio (SSNR) of incoming signal and on degree of synchronization. Ability of DTTL to maintain synchronization depends partly on SSNR and partly on data-transition density.

Nguyen, Tien M.↗

DOE OSTI2015

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Active learning using hybrid surrogate tool life modeling for machining process optimization

Here, this paper describes an active learning approach for part-to-part iterative machining process optimization using a hybrid surrogate tool life model. A probabilistic interpolating tool life model is developed by combining the empirical Taylor-type tool life equation and the model fit error. The probabilistic tool life model is then used to calculate the machining cost per part distribution. The optimal machining parameters are selected using an expected improvement in machining cost per part criterion. The method is validated numerically using experimental results; the results show a median convergence error of 2.2% after three tests over 400 simulations. The method is validated experimentally on two industrial applications for Ti-6Al-4V roughing resulting in a cost per part reduction greater than 23% after two tests. The described method is a robust solution for rapid convergence to optimal machining parameters in an industrial production environment.

Active learning↗

DOE OSTI2016

A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute “dual-weighted” a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

97 MATHEMATICS AND COMPUTING↗