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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Experimental Validation of Exact Burst Pressure Solutions for Thick-Walled Cylindrical Pressure Vessels

Burst pressure is one of the critical strength parameters used in the design and operation of pressure vessels because it represents the maximum pressure that a vessel can withstand before failing. Historically, the Barlow formula was used as a design base for estimating burst pressure. However, it does not consider the plastic flow response for ductile steels and is applicable only to thin-walled cylinders (i.e., the diameter to thickness ratio D/t ≥ 20). A new multiaxial plastic yield theory was developed to consider the plastic flow response, and the associated theoretical (i.e., Zhu–Leis) solution of burst pressure was obtained and has gained extensive applications in the pipeline industry because it was validated by different full-scale burst test datasets for large-diameter, thin-walled pipelines in a variety of steel grades from Grade B to X120. The Zhu–Leis flow theory of plasticity was recently extended to thick-walled pressure vessels, and the associated exact flow solution of burst pressure was obtained and is applicable to both thin and thick-walled cylindrical shells. Many full-scale burst tests are available for thin-walled line pipes in the pipeline industry, but limited pressure burst tests exist for thick-walled vessels. To validate the newly developed exact solutions of burst pressure for thick-walled cylinders, this paper conducts a series of burst pressure tests on small-diameter, thick-walled pipes. In particular, six burst tests are carried out for three thick-walled pipes in Grade B carbon steel. These pipes have a nominal diameter of 2.375 inches (60.33 mm) and three nominal wall thicknesses of 0.154, 0.218, and 0.344 inches (3.91, 5.54, and 8.74 mm), leading to D/t = 15.4, 10.9, and 6.9, respectively. With the burst test data, comparisons show that the Zhu–Leis flow solution of burst pressure matches well the burst test data for thick-walled pipes. Thus, these burst tests validate the accuracy of the Zhu–Leis flow solution of burst pressure for thick-walled cylindrical vessels.

42 ENGINEERING↗
DOE OSTI2020

Effective theories for a nonrelativistic field in an expanding universe: Induced self-interaction, pressure, sound speed, and viscosity

A massive, nonrelativistic scalar field in an expanding spacetime is usually approximated by a pressureless perfect fluid, which leads to the standard conclusion that such a field can play the role of cold dark matter. In this paper, we systematically study these approximations, incorporating subleading corrections. We provide two equivalent effective descriptions of the system, each of which offers its own advantages and insights: (i) A nonrelativistic effective field theory (EFT) with which we show that the relativistic corrections induce an effective self-interaction for the nonrelativistic field. As a byproduct, our EFT also allows one to construct the exact solution, including oscillatory behavior, which is often difficult to achieve from the exact equations. (ii) An effective (imperfect) fluid description, with which we demonstrate that, for a perturbed Friedmann-Lemaître- Robertson-Walker (FLRW) universe: (a) The pressure is small but nonzero (and positive), even for a free theory with no tree-level self-interactions. (b) The sound speed of small fluctuations is also nonzero (and positive), reproducing already known leading-order results, correcting a subdominant term, and identifying a new contribution that had been omitted in previous analyses. (c) The fluctuations experience a negative effective bulk viscosity. The positive sound speed and the negative bulk viscosity act in favor of and against the growth of overdensities, respectively. The net effect may be considered a smoking gun for ultra-light dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗
DOE OSTI2022

Mass Transport in Membrane Systems: Flow Regime Identification by Fourier Analysis

The numerical calculation of local mass distributions in membrane systems by computational fluid dynamics (CFD) offers indispensable benefits. However, the concept to calculate such distributions in response to separate variations of operation conditions (OCs) makes it difficult to address overall, flow-physics-related questions, which require the consideration of the collective interaction of OCs. It is shown that such understanding-related relationships can be obtained by the analytical solution of the advection–diffusion equation considered. A Fourier series model (FSM) is presented, which provides exact solutions of an advection–diffusion equation for a wide range of OCs. On this basis, a new zeroth-order model is developed, which is very simple and as accurate as the complete FSM for all conditions of practical relevance. Advection-dominated blocked and diffusion-dominated unblocked flow regimes are identified (depending on a Péclet number which compares the flow geometry with a length scale imposed by the flow), which implies relevant requirements for the use of lab results for pilot- and full-scale applications. Analyses reveal the equivalence of variations of OCs, which offers a variety of options to accomplish desired flow regime changes.

Heinz, Stefan (ORCID:0000000248712416)↗
DOE OSTI2021

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders n ϵ R> 0 and exact solutions are also constructed for reaction orders n ϵ N : n ≤ 3. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Integrating Multi-Source Data for Bi-Level Traffic Simulator Calibration: A Literature Review and Highway Case Study

Traffic simulation serves as a powerful tool for pre-evaluating policies and technologies. In this context, simulation-based Dynamic traffic assignment (DTA) models are capable of capturing traffic dynamics. They are well-known as critical tools in controlling and predicting traffic situations. The reliability of simulation results heavily depends on the calibration process. Most studies in the literature formulate and calibrate simulators based on a single source of collected data or multiple data sets with the same spatiotemporal characteristics. However, in practice, traffic data is collected by various tools with usually different spatial and temporal resolutions. This study introduces a novel approach to taking into account diverse input data from a variety of sources. An iterative bi-level solution is proposed. to equally treat traffic flow and speed data. The upper level solves flow calibration with the exact solution method, and the lower level calibrates the speed with the simultaneous perturbation stochastic approximation (SPSA) algorithm. Subsequently, the effectiveness of the proposed model is investigated using data from a six-mile section of Nashville's I-24 highway in Tennessee. The results demonstrate that our proposed model creates an effective feedback loop between the optimizer and the simulator for calibrating flow and speed to reduce the error between simulated and real data.

42 ENGINEERING↗
DOE OSTI2020

Pressure falloff testing to characterize CO 2 plume and dry-out zone during CO 2 injection in saline aquifers

The fluid mobilities and the lateral extent of the CO 2 plume and the dry-out zone are among important unknowns required to effectively manage CO 2 storage in saline aquifers projects. These unknowns can be derived from pressure falloff testing which has been widely used to characterize the subsurface. This paper provides a three-region analytical solution for falloff pressure during the infinite-acting period of CO 2 injection in saline aquifers. The solution is derived using Laplace transformation technique of the governing diffusivity equations and the accompanying initial and boundary conditions. The exact solution is validated against numerical results obtained from a black-oil reservoir simulator for two cases. The solution is approximated into simple forms in real-time domain considering different time periods. Then, a graphical semi-log analysis technique based on the approximate solutions is provided as an interpretation tool of falloff tests where the fluid mobilities and the extents of dry-out zone and CO 2 plume can be inferred. The interpretation technique is applied to synthetic falloff test data to investigate its potential and reliability.

02 PETROLEUM↗
DOE OSTI2022

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A minimally invasive, efficient method for propagation of full-field uncertainty in solid dynamics

In this work, we present a minimally invasive method for forward propagation of material property uncertainty to full-field quantities of interest in solid dynamics. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi-one-dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.

42 ENGINEERING↗
DOE OSTI2022

Comprehensive uncertainty quantification (UQ) for full engineering models by solving probability density function (PDF) equation

This report details a new method for propagating parameter uncertainty (forward uncertainty quantification) in partial differential equations (PDE) based computational mechanics applications. The method provides full-field quantities of interest by solving for the joint probability density function (PDF) equations which are implied by the PDEs with uncertain parameters. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known apriori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the driving (dynamics) term of the PDEs based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the dynamics term of the governing PDEs. The efficacy of the method is demonstrated by applying it to two target problems: solid mechanics explicit dynamics with uncertain material model parameters, and reacting hypersonic fluid mechanics with uncertain chemical kinetic rate parameters. A minimally invasive implementation of the method for representative codes SPARC (reacting hypersonics) and NimbleSM (finite- element solid mechanics) and associated software details are described. For solid mechanics demonstration problems the method shows order of magnitudes improvement in accuracy over traditional stochastic collocation. For the reacting hypersonics problem, the method is implemented as a streamline integration and results show very good accuracy for the approximate sample solutions of re-entry flow past the Apollo capsule geometry at Mach 30.

42 ENGINEERING↗
DOE OSTI2021

Critical percolation on the kagome hypergraph

In this report we study the percolation critical surface of the kagome lattice in which each triangle is allowed an arbitrary connectivity. Using the method of critical polynomials, we find points along this critical surface to high precision. This kagome hypergraph contains many unsolved problems as special cases, including bond percolation on the kagome and (3, 12 2 ) lattices, and site percolation on the hexagonal, or honeycomb, lattice, as well as a single point for which there is an exact solution. We are able to compute enough points along the critical surface to find a very accurate fit, essentially a Taylor series about the exact point, that allows estimations of the critical point of any system that lies on the surface to precision rivaling Monte Carlo and traditional techniques of similar accuracy. We find also that this system sheds light on some of the surprising aspects of the method of critical polynomials, such as why it is so accurate for certain problems, like the kagome and (3, 12 2 ) lattices. The bond percolation critical points of these lattices can be found to 17 and 18 digits, respectively, because they are in close proximity, in a sense that can be made quantitative, to the exact point on the critical surface. We also discuss in detail a parallel implementation of the method which we use here for a few calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Variational Discrete Action Theory

In this work, we propose the variational discrete action theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathscr{N}$, which monotonically approaches the exact solution with increasing $\mathscr{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green’s function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model and the d = ∞ Hubbard model. For the latter, we evaluate $\mathscr{N}$ = 2 – 4, where $\mathscr{N}$ = 2 recovers the Gutzwiller approximation (GA), and we show that $\mathscr{N}$ = 3, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to that of the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Comments on 'Do ultrafine cloud condensation nuclei invigorate deep convection?'

Here we elaborated on the deficiencies associated with the theoretical arguments and model simulations in Grawbowski and Morrison (2020; GM20), and showed that the concept of convective invigoration by aerosols can be supported by both accurate theoretical analysis and explicit physics modeling with prognostic aerosols and supersaturation. Above the freezing level, droplet freezing itself does not change mass loading and the latent heat release resulting from freezing leads to an increase in the buoyancy. The derivation in GM20 is erroneous because of omitting the liquid water sink term. They also ignored the effect of enhanced latent heating from the subsequent growth processes (deposition and riming) after freezing. Regarding aerosol effect on condensational growth, the quasi-steady assumption for supersaturation as adopted in GM20 is invalidated especially when droplet number concentration is low and updraft is strong from both theoretical analysis and our bin microphysics modeling results. The quasi-steady assumption makes condensation independent of droplet number and size and therefore reduces the overall aerosol effects on cloud dynamics. Studying aerosol effects on clouds particularly deep convective clouds requires the exact solution of supersaturation. Any assumption imposed to supersaturation such as saturation adjustment and quasi-steady approximation leads to incorrect aerosol effects on diffusional growth. The exact supersaturation equation clearly shows that condensation depends on droplet number and size, and more droplets in the polluted clouds increase condensation (thus lower supersaturation), leading to enhanced buoyancy and updraft speeds.

Convective invigoration, deep convective clouds, a↗
DOE OSTI2022

Quantum optimization of maximum independent set using Rydberg atom arrays

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the maximum independent set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find that the problem hardness is controlled by the solution degeneracy and number of local minima, and we experimentally benchmark the quantum algorithm’s performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.

Science & Technology - Other Topics↗
DOE OSTI2020

Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential

In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Alluvial fan morphology: A self-similar free boundary problem description

In this work, we examine approximate geometrically self-similar solutions to a parabolic free boundary value problem applied to alluvial fan surface morphology and growth. Alluvial fans are fan- or cone-shaped sedimentary deposits caused by the rapid deposition of sediment from a canyon discharging onto a flatter plain. Longitudinal, topographic profiles of fans can be readily described by a seemingly time independent dimensionless profile (DeChant et al., 1999). However, because an alluvial fan can be expected to grow over time, it is clear that this “steady” profile is certainly time dependent and can be described using a space-time self-similar solution. In an experimental and theory-based study, Guerit et al. (2014) developed a self-similar (or as they describe it a self-affine) linear solution based upon an approximate first order small parameter expansion solution for a 1-d homogeneous nonlinear diffusion equation. Direct substitution of this result into a linear diffusion equation suggests that this first order expression may not fully satisfy the associated governing equation. In contrast, we develop a more complete solution based upon a modeled approximation for the axi-symmetric formulation such that the associated temporal behavior is consistent with a 1/3 time power-law as described by Reitz and Jerolmack (2014). The resulting expression is an exact solution to a linear heat equation. Furthermore, we emphasize that a small parameter is not inherent to the resulting profile result and is not included in our model development. Though developed using rather different approaches, the formal solution developed here is in good agreement with the simple polynomial described by DeChant et al. (1999) suggesting that this self-similar solution is a suitable time dependent representation of alluvial fan longitudinal profile form and improves on earlier work.

58 GEOSCIENCES↗
DOE OSTI2024

Enhancing scalability and accuracy of quantum poisson solver

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the problem and thus have no practical usage. In this regard, our previous work showed a proof-of-concept demonstration in advancing quantum Poisson solver algorithm and validated preliminary results for a simple case of 3 x 3 problem. In this work, we delve into comprehensive research details, presenting the results on up to 15 x 15 problems that include step-by-step improvements in Poisson equation solutions, scaling performance, and experimental exploration. In particular, we demonstrate the implementation of eigenvalue amplification by a factor of up to 2 8 , achieving a significant improvement in the accuracy of our quantum Poisson solver and comparing that to the exact solution. Additionally, we present success probability results, highlighting the reliability of our quantum Poisson solver. Moreover, we explore the scaling performance of our algorithm against the circuit depth and width, demonstrating how our approach scales with larger problem sizes and thus further solidifies the practicality of easy adaptation of this algorithm in real-world applications. We also discuss a multilevel strategy for how this algorithm might be further improved to explore much larger problems with greater performance. Finally, through our experiments on the IBM quantum hardware, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the CNOT gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Electron-scale temperature gradients in kinetic equilibrium: MMS observations and Vlasov–Maxwell solutions

For an ideal gas, the notion of thermodynamic equilibrium requires that the system’s temperature be spatially uniform. We demonstrate that for a collisionless plasma, kinetic equilibrium can be achieved even in the presence of a temperature gradient. Motivated by recent MMS magnetopause observations of thin current layers exhibiting electron-scale temperature gradients, here we present an exact solution to the Vlasov-Maxwell system which accounts for the observed electron temperature gradient and reproduces much of the plasma’s spatial variation along one dimension. Furthermore, the current layer in the Vlasov-Maxwell model is self-consistently supported by a prominent crescent shaped electron velocity distribution that naturally arises due to the temperature transition, which agrees with the electron distribution structures measured by MMS during two asymmetric current layers encountered at the magnetopause.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗