Search NASA⌕ Search

SEARCH · Search NASA

Results for “discretization methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Final Technical Report: Using Solid Particles as Heat Transfer Fluid for use in Concentrating Solar Power (CSP) Plants

In today’s industrial economy, energy consumption has never been higher. Over the last 15 years the US alone has consumed an average of nearly 100 quadrillion BTUs per year [21]. A need for clean and renewable energy sources has become quite apparent. The SunShot Initiative is an ambitious effort taken on by the United States Department of Energy that targets the development of solar energy that is cost-competitive with other methods for generating electricity. Specifically, this work is concerned with the development of concentrating solar power plants (CSPs) with granular media as the heat transfer fluid (HTF) from the solar receiver. Unfortunately, the prediction of heat transfer in multiphase flows is not well understood. For this reason, our aim is to fundamentally advance the understanding of multiphase heat transfer, particularly in gas-solid flows, while providing quantitative input for the design of a near black body receiver (NBB) that uses solid grains (like sand) as the HTF. Over the course of this three-year project, a wide variety of contributions have been made to advance the state-of-the art description for non-radiative heat transfer in dense, gas-solid systems. Comparisons between a state-of-the-art continuum heat transfer model and discrete element method (DEM) simulations have been drawn. The results of these comparisons brought to light the limitations of the continuum model due to inherent assumptions in its derivation. A new continuum model was then developed for heat transfer at a solid boundary by rigorously accounting for the most dominant non-radiative heat transfer mechanism (particle-fluid-wall conduction). The new model is shown to be in excellent agreement with DEM data and captures the dependence of heat transfer on particle size, a dependency that previous continuum models were not capable of. DEM and the new continuum model were then employed to model heat transfer in a variety of receiver geometries. The results provided crucial feedback on the efficiency and feasibility of various designs. Namely, a prototype design consisting of an array of heated hexagonal tubes was later supplanted by a vertical conduit with internal baffles. Due to low solids heat transfer on the bottom faces of the hexagonal tubes in the prototype, the predicted wall temperature gradients exceeded the design limitations. By contrast, the vertical conduit can be constructed to continually force particle-wall contacts, and thus, result in more desirable solids heat transfer and wall temperature gradients. Finally, a new heat flux boundary condition was developed for DEM simulations to assess the aforementioned wall temperature gradients. The new boundary condition advances current state-of-the-art techniques by allowing the heat fluxes to each phase to vary with space and time while the total flux remains constant. Simulations with the new boundary condition show that the total boundary heat flux is in good agreement with the imposed total boundary heat flux. While the methods we have utilized here are primarily numerical and fundamental by nature, they offer some key advantages of: (i) being robust and valid over a large range of conditions, (ii) able to quickly explore large parameter spaces, and (iii) aid in the construction of experiments. We have ultimately leveraged our computational capabilities to provide feedback on the design of a CSP which possesses great potential to become a cost effective source of clean and renewable electricity. Overall, ensuring that future energy demands are met in a responsible and efficient manner has far reaching impacts that span both ecologic and economic concerns. Regarding logistics, the project was successfully re-negotiated after the go/no-decisions of Years 1 and 2. All milestones were successfully completed.

14 SOLAR ENERGY↗
DOE OSTI2013

Residual a posteriori error estimation of a mimetic/virtual element method

A posteriori error estimation and adaptivity are very useful in the context of the mimetic finite difference method due to the flexibility of the meshes to which this family of numerical schemes can be applied. Nevertheless, developing error estimators for mimetic methods is not a straightforward task due to the lack of knowledge of the basis functions. This issue is tackled by the virtual element method recently introduced in [4], which can be interpreted as a Galerkin reformulation of the mimetic finite difference method. In the new virtual element setting, we develop a residual based a posteriori error estimator that immediately applies to its mimetic counterpart. For such estimator we prove the reliability and we show the numerical performance when it is combined with an adaptive strategy for the mesh refinement. For the lowest-regular approximation we also developed an hp-adaptive strategy based on the comparison between the numerical solution on a base mesh and on a reference mesh.

a posteriori error estimation↗
NASA NTRS2010

Charge-Spot Model for Electrostatic Forces in Simulation of Fine Particulates

The charge-spot technique for modeling the static electric forces acting between charged fine particles entails treating electric charges on individual particles as small sets of discrete point charges, located near their surfaces. This is in contrast to existing models, which assume a single charge per particle. The charge-spot technique more accurately describes the forces, torques, and moments that act on triboelectrically charged particles, especially image-charge forces acting near conducting surfaces. The discrete element method (DEM) simulation uses a truncation range to limit the number of near-neighbor charge spots via a shifted and truncated potential Coulomb interaction. The model can be readily adapted to account for induced dipoles in uncharged particles (and thus dielectrophoretic forces) by allowing two charge spots of opposite signs to be created in response to an external electric field. To account for virtual overlap during contacts, the model can be set to automatically scale down the effective charge in proportion to the amount of virtual overlap of the charge spots. This can be accomplished by mimicking the behavior of two real overlapping spherical charge clouds, or with other approximate forms. The charge-spot method much more closely resembles real non-uniform surface charge distributions that result from tribocharging than simpler approaches, which just assign a single total charge to a particle. With the charge-spot model, a single particle may have a zero net charge, but still have both positive and negative charge spots, which could produce substantial forces on the particle when it is close to other charges, when it is in an external electric field, or when near a conducting surface. Since the charge-spot model can contain any number of charges per particle, can be used with only one or two charge spots per particle for simulating charging from solar wind bombardment, or with several charge spots for simulating triboelectric charging. Adhesive image-charge forces acting on charged particles touching conducting surfaces can be up to 50 times stronger if the charge is located in discrete spots on the particle surface instead of being distributed uniformly over the surface of the particle, as is assumed by most other models. Besides being useful in modeling particulates in space and distant objects, this modeling technique is useful for electrophotography (used in copiers) and in simulating the effects of static charge in the pulmonary delivery of fine dry powders.

Walton, Otis R.↗
DOE OSTI2021

Experiment and computational fluid dynamics investigation of biochar elutriation in fluidized bed

Here, in fluidized bed biomass fast pyrolysis, the biomass is converted to biochar and elutriated. The elutriation rate is a key parameter in reactor designs and operations. This research presents a video-based continuous measurement of biochar elutriation rate in a fluidized bed with sands and biomass as bed materials. The fluidized bed is simulated with the Computational Fluid Dynamics - Coarse-Grained Discrete Element Method (CFD-CGDEM) in MFiX. The fluidization behavior of non-spherical sands can be more accurately captured when a rolling friction model is used. The predicted elutriation rate is close to the experimental measurement when the particle size distributions are considered and the filtered drag with a shape correction is used. These results validated the accuracy of the MFiX based CFD framework for the prediction of biochar elutriations in the fluidized bed biomass fast pyrolysis reactor.

09 BIOMASS FUELS↗
DOE OSTI2012

Element orbitals for Kohn-Sham density functional theory

We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, which is a small part of the global domain containing multiple atoms. We demonstrate that the resulting basis set achieves meV accuracy for 3D densely packed systems with a small number of basis functions per atom. The procedure is applicable to insulating and metallic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

A fast high-order method to calculate wakefield forces in an electron beam

In this paper we report on a high-order fast method to numerically calculate wakefield forces in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT method for discrete summation that results in an O(Nlog(N)) computational cost, where N is the number of grid points. Using the Simpson quadrature rule with an accuracy of O(h4), where h is the grid size, we present numerical calculation of the wakefields from a resonator wake function model and from a one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the fast speed and high numerical accuracy, the calculation using the direct line density instead of the first derivative of the line density avoids numerical filtering of the electron density function for computing the CSR wakefield force. I. INTRODUCTION

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

Discrete element modeling of indentation tests to investigate mechanisms of CO 2 -related chemomechanical rock alteration

During CO 2 injection into geological formations, petrophysical and geomechanical properties of host formations can be altered due to mineral dissolution and precipitation. Field and laboratory results have shown that sandstone and siltstone can be altered by CO 2 -water mixtures, but few quantitative studies have been performed to fully investigate underlying mechanisms. Based on the hypothesis that CO 2 -water mixtures alter the integrity of rock structure by attacking cements rather than grains, we attempt to explain the degradation of cementation due to long-term contact with CO 2 and water and mechanisms for changes in rock mechanical properties. Many sandstones, including calcite-cemented quartzitic sandstone, chlorite-cemented quartzitic sandstone, and hematite-cemented quartzitic sandstone, contain interparticle cements that are more readily affected by CO 2 -water mixtures than grains. A model that couples the discrete element method and the bonded-particle model is used to perform simulations of indentation tests on synthetic rocks with crystal and random packings. The model is verified against the analytical cavity expansion model and validated against laboratory indentation tests on Entrada sandstone with and without CO 2 alteration. Sensitivity analysis is performed for cementation microscopic parameters including stiffness, size, axial, and shear strength. The simulation results indicate that the CO 2 -related degradation of mechanical properties in bleached Entrada sandstone can be attributed to the reduction of cement size rather than cement strength. Finally, our study indicates that it is possible to describe the CO 2 -related rock alteration through particle-scale mechanisms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Discrete numerical simulations of torpedo anchor installation in granular soils

Torpedo anchors are a viable approach for mooring marine hydrokinetic (MHK) energy devices to the seafloor. These anchors can serve to maintain station and to provide the reaction force for an MHK device. The ability of the anchor to perform these duties is a strong function of its penetration depth during installation. This is a large-strain problem not amenable to typical continuum numerical approaches. In the current work, we propose that the discrete element method (DEM) is a more appropriate tool to investigate the shallow penetration of torpedo anchors in sands. The effects of anchor mass, impact velocity, and soil interparticle friction are considered in the DEM simulations. The relative maximum penetration depths for different penetration conditions are quantified and presented. Granular material response at the microscale during penetration are used to provide insight into system response. Energy dissipation in the assembly by both friction and collision at the particle scale are considered. Results show that anchor penetration increases approximately linearly with an increase in impact velocity or anchor weight. Penetration decreases with an increase in interparticle friction (i.e., soil strength). Observations of microscale behaviors and energy calculations are used to provide insight into overall system response.

58 GEOSCIENCES↗
DOE OSTI2023

Discrete element model for powder grain interactions under high compressive stress

A reduced order, nonlocal model is proposed for the contact force between initially spherical particles under compression. The model in effect provides the normal component of the interaction force between elements in the discrete element method (DEM). It is applicable to high relative density and large stress in powder compaction. It takes into account the mutual interaction between multiple points of contact, in contrast to the usual assumption in DEM of pair interactions. The mathematical form of the model is derived from a variational formulation that leads to the momentum balance for the forces on each grain. The model is calibrated mainly using detailed three dimensional peridynamic simulations of single grains under compressive loading by rigid plates that move radially with prescribed velocity. This calibration takes into account the large deformation and fracture of the grains. The interaction model also includes terms for the unloading behavior and adhesion. Finally, as validation, the model is applied to test data on the compaction of microcrystalline cellulose bulk powder.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing

This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Effects of curvature-related DEM contact model on the macro- and micro-mechanical behaviours of granular soils

The presented paper conducted a comprehensive comparison between the Hertz-Mindlin model and the linear spring model in true triaxial shear simulations of granular soils using the discrete element method (DEM). The no-slip Hertz-Mindlin model for general elastic non-spherical particles with smooth surfaces was revisited, and implemented for superellipsoidal particles in an in-house DEM code. Three groups of specimens with a grain size distribution of Ottawa 20-30 sands, consisting of spheres, ellipsoids, and superellipsoids, respectively, were subjected to triaxial shear DEM simulations with the Hertz-Mindlin model and the linear spring model. The corresponding mechanical behaviours were examined in terms of a series of macro-and micro-parameters. It is found that the linear spring model is able to resemble the Hertz-Mindlin model on aspects of both microscopic and macroscopic mechanical behaviours of granular media with spherical and/or non-spherical particles. This finding suggests that the linear spring model can be used to investigate micro-mechanical behaviours of granular soils even with complex particle shapes.

42 ENGINEERING↗
NASA NTRS1997

Experiments in Aircraft Roll-Yaw Control using Forebody Tangential Blowing

Advantages of flight at high angles of attack include increased maneuverability and lift capabilities. These are beneficial not only for fighter aircraft, but also for future supersonic and hypersonic transport aircraft during take-off and landing. At high angles of attack the aerodynamics of the vehicle are dominated by separation, vortex shedding and possibly vortex breakdown. These phenomena severely compromise the effectiveness of conventional control surfaces. As a result, controlled flight at high angles of attack is not feasible for current aircraft configurations. Alternate means to augment the control of the vehicle at these flight regimes are therefore necessary. The present work investigates the augmentation of an aircraft flight control system by the injection of a thin sheet of air tangentially to the forebody of the vehicle. This method, known as Forebody Tangential Blowing (FTB), has been proposed as an effective means of increasing the controllability of aircraft at high angles of attack. The idea is based on the fact that a small amount of air is sufficient to change the separation lines on the forebody. As a consequence, the strength and position of the vortices are altered causing a change on the aerodynamic loads. Although a very effective actuator, forebody tangential blowing is also highly non-linear which makes its use for aircraft control very difficult. In this work, the feasibility of using FTB to control the roll-yaw motion of a wind tunnel model was demonstrated both through simulations and experimentally. The wind tunnel model used in the experiments consists of a wing-body configuration incorporating a delta wing with 70-degree sweep angle and a cone-cylinder fuselage. The model is equipped with forebody slots through which blowing is applied. There are no movable control surfaces, therefore blowing is the only form of actuation. Experiments were conducted at a nominal angle of attack of 45 degrees. A unique apparatus that constrains the model to two degrees-of-freedom, roll and yaw, was designed and built. The apparatus was used to conduct dynamic experiments which showed that the system was unstable, its natural motion divergent. A model for the unsteady aerodynamic loads was developed based on the basic physics of the flow and results from flow visualization experiments. Parameters of the aerodynamic model were identified from experimental data. The model was validated using data from dynamic experiments. The aerodynamic model completes the equations of motion of the system which were used in the design of control laws using blowing as the only actuator. The unsteady aerodynamic model was implemented as part of the real-time vehicle control system. A control strategy using asymmetric blowing was demonstrated experimentally. A discrete vortex method was developed to help understand the main physics of the flow. The method correctly captures the interactions between forebody and wing vortices. Moreover, the trends in static loads and flow structure are correctly represented. Flow visualization results revealed the vortical structure of the flow to be asymmetric even for symmetric flight conditions. The effects of blowing, and roll and yaw angles on the flow structure were determined. It is shown that superimposing symmetric and asymmetric blowing has a linearizing effect on the actuator characteristics. Transient responses of roll and yaw moments to step input blowing were characterized, and their differences were explained based on the physical mechanisms through which these loads are generated.

Pedreiro, Nelson↗
NASA NTRS1999

Some Continuum Aspects of Data Assimilation

A long-sought goal in data assimilation is to build more fully the time dimension into the data assimilation process. Truly four-dimensional data assimilation requires evolving second-moment information, namely the estimation error covariance, along with the state estimate itself. The continuum evolution equations for the estimation error covariance constitute a system of partial differential equations in six space dimensions, forced by a model error covariance and by the observations themselves. The high dimensionality of this system poses a difficult computational problem. Numerous methods have been proposed for approximate, discrete solution of this system of equations. Four-dimensional variational schemes solve these equations indirectly, while schemes based on Kalman filtering solve the equations more directly, usually on a small subspace of the full six-dimensional space. In both cases, most proposed solution methods are not derived from the continuum covariance evolution equations themselves. Instead, most methods simply inherit the discretization used for evolving the state estimate, either in the form of a discrete tangent linear model or, in the case of ensemble schemes, in the form of a fully nonlinear discrete model. In this lecture we show that solutions of the continuum covariance evolution equations possess simple properties that are not readily satisfied upon discretization of the equations. we give numerical examples illustrating that "inherited" discretizations sometimes fail to produce meaningfully accurate solutions. Finally, we suggest alternative discretization methods that may yield more faithful approximate solutions of the continuum problem.

Cohn, Stephen E.↗
DOE OSTI2015

Acoustically induced slip in sheared granular layers: Application to dynamic earthquake triggering: TRIGGERED SLIP IN SHEARED GRANULAR GOUGE

A fundamental mystery in earthquake physics is “how can an earthquake be triggered by distant seismic sources?” We use discrete element method simulations of a granular layer, during stick slip, that is subject to transient vibrational excitation to gain further insight into the physics of dynamic earthquake triggering. We also observe delayed triggering of slip in the granular gouge, using Coulomb friction law for grains interaction. We find that at a critical vibrational amplitude (strain) there is an abrupt transition from negligible time-advanced slip (clock advance) to full clock advance; i.e., transient vibration and triggered slip are simultaneous. Moreover, the critical strain is of order 10 -6 , similar to observations in the laboratory and in Earth. The transition is related to frictional weakening of the granular layer due to a dramatic decrease in coordination number and the weakening of the contact force network. Associated with this frictional weakening is a pronounced decrease in the elastic modulus of the layer. The study has important implications for mechanisms of triggered earthquakes and induced seismic events and points out the underlying processes in response of the fault gouge to dynamic transient stresses.

58 GEOSCIENCES↗
DOE OSTI2017

On the micromechanics of slip events in sheared, fluid-saturated fault gouge

We used a three-dimensional discrete element method coupled with computational fluid dynamics to study the poromechanical properties of dry and fluid-saturated granular fault gouge. The granular layer was sheared under dry conditions to establish a steady state condition of stick-slip dynamic failure, and then fluid was introduced to study its effect on subsequent failure events. The fluid-saturated case showed increased stick-slip recurrence time and larger slip events compared to the dry case. Particle motion induces fluid flow with local pressure variation, which in turn leads to high particle kinetic energy during slip due to increased drag forces from fluid on particles. The presence of fluid during the stick phase of loading promotes a more stable configuration evidenced by higher particle coordination number. Our coupled fluid-particle simulations provide grain-scale information that improves understanding of slip instabilities and illuminates details of phenomenological, macroscale observations.

58 GEOSCIENCES↗
DOE OSTI2017

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach: STICK-SLIP IN SATURATED FAULT GOUGE

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this study, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that the (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Finally, our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.

58 GEOSCIENCES↗
DOE OSTI2019

Breakage of wet flexible fiber agglomerates impacting a plane

Abstract The breakage of an agglomerate of wet flexible fibers impacting a plane is computationally investigated in this work using the discrete element method. In the agglomerate, the fibers stick together due to cohesive liquid bridge forces. Agglomerate breakage with various impact conditions, initial configurations, fiber properties, and liquid bridge properties is systematically investigated. The degree of breakage is governed by the impact energy, the cohesion energy due to liquid bridges, the energy dissipation/absorption through fiber–fiber contacts and fiber deformation, and the efficiency of force transmission within the agglomerate. More specifically, breakage is promoted by increasing impact velocity, decreasing agglomerate size, increasing initial compaction, increasing fiber bending modulus, decreasing liquid surface tension, and decreasing liquid‐to‐solid volume ratio. Breakage is strongly dependent on the modified Weber number, that is, the ratio of the Weber number to a dimensionless rupture distance, which is a measure of the impact energy relative to the cohesion energy.

Yang, Jiecheng↗