Energy-Conserving Pseudo-spectral Particle-in-Cell Methods
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Mathematics↗
SEARCH · Engineering Papers
Results for “energy conservation”
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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Space Shuttle Main Engine performance analysis
For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.
Santi, L. Michael↗
Energetically consistent model reduction for metriplectic systems
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not preserve the metriplectic structure which governs long-term stability of the system. Based on proper orthogonal decomposition, a provably convergent metriplectic reduced-order model is formulated which is guaranteed to maintain the algebraic structure necessary for energy conservation and entropy formation. Further, numerical results on benchmark problems show that the proposed method is remarkably stable, leading to improved accuracy over long time scales at a moderate increase in cost over naive methods.
42 ENGINEERING↗
Gas bearings
The present work deals with the fundamentals of gas lubrication theory, which forms the foundation of all analytical design tools for gas bearings. Most of the hard lessons learned in the past are outlined with reference to dry contact, debris ingestion, sliding speed, and chemical stability of lubricant. The mathematical theory of gas lubrication is described for scaling rules in thin-film viscous flow, momentum conservation, mass conservation, energy conservation, isothermal gas bearing theory, coupling effects, and global bearing characteristics. Particular attention is given to the governing differential equations for common bearing configurations. Also discussed are representative solutions of self-acting gas bearings, externally pressurized bearings, and time-dependent effects.
Pan, C. H. T.↗
An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes
Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.
vegetation remote sensing; stochastic radiative tr↗
NASA Technology Utilization House technical support package Summary of results and house description
The Technology Utilization House (Tech House) was designed and constructed to demonstrate to the building industry and the public the benefits of aerospace technology and other new technology that are presently available or will be in very near future. Use of solar energy, conservation of energy and of water, safety, and security were incorporated in the design of the house. The terms to be incorporated into the house and to assist in the design of the house were evaluated. An architectural engineering team was employed to investigate energy conservation ideas, determine cost effectiveness of new materials and systems, and prepare specifications and drawings for the house. The Tech House was constructed during the spring of 1976. All the systems were monitored to insure proper operation, and data were collected during a one year occupancy. Results obtained during the family live-in period, comments on the acceptance of the various energy-saving systems by the family, and suggestions for improvement of the systems are presented.
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Digital quantum magnetism on a trapped-ion quantum computer
Digital quantum matter—realized when discrete quantum gates approximate continuous time evolution—is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviours observed in equilibrium systems, ranging from the non-trivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here we use Quantinuum’s H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics owing to approximate energy conservation and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Furthermore, our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of 99.94(1)%) and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.
Information theory and computation↗
Multigrid methods in structural mechanics
Although the application of multigrid methods to the equations of elasticity has been suggested, few such applications have been reported in the literature. In the present work, multigrid techniques are applied to the finite element analysis of a simply supported Bernoulli-Euler beam, and various aspects of the multigrid algorithm are studied and explained in detail. In this study, six grid levels were used to model half the beam. With linear prolongation and sequential ordering, the multigrid algorithm yielded results which were of machine accuracy with work equivalent to 200 standard Gauss-Seidel iterations on the fine grid. Also with linear prolongation and sequential ordering, the V(1,n) cycle with n greater than 2 yielded better convergence rates than the V(n,1) cycle. The restriction and prolongation operators were derived based on energy principles. Conserving energy during the inter-grid transfers required that the prolongation operator be the transpose of the restriction operator, and led to improved convergence rates. With energy-conserving prolongation and sequential ordering, the multigrid algorithm yielded results of machine accuracy with a work equivalent to 45 Gauss-Seidel iterations on the fine grid. The red-black ordering of relaxations yielded solutions of machine accuracy in a single V(1,1) cycle, which required work equivalent to about 4 iterations on the finest grid level.
Raju, I. S.↗
Energy and Water Conservation and Renewable Energy Program
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Jennifer Hill↗
Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates
The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating terms containing the covariant component B Ψ P of the magnetic field vector with respect to the poloidal flux function Ψ P . In an unperturbed plasma, B Ψ P can be eliminated via exact coordinate transformations, but, in general, one relies on approximations, assuming that the effect of B Ψ P is small. In this work, we are interested in the question whether Hamiltonian conservation laws are still satisfied when B Ψ P is retained in the presence of fluctuations. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency, and a single toroidal mode number n, we show that simulations using the code ORBIT with and without B Ψ P yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the appendix), which show that the unabridged GC Lagrangian with B Ψ P retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) and (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen) modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Conservation as an alternative energy source
A speech is given outlining the energy situation in the United States. It is warned that the existing energy situation cannot prevail and the time is fast running out for continued growth or even maintenance of present levels. Energy conservation measures are given as an aid to decrease U.S. energy consumption, which would allow more time to develop alternative sources of energy.
Allen, D. E.↗
Semiclassical theory of vibrational excitation for diatomic molecules with conserved collision energy
Inelastic collision effects on vibrational excitation of diatomic molecules with conserved energy
Hansen, C. F.↗
Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds
Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite the continuous effort. Without such local conservation laws, energy and momentum can be instantaneously transported across spacetime, which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory. The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic fields reside on different manifolds. To overcome this difficulty, we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact, local conservation laws, in particular the energy-momentum conservation laws, for the electromagnetic gyrokinetic system. A weak Euler-Lagrange equation is established to replace the standard Euler-Lagrange equation for the particles. It is discovered that an induced weak Euler-Lagrange current enters the local conservation laws. And it is the new physics captured by the high-order field theory on heterogeneous manifolds. A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy-momentum conservation laws electromagnetic gauge-invariant.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
State Technical Assistance - New Mexico Energy and Conservation Management Division Report [Slides]
The New Mexico Energy and Conservation Management Division (ECMD) sought technical assistance to enhance their ability to evaluate program impacts using the Low-Income Energy Affordability Data (LEAD) tool. NLR assisted ECMD in leveraging the LEAD tool to calculate and analyze energy burden across electric utility service areas, enabling them to assess program outcomes more effectively. To meet ECMD's goals, NLR developed a customized methodology to calculate utility-specific energy burden metrics using census tract data and available utility service area information from the Energy Information Administration (EIA). While acknowledging some limitations in the EIA dataset, NLR estimated the percentage of households within each service territory and incorporated relevant filters such as income, housing characteristics, and other demographics from the LEAD tool. The analysis provided ECMD with a new capability to evaluate program success based on energy savings, reductions in energy burden, and other performance indicators. The data and methodology also support discussions with utilities to improve the accuracy of service territory datasets. ECMD can use the outputs to track program effectiveness and plan future initiatives. NLR offered the possibility of follow-on work, including capacity-building for ECMD to repeat the analysis independently and the option to refine the analysis with updated service.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Three strategies for conservation
The three strategies considered as energy conservation oriented were given: national energy conservation, electrification, and diversification. The first one applies to the near term period (now-1985), the second one to the mid term (1985-2000), and the third one to the far term (2000- ). The rest of this section was focussed on the near term period. The following proposed actions were considered: (1) roll back the price of newly discovered oil, (2) force conversion of many power plants from gas and oil to coal, (3) freeze gasoline production for three years at 1972 levels, (4) mandate automobile mileage requirements, (5) require industry to improve energy efficiency, and (6) require manufacture of household appliances with greater efficiency. Each of these six actions was described and discussed in more detail.
Source record↗
Evaluating the Conservation of Energy Variables in Simulations of Deep Moist Convection
Abstract It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE − IB and MSE + KE, wherein IB is the path integral of buoyancy ( B ) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE − IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE − IB is better conserved in isolated deep convection, whereas MSE − IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE − IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE − IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE − IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats.
54 ENVIRONMENTAL SCIENCES↗
Two (or more) for one: Identifying classes of household energy- and water-saving measures to understand the potential for positive spillover
A key component of behavior-based energy conservation programs is the identification of target behaviors. A common approach is to target behaviors with the greatest energy-saving potential. The concept of behavioral spillover introduces further considerations, namely that adoption of one energy-saving behavior may increase (or decrease) the likelihood of other energy-saving behaviors. This research aimed to identify and describe household energy- and water-saving measure classes within which positive spillover is likely to occur (e.g., adoption of energy-efficient appliances may correlate with adoption of water-efficient appliances), and explore demographic and psychographic predictors of each. Nearly 1,000 households in a California city were surveyed and asked to report whether they had adopted 75 different energy- and/or water-saving measures. Principal Component Analysis and Network Analysis based on correlations between adoption of these diverse measures revealed and characterized eight water-energy-saving measure classes: Water Conservation, Energy Conservation, Maintenance and Management, Efficient Appliance, Advanced Efficiency, Efficient Irrigation, Green Gardening, and Green Landscaping. Understanding these measure classes can help guide behavior-based energy program developers in selecting target behaviors and designing interventions.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
A phase-field diffraction model for thermo-hydro-mechanical propagating fractures
This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.
Diffraction systems↗