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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1995

Nozzle flow with vibrational nonequilibrium

This research concerns the modeling and numerical solutions of the coupled system of compressible Navier-Stokes equations in cylindrical coordinates under conditions of equilibrium and nonequilibrium thermodynamics. The problem considered was the modeling of a high temperature diatomic gas N2 flowing through a converging-diverging high expansion nozzle. The problem was modeled in two ways. The first model uses a single temperature with variable specific heats as functions of this temperature. For the second model we assume that the various degrees of freedom all have a Boltzmann distribution and that there is a continuous redistribution of energy among the various degrees of freedom as the gas passes through the nozzle. Each degree of freedom is assumed to have its own temperature and, consequently, each system state can be characterized by these temperatures. This suggests that formulation of a second model with a vibrational degree of freedom along with a rotational-translation degree of freedom, each degree of freedom having its own temperature. Initially the vibrational degree of freedom is excited by heating the gas to a high temperature. As the high temperature gas passes through the nozzle throat there is a sudden drop in temperature along with a relaxation time for the vibrational degree of freedom to achieve equilibrium with the rotational-translation degree of freedom. That is, we assume that the temperature change upon passing through the throat is so great that the changes in the vibrational degree of freedom occur at a much slower pace and consequently lags behind the rotational-translational energy changes. This lag results in a finite relaxation time. In this context the term nonequilibrium is used to denote the fact that the energy content of the various degrees of freedom are characterized by two temperatures. We neglect any chemical reactions which could also add nonequilibrium effects. We develop the energy equations for the nonequilibrium model from first principles. The resulting equations, which model the nozzle flow, can be expressed in various forms. In most forms the resulting equations are coupled systems of nonlinear partial differential equations subject to certain boundary conditions. To solve the resulting coupled system of nonlinear partial differential equations, several numerical techniques were investigated: (1) the explicit MacCormack method, (2) the explicit-implicit MacCormack method, (3) the method of operator splitting, (4) factorization schemes, and (5) the Steger-Warming scheme.

Heinbockel, J. H.↗
NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Jiang, Bo-Nan↗
NASA NTRS2013

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, Linda Neergaard↗
NASA NTRS2013

Modeling of Particle Acceleration at Multiple Shocks via Diffusive Shock Acceleration: Preliminary Results

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box. We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (E(sub max)) appropriate for quasi-parallel and quasi-perpendicular shocks and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, L. Neergaard↗
NASA NTRSDate not supplied

Wear Test of the 12.5-kW Advanced Electric Propulsion System Engineering Test Unit Hall Thruster

This work presents a summary of the first wear test of the 12.5 kW Advanced Electric Propulsion System Engineering Test Unit 2 (AEPS ETU-2) thruster produced by Aerojet Rocketdyne. The ETU-2 Wear Test accumulated approximately 730 hours of operation split between the nominal 600 V/12.5 kW condition and the 300 V/6.25 kW condition previously identified as the worst-case erosion condition.

Jason D. Frieman↗
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 OSTI2020

Multiphysics coupling plan

In this chapter, multiphysics coupling simulations of nuclear reactor systems are reviewed. On the one hand, the mainstream methods of multiphysics coupling are demonstrated. The fundamental theory and coupling scheme of operator splitting methods, Jacobian-free Newton–Krylov methods, and approximate block Newton methods are summarized and presented. On the other hand, some significant works on neutronic and thermal-hydraulic codes coupling, and large research project, including NURESAFE European project, Multiphysics Object-Oriented Simulation Environment plan, and Consortium for the Advanced Simulation of Light Water Reactors project, are reviewed. This chapter helps the readers have a better understanding on the worldwide current status of multiphysics coupling research.

Gui, Miao↗
NASA NTRSDate not supplied

Extended Wear Testing of the 12-kW Advanced Electric Propulsion System Engineering Test Unit Hall Thruster

This work presents a summary of the first wear test of the 12 kW Advanced Electric Propulsion System (AEPS) intended to isolate the impact of discharge current on component wear rates. Testing was led by Aerojet Rocketdyne and performed with the AEPS Engineering Test Unit 2 (ETU-2) thruster. In total, approximately 860 hours of operation were accumulated split between operating conditions of 600 V/9 kW, 600 V/11 kW, and 600 V/12 kW. Thruster performance and stability were invariant throughout the wear test for all thruster throttle conditions and shown to be equal to the values previously measured with ETU-2. Inner front pole cover erosion rates were found to be invariant to discharge current as the measurements at all three operating conditions were equal to within the empirical uncertainty. Outer front pole cover erosion rates were found to be equal for the 600 V/9 kW and 600 V/12 kW conditions with operation at 600 V/11 kW yielding elevated erosion rates. Overall, the data shows that the AEPS thruster design has a high probability of meeting lifetime and performance requirements as the design proceeds to flight production and qualification.

Jason D Frieman↗
NASA NTRSDate not supplied

Extended Wear Testing of the 12-kW Advanced Electric Propulsion System Engineering Test Unit Hall Thruster

This work presents a summary of the first wear test of the 12 kW Advanced Electric Propulsion System (AEPS) intended to isolate the impact of discharge current on component wear rates. Testing was led by Aerojet Rocketdyne and performed with the AEPS Engineering Test Unit 2 (ETU-2) thruster. In total, approximately 860 hours of operation were accumulated split between operating conditions of 600 V/9 kW, 600 V/11 kW, and 600 V/12 kW. Thruster performance and stability were invariant throughout the wear test for all thruster throttle conditions and shown to be equal to the values previously measured with ETU-2. Inner front pole cover erosion rates were found to be invariant to discharge current as the measurements at all three operating conditions were equal to within the empirical uncertainty. Outer front pole cover erosion rates were found to be equal for the 600 V/9 kW and 600 V/12 kW conditions with operation at 600 V/11 kW yielding rates that were comparable to those on the inner front pole cover. Overall, the data shows that the AEPS thruster design has a high probability of meeting lifetime and performance requirements as the design proceeds to flight production and qualification.

HERMeS↗
NASA NTRS1986

The effects of various implicit operators on a flux vector splitting method

Three different implicit operators in a numerical method for solving the two-dimensional steady Euler equations using flux vector splitting are investigated. These include the implementation of the true Jacobian matrices in the implicit part, the use of their splitting approximate form, and a modification of the implicit part of the scheme that uses the scalar form of the implicit part based on the spectral radii of the split Jacobian matrices. The three versions of the basic algorithm are compared with the results given by two common numerical methods using several two-dimensional test cases. Special attention is paid to the quality of results as well as computational efficiency and convergence properties.

Von Lavante, E.↗
DOE OSTI2021

Substation-Level Grid Topology Optimization Using Bus Splitting: Preprint

Operations of substation circuit breakers are of high significance for performing system maintenance and topology optimization. Bus splitting is one type of topology changes where the two bus-bars at a substation become electrically disconnected after certain actions of circuit breakers. As these events involve detailed substation modeling, they are not typically considered in power system routine operation and control. In this paper, an improved substation-level topology optimization is developed by expanding traditional line switching with breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bi-linear terms in the resultant topology optimization model. Thus, a tractable mixed-integer linear program formulation is presented which can be efficiently solved for real-time control. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the performance and economic benefits of the proposed topology optimization approach.

bus split↗
DOE OSTI2023

Protecting Customer Privacy Through Distributed Energy Resource Anonymization

Due to their stochastic nature, the increase of Renewable Energy Resources (RERs) as a primary source of energy for power grids creates challenges regarding the reliability and resilience of the system. In order to combat these obstacles, expansion of Distributed Energy Resources (DERs) and their participation in Demand Response (DR) programs is necessary. Widespread participation requires prioritizing customer privacy and addressing concerns that may arise regarding communication between DERs and the Grid Service Provider (GSP). This paper discusses the use of flow reservation resources to split the operating cycles of DER load profiles into unique phases. The splitting of phases increases anonymization of the DERs by making it more difficult to determine the individual characteristics of the device. We discuss an example of this using simulated DER load profile data and examine the resulting effectiveness by using a machine learning algorithm for classification, called Support Vector Machine (SVM).

Distributed Energy Resource, Anonymization, Renewa↗
NASA NTRS1934

Preliminary Wind-Tunnel and Flight Tests of a Balanced Split Flap, Special Report

One disadvantage that has been apparent in the operation of split flaps as used to date is the time and effort required to operate them. In this communication an investigation is being made of possible means for balancing them aerodynamically to make their operation easier. Several arrangements have been tested in the 7 by 210 foot wind tunnel, and the results of the wind-tunnel tests as well as preliminary flight tests on one of the more promising forms are given in this paper.

Weick, Fred E.↗
NASA NTRS1972

Computational efficiency achieved by time splitting of finite difference operators.

A technique is presented for computing multidimensional time-dependent flow fields that avoids much of the inefficiency typically found in finite difference calculations. The technique initially divides the flow field into regions, each containing a mesh of general quadrilateral cells chosen to provide spatial resolution of the local features of the flow. A finite difference operator of second order accuracy, consisting of a sequence of one-dimensional operators (each operating at near maximum Courant-Friedrich-Lewy number) is then constructed for each region. Numerical results illustrating the technique for inviscid flows about simple bodies that generate shock waves, embedded shock waves, and expansion fans are presented and compared with exact theory.

Maccormack, R. W.↗
DOE OSTI2021

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as O(Ne4) where Ne is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to O(Ne 3 ) in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the O(Ne 3 ) complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. In this work, we demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗