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DOE OSTI2021

Network-Level Optimization for Unbalanced Power Distribution System: Approximation and Relaxation

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. Finally, it is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLPD-OPF model for the same distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic-level insight into photochemistry. Here, we performed a time-resolved study of ultrafast molecular symmetry breaking through geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft x-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry-broken cation, which were detected in the x-ray signal. These oscillations were damped within 58 ± 13 femtoseconds because vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens avenues for exploring complex systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Design and Scoping Tests on Alloy 617 Using Notched Specimen Geometry to Validate Methods for Multiaxial Stress Relaxation

In FY 2022, a development effort was initiated at the US Department of Energy’s Oak Ridge National Laboratory (ORNL) to examine the multiaxial stress-relaxation behavior and multiaxial stress-state effect on the creep-fatigue (CF) performance for Alloy 617 at elevated temperatures. This effort supported the development of the design rules in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), Section III, Division 5. In this work, two types of the notch specimen geometries were designed. An inelastic constitutive model was used to investigate the stress triaxiality and elastic follow-up effects on the notch specimens under CF deformation in the finite element (FE) simulations. The numerical study demonstrated that the stress triaxiality and elastic follow-up caused by the notches both play significant roles in the stress-relaxation behavior. In addition, Alloy 617 CF experiments were designed, and the testing on the notch specimens is ongoing. CF test failure data will be generated on the specimens with notches under various conditions in FY 2023, and the results will be used to validate methods for accounting for the multiaxial stress relaxation effect in the design code.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Modified 316H constitutive model updated with high temperature stress relaxation test data

This report describes the calibration of a new high temperature constitutive model for 316H stainless steel, suitable for use with the ASME Boiler & Pressure Vessel Section III, Division 5, Class A rules for design by inelastic analysis. The model retains the same mathematical form used by the reference model included in Nonmandatory Appendix Z of the Code, but refits the model to an expanded dataset including all the data used to fit the original model plus seven new stress relaxation tests. The addition of these high temperature stress relaxation tests improves the model's accuracy in predicting relaxation at temperatures greater than 700 ⁰C, without compromising the accuracy of the model versus the original calibration data.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Optical Photometric Indicators of Galaxy Cluster Relaxation

Abstract The most dynamically relaxed clusters of galaxies play a special role in cosmological studies as well as astrophysical studies of the intracluster medium (ICM) and active galactic nucleus feedback. While high-spatial-resolution imaging of the morphology of the ICM has long been the gold standard for establishing a cluster’s dynamical state, such data are not available from current or planned surveys, and thus require separate, pointed follow-up observations. With optical and/or near-IR photometric imaging, and red-sequence cluster finding results from those data, expected to be ubiquitously available for clusters discovered in upcoming optical and millimeter-wavelength surveys, it is worth asking how effectively photometric data alone can identify relaxed cluster candidates, before investing in, e.g., high-resolution X-ray observations. Here we assess the ability of several simple photometric measurements, based on the redMaPPer cluster finder run on Sloan Digital Sky Survey data, to reproduce X-ray classifications of dynamical state for an X-ray selected sample of massive clusters. We find that two simple metrics contrasting the bright central galaxy (BCG) to other cluster members can identify a complete sample of relaxed clusters with a purity of ∼40% in our data set. Including minimal ICM information in the form of a center position increases the purity to ∼60%. However, all three metrics depend critically on correctly identifying the BCG, which is presently a challenge for optical red-sequence cluster finders.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

XRISM Reveals Low Nonthermal Pressure in the Core of the Hot, Relaxed Galaxy Cluster A2029

We present XRISM Resolve observations of the core of the hot, relaxed galaxy cluster Abell 2029 (A2029). We find that the line-of-sight bulk velocity of the intracluster medium (ICM) within the central 180 kpc is at rest with respect to the brightest cluster galaxy, with a 3σ upper limit of ∣vbulk∣ < 100 km s−1. We robustly measure the field-integrated ICM velocity dispersion to be σv = 169 ± 10 km s−1, obtaining similar results for both single-temperature and two-temperature plasma models to account for the cluster cool core. This result, if ascribed to isotropic turbulence, implies a subsonic ICM with Mach number M 3D ≈ 0.22 and a nonthermal pressure fraction of 2.6 ± 0.3%. The turbulent velocity is similar to what was measured in the core of the Perseus cluster by Hitomi, but here in a more massive cluster with an ICM temperature of 7 keV, the limit on the nonthermal pressure fraction is even more stringent. Our result is consistent with expectations from simulations of relaxed clusters, but it is on the low end of the predicted distribution, indicating that A2029 is an exceptionally relaxed cluster with no significant impacts from either a recent minor merger or active galactic nucleus activity.

Audard, Marc (ORCID:000000034721034X)↗

NASA NTRS1972

Study of excitation transfer in flowing helium afterglow pumped with a tuneable dye laser. 2: Measurement of the rate coefficient for the rotational relaxation of He2(3p (3 Pi g))

The rotational relaxation of the He2(3p(3pi g)) state is examined by optically pumping a flowing helium afterglow with a tuneable dye laser. The population of the J = 8 rotational state is enhanced by optically saturating the R sub 7 component of the transition connecting this state with the metastable He2(2s (3 Sigma u +)) molecular state. From the lifetime and yield of the Q sub 7 component, the rate coefficient for the rotational relaxation via the forbidden delta J = 1 channel is determined to be of the order of 2 x 10 to the minus 11th power cm3/sec. It is found that this represents about half of the total rate of rotational relaxation in this state.

Collins, C. B.↗

NASA NTRS1973

A general relaxation theory of simple liquids

A relatively simple relaxation theory to account for the behavior of liquids under dynamic conditions was proposed. The general dynamical equations are similar in form to the phenomenological relaxation equations used in theories of viscoelasticity, however, they differ in that all the coefficients of the present equations are expressed in terms of thermodynamic and molecular quantities. The theory is based on the concept that flow in a liquid distorts both the radial and the velocity distribution functions, and that relaxation equations describing the return of these functions to their isotropic distributions, characterizing a stationary liquid, can be written. The theory was applied to the problems of steady and oscillatory shear flows and to the propagation of longitudinal waves. In all cases classical results are predicted for strain rates, and an expression for the viscosity of a liquid, simular to the Macedo-Litovitz equation, is obtained.

Merilo, M.↗

NASA NTRS1973

Relaxation of the V = 4,5,6,7, Sigma g/+/ vibrational levels of carbon monoxide studied by laser absorption.

The vibrational relaxation of individual vibration rotation levels of carbon monoxide behind incident shock waves of carbon monoxide has been studied by the method of laser absorption. For the particular vibrational states (V = 4 to 7) and temperature range (2500 to 5500 K) studied, it is concluded that the characteristic relaxation times are in excellent agreement with those obtained via previous measurements of 'bulk' gas properties. Further, the data furnish strong corroboration of the idea that the individual levels are in Boltzmann vibrational equilibrium during the relaxation process.

Chackerian, C., Jr.↗

NASA NTRS1973

Relaxation time in disk galaxy simulations.

An initially stationary and stable axisymmetric disk of stars with a mass spectrum of stars is used to determine the collisional relaxation time. The relaxation time as determined from the rate of energy equipartition was found to be 560 rotation periods for stars with 10 times the mean star mass and was 1700 rotation periods for stars with 0.55 times the mean star mass. These times are in general agreement with theoretical predictions for the relaxation time of the two mass groups. The results show that the model used for the large-scale gravitational N-body calculations is indeed 'collisionless.'

Hohl, F.↗

NASA NTRS1974

Thermal relaxation of a two dimensional plasma in a dc magnetic field. Part 2: Numerical simulation

The thermal relaxation process for a spatially uniform two dimensional plasma in a uniform dc magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computer Boltzman H-function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square and ratio of gyrofrequency to plasma frequency.

Hsu, J. Y.↗

NASA NTRS1974

Relaxation of an unsteady turbulent boundary layer on a flat plate in an expansion tube

An analysis is presented for the relaxation of a turbulent boundary layer on a semi-infinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion-tube flows. The flow-governing equations have been transformed into the Crocco variables, and a time-similar solution is presented in terms of the dimensionless distance-time variable alpha and the dimensionless velocity variable beta. An eddy-viscosity model, similar to that of time-steady boundary layers, is applied to the inner and outer regions of the boundary layer. A turbulent Prandtl number equal to the molecular Prandtl number is used to relate the turbulent heat flux to the eddy viscosity. The numerical results, obtained by using the Gauss-Seidel line-relaxation method, indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin friction than a laminar boundary layer. The results also give a fairly good estimate of the local skin friction and heat transfer for near steady-flow conditions.

Gurta, R. N.↗

NASA NTRS1973

Vibrational relaxation of carbon monoxide studied by two-wavelength infrared emission

Experimental results are presented for the vibrational relaxation of pure carbon monoxide behind incident shock waves over the temperature range 4000 to 6300 K. The data were obtained as infrared emission from the fundamental and overtone vibrational band systems (in some of the experiments the two-band systems were recorded simultaneously). The data are consistent with present theories for the vibrational relaxation of diatomic molecules and can be interpreted in terms of an initial Boltzmann vibrational distribution relaxing toward final equilibrium via a continuous sequence of intermediate Boltzmann distributions.

Chackerian, C., Jr.↗

NASA NTRS1973

Relaxation of the accelerating-gas boundary layer to the test-gas boundary layer on a flat plate in an expansion tube

An analytic investigation of the relaxation of the accelerating-gas boundary layer to the test-gas boundary layer over a flat plate mounted in an expansion tube has been conducted. In this treatment, nitrogen has been considered as the test gas and helium as the accelerating gas. The problem is analyzed in two conically similar limits: (1) when the time lag between the arrival of the shock and the interface at the leading edge of the plate is very large, and (2) when this time lag is negligible. The transient laminar boundary-layer equations of a perfect binary-gas mixture are taken as the flow governing equations. These coupled equations have been solved numerically by Gauss-Seidel line-relaxation method. The results predict the transient behavior as well as the time required for an all-helium accelerating-gas boundary layer to relax to an all-nitrogen boundary layer.

Gupta, R. N.↗

NASA NTRS1975

Stress relaxation and mechanical properties of RL-1973 and PD-200-16 silicone resin sponge materials

Stress relaxation tests were conducted by loading specimens in double-lap shear to a preselected strain level and monitoring the decay of stress with time. The stress relaxation response characteristics were measured over a temperature range of 100 to 300 K and four strain levels. It is concluded that only a slight amount of stress relaxation was observed, and the stiffness increased approximately two orders of magnitude over the range of temperatures.

Saylak, D.↗

NASA NTRS1977

Over-relaxation applied to the MacCormack finite-difference scheme

An over-relaxation procedure is applied to the MacCormack finite-difference scheme in order to reduce the computation time required to obtain a steady-state solution. The implementation of this acceleration procedure to an existing computer program using the regular MacCormack method is extremely simple and does not require additional storage. The over-relaxation procedure does not alter the steady-state solution, which is second-order accurate. The method is first applied to Burgers' equation. A stability condition and an expression for the increase in the rate of convergence are derived. The method is then applied to the calculation of the hypersonic viscous flow over a flat plate, using the complete Navier-Stokes equations, and the inviscid flow over a wedge. Reductions in computing time by factors of 3 and 1.5, respectively, are obtained by over-relaxation.

Desideri, J.-A.↗

NASA NTRS1977

Sound-tube measurements of the relaxation frequency of moist nitrogen

At audible frequencies, the vibrational relaxation of nitrogen contributes significantly to the absorption of sound in still air. The accurate measurement of the humidity dependence of the relaxation frequency of nitrogen, as yet, has eluded careful measurement due to the difficulty in measuring small absorption at low frequencies. Recently, equipment has been constructed for measuring sound absorption in air as a function of humidity over the frequency range from 4 to 100 kHz. In the experiment described here, the temperature and humidity range of this equipment has been extended so that it can be used to study the relaxation absorption in nitrogen at temperatures from 311 K to 418 K. The results indicate that, over this temperature range, the frequency of maximum absorption in moist nitrogen, f, can be given by f/P = 260 x h, Hz/atm, where h is the percent mole fraction of water, and P is the pressure in atm. To the accuracy of the measurements reported here, f is independent of temperature over the range of temperatures at which the measurements were made.

Chang, D.↗

NASA NTRS1978

Wall region of a relaxing three-dimensional incompressible turbulent boundary layer

A three-dimensional turbulent boundary layer relaxing behind a transverse hump (shaped as a 30-deg swept 5-ft chord wing-type model) was studied in a low-speed wind tunnel. Data obtained with hot-wire probes showed that the apparent dimensionless velocity profiles in the viscous sublayer prevail universally; evidence for wall similarity in the relaxing flow field was confirmed in the form of a log law. An unusual region of slightly decreasing cross-flow angle was found in collateral regions, and a near-wall noncollateral flow was posited. Streamwise relaxation of the mean flow field was also investigated.

Hebbar, K. S.↗