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NASA NTRS1991

An error bound for instantaneous coverage

An error bound is derived for a reliability model approximation method. The approximation method is appropriate for the semi-Markov models of reconfigurable systems that are designed to achieve extremely high reliability. The semi-Markov models of these system are complex, and a significant amount of their complexity arises from the detailed descriptions of the reconfiguration processes. The reliability model approximation method consists of replacing a detailed description of a reconfiguration process with the probabilities of the possible outcomes of the reconfiguration process. These probabilities are included in the model as instantaneous jumps from the fault-occurrence state. Since little time is spent in the reconfiguration states, instantaneous jumps are a close approximation to the original model. This approximation procedure is shown to produce an overestimation for the probability of system failure, and an error bound is derived for this overestimation.

White, Allan L.↗

DOE OSTI2025

Temperature sensitivity of the equilibrium neutronics and accident analysis of the HTR-10

Pebble-Bed High-Temperature Gas-cooled Reactors (PB-HTGR) are moderated by the graphite in the fuel pebbles and the graphite reflector surrounding the pebble-bed. Because graphite is by far the most abundant material in PB-HTGRs and the primary moderator, accurate modeling of the graphite material, including density, impurities, and temperatures, is crucial for accurate computational modeling and simulation of these reactors. While main characteristics of the graphite components are often known, the local temperature is less well known and often averaged over all components. Here, this work studies the impact of considering accurate temperature profiles in the graphite material on the generation of a small PB-HTGR model at the state of equilibrium operation and on short-term accident progression. The fuel compositions for the PB-HTGR were determined using a jump-in equilibrium modeling method, the Axial Radial Zone Equilibrium Modeling (AR-ZEM) method. In contrast to previous work, the AR-ZEM method was used considering thermal-hydraulic feedback from the MELCOR code to determine temperatures of the fuel pebbles and the surrounding graphite reflector. The consideration of an axial and radial temperature profile in the core and reflector, as opposed to uniform material temperatures, had an impact of almost 1,300 pcm on the equilibrium core eigenvalue and caused significant differences in the discharged plutonium fuel inventory with up to 4.9% and 11.0% for Pu-239 and Pu-242, respectively. To assess the impact on short-term accident progression, two Anticipated Transient Without SCRAM (ATWS) events, a Pressurized Loss of Forced Coolant (PLOFC) and a Control Rod Withdrawal (CRW) with loss of flow, were simulated with MELCOR. The use of temperature profiles in the equilibrium core models did not reveal a significant impact on the temperature, power, or reactivity responses during the transients. In conclusion, a need for consideration of accurate temperature profiles, in particular for the graphite reflector, was found for the generation of equilibrium PB-HTGRs core models using jump-in methods, but detailed temperature profiles may not be necessary when performing conservative transient analysis.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1988

JPL pulsar timing observations. V - Macro and microjumps in the Vela pulsar 0833-45

In this paper, 14.5 yr of JPL timing data are analyzed to study the spindown of the Vela pulsar. Discontinuities in the spin frequency and its derivatives have bimodal amplitude distributions. Macrojumps are characterized by relative changes in spin rate of about 10 to the -6th with a derivative of 0.01, while microjumps have relative changes in spin rate of less than about 10 to the -9th with derivative of less than about 0.0001. Macrojumps display a (+,-) signature with a well-defined ratio of the amplitudes. Microjumps, however, show all possible signs of events and a larger range in signature. Six macrojumps and their associated transients are quantified using a 10-parameter model for each jump. Amplitude and decay time parameters vary by a factor of about five over the set of jumps. The results are discussed in terms of superfluid vortex models. The macrojumps are consistent with a model in which angular momentum is suddenly transferred to the crust from a more rapidly rotating superfluid core, followed by relaxation of the spin-down rate.

Cordes, J. M.↗

DOE OSTI2023

3-D Simulations of earthquakes rupture jumps: 1. Homogeneous pre-stress conditions

SUMMARY Observational and modelling studies indicate that earthquake ruptures can jump between fault sections as large as ∼3 and ∼5 km for compressional and extensional offsets, respectively. Here, we compare characteristics of the rupture jump process on parallel but offset fault sections from traditional 3-D dynamic rupture simulations governed by slip weakening friction using the finite element code, FaultMod, to those from quasi-dynamic simulations governed by rate- and state-dependent friction (rate-state friction) using the code RSQSim. These simulations use spatially uniform initial stresses. For a variety of measures the rupture renucleation position on the offset fault, the rate-state friction and slip weakening friction models produce very similar results. The principal difference is the additional occurrence of delayed rupture jumps that arise from the time- and stress-dependent nucleation that is characteristic of rate-state friction. For immediate rupture jumps, models with slip weakening friction span greater offsets than those with rate-state friction. However the jump distances are nearly identical when delayed rupture jumps are included in the comparisons. We propose that delayed rupture jumps are the likely mechanism for adjacent large-earthquake pairs and clusters. Based on the similarity of renucleation positions with both dynamic and quasi-dynamic models, we conclude that the renucleation positions for rupture initiation on the receiver fault (separated by less than ∼3 km from the source fault) are primarily controlled by static stress changes induced by slip on the initiating fault. However, in light of the slightly greater maximum jump distances (>3 km) seen with the dynamic slip weakening friction model, dynamic stress changes from seismic waves play an increasingly important role as offset distances increase.

, RSQSim↗

NASA NTRS1991

Shock interactions in the outer heliosphere

The results of recent simulations of the nonlinear evolution of the solar wind structures are reviewed, emphasizing theoretical development and the shock interactions model (SIM). Models which calculate jumps in flow properties across shocks without using exact Rankine-Hugoniot relations and models which do use them are addressed. The development of a computer code and some basic applications to the SIM are considered. Simulation results for the formation and propagation of forward-reverse shock pairs and the collision and merging of shocks are shown. Two studies which used the SIM to simulate nonlinear evolution of large-scale solar wind structures in the outer heliosphere are examined, and the SIM is then applied to study the heating of the solar wind in the outer heliosphere. The results support the hypothesis that shocks are mainly responsible for the heating of the solar wind plasma in the outer heliosphere at least up to 30 AU.

Whang, Y. C.↗

NASA NTRS2014

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; AMS 10th Satellite Symposium) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014; this conference) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end to end physical and dynamical basis for relating lightning rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relation to updraft strength, updraft volume, precipitation‐sized ice mass, etc.; however, relation specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler techniques to resolve the physical and dynamical storm characteristics specifically around the time of the lightning jump. This information will help forecasters anticipate lightning jump occurrence, or even be of use to determine future characteristics of a given storm (e.g., development of a mesocyclone, downdraft, or hail signature on radar), providing additional lead time/confidence in the severe storm warning paradigm.

Shultz, Christopher J.↗

NASA NTRS2013

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

Key points this analysis will address: 1) What physically is going on in the cloud when there is a jump in lightning? -- Updraft variations, Ice fluxes 2) How do these processes fit in with severe storm conceptual models? 3) What would this information provide an end user? --Relate LJA to radar observations, like changes in reflectivity, MESH, VIL, etc. based multi -Doppler derived physical relationships

Schultz, Chris↗

NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

Hall, Kenneth C.↗

NASA NTRS2012

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

Key points that this analysis will begin to address are: 1)What physically is going on in the cloud when there is a jump in lightning? - Updraft variations, ice fluxes. 2)How do these processes fit in with severe storm conceptual models? 3)What would this information provide an end user (i.e., the forecaster)? - Relate LJA to radar observations, like changes in reflectivity, MESH, VIL, etc. based multi-Doppler derived physical relationships 4) How do we best transistionthis algorithm into the warning decision process. The known relationship between lightning updraft strength/volume and precipitation ice mass production can be extended to the concept of the lightning jump. Examination of the first lightning jump times from 329 storms in Schultz et al. shows an increase in the mean reflectivity profile and mixed phase echo volume during the 10 minutes prior to the lightning jump. Limited dual-Doppler results show that the largest lightning jumps are well correlated in time with increases in updraft strength/volume and precipitation ice mass production; however, the smaller magnitude lightning jumps appear to have more subtle relationships to updraft and ice mass characteristics.

Schultz, Christopher J.↗

NASA NTRS1986

Full-potential modeling of blade-vortex interactions

A comparison is made of four different models for predicting the unsteady loading induced by a vortex passing close to an airfoil. (1) The first model approximates the vortex effect as a change in the airfoil angle of attack. (2) The second model is related to the first but, instead of imposing only a constant velocity on the airfoil, the distributed effect of the vortex is computed and used. This is analogous to a lifting surface method. (3) The third model is to specify a branch cut discontinuity in the potential field. The vortex is modeled as a jump in potential across the branch cut, the edge of which represents the center of the vortex. (4) The fourth method models the vortex expressing the potential as the sum of a known potential due to the vortex and an unknown perturbation due to the airfoil. The purpose of the current study is to investigate the four vortex models described above and to determine their relative merits and suitability for use in large three-dimensional codes.

Jones, H. E.↗

NASA NTRS1986

Full potential modeling of blade-vortex interactions

A comparison is made of four different models for predicting the unsteady loading induced by a vortex passing close to an airfoil. (1) The first model approximates the vortex effect as a change in the airfoil angle of attack. (2) The second model is related to the first but, instead of imposing only a constant velocity on the airfoil, the distributed effect of the vortex is computed and used. This is analogous to a lifting surface method. (3) The third model is to specify a branch cut discontinuity in the potential field. The vortex is modeled as a jump in potential across the branch cut, the edge of which represents the center of the vortex. (4) The fourth method models the vortex expressing the potential as the sum of as known potential due to the vortex and an unknown perturbation due to the airfoil. The purpose of the current study is to investigate the four vortex models described above and to determine their relative merits and suitability for use in large three-dimensional codes.

Jones, H. E.↗

NASA NTRS2013

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. In order to become a viable option for operational forecasters to incorporate into their severe storm monitoring process, the total lightning jump must be placed into the framework of several severe storm conceptual models (e.g., radar evolution, storm morphology) which forecasters have built through training and experience. Thus, one of the goals of this study is to examine and relate the lightning jump concept to often used radar parameters (e.g., dBZ vertical structure, VIL, MESH, MESO/shear) in the warning environment. Tying lightning trends and lightning jump occurrences to these radar based parameters will provide forecasters with an additional tool that they can use to build an accurate realtime depiction as to what is going on in a given environment. Furthermore, relating the lightning jump concept to these parameters could also increase confidence in a warning decision they have already made, help tip the scales on whether or not to warn on a given storm, or to draw the forecaster s attention to a particular storm that is rapidly developing. Furthermore the lightning information will add vital storm scale information in regions that are not well covered by radar, or when radar failures occur. The physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relation to updraft strength, updraft volume, precipitation -sized ice mass, etc.; however, very few have related the concept of the lightning jump and manifestation of severe weather to storm dynamics and microphysics using multi -Doppler and polarimetric radar techniques. Therefore, the second half of this study will combine the lightning jump algorithm and these radar techniques in order to place the lightning jump concept into a physical and dynamical framework. This analysis includes examining such parameters as mixed phase precipitation volume, charging zone, updraft strength and updraft volume. Such a study should provide increased understanding of and confidence in the strengths and limitations of the lightning jump algorithm in the storm warning process.

Schultz, Christopher J.↗

NASA NTRS1982

Pressure distributions and shock shapes for a bent-nose biconic at incidence

Initial results of a NASA study of the lift-drag characteristics of a 12.84/7 deg biconic model intended for airbraking during atmospheric entry of probes to Mars, Venus, Saturn, and Titan are reported. Pressure distributions and shock shapes were measured in the Langley 20 in. Mach 6 tunnel with the spherically blunted bent-nose model set at angles from 0-25 deg. Pressure distributions and shock shapes where computed using the STEIN flowfield code, which features a MacCormack scheme to integrate the three-dimensional Euler equations, the Rankine-Hugoniot jump conditions to model shock waves as discontinuities, and requires a supersonic condition at every step. A comparison was made between measured and predicted values. The leeward shock angle was found to be predictable to within 3% for all angles of attack, while parabolized Navier-Stokes equations are regarded as offering more accurate results than the STEIN code for surface pressure distributions.

Miller, C. G., III↗

NASA NTRS1988

Application of unsteady aerodynamic methods for transonic aeroelastic analysis

Aerodynamic methods for aeroelastic analysis are applied to various flow problems. These methods include those that solve the three dimensional transonic small disturbance (TSD) potential equation, the two dimensional (2-D) full potential (FP) equation, and the 2-D thin layer Navier-Stokes equations. Flutter analysis performed using TSD aerodynamics show that such methods can be used to analyze some aeroelastic phenomena. For thicker bodies and larger amplitude motions, a nonisentropic FP method is presented. The unsteady FP equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. Pressures calculated on the NLR 7301 and NACA 64A010A airfoils using the nonisentropic FP method are presented. It is shown that modeling shock generated entropy extends the range of validity of the FP method. A Navier-Stokes code is correlated with pressures measured on a supercritical airfoil at transonic speeds. When corrections are made for wind tunnel wall effects, the calculations correlate well with the measured data.

Whitlow, Woodrow, Jr.↗

DOE OSTI2023

Stochastic Price Generation for Evaluating Wholesale Electricity Market Bidding Strategies

This work presents a novel method for generating electricity price scenarios from statistical properties of past electricity prices using a hybrid statistical and reduced-form stochastic model. Previous work in applying stochastic differential equations (SDE) to model electricity prices has focused on daily average prices. To extend stochastic price generation methods to hourly or sub-hourly pricing, we address several weaknesses in the state-of-the-art: (1) we replace the mean-reversion component of the SDE with an ARIMA process that is better able to characterize the daily and weekly trends; (2) we extend the price-spike, or jump process to account for conditional probabilities of price spikes occurring in consecutive time steps by replacing the traditional Poisson process for modeling jumps with a generalized point process model inspired by brain neuron models; and (3) we replace the traditional method of estimating spike intensity with empirical variance with a Markov process based on observed price spike intensity transitions. The method is demonstrated with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the day-ahead and real-time energy markets of ERCOT using stochastic optimization methods. Results show that the the synthetic price model out performs a (naive) persistence forecast model by resulting in 24% to 47% more in profits over 168 simulated days.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS2018

From S-N to the Paris Law with a New Mixed-Mode Cohesive Fatigue Model

The relationship between fatigue life and fatigue crack propagation rate is explored with a new cohesive damage model. The parameters of the model are obtained from idealizations of S-N diagrams used in engineering design. The model is based on the hypothesis that both stable tearing damage and damage due to cyclic loading are representations of a density of microcracks and, therefore, a single damage variable can describe the state of damage. This assumption implies that the quasi-static cohesive law that describes tearing is also the envelope of the fatigue damage. Fatigue damage within the cohesive envelope is assumed to accumulate at a rate that depends on the displacement jumps. The fatigue model was implemented as a UMAT subroutine for Abaqus cohesive elements by adding fatigue damage accumulation to a cohesive model based on the Turon mixed-mode cohesive laws. The analyses were conducted using a simplified cyclic loading procedure in which the maximum applied load is kept constant and the computational expense of cycling the load is avoided. The predicted propagation rates in mode I and mixed mode were compared to experimental results for IM7/8552 graphite/epoxy tape. Several aspects of the results were investigated, including the effect of R-curves, the stress ratio R, and the difference between displacement control and force control.

Davila, Carlos G.↗

NASA NTRS2018

A Cohesive Fatigue Model Based on the S-N Diagram

The relationship between fatigue life and fatigue crack propagation rate is explored with a new cohesive damage model. The parameters of the model are obtained from idealizations of S-N diagrams used in engineering design. The model is based on the hypothesis that both stable tearing damage and damage due to cyclic loading are representations of a density of microcracks and, therefore, a single damage variable can describe the state of damage. This assumption implies that the quasi-static cohesive law that describes tearing is also the envelope of the fatigue damage. Fatigue damage within the cohesive envelope is assumed to accumulate at a rate that depends on the displacement jumps. The fatigue model was implemented as a UMAT subroutine for Abaqus cohesive elements by adding fatigue damage accumulation to a cohesive model based on the Turon quasi-static cohesive law. The analyses were conducted using a simplified cyclic loading procedure in which the maximum applied load is kept constant and the computational expense of cycling the load is avoided. The predicted propagation rates for a double cantilever beam (DCB) specimen were compared to experimental results for IM7/8552 graphite/epoxy tape.

Dávila, Carlos G.↗