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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Foot-scale Evaluation of CO2-Responsive Polymer and CO2 Binary Fluid as an Alternative Fracturing Fluid for Enhanced Geothermal Systems

A foot-scale high-temperature true-triaxial fracturing apparatus was used to conduct hydraulic fracture tests on rock samples. The fracturing tests used different fluids including water, CO2, CO2 with water, and CO2 with a 1% polyallylamine (PAA)/water solution. The tests were conducted with both constant pressure injection and constant flow rate injection modes. CO2-based fracturing fluids were found to produce higher breakdown pressures, high transient flow rates, and produce higher-conductivity fractures as compared to water-based fracturing fluids. Additionally, faster pressurization rates with CO2-based fracturing fluids (obtained when fracturing at constant flow rate mode) are found to be associated with higher fracture conductivities. When fracturing with CO2-based fluids in the presence of a PAA aqueous solution, for example if the rock is saturated with 1wt% PAA in water, the volume expansion caused by CO2-induced crosslinking of PAA leads to a faster pressure increase due to the associated volume expansion and increase in viscosity. It was also found that CO2 as a fracturing fluid injected in hot dry rock (HDR) attain the highest fracture conductivity only when injected at very high flow rates, followed very closely by the CO2/PAA fracturing fluid system that generates fractures with, on average, similarly high conductivity values though independently of injection flow rate and using 1/6 of the mass of CO2 as compared to CO2 in HDR. Breakdown pressures were also similar for CO2 stimulation in HDR and CO2/PAA fluid system under identical injection flow rates. Finally, the well-known low viscosity of CO2 phase prevents the efficient transport of proppants while the reacted CO2/PAA fluid system is known to form a high viscosity binary fracturing fluid system with the potential to carry proppant in addition of being a fine fracturing fluid.

Enhanced Geothermal Systems, polyallylamine, Co2-r↗
DOE OSTI2021

Generation of excited species in a streamer discharge

At or near atmospheric pressure, most transient discharges, particularly in molecular gases or gas mixture containing molecular gases result in a space-charge dominated transport called a streamer discharge. The excited species generation in such discharges forms the basis for plasma chemistry in most technological applications. In this paper we simulate the propagation of streamers in atmospheric pressure N 2 to understand the energy partitioning in the formation of various excited species and compare the results to a uniform Townsend discharge. The model is fully two-dimensional with azimuthal symmetry. Results show a significantly larger fraction of the energy goes into vibrational excitation of the N 2 ground state in a streamer-type discharge in comparison to a Townsend discharge. For lower applied voltages, the anode-directed (negative) steamer is slightly more efficient in channeling energy for excited species production in comparison to a cathode-directed (positive) streamer. Near 70% overvoltage both types of streamers show very similar energy partitioning but quite different from a Townsend discharge.

42 ENGINEERING↗
DOE OSTI2021

Role of surface diffusion in formation of unique reactivity for graphite oxidation: Time-resolved measurements in a pulsed diffusion reactor

Quantification of oxidation kinetics is essential to develop graphitic materials for diverse applications: from refractories found in gas-cooled nuclear reactors to catalysts needed for chemical manufacturing. In this work, using well-defined highly oriented pyrolytic graphite, low-pressure isotopic transient experiments combined with controlled annealing periods, we resolve the role of surface diffusion and quantify oxidation kinetics with nanomole-precision. We observe an unexpected increase in reactivity following annealing which is explained by the role of surface diffusion increasing the probability for trapping mobile oxygen at more reactive edge sites. Here, the locus of adsorption and spillover to the basal plane is distinct from the trapping location creating a more active oxygen species. Isotopic products reflect the population dynamics of oxygen added at the edge and surface diffusion that relocates basal plane oxygen to more reactive edge sites. Since this process proceeds in parallel with direct oxidation reactions, it is not likely to be observed using steady-state or conventional ‘bulk’ characterization techniques. Our unique time-resolved non-equilibrium measurement in a well-defined transport regime, enables observation of three distinct behaviors: short-term deactivation due to the balance of rates in oxygen supply/product formation, reactivity increases due to surface diffusion and longer-term reactivity increase with oxygen accumulation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A multi-dimensional dataset for two-phase instability in low pressure natural circulation based on direct transient local measurement

Thermal hydraulic instability can challenge the control and the safety of nuclear reactors. This experimental research captures and investigates the instability in a low-pressure (1–10 atmospheres) natural circulation loop with an adiabatic chimney installed above the heated section. Direct transient local measurement of two-phase flow is performed at multiple axial locations along the flow channel with thermocouples and conductivity probes traversed by customized high-precision mechanisms. Based on the periodicity of oscillations, a post-processing method is proposed to align the data captured non-simultaneously to reconstruct the instability behavior in one representative period. The averaging operation over multiple oscillation cycles is performed to reduce the random errors. Cyclic phenomena are clearly demonstrated by the post-processed data, and rapid void fraction change induced by the flashing is observed to be significant in the driving mechanism for low pressure oscillations. Parametric effects of inlet subcooling, heat flux, inlet flow restriction and system pressure are studied within the experiment range, and qualitative results are explained and compared with existing literature. The ratio between the oscillation period and the travelling time of the fluid particle through the test section is compared with the theoretical value for the density wave oscillation. The new dataset contains directly measured transient multi-dimensional two-phase data along the flow channel for natural circulation under density wave oscillations. The generated dataset is valuable for the validation of system analysis codes and CFD codes in the simulation of natural circulation phenomena and dynamic two-phase flow.

42 ENGINEERING↗
DOE OSTI2024

CCUS 2024, Interpreting the strain tensor Larry Murdoch Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring during CCUS. We have demonstrated this method by deploying strainmeters at shallow depths (30 to 40m) and then conducting injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. We have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS. Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and our objective was to evaluate opportunities for strain monitoring during characterization and monitoring for CCUS. Our approach was to deploy strainmeters at shallow depths (30 to 40m) and then conduct injection well tests in an underlying reservoir at 530m depth. The results indicate that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. In conclusion, we have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS.

Murdoch, Larry↗
DOE OSTI2023

Limitations of cetane number to predict transient combustion phenomena in high-pressure fuel sprays

Fundamental understanding of in-cylinder processes in diesel engines is important to screen emerging biofuels and advanced combustion modes that can reduce greenhouse gas emissions and regulated pollutants including soot. In this study, the role of fuel properties on spray development and combustion is investigated by systematically isolating chemical and thermophysical effects. Three different fuels are considered, two with similar chemical properties and two with similar thermophysical properties with one fuel common to both groups. Experiments are performed in a constant-pressure flow chamber de-signed to provide stable test conditions and facilitate acquisition of at least 150 injections in quick succession for each fuel under reacting conditions at high-pressure, high-temperature ambient conditions using a modified conventional diesel engine injector. Further, high speed optical diagnostics including rainbow schlieren deflectometry, OH* chemiluminescence, and a two-color pyrometry system are employed to simultaneously image the transient spray and reacting jets. Image analysis is performed to determine liquid length, vapor penetration length, timing and location of first stage and main ignition events, lift-off location, total soot mass, and more. Results show that fuels with similar chemical properties or cetane number (CN) exhibit similar delay times for first stage and main ignition events as may be expected, but very different liquid length, first stage and main ignition locations, lift-off length, apparent turbulent flame speed, and soot formation. As such, the ability to characterize candidate biofuels with CN or other parameters derived from simple flame configurations is called into question. In this study, thermo-physical properties controlling the liquid length are identified as the main contributing factor for the observed differences.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Stereoscopic high-speed microscopy to understand transient internal flow processes in high-pressure nozzles

The flow and cavitation behavior inside fuel injectors is known to affect spray development, mixing and combustion characteristics. We discuss that while diesel fuel injectors with converging and hydro-eroded holes are generally known to limit cavitation and feature higher discharge coefficients during the steady period of injection, less is known about the flow during transient periods corresponding to needle opening and closing. Multiple injection strategies involve short injections, multiplying these aspects and giving them a growing importance as part of the fuel delivery process. In this study, single-hole transparent nozzles were manufactured with the same hole inlet radius and diameter as the Engine Combustion Network Spray D nozzle, mounted to a modified version of a common-rail Spray A injector body and needle. Needle opening and closing periods were visualized with stereoscopic high-speed microscopy at injection pressures relevant to modern diesel engines. Time-resolved sac pressure was extracted via elastic deformation analysis of the transparent nozzles. Sources of cavitation were observed and tracked, enabling the identification of a gas exchange process after the end of injection with ingestion of chamber gas into the sac and orifice. We observed that the gas exchange contributed widely to disrupting the start of injection and outlet flow during the subsequent injection event.

42 ENGINEERING↗
DOE OSTI2021

Ultrafast olivine-ringwoodite transformation during shock compression

Meteorites from interplanetary space often include high-pressure polymorphs of their constituent minerals, which provide records of past hypervelocity collisions. These collisions were expected to occur between kilometre-sized asteroids, generating transient high-pressure states lasting for several seconds to facilitate mineral transformations across the relevant phase boundaries. However, their mechanisms in such a short timescale were never experimentally evaluated and remained speculative. Here, we show a nanosecond transformation mechanism yielding ringwoodite, which is the most typical high-pressure mineral in meteorites. An olivine crystal was shock-compressed by a focused high-power laser pulse, and the transformation was time-resolved by femtosecond diffractometry using an X-ray free electron laser. Our results show the formation of ringwoodite through a faster, diffusionless process, suggesting that ringwoodite can form from collisions between much smaller bodies, such as metre to submetre-sized asteroids, at common relative velocities. Even nominally unshocked meteorites could therefore contain signatures of high-pressure states from past collisions.

42 ENGINEERING↗
DOE OSTI2024

Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring. We have deployed strainmeters and then conducted injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters (30 to 40m depth) was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 n/d over a few days. The signal at two strainmeters at shallow depth were consistent, although the magnitude of the horizontal strains were different reflecting the different radial directions from the well. The signal at a deep strainmeter deployed at reservoir depth was much different, with tensile vertical strains and compressive horizontal strains. These data can be interpreted by inverting poroelastic forward models developed using numerical and analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. This model is fast and can be inverted to estimate reservoir stiffness and geometry. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. The proxy model is periodically updated and refined using the finite element model to ensure accuracy. This approach significantly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. We have shown that the strain tensor in the caprock is sensitive to pressure in the reservoir, boundaries in the reservoir, and pressure in the caprock caused by leaks. These results indicate that coupling strain tensor data with inversion has the potential to help evaluate reservoirs during initial characterization, and to monitor them during the CO2 injection and storage process.

Murdoch, Larry↗
DOE OSTI2025

Operation of helium sub-atmospheric multistage cryogenic centrifugal compressor trains: Part 2 – Transient modeling and pump-down path selection

Low-pressure conditions required for operation of helium cryogenic systems below the normal boiling point (i.e. 4.2 K) are established through a transient process, commonly referred to as ‘pump-down’. This process is defined as the transition from pressures above atmospheric conditions to the saturation pressure which corresponds to a specified operational temperature. The FRIB 2 K system consists of five cryogenic centrifugal compressors which are operated in series. Historically, the pump-down process path has been established through empirical methods and system operator experience. Investigation into the pump-down process at FRIB aimed to develop a pump-down methodology which relies on theoretical model predictions rather than empirically developed process paths. Ensuring stable operation during the pump-down process involved application of a centrifugal compressor performance prediction model, which is described in Part 1 of this paper. Compressor performance maps can be directly used to evaluate the stability of a selected pump-down path and anticipate the overall reliability of the selected path. In conjunction with the compressor performance maps, a system pressure model was developed to estimate the transient pressure response during the pump-down process. Lastly, an explicit equation was developed to establish a mass flow rate profile for the pump-down process. Implementation of the presented methodology (including the developed models) allows for the system operator to determine a continuous pump-down path which maintains compressor stability while conforming to overall system capabilities. Altogether, the methodology presented has resulted in simplification of transient pump-down operations and increased the reliability, stability and efficiency of the pump-down process.

Compressor train control↗
DOE OSTI2023

Sensitivity Analysis of Transient Critical Heat Flux by RIA Under High-Pressure Flow Boiling Conditions in TRTL

A reactivity-initiated accident (RIA) is a design-basis accident under which critical heat flux (CHF) is likely to be exceeded. The operational margin for RIAs is currently determined using steady-state CHF lookup tables, which provide conservative estimates relative to transient CHF phenomena. The Transient Reactor Test Loop (TRTL) facility at Oregon State University is capable of performing out-of-pile rapid heating experiments representative of a RIA at conditions representative of a pressurized water reactor (PWR). Here, to further our understanding of and ability to predict transient CHF under PWR conditions, we performed a sensitivity analysis on a RELAP5-3D model of the TRTL facility coupled to the RAVEN code framework to define a proposed experimental test matrix to be performed at the TRTL facility. We then implemented a flow boiling CHF correlation into RELAP5-3D and performed a secondary sensitivity analysis inspecting the impact of the built-in RELAP5-3D CHF and heat transfer multipliers on both the prediction of CHF and key safety parameters, such as peak cladding temperature and heat flux. The results show that the multiplier with the highest influence toward the prediction of CHF occurrence and the safety parameters is the transient CHF multiplier. Operational performance envelopes have been developed for each of the test matrix cases and will be used for validation once the experiments are performed. The TRTL facility is currently performing shakedown testing to verify system performance prior to proceeding with the experimental campaign. Restart testing results include pump curve restart testing, pressure tests, and heater rod thermocouple transients.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Coupling of Pronghorn and RELAP-7 for a Pebble Bed Reactor

High temperature gas cooled reactors (HTGR) are a candidate for timely Gen-IV reactor technology deployment because of high technology readiness and walk-away safety. Among HTGRs, pebble bed reactors (PBRs) have attractive features such as low excess reactivity and online refueling. Pebble bed reactors pose unique challenges to analysts and reactor designers such as continuous burnup distribution depending on pebble motion and recirculation, radiative heat transfer across a variety of gas-filled gaps, and long design basis transients such as pressurized and depressurized loss of forced circulation. Modeling and simulation is essential for both the PBR’s safety case and design process. In order to verify and validate the new generation codes the Nuclear Energy Agency (NEA) Data bank provide a set of benchmarks data together with solutions calculated by the participants using the state of the art codes of that time. An important milestone to test the new PBR simulation codes is the OECD NEA PBMR-400 benchmark which includes thermal hydraulic and neutron kinetic standalone exercises as well as coupled exercises and transients scenarios. In this work, the reactor multiphysics code MAMMOTH and the thermal hydraulics code Pronghorn, both developed by the Idaho National Laboratory (INL) within the multiphysics object-oriented simulation environment (MOOSE), have been used to solve Phase 1 exercises 1 and 2 of the PBMR-400 benchmark. The steady state results are in agreement with the other participants’ solutions demonstrating the adequacy of MAMMOTH and Pronghorn for simulating PBRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Investigating bubble pressures in irradiated UO 2 for understanding fragmentation of high burnup structure

This report summarized work carried out to investigate mechanisms relevant to fragmentation of high burnup UO 2 fuel. High pressure bubbles that form in high burnup structure are thought to be responsible for fragmentation and pulverization, when exposed to a temperature ramp during a transient. The over-pressurization of the bubbles during normal operation is a pre-requisite for this mechanism to occur. Therefore, in this work we investigate the role of interstitials, produced through irradiation, in over-pressurizing the bubbles by using a combined molecular dynamics (MD) and cluster dynamics approach. Firstly, the energies for the annihilation of interstitials and vacancies at bubbles have been determined from MD as a function of bubble pressure. Secondly, these reaction energies have been implemented in the cluster dynamics code Centipede to determine the steady-state defect concentrations and bubble pressure under irradiation. It was found that there is a transition from low pressure bubbles, at high temperature, to high pressure bubbles, at low temperatures. This indicates the formation of over-pressurized bubbles in the low temperature periphery of the pellet, where high burnup structure forms. This result supports the hypothesis that over-pressurized bubbles form during steady-state operation and can then contribute to fragmentation during a transient. Future work will examine the influence of bubble pressure on Xe diffusion and study the impact of other sinks (e.g. grain boundaries and dislocations) that are relevant to high burnup structure. Ultimately, the goal is to provide predictions of the bubble pressure as a function of burnup that can be used to derive a more mechanistic fragmentation threshold for use in BISON.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A two-equation soot-in-flamelet modeling approach applied under Spray A conditions

Soot production (including formation and oxidation) is studied in the transient, high-pressure and turbulent n-dodecane Spray A flames from the Engine Combustion Network (ECN) using computational fluid dynamics (CFD) simulations. A two-equation soot-in-flamelet modeling approach is applied within the framework of the Unsteady Flamelet Progress Variable (UFPV) model and results are validated against experimental data. Equations for soot mass fraction and soot number density derived in the mixture fraction space are solved in the context of detailed flamelet calculations. Source terms for the different steps in the soot chemistry are tabulated and incorporated in the flamelet manifold. For the reference condition, the modeling approach based on the tabulated flamelet manifold reduces the computational cost of a CFD calculation by approximately 40 times compared to a non-tabulated well-mixed (WM) modeling approach. The soot-in-flamelet approach is then extended to study the effect of ambient oxygen concentration, ambient mixture composition and ambient temperature on soot production. Results show that the modeling approach is able to capture the experimental trends for the soot volume fraction (SVF) with good quantitative agreement, especially in the soot ramp-up region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Design of the high-yield time-gated x-ray hot-spot imager for OMEGA

Time-resolved x-ray self-emission imaging of hot spots in inertial confinement fusion experiments along several lines of sight provides critical information on the pressure and the transient morphology of the hot spot on the University of Rochester’s OMEGA Laser System. At least three quasi-orthogonal lines of sight are required to infer the tomographic information of the hot spots of deuterium–tritium cryogenic layered implosions. OMEGA currently has two time-gated x-ray hot-spot imagers: the time-resolved Kirkpatrick–Baez x-ray microscope and the single-line-of-sight, time-resolved x-ray imager (SLOS-TRXI). The time-gated x-ray hot-spot imager (XRHSI) is being developed for use on OMEGA as the third line of sight for the high-yield operation of up to 4 × 10 14 neutrons. XRHSI follows the SLOS-TRXI concept; however, it will have improved spatial and temporal resolutions of 5 μm and 20 ps, respectively. The simultaneous operation of the three instruments will provide 3-D reconstructions of the assembled hot-spot fuel at various times through peak thermonuclear output. The technical approach consists of a pinhole array imager and demagnifying time-dilation drift tube that are coupled to two side-by-side hybrid complementary metal–oxide semiconductor (hCMOS) image sensors. To minimize the background and to harden the diagnostics, an angled drift-tube assembly shifting the hCMOS sensors out of the direct line of sight and neutron shielding will be applied. As a result, the technical design space for the instrument will be discussed and the conceptual design will be presented.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Pressure Spike in The LBNF Absorber Core s Gun Drilled Cooling Channel from an Accident Beam Pulse

The LBNF Absorber consists of thirteen 6061-T6 aluminum core blocks. The core blocks are water cooled with de-ionized (DI) water which becomes radioactive during beam operations. The cooling water flows through gun-drilled channels in the core blocks. The cooling water is supplied by the LBNF Absorber Radioactive Water (RAW) cooling system which is designed as per ASME B31.3 Normal Fluid Service [1]. An uninhibited beam accident pulse striking the water channels was identified as a credible accident scenario. In this study, it is assumed that the beam pulse hits the Absorber directly without interacting with any of the other upstream beamline components. The beam parameters used for the LBNF beam are 120 GeV, 2.4 MW with a 1.2 s cycle time. The accident pulse lasts for 10 μs. The maximum energy is deposited in the 3rd aluminum core block. For the sake of simplicity, it is assumed that the accident pulse strikes the 1 in. ID water channel directly. The analysis here simulates the pressure rise in the water during and after the beam pulse and its effects on the aluminum piping components that deliver water to the core blocks. The weld strengths as determined by the Load and Resistance Factor Design (LRDF) and the Allowable Strength Design (ASD) are compared to the forces generated in the weld owing to the pressure spike. A transient structural analysis was used to determine the equivalent membrane, peak, and bending stresses and they were com-pared to allowable limits.

43 PARTICLE ACCELERATORS↗