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At least 37 records · Page 2

Thermal-Fluid and Thermal-Structural Response of the T-Tube Modular Divertor to Spatiotemporally Varying Heat Loads

Tungsten (W) is the leading candidate for divertor target plates because of its high melting point (>3000°C), thermal conductivity, and ultimate tensile stress. While W and its alloys are the only solid materials that can survive the high heat fluxes incident on the divertor, W’s low-ductility high ductile-to-brittle transition temperature of ~600°C and relatively low recrystallization temperature (RT) of ~1300°C pose structural (among other) challenges. The objective of this work is to estimate the thermal-fluid and thermal-structural performance of the helium (He)-cooled T-tube divertor, which was originally developed by the Advanced Reactor Innovation and Evaluation Study (ARIES) using numerical simulations. Here, predictions of temperature distributions across the plasma-facing structural component and surface pressures from computational fluid dynamics simulations are used to determine stress distributions using commercial structural finite element modeling software over a range of fusion-relevant conditions. The maximum allowable incident heat fluxes are determined based on the temperature limits imposed by the ITER elastic Structural Design Criteria for In-vessel Components (SDC-IC) and the maximum RT over a range of He mass flow rates and presented in the form of performance design charts. Our recent work found that thermal- structural criteria accounting for the low ductility of W in a finger-type modular divertor constrain the maximum incident heat fluxes to values well below the ITER specifications, and those based on considering only the RT demonstrate that integrated thermal-fluid and elastic structural performance evaluation are required for accurate assessment of divertor performance. This novel analysis of the T-tube considers how nonuniform and transient incident heat fluxes affect its thermal-fluid and thermal-structural performance, as well as the effect of volumetric heating, which can be as great as 27% of the power incident on the divertor surface. The W tile of the T-tube, with its relatively large plasma-facing area of ~15 cm 2 , will likely experience significant spatial variations in incident heat flux. This work therefore assesses whether steady-state incident heat flux profiles with a peak of 10 MW/m 2 and maximum heat flux gradients of 200 MW/m 2 per m exceed the structural limits imposed by the ITER elastic SDC-IC and the maximum RT over a range of fusion-relevant conditions. The effect of transient heat fluxes typical of plasma detachment and reattachment from the target plate due, for example, to gas injection are also evaluated

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Damage progression and failure of SiC/SiC composite tubes under hard-contact radial expansion

The response of silicon carbide (SiC) fiber-reinforced SiC matrix (SiC/SiC) composite cladding to mechanical interaction with fissile fuel is a knowledge gap that must be overcome to design and assess SiC-based cladding systems for advanced nuclear applications. This study developed the relevant mechanical testing capability and identified the failure behavior and the critical microstructural features and processing defects. Sections of SiC composite tube were subjected to a modified expansion-due-to-compression (EDC) test in an X-ray computed tomography microscope: a polyurethane plug pressed surrogate Al 2 O 3 into the inner walls of the SiC/SiC composite tubes to achieve hard contact. A pure EDC test with just a polyurethane plug was also performed as a reference. Through the use of displacement fields, digital volume correlation revealed inhomogeneous deformation fields in the tubes, even for pure EDC, which was related to the inherent defects in the structure. Deep learning–aided segmentation and systematic data analysis revealed that the presence of inhomogeneous deformation applied by the hard contact was exaggerated by the presence of inner surface imperfections left behind from the matrix densification process. In conclusion, the findings provide insights into the applications, highlighting the necessity for improvements in inner surface roughness and the incorporation of localized contacts in pellet–cladding mechanical interaction computational models.

Composites↗

Damage modeling of power tower receiver tubes using the SRLIFE tool

Concentrating Solar Power (CSP) molten-salt central receivers are subject to high, transient incident flux during daily operation. The resulting creep-fatigue damage impacts the receiver’s reliability and restricts the permissible incident flux distribution for a given receiver. This paper aims to reduce CSP plants’ levelized cost of electricity by developing a methodology to predict lifetime and identifies the primary damage mechanism (creep vs fatigue) for any given fluid temperature and temperature gradient. Results are presented in the form of a damage map that serves as a valuable operation guide and design tool. Damage maps can be used to reduce maintenance costs by improving reliability and reduce receiver capital costs by better utilizing the receiver area. FEA simulation and damage modeling of tubes subject to asymmetrical flux conditions is performed in the open-source receiver design tool srlife. Parametric studies are performed over a range of inner tube temperatures and thermal gradients for A230, 316H, 740H, A282, A617, and 800H high temperature alloys. Damage maps are presented for each alloy. A parametric, FEA-based methodology is presented for comparison of fatigue-creep ratios and prediction of tube lifetime based on the critical thermal operating conditions. Fatigue is found to be negligible compared to creep for almost every case. Here, this finding suggests that fatigue effects associated with cloud events are insignificant compared to creep at these high temperature operating conditions. Additionally, lifetime predictions identify thermal conditions where small changes in operating conditions can result in large changes in predicted lifetime.

14 SOLAR ENERGY↗

Anode sensitivity calibration of photomultiplier tubes used as a readout of the ELOSS detector

We present and discuss the methodology and results for an anode sensitivity calibration of Photomultiplier Tubes (PMTs) that serve as the optical readout of the Energy Loss Optical Scintillation System (ELOSS). The ELOSS detector, under development at the Facility for Rare Isotope Beams (FRIB), is a gaseous Xe scintillation-based detector designed to identify the atomic number (Z) of nuclear reaction fragments by energy-loss measurement. Variation in the anode sensitivity from tube to tube of commercially available PMTs limits ELOSS from reaching its ultimate Z resolution. A methodical approach to calibrating PMT anode sensitivities to a single target value by systematic PMT gain corrections is presented. Although the calibration process is discussed in terms of its impact on ELOSS performance, the presented method is applicable to any optical detector system composed of a large number of PMTs needing anode sensitivity calibration.

Instrumentation for heavy-ion accelerators↗

Beam Loss Assessment Through Use of Photomultiplier Tubes

The first machine in the Fermilab Accelerator chain, the Linac, delivers a 400 MeV proton beam. The first portion of the Fermilab Linac, the Drift Tube Linac, lacks the degree of instrumentation necessary for beam tuning. To compensate for this, photomultiplier tube (PMT s) based loss monitors were installed on either side of the first two drift tube tanks, but are not yet operational. One of the main goals in this is to make PMT's operational beam loss monitors for tuning. Noise reduction and peak finding on the PMT data is a requirement for this. A method for noise reduction and peak finding has been developed and implemented to produce a consistent and stable output. Future work includes integration with ACNET to automate input and output of data for analysis of beam loss.

Waggoner, Alexander↗

Fatigue Testing and Characterization of Pre-hydrided Zircaloy-4 Cladding Tubes

The solubility of hydrogen in Zircaloy-4 (Zry-4) at the cladding operating temperature is near 100 wt. ppm. Above this solubility limit, excess hydrogen precipitates as δ-hydride platelets in the cladding material. Because of the effect of the thermal gradient across the cladding thickness on the migration and precipitation of hydrogen, hydride rims are often observed at the cladding outer surface; under excessive corrosion conditions hydride blisters are possible. It is well known that the fatigue of metal alloys, especially high cycle fatigue, is sensitive to the status of surface including the microstructure, roughness, and residual stress. Thus, the question considered herein, is whether excessive hydrogen pickup modifies the microstructure such that it has a degradation effect on the fatigue performance of cladding during operation. This report describes the evaluation of fatigue performance of a pre-hydrided Zry-4 cladding. A commercial Zry-4 was polished and pre-hydrided to 800 ppm and 1300 ppm H contents. The fatigue testing was conducted under strain control at 5 Hz with fully-reversed bending by using a cyclic integrated reversible bending fatigue tester (CIRFT). Six specimens with 1300 ppm and one specimen with 800 ppm were tested. Significant variation in test results were observed. While two of the 1300 ppm specimens failed with less than 1 ×10 5 cycles (at 0.32% and 0.41%), the four other samples did not fail over the strain amplitude range of 0.25% to 0.38%. Interestingly, the fracture initiation site of the failed samples was on the outside diameter (OD) surface rather than on the inside diameter (ID) surface as is typical for the as-polished cladding. This suggested a degrading effect of the hydriding process. Subsequently, three of the unfailed specimens were then further tested at ~0.43% to observe where failure initiation occurred. Significant variation was also observed in these three specimens. One specimen failed at ~9000 cycles while the two others failed at 43000 and 1.06 ×10 5 cycles. The performance here correlated to the location of failure initiation; failure initiated on the OD in the sample that failed after 9000 cycles while it initiated on the ID in the sample that failed after 43000 and 1.06 ×10 5 cycles. Flat features at the OD initiation sites suggest a brittle hydride feature on the surface of those samples was the cause of the degradation in fatigue performance, though the overall hydrogen levels in all samples was similar. A summary of all the observations is provided below: • The un-failed specimens with 1300 ppm H were cycled to failure with a higher amplitude near 0.43%. In addition, the fatigue-treated specimen tended to have a longer fatigue at the same induced amplitude. • Fractography revealed a mixed failure mode for the pre-hydrided specimen. Particularly, the specimen with fracture initiation site (FIS) located on the outer diameter surface of tube tended to have a shorter fatigue life than that of FIS on the inner diameter surface. • Etched cross section was shown to have hydride platelets aligned with tube longitudinal axis as expected, and the density of hydrides is at the similar level as in literature data. Meanwhile, a LECO procedure was applied for hydrogen concentration measurement, which showed the measured hydrogen contents are close to the nominal value. • With the polished cladding tube as baseline, O’Donnell-Lager (O-L) analysis showed that a decrease of about 50% in reduction-of-area (RA) would be needed for the O-L fitting to the fatigue data of 1300 ppm cladding. The suggestion for the next steps is provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Analysis of pressure test results of tube fittings for the potential application in cryo systems for helium leak rate reduction

Due to the nature of Helium, it is notoriously difficult to maintain a closed system without experiencing helium inventory loss through leakage in large tubing and piping runs. There are two standard fitting options readily available for piping and tubing assemblies, welded fittings or Swagelok ® . Welding is the best option for leak rate reduction, but more costly than Swagelok ® . A new style of fitting has come to the attention of BNL C-AD Cryo group, and a pressure test and leak rate analysis were performed to evaluate the viability of incorporating this new style fitting into current engineering design of warm helium tubing runs for the purpose of leak rate reduction.

43 PARTICLE ACCELERATORS↗

Experimental investigation on phase change material–based finned tube heat exchanger for thermal energy storage and building envelope thermal management

Phase change materials (PCMs) are attractive solutions for thermal energy storage (TES) applications by absorbing and releasing large amounts of latent heat during solid–liquid phase transitions. However, their relatively low thermal conductivity requires novel heat exchanger–based solutions to improve the power density and overall energy storage efficiency of the TES system. This work presents the design and experimental results of a finned tube heat exchanger to store collected natural thermal energy from a building envelope in a latent-based TES and to release it later for building heating/cooling applications. We experimentally evaluate the finned tube heat exchanger and evaluate the performance of TES in reducing building heating and cooling loads over 3–4 h of desired time of operation (e.g., peak load). The optimized design allows for maximum energy density by minimizing the heat exchanger volume, and the system is evaluated experimentally using commercially available heat exchanger materials and an organic PCM. Here, the experimental results reveal that the TES system is able to charge and discharge stored latent energy within 3–4 h, matching peak building electricity demand duration under an average fluid flow rate of 0.136 kg/s and temperature difference of 5.55 °C. Importantly, such optimized designs illuminate a path toward TES designs that are low-cost, scalable, and optimized for thermal energy and power availability under the desired time of operation.

25 ENERGY STORAGE↗

Performance evaluation of finned tube heat exchanger using curved wavy delta winglet vortex generators with circular perforations

Vortex generation is recognized as an effective passive approach to improve the heat transfer rate in fin and tube heat exchangers (FTHEs). The current study proposed innovative designs of curved wavy delta winglet vortex generators (CWDWVGs), both without and with circular perforations, to improve the heat transfer efficiency of FTHEs. There is potential to increase heat transfer performance further through various CWDWVG designs. Here, this study explores seven unique CWDWVG configurations, from 1-wave to 7-wave. A 3-D computational numerical model is utilized to evaluate the Thermo-hydraulic performance of FTHEs fitted with these different CWDWVG configurations across Reynolds numbers from 400 to 2000. This comparative analysis of the Thermo-hydraulic performance of FTHEs featuring four parallel circular tube layouts assesses configurations both with and without vortex generators (VGs) and various hole configurations. The evaluation of Thermo-hydraulic performance involves different parameters, including the London area goodness factor (LAGF), Colburn factor (j), friction factor (f), pressure drop (?P), and Nusselt number (Nu). Results demonstrate that the various CWDWVG configurations and the number of holes in them substantially affect the efficiency, as evaluated by the dimensionless Performance Evaluation Criteria (PEC). Notably, the 7-wave CWDWVGs surpassed other configurations, and integrating circular punched perforations further improved the thermal-hydraulic performance of FTHE. Specifically, the 7-wave CWDWVGs without holes demonstrated superior performance over other configurations, showing a significant increase in Nusselt number by 75.18% and 85.16% at Reynolds numbers of 2000 and 400, respectively, alongside an increase in pressure drop by 216.38% to 224.96%. Meanwhile, the 7-wave CWDWVGs with eight holes, in comparison to those without holes, exhibited a Nusselt number increase of 0.85%, a pressure drop decrease of 7.31%, and a reduction in the friction factor by 5.82%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluation and development of flow condensation correlations using the data from low GWP refrigerants in an axial micro-fin aluminum tube

To mitigate global warming, the world is transitioning to refrigerants with low global warming potential (GWP). Supporting this shift requires a model that can accurately predict the heat transfer and pressure drop of new refrigerants, crucial for designing efficient heat exchangers. Existing models, however, are largely based on currently deployed refrigerants and primarily developed for unexpanded micro-fin tubes with spiral angles of 6° to 30°. Their applicability to new refrigerants, especially in expanded micro-fin tubes, is uncertain. This study assesses the performance of four well-known condensation models for six emerging refrigerants—R-32, R-454B, R-454C, R-455A, R-1234yf, and R-1234ze(E)—against experimental data. Initially, the Han and Lee (2005) model shows the best prediction accuracy with a mean absolute deviation (MAD) of 22.1 %. To enhance the accuracy of heat transfer models for new refrigerants and geometries with large temperature glides, two approaches are proposed. Here, the first approach applies a simple correction factor, reducing the MAD of the Cavallini et al. (2009) model from 68.2 % to 15.4 %. The second approach uses the variable metric method for minimization, fitting new constants to the data. This optimization results in the Kedzierski and Goncalves (1997) model achieving the highest accuracy, with a MAD of 13.1 %. For pressure drop models, the Cavallini et al. (1997) model is the most accurate with a MAD of 6.4 %, followed by the Haraguchi et al. (1993) model with a MAD of 9.4 %. Due to its simplicity, the Haraguchi et al. (1993) model is a practical option for predicting frictional pressure drop.

Axial micro-fin tubes↗

A 24-channel ultra-low-noise preamplifier for dN/dx measurements with drift tube detectors

Cluster counting $(dN/dx)$ is a promising method to enhance particle identification for gaseous detectors, especially in next-generation collider experiments like the FCC-ee, where good $π/K$ separation over a broad momentum range is essential. However, its implementation in large-scale systems has been limited by the challenging requirements for high-resolution signal amplification and readout. This paper presents a 24-channel ultra-low-noise preamplifier board designed for drift tube detectors to enable $dN/dx$ measurements. The three-stage amplification topology employs SiGe transistors and integrates dedicated noise-minimization techniques, achieving a charge gain of 21.11 mV/fC from 0.3 fC to 50 fC, a bandwidth of 542 MHz, and a voltage gain of 47.8 dB. The measured voltage noise density is 0.35 nV/$\sqrt{\textrm{Hz}}$ , surpassing most of the state-of-the-art preamplifiers for gaseous and silicon detectors. Validation tests conducted on the sMDT chambers at the CERN Proton Synchrotron test beam facility demonstrate that the proposed design meets the stringent preamplifier requirements for implementing the $dN/dx$ method in drift-tube detector systems, achieving an equivalent noise charge of 0.14 fC and a signal-to-noise ratio of 73 when operated with a He:iC 4 H 10 (90:10) gas mixture. The design also shows promise for broader application in other gaseous or semiconductor detectors.

Drift tube detector↗

Fractional Skyrmion Tubes in Chiral‐Interfaced 3D Magnetic Nanowires

Magnetic skyrmions are chiral spin textures with rich physics and great potential for unconventional computing. Typically, skyrmions form in bulk crystals with reduced symmetry or ultrathin film multilayers involving heavy metals. Here, the formation of fractional Bloch skyrmion tubes at room temperature is demonstrated by 3D printing ferromagnetic double‐helix nanowires with two regions of opposite chirality. Using X‐ray microscopy and micromagnetic simulations, it is shown that the coexistence of vortex and anti‐parallel spin states induces the formation of fractional skyrmion tubes at zero magnetic fields, minimizing the energy cost of breaking the coupling between geometric and magnetic chirality. Control over zero‐field states is also demonstrated, including pure vortex, or mixed skyrmion‐vortex states, highlighting the magnetic reconfigurability of these 3D nanowires. This work shows how interfacing chiral geometries at the nanoscale can enable advanced forms of topological spintronics.

X-ray microscopy↗

Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory

We construct a novel flux tube entanglement entropy (FTE 2 ), defined as the excess entanglement entropy relative to the vacuum of a region of color flux stretching between a heavy quark-anti-quark pair in pure gauge Yang-Mills theory. We show that FTE 2 can be expressed in terms of correlators of Polyakov loops, is manifestly gauge-invariant, and therefore free of the ambiguities in computations of the entanglement entropy in gauge theories related to the choice of the center algebra. Employing the replica trick, we compute FTE 2 for SU(2) Yang-Mills theory in (2+1)D and demonstrate that it is finite in the continuum limit. We explore the properties of FTE 2 for a half-slab geometry, which allows us to vary the width and location of the slab, and the extent to which the slab cross-cuts the color flux tube. Following the intuition provided by computations of FTE 2 in (1+1)D, and in a thin string model, we examine the extent to which our FTE 2 results can be interpreted as the sum of an internal color entropy and a vibrational entropy corresponding to the transverse excitations of the string.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Experimental investigation of Multi-Mode heat transfer to a Free-Falling dilute particle cloud in a heated vertical tube

The development of dilute particle heat exchangers and reactors for advanced energy systems requires an understanding of the multi-mode heat transfer from a heated wall to falling particles. This study presents experimental results of the overall heat transfer coefficient for a free-falling, dilute flow of particles with solid volume fraction from 0.0005 to 0.006 corresponding to feed rates from 3.7 kg s -1 m -2 to 44 kg s -1 m -2 in a vertical, heated tube containing quiescent air at atmospheric pressure. Tube wall temperatures are varied between 300°C to 900°C while keeping the particle inlet temperature constant. The experimental results show that the overall heat transfer coefficient is a strong function of particle feed rate and surface temperature. Good agreement was obtained with prior studies conducted at comparable temperatures but lower particle feed rates (< 4 kg m -2 s -1 ). The established correlations for particle-to-wall radiation and particle-to-gas convection were used to estimate the wall-to-gas convective contribution from the measured overall heat transfer coefficient. The experimental results indicated a 4 to 6 times improvement in the wall convection in the solid-gas mixture compared to that expected from natural convection in a single-phase gas. Furthermore, the data presented here are applicable to characterize heat transfer in dilute particle heat exchangers, furnaces, and solar receivers.

14 SOLAR ENERGY↗

Nonseeded linewise temperature measurements by resonantly ionized photoemission thermometry in a Mach 4 Ludwieg tube

A one-dimensional (1D) thermometry using oxygen-tagging resonantly ionized photoelectron thermometry (O 2 RIPT) was employed to investigate thermal gradients within a Mach 4 Ludwieg tube. The Ludwieg tube is pulsed with a test duration of approximately 100 ms, providing a cold supersonic flow at Mach 4 ideal for studying aerothermal effects. This study focused on measuring freestream temperatures, capturing shock-induced heating behind a detached bow shock from a blunt cylinder, and resolving sharp temperature variations across a bow shock generated by a cylinder. The O 2 RIPT technique produced strong emission signals extending approximately 4 cm long, demonstrating its capability for precise temperature measurements in high-speed wind tunnel environments. The results confirm that O 2 RIPT is well-suited for applications in large-scale aerodynamic testing facilities, particularly in regions with strong compression effects, enabling the resolution of sharp thermal gradients. This method presents a promising solution for thermometry in dynamic flow conditions relevant to various experimental ground-test facilities.

McCord, Walker (ORCID:0000000179747550)↗

Upgrade to Fixed and Translating Scintillation-based Loss Detector System in the Fermilab Drift Tube Linac

The closed-off structure of the Fermilab Drift Tube Linac precludes a robust array of instrumentation from directly monitoring the H- beam that is accelerated from 750 keV to 116 MeV. To improve beam tuning and operational assessment of Drift Tube Linac performance, scintillator-based loss monitors were previously installed along the exterior of the first two accelerating cavities to assess low energy beam losses. Here we present a recent upgrade to the loss monitor system, including significant improvements in analog signal processing to address baseline-interfering noise; digitization of the signals to enable regular operational use and tuning; and a new remote operation upgrade of the translating loss monitor with precise positioning of the loss monitor along its nine-foot track. Data from the fixed and translating detectors collected under varying beam conditions validate the utility of the upgrade.

Chen, E. V. [Fermilab]↗

Optimizing the Heisenberg Vortex Tube for Hydrogen Cooling (Final Technical Report)

Hydrogen utilization at Plug Power sites ranges between 70-93% with the remainder vented and lost to the atmosphere. The goal of this project was to improve hydrogen utilization at Plug Power fulfillment centers via the patented Heisenberg vortex tube (HVT). The HVT combines conventional counterflow vortex tubes with para-orthohydrogen conversion catalyst to allow the cooling of hydrogen flows with no moving parts or external energy inputs. In year 1 of this project the HVT was evaluated to improve hydrogen utilization via the following concepts: 1) increasing liquid hydrogen pump volumetric efficiency by 20% through vapor separation and subcooling of the liquid, 2) reducing liquid hydrogen storage tank boil-off losses by 20% through thermal vapor shielding (TVS), and 3) increase isentropic efficiency of supercritical hydrogen expansion at 40-50 K, from 31% to over 40%. The TVS concept was selected as the most favorable application for further development. While the conceptual analysis was underway, the cryocatalysis hydrogen experiment facility (CHEF) was retrofitted with a new cryocooler, higher pressure condenser tanks, and in-situ fiber-optic Raman probes for ortho-parahydrogen composition analysis at the inlets and outlets of the HVT. To our knowledge this is the first in-situ implementation of cryogenic Raman probes for ortho-parahydrogen analysis. Subsequent testing of catalyzed and non-catalyzed HVT identified a low flow rate, high-conversion efficacy regime well suited for TVS development. Computational fluid dynamics (CFD), Reduced order modeling (ROM), and quantum Monte Carlo atomistic simulations were applied to optimize the design of the HVT implemented for TVS. The simulations and analysis identified a ruthenium-based catalyst as the most optimal for high conversion with little pressure losses and was matched to experimental measurements. These results indicated the design could achieve the 20% boil-off reduction target. An HVT field-trial was designed and constructed by Plug Power and implemented at a customer site. However, budget limitations reduced the amount of catalyst that could be applied to the HVT. With the reduced amount of catalyst, CFD analysis estimated about 3% reduction in boil-off. A similar amount of boil-off reduction was observed during preliminary measurements during tank commissioning. However, the results have a large margin for error and were operated at relatively low tank temperatures when the HVT has the lowest potential for improvement. This project demonstrated the use of para-orthohydrogen catalysis for reducing liquid hydrogen tank boil-off losses. The field trial system is anticipated to provide long-term experimental measurements on tank operational performance that will allow Plug Power to instrument additional tanks in the future. Recommendations for future work include the development of higher activity, lower cost para-orthohydrogen conversion catalyst for use in the HVT. Tank process optimizations could maximize the efficacy of the HVT and further improve hydrogen utilization.

08 HYDROGEN↗

Euler equations and the Sod shock tube problem

The Euler equations are a subset of the magnetohydrodynamic (MHD) equations in the infinitely collisional, unmagnetized limit. MHD modeling is central to many areas of plasma physics, ranging from low-temperature glow discharges to inertial confinement fusion. An important aspect of the Euler equations is their ability to describe states with discontinuities, such as shock waves. A standard benchmark test for numerical implementation of the Euler equations is the Sod shock tube. In this test, the system is initialized at rest with a pressure and density discontinuity, which results in a shock wave traveling into the low-pressure region and a rarefaction wave traveling into the high-pressure region. Starting with the presentation of the Euler equations, a numerical algorithm is presented here to solve these equations in one dimension. This is followed by an overview of the Sod shock tube problem that includes the precise initial setup and the analytic solution. Finally, the analytic solution is compared with results from numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗