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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Retention and surface morphology evaluation of fine-grain dispersion-strengthened tungsten for plasma-facing component applications

This study exposed novel fine-grain dispersion-strengthened tungsten (W) to high fluence, low energy deuterium (D) and helium (He) plasmas to evaluate how material microstructure and composition affect hydrogen retention and surface morphology. Tested materials included fine-grain dispersion-strengthened tungsten (DSW) with 3 wt% zirconium carbide (ZrC) dispersoids, fine-grain dense W without any dispersoids (FGW), and coarse-grained polycrystalline ‘ITER-grade’ W. Samples were exposed to D 2 + and He + plasmas at fusion-relevant fluences (∼10 25 m -2 ) and ion energies (75 eV) over a range of temperatures (200 °C, 300 °C, 450 °C for D, 850 °C for He). Helium ion microscopy was performed on the exposed samples to evaluate surface morphology changes and material integrity. After D plasma exposure, the ZrC dispersoids showed near-surface degradation at exposure temperatures above 300 °C, but no detrimental morphology changes were observed for the adjacent W grains. After He plasma-exposure, nano-structured fuzz formation was observed in the tungsten matrix of all samples. The ZrC dispersoids maintained their integrity despite the surrounding fuzz growth, with clear delineation between the W fuzz and dispersoid regions. Thermal desorption spectroscopy showed that ZrC DSW consistently retained more D than the FGW by about a factor of 2 across all temperatures. At 200 °C and 300 °C, the ITER-W displayed lower D retention than both the DSW and FGW, however at 450 °C ITER-W showed the highest retention, about 50% more than DSW. He retention was comparable across all samples, with the highest retention observed in the fine-grain W, only 26% higher than in ITER-W. These insights on retention behavior will inform further optimization of these novel fine-grained tungsten materials with and without dispersoid additives.

Dispersion-strengthened tungsten↗
DOE OSTI2024

A simulation study of the ability to detect power distribution perturbations in the texas A&M TRIGA reactor with self-powered neutron detectors

Given the variety of ways that nuclear reactor core power may be perturbed, reactor operators and developers are keen on understanding the accuracy and convergence time during which perturbations in reactor power distribution may be synthesized (i.e., inferred) from an array of in-core radiation detectors. A simulation study was conducted as described herein using a highly detailed model of the Texas A&M Training, Research, Isotopes, General Atomics Reactor, in which an array of self-powered neutron detectors (SPNDs) was considered for input to the power synthesis methodology. The core power synthesis is conducted using a point-based iterative method with an iterative loop built in to ensure working equation consistency. The forward problem of SPND response to simulated perturbations in reactor power was solved for Gaussian peak-type perturbations in the reactor power distribution. These perturbations varied in variance, amplitude, and core location to assess their impact on synthesis error and to determine the number of iterations required for convergence. A relation between the unique resolvability limit and perturbation width was identified such that the maximum synthesis error increased rapidly when the peak width went beneath this limit (a width approximating half the reactor’s fuel pin-to-pin pitch); this resolvability limit is specific to the SPND configuration and fuel segmentation considered herein. The synthesis error increased linearly with perturbation peak amplitude, whereas the convergence time increased nonlinearly. Perturbations located closer to the center of the core were synthesized more accurately, albeit with a higher number of required iterations. These findings provide a qualitative and quantitative understanding of the accuracy and speed at which different types of spatial power perturbations can be resolved in light-water reactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

Quantum annealing for systems of polynomial equations

Abstract Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of 10 −8 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Shattered pellet injection simulations with NIMROD

Optimal strategies for disruption mitigation benefit from the understanding of details both spatially and temporally. Beyond the assessment of the efficacy of a particular proposed Disruption Mitigation System (DMS), ITER's longevity will require accounting of both mitigated and unmitigated disruptions. Accurate models and validated simulations that detail multiple ITER scenarios with mitigated and unmitigated disruptions are essential for accurate estimates of load damage. The primary candidate for ITER's DMS is Shattered Pellet Injection (SPI); its efficacy must be evaluated within the next several years. To perform critical time dependent 3-D nonlinear simulations, we have developed a particle based SPI model in the NIMROD code coupled to its modified single fluid equations with impurity and radiation [Izzo, Nucl. Fusion 46(5), 541 (2006)]. SPI validation simulations of the thermal quench and comparisons to DIII-D impurity scan experiments [Shiraki et al., Phys. Plasmas 23(6), 062516 (2016)] are presented. We also present an initial ITER Q = 10 pure neon SPI simulation and compare it with the DIII-D SPI simulations. NIMROD SPI simulations demonstrate that the ablating fragment drives strong parallel flows that transport the impurities and governs the thermal quench. Analysis of SPI simulations shows that the mixed deuterium/neon SPI results in a more benign thermal quench due to the enhanced transport caused by the additional deuterium. These results suggest that an optimal pellet mixture exists for the SPI system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

Monte Carlo (MC) simulation is widely used to solve the eigenvalue form of the Boltzmann transport equation that mathematically represents the neutron transport process through complex multiplying (fissionable) systems. Monte Carlo eigenvalue simulation starts with an assumed fission source distribution and uses the fission sites from the previous iteration (cycle) as the starting source in the current iteration. Important system parameters (MC tallies) such as fuel pin-power distribution are estimated over several cycles after the convergence of the fission source distribution to a stationary distribution. However, the MC fission source iteration algorithm that uses fission source sites from the previous cycle introduces a cycle-to-cycle correlation. Monte Carlo simulations that do not account for the cycle-to-cycle correlation systematically underestimate the variance of the estimated system parameters (sample mean). This paper presents the relationship between the spectral density in the frequency domain at frequency zero and the variance of the sample mean. This paper introduces a novel method in the frequency domain for the MC variance estimation. For the three test problems used in this paper, researchers have observed that the new method results in an improvement of more than one order of magnitude to the standard deviation of the sample mean. The new method also compares favorably with the previously introduced batch, bootstrap, and covariance-adjusted methods when applied to the three test problems investigated in this paper. This new method does not require modification of the MC eigenvalue algorithm (power iteration), is code agnostic, and is therefore easy to use when implementing in any existing MC code. In conclusion, the new estimate can be calculated without saving tally results of all active/stationary cycles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗
DOE OSTI2024

One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A multi-machine scaling of halo current rotation

Halo currents generated during unmitigated tokamak disruptions are known to develop rotating asymmetric features that are of great concern to ITER because they can dynamically amplify the mechanical stresses on the machine. This paper presents a multi-machine analysis of these phenomena. More specifically, data from C-Mod, NSTX, ASDEX Upgrade, DIII-D, and JET are used to develop empirical scalings of three key quantities: the machine-specific minimum current quench time, $ \newcommand{\tauCQ}{\tau_{{\rm CQ}}} \tauCQ$; the halo current rotation duration, $ \newcommand{\trot}{t_{{\rm rot}}} \newcommand{\tr}{{\rm tr}} \trot$ ; and (3) the average halo current rotation frequency, $ \newcommand{\favg}{\langle f_{{\rm h}} \rangle} \favg$ . These data reveal that the normalized rotation duration, $ \newcommand{\tauCQ}{\tau_{{\rm CQ}}} \newcommand{\trot}{t_{{\rm rot}}} \newcommand{\tr}{{\rm tr}} \trot/\tauCQ$ , and the average rotation velocity, $ \newcommand{\vavg}{\langle {v}_{{\rm h}} \rangle} \vavg$ , are surprisingly consistent from machine to machine. Furthermore, comparisons between carbon and metal wall machines show that metal walls have minimal impact on the behavior of rotating halo currents. Finally, upon projecting to ITER, the empirical scalings indicate that substantial halo current rotation above $ \newcommand{\favg}{\langle \,f_{{\rm h}} \rangle} \favg=20$ Hz is to be expected. More importantly, depending on the projected value of $ \newcommand{\tauCQ}{\tau_{{\rm CQ}}} \tauCQ$ in ITER, substantial rotation could also occur in the resonant frequency range of 6–20 Hz. In conclusion, the possibility of damaging halo current rotation during unmitigated disruptions in ITER cannot be ruled out.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

The role of edge resonant magnetic perturbations in edge-localized-mode suppression and density pump-out in low-collisionality DIII-D plasmas

Two-fluid nonlinear MHD simulations using the TM1 code demonstrate that the formation of magnetic islands at the top and bottom of the H-mode pedestal, together with the strong screening of resonant fields in the gradient region of the pedestal, can account for ELM suppression and density pump-out by n = 2 resonant magnetic perturbations (RMPs) in low-collisionality DIII-D ITER similar shape (ISS) plasmas. Using experimentally relevant transport coefficients, neoclassical resistivity, electron collisionality, and RMP amplitudes, nonlinear MHD simulations reproduce the observed level of density reduction (density pump-out) in DIII-D due to the formation of narrow magnetic islands in the resistive foot of pedestal. For large amplitude RMPs ( B r / B t > 1 × 10 -4 ) simulations predict resonant field penetration and resulting in pressure reduction at the top of the pedestal, consistent with experimental observations at the onset of ELM suppression. The predicted reduction in the height and width of the pedestal by magnetic island enhanced collisional transport provides a quantitative mechanism for the stabilization of the peeling-ballooning mode (PBM). Importantly, these simulations predict strong screening of resonant fields in the steep gradient region of the pedestal due to strong E × B rotation and diamagnetic flows. Yet, if the plasma resistivity is made artificially larger (~ 10X) than neoclassical, the simulations predict magnetic stochasticity throughout the plasma edge and the collapse of the pedestal due to the reduction in the penetration threshold with increasing resistivity. A scaling relation for resonant field penetration at the pedestal top, using several hundred nonlinear simulations, reproduces the density and E × B rotation dependence of the ELM suppression threshold observed in DIII-D. Simulations using ITER model equilibria indicate that the penetration threshold at the top of the ITER pedestal will be lower than in DIII-D due to the anticipated lower perpendicular flow velocities in ITER, resulting in the weaker screening of resonant fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Advances in the long-pulse steady-state high beta H-mode scenario with active controls of divertor heat and particle fluxes in EAST

Since the last IAEA-Fusion Energy Conference, the Experimental Advanced Superconducting Tokamak (EAST) research program has been, in support of ITER and CFETR, focused on development in terms of the long-pulse steady-state (fully noninductive) high beta H-mode scenario with active controls of the stationary and transient divertor heat and particle fluxes. The operational domain of the steady-state H-mode plasma scenario has been significantly extended with ITER-like tungsten mono-block divertor, plasma control and heating schemes. EAST has achieved several important milestones in the development of high β p H-mode scenario and its key physics and technologies. A 60 s-scale long-pulse steady-state high β p H-mode discharge with the major normalized plasma parameters similar to the designed performance of the CFETR 1GW fusion power operation scenario has been successfully established and sustained by pure RF heating and current drive. Several feedback control schemes have been developed for a sustained detachment with good core confinement. This includes control of the total radiation power, target electron temperature, and particle flux measured using divertor Langmuir probes or a combination of the control of target electron temperature and AXUV radiation near the X point. The detachment feedback control schemes have been integrated with small-ELM regimes and high β p scenario via neon seeding, enabling a core and edge compatible integrated high-beta scenario applicable to long-pulse operations. ELM suppression has been achieved using various methods, including resonant magnetic perturbations and impurity seeding. Full suppression of ELMs by using n=4 RMPs has been demonstrated for ITER for the first time in low input torque plasmas in EAST. Finally, EAST has been operated with helium to support the ITER research requirements for the first time. For a long-pulse, high bootstrap current fraction operation, a new lower tungsten divertor with active water-cooling has been installed, along with improvements in the heating and current drive capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Progress towards edge-localized mode suppression via magnetic perturbations in hydrogen plasmas

Abstract The suppression of edge-localized modes (ELMs) by applying resonant magnetic perturbations (RMPs) is well studied in low collisionality deuterium plasmas as a measure to reduce transient divertor heat loads. However, ELM suppression has yet to be demonstrated in non-nuclear fuels such as hydrogen and hydrogen + helium mixtures which are the main ion species to be used in the ITER pre-fusion power operation (PFPO) phase. For the first time, attempts have been made to access ELM suppression with RMPs in ITER-like low collisionality hydrogen plasmas at DIII-D and ASDEX Upgrade. The DIII-D experiments focused on operation with injected power slightly above the L–H power threshold similar to the expected conditions in the ITER PFPO phase with limited external heating power. The RMPs were found to trigger H–L backtransitions, which is shown to be avoided by reducing the L–H power threshold by diluting the plasma with helium. The additional helium combined with a larger measured neutral density of hydrogen inside the separatrix compared to ELM suppressed deuterium plasmas precluded access to a pedestal top density below the known RMP-ELM suppression threshold. At ASDEX Upgrade, RMP-ELM suppression has been achieved when the concentration of 1 H in the hydrogen isotope mix is below 40 % . While all known access criteria for RMP-ELM suppression were met above this threshold, full ELM suppression was replaced by strong mitigation. The most prominent difference between the hydrogen and deuterium plasmas was a change of turbulence characteristics in the pedestal where Doppler reflectometry measurements suggest a significant reduction of turbulence even at small hydrogen concentrations. In conclusion, these experiments not only identify issues that may prevent access to RMP-ELM suppression in the ITER PFPO phase, but also highlight missing physics in our current understanding of RMP-ELM suppression such as potentially the role of turbulence in the pedestal gradient region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Transient magneto-hydrodynamic (MHD) events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here in a concise way to provide a complete overview, while we refer to the original publications for details. Experimental validation for unmitigated vertical displacement events progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection was simulated in JET, KSTAR, ASDEX Upgrade (AUG) and ITER. Benign runaway electron beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f particle in cell models for ion temperature gradient and trapped electron modes were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle interactions with MHD were studied. Flux pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in $l$ = 2 stellarators, while verification for advanced stellarators progresses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Efficient 3-D velocity model building using joint inline and crossline plane-wave wave-equation migration velocity analyses

SUMMARY Wave-equation migration velocity analysis (WEMVA) is an image-domain inversion method for velocity model building. Automatic plane-wave WEMVA (PWEMVA) calculates the moveouts of plane-wave common-image gathers (CIGs) by searching a best-fitting parabola with semblance analysis and backprojects residual CIG moveouts into wavefield wave paths with a reflection tomographic kernel. However, 3-D PWEMVA is very computationally expensive because 3-D reflection tomographic inversion requires at least five 3-D reverse-time migrations per iteration and stores two types of source wavefields at model boundaries. We develop a joint inline and crossline PWEMVA method for efficient 3-D velocity model building. We alternatively implement the inline and crossline PWEMVAs with a constraint for each other, in which we iteratively construct the 3-D velocity model update through 1-D spline interpolation of 2-D gradients. The inline and crossline joint inversion is practical since PWEMVA only inverts for low-wavenumber velocity perturbations along wave paths, and the method can take less than 1 per cent of the computational cost of full 3-D PWEMVA. To construct unaliased plane waves for our joint inline and crossline PWEMVA, we develop a 3-D data interpolation method in the frequency–wavenumber (FK) domain to recover regularly and randomly missing traces. The method minimizes the misfit on sufficiently localized data subsets with iterative optimal step lengths and a gradient preconditioner that iteratively selects dominant dips along different azimuths. In numerical experiments, we use a 3-D synthetic seismic data set and a land 3-D field seismic data set acquired at the Farnsworth CO2-EOR (enhanced oil recovery) field to demonstrate the efficacy of our velocity model building and data interpolation methods.

Liu, Xuejian↗
DOE OSTI2018

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II↗
DOE OSTI2018

Improving the Convergence Rate of Parareal-in-time Power System Simulation using the Krylov Subspace

The performance of parareal-in-time algorithms is determined on the number of sequential, coarse step iterations. A common tradeoff in designing an efficient parareal-in-time algorithm is between accuracy of the coarse solver and the number of iterations. Traditional parareal implementation for the power system simulation can also have difficulties handling complex power systems. In this paper, we propose a Krylov subspace enhanced parareal algorithm to reduce the number of coarse iterations. The proposed approach is demonstrated on a single-machine-infinite-bus system and the IEEE 10-machine 39-bus system. Noticeable decrease of number of iterations is observed in both cases.

Duan, Nan↗
DOE OSTI2022

Numerical Analysis of Liquid Metal MHD Flow and Heat Transfer for Open-Surface Li Divertor in FNSF

Within the ongoing U.S.-based program on the development of liquid metal plasma-facing components, numerical simulations and analyses are performed to address the feasibility of the open-surface Li divertor. In the previous scoping studies (Smolentsev, 2021), heat-removal capabilities of the divertor were assessed using a simplified flow model for a slug-type velocity profile and constant flow thickness. Here, new analyses take into account forces acting on the flowing Li layer. Three reduced-order mathematical models are applied under the conditions of the U.S. Fusion Nuclear Science Facility (FNSF) to access magnetohydrodynamic (MHD) flow development effects, velocity distribution, and surface waves: 1) fully developed MHD flow; 2) quasi-2-D developing MHD flow; and 3) multiphase MHD flow. The obtained results for MHD flows and the surface heat flux computed with the plasma code scrape-off layer plasma simulation for ITER (SOLPS-ITER) are then used as input data to compute the temperature distribution in the divertor by solving the convection–diffusion energy equation.

Smolentsev, Sergey↗
DOE OSTI2019

A Kriging Surrogate Model for Computing Gas Mixture Equations of State

Accurate simulation of the complex flow following the detonation of an explosive material is a challenging problem. In these flows, the detonation products of the explosive must be treated as a real gas while the surrounding air is treated as an ideal gas. As the detonation process unfolds and the blast wave moves into the surrounding ambient air, the products of detonation expand outward and interact with the air creating a mixture region. In this region, both of the state equations for air and the products must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between the equations of state until both pressure and temperature reach an equilibrium inside of a computational cell. Since this mixture region moves and grows over time, this algorithm must be performed millions, or even billions, of times in a typical detonation simulation. As such, these calculations can account for a large percentage of the overall solution time. This work aims to use a kriging surrogate model to replace this process. The iterative method solves a nonlinear system of equations created from the gas mixture density, internal energy, and composition using a Broyden iterative solver to obtain an output pressure and temperature. Kriging is used to produce curve fits which interpolate selected pressures and temperatures from this solver from appropriate ranges of the mixture input quantities. Using a finite volume hydrocode, the performance of the model with respect to the iterative solver is demonstrated in the simulation of a pentaerythritol tetranitrate (PETN) charge detonation. The model's computational speed and accuracy are quantified as a function of the choice of sampling points in order to try optimize the combination as well as to show the benefits of this novel approach.

Engineering↗