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At least 19 records

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DOE OSTI2021

Alluvial fan morphology: A self-similar free boundary problem description

In this work, we examine approximate geometrically self-similar solutions to a parabolic free boundary value problem applied to alluvial fan surface morphology and growth. Alluvial fans are fan- or cone-shaped sedimentary deposits caused by the rapid deposition of sediment from a canyon discharging onto a flatter plain. Longitudinal, topographic profiles of fans can be readily described by a seemingly time independent dimensionless profile (DeChant et al., 1999). However, because an alluvial fan can be expected to grow over time, it is clear that this “steady” profile is certainly time dependent and can be described using a space-time self-similar solution. In an experimental and theory-based study, Guerit et al. (2014) developed a self-similar (or as they describe it a self-affine) linear solution based upon an approximate first order small parameter expansion solution for a 1-d homogeneous nonlinear diffusion equation. Direct substitution of this result into a linear diffusion equation suggests that this first order expression may not fully satisfy the associated governing equation. In contrast, we develop a more complete solution based upon a modeled approximation for the axi-symmetric formulation such that the associated temporal behavior is consistent with a 1/3 time power-law as described by Reitz and Jerolmack (2014). The resulting expression is an exact solution to a linear heat equation. Furthermore, we emphasize that a small parameter is not inherent to the resulting profile result and is not included in our model development. Though developed using rather different approaches, the formal solution developed here is in good agreement with the simple polynomial described by DeChant et al. (1999) suggesting that this self-similar solution is a suitable time dependent representation of alluvial fan longitudinal profile form and improves on earlier work.

58 GEOSCIENCES↗

NASA NTRS1997

Diffuse-Interface Methods in Fluid Mechanics

The authors review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. The authors discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, the authors address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, related computational approaches to describe interfacial phenomena, and related approaches describing fully-miscible fluids.

SURFACE DIFFUSION↗

DOE OSTI2023

Toroidal modeling of plasma flow damping and density pump-out by RMP during ELM mitigation in HL-2A

Reduction of both the plasma density and toroidal flow speed, due to application of the predominantly n = 1 (n is the toroidal mode number) resonant magnetic perturbation (RMP) for controlling the edge localized mode in the HL-2A tokamak, is numerically investigated utilizing the quasi-linear initial-value code MARS-Q (Liu et al 2013 Phys. Plasmas 20 042503). Simulation results reveal that the neoclassical toroidal viscosity (NTV) due to three dimensional fields plays the key role in modifying the plasma momentum and particle transport in the HL-2A discharge. By comparing the modeling results with the measured density pump-out in the experiment, the electron NTV particle flux model, in combination with the free-boundary condition for the axisymmetric change of the density at the plasma edge, is found to yield the best agreement in terms of both the pump-out level and the overall time scale. Further sensitivity studies show that the simulated density pump-out level is reasonably robust against variations in the model assumptions, including the particle diffusion model and the non-ambipolar versus ambipolar NTV particle flux. The latter however affects the time scale for reaching the steady state solution. Finally, it is found that the plasma edge-peeling response, the NTV torque, as well as the plasma momentum and particle transport, all are sensitive to the toroidal phase difference between the upper and lower rows of the RMP coil currents in HL-2A, with the 30 ∘ coil phasing producing the minimal side effects on the plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1987

Redesign of a supercritical wing in the presence of an engine nacelle

If an obstacle, such as an engine nacelle, is placed in the flow near a virtually shockless wing, shocks of substantial magnitude may appear on the wing. A source distribution method is presently employed in the modeling of an engine nacelle in compressible flow, through incorporation into a free-boundary supercritical wing design code. Code calculation results are presented which show the transonic shock to appear, on average, 10 percent forward of its position on the clean wing. Attention is also given to an associated method for the calculation of wave drag.

Ross, David S.↗

DOE OSTI2026

Minimizing the Electromechanical Stresses in Poloidal Field Coils by Optimizing their Numbers and Locations using FREDA Framework

Poloidal field (PF) and central solenoid (CS) coils play a crucial role in sustaining the equilibrium and preserving the shape of highly confined tokamak plasmas. Ensuring that PF coil current and mechanical stress stay within superconducting and structural limitations is an important check in the design assessment. Minimizing the PF coil currents and mechanical stresses influences reliability, cost, and performance. A free-boundary MHD equilibrium code—FreeGS is employed within the fusion reactor design and assessment (FREDA) whole facility modeling (WFM) framework to construct the plasma equilibrium based on the configuration and currents in the PF coils. Here, we present the capability of the FreeGS code to minimize the currents, forces, and electromagnetic stresses on the PF coils by optimizing their number, sizes, structures, and locations while maintaining an MHD stable plasma configuration with a large confinement factor. The workflow is initialized with a configuration of plasma parameters and coils’ locations from the 0-D tokamak build systems code in the FREDA framework. Then, FreeGS is called to calculate the initial equilibrium at the minimum total current in PF coils. Thereafter, FreeGS’s internal optimizer minimizes the currents and hoop and central forces on the PF coils while maintaining the reference equilibrium. Finally, the input configuration is updated with the optimized parameters for equilibria over the ramp-up phase of a burning-plasma operation. FREDA’s whole facility optimization capability, which includes all magnetic field coil systems, blanket, vacuum vessel (VV), first wall, divertor, etc., is under development and out of the scope for this study.

Hassan, Ehab [ORNL] (ORCID:0000000181060301)↗

NASA NTRS1984

Boundary-layer model of pattern formation in solidification

A model of pattern formation in crystal growth is proposed, and its analytic properties are investigated. The principal dynamical variables in this model are the curvature of the solidification front and the thickness (or heat content) of a thermal boundary layer, both taken to be functions of position along the interface. This model is mathematically much more tractable than the realistic, fully nonlocal version of the free-boundary problem, and still recaptures many of the features that seem essential for studying dendritic behavior, for example. Preliminary numerical solutions produce snowflakelike patterns similar to those seen in nature.

Ben-Jacob, E.↗

DOE OSTI2022

Neural net modeling of equilibria in NSTX-U

Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two NNs relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a free-boundary equilibrium solver trained on the EFIT01 (Equilibrium FITtting 01) reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The NNs are trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, Eqnet can use magnetic diagnostics as inputs and act as an EFIT-like reconstruction algorithm, or, by using pressure and current profile information the NN can act as a forward Grad–Shafranov equilibrium solver. This forward-mode version is envisioned to be implemented in the suite of tools for simulation of plasma scenarios. The reconstruction-mode version gives some performance improvements compared to the online reconstruction code real-time EFIT, especially when vessel eddy currents are significant. Here, we report strong performance for all NNs indicating that the models could reliably be used within closed-loop simulations or other applications. Some limitations are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Real-time estimation and control of divertor surface heat flux on the DⅢ-D tokamak

We report Future tokamaks will require robust technologies for the mitigation of heat exhaust onto the plasma-facing components. As a first step towards this development, a system has been developed at DIII-D that estimates and controls in real-time the heat flux to the PFCs. Real-time estimation of the peak power flux from this model-based approach is validated with off-line infra-red measurements for various DIII-D plasma discharges. A nonlinear free-boundary simulation code (GSevolve) is used for simulating the closed loop response and for the off-line determination of the control parameters. The implementation and first experimental results of the application during the DIII-D plasma campaign are reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

Green Run Modal Test of the NASA Space Launch System Core Stage

The Core Stage of the new NASA Space Launch System (SLS) is a 212-foot-tall rocket assembly—consisting primarily of two cryogenic propellant tanks, an engine section, and four RS-25 rocket engines—that will send crew and large payloads to the moon and beyond for NASA’s Artemis program. Prior to SLS assembly, the Core Stage completed a series of structural and functional tests in the B-2 Test Stand at Stennis Space Center, designated Green Run. The goal of Green Run was to verify analytical models, confirm proper subsystem operation, and test-fire all four RS-25 engines of the Core Stage. In January 2020, Green Run testing began with an experimental modal analysis test, performed by the Marshal Space Flight Center modal test team. A free-boundary test condition of the Core Stage was simulated as close as possible by suspending the massive launch vehicle from the B-2 Test Stand crane. Modal excitation was provided by a pair of 250-lb electro-dynamic shakers for multi-shaker random vibration testing, as well as a 12-pound instrumented hammer for impact testing. Modal response was measured with 550 accelerometer channels distributed on both the Core Stage and the B-2 Test Stand derrick crane. Following one very long day of testing, frequency response functions were calculated from the measured time histories in the target mode frequency range of 5 Hz to 15 Hz, and mode shapes, frequencies, and damping values were successfully estimated. The case-study presented in this paper will discuss Green Run, the SLS Core Stage, the modal test setup and execution, as well as a brief overview of the test results. Challenges associated with testing such a large, suspended structure in an outdoor environment will be discussed as well.

Space Launch System↗

NASA NTRS1993

Cost-effective test methods for Shuttle payloads

Techniques are discussed for deriving constrained vibration mode shapes for Space Shuttle payloads using unconstrained or free-boundary dynamic properties. Application of the residual flexibility method requires measurement of a set of free-boundary modes plus the residual flexibility of the payload-to-orbiter interfaces. The mass-additive approach involves the measurement of unconstrained modes and frequencies of a payload with large masses attached to the interfaces. In either case, the orbiter interfaces of the test-verified payload model are analytically constrained to provide the mode shapes for the Shuttle-constrained configuration. Use of these methods or a hybrid combination of them for structures to which they are applicable allows the difficult and expense associated with development and verification of fixed-base test fixtures to be avoided.

Tinker, Michael L.↗

DOE OSTI2023

FES 2023 Theory & Simulation Performance Target

The Report for the 2023 Theory & Simulation Performance Target (TSPT) is presented herein. The 1st, 2nd and 3rd Quarter Reports are given in Sec. I, Sec. II and Sec. III. These are unchanged from those previously submitted, except that in this final document the equations, figures and citations have been automatically renumbered. The 4th Quarter Report is given in Sec. IV. The following material presents verification calculations of several widely used three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium codes in strongly shaped configurations; for both fixed and free-boundary equilibria; for the so-called vacuum case and for the case of high plasma pressure; and, for magnetic fields that have nested magnetic surfaces and for fields that have a magnetic island. The configurations studied includes the recently discovered “precise-QA” case [Phys. Rev. Lett., 128, 035001 (2002)] and other highly optimized configurations. Because of the strong (extreme) shaping, the latter of these pose challenges to the 3D MHD codes. A new method is introduced for constructing coordinates in arbitrarily shaped toroidal domains, and this can improve the robustness of 3D equilibrium calculations. Beyond the equilibrium calculation, this report demonstrates the capability of performing non-linear extended-MHD modelling of optimized stellarator equilibria. This capability allows the assessment not only of linear stability thresholds but also of the nonlinear evolution of unstable equilibria to new configurations that might be far from the original configuration, with significantly different transport properties and magnetic topology. They also enable the self-consistent determination of pressure profiles in non-integrable magnetic topology through the use of highly anisotropic thermal-transport equations. The calculations presented here represent the first demonstration of extended-MHD calculations in strongly-shaped, optimized quasi-symmetric configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

First snowflake divertor experiments in MAST-U tokamak

First snowflake (SF) divertor experiments in the MAST-U tokamak demonstrated steady-state snowflake-plus divertor configurations in 450 kA ohmic L-mode plasmas. The SF divertor configuration features a second poloidal field (PF) null in the divertor region close by or overlapping with the main X-point. The resulting low PF region and two additional divertor legs (strike points) may lead to additional power and particle flux sharing via a hypothesized convective cell, and increased plasma-wetted area and radiation. The free-boundary Grad–Shafranov equilibrium code FIESTA was used to design SF configurations with several inter-null distances and orientations. In the experiment, the SF configurations with inter-null distances 0.13–0.20 m and lasting 0.2–0.3 s were obtained. Parallel connection lengths between the midplane and the outer strike point in the SF configurations (evaluated at field lines 1–2 mm from the separatrix in the midplane) were 25–30 m, higher than in the standard divertor (20–25 m) or the Super-X divertor (25 m). Diagnostic measurements highlighted salient SF features. The infra-red video bolometer diagnostic showed that the radiated power peaking in the PF null region was not as pronounces as in the standard divertor. Divertor ion fluxes measured by target Langmuir probes showed increased ion flux in the plate region where a secondary SF strike point landed, concomitantly with the SF formation. These measurements may suggest that some particle and heat redistribution was taking place in the convective SF zone. The first SF experiments provide a basis for future SF studies in MAST-U tokamak with higher input power, improved plasma control and diagnostic measurements, to be compared with the modeling predictions of plasma convective SF mixing and lower density strike point detachment threshold.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

Here, in this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial degree for analytic and cross-code test cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

High Performance Equilibrium Solvers for Integrated Magnetic Fusion Simulations

With the funding provided by this award, we developed numerical codes for the study of magnetically confined plasmas for fusion applications. Accordingly, our work can be divided into two separate categories: 1) the design and analysis of novel numerical methods providing high accuracy and high efficiency; 2) the study of the equilibrium and stability of magnetically confined plasmas with some of these numerical codes, as well as the study of the nature of the turbulent behavior which may arise in the presence of instabilities. We first developed new numerical schemes based on integral equation methods for the computation of steady-state magnetic configurations in fusion experiments, providing high accuracy for the magnetic field and its derivatives, which are required for stability and turbulence calculations. We employed different integral formulations depending on the application of interest: axisymmetric or non-axisymmetric equilibria, force-free or magnetohydrodynamic equilibria, fixed-boundary equilibria or free-boundary equilibria. While efficient, these methods do not yet apply to plasma boundaries which are not smooth, a situation which is fairly common in magnetic confinement experiments. To address this temporary weakness, we also constructed a new steady-state solver based on the Hybridizable Discontinuous Galerkin (HDG) method, which provides full geometric flexibility. In addition to these numerical tools focused on steady-states, we also contributed to the improvement of the speed and accuracy of codes simulating the plasma dynamics of fusion plasmas, by developing a novel velocity space representation for the efficient solution of kinetic equations, which most accurately describe the time evolution of hot plasmas in fusion experiments. Using the tools discussed above, we studied several questions pertaining to the equilibrium and stability of magnetically confined plasmas. In particular, we derived a new simple model for axisymmetric devices called tokamaks, to predict how elongated a fusion plasma can be before it becomes unstable and collapses. We also looked at the effect of the shape of the outer plasma surface on key properties of the steady-state magnetic configurations, and how these properties impact turbulence in fusion plasmas, and the corresponding transport of momentum. Likewise, we studied the role of large localized flows on the steady-state magnetic configurations, and how they may influence plasma stability and turbulence. Non-axisymmetric steady-state magnetic configurations are inherently more complex than axisymmetric steady-state configurations, and the subject of ongoing controversies regarding the regularity of the equations determining such steady-states, and their solutions. Implementing an existing NYU code in a new geometry, we studied the nature of the singularity of the solutions observed in the code, and methods to eliminate them. Our main conclusion is that by appropriately tailoring the plasma boundary, it is possible to eliminate the singularities otherwise appearing in our simulations, and to obtain steady-states which appear to be smooth. To gain further insights on incompletely understood turbulence phenomena, we proposed a new reduced model capturing most of these phenomena, which is simple enough to not require expensive numerical simulations on massive supercomputers to investigate them. We demonstrated the strong similarity between our simulations and published results obtained from computationally expensive simulations, and plan to rely on our reduced model to identify the key mechanisms determining the evolution and strength turbulent driven transport in fusion plasmas. Finally, we proposed a new framework for tokamak reactor design studies, enabling us to consider the relative merits of steady-state versus pulsed fusion reactors. We found that pulsed fusion reactors may benefit most from recent advances in magnet technology, and the availability of very high field magnets. As such, they may become more desirable than steady-state tokamak reactors for cost efficient electricity generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1981

Eruptive solar magnetic fields

The quasi-steady evolution of solar magnetic fields in response to gradual photospheric changes is considered, with particular attention given to the threshold of a sudden eruption in the solar atmosphere. The formal model of an evolving, force-free field dependent on two Cartesian coordinates is extended to a field which is not force free but in static equilibrium with plasma pressure and gravity. The basic physics is illustrated through the evolution of a loop-shaped electric current sheet enclosing a potential bipolar field with footpoints rooted in the photosphere. A free-boundary problem is posed and then solved for the equilibrium configuration of the current sheet in a hydrostatically supported isothermal atmosphere. As the footpoints move apart to spread a constant photospheric magnetic flux over a larger region, the equilibria available extend the field to increasing heights.

Low, B. C.↗

NASA NTRS1993

Cost-effective test methods for Shuttle payloads

Techniques are discussed for deriving constrained vibration mode shapes for space shuttle payloads using unconstrained or free-boundary dynamic properties. Application of the residual flexibility method requires measurement of a set of free boundary modes plus the residual flexibility of the payload-to-orbiter interfaces. The mass-additive approach involves the measurement of unconstrained modes and frequencies of a payload with large masses attached to the interfaces. In either case, the orbiter interfaces of the test-verified payload model are analytically constrained to provide the mode shapes for the shuttle-constrained configuration. Use of these methods or a hybrid combination of them for structures to which they are applicable allows the difficulty and expense associated with development and verification of fixed-base test fixtures to be avoided.

Tinker, Michael L.↗

NASA NTRS1994

Measurement of Residual Flexibility for Substructures Having Prominent Flexible Interfaces

Verification of a dynamic model of a constrained structure requires a modal survey test of the physical structure and subsequent modification of the model to obtain the best agreement possible with test data. Constrained-boundary or fixed-base testing has historically been the most common approach for verifying constrained mathematical models, since the boundary conditions of the test article are designed to match the actual constraints in service. However, there are difficulties involved with fixed-base testing, in some cases making the approach impractical. It is not possible to conduct a truly fixed-base test due to coupling between the test article and the fixture. In addition, it is often difficult to accurately simulate the actual boundary constraints, and the cost of designing and constructing the fixture may be prohibitive. For use when fixed-base testing proves impractical or undesirable, alternate free-boundary test methods have been investigated, including the residual flexibility technique. The residual flexibility approach has been treated analytically in considerable detail and has had limited frequency response measurements for the method. This concern is well-justified for a number of reasons. First, residual flexibilities are very small numbers, typically on the order of 1.0E-6 in/lb for translational diagonal terms, and orders of magnitude smaller for off-diagonal values. This poses difficulty in obtaining accurate and noise-free measurements, especially for points removed from the excitation source. A second difficulty encountered in residual measurements lies in obtaining a clean residual function in the process of subtracting synthesized modal data from a measured response function. Inaccuracies occur since modes are not subtracted exactly, but only to the accuracy of the curve fits for each mode; these errors are compounded with increasing distance from the excitation point. In this paper, the residual flexibility method is applied to a simple structure in both test and analysis. Measured and predicted residual functions are compared, and regions of poor data in the measured curves are described. It is found that for accurate residual measurements, frequency response functions having prominent stiffness lines in the acceleration/force format are needed. The lack of such stiffness lines increases measurement errors. Interface drive point frequency respose functions for shuttle orbiter payloads exhibit dominant stiffness lines, making the residual test approach a good candidate for payload modal tests when constrained tests are inappropriate. Difficulties in extracting a residual flexibility value from noisy test data are discussed. It is shown that use of a weighted second order least-squares curve fit of the measured residual function allows identification of residual flexibility that compares very well with predictions for the simple structure. This approach also provides an estimate of second order residual mass effects.

Tinker, Michael L.↗