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At least 163 records · Page 9

Verification of Anisotropic Mesh Adaptation for Complex Aerospace Applications

The stabilized finite element solver, FUN3D-SFE, along with the grid mechanics package refine are verified for aerospace applications of laminar and turbulent flow simulations. The current verification exercise represents an extension of previous research using FUN3D-SFEwith adjoint-based mesh adaptation to generate highly anisotropic adapted meshes for inviscid problems. Adaptations are performed using a solution-based approach that controls the Lpnorm of Mach number interpolation error and an adjoint-based approach that controls the error in some output functional. Adaptive results are shown for laminar subsonic flow over a delta wing, laminar subsonic flow over ONERA M6 wing, inviscid supersonic flow over a sonic boom test case, and a turbulent flow over a high lift configuration (JAXA Standard Model). Mesh convergence results are also compared with results from FUN3D-FV (Finite Volume) whenever available. For all test cases considered, FUN3D-SFE gives significantly better accurate results than FUN3D-FV on coarse meshes.

Aravind Balan↗

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

Berger, Marsha↗

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.

Park, Michael A.↗

Initial Atmospheric Transport of Particles

A new version of the Initial Atmospheric Transport (IAT) model has been developed. This report fully characterizes the new model. IAT is designed to model heat release into the atmosphere that contains contaminated particles. The heat release forms a buoyant puff or plume. Buoyancy is quickly dissipated in 10's to 100's of seconds through drag and entrainment of ambient air. The final location of contaminant particles in the atmosphere after dissipation of abnormal heat is an important input to long term transportation codes such as the National Oceanic and Atmospheric Administration's (NOAA) Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) code. Ultimately the settling of contaminants after long term transport provides a basis for estimating health consequences. In comparison to the old version, the new model includes explicit simulation of particles, newly formulated equations of motion for a rising puff, and a new plume model. The plume model releases many instances of a single puff along a single trajectory in a way that balances energy released over a longer period than would be appropriate for a single puff. The puff model has additions for vorticity, turbulence, virtual mass, drag, and entrainment. The particle model leads to direct interfacing between IAT and the long-term transport code HYSPLIT. Previously, particle locations were given a pattern based on IAT's puff trajectory with no particle simulation. Now, particles are explicitly simulated, and 3-D spatial distributions of particles are output based on final positions. Ballistic particles are thrown outward at high velocity from explosive events and tend to hit the ground before the end of the simulation. Non-ballistic particles tend to get pulled into the rising puff s ring of vorticity with some escaping to ambient conditions as buoyant energy dissipates. A new model verification and validation effort was made for the new plume model. The Wallops Island Solid Rocket Propellant (SRP) fire plume was extracted to a 3-D transient dataset. After calibration, the model performs better than previous single puff attempts. Even so, error levels in the process used to estimate location and ambient weather conditions approach 30%. This leads to the conclusion that unplanned photogrammetry evaluations of the IAT model are useful but not sufficiently accurate to quantify model parameters. Like previous attempts, the vertical motion entrainment parameters come out much too high in comparison to values for other studies in the literature. It is suspected that a new model of shear entrainment would alleviate this problem. Unfortunately, IAT already has more calibration parameters than the data comparisons thus far can resolve with statistical certainty. This underscores the need to verify and validate the IAT model using detailed CFD studies that allow ideal statistical comparison with the IAT model for hundreds of cases. Even so, validation by comparison to carefully planned experiments (i.e. with acceptable error levels) is also necessary because the dynamics of entrainment are at a sub-grid level for CFD. Though better validation and verification are most important, many new enhancements are still envisioned for future IAT development. These include particle rain out due to condensation and agglomeration of water, direct connection to the North American Mesoscale (NAM) weather dataset, dynamic weather conditions, including ambient particle entrainment into the puff, and detrainment at the puff to ambient mixing interface. In general, including detailed aerosol dynamics is the greatest coming challenge which will require an entire new sub-model in IAT. This is very important if contaminant particles change in such a way that they increase or decrease in their potential harm to the environment.

54 ENVIRONMENTAL SCIENCES↗

Advanced natural laminar flow airfoil with high lift to drag ratio

An experimental verification of a high performance natural laminar flow (NLF) airfoil for low speed and high Reynolds number applications was completed in the Langley Low Turbulence Pressure Tunnel (LTPT). Theoretical development allowed for the achievement of 0.70 chord laminar flow on both surfaces by the use of accelerated flow as long as tunnel turbulence did not cause upstream movement of transition with increasing chord Reynolds number. With such a rearward pressure recovery, a concave type deceleration was implemented. Two-dimensional theoretical analysis indicated that a minimum profile drag coefficient of 0.0026 was possible with the desired laminar flow at the design condition. With the three-foot chord two-dimensional model constructed for the LTPT experiment, a minimum profile drag coefficient of 0.0027 was measured at c sub l = 0.41 and Re sub c = 10 x 10 to the 6th power. The low drag bucket was shifted over a considerably large c sub l range by the use of the 12.5 percent chord trailing edge flap. A two-dimensional lift to drag ratio (L/D) was 245. Surprisingly high c sub l max values were obtained for an airfoil of this type. A 0.20 chort split flap with 60 deg deflection was also implemented to verify the airfoil's lift capabilities. A maximum lift coefficient of 2.70 was attained at Reynolds numbers of 3 and 6 million.

Viken, Jeffrey K.↗

Uncertainty Assessment of Hypersonic Aerothermodynamics Prediction Capability

The present paper provides the background of a focused effort to assess uncertainties in predictions of heat flux and pressure in hypersonic flight (airbreathing or atmospheric entry) using state-of-the-art aerothermodynamics codes. The assessment is performed for four mission relevant problems: (1) shock turbulent boundary layer interaction on a compression corner, (2) shock turbulent boundary layer interaction due a impinging shock, (3) high-mass Mars entry and aerocapture, and (4) high speed return to Earth. A validation based uncertainty assessment approach with reliance on subject matter expertise is used. A code verification exercise with code-to-code comparisons and comparisons against well established correlations is also included in this effort. A thorough review of the literature in search of validation experiments is performed, which identified a scarcity of ground based validation experiments at hypersonic conditions. In particular, a shortage of useable experimental data at flight like enthalpies and Reynolds numbers is found. The uncertainty was quantified using metrics that measured discrepancy between model predictions and experimental data. The discrepancy data is statistically analyzed and investigated for physics based trends in order to define a meaningful quantified uncertainty. The detailed uncertainty assessment of each mission relevant problem is found in the four companion papers.

Bose, Deepak↗

A multipurpose lifting-line flow solver for arbitrary wind energy concepts

Abstract. In this work, we extend the AeroDyn module of OpenFAST to support arbitrary collections of wings, rotors, and towers. The new standalone AeroDyn driver supports arbitrary motions of the lifting surfaces and complex turbulent inflows. Aerodynamics and inflow are assembled into one module that can be readily coupled with an elastic solver. We describe the features and updates necessary for the implementation of the new AeroDyn driver. We present different case studies of the driver to illustrate its application to concepts such as multirotors, kites, or vertical-axis wind turbines. We perform verification and validation of some of the new features using the following test cases: elliptical wings, horizontal-axis wind turbines, and 2D and 3D vertical-axis wind turbines. The wind turbine simulations are compared to existing tools and field measurements. We use this opportunity to describe some limitations of current models and to highlight areas that we think should be the focus of future research in wind turbine aerodynamics.

17 WIND ENERGY↗

Effects of rotation on coolant passage heat transfer. Volume 2: Coolant passages with trips normal and skewed to the flow

An experimental program was conducted to investigate heat transfer and pressure loss characteristics of rotating multipass passages, for configurations and dimensions typical of modem turbine blades. This experimental program is one part of the NASA Hot Section Technology (HOST) Initiative, which has as its overall objective the development and verification of improved analysis methods that will form the basis for a design system that will produce turbine components with improved durability. The objective of this program was the generation of a data base of heat transfer and pressure loss data required to develop heat transfer correlations and to assess computational fluid dynamic techniques for rotating coolant passages. The experimental work was broken down into two phases. Phase 1 consists of experiments conducted in a smooth wall large scale heat transfer model. A detailed discussion of these results was presented in volume 1 of a NASA Report. In Phase 2 the large scale model was modified to investigate the effects of skewed and normal passage turbulators. The results of Phase 2 along with comparison to Phase 1 is the subject of this Volume 2 NASA Report.

Johnson, B. V.↗

Thermal environment around the Space Shuttle with hot-gas jets for ice suppression

To prevent prelaunch ice formation on the external tank of the Space Shuttle, the final selected approach is to heat the surrounding air with vertical hot-gas jets located at the launch pad. This approach was considerably more cost-effective than other ice suppression methods considered, although its feasibility was not easily discernible due to the complex flowfield interactions. This paper describes how the use of vertical jets was first evaluated with the aid of a computational fluid dynamics (CFD) technique. An existing general-purpose CFD program (PHOENICS) was used to predict the thermal environment around the Shuttle under various jet configurations and wind conditions. The program accounts for effects of buoyancy, turbulence, and structural obstructions in the flowfield. The computed results showed physically plausible and consistent trends. The wind wake effects were found to be significant, and normally resulted in higher temperatures on the leeward side of the tank. High wind conditions were found to be more severe than calm wind conditions. The use of four jets with two different temperatures was identified as a promising option in which the air temperatures were raised sufficiently to prevent ice formation on the external tank, without excessive increase in Orbiter surface temperature. The use of the numerical model also facilitated the selection of test configurations and a test matrix for verifying the approach. Selected results of an experimental verification (by using a 2 percent scale model in a wind tunnel) are also presented.

Singhal, A. K.↗

Nek5000 developments in support of industry and the NRC

This year, the Nuclear Energy Advanced Modeling Simulation program (NEAMS) thermal-hydraulics verification and validation (V&V) work has focused in three areas of Nek5000 V&V-driven development. First, in a close collaborative effort with the U. S. Nuclear Regulatory Commission (NRC) staff, we have continued V&V efforts for the HYMERES-2 project using the OECD/NEA sponsored testing in the PSI PANDA facility. This year’s focus of ANL-NRC collaboration involves Nek5000 setups and validation for a range of problems relevant to and including the HYMERES-2 benchmark from PSI. The primary outcome of this year efforts is a more efficient geometry and inlet modeling simplification after a careful sensitivity study of the inlet profiles and pipe geometries. The resulting modeling choice of a short recycling/fully-developed turbulent inlet is within the experimental uncertainty estimate. This finding simplifies the next step of the cross-V&V HYMERES-2 project. In addition, the ANL team continue to provide assistance to the NRC staff in the form of Nek5000 application support in general and on the use of the HPC platforms of ALCF and INL in particular. This supports the NRC’s assessment of Nek5000 for use with the NRC Blue CRAB code suite. Second, we have implemented and tested more robust model of URANS, namely the k – τ model, a variant of the k-ω model, along with other improvements to RANS Nek5000 modeling in general. Because of its demonstrated robustness and stability, the k – τ model is the only RANS model that has been implemented in the new GPU version of the Nek5000 code, nekRS. Lastly, we report the initial implementation of Jacobian-free Newton Krylov approach to the direct Newton method for steady fluid solvers aimed at acceleration of RANS modeling and at IC improvement for LES campaigns. Also leveraging the Exascale Computing Project (ECP) ANL/CEED & SMR team’s software development effort to support NEAMS problems at large scale of the advanced computing architectures, NekRS, a GPU variant of Nek5000, built on top of kernels from libParanumal using OCCA for portability, has been successfully run on the full system of Summit (4608 nodes, 27648 GPUs).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multi-species collisions for delta-f gyrokinetic simulations: Implementation and verification with GENE

A multi-species linearized collision operator based on the model developed by Sugama et al. has been implemented in the nonlinear gyrokinetic code, GENE. Such a model conserves particles, momentum, and energy to machine precision, and is shown to have negative definite free energy dissipation characteristics, satisfying Boltzmann’s H-theorem, including for realistic mass ratio. Finite Larmor Radius (FLR) effects have also been implemented into the local version of the code. For the global version of the code, the collision operator has been developed to allow for block-structured velocity space grids, allowing for computationally tractable collisional global simulations. The validity of the collision operator has been demonstrated by relaxation and conservation tests, as well as appropriate benchmarks. The newly implemented operator shall be used in future simulations to study magnetically confined fusion plasma turbulence and transport in more extreme regions with higher collisionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multi-species collisions for delta-f gyrokinetic simulations: Implementation and verification with GENE

we report a multi-species linearized collision operator based on the model developed by Sugama et al. has been implemented in the nonlinear gyrokinetic code, GENE. Such a model conserves particles, momentum, and energy to machine precision, and is shown to have negative definite free energy dissipation characteristics, satisfying Boltzmann’s H-theorem, including for realistic mass ratio. Finite Larmor Radius (FLR) effects have also been implemented into the local version of the code. For the global version of the code, the collision operator has been developed to allow for block-structured velocity space grids, allowing for computationally tractable collisional global simulations. The validity of the collision operator has been demonstrated by relaxation and conservation tests, as well as appropriate benchmarks. The newly implemented operator shall be used in future simulations to study magnetically confined fusion plasma turbulence and transport in more extreme regions with higher collisionality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

CFD Code Validation of Wall Heat Fluxes for a G02/GH2 Single Element Combustor

This paper puts forth the case for the need for improved injector design tools to meet NASA s Vision for Space Exploration goals. Requirements for this improved tool are outlined and discussed. The potential for Computational Fluid Dynamics (CFD) to meet these requirements is noted along with its current shortcomings, especially relative to demonstrated solution accuracy. The concept of verification and validation is introduced as the primary process for building and quantifying the confidence necessary for CFD to be useful as an injector design tool. The verification and validation process is considered in the context of the Marshall Space Flight Center (MSFC) Combustion Devices CFD Simulation Capability Roadmap via the Simulation Readiness Level (SRL) concept. The portion of the validation process which demonstrates the ability of a CFD code to simulate heat fluxes to a rocket engine combustor wall is the focus of the current effort. The FDNS and Loci-CHEM codes are used to simulate a shear coaxial single element G02/GH2 injector experiment. The experiment was conducted a t a chamber pressure of 750 psia using hot propellants from preburners. A measured wall temperature profile is used as a boundary condition to facilitate the calculations. Converged solutions, obtained from both codes by using wall functions with the K-E turbulence model and integrating to the wall using Mentor s baseline turbulence model, are compared to the experimental data. The initial solutions from both codes revealed significant issues with the wall function implementation associated with the recirculation zone between the shear coaxial jet and the chamber wall. The FDNS solution with a corrected implementation shows marked improvement in overall character and level of comparison to the data. With the FDNS code, integrating to the wall with Mentor s baseline turbulence model actually produce a degraded solution when compared to the wall function solution with the K--E model. The Loci-CHEM solution, produced by integrating to the wall with Mentor s baseline turbulence model, matches both the heat flux rise rate in the near injector region and the peak heat flux level very well. However, it moderately over predicts the heat fluxes downstream of the reattachment point. The Loci-CHEM solution achieved by integrating to the wall with Mentor s baseline turbulence model was clearly superior to the other solutions produced in this effort.

Lin, Jeff↗

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗

Testing and Performance Verification of a High Bypass Ratio Turbofan Rotor in an Internal Flow Component Test Facility

A 1/5 scale model rotor representative of a current technology, high bypass ratio, turbofan engine was installed and tested in the W8 single-stage, high-speed, compressor test facility at NASA Glenn Research Center (GRC). The same fan rotor was tested previously in the GRC 9x15 Low Speed Wind Tunnel as a fan module consisting of the rotor and outlet guide vanes mounted in a flight-like nacelle. The W8 test verified that the aerodynamic performance and detailed flow field of the rotor as installed in W8 were representative of the wind tunnel fan module installation. Modifications to W8 were necessary to ensure that this internal flow facility would have a flow field at the test package that is representative of flow conditions in the wind tunnel installation. Inlet flow conditioning was designed and installed in W8 to lower the fan face turbulence intensity to less than 1.0 percent in order to better match the wind tunnel operating environment. Also, inlet bleed was added to thin the casing boundary layer to be more representative of a flight nacelle boundary layer. On the 100 percent speed operating line the fan pressure rise and mass flow rate agreed with the wind tunnel data to within 1 percent. Detailed hot film surveys of the inlet flow, inlet boundary layer and fan exit flow were compared to results from the wind tunnel. The effect of inlet casing boundary layer thickness on fan performance was quantified. Challenges and lessons learned from testing this high flow, low static pressure rise fan in an internal flow facility are discussed.

VanZante, Dale E.↗

Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

In this work, the saturation physics of ion temperature gradient (ITG) turbulence is probed by studying how amplitudes and scalings with key parameters vary across a hierarchy of reduced models. The models derive from nonlinear fluid equations for toroidal ITG turbulence under approximations to the mode coupling interactions in wavenumber space and the representation of turbulent decorrelation. Mode coupling approximations include local-in-wavenumber treatments like the spectral density of flux in quasilinear theory, a truncation to three nonlinearly interacting waves, and the interactions in a cascade to high radial wavenumber mediated by a single zonal flow. Turbulent decorrelation treatments are based on the triplet correlation time with and without eddy damping. Model fidelity is assessed by the scalings and magnitudes of the squared amplitudes of unstable mode, stable mode, and zonal flow with respect to the flow-damping rate and temperature gradient. It is shown that all models reproduce fundamental scalings, provided they incorporate the coupling of unstable mode, stable mode, and zonal flow. Accurate amplitude prediction requires eddy damping in the triplet correlation time and proper representation of the zonal-flow drive by interactions associated with the radial wavenumber cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Observations on CFD Verification and Validation from the AIAA Drag Prediction Workshops

The authors provide observations from the AIAA Drag Prediction Workshops that have spanned over a decade and from a recent validation experiment at NASA Langley. These workshops provide an assessment of the predictive capability of forces and moments, focused on drag, for transonic transports. It is very difficult to manage the consistency of results in a workshop setting to perform verification and validation at the scientific level, but it may be sufficient to assess it at the level of practice. Observations thus far: 1) due to simplifications in the workshop test cases, wind tunnel data are not necessarily the “correct” results that CFD should match, 2) an average of core CFD data are not necessarily a better estimate of the true solution as it is merely an average of other solutions and has many coupled sources of variation, 3) outlier solutions should be investigated and understood, and 4) the DPW series does not have the systematic build up and definition on both the computational and experimental side that is required for detailed verification and validation. Several observations regarding the importance of the grid, effects of physical modeling, benefits of open forums, and guidance for validation experiments are discussed. The increased variation in results when predicting regions of flow separation and increased variation due to interaction effects, e.g., fuselage and horizontal tail, point out the need for validation data sets for these important flow phenomena. Experiences with a recent validation experiment at NASA Langley are included to provide guidance on validation experiments.

Computational Fluid Dynamics↗

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗