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Korean Modeling Effort : C2 Code J.M. Park NFRC/ORNL In collaboration with Sun Hee Kim, Ki Min Kim, Hyun-Sun Han, Sang Hee Hong Seoul National University presented at ITPA CDBM TG Meeting Princeton, NJ April 25, 2006

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The KSTAR main structures are almost completed. The significant progresses, especially on the manufacture and test of TF and PF superconducting magnets, have been achieved. (16 TF coils encased, 4 CS coils completed, 4 Large PF coilds ready for assembly) Machine assembly has to be finished by Aug. of 2007, then commisioning for integration will follow. If the SCMS are commisioned successfully, the first plasma shot is expected in June of 2998. KSTAR will open to the fusion research society not only domestically, but also internationally. Current Status of KSTAR Project

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Integrated Discharge Simulation Code for KSTAR

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1 Plasma continuity 2 Parallel momentum balance 3 Electron/Ion energy 4 Current continuity 5 Magnetic field diffusion C2 : Coupled 2-Dimensional Finite volume method pressure-correction 1 Finite volume method in unstructured multi-block grid 2 All-speed compressible pressure-correction algorithm Fully implicit 3 Fully implicit time advancing physics-base preconditioner 4 BiCGStab solver with physics-base preconditioner domain decomposition 5 Parallel computing: domain decomposition A 2-D multi-fluid model extending the previous formulations of 1-D core and 2-D edge/divertor transports: Valid not only in the collisional edge/divertor regions but also in the high temperature core region. A parallel transient 2-D numerical method * ExB drift * Diamagnetic drift

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C2 Equations Self-consistent ExB and diamagnetic drifts Parallel viscous force o local form with neoclassical viscosity coefficients valid in all collisional regimes, ij standard neoclassical expression if flux-surface averaged 1-D magnetic field diffusion equation (flux-surface averaged) Normalized poloidal velocity

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C2 Parallel Computation Sub-Domain Domain Decomposition Method with MPI

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Radial profile of electron & ion temperatures Benchmark with ASTRA* : Ohmic Discharge, I p = 2 MA * ASTRA : Automated System for Transport Analysis in a Tokamak (1.5-D core transport code) (C2 run with prescribed boundary conditions at core-edge interface) C2 Validation: Core Region Temperature evolution at magnetic axis

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Benchmark with B2SOLPS : T e = T i = 100 eV, n i = 2 x 10 19 m -3 (C2 run with prescribed boundary conditions at core-edge interface) C2 Validation: Edge/SOL Region C2 B2SOLPS C2 B2SOLPS C2 B2SOLPS C2

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C1 : Coupled 1-Dimensional Assume boundary T* Advance core transport equations with boundary condition T* Calculate q u * Advance Edge-SOL transport equations with boundary condition q u * Check T*=T** Next time step Calculate T** 1.5D transport Code with 1D SOL model

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Module Code Feature Remark NBI NUBEAM Monte-Carlo NTCC* NBEAMS Semi-Analytic NTCC SINBI Semi-Analytic SNU ICRF/FWCD TORIC Full wave IPP CURRAY Ray-tracing NTCC LH LSC Ray-tracing NTCC MHD EQ FEQ Free boundary/FDM SNU ROTEQ Fixed boundary/FEM SNU Transport MMM95 Multi-Mode Mode NTCC NCLASS Neoclassical Model NTCC ECCD TORAY** Ray-tracing NTCC ESC Fixed boundary/Moment NTCC ICRAY Ray-tracing NTCC FWCDSC Full wave SNU Neutral GTNEUT TEP NTCC NTRANS** Monte-Carlo SNU Integrated Computational Modules * NTCC : National Transport Code Collaboration Libraries (http://w3.pppl.gov/ntcc) ** Coupling algorithm under development

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Predictive Hybrid Scenario Modeling Pre-heating L-H transition Ip = 1.0 MA, B = 2.0 T, P NBI = 8MW, /n GW = 0.5 Current ramp-up rates of KSTAR superconducting coils are too slow to adopt a conventional fast ramp-up method. o Current ramp-up rate of KSTAR : ~ 0.5 MA/sec o Necessary NBI preheating power : ~ 4 MW at t = 0.5 sec unrealistic scenario for KSTAR

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Predictive Hybrid Scenario Modeling Pre-heating Off-axis current drive Ip = 1.0 MA, B = 2.0 T, P NBI = 8MW, P LH = 1.5 MW, /n GW = 0.5 The desired q-profiles can be obtained with the baseline heating and current drive systems of KSTAR by earlier central heating and subsequent off-axis current drive during the current rise phase. o Lower hybrid power for off-axis current drive : 1.5 MW o Necessary NBI preheating power : ~ 2 MW at t = 0.5 sec

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Electron temperature Te : keV Ion temperature Ti : keV Ion density n i Neutral density Log(n n ) x10 19 Self-consistent 2-D Profiles in the Entire Region of KSTAR B = 3.5 T, I p = 2 MA, = 5.0x10 19 m -3, P nbi = 6 MW

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1 2 3 12 3 Self-consistent 2-D Profiles in the Entire Region of KSTAR

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Edge Pedestal Temperature during ELMs (B = 3.5 T, I p = 2 MA, = 5.0x10 19 m -3, P nbi = 8 MW) Edge Pedestal Temperature T ped : Limited by ELM Temporal evolution of ion pedestal temperature during ELM Temporal evolution of radial ion temperature profile during ELM Simplified ELM model (Ballooning)

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Divertor Heat load during ELMs Rapid Emissions of Plasma Energy and Particles during ELM Large transient heat loads onto divertor plates Temporal evolution of maximum Heat flux onto outer divertor Temporal evolution of electron temperature

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A newly developed integrated simulation code C2 has been applied to predict high performance discharges of hybrid and standard H-mode scenario in the KSTAR tokamak. The simulations have focused on o finding optimum operation scenarios to establish and sustain a broad current profiles with q0 1. o estimating edge pedestal parameters and divertor heat load The desired q-profiles can be obtained with the baseline heating and current drive systems of KSTAR by earlier central heating and subsequent off-axis current drive during the current rise phase, although the current ramp-up rates of KSTAR superconducting coils are too slow to adopt a conventional fast ramp-up method. Both the temperatures at the top of the edge pedestal and divertor heat load are estimated self-consistently during ELMs in the main heating phase. Summary

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