Korean Modeling Effort : C2 Code

transcript

J.M. ParkNFRC/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

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

Integrated Discharge Simulation Code for KSTAR

Neutral- GTNEUT- NTRANS

LHCD- LSC

NBI- NUBEAM- NBEAMS- SNBI

ICRH- TORIC- CURRAY

MHD Eq- ESC- ROTEQ - FEQ

Transport- MMM95- GLF23- IFS/PPPL- NCLASS

EdgeTurbulence

- ETB3D*

EdgeTurbulence

- ETB3D*

ELM- Ballooning

Coupled Core-Edge-SOL2-D Transport Code

C2 (Coupled 2-D)*

Coupled Core-Edge-SOL2-D Transport Code

C2 (Coupled 2-D)*

1 Plasma continuity2 Parallel momentum balance 3 Electron/Ion energy4 Current continuity5 Magnetic field diffusion

C2 : Coupled 2-Dimensional

1 Finite volume methodFinite volume method in unstructured multi-block grid2 All-speed compressible pressure-correctionpressure-correction algorithm3 Fully implicitFully implicit time advancing4 BiCGStab solver with physics-base preconditionerphysics-base preconditioner5 Parallel computing: domain decompositiondomain 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

C2 Equations

Self-consistent ExB and diamagnetic drifts

Parallel viscous forceo local form

with neoclassical viscosity coefficients valid in all collisional regimes, ij

standard neoclassical expression if flux-surface averaged

211 12

3/ 2 1// // //2

3B B u V

1-D magnetic field diffusion equation (flux-surface averaged)

3/ 2 2// // //2

3 5 5 ii

B B q pVB p

Normalized minor radius0.1 0.2 0.3 0.4 0.5-5000

C2NCLASS

Normalized poloidal velocity

C2 Parallel Computation

Sub-Domain

Domain Decomposition Method with MPI

Number of Processor

0 5 10 15 20 250

Minor radius (m)

0 0.1 0.2 0.3 0.4 0.5 0.60

broken line : ASTRAsolid line : C2

Radial profile of electron & ion temperatures

Benchmark with ASTRA* : Ohmic Discharge, Ip = 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

Time (sec)

0 0.5 1 1.5 20

broken line : ASTRAsolid line : C2

Temperature evolution at magnetic axis

Benchmark with B2SOLPS : Te = Ti = 100 eV, ni = 2 x 10 19 m-3

(C2 run with prescribed boundary conditions at core-edge interface)

C2 Validation: Edge/SOL Region

B2SOLPS

C1 : Coupled 1-Dimensional

SOL Region

Core Region

divertor

X-point

midplane

SOL Region

Core Region

divertor

X-point

midplane

MidplaneX-point

DivertorPlate

Heat Source Region

MidplaneX-point

DivertorPlate

Heat Source Region

Assume boundary T*

Advance core transport equations with boundary condition T*

Calculate qu*

Advance Edge-SOL transport equationswith boundary condition qu*

Check T*=T**

Next time step

Calculate T**

1.5D transport Code with 1D SOL model

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

0 1 2 3 4 5 60

<n>/nGW

0 1 2 3 4 5 60

PNBI/4

0 1 2 3 4 5 60

Predictive Hybrid Scenario Modeling

Pre-heating L-H transition

Ip = 1.0 MA, B = 2.0 T, PNBI = 8MW, <n>/nGW = 0.5

0 1 2 3 4 5 60

<n>/nGW

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/seco Necessary NBI preheating power : ~ 4 MW at t = 0.5 sec unrealistic scenario for KSTAR

Predictive Hybrid Scenario Modeling

Pre-heatingOff-axis current drive

Ip = 1.0 MA, B = 2.0 T, PNBI = 8MW, PLH = 1.5 MW, <n>/nGW = 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 MWo Necessary NBI preheating power : ~ 2 MW at t = 0.5 sec

0 1 2 3 4 5 60

PNBI/4

0 1 2 3 4 5 60

<n>/nGW

0 1 2 3 4 5 60

<n>/nGW

1 1.5 2 2.5-1.5

400 eVContour spacing 500 eV

100 eV

Electron temperatureTe : keV

1 1.5 2 2.5-1.5

400 eVContour spacing 500 eV

50 eV75 eV

125 eV100 eV

Ion temperatureTi : keV

Ion densityni

Neutral densityLog(nn)

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

B = 3.5 T, Ip = 2 MA, <n> = 5.0x1019 m-3, Pnbi = 6 MW

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

Edge Pedestal Temperature during ELMs

minor radius (m)Io

2 2.1 2.2 2.3

Time (sec)

0.2 0.4 0.6 0.8 1

H-mode transition

Pedestaltemperature

(B = 3.5 T, Ip = 2 MA, <n> = 5.0x1019 m-3, Pnbi = 8 MW)

Edge Pedestal Temperature Tped : Limited by ELM

Temporal evolution of ion pedestal temperature during ELM

Temporal evolution of radial ion temperature profile during ELM

Simplified ELM model (Ballooning)

Divertor Heat load during ELMs

Time (sec)

0.2 0.4 0.6 0.8 1

rRapid Emissions of Plasma Energy and Particles during ELM

1 1.5 2-1.4

189168147126105846342210

Large transient heat loads onto divertor plates

Temporal evolution of maximumHeat flux onto outer divertor

Temporal evolution of electrontemperature

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 ono 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

Korean Modeling Effort : C2 Code

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