Kansas Annual NSF EPSCoR Statewide ConferenceWichita, KS January 12-13, 2012

Simulation of pellet ablation in DIII-D

Tianshi Lu

Patrick Rinker

Department of MathematicsWichita State University

In collaboration with

Roman Samulyak, Stony Brook University

Paul Parks, General Atomics

Model for pellet ablation in tokamak

• MHD system at low ReM

• Explicit discretization• EOS for partially ionized gas• Free surface flow• System size ~ cm, grid size ~ 0.1 mm

Courtesy of Ravi Samtaney, PPPL

Tokamak (ITER) Fueling

• Fuel pellet ablation• Striation instabilities• Killer pellet / gas ball for

plasma disruption mitigation

Schematic of pellet ablation in a magnetic field

Schematic of processes in the ablation cloud

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1.Spherical model• Excellent agreement with NGS model

2.Axisymmetric pure hydro model• Geometric effect found to be minor (Reduction by 18% rather than 50%)

3.Plasma shielding without rotation• Subsonic ablation flow everywhere in the channel• Ablation rate depending on the ramp-up time

4.Cloud charging and rotation• Supersonic rotation causes wider channel and faster ablation• Ablation rate independent of the ramp-up time

Simulation results of pellet ablation

Spherical model Axis. hydro model Plasma shielding

Plasma shielding without rotation

Mach number distribution

Double transonic flow evolves to subsonic flow

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-.-.- tw = 5 s, ne = 1.6 1013 cm-3

___ tw = 10 s, ne = 1014 cm-3

----- tw = 10 s, ne = 1.6 1013 cm-3

Formation of the ablation channel and ablation rate strongly depends on plasma pedestal properties and pellet velocity.

Plasma shielding without rotation

Supersonic rotation of the ablation channel

Cloud charging and rotation

Isosurfaces of the rotational Mach number in the pellet ablation flow

Density redistribution in the ablation channel

Steady-state pressure distribution in the widened ablation channel

2TB

• Gsteady of a rotating cloud is independent of tramp

• G(tramp) < Gsteady

• G(tramp) increases with tramp

• Fast pellet

• Short ramp-up distance

Fixed pellet: effect of ramp up time

Shrinking pellet: tumbling pellet model

“Pancake” pellet

• Due to anisotropic heating, the pellet would evolve to a pancake shape.

• In reality, the pellet is tumbling as it enters the tokamak, so its shape remains approximately spherical.

• In the simulation, the pellet shrinking velocity is averaged over the surface to maintain the spherical shape.

Tumbling spherical pellet

Shrinking pellet: DIII-D temperature profile

DIII-D Temperature and Density Profile G from simulation agrees with 0.8 GNGS

Conclusions and future work

Conclusions

• Supersonic rotation causes wider channel and faster ablation• Good agreement with NGS model for DIII-D profile • Smaller Ablation rate during fast ramp-up

Future work

• Inclusion of grad-B drift in the simulation• Non-transient radial current for smaller B field – finite spin up• Mechanism of striation