1. Modeling the effect of viscosity on melt layer losses during plasma instabilities
Walter Schostak
Center for Materials Under eXtreme Environment
School of Nuclear Engineering, Purdue University
CMUXE Seminar Series
August 3, 2011 1

2. Outline Problem Introduction Physics Model
Computational Model and OpenFOAM
Kelvin-Helmholtz Instability
Simulation Results
Summary 2

3. Background High erosion due to the loss of tungsten melt layer
Ablation physics of macroscopic material is the governing mechanism
Tungsten plate in TEXTOR tokamak
Sergienko et al., Phys. Scr. T128 (2007) 81
ELMs
J.PAMELA, V. PHILIPPS 18 (36) 17th PSI Conference, Hefei, China 22 May 2006
10 pulses
60 pulses
80 pulses
The melt loss is due to plasma impact and/or Lorentz force
Tungsten plate in QSPA and MK-200UG plasma guns
Federici et al., Journal of Nuclear Materials 337–339 (2005) 684 3 3

4. Melt Layer Motion and Splashing in TEXTOR
Tungsten melt layer spraying and splashing: fine spray of small droplets & melt splashes with large droplets
Coenen et al., Nucl. Fusion 51 (2011) 4

5. The Problem
My research has been on creating a comprehensive computational model to accurately predict the development and effect of these instabilities
With an accurate model, changes can be made to the reactor system to prevent or reduce the effect of this splashing 5

6. OpenFOAM
A package of C++ libraries to facilitate Fluid Dynamics Calculations
Includes over 80 different solvers to do a wide range of CFD problems
Electromagnetics
Thermodynamics
Combustion
VOF
Designed so that users can take advantage of the libraries and create their own niche solvers.
Able to do implicit and explicit calculations depending on the circumstance 6

7. interFoam 7

8. VofmhdFOAM
Custom built solver that combines the functionality of interFoam (a VOF solver) and mhdFoam (a MHD solver)
Based on the functionality of interFoam
Calculates weighted averages of properties based on the phase fraction 
Includes the effects of viscosity 8

9. Governing Equations The Navier-Stokes Equations: Mass Continuity
Momentum
Maxwell's Equations combined with Ohm’s Law:
Combined form: 9

10. Basic Parameters All of the test cases are over a uniform domain
Cyclic boundaries on the left and right
Open top
Solid bottom
Initially a sinusodial perturbation is impressed on the fluid interface 10

11. Challenges in Modeling
A very high resolution mesh is needed to show the minute structures that develop
Prominences rising out of the tungsten
Splashing of the tungsten melt
With such a large difference between the properties of plasma and the properties of tungsten a lot of time is needed to make the calculations.
Simply getting time on Steele and Blacklight is challenging, the queues are very long 11

12. Results K-H Instability in the Air-Air Case -Density = 1.25 kg/m^3
Parameters:
-Density = 1.25 kg/m^3
-Viscosity = 1.73e-5 Pa s
-Phase 1 Velocity = m/s
-Phase 2 Velocity = -50 m/s 12

13. Linear Stability Analysis of Inviscid and Viscous Potential Plasma-Melt Flow
Miloshevsky & Hassanein, Nucl. Fusion 50 (2010) ; J. Nucl. Mater. (2010) 13

14. Results K-H Instability in viscous plasma-tungsten case -Phase 1:
Parameters:
-Phase 1:
-Viscosity = 7e-3 Pa s
-Density = kg/m^3
-Velocity = +1m/s
-Phase 2:
-Viscosity = 5e-5 Pa s
-Density = 10e-6 kg/m^3
-Velocity = +10e5 m/s
Surface Tension = 2.5 kg/s^2 14

15. Results

16. Conclusions
Control and understanding of plasma instabilities are critical in successful operations of magnetic fusion energy systems
Melt layer losses during various instabilities can significantly reduce reactor lifetime
It is clear that viscosity has a large and important effect on these systems
Other factors include the magnetic field, reactor design, properties of the plasma and metals, etc.
More research needs to be done into what happens at longer time scale and the overall losses of melt layers of metallic components due to various forces and the interaction of these forces during instabilities 16