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

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

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

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) 083008. 4

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

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

interFoam 7

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

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

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

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

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 = +50 m/s -Phase 2 Velocity = -50 m/s 12

Linear Stability Analysis of Inviscid and Viscous Potential Plasma-Melt Flow Miloshevsky & Hassanein, Nucl. Fusion 50 (2010) 115005; J. Nucl. Mater. (2010) 13

Results K-H Instability in viscous plasma-tungsten case -Phase 1: Parameters: -Phase 1: -Viscosity = 7e-3 Pa s -Density = 17600 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

Results

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