Modeling the effect of viscosity on Modeling the effect of viscosity on melt layer losses during plasma melt layer losses during plasma

instabilitiesinstabilities

Walter Schostak

Center for Materials Under eXtreme Environment

School of Nuclear Engineering, Purdue University

CMUXE Seminar Series

August 3, 2011

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Outline Problem Introduction

Physics Model

Computational Model and OpenFOAM

Kelvin-Helmholtz Instability

Simulation Results

Summary

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J.PAMELA, V. PHILIPPS 18 (36) 17th PSI Conference, Hefei, China 22 May 2006

Tungsten plate in TEXTOR tokamakSergienko et al., Phys. Scr. T128 (2007) 81

Tungsten plate in QSPA and MK-200UG plasma gunsFederici et al., Journal of Nuclear Materials 337–339 (2005) 684

BackgroundBackground High erosion due to the loss of tungsten melt layer

Ablation physics of macroscopic material is the governing mechanism

The melt loss is due to plasma impact and/or Lorentz force

ELMs

10 pulses 60 pulses 80 pulses

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Melt Layer Motion and Splashing in TEXTORMelt Layer Motion and Splashing in TEXTOR

Coenen et al., Nucl. Fusion 51 (2011) 083008.

Tungsten melt layer spraying and splashing: fine spray of small droplets & melt splashes with large droplets

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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

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OpenFOAM A package of C++ libraries to facilitate Fluid Dynamics

CalculationsIncludes 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

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interFoam

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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

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Governing Equations The Navier-Stokes Equations:

•Mass Continuity•Momentum•Maxwell's Equations combined with Ohm’s Law:

•Combined form:

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Basic ParametersAll 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

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Challenges in ModelingA 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

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Results K-H Instability in the Air-Air Case

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

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Linear Stability Analysis of Inviscid and Viscous Linear Stability Analysis of Inviscid and Viscous Potential Plasma-Melt Flow Potential Plasma-Melt Flow

Miloshevsky & Hassanein, Nucl. Fusion 50 (2010) 115005; J. Nucl. Mater. (2010)

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Results K-H Instability in viscous plasma-tungsten case

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

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Results

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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