Observations of Thermo-Electric MHD Driven Flows in the SLiDE Apparatus

Transcription

1 Observations of Thermo-Electric MHD Driven Flows in the SLiDE Apparatus M.A. Jaworski, Wenyu Xu, M. Antonelli, J.J. Kim, M.B. Lee, V. Surla and D.N. Ruzic Department of Nuclear, Plasma and Radiological Engineering University of Illinois at Urbana-Champaign Correspondence:

2 Introduction SLiDE experiment overview (1 viewgraph) Apparatus (6) Electron beam system Tray diagnostic system Flow observation Theory: Thermocapillary and thermoelectric flows (1) Experimental Results: thermoelectric flow observation (5) Qualitative tests Quantitative results Discussion: Potential uses for TEMHD (1) Conclusions (1)

3 Solid/Liquid Lithium Divertor Experiment Developed to explore passive lithium flows under applied heat fluxes CDX-U electron beam results motivated facility Examine thermocapillary (a.k.a. Marangonic) convection with MHD damping Three main elements An external magnetic field An internal electron beam which is guided along the field A tray which contains the lithium and provides cooling Future iterations will tilt the field with respect to the vertical axis

4 Electron Beam Design Designed to mimic current fusion experiment divertors Peak heat flux, q0 Heat flux gradient, dq/dx Line stripe heat flux (straightened out radial SOL profile) Obtained Range of dq/dx MW/m2-m Developed from Pierce geometry Beam transport and electrodes modeled in 3D (FieldP) Engineering drawings made with Pro/E Fabricated with local machine shop

5 Electron Beam Performance Electron beam characterized with two methods Faraday cup at low power levels to measure Gaussian profile Beam Visualization Tool (BVT) at higher power levels to measure stripe length Heat flux results summarized in table Current distribution with 542 [G] external magnet current. Similar to divertor peak heat fluxes and heat flux gradients Values continuously variable beneath maximum value by changing input power Power supply and hardware capable of 15,000W input power ~300W utilized for these tests only

6 Tray System Tray system provides active cooling Sandwich thermocouple sensor design utilized Enables steady-state operation Additional measure of incident beam power (lower bound) Air and water cooling enables wide range of input power with liquid lithium temperatures Coolant system overview (water). Air cooling includes additional measurements for moisture content. Multiple plates stacked together Thermocouples inserted and cemented into place Stainless steel used initially Cost effective and higher signal levels Trade-off is a limitation on maximum power before excessive temperatures reached Diagram of local heat flux sensor.

7 Tray Calibration Tray system calibrated with simple test rig External electric resistance heater Well insulated Both water and air cooling Calibration results Single thermal resistance loss to environment brings entire data set into line Heat flux sensors individually calibrated to account for assembly variations Equivalent distances to interface calibrated on an individual bases as well Raw calorimetric measurements system in insulated test rig. of Example calibration curve for embedded heat flux sensor.

8 Lithium Containment System Several design iterations tested Original system had welded walls for buckling rigidity too rigid with buckling of the interior plate Second design utilized floating walls on tungsten wetting barriers lack of heat shield or beam blocks led to failure of shim-stock joiner, though the wetting barriers worked Third design current used without incident Third tray design iteration. Welded tray walls replaced with floating design for strain relief. Version 2.0 notes: Segmented tray design adopted due to fabrication concerns Buckling remains a problem and a monolithic system may be necessary Image of tray during fabrication.

9 Flow Observation Webcam or high-definition hand-held camera provide flow observation Electron beam blocks direct line-of-sight Mirror provides view around the obstruction Webcam allows real-time monitoring when HD camera not in use Webcam or other system diagram. optical observation Example image shown at right Mirror and tray outlined Lighting provided by electron beam filaments Webcam live image from chamber interior.

10 Theory: TCMHD and TEMHD Thermocapillary and TEMHD produce different flow patterns TC forces act parallel to surface gradients in surface tension force vectors radiate away from heat stripe (induce poloidal flow) TEMHD forces are produced in the bulk lithium due to gradients at the lithium-steel interface TE current the same process as produces voltages in thermocouple junctions Cross-product of J and B results in TEMHD azimuthal flow Beam generated forces (JxB) also result in an azimuthal flow (current converges into impact point) sense of rotation is opposite of TEMHD Thermocapillary force vectors. Increased field damps both flows TCMHD is damped by B-2 TEMHD is damped as B-1 at high fields (due to thermoelectric propulsive force) Math available on request but neglected here due to time constraints TEMHD current diagram.

11 Results: Azimuthal Flow No strong poloidal flows observed Azimuthal flows observed at small to large fields (60 800[G]) Some initial experiments to establish TE effect Flow reverses when magnetic field is reversed Flow direction is consistent with the TE effect, counter the sense of beam generated forces Placing a quartz insulated between Li and steel stops rotation (and all observed flow) Movie of swirling flow 40AmpSS.mov

12 Qualitative test: Spin Down Tests Test based on the time required for the lithium to come to a stop Viscous damping brings fluid to a rest without additional forces to maintain flow (seconds) Magnetic fields enhance the destruction of kinetic energy and spin down faster (confirmed with a mercury test) If thermoelectric currents exist, these will decay at the thermal time constant of the lithium-tray system (minutes) Maintaining the magnetic field will sustain the flow, as opposed to damping it Turning magnetic field back on after a viscous spin-down should induce motion once more Test procedure: 1.Obtain steady thermal conditions and lithium flow 2.Shut off beam and magnetic field and measure spin-down time 3.Return system to steady thermal conditions and lithium flow 4.Shut off beam but maintain magnetic field measure spin-down time 5.Repeat step 2, but turn magnetic field back on after flow comes to rest and look for spin startup Movie of spin-down test spindown.mov

13 Quantitative Analysis: Velocity Goal: combine measured velocity with measured tray temperatures to test TEMHD flow prediction Velocity taken from frameanalysis of movies Individual particle measured over several frames More frames with a single particle reduce error Several particles from any given case obtained (usually about 5) Radial distance from flow center also measured

14 Heat Flux Measurements: Thermal Transport Tray heat fluxes found to have radial distribution Azimuthal flow velocity creates a large Peclet number in this direction Pe>>1 is convection dominated transport Smears out line stripe, Gaussian heat flux New profile varies as ~arcsin( 2.5 a0 r-1 ) Negligible flow in the poloidal direction means conduction dominates Heat fluxes for 540[G], 1.5[cm] Lithium with 350 [W] input power. Problem modeled in OpenFOAM with axisymmetric, pure conduction energy transport Tray warping increased error from original calibration (eliminated some sensors) making more quantitative comparison impossible at present OpenFOAM conduction model.

15 Interface Temperature Reconstruction Measured power fluxes used to reconstruct interface temperature Used alongside calibration for equivalent distance to interface for each individual thermocouple Linear extrapolation applied from measured temperature at a given point Parabolic curve fitted to resulting data Heat fluxes for 540[G], 1.5[cm] Lithium with 350 [W] input power. Best fit of data used to calculate interface temperature gradient Schematic diagram of sensor locations

16 Quantitative Prediction Moderate Hartmann number regime TEMHD and MHD braking in equilibrium Dependent on thermoelectric power of the metal pair, P Temperature gradient along the interface determines flow velocity (for Ha > 1) Mean current density due to TE currents depends on geometry and conductivities (C variable) 1D current driven flow in a semi-infinite domain. Velocity prediction can be converted to Reynolds number using depth as the characteristic length scale

17 Quantitative Comparison Flow rate predicted based on temperature gradients Field Strength [G] 271 Depth [m] Hartmann U U [-] predicted measured [cm/s] [cm/s] / Largest source of error is due to tray warping Indicates the torque due to TEMHD is nearly balanced by MHD drag for Ha >> 1 (as opposed to viscous recirculation) Data exists for Ha <10, but is still being processed

18 Discussion: Utilizing TEMHD Pumping Passive pumping system Thin porous layer could hold lithium TEMHD currents exist within walls of porous structure Primary heat flux gradient into the material would drive a radial flow Pore size can be optimized for a given magnetic environment Flow velocities of 10s of cm/s possible for steady replenishment TEMHD pumping through a porous material. Lithium-Vanadium system with 10MW/m2. Secondary heat flux gradient (in the radial direction) would produce forces in the vertical direction Ejection from the foam dependent on net body forces and capillary action No solid answers, but potential

19 Summary SLiDE apparatus constructed and fully operational Results demonstrate the ability of thermoelectric currents to propel liquid lithium under moderate heat loads ~0.7 MW/m2 peak heat flux ~180 MW/m2-m peak heat flux gradient Reasonable quantitative agreement obtained with measured velocities and internal thermocouple measurements Sources of error in the experiment identified and remedies suggested (tray redesign) TEMHD pumping provides new possibilities for liquid metal control and transport within a fusion machine

20 Thank you Questions?