Power input measurements in Lorentz force-driven turbulent flow - - PowerPoint PPT Presentation

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Power input measurements in Lorentz force-driven turbulent flow

Barbara E. Brawn & Daniel P. Lathrop

Institute for Research in Electronics and Applied Physics Department of Physics University of Maryland College Park

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Goals

u F

P

⋅

=

• measure local velocity in a flow driven by known Lorentz forces
• use velocity measurements to yield local power input

L

F J B ρ = ×

• correspondence to steady-state Fluctuation Theorem?

1 Pr( ) lim lnPr( ) P P P

τ

τ

→∞

= −

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Experimental Set Up

Cu Cu Cu Cu Na

Quadrupole Dipole

Electrode Configurations

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Dipole Quadrupole

• 1
• 0 .8
• 0 .6
• 0 .4
• 0 .2

0 .2 0 .4 0 .6 0 .8 1

• 2
• 1 .5
• 1
• 0 .5

0 .5 1 1 .5 2 x N o rm a liz e d F itte d F u n c tio n s , Q u a d ru p o le J (x ) (a m p s ) B (x ) (g a u s s ) F L (x ) (N e w to n s )

• 1
• 0 .8
• 0 .6
• 0 .4
• 0 .2

0 .2 0 .4 0 .6 0 .8 1 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2 2 . 2 2 . 4 2 . 6 x N o rm a liz e d F itte d F u n c tio n s , D ip o le J (x ) (a m p s ) B (x ) (g a u s s ) F L (x ) (N e w t o n s )

Lorentz Force

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Velocity Profiles

t B Field Vs Mean Velocity t

Dipole Quadrupole

x (cm) t (s) v (cm/s) mean velocity (cm/s)

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Power

Dipole 10 A 300 G Power vs. Pr (P) Probability Distribution P (W) Pr (P) Pr( -P) / Pr(P)

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Continuing Power Analysis

• 1

.8

.6

.4

.2 .2 .4 .6 .8 1

.0 1 .0 1 .0 2 .0 3 .0 4 .0 5 .0 6 x Power P (x ) D ip

• le

, 2 A m p s, 3 G a u s s

• 1

.8

.6

.4

.2 .2 .4 .6 .8 1

.0 1 .0 1 .0 2 .0 3 .0 4 .0 5 .0 6 .0 7 .0 8 x Power P (x ) D ip

• le

, 3 A m p s , 3 G a u s s

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Summary

• Turbulent flow from body force

Reynolds number Re=1.5104, where Re=(vmaxD)/ν (Na kinematic viscosity ν = 0.008 cm2/s) Schumacher and Eckhardt, PHYSICA D-NONLINEAR PHENOMENA 187 (1-4): 370-376 JAN 1 2004

• Fluctuation Theorem holds outside standard context

(local vs. global power) Mazonka and Jarzynski, ARXIV:COND-MAT/9912121 V1: 7 DEC 1999