Liquid metal flow under inhomogeneous magnetic

field O. Andreev, E. Votyakov,A. Thess, Y. Kolesnikov

TU Ilmenau, Germany

ElectromagneticBrake (EMBR)

magnet system

Main goal

1. Smooth meanvelocity profile

Avoid flow instability

Avoid sources of instability

2. Brake generated and introduced velocity fluctuations

Experimental setup

y

permanentmagnet

honeycomb

Plexiglas cover blocks

Bz magnetic field

Vivesprobe

potentialprobe

In- Ga -Sn

outletdiffuser

inletcontractor

N

S

lx

top viewly

side view

lx

N

S

30 mm

Permanent magnet

Channel: S = 210 cm L = 90 cm

Coordinate system

Liquid metal: GaInSn

General view of test-section

M-shape velocity profile

0,25

0,5

-105 -75 -45 -15 15 45 75 105

-50

-25

0

25

50

0,5

Y, mm

X, mm

zyx BjF ~

maxB

Bz

/jBV

Flow

0,25

B

Governing parameters

Reynolds number:

Re=U0H/ Re<15000

Hartmann number:

Ha=B0H(/)1/2 Ha=400

MHD interaction parameter:

N=Ha2/Re N>40

U0 < 35cm/s, B0=0.5T, H=2cm

Flow

x= - 106 mm - 29

0

20

0

0,01

0,02

0,03

0,05

0,06

0,07

0,08

-50 -40 -30 -20 -10 0 10 20 30 40 50

X, mm

0E

Ey

(b)

-0,5

0

0,5

1

2

2,5

3

3,5

-50 -40 -30 -20 -10 0 10 20 30 40 50 Y, mm

0EEy

(a)

Streamwise velocity in the middle plane of channel

potential velocimetry Re 4000

U

Streamwise velocity in the middle plane of channel

ultrasound velocimetry Re 4000magnet

flow

flow

Decay of velocity fluctuations under the external magnetic field

Mag

net

Flow

Re =4000I.

turbulence suppression

region

II.vorticalregion

III.wall jet region

u´/U0%

5.0

7.5

2.5

10

0-5 -2.5 0 2.5 7.55 10

on the axes

12.5

near walls

15

B

Accuracy of

potential velocimetryin the region of

inhomogeneousmagnetic field

is ?!

Principles of potential velocimetry

zy BUy

j

from

Ohm’s law

streamwisevelocity

z

y

z B

j

yBU

1

measurablevalues

physical

ERRORof the potential velocimetry

y

x

electrical current in the middle

plane

spanwiseJy

electricalcurrent

negative values of el.current

positivevalues of el.current

positivevalues of el.current

z

y

z B

j

yBU

1

overestimatedvalues of velocity

overestimatedvalues of velocityunder

estimatedvalues

directnumericalsimulation

byE. Votyakov,

E. Zienike

voltmeter

flow

potential difference between the side walls

dyjBBH

Qy

zz 11

flow rate through the channel integral estimation of

error

movable electrodes onthe side walls

0

0.5

1

1.5

2

2.5

3

3.5

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6x/H, dimensionless streamwise coordinate

Re=271640145312661179099207105051180413102Magnetic field

overestimatedvalues of flow rate

overestimatedvalues of flow rate

underestimated

valuesQB

H

z

flow

potentialdifference

flow rate

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

-50 -30 -10 10 30 50

X/H=0streamwise

velocity

0U

UDOP2000

potentialprobe

Comparison of ultrasound and potential velocimetry

flowRe 4000

0

0.5

1

1.5

2

2.5

3

3.5

4

-50 -30 -10 10 30 50

X/H=-3streamwise

velocity

0U

U

DOP2000

potentialprobe

Comparison of ultrasound and potential velocimetry

flowRe 4000

Vivesprobe

0

1

2

3

4

5

6

7

8

9

-50 -30 -10 10 30 50

X/H=2streamwise

velocity

0U

U

DOP2000

potentialprobe

Comparison of ultrasound and potential velocimetry

flowRe 4000

Vivesprobe

0

1

2

3

4

5

6

7

-50 -30 -10 10 30 50

X/H=6streamwise

velocity

0U

U

DOP2000

flowRe 4000

Vivesprobe

Comparison of ultrasound and potential velocimetry

potentialprobe

0

0.5

1

1.5

2

2.5

3

3.5

-50 -30 -10 10 30 50

X/H=8streamwise

velocity

0U

UDOP2000

flowRe 4000

Vivesprobe

Comparison of ultrasound and potential velocimetry

Summary remarks• The laboratory flow was investigated in the

following range of the governing parameters:

Ha = 400, Re<15000, N>10.

• Potential probe qualitatively reproduces velocity field within the region of two magnet gaps in streamwise direction.

• Vives probe is strongly influenced by the external electric potential and could be applied on the distance which exceeds 5-6 gaps of magnet.