Digital image processing 1
Liquid metal
sodium hydroxide
mirror (upper surface)
free surface
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Small surface waves 1
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Dynamics of the free surface 1Spectrum of different wavelengths
(gravity, capillary)Amplitudes increase upon increasing I0a = 3 mm,
H = 24 mm, L = 17 mm, f = 21.9 kHz, I = 120 A
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Static surface deformation 1
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Dynamics of the free surface 2a = 3 mm, H = 24 mm, L = 17 mm, f
= 21.9 kHz, I = 127 AWavelength corresponding to skin depth: 1 ~ 2p
d
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Pinch
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a = 3 mm, H = 24 mm, L = 17 mm, f = 47.2 kHz, I = 123 A Pinch
development
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Magnetohydrodynamics 2003Theoretical ModelHele Shaw
approximationSkin depth approximationKarcher, MohringCartesian
geometry2dLiquid metalr,u,sHLxy,vh(y,t)zI coswtnz,wpa, pMI
coswtpgLorentz force:j, B from vector potentials Ai, Aamagnetic
pressure:
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governing equationsboundary conditions
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evolution equationMost dangerous modeNeutral instability
HPhysical interpretationConclusionsLinear stabilty analysis for
basic state
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Measurement vs. theorya = 3 mm, H = 30 mm
Tabelle1
a in mmH in mmL in mmf in HzIkrit in AIkritneu
1241721500100
124172410097
124172770093
124173360088
124174620084
1242221200112
1242223600110
1242227100106
1242233000102
124224540095
3241721900130
3241724400129
3241728100128
3241734100125
3241747200123
3301222552108.32
3301225160104.3
3301228933103.38
3301235093101.81
330124829099.71
33014.522182115.85
33014.524750113.81
33014.528416113.25
33014.534503110.73
33014.547490107.94
3301721870125.44
3301724405122.93
3301728045121.08
3301734043118.34
3301746877115.44
33019.521594136.11
33019.524084132.48
33019.527696130.17
33019.533598128.17
33019.546258125.46
3302221370146.04
3302223859141.51
3302227418139.91
3302233273137.18
3302245826133.67
3202221423152
3202223893149
3202227480146
3202233359143
3202245943140
322.52221418149.35
322.52223893146.78
322.52227468144
322.52233325142.27
322.52245884138.76
3252221380147.6
3252223851145.93
3252227419143.74
3252233291140.58
3252245800138.74
327.52221405143.53
327.52223885140.45
327.52227421138.72
327.52233313136.05
327.52245878133.3
3302221387142.68
3302223875140.36
3302227410139.41
3302233289136.23
3302245830133.39
332.52221336142.76
332.52223807140.66
332.52227362139.87
332.52233194136.5
332.52245721133.3
6241722000186
6241724500184
6241728200181
6241734200178
6241747000175
6242221500213214.6500155328262.2034508866
6242223900204209.987056653255.1029058274
6242227500200204.1277414349246.2364185535
6242233400194196.3210729988234.521896047
6242246000183.997302295216.266408157
10241722400240
10241725000227
10241728800220
10241735000210
10241748400200
I(f) Par. a
100130186240
97129184227
93128181220
88125178210
84123175200
Frequenz in Hz
Strom in A
Pincheffekt: Induktorstrom in Abhngigkeit der Frequenz f. a = 3
mm. Parameter: Flssigkeitshhe H, Koppelspalt L
I(f) Par. H
152149.35147.6143.53142.68142.76
149146.78145.93140.45140.36140.66
146144143.74138.72139.41139.87
143142.27140.58136.05136.23136.5
140138.76138.74133.3133.39133.3
I(f) Par. L
108.32115.85125.44136.11146.04
104.3113.81122.93132.48141.51
103.38113.25121.08130.17139.91
101.81110.73118.34128.17137.18
99.71107.94115.44125.46133.67
Tabelle2
L in mmH in mmmf in Hza in mmI in A
172425000195.8239905885
1724250003128.7296656531
1724250006183.4241656549
17242500010229.3763818669
172430000191.8502726113
1724300003126.9790664132
1724300006180.7385482068
17243000010220.1491846731
172435000188.6193806341
1724350003125.517541966
1724350006178.4985917706
17243500010212.6378950077
172440000185.9126630435
1724400003124.2651162876
1724400006176.5807046988
17244000010206.3387892624
172445000183.593873595
1724450003123.1707755926
1724450006174.906120326
17244500010200.9376551059
I(a) Par. f
95.823990588591.850272611388.619380634185.912663043583.593873595
128.7296656531126.9790664132125.517541966124.2651162876123.1707755926
183.4241656549180.7385482068178.4985917706176.5807046988174.906120326
229.3763818669220.1491846731212.6378950077206.3387892624200.9376551059
f = 25000 Hz
f = 30000 Hz
f = 35000 Hz
f = 40000 Hz
f = 45000 Hz
Spaltbreite a in mm
Induktorstrom in A
Pincheffekt: Induktorstrom in Abhngigkeit der Spaltbreite. H =
24 mm, L = 17 mm.Parameter: Frequenz f
Tabelle3
a in mmL in mmf in HzH in mmH/deltaI in A
32225000209.629356884148.4168833694
3222500022.510.8330264945146.3569290731
322250002512.036696105145.2163247187
3222500027.513.2403657155140.4148326931
322250003014.444035326140.2074435116
3222500032.515.6477049365140.5460537647
322300002010.5484319593145.5867220948
3223000022.511.8669859542143.9067300537
322300002513.1855399491143.0275314831
3223000027.514.504093944138.0590775177
322300003015.822647939138.0010218505
3223000032.517.1412019339138.2763065617
322350002011.3936087172143.2360008352
3223500022.512.8178098068141.8671460989
322350002514.2420108965141.2026917062
3223500027.515.6662119861136.0981761032
322350003017.0904130758136.1626300748
3223500032.518.5146141654136.3858838389
322400002012.1802800625141.2304156784
3224000022.513.7028150703140.1237585626
322400002515.2253500781139.6407737069
3224000027.516.7478850859134.4220927526
322400003018.2704200937134.5899501068
3224000032.519.7929551015134.7692283084
322450002012.9191379434139.4846866035
3224500022.514.5340301863138.6037735744
322450002516.1489224292138.2774115642
3224500027.517.7638146721132.960824137
322450003019.3787069151133.2178323222
3224500032.520.993599158133.3591507993
I(H) Par. f
148.4168833694145.5867220948143.2360008352141.2304156784139.4846866035
146.3569290731143.9067300537141.8671460989140.1237585626138.6037735744
145.2163247187143.0275314831141.2026917062139.6407737069138.2774115642
140.4148326931138.0590775177136.0981761032134.4220927526132.960824137
140.2074435116138.0010218505136.1626300748134.5899501068133.2178323222
140.5460537647138.2763065617136.3858838389134.7692283084133.3591507993
f = 25000 Hz
f = 30000 Hz
f = 35000 Hz
f = 40000 Hz
f = 45000 Hz
Flssigkeitshhe H in mm
Induktorstrom in A
Pincheffekt: Induktorstrom in Abhngigkeit der Flssigkeitshhe H.
a = 3 mm, L = 22 mm.Parameter: Frequenz f
I(H_delta)
148.4168833694
146.3569290731
145.2163247187
140.4148326931
140.2074435116
140.5460537647
145.5867220948
143.9067300537
143.0275314831
138.0590775177
138.0010218505
138.2763065617
143.2360008352
141.8671460989
141.2026917062
136.0981761032
136.1626300748
136.3858838389
141.2304156784
140.1237585626
139.6407737069
134.4220927526
134.5899501068
134.7692283084
139.4846866035
138.6037735744
138.2774115642
132.960824137
133.2178323222
133.3591507993
Tabelle4
a in mmH in mmf in HzL in mmI in A
3302500012105.5304466597
3302500014.5114.2432493064
3302500017122.8851406254
3302500019.5132.5457788487
3302500022141.947091978
3303000012103.7032131772
3303000014.5112.3798371489
3303000017120.5220660896
3303000019.5130.1558261248
3303000022139.2022285868
3303500012102.1830144608
3303500014.5110.8280770567
3303500017118.5596026222
3303500019.5128.1688015575
3303500022136.922930977
3304000012100.884183164
3304000014.5109.5012115563
3304000017116.8854875377
3304000019.5126.4720992182
3304000022134.9787026406
330450001299.7522430979
3304500014.5108.3440252948
3304500017115.4284460458
3304500019.5124.9941551417
3304500022133.2866996526
I(L) Par. f
105.5304466597103.7032131772102.1830144608100.88418316499.7522430979
114.2432493064112.3798371489110.8280770567109.5012115563108.3440252948
122.8851406254120.5220660896118.5596026222116.8854875377115.4284460458
132.5457788487130.1558261248128.1688015575126.4720992182124.9941551417
141.947091978139.2022285868136.922930977134.9787026406133.2866996526
f = 25000 Hz
f = 30000 Hz
f = 35000 Hz
f = 40000 Hz
f = 45000 Hz
Coupling gap in mm
Inductor current in A
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ConclusionsElectromagnetic shaping with high-frequency magnetic
fields Squeezing of drops up to 15% possible Onset of drop
instabilities; critical parameters depending on drop volume and
inductor current frequeny3 Types of surface instabilities: small
surface waves, large-amplitude static deformation, electromagnetic
pinch First instability well-predicted by simple model based on
Hele Shaw and skin depth approximation High-frequency fields not
suited for sealing purposesAcknoledgementsDFG: Research Group
MagnetofluiddynamicsDAAD: PROCOPE program with EPM Grenoble
(Professor Yves Fautrelle)
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Proposal for Collaboration ILorentz force velocimetry (Thess,
Kolesnikov, Karcher: Patent 2005) BMBF project; start
01.07.2006Measurement of mass flow in liquid aluminum, steel,
glass, semiconductor melts
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Proposal for Collaboration II
