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LICOR - Liquid Columns' Resonances

WL-FPM-LICOR

D. L a n g b e i n , ZARM B r e m e n , G e r m a n y F. Falk, IPHT J e n a , G e r m a n y R, Grofibach, tecS S t e i n b a c h , G e r m a n y

W. H e i d e , ANTEC Kelkheim, G e r m a n y H. B a u e r , B u n d e s w e h r u n i v e r s i t d t M i i n c h e n , G e r m a n y ]. M e s e g u e r , J.M. P e r a l e s , A. S a n z , ETSI A e r o n a u t i c o s M a d r i d , S p a i n

A b s t r a c t

The aim of the experiment LICOR was the investigation of the a x i a l r e s o n a n c e s oi cylindrical liquid columns supported by equal circular coaxiaJ disks. In preparation ot the D-2 experiment a •heoreiical model has been developed, which exactly describes the small amplitude oscillations of finite cylindrical columns between coaxial circular disks. In addition, in terrestrial experiments the resonance frequencies of small liquid columns with up to 5 mm in diameter have been determined and investigations with density-matched liquids (silicon oil in a waierlmethanol mixture) have been performed. For the D-2 experiment LICOR the front disk and the rear disk lor use in the AFPM have been constructed and equipped with pressure sensors and the necessary electronics. The pressure exerted by the oscillating liquid column on trie supporting disks vsas as low as 10 Pa. Since the data downlink of the Materials Research Laboratory was just one signal oer s e c o n d and channel, it was necessary to determine amplitude and phase of the pressure already in the LICOR disks. The D-2 experiment has been successfully performed. It has fully confirmed the theoretical models and remarkably supplements the experiments on small liquid columns and on density-matched columns.

I n t r o d u c t i o n

It w a s the a i m oi the D-2 experiment LICOR to achieve a consistent u n d e r s t a n d i n g of the axial oscillations of cylindrical liquid columns s u p p o r t e d by c o a x i a l circular disks. Configu-rations of this type occur in the floating zone method of crystal growth. Of s p e c i a l interest a r e the frequencies of the r e s o n a n c e s , where at the nth r e s o n a n c e n n o d e s of the surface deflection a r e o b s e r v e d . The first r e s o n a n c e frequency a p p r o a c h e s zero, if by increasing its length the column r e a c h e s its stability limit. For r e s o n a n c e d e t e c t i o n t h r e e different methods h a v e b e e n a p p l i e d , namely visual observation, monitoring the p r e s s u r e on the vibrating s u p p o r t i n g disks a n d i m a g e pro-cessing of the video recordings.

The D-2 experiment LICOR h a s b e e n b a s e d on four s u p p l e m e n t a r y methods, s e e Fig. 1. A nearly cylindrical column between circular disks requires a low Bond n u m b e r

B = aA£fl!

(})

a

w h e r e R is the column r a d i u s , g the a c c e l e r a -tion d u e to gravity, A p the density difference b e t w e e n the fluid of the column a n d the sur-rounding m e d i u m , a n d a the surface tension of the fluid u n d e r consideration.

In a n experiment a low Bond number may be a c h i e v e d by

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Fig. 1: The four supplementary methods for stu-dying the behaviour of liquid columns with low Bond number.

• i n v e s t i g a t i o n s with d e n s i t y a d j u s t e d liquids (Ap small)

• experiments in low gravity conditions (g small).

T h e o r y

The r e s o n a n c e frequencies of liquid columns a r e d e t e r m i n e d by the b a l a n c e between the kinetic e n e r g y of the liquid motion a n d the potential e n e r g y of the resultant surface d e -formation. This m e a n s that the r e s o n a n c e fre-q u e n c i e s e r e properly s c a l e d by

kinetic energy £ j R _ £ (®K)_ _ P CO fl ._.

surface energy O R L O

The s h a r p n e s s of the r e s o n a n c e frequencies is d e t e r m i n e d by the liquid viscosity. It is properly s c a l e d by the ratio of the transient time i<yo of liquid motions d u e to surface d e

-formations over their d a m p i n g time «/«. This d i m e n s i o n l e s s n u m b e r

or else its s q u a r e root a r e d e n o t e d a s O h n e -sorge number, capillary n u m b e r or modified Reynolds number, p a n d v a r e the density

a n d the kinematic viscosity, n = p v is the dy-namic viscosity of the liquid considered.

The three scientific t e a m s involved in LICOR have developed different theoretical models which yield slightly different r e s o n a n c e fre-q u e n c i e s in a g r e e m e n t with tire different sim-plifications m a d e .

The Madrid t e a m h a s investigated two differ-ent o n e - d i m e n s i o n a l models, both of which a r e a p p l i c a b l e to slender liquid columns a n d low frequencies [1 - 4]. In the one-dimensional slice model only the contribution of the axial liquid motion to the kinetic energy is taken into account. The r a d i a l contribution is disre-g a r d e d . The liquid motion t h r o u disre-g h e a c h r a d i a l c r o s s - s e c t i o n is o b t a i n e d from the c h a n g e of the liquid volumes on both sides. This lower estimate to the kinetic energy gives rise to too high r e s o n a n c e frequencies. The neglection of the r a d i a l motion is the more critical, the shorter the considered liquid col-umn is. An upper bound to the kinetic energy is obtained, if one takes the axial flow for g r a n t e d a n d c a l c u l a t e s the radial flow from the continuity e q u a t i o n . In c o n s e q u e n c e of this treatment too low r e s o n a n c e frequencies arise, in particular for oscillations exhibiting several n o d e s . This a p p l i e s to the C o s s e r a t model.

The m o d e ! d e v e l o p e d by the Munchen t e a m [5 - 7] treats the oscillations of infinite liquid columns. Among these it selects those which satisfy the correct b o u n d a r y conditions on the flow velocity at the periphery of the supporting disks. The c o r r e s p o n d i n g b o u n d a r y condi-tions at smaller radii a r e d i s r e g a r d e d . With the flow velocity being less restricted in that model than in the experiment, too low reson-a n c e frequencies reson-a r e o b t reson-a i n e d .

The model d e v e l o p e d by the Frankfurt t e a m [8 - 10] is principally exact. The only limitation is the linearization of the b a s i c e q u a t i o n s which is correct for small a m p l i t u d e oscilla-tions. It is b a s e d on the following steps:

• The solutions of the m o m e n t u m e q u a t i o n plus the continuity e q u a t i o n in cylindrical coordinates a r e determined.

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ex-p o n e n t i a l functions exex-pdmiex-p 4- iqz) in the a z i m u t h f a n d in the r a d i a l coordinate z.

. T h e s e solutions a r e used for satisfying the b o u n d a r y conditions on the r a d i a l compo-nent a n d the two t a n g e n t i a l c o m p o n e n t s of the stress tensor a l o n g the surface of a n infinite liquid column.

. Satisfying three b o u n d a r y conditions by m e a n s of three linearly i n d e p e n d e n t solu-tions r e n d e r s a 3x3 secular determinant.

• The solutions of this secular determinant for real axial w a v e n u m b e r q a n d complex frequency a a r e the natural frequencies of inifinitely long columns.

• I n s t e a d of t h e s e natural oscillations the enforced oscillations lor real frequences complex a x i a l w a v e n u m b e r q ate deter-mined.

• T h e s e a r e axially increasing or d e c r e a s -ing oscillations of the liquid column.

• From the i n c r e a s i n g or d e c r e a s i n g oscilla-tions linear superposioscilla-tions a r e formed, which satisfy the b o u n d a r y conditions on the flow velocity a l o n g the s u p p o r t i n g disks.

« Satisfying the b o u n d a r y conditions at a n y position a c r o s s the disks would require taking into a c c o u n t a n infinite set of solu-tions.

• Meeting the b o u n d a r y conditions there-fore is r e d u c e d toW radii on the supporting disks, which requires 2N solutions.

• Taking into a c c o u n t N = 12 such radii re-d u c e s the error to less than two percent even without optimizing their s p a c i n g .

Among the most important results of this pro-c e d u r e let us mention:

• The surface s h a p e resulting at low fre-q u e n c i e s is that unduloid, which fits with respect to length a n d to volume.

• The p r e s s u r e on the supporting disks is proportional to the amplitude of the exci-t a exci-t i o n a n d is c o n v e n i e n exci-t l y s c a l e d by

2 P " / a

a-• R e s o n a n t oscillations arise if the axially d e c r e a s i n g w a v e s r e a c h the o p p o s i t e d i s k s a n d a r e reflected with a d e q u a t e p h a s e .

• The latter requirement generally is satis-fied by the first two p a i r s of solutions only,

such that the r e s o n a n c e frequencies basi-cally follow from t h e s e solutions. • T h e first r e s o n a n c e i r e q u e n c y a p

-p r o a c h e s zero when the length L of the c o l u m n r e a c h e s its circumference 2nR (Rayleigh instability).

• The height of the p r e s s u r e maxima at the r e s o n a n c e f r e q u e n c i e s v a r i e s propor-tional tO "VPv/ofl.

• The s h a r p n e s s of the r e s o n a n c e s de-c r e a s e s with i n de-c r e a s i n g n u m b e r r. of n o d e s , i.e. only a finite number of reson-a n c e f r e q u e n c i e s c reson-a n b e f o u n d ex-perimentally.

• D e c r e a s i n g i"*/aH by one order of

magni-tude e n a b l e s detection of two or three fur-ther r e s o n a n c e s .

• At high frequencies surface waves arise, i.e. the liquid motion along the axis van-ishes.

Figs. 2 a n d 3 show the p r e s s u r e on the vibrat-ing disk in d e p e n d e n c e on frequency a n d the flow profile of the s e c o n d resonant oscillation according to the calculations.

100r

L/2FU3.0 5

Fig. 2: The amplitude of tire pressure pR~/cc at the vibrating disk versus the reduced frequency \p« fl/c for varying damping parameter Pv/a/i.

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L

•nun i«nii

•mil'

nun

mill

r

i r

i f

1 J a = 2 inn to a - 5 urn. The frequon-•• cies c a n bo set manually or else a frequency r a m p of variable rate may be a p p l i e d .

"',','.'.' ',',',''' The oscillations were observed bv m o a n s of a telemicroscope a n d V,'.'.'.'.' '.'.'.'.'. were video recorded. By using stro-".'..'.'.''•' '•'.'.'.'.'.'. boscopic illumination a resting

pic-'•'•'•'.'•'.'.'.'.'.'.'.'..'.'.'•'.'•••'•'•'•'•'•'•'•• lure could b e a c h i e v e d a t a n y ••••'•.'.'.'..'.'.'.'.'.'.'.'.'.'.','.'.'. p h a s e . Applying a s l o w p h a s e vari-...','.7'///77777'.'".. ation resulted in a slow motion

pic-ture. This is of particular import-...'1'"'''''"''"..'..'. a n c e at high frequencies, where

the oscillations b e c o m e non-linear.

For quantitative detection of the | r e s o n a n c e frequencies the press-ure of the liquid column on the

sup-• . I | t j porting disks h a s b e e n m e a s u r e d .

~7~ The nominal sensity of the press-ure s e n s o r s w a s 15 uV/Pa. For cali-" 7 7 7 7 7 7 7 7 7 «cali-"cali-"•' cali-"cali-"cali-" bration of the pressure sensors the >,, ,„ »»,m,, n„„ii,i ga s v o l u m e i n a 1 liter b o t t l e h a s

"",',,',',','.',"M"M!'.',,I',,',',',"", IIIII'I' ' '"mi b e e n v a r i e d b y 5 0 m m b y m e a n s

,'.'.'.' '.'.'. m i " " "' "',',',',','!,'!!!!!!!!!!!!',!!l",lu ° ' a motor driven microsyringe.

.';;.'.'.'.'.'.'.'.' '•'.'.'.'.'.•.•.'. -».'•'•' '-'-- " " " " - " ^ T h e liquids u s e d in ihe experi-'.'.'.'.".'.'.'.'.'.'.'.'.'.'• '.'.'.'.'.'.'.'.'. '.'.'..'. - — — merits were water a n d a water/

- ^ . , -//// glycerol mixture (Table 1).

'•••••77777777777'....' 'i"',777777777777m iimim.,,,,,imiiMimii// With both liquids systematic m e a s -mi,,,,,,, „,i, Mlllll, , Mllm u r e m e n l s with disks of 5 mm in

'.'.'.."'77.'.'.'...' "!",','.'.". 777,'" ""'""" ,,,„mm d i a m e t e r a n d a frequency r a m p ",..'„,','.'„ from 15 Hz to 150 Hz were

per-formed. The rise in frequency w a s """ , 1 Hz per s e c o n d . The a s p e c t ratio A = L/2R w a s systematically varied

Fig. 3: The flow pattern of the second resonant oscillation in a from 0.8 to 1.1. Fig. 5 deoicts the

column with aspect ratio '•/?. R = 2.4 and tlie damping parameter [ i r s t ,W Q r e s o n a n c e frequencies of

pv/a/i = 10'. a w a t e r c o l u m n with 5 m m in

d i a m e t e r a n d 3.5 mm in height. Fig. 6 s h o w s t h e r e s o n a n c e f r e q u e n c i e s versus the a s p e c t ratio. The r e s o n a n c e fre-q u e n c i e s o b t a i n e d with water (x) a r e some-what lower than those o b t a i n e d with the wa-ter/glycerol mixture ( +). This contradicts the-ory, since for the mixture the Bond number a n d a l s o the O h n e s o r g e n u m b e r is slightly higher, which s u g g e s t s slightly lower reson-a n c e frequencies. The full lines in Fig. 6 give the r e s o n a n c e frequencies a c c o r d i n g to the exact theory, the d a s h e d lines those accord-ing to the Cosserat model. The m e a s u r e d r e s o n a n c e frequencies a g r e e excellently with the exact model.

S m a l l L i q u i d C o l u m n s

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liquid

water/glycerol 25 %

1.00 0.01

1.06 0.021

/m Nm

50.3

48.5

B (2R = 5 mm)

1,22

1,34

Table 1: Physical d a t a ot the liquids u s e d in terrestrial experiments on small columns

(V2fl)mc

,43

1,33

P l a t e a u S i m u l a t i o n 1st resonance

P l a t e a u s i m u l a t i o n , i. e . t h e u s e of d e n s i t y a d j u s t e d l i q u i d s , o f t e n is d i s q u a l i f i e d b y t h e a r g u m e n t t h a t t h e e x t e r i o r fluid m u s t a l s o o s c i l l a t e , s u c h t h a t n o c l e a r c o m p a r i s o n w i t h t h e o r y is p o s s i b l e . I n a d d i t i o n to t h e d e n s i t y a n d t h e v i s c o s i t y of t h e o u t e r l i q u i d b a t h , t h e

s h a p e of I h e c o n t a i n e r u s e d a n d of t h e l e a d s to t h e s u p p o r t i n g d i s k s h a v e to b e t a k e n i n t o a c c o u n t . A n e x a c t c a l c u l a t i o n of t h e r e s o n a n c e f r e q u e n c i e s t h e r e f o r e is p o s s i b l e b y n u -m e r i c a l -m e t h o d s only. O n t h e o t h e r h a n d , c o n s i d e r i n g t h a t t h e v i s c o s i t y s t r o n g l y a f f e c t s t h e s h a r p n e s s of t h e r e s o n a n c e f r e q u e n c i e s , b u t o n l y s l i g h t l y t h e i r p o s i t i o n , it s h o u l d b e

R

\

2nd resonance

(•TO

llirif ~ • to^Ai^J

7 T

\

/

CCOVy

Fig. 4: The device u s e d for investigating the reson-a n c e frequencies of smreson-all liquid columns.

Fig. 5: The 1st a n d 2nd r e s o n a n t oscillations of a water column with 5 m m in diameter a n d 3.5 mm in length.

a ) Stroboscopic pictures oi the extreme deforma-tions;

b) Superposition oi tire silhouettes of the extreme deformations.

p o s s i b l e t o o b t a i n u s e f u l r e s u l t s a l s o b y m e a n s of P l a t e a u s i m u l a t i o n .

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..

re

__. .. —_.__—- 1 l e n g t h / m m

a m p l i t u d e / m m

j o n a n c e f r e q u e n c y / Hz

1

2

3

4

b

6

29.8

2.0

0.30

1.3G

3.10

-~ ~

40.3

2.0

0.50

1.22

2.0G

3.02

> 4.00

. . . „

53.4

2.0

0.30

0.72

1.26

1.00

2.G8

3.52

70.0

3.0

0.24

0.43

0.70

1.20

i .S3

2.20

Table 2: The resonance frequencies of a cylindrical liquid column with 30 mm in diameter as determined in the Plateau tank in the COLUMBUS mockup. Liquid column: silicon oil; Liquid bath: water + methanol.

3.0

0.2 0.4 0.6 0.8 1.0

aspect ratio L/2nR

Fig. 6: Comparison of tire resonance frequencies obtained in tire Plateau tank with tire exact theoreti-cal model. Stheoreti-caling of the frequency has beon chosen according to the best fit. Solid lines: experiment; dash-dotted lines: theory.

This P l a t e a u tank h a s b e e n provided by the Madrid team, which h a s a long experience with this technique. Alter the first training with the science a s t r o n a u t s , a frequency r a m p from 0 Hz to 5 Hz with a frequency rise by 1 Hz within 90 s h a s b e e n a d d e d . This proved par-ticularly useful during the s e c o n d training performed.

By r e p e a t e d l y studying the video recordings, i. e. after some visual practice, the r e s o n a n c e frequencies may be d e t e r m i n e d up to 0.02 Hz. With four columns with d i a m e t e r 30 mm a n d different a s p e c t ratio the r e s o n a n c e frequen-cies shown in Tab. 2 have b e e n o b t a i n e d .

Plotting the r e s o n a n c e frequencies versus the a s p e c t ratio renders Fig. 6. Scaling of the ordinate h a s b e e n c h o s e n such that optimum fitting of the theoretical results is achieved. The g o o d a g r e e m e n t of the experimental with the theoretical curves reveals that the reson-a n c e frequencies in the P l reson-a t e reson-a u treson-ank show similar behaviour a s those of free liquid col-u m n s . The only a d a p t e d p a r a m e t e r is the frequency scaling.

D e s i g n a n d P e r f o r m a n c e of the LICOR D i s k s

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test chamber

permanent magnet

at a rate of 4 Hz a n d with a n accu-racy of 16 bit.

Iront disk

Run I oJ LICOR

rear disk

Fig. 7: The front disk a n d the rear disk developed for implemen-tation in the AFPM. The hole for liquid injection is in the front disk. The rear disk is exited to vibrations. The built-in electronics evalu-a t e s tire p r e s s u r e evalu-a m p l i t u d e evalu-a n d p h evalu-a s e .

shown in Fig. 7 h a v e b e e n d e s i g n e d . The hole ior liquid injection is in the centre of the front disk. The rear disk c a n be vibrated. Since the d a t a t r a n s m i s s i o n rate from the Materials Re-s e a r c h Laboratory to g r o u n d w a Re-s a Re-s low a Re-s 1 Hz, the s i g n a l s of the p r e s s u r e sensors were transformed into a m p l i t u d e a n d p h a s e al-r e a d y in the disks. The p h a s e w a s counted relative to the vibration of the rear disk. In order to i n c r e a s e the d a t a rate to 4 Hz, e a c h of the a m p l i t u d e a n d p h a s e s i g n a l s from the front disk a n d from the rear disk w a s dis-tributed to four different c h a n n e l s with a time shift of 1/4 s. The c h a n n e l s originally were d e s i g n e d to serve the transmission of sixteen t e m p e r a t u r e s i g n a l s . After transmission to g r o u n d the d a t a were r e a r r a n g e d accord-ingly.

The d a t a p r o c e s s i n g in the disks e v a l u a t e s p r e s s u r e s i g n a l s from 0.5 Pa to 10 Pa in the frequency r a n g e from 1 Hz to 5 Hz. In that w a y it w a s p o s s i b l e to transmit to ground

• the a m p l i t u d e of the pressure at the front disk

• the p h a s e of the p r e s s u r e a! the front disk

• the a m p l i t u d e of the p r e s s u r e at the rear disk

• the p h a s e of the p r e s s u r e at the rear disk

The experiment LICOR was sche-d u l e sche-d in the D-2 timeline from MET 1/23:18 to MET 2/02:50 (MET = Mission E l a p s e d Time). It h a s b e e n p l a c e d in such a way that during the essential steps (the frequency r a m p s ) Real Time TV w a s avail-a b l e . LICOR h avail-a s b e e n performed by PS-1, Dr. Ulrich Walter.

LICOR w a s the second experiment to run in the AFPM following the experiment STACO. Due to several d e l a y s during p r e p a r a t i o n of the AFPM, the latter experiment h a d s u f f e r e d by s e v e r e t i m e con-straints. Due to that experience, staying within the given time frame w a s strongly watched during the LICOR p e r f o r m a n c e . It w a s essential that the i n t e n d e d frequency r a m p s from 0 Hz to 5 Hz, e a c h lasting 7:30 min, could be observed, r e c o r d e d a n d p r o c e s s e d in RT-TV. The video s i g n a l w a s transmitted via ITALSAT to MARS Center, Napoli, to b e i m a g e processed a n d w a s returned on-line.

First a column from 10 cSt silicon oil with. 30 mm in d i a m e t e r a n d nominally 47.4 mm in l e n g t h w a s c r e a t e d . PS-1 started the fre-q u e n c y r a m p at MET 2/00:27:00 (= GMT 118/15:17:00). In addition to the video signal of the oscillating columns the pressure d a t a were received on g r o u n d . The amplitude of the p r e s s u r e on the vibrating disk w a s plotted on o n e of the monitors at G S O C a n d excel-lently a g r e e d with the precalculated curve. The p r e s s u r e m a x i m a , i.e. the r e s o n a n c e fre-q u e n c i e s , could b e easily identified from t h e s e d a t a . This w a s m u c h more than PS-1 a n d all other observers of LICOR could real-ize, w h o s a w the video picture of the oscillat-ing c o l u m n only, s e e Fig. 8.

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r e g i o n s with high flow velocity a n d r a t h e r m o v e d to the flow

* • + •

-m

H

G M T 118-15:17:00 ; start of frequency ramp

G M T 118 15 17 43 1st icson nice 0 53 11/

G M T 118 15 13 47 , 2nd t c - o n a n t e 1 20 11/

A ^ ^

- HP™" V J^ — * « S L «

G M T 1 1 " 15 20 03 , 3rd ^ s o n t i K C 2 13 11/

G M T 118:15:22:06 ; 4th resonance 3.12 Hz

I P F

3 8

^ ?

W

r i > ' V

GMT 118:15:23:28 : 5th resonance : 4.28 Hz

Fig. 8: The fijst five resonant oscillations of the column of silicon oil with 30 m m in diameter a n d 49.1 mm in length.

After application of the frequency r a m p , several frequencies close to the r e s o n a n c e s noted by the PS a n d the PI were set manually in s t e p s of .04 Hz a n d the respective oscillations were observed in de-tail.

Subsequently, the length of the column w a s reduced to nominally 40 mm a n d the frequency r a m p a n d the m a n u a l settings were re-p e a t e d . As b e f o r e , e v e r y t h i n g worked very well a n d g o o d a g r e e -ment with theory w a s obtained. Due to a n a g r e e m e n t of the Pis a n a x i a l line with equidistant radial ticks h a d b e e n p l a c e d between tire b a c k g r o u n d illumination a n d the liquid column. It g a v e valu-a b l e valu-a d d i t i o n valu-a l informvalu-ation. The start of the frequency r a m p c a n be s e e n from the motion of the ticks much earlier t h a n from the sur-face deformation. Residual ac-c e l e r a t i o n s ac-c a n b e ac-c l e a r l y ob-served, which not at all were de-tected by the Microgravity Meas-urement Assembly, MMA. Non-ax-isymmetric surface deformations could be easily identified.

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'! I.

\ \ „ Ircqucncy (H;|

Uequency (Hz.;

Fig- 3: The amplitude of pressure at the vibrating disk (a) and at the resting disk (b) during the fre-quency ramp applied to the column of 49.1 mm in length; solid lines: Cosserat model; dash-dotted lines; exact model.

Fig. 10: The phase of pressure at the vibrating disk (a) and at the resting disk (b) during thedrequency ramp applied to the column of 49.1 mm in length; solid lines: Cosserat model.

Run II of LICOH

On the third d a y of the D-2 Mission, the AFPM h a d fully b r o k e n down electronically. How-ever, alter intensive simulations of the AFPM support t e a m with the e n g i n e e r i n g m o d e l a v a i l a b l e at G S O C a n d a two to three hour air-to-ground repair activity, the AFPM could be reactivated by the crew. Since the S p a c e -l a b mission w a s e x t e n d e d by one day, a sec-ond run of LICOR w a s e n a b l e d by m e a n s ol a r e p l a n n i n g r e q u e s t .

In order to s a v e crev/ time, Run II of LICOR w a s performed with the 5 cSt silicon oil u s e d in the p r e c e d i n g experiment ONSET (Onset of oscillatory M a r a n g o n i flows). In order to a c -count for the lower viscosity, the a m p l i t u d e of excitation of the r e a r disk w a s r e d u c e d from

1 m m to 0.5 mm. The front disk, d u e to the p r e c e d i n g p r o c e d u r e s , still w a s shifted lat-erally by 0.7 mm. The request to r e a r r a n g e it coaxially w a s r e n o u n c e d , since this w a s the s t e p w e r e the AFPM h a d broken down earlier.

As in Run I, the science astronaut w a s Dr. Ulrich Walter. He c r e a t e d a liquid column with 40 mm in length a n d a p p l i e d the frequency r a m p from 0 Hz to 5 Hz. As before, s h a r p m a x i m a of p r e s s u r e versus frequency showed up. The first r e s o n a n c e frequencies could b e . clearly identified, s e e Table 3. However, alter p a s s i n g the third r e s o n a n c e frequency the oscillation b e c a m e so intense that a strong lateral motion a r o s e a n d the liquid spilled over the s h a r p e d g e of the rear disk. The column s u b s e q u e n t l y broke. Since no un-u s un-u a l a c c e l e r a t i o n s w e r e recorded by the Microgravity M e a s u r e m e n t Assembly, the possible r e a s o n s for the spillage a r e

• the l a t e r a l shift of the Front Disk by 0.7 mm

• the r e t a r d a t i o n of the full development of the r e s o n a n t oscillations relative to the a p p e a r e n c e of the pressure maximum.

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aspect ratio L/2R

Fig. 11: The first five r e s o n a n c e frequencies o b t a i n e d with columns of different length in the experiment LICOR together with the r e s o n a n c e fre-q u e n c i e s of small lifre-quid columns; (d) D-2 experiments; (x) small columns of water, (-H) small columns of water/glycerol 25 %; solid lines: exact theory, d a s h e d lines: C o s s e r a t model.

Conclusions

The D-2 experiment LICOR perfectly supple-ments the experisupple-ments on small liquid col-u m n s a n d those b a s e d on density-adjcol-usted liquids. At the s a m e time, it h a s given new insight into the immediate a p p e a r e n c e ol the p r e s s u r e m a x i m a , the visual observation of r e s o n a n c e s a n d the retardation of the fully d e v e l o p e d oscillations. The a u t o m a t i c

detec-tion of the r e s o n a n c e s by m e a n s of p r e s s u r e sen-sors h a s proven very ef-fective.

The u n i n t e n d e d l a l e r a i shift of the front disk, which h a s n ' t b e e n cor-rected due to this risk o: b r e a k d o w n of the AFPM, h a s shown the sensitivity of liquid columns to non-axial perturbations. It was most likely the r e a s o n for the b r e a k a g e of the col-umn in Run II. In the sub-sequent re-run of the ex-p e r i m e n t STACO a col-umn of silicon oil between circular disks with the un-e q u a l d i a m un-e t un-e r s 30 mm a n d 28 mm h a s b e e n es-t a b l i s h e d . T h e c o l u m n s t a r t e d to o s c i l l a t e lat-e r a l l y with a p lat-e r i o d of 4.75 s a n d b r o k e after a b o u t 3 min. The u n e q u a l disk d i a m e t e r s bring about three different surface s h a p e s , which differ only slightly in energy. All of these surfaces a r e sections of unduloids. B r e a k a g e occurred after the en-ergy of the lateral motion c a u s e d the column to switch from the unduloid with lowest energy to the one with next higher energy.

This underlines the importance of non-axial oscillations of liquid columns a n d of

oscilia-silicon oil

lOcSt

lOcSt

5 c S t

l e n g t h / mm

49.1

41.7

39.7

disk

vibrating resting

video

vibrating resting

video

vibrating resting

video

1

0.53 0.53 0.48

0.69 0.S9 0.64

0.80 0.80 0.73

r e s o n a n c e frequency / Hz

2

1.20 1.21 1.20

1.53 1.58 1.53

1.77 1.78 1.77

3

2.13 2.19 2.04

2.70

2.70

3.00

3.00

4

3.12 3.38 3.40

3.96

3.36

5

4.23 4.30 4.31

4.98

Table 3: The r e s o n a n c e frequencies o b t a i n e d from the p r e s s u r e maxima a n d by visual recordings.

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lions with a z i m u t h a l w a v e n u m b e r s m > = 1. They s h o w a m u c h lower d a m p i n g than the a x i a l oscillations with m = 0.

There a r e g o o d r e a s o n s to a s s u m e that the oscillatory M a r a n g o n i convection, which h a s b e e n r e p e a t e d l y o b s e r v e d in liquid columns, is coupled to capillary oscillations with m = 1. M a r a n g o n i convection a r i s e s , if the disks sup-porting the column a r e h e a t e d to different t e m p e r a t u r e s . A g r a d i e n t in surface tension from hot to cold a r i s e s together with a surface convection in the s a m e direction. It b e c o m e s oscillatory, if the a p p l i e d t e m p e r a t u r e dif-ference e x c e e d s a critical value. In that c a s e the convective flow starts to rotate azimu-thally. This a p p e a r s to be a n oscillator,' flow in a m e r i d i a n light-cut. The rotating flow gives rise a n d in turn is s u p p o r t e d by a correspond-ing surface deformation. E a c h investigation of oscillatory M a r a n g o n i flows therefore re-quires the exact knowledge of all non-axial capillary deformations.

A c k n o w l e d g e m e n t s

The p r e p a r a t i o n a n d p e r f o r m a n c e of the D-2 experiment LICOR h a s b e e n s p o n s o r e d by the D e u t s c h e A g e n t u r fur R a u m f a h r t a n g e -legenheiten, DARA. The flight opportunity in the A d v a n c e d Fluid Physics Module, AFPM, h a s b e e n provided by the E u r o p e a n S p a c e Agency, ESA. We t h a n k the support t e a m of the E u r o p e a n S p a c e T e c h n o l o g y Center, ESTEC, for the e n g a g e d c a r e of the AFPM d e v e l o p m e n t a n d of the experiments. LICOR h a s b e e n p e r f o r m e d with g r e a t skill by Science Astronaut Dr. Ulrich Waller. During t h e t r a i n i n g s e s s i o n s a t t h e e n g i n e e r i n g m o d e l of the AFPM all Science Astronauts g a v e v a l u a b l e hints o n the experiment perfor-m a n c e . We t h a n k the Microgravity A d v a n c e d R e s e a r c h C e n t e r , MARS, N a p o l i for t h e on-line t r a n s m i s s i o n a n d processing of our d a t a via ITALSAT. An experiment just must

perform well, if F. Sacerdoti s e n d s m e s s a g e s to the sky a n d G. R Evangelista r e s p o n d s from MARS!

R e f e r e n c e s

[11 M e s o g u e r J., S a n z A., P e r a l e 3 J.M.,

Axisymmetric long liquid b r i d g e s stability a n d r e s o n a n c e s , Appl. Microgravifv Teclmol. 2

(1989). 186-192

[2] M e s c g u e r ]., The b r e a k i n g oi axisymmetric slender liquid bridges, /. Fluid Mech. 1 30

(1983), 123-15!

13] M e s e g u c r I., Percdes ].M., Viscosity Effects on the Dynamics of Long Axisymmetric Liquid Bridges, in: Micrograivty Fluid Mechanics. H.J.

Rath (ed.), Springer, Bad in (1992), 37-15

[4] S a n z A.., The influence of the outer bath on the d y n a m i c s of axisymmetric liquid bridges, /.Fluid Mech. 156(19851, 101-140

[5] B a u e r H.F., Natural d a m p e d frequencies of a n iirfinitely long column of immiscible viscous liauids, Z. angew. Math. Mech. 64 (1984), 475-490

[81 B a u e r H.F., Free surface a n d interface oscilla-tions of a n infinitely long visco-elastic liquid column, Acta Astronautica 13 (1S86), 9-22

[7] B a u e r H.F., Axial r e s p o n s e oi differently excited a n c h o r e d viscous liquid b r i d g e s in zero-grav-ity, Arch. Appl Mech 63 (1932), 322-338

[8] L a n g i x u n D., Rischbieter F., Form, Schwingun-g e n u n d Stabilildt von FuissiSchwingun-gkeitsSchwingun-grenz- Fuissigkeitsgrenz-iluchen, Battelle Franklurt/M.

1984,ScliluBbe-ncht fur das BMFT, 01 QV 242: 1-130. Form.

S c h w i n g u n g c n u n d Stabilitcit von Flussigkeits-grenzfiachen, Borrtcile FranklurtlM. 138G.

For-sdmngsbericht W 86-029 des BMFT

[31 L a n g b e m D.. Oscillations of Finite Liquid Col-u m n s , Microg/orvify sci. technoi. V (1992). 73-85 [101 L a n g b e i n D., Oscillations of Finite Liquid

Col-umns, ESA SP-353 (19S2), 419-442

[11] A l l i e n s S.. Faik F. G r o B b a c h R.. L a n b e i n D., Experiments on Oscillations of Small Liquid Bridges, Microgravity sci. techno!. Vil (1394), 2-5

[12] M a r t i n e z I., Rivas D., Plateau Tank Facility for Simulation of S p a c e l a b Experiments, Acta

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