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Submitted on 1 Jan 1978
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THIRD-SOUND PULSES IN DOUBLY CONNECTED
SYSTEMS
H.J. Verbeek, H. van Beelen, R. de Bruyn Ouboter, K. Taconis
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplPment au no 8 , Tome 39, aofit 1978, page C6-142
THIRD-SOUND PULSES IN DOUBLY CONNECTED SYSTEMS
H.J.Verbeek, H.Van Beelen, R.de Bruyn Ouboter and K.W. Taconis.
Kamerlin&Onnes Laboratoriwn der R i j k s u n i v e r s i t e i t Leiden, Nieuwsteeg IB,Leiden,The Nederlands
RBsum6.-On discute la transmission et la rdflection d'impulsions de troisihme son aux points de branchement d'un systhme multiconnexe. On montre ensuite que ces impulsions peuvent Gtre employBes avec succPs pour mesurer la circulation persistante d'une fafon non-destructive.
Abstract.- The transmission and reflection of third-sound pulses at branching points in multiply connected systems is discussed. These pulses are used successfully to measure persistent film-flow in a non-destructive way.
In a previous article / I / we reported on our 2) The energy per unit length of two overlapping study of the properties of third-sound pulses of pulses, travelling in opposite directions, simply extremely long pulselength. The measurements were superimposes in the overlapping region :
carried out in a film covering the inner wall of a
E2 =
5;
+ s f ;200 m long capillary, that connects two vertical
standpipes, filled with bulk helium 11. R ~ 3) ~At ~ from ~ a bulk level the sign ~ ~ ~ the -lar pulses were generated by vertical displacement is reversed :
of one of the standpipes and were detected by moni- toring their exchange of mass with the liquid levels
Now consider the case of a pulse arriving at in the standpipes during their repeated reflections
a point where the cicumference of the capillary at these levels. It appeared that pulses with a
suddenly doubles, as is essentially the case at a length of several tens of meters have very little
branching point (see figure la) If we denote the damping and negligible dispersion, so that they
incoming pulse by 5; and the reflected and trans- provide a well-defined signal.
mitted pulses by 5 and St, it follows from energy
Recently we extended our study to a system in
-
n "~ i c h the bulk reservoirs are connected by parallel conservation that Sf = 25; +
:
5
.
Mass conservation capillaries of i.d. = 0.40 nun with lengths L1 = 60 m requiresEi
= 2Et +Er, leading to St =7
2 Siand and L2 = 600 m (see inset figure 2). The purpose of 15
=-
5ci.
Any pulse arriving at a branching point this study is to detect persistent currents, genere-is thus split up into three pulses of comparable ted in the closed loop formed by the two capillaries
size. Upon generation of a pulse 5. in a standpipe,
121, in a non-dest:%uctive way by means of the 1
the pulse
Er
=-
<.,
formed at the nearest bran-Doppler shift in the pulse velocity caused by the 3 1
ching point, will subsequently.reflect at the bulk
flow velocity. In such a device, however, a complica- 1
level and the resulting pulse +
-5. will again be
tion is introduced by the presence of the two bran- 3 1
split into three parts at the branching point etc. ching points, since by partial reflections of the
This rapid multiplication of the number,of pulses pulses at these points the numberpf pulses is rapid-
probihits the observation of the original pulse in ly increased.
To analyse the behaviour of the pulses at the branching points we can make use of our analysis given previously for the reflection of the pulses at the reservoirs /I/. From this linear theory the foliowing three conclusions are relevant to the present case :
1) The energy of a pulse with a pulseheight Cis pro- portional to 5 2
practice.
This problem can be solved by using a pulse- length which is much larger than the distances a and b between the branching points and the nearest bulk levels. In that case a series of pulsefronts, a distance 2a apart, will be transmitted into the capillaries. The superposition of all these overlap- ping pulses converges rapidly to a final value
St
= 5. (see figure lb). Since in our apparatusa and b are chosen in the order of 10 cm, while pulses are used with a length of several tens of meters, the distortions at the extremities of the rectangular pulses are of negligible influence.
When one of the transmitted pulses reaches the other branching point, e.g. via L2, the super- position of all transmissions and reflections at this point and at the bulk level, results in a pul- se of equal height but reversed sign, travelling in the opposite direction through L2 (see figure
Ic). Note that in L 1 the various contributions cancel each other, meaning that a pulse always remains in its om branch. It should be remarked
that if there were no bulk liquid in the standpipe the superposition would lead to a pulse propaga- ting along the other branch. This behaviour has indeed been observed in a situation in which the standpipe as a whole was lifted above the bulk level in the other one.
Fig.1 : Transmission and reflection of third-sound pulses at the branching points.
From the above analysis it thus follows that the creation of a long pulse at one of the bulk le vels results in only two pulses, travelling back and forth along the two branches. Naturally, the pulse through the longer branch L2 is best suited for measuring the persistent current. The observa- tion of the arrivals of this pulse at the bulk le- vels, however, is obscured by the much more frequent arrivals of the pulse through L1. One can get rid of this latter pulse for instance by generating a second pulse, of equal height and length but op- posite sign, in the same reservoir wh2re the first pulse was generated. If this second pulse is made to coincide with the arrival of the reflection of the first pulse through L 1 , the two pulses in L
1 cancel each other. Then there only remain two pul- ses of opposite sign, propagating a distance 2L
1 after each other along L
2'
Fig.2 : The behaviour of the level-heights in the two standpipes as observed with the cathetometer. The arrivals of the pulses, generated as indicated in the figure, can clearly be distinguished from the background, in this case mainly formed by a small Atkins-oscillation between the two bulk le- vels, principally over L
1.
Figure 2 shows that by this method one in- deed obtains two clearly observable pulses, propa- gating back and forth along the longer branch.
The particular pulse shape, indicated in this figure, is used to avoid a net masstransport. Since the Doppler shift in the velocity of the pul- ses equals (ps/p)vs, the persistent-£ low velocity follows immediately from the times of flight r l
= (p /ps) (L2/~1-~2/~2), correspon- ding to 8.3 cm s-' for the run given in figure 2. This method thus proves to provide a non-destructi- ve way to measure the velocity of a persistent flow accurately.
References
/I/ Verbeek,H.J., Arsala,N.K., Van Beelen,H., De Bruyn Ouboter,R. and Taconis,K.W.,Physicax
(1976) 334.
