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Thermoacoustic oscillations in cryostats: New results
Thermoacoustic oscillations in cryostats: n e w results A.G. Kuzmina Scientific and Industrial Association of Cryogenic Engineering, 67 Lenin Avenue, Moscow Region 143900, Balashiha 7, USSR Received 20 March 1991; revised 29 July 1991 Thermoacoustic oscillations occurring in pipes of cryogenic equipment cause increased evaporation of liquid helium. According to scientific publications the heat inflow generated due to thermoacoustic oscillations is not in excess of 1 - 4 W. However, the present authors have obtained heat inflow values of 2 0 0 - 3 0 0 W in standard helium cryostats with a capacity of 40 dm 3. They have called the thermoacoustic oscillations causing such heat inflows anomalous or resonance oscillations and a hypothesis about their physical nature is suggested.
Keywords: thermoacoustics; cryostats; helium
Nomenclature q L Ap D
Heat inflow (W) Length of thermoacoustic element (m) Complete amplitude of pressure oscillations (MPa) Diameter (ram)
In a number of cases when testing cryogenic equipment extremely large heat inflows have been observed, the cause of which, in the present authors' opinion, is thermoacoustic oscillations. The main aim of most investigators has been to remove these oscillations; an aim which is usually successful. But, as a rule, the conditions of and reasons for the onset of these oscillations have not been studied. In Reference 1 the process of filling a 25 d m ~ helium cryostat is described, where, when using a new overflow device such strong thermoacoustic oscillations occurred that the authors failed to fill the cryostat with helium until the design of the overflow device was changed. The present authors have observed a similar phenomenon when testing the processes involved in helium cryostat filling; they encountered heat inflows of 5 0 - 1 0 0 W, according to their evaluations. In addition, heat inflows of 1 - 4 W have been described in work dedicated to the investigation of thermoacoustic oscillations at helium temperatures. According to Reference 2, where an investigation was carried out with a wide range of tube sizes ( 2 - 1 2 mm in diameter, 1 2 2 - 2 1 4 mm in length), the largest value of heat inflow obtained was 1.2 W. The heat inflow values observed in closed U-shaped tubes were an order of magnitude lower ~. The problem posed is, therefore,
h T t
Height (ram) Temperature (K) Time (s)
Greek letter Oscillation frequency (Hz)
to find out the conditions at which thermoacoustic oscillations of increased intensity occur and to try to define their physical nature.
Description of experimental procedure The tests were conducted in standard helium cryostats (STG-40) with a capacity of 40 dm 3. The thermoacoustic element (TE) consisted of two parts: a thermoacoustic tube (TT) open at both ends (one end of the tube was immersed in the liquid helium of the cryostat and the other was placed outside the cryostat) and a warm portion. The TT was designed as follows: a section of the tube with an internal diameter of 3 - 8 mm, a wall thickness of 0 . 3 - 1 mm and 1 1 0 0 - 1 6 5 0 mm in length was taken. On the outside this tube was covered with a tube of larger diameter but of smaller length. The ends of the outer tube were soldered to the lateral surface of the inner tube, thus forming the enclosure which, during immersion into liquid helium, formed a vacuum due to air condensation in the clearance between the tubes. The warm portion (though it was not always warm enough) was a hose made of vacuum rubber, the inner diameter of the hose and its wall thickness being 5 - 9 mm. The hose was put on the upper portion of the TT, outside the cryostaL or on a metal tube, connected with the TT, on
0011 2275/92/010Oll 09 ,, 1 9 9 2 B u t t e r w o r t h Heinernann Ltd
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Thermoacoustic oscillations in cryostats: A.G. Kuzmina the lateral tee of which a pressure transducer was mounted. Sometimes the pressure transducer was placed near the warm end of the vacuum hose. Thermoacoustic oscillations occurred in cases of vacuum hose pinching, the location of pinching determining the length of the warm portion and the entire TE. The pressure oscillations were registered on photographic paper using an oscillograph. Evaporated helium was warmed up and fed to a gas meter, and the heat inflow was determined as the product of mass flow rate and evaporation heat. When the heat inflow was in excess of 5 0 - 6 0 W, it was evaluated according to the rate of pressure rise in the closed vessel. The evaluation was two-fold: the gas discharge to the gas holder through the gas meter, conducted after the pressure rise, and, in addition, the quantity of heat required for liquid warm-up, for its evaporation and for vapour warm-up was calculated.
Additional tests have shown that during the pressure rise due to thermoacoustic oscillations in the tube, one end of which is immersed in liquid helium, helium is held in an equilibrium state due to active mixing. Thus, liquid warm-up to the equilibrium temperature was taken into account in the heat inflow evaluation according to the rate of pressure rise. The vapour warm-up was determined using the temperature sensitive elements, which were situated in the vapour space. On completing the measurements, the clamp on the vacuum hose was opened, at the end of which a cylindrical vessel with a capacity of 150 dm 3 was mounted, and the oscillations stopped. To measure temperatures below 70 K semiconductive resistance thermometers (crystals with no enclosure) were used to decrease the lag. On the outer surface of the warm portion of the TE the temperature was measured using copper-constantan and copper-iron thermocouples. A necessary condition of the experiment was the preliminary blow of the element with cold helium, thus avoiding air freezing inside the tube and creating the temperature distribution along the element required for the onset of oscillations. A diagram of the test rig is shown in Figure 1 and the characteristics of the elements tested are given in Table 1. The boundary of the area of existence of thermoacoustic oscillations may be determined by calculation, the calculation results being in good agreement with those from the experiment. The present task consisted of monitoring the anomalous oscillations of high intensity within this area and determining the conditions under which they occur.
8
~'11
Experimental results Resonance oscillations differ from normal ones due to their extraordinarily high intensity. The maximum values observed were Ap = 0.2--0.25 MPa and q --~ 350 W. However, resonance oscillations were also observed where q ~ 4 - 5 W; the waveform makes it possible to distinguish them from normal oscillations. Normal thermoacoustic oscillations have a waveform similar to a sinusoidal one and the waves are practically symmetric about the axis Ap = p -- P0 = 0, where P0 is the pressure in the cryostat and p is the pressure in a warm portion of the TE (Figure 2). For resonance oscillations the waves are almost completely located in the field of positive Ap; pressure rise ('inhalation') takes up to 0.8 of the period and pressure
Figure
1 Diagram of test rig. 1. Helium cryostat; 2, nitrogen shield; 3, temperature transducer; 4, vacuum enclosure; 5, thermoacoustic tube; 6, manometer; 7, transient element; 8, pressure gauge; 9, vacuum hose; 10, flow rate meter; 1 1, heater
Table 1
Performance of thermoacoustic elements tested
Name of element
1
2
3
4
5
6
7
8
9
10 a
115
Inner diameter of TT (mm) Wall thickness of TT (mm) Length of T T ( m m ) Length of portion without insulation (mm) Internal diameter of vacuum hose (mm) qma×(W)
5.4 0.3 1160
5.4 0.3 1160
5.4 0.3 1160
5.4 0.3 1160
5.4 0.3 1160
4.0 1.0 1160
3.0 0.5 1160
5.4 0.3 1160
6.0 1.0 1160
5.0 0.5 1160
5.4 0.3 1300
20
20
380
720
1160
380
380
720
20
20
20
8 80
5 3
8 38
8 10
8 6
6.5 18
6.5 9
8 15
8 300
5 1.5
8 30
alnternal tube made of copper (cf. in other cases, stainless steel) bA tip was made in the form of diffuser on the TT cold end
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Cryogenics 1992 Vol 32, No 1
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Thermoacoustic oscillations in cryostats: A.G. Kuzmina 0.004 -a
0.002 n
1 D.3
~" 0.000
-0.002
40
30
b
20
j
0.06
~°-~0.04/ 0.02 0.00
10 I
2
L (m)
I
.
~
0.3
.
1
0.06
t (s) D. z~ 0.04 13.
<
~ [ . . . . .
,.^^
^
A
1 . . . . . . . .
~2"-
^A
^
. . . . . . .
L,,. ~-
0.02
t (s) Figure 2 Waveforms for: (a) usual thermoacoustic oscillations; (b) resonance oscillations in resonance moment; (c) unsteady resonance oscillations
drop ('expiration') only 0.2. This correlation is typical for the resonance peak fields observed during investigation of the dependences Ap(L), q(L) and ~(L). Such peaks are clearly seen in Figure 3, where test results for resonance oscillations (TE N1) and normal oscillations (TE N2) are presented. A description of the TE and the maximum heat inflow values are given in Table 1. The heat inflow peaks for TE N1 corresponded to L = 3.9 and 5.2 m and a frequency of 8 and 7 Hz, respectively. Reruns of the experiment have shown the stability of the first peak, though its value differed from 25 to 80 W. The value of the second peak was always smaller than the first and its position was sometimes slightly shifted along the L axis. It should be noted that the peak values of ,Sp were consistent, as a rule, with the peak values of q. The dependence of oscillation frequency on TE length in the extreme range had steps, as usual, and sometimes even small maximum values. It is seen in Figure 3 (curve i) that a maximum L v2 was noted only for L = 3.9 m, i.e. for the first extreme dependence of q(L). Once removed from the resonance peak, the oscillation amplitude decreases, but often alternating waves of different intensity arise, which can be ordered or chaotic. An example of such chaotic oscillations is given in Figure 2c. In this case, for TT N9, a vacuum hose and reducer are substituted for the cylindrical volume, with V = 220 cm 2 and D = 70 mm. The oscillations assumed the character presented in Figure 2b when a
I
6
I 2
I 4
1 6
i 8
{ 10
L (m) Figure 3
Test results for specimens: 1, N1; 2, N2 (see Table 1)
metal reducer, with D = 12 x 1 mm and L = 300 mm, was set up between the TT and the volume. After a number of specimen test runs it has been clarified that thermoacoustic oscillations of anomalously high intensity and with abrupt extremes, similar to the resonance phenomenon, occurred in cases where the following conditions were satisfied: 1 the flow area of the warm portion exceeded the flow area of the cold portion (TT) by not less than 2 - 2 . 5 times; 2 the lateral surface of the thermoacoustic tube (cold section) was well heat insulated (for example by vacuum);
Cryogenics
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Vol 32, No 1
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Thermoacoustic oscillations in cryostats: A.G. Kuzmina
3 the tube end, immersed into liquid helium, was placed not less than 3 0 - 4 0 mm from the vessel bottom; and 4 the transition to the warm section was smooth, without bends, and the tube had no restrictions (including wires) in the cold portion.
30 3 20 I
When these conditions were met the reproducibility of the results was satisfactory. This is explained by the fact that not all the conditions determining oscillation intensity were checked and reproduced during the experiments. In particular, the temperature distribution along the thermoacoustic element, which is a major factor for the onset and maintaining of the oscillations, was not controlled. The intensity of oscillations and the character of the dependences q(L), Ap(L) and ~,(L) depended on many circumstances. Let us now determine the main ones.
10
5 L (m)
g
0.04
0.02
Insulation effect of TE cold portion It is noted in a number of works, including Reference 4, that improvement of TE cold portion insulation causes the thermoacoustic oscillations to be weakened and sometimes stopped altogether. The present experiments have shown that these observations refer only to normal oscillations. For resonance oscillations improvement of TE cold portion insulation causes an intensification of the thermoacoustic oscillations. The dependences q(L) for elements N 3, 4 and 5 are given in Figure 4. The lower portion of elements N 3 and 4, with a height of up to 380 and 720 mm, respectively, had no vacuum enclosure, i.e. it was not insulated. The presence of the uninsulated portion reduced the value of q and smoothed out the peaks. The significant reduction of qmax for element N 4 is explained by the fact that the vacuum enclosure existed in the warm zone and thus the quality of the vacuum insulation itself was worse. Structurally, element N 5 was enclosed along its entire length, but the tightness of seal was disturbed: the lower weld of the outer tube was left unsoldered. The values of q obtained are small.
Effect of helium level in vessel It was necessary to observe the influence of vessel filling rate on the intensity of oscillations in order to know whether the helium vessel is the original cavity for the oscillations. We failed to observe this effect for the tube insulated along its entire length; besides, the level readily dropped due to large heat inflows. In the partial absence of insulation the oscillation intensity was increased with decreasing helium level in the vessel, but only slightly. This seems to be connected with that fact that in the absence of a vacuum enclosure, the change of helium level is accompanied by a change in the heat exchange conditions on the TT surface. So far as heat transfer to gas is much less than that to liquid, a decreasing helium level is equivalent to the best insulation of the lateral surface and should cause strengthening of the oscillation intensity. Such an increase was indeed observed when testing specimen N 6, the results of which are given in Figure 5; but again
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Cryogenics 1992 Vol 32, No 1
I
0.00
I
I
I
I
I 8
f 10
L (m) 10
%-
8
-1v
6~-
4 I 2
I 4
I 6
12
L (m) Figure 4
Test results for specimens: 3, N3; 4, N4; 5, N5 (see
Table 1 )
the change was slight. Instability of the first peak was more characteristic of this specimen, with D = 4 ram. Compared to results for specimens of larger diameter, this peak was observed at a smaller length of TE: L = 1 . 7 - 2 m. In a number of cases it was removed and, if observed, it was smaller than a more stable second peak, corresponding to L = 2 . 7 - 3 m and a frequency of 8 Hz.
Influence of thermoacoustic tube diameter Comparing Figures 3 and 5 we can see that with decreasing TT diameter the region of resonance oscillations is restricted and displaced along the L axis to the left. Figure 6 shows the results of testing two elements, N 7 and N 6, which confirm this conclusion. Both tubes had no insulation up to a height of 380 mm. It can also be seen from the given figures that oscillation intensity, estimated from the heat inflow value, was decreasing. Data on the amplitude of pressure oscillations are given only when carrying out the calibration of the oscillograph. Qualitative estimation of the amplitude of the pressure oscillations has shown that it increased with decreasing TT diameter for the same values of q.
Thermoacoustic oscillations in cryostats: A.G. Kuzmina and vapour phase. The restriction of the oscillation area, the displacement of qma× to the left and the loss of qma× itself are characteristic of the vapour phase. In addition, steps were missing on the u(L) curve for the vapour phase. The oscillation intensity decreased for the case where the cold end of the tube was removed from the liquid level. The oscillation frequency was practically doubled, an observation which has also been made by other investigators.
16
12
(3"
8
Effect
of cryostat
design
×
It was indicated in Reference 1 that observed heat inflows, being stipulated by thermoacoustic oscillations in an overflow siphon, were especially large in a 25 dm 3 metal cryostat, and were much less in a cylindrical glass cryostat. In the present experiments the main tests were conducted in a cylindrical metal vessel with
4
I
I
I
I
t
L (m) I0
"~
12
8
6
- :i
t~
4
I 2
I 4
I 6 L (m)
I 8
I 10
12
I
I
L
L
I
I
L (m)
Figure5 Test results for specimen N6 w i t h d i f f e r e n t a m o u n t s of liquid helium in S T G - 4 0 : x, 5 dm3; - - e - - , 17 dm3; - - , 3 2 dm 3 0.04
Due to the restriction of the area of thermoacoustic oscillation stability we should expect that, with increasing diameter, the oscillation intensity will reach a maximum value and begin to decrease. The present experiments with element N 9 (D = 6 ram) showed that this maximum had not yet been achieved. In connection with very large heat inflows, the authors succeeded in estimating, but only schematically, the dependence q(L) for element N 9 (Figure 7) and confirming that with increasing thermoacoustic tube diameter, the maximum values of q were achieved at relatively small values of
zXp.
Transition
to
vapour
phase
In accordance with the experiments previously described, the cold end of the thermoacoustic tube was placed below the helium level. During the experiments it was observed that the oscillation frequency was increasing and the intensity was decreasing when the helium in the vessel was exhausted. In one of the experiments the cold end of the tube was held 10 mm above the helium level and the position was corrected before each measurement. Figure 6 shows the results of testing element N 6 with the cold end placed in the liquid
n
0.02
10
I
I
I
8
2O
6
16
I 2
'4 4
I 6 L (m)
Figure6 Test results for specimens: in v a p o u r phase; x, N7 in liquid
I 8 --
I 10
, N6 in liquid; . . . , N6
C r y o g e n i c s 1 9 9 2 V o l 32, N o 1
15
Thermoacoustic oscillations in cryostats: A.G. Kuzmina 200
150
100
50
) L (m)
0.12 (3. 0.08
0.04
L (m)
12
10
8
6
I
I
I
I
I
I
2
4
6
8
10
12
L (m)
Figure 7 Test results for specimen N9
an elliptic bottom and a capacity of 40 dm 3. The vessel inner diameter is 400 mm and height 380 mm, and the inner diameter of the neck is 24.4 mm and its height 460 mm. In addition, tests have been conducted in a helium vessel (STG-100) with a capacity of 100 rim3: its inner diameter is 450 mm, its height is 270 mm and the neck height is 300 mm. Unfortunately all previously tested elements for this cryostat were too short and a new element (N 11) with a diffuser on the end has been manufactured. For this element, insulated along its entire length, qmax = 30 W for cryostat STG-40 and qmax = 15 W for cryostat STG100. For the element with no insulation on the lateral surface (N 4 in STG-40 and N 8 in STG-100) the test results differed a little. It is difficult to make a final conclusion because of the insignificant number of tests carried out in the 100 dm 3 vessel. It is only possible to note that none of the most intensive oscillations seen in cryostat STG-100 were observed in cryostat STG-40. Influence
of w a r m
portion
insulation
As was noted, generally the thermoacoustic ele-
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Cryogenics 1992 Vol 32, No 1
ment consisted of a tube with an enclosure and a vacuum rubber hose. As far as rubber is a heat insulator, its existence at the warm end can affect the oscillation intensity. The hose wall elasticity may also be important. That is why in some experiments transient elements made of a metal tube (D = 10 ram) were used, one end of which was connected to the TT, with the rubber hose put on the other end. It was found that with such a reducer, the oscillation intensity increased. So, for element N1, when L = 3.9 mm, with the reducer, q = 8 0 - 8 5 W and without it, q = 4 5 - 5 0 W. On the other hand, it was noted that oscillation intensity was not directly proportional to the heat supplied to the warm end. From this point of view, the results of the following experiments are characteristic. The reducer was manufactured with a heater wound on its surface, and it was covered with a layer of super-thin glass fibre insulation 5 0 - 7 0 mm thick, and then it was covered with a lavsan film. The temperature inside the reducer at the point of its connection with the TT reached 100 K and increased to 270 K at a distance of 0.5 m with the heater switched off. The maximum heat inflow to the liquid helium (L = 3.9 m) was set up after 4 - 5 min and reached 48 W. According to such an evaluation, the heat inflow on the warm end of the thermoacoustic element was not greater than 1 0 - 1 5 W. With the heater switched on and its capacity increased to 40 W, the temperature at the point of connection of the TT to the reducer inside the tube increased to 300 K, heat was ejected through the insulation and, in fact, the heater burnt out. But the oscillation intensity was unchanged, with a measured value of q of 45 W. This adds weight to the assumption that oscillation intensity depends not only on the amount of heat supplied but also on the temperature level at which it is supplied. In this case the decrease in heat inflow at the cost of the reducer heat insulation and the heat supply at a temperature = 300 K were similarly unfavourable. The maximum heat inflow was observed with an uninsulated reducer (L _> 300 mm); in this case at the moment when q=qm~=80W at the outlet from the TT of N1, temperature oscillations in the range 7 0 - 1 0 0 K were observed. Temperature
measurement
Measurement of the temperature distribution along the thermoacoustical element is one of preconditions for the possibility of numerical calculation, which is why it is of interest. However, measurement of temperature inside the TT turned out to be a complicated problem. Though a miniature crystal semiconductive transducer was used, its insertion, together with the conducting wires inside the TT, changed the oscillation intensity: anomalous strong oscillations were transformed into normal weak ones. Outlet temperature measurement from the cold end of the thermoacoustic tube turned out to be the most successful method. The transducer was installed 10 mm lower than the outlet. Under weak oscillations, harmonic temperature oscillations with a frequency equal to the pressure oscillation frequency and amplitude (0.02 K) were observed. Under anomalous strong oscillations the temperature of the oscillations turned out to be complex and non-harmonic:
Thermoacoustic oscillations in cryostats: A.G. Kuzmina In one of the tests, where q = 250 W, the cryostat was left in the open position, in order to observe the evolution of the resulting process. The results of this test, in the form of the relations of the wall temperature and oscillation amplitude to time, are illustrated in Figure 9. In this test the metal reducer was set up between the TT and the vacuum hose, its total length being 1000 ram: 100mm of D = 12 x 1 mm and 900mm of D = 12 × 0.3 ram. The transducers were mounted on the reducer: the first one at a distance of 50 ram, the second at a distance of 550 mm and the third at a distance of 950 mm from the point of connection of the reducer to the TT. It was characteristic that the greatest oscillation intensity was observed at the beginning, then there was a temporary drop, then another peak, followed by a gradual decrease in the oscillation intensity. The intensity decrease agrees with the theory which states that a sudden temperature jump is the most favourable condition for the existence of thermoacoustic oscillations,
a
10 8 6
4 I
b 12108-
Thermoacoustic
6-
I
I
200 h (ram)
I
300
Figure8 Temperature distribution along c r y o s t a t height w i t h (a) q = 25 W and (b) q = 2 5 0 W : 1, initially; 2, after TE operation w i t h gas discharge closed. - , Liquid helium level in STG-40
against a background of weak oscillations in the range 4.3 - 4 . 4 K, irregular peaks of = 4 . 8 K with a frequency of 1 - 2 Hz were observed. Furthermore, the character of the oscillations turned out to be complicated. A pulsing vapour bubble was formed at the end of the tube. Such a picture was observed with q = 50 W and Ap = 0.05 MPa, when operating with the gas discharge vent open. Similar measurements were carried out for more powerful oscillations, where q = 2 0 0 - 2 5 0 W and when the time of the pressure rise was measured from 0, 1 to 0.16 MPa. In this test, the lower transducer did not register any oscillation and the temperature was increasing smoothly, in accordance with the rising pressure. The transducers, located in the vapour phase, registered the temperature increase (the more intensive the oscillations the greater the temperature increase) (see Figure 8). This, at the same time as checking the heat inflow value by two methods, disproved the authors' initial assumption that anomalously greater heat inflows are connected with the carryover of drops into the drainage system. The temperature change on the warm end of the element was also of interest. Usually, for purposes of helium economy, the relations q(L), Ap(L) and ~(L) were recorded during the first 1 - 2 rain and, under strong oscillations, during the first 2 0 - 3 0 s after the oscillations had been generated. The temperature of the element warm end could not set, and an unsteady process proceeded, so that it was difficult to estimate the heat inflow from the outside.
in cryostat
neck
During the course of the tests, thermoacoustic oscillations were observed in the cryostat neck. Their intensity increased with increasing rate, which is why these oscillations reached a substantial value in the resonance areas. It was of interest to determine whether the resonance peaks in relations q(L) and Ap(L) were the result of the resonance of two oscillations: those in the thermoacoustic tube and in the cryostat neck.
4-
100
oscillations
300 --
3
200 ! w"
100
l
I
I
I
t
I
t (s)
0.12 EL v
0
.
1
0
0.08 I
20
I
40
I
60 t(s)
I
80
I
1oo
Figure 9 Change of oscillation amplitude and t e m p e r a t u r e on metal reducer surface w i t h time for specimen N8 w i t h qmax (1, 2 and 3 indicate the number of the transducer)
Cryogenics 1992 Vol 32, No 1
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Thermoacoustic oscillations in cryostats: A.G, Kuzmina The oscillation frequency in the STG neck is 4 0 - 4 2 Hz. Numerous joint recordings of oscillations on one tape do not lead to the proposal of mutual influence of the two oscillations. There is, however, an indirect influence: with oscillation intensity rising in the TT, the gas flow rate increases and this causes an increase in oscillation intensity in the neck. The following factor was a determinant which ruled out the effect of the resonance of two oscillations: at the moment of the most intensive oscillations in the thermoacoustic tube the gas discharge in the neck was so great that the temperature in the top part decreased and the oscillations in the neck stopped completely. This did not influence the oscillation intensity in the thermoacoustic tube. It was shown by a special test, where the heater was used to create a vapour flow in the neck and the generated power was registered, that the thermoacoustic oscillations in the cryostat neck did not influence the quantity of evaporating helium.
Reproducibility of results obtained As far as it was impossible to maintain a definite temperature profile, the reproducibility of the results in some cases was only satisfactory. Most of the questions arising from this work arose from the following scenario, however. The oscillation intensity, especially in the field of resonance peaks, depended on tube 'training'. With the initial mounting of a newly manufactured tube, generally only weak oscillations were observed. Repeated tests showed the anomalous oscillations, with the heat inflow continuing to increase in the region of peaks and reaching the ultimate stationary values after four or five tests. If the tube was kept for half a year or more between tests, it showed average intensity anomalous oscillations with the first new test.
Analysis of results It has been shown that in tubes, one end of which was
immersed in liquid helium with the other at room temperature, there were anomalous strong thermoacoustic oscillations, the amplitude of the pressure oscillations being more than 0.1 MPa. The heat inflow introduced by these oscillations can reach 250-300 W. The basic conditions for the onset of such oscillations a heat-insulated cold part and tube expansion in the heat supply zone - are quite characteristic of many cryogenic devices. One of the possible interpretations of the physical nature of these resonance thermoacoustic oscillations is dealt with in an asymmetric form of the pressure variation curve (Figure 10). Of the total period, =0.8 is spent on the pressure rise ('inhalation') and 0.2 on pressure drop ('expiration'). The 'inhalations' and 'expirations' of ordinary thermoacoustic oscillations are nearly equal in duration. 'Inhalation' at the beginning of resonance oscillations proceeds similarly to that for ordinary ones when liquid is present at the cold end, i.e. with a reduced speed. Meanwhile, 'expiration' almost exactly repeats the analogous process in ordinary oscillations in a gaseous medium, i.e. it proceeds rapidly. Calculations show that 'expiration' can take 0.2
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Cryogenics 1992 Vol 32, No 1
0"20I
).104 D.. ).102 cf
~0.15
0.1
0.10
0.1
t (s)
0.2
Figure 10 Recording of pressure oscillations: p, pressure in TE; Pl,
pressure in STG-40
of the period only in the case of absolute absence of liquid in the TT. Evidently, some event takes place between the first part of the 'inhalation' and the beginning of 'expiration'. This leads to partial liquid evaporation and partial liquid retreat to the cryostat and induces a more sharp pressure rise in the warm portion of TE than at the beginning of the process. Such a short-term event could be the explosive boiling of helium. But explosive boiling is observed only with superheated liquids. Extrapolating known experimental results, the lifetime of liquid helium overheated by 0 . 2 5 - 0 . 3 K is =0.01 s. Can helium in the TT superheat? Yes, it can. This is possible not only due to heat exchange with the wall but also due to the velocity increase which lowers the pressure in the flow. Simple calculations show that for a frequency of 10 Hz and a liquid rise up to the middle of the TT (approximately the quantity of liquid evaporated at qmax, the flow velocity reaches 24 m s-~ and pressure inside the flow drops by 0.03 MPa, which corresponds to superheating by 0.3 K. Thus, we propose the following sequence of events. The process begins with drawing liquid into the TT as with ordinary tbermoacoustic oscillations, but continues more intensively because there is an expansion at the warm end that acts as a weakened spring. The presence of vacuum insulation on the TT helps to preserve the wall heat of the previous cycle which is necessary for liquid superheating. Having achieved a maximum velocity, liquid boils up, pressure in the tube grows and the resulting vapour-liquid mixture is pushed out of the TT in both directions. At the outlet to the warm tube part, most of the liquid evaporates and vapour is warmed up due to the heat of the walls. At the moment of the pressure peak measured at the TE warm end, there is no liquid in the TT and generated vapour is pushed back into the cryostat due to the pressure difference. If these processes stay exactly within the period typical for ordinary thermoacoustic oscillations in a liquid, a resonance peak - a highest oscillation intensity and a highest heat inleak - is observed. If this coincidence is not complete, the system itself begins to regulate the process, and alternating oscillations of different intensity are observed, which are typical for other cases of parametric resonance. To validate the suggested hypothesis several additional experiments were carried out. For TT N9 a
Thermoacoustic oscillations in cryostats: A.G. Kuzmina simultaneous pressure recording in the TE warm portion and in the cryostat vapour space was performed. If helium boiling takes place inside the TT, the pressure in the cryostat would start rising to reach P .... in the TT. The recorded results, shown in Figure 10, illustrate this. Now, for the same TT, in its joint with the reducer, a diffusor was set up, i.e. hydraulic resistance was reduced. In this case separate peaks of Ap = 0 . 2 0.25 MPa instead of Ap = 0 . 1 - 0 . 1 2 MPa were observed. This indicates that in the process of 'inhalation' the pressure in the TT rises more intensively than in the TE warm portion, i.e. boiling takes place inside the TT. All the main test results have been analysed and they do not seem to contradict the suggested physical model. The initial step of vessel hard wall 'work-down" is well
known in thermal physics. According to the present author's estimations, which need careful verification, in some cases the heat supply at the warm end was less than the heat inflow to the cold zone. Evidently, this can be explained by the fact that in the calculations the evaporation heat was specified for normal conditions, while in reality the conditions differed greatly from the normal.
References 1 Clement, J.R. and Gaffney, J. Thermal oscillations in low temperature apparatus Adv Cryog Eng (1953) 1 3 0 2 - 3 0 6 2 Banister, J.D. Spontaneous pressure oscillations in tube connecting liquid helium reservoirs Bull hit hzst R£fi'ig (1966) 5 127-134 3 Ya~ki, T., Tominaga, A. and Narahara, Y. Large heat transport due to spontaneous gas oscillations induced in a tube with steep temperature gradients l)'ans ASME: J Heat Tran~j~,r (1983) 105 8 8 9 - 8 9 4
Cryogenics 1992 Vol 32, No 1
19
Keywords: thermoacoustics; cryostats; helium
Nomenclature q L Ap D
Heat inflow (W) Length of thermoacoustic element (m) Complete amplitude of pressure oscillations (MPa) Diameter (ram)
In a number of cases when testing cryogenic equipment extremely large heat inflows have been observed, the cause of which, in the present authors' opinion, is thermoacoustic oscillations. The main aim of most investigators has been to remove these oscillations; an aim which is usually successful. But, as a rule, the conditions of and reasons for the onset of these oscillations have not been studied. In Reference 1 the process of filling a 25 d m ~ helium cryostat is described, where, when using a new overflow device such strong thermoacoustic oscillations occurred that the authors failed to fill the cryostat with helium until the design of the overflow device was changed. The present authors have observed a similar phenomenon when testing the processes involved in helium cryostat filling; they encountered heat inflows of 5 0 - 1 0 0 W, according to their evaluations. In addition, heat inflows of 1 - 4 W have been described in work dedicated to the investigation of thermoacoustic oscillations at helium temperatures. According to Reference 2, where an investigation was carried out with a wide range of tube sizes ( 2 - 1 2 mm in diameter, 1 2 2 - 2 1 4 mm in length), the largest value of heat inflow obtained was 1.2 W. The heat inflow values observed in closed U-shaped tubes were an order of magnitude lower ~. The problem posed is, therefore,
h T t
Height (ram) Temperature (K) Time (s)
Greek letter Oscillation frequency (Hz)
to find out the conditions at which thermoacoustic oscillations of increased intensity occur and to try to define their physical nature.
Description of experimental procedure The tests were conducted in standard helium cryostats (STG-40) with a capacity of 40 dm 3. The thermoacoustic element (TE) consisted of two parts: a thermoacoustic tube (TT) open at both ends (one end of the tube was immersed in the liquid helium of the cryostat and the other was placed outside the cryostat) and a warm portion. The TT was designed as follows: a section of the tube with an internal diameter of 3 - 8 mm, a wall thickness of 0 . 3 - 1 mm and 1 1 0 0 - 1 6 5 0 mm in length was taken. On the outside this tube was covered with a tube of larger diameter but of smaller length. The ends of the outer tube were soldered to the lateral surface of the inner tube, thus forming the enclosure which, during immersion into liquid helium, formed a vacuum due to air condensation in the clearance between the tubes. The warm portion (though it was not always warm enough) was a hose made of vacuum rubber, the inner diameter of the hose and its wall thickness being 5 - 9 mm. The hose was put on the upper portion of the TT, outside the cryostaL or on a metal tube, connected with the TT, on
0011 2275/92/010Oll 09 ,, 1 9 9 2 B u t t e r w o r t h Heinernann Ltd
Cryogenics 1992 Vol 32, No 1
11
Thermoacoustic oscillations in cryostats: A.G. Kuzmina the lateral tee of which a pressure transducer was mounted. Sometimes the pressure transducer was placed near the warm end of the vacuum hose. Thermoacoustic oscillations occurred in cases of vacuum hose pinching, the location of pinching determining the length of the warm portion and the entire TE. The pressure oscillations were registered on photographic paper using an oscillograph. Evaporated helium was warmed up and fed to a gas meter, and the heat inflow was determined as the product of mass flow rate and evaporation heat. When the heat inflow was in excess of 5 0 - 6 0 W, it was evaluated according to the rate of pressure rise in the closed vessel. The evaluation was two-fold: the gas discharge to the gas holder through the gas meter, conducted after the pressure rise, and, in addition, the quantity of heat required for liquid warm-up, for its evaporation and for vapour warm-up was calculated.
Additional tests have shown that during the pressure rise due to thermoacoustic oscillations in the tube, one end of which is immersed in liquid helium, helium is held in an equilibrium state due to active mixing. Thus, liquid warm-up to the equilibrium temperature was taken into account in the heat inflow evaluation according to the rate of pressure rise. The vapour warm-up was determined using the temperature sensitive elements, which were situated in the vapour space. On completing the measurements, the clamp on the vacuum hose was opened, at the end of which a cylindrical vessel with a capacity of 150 dm 3 was mounted, and the oscillations stopped. To measure temperatures below 70 K semiconductive resistance thermometers (crystals with no enclosure) were used to decrease the lag. On the outer surface of the warm portion of the TE the temperature was measured using copper-constantan and copper-iron thermocouples. A necessary condition of the experiment was the preliminary blow of the element with cold helium, thus avoiding air freezing inside the tube and creating the temperature distribution along the element required for the onset of oscillations. A diagram of the test rig is shown in Figure 1 and the characteristics of the elements tested are given in Table 1. The boundary of the area of existence of thermoacoustic oscillations may be determined by calculation, the calculation results being in good agreement with those from the experiment. The present task consisted of monitoring the anomalous oscillations of high intensity within this area and determining the conditions under which they occur.
8
~'11
Experimental results Resonance oscillations differ from normal ones due to their extraordinarily high intensity. The maximum values observed were Ap = 0.2--0.25 MPa and q --~ 350 W. However, resonance oscillations were also observed where q ~ 4 - 5 W; the waveform makes it possible to distinguish them from normal oscillations. Normal thermoacoustic oscillations have a waveform similar to a sinusoidal one and the waves are practically symmetric about the axis Ap = p -- P0 = 0, where P0 is the pressure in the cryostat and p is the pressure in a warm portion of the TE (Figure 2). For resonance oscillations the waves are almost completely located in the field of positive Ap; pressure rise ('inhalation') takes up to 0.8 of the period and pressure
Figure
1 Diagram of test rig. 1. Helium cryostat; 2, nitrogen shield; 3, temperature transducer; 4, vacuum enclosure; 5, thermoacoustic tube; 6, manometer; 7, transient element; 8, pressure gauge; 9, vacuum hose; 10, flow rate meter; 1 1, heater
Table 1
Performance of thermoacoustic elements tested
Name of element
1
2
3
4
5
6
7
8
9
10 a
115
Inner diameter of TT (mm) Wall thickness of TT (mm) Length of T T ( m m ) Length of portion without insulation (mm) Internal diameter of vacuum hose (mm) qma×(W)
5.4 0.3 1160
5.4 0.3 1160
5.4 0.3 1160
5.4 0.3 1160
5.4 0.3 1160
4.0 1.0 1160
3.0 0.5 1160
5.4 0.3 1160
6.0 1.0 1160
5.0 0.5 1160
5.4 0.3 1300
20
20
380
720
1160
380
380
720
20
20
20
8 80
5 3
8 38
8 10
8 6
6.5 18
6.5 9
8 15
8 300
5 1.5
8 30
alnternal tube made of copper (cf. in other cases, stainless steel) bA tip was made in the form of diffuser on the TT cold end
12
Cryogenics 1992 Vol 32, No 1
12
Thermoacoustic oscillations in cryostats: A.G. Kuzmina 0.004 -a
0.002 n
1 D.3
~" 0.000
-0.002
40
30
b
20
j
0.06
~°-~0.04/ 0.02 0.00
10 I
2
L (m)
I
.
~
0.3
.
1
0.06
t (s) D. z~ 0.04 13.
<
~ [ . . . . .
,.^^
^
A
1 . . . . . . . .
~2"-
^A
^
. . . . . . .
L,,. ~-
0.02
t (s) Figure 2 Waveforms for: (a) usual thermoacoustic oscillations; (b) resonance oscillations in resonance moment; (c) unsteady resonance oscillations
drop ('expiration') only 0.2. This correlation is typical for the resonance peak fields observed during investigation of the dependences Ap(L), q(L) and ~(L). Such peaks are clearly seen in Figure 3, where test results for resonance oscillations (TE N1) and normal oscillations (TE N2) are presented. A description of the TE and the maximum heat inflow values are given in Table 1. The heat inflow peaks for TE N1 corresponded to L = 3.9 and 5.2 m and a frequency of 8 and 7 Hz, respectively. Reruns of the experiment have shown the stability of the first peak, though its value differed from 25 to 80 W. The value of the second peak was always smaller than the first and its position was sometimes slightly shifted along the L axis. It should be noted that the peak values of ,Sp were consistent, as a rule, with the peak values of q. The dependence of oscillation frequency on TE length in the extreme range had steps, as usual, and sometimes even small maximum values. It is seen in Figure 3 (curve i) that a maximum L v2 was noted only for L = 3.9 m, i.e. for the first extreme dependence of q(L). Once removed from the resonance peak, the oscillation amplitude decreases, but often alternating waves of different intensity arise, which can be ordered or chaotic. An example of such chaotic oscillations is given in Figure 2c. In this case, for TT N9, a vacuum hose and reducer are substituted for the cylindrical volume, with V = 220 cm 2 and D = 70 mm. The oscillations assumed the character presented in Figure 2b when a
I
6
I 2
I 4
1 6
i 8
{ 10
L (m) Figure 3
Test results for specimens: 1, N1; 2, N2 (see Table 1)
metal reducer, with D = 12 x 1 mm and L = 300 mm, was set up between the TT and the volume. After a number of specimen test runs it has been clarified that thermoacoustic oscillations of anomalously high intensity and with abrupt extremes, similar to the resonance phenomenon, occurred in cases where the following conditions were satisfied: 1 the flow area of the warm portion exceeded the flow area of the cold portion (TT) by not less than 2 - 2 . 5 times; 2 the lateral surface of the thermoacoustic tube (cold section) was well heat insulated (for example by vacuum);
Cryogenics
1992
Vol 32, No 1
13
Thermoacoustic oscillations in cryostats: A.G. Kuzmina
3 the tube end, immersed into liquid helium, was placed not less than 3 0 - 4 0 mm from the vessel bottom; and 4 the transition to the warm section was smooth, without bends, and the tube had no restrictions (including wires) in the cold portion.
30 3 20 I
When these conditions were met the reproducibility of the results was satisfactory. This is explained by the fact that not all the conditions determining oscillation intensity were checked and reproduced during the experiments. In particular, the temperature distribution along the thermoacoustic element, which is a major factor for the onset and maintaining of the oscillations, was not controlled. The intensity of oscillations and the character of the dependences q(L), Ap(L) and ~,(L) depended on many circumstances. Let us now determine the main ones.
10
5 L (m)
g
0.04
0.02
Insulation effect of TE cold portion It is noted in a number of works, including Reference 4, that improvement of TE cold portion insulation causes the thermoacoustic oscillations to be weakened and sometimes stopped altogether. The present experiments have shown that these observations refer only to normal oscillations. For resonance oscillations improvement of TE cold portion insulation causes an intensification of the thermoacoustic oscillations. The dependences q(L) for elements N 3, 4 and 5 are given in Figure 4. The lower portion of elements N 3 and 4, with a height of up to 380 and 720 mm, respectively, had no vacuum enclosure, i.e. it was not insulated. The presence of the uninsulated portion reduced the value of q and smoothed out the peaks. The significant reduction of qmax for element N 4 is explained by the fact that the vacuum enclosure existed in the warm zone and thus the quality of the vacuum insulation itself was worse. Structurally, element N 5 was enclosed along its entire length, but the tightness of seal was disturbed: the lower weld of the outer tube was left unsoldered. The values of q obtained are small.
Effect of helium level in vessel It was necessary to observe the influence of vessel filling rate on the intensity of oscillations in order to know whether the helium vessel is the original cavity for the oscillations. We failed to observe this effect for the tube insulated along its entire length; besides, the level readily dropped due to large heat inflows. In the partial absence of insulation the oscillation intensity was increased with decreasing helium level in the vessel, but only slightly. This seems to be connected with that fact that in the absence of a vacuum enclosure, the change of helium level is accompanied by a change in the heat exchange conditions on the TT surface. So far as heat transfer to gas is much less than that to liquid, a decreasing helium level is equivalent to the best insulation of the lateral surface and should cause strengthening of the oscillation intensity. Such an increase was indeed observed when testing specimen N 6, the results of which are given in Figure 5; but again
14
Cryogenics 1992 Vol 32, No 1
I
0.00
I
I
I
I
I 8
f 10
L (m) 10
%-
8
-1v
6~-
4 I 2
I 4
I 6
12
L (m) Figure 4
Test results for specimens: 3, N3; 4, N4; 5, N5 (see
Table 1 )
the change was slight. Instability of the first peak was more characteristic of this specimen, with D = 4 ram. Compared to results for specimens of larger diameter, this peak was observed at a smaller length of TE: L = 1 . 7 - 2 m. In a number of cases it was removed and, if observed, it was smaller than a more stable second peak, corresponding to L = 2 . 7 - 3 m and a frequency of 8 Hz.
Influence of thermoacoustic tube diameter Comparing Figures 3 and 5 we can see that with decreasing TT diameter the region of resonance oscillations is restricted and displaced along the L axis to the left. Figure 6 shows the results of testing two elements, N 7 and N 6, which confirm this conclusion. Both tubes had no insulation up to a height of 380 mm. It can also be seen from the given figures that oscillation intensity, estimated from the heat inflow value, was decreasing. Data on the amplitude of pressure oscillations are given only when carrying out the calibration of the oscillograph. Qualitative estimation of the amplitude of the pressure oscillations has shown that it increased with decreasing TT diameter for the same values of q.
Thermoacoustic oscillations in cryostats: A.G. Kuzmina and vapour phase. The restriction of the oscillation area, the displacement of qma× to the left and the loss of qma× itself are characteristic of the vapour phase. In addition, steps were missing on the u(L) curve for the vapour phase. The oscillation intensity decreased for the case where the cold end of the tube was removed from the liquid level. The oscillation frequency was practically doubled, an observation which has also been made by other investigators.
16
12
(3"
8
Effect
of cryostat
design
×
It was indicated in Reference 1 that observed heat inflows, being stipulated by thermoacoustic oscillations in an overflow siphon, were especially large in a 25 dm 3 metal cryostat, and were much less in a cylindrical glass cryostat. In the present experiments the main tests were conducted in a cylindrical metal vessel with
4
I
I
I
I
t
L (m) I0
"~
12
8
6
- :i
t~
4
I 2
I 4
I 6 L (m)
I 8
I 10
12
I
I
L
L
I
I
L (m)
Figure5 Test results for specimen N6 w i t h d i f f e r e n t a m o u n t s of liquid helium in S T G - 4 0 : x, 5 dm3; - - e - - , 17 dm3; - - , 3 2 dm 3 0.04
Due to the restriction of the area of thermoacoustic oscillation stability we should expect that, with increasing diameter, the oscillation intensity will reach a maximum value and begin to decrease. The present experiments with element N 9 (D = 6 ram) showed that this maximum had not yet been achieved. In connection with very large heat inflows, the authors succeeded in estimating, but only schematically, the dependence q(L) for element N 9 (Figure 7) and confirming that with increasing thermoacoustic tube diameter, the maximum values of q were achieved at relatively small values of
zXp.
Transition
to
vapour
phase
In accordance with the experiments previously described, the cold end of the thermoacoustic tube was placed below the helium level. During the experiments it was observed that the oscillation frequency was increasing and the intensity was decreasing when the helium in the vessel was exhausted. In one of the experiments the cold end of the tube was held 10 mm above the helium level and the position was corrected before each measurement. Figure 6 shows the results of testing element N 6 with the cold end placed in the liquid
n
0.02
10
I
I
I
8
2O
6
16
I 2
'4 4
I 6 L (m)
Figure6 Test results for specimens: in v a p o u r phase; x, N7 in liquid
I 8 --
I 10
, N6 in liquid; . . . , N6
C r y o g e n i c s 1 9 9 2 V o l 32, N o 1
15
Thermoacoustic oscillations in cryostats: A.G. Kuzmina 200
150
100
50
) L (m)
0.12 (3. 0.08
0.04
L (m)
12
10
8
6
I
I
I
I
I
I
2
4
6
8
10
12
L (m)
Figure 7 Test results for specimen N9
an elliptic bottom and a capacity of 40 dm 3. The vessel inner diameter is 400 mm and height 380 mm, and the inner diameter of the neck is 24.4 mm and its height 460 mm. In addition, tests have been conducted in a helium vessel (STG-100) with a capacity of 100 rim3: its inner diameter is 450 mm, its height is 270 mm and the neck height is 300 mm. Unfortunately all previously tested elements for this cryostat were too short and a new element (N 11) with a diffuser on the end has been manufactured. For this element, insulated along its entire length, qmax = 30 W for cryostat STG-40 and qmax = 15 W for cryostat STG100. For the element with no insulation on the lateral surface (N 4 in STG-40 and N 8 in STG-100) the test results differed a little. It is difficult to make a final conclusion because of the insignificant number of tests carried out in the 100 dm 3 vessel. It is only possible to note that none of the most intensive oscillations seen in cryostat STG-100 were observed in cryostat STG-40. Influence
of w a r m
portion
insulation
As was noted, generally the thermoacoustic ele-
16
Cryogenics 1992 Vol 32, No 1
ment consisted of a tube with an enclosure and a vacuum rubber hose. As far as rubber is a heat insulator, its existence at the warm end can affect the oscillation intensity. The hose wall elasticity may also be important. That is why in some experiments transient elements made of a metal tube (D = 10 ram) were used, one end of which was connected to the TT, with the rubber hose put on the other end. It was found that with such a reducer, the oscillation intensity increased. So, for element N1, when L = 3.9 mm, with the reducer, q = 8 0 - 8 5 W and without it, q = 4 5 - 5 0 W. On the other hand, it was noted that oscillation intensity was not directly proportional to the heat supplied to the warm end. From this point of view, the results of the following experiments are characteristic. The reducer was manufactured with a heater wound on its surface, and it was covered with a layer of super-thin glass fibre insulation 5 0 - 7 0 mm thick, and then it was covered with a lavsan film. The temperature inside the reducer at the point of its connection with the TT reached 100 K and increased to 270 K at a distance of 0.5 m with the heater switched off. The maximum heat inflow to the liquid helium (L = 3.9 m) was set up after 4 - 5 min and reached 48 W. According to such an evaluation, the heat inflow on the warm end of the thermoacoustic element was not greater than 1 0 - 1 5 W. With the heater switched on and its capacity increased to 40 W, the temperature at the point of connection of the TT to the reducer inside the tube increased to 300 K, heat was ejected through the insulation and, in fact, the heater burnt out. But the oscillation intensity was unchanged, with a measured value of q of 45 W. This adds weight to the assumption that oscillation intensity depends not only on the amount of heat supplied but also on the temperature level at which it is supplied. In this case the decrease in heat inflow at the cost of the reducer heat insulation and the heat supply at a temperature = 300 K were similarly unfavourable. The maximum heat inflow was observed with an uninsulated reducer (L _> 300 mm); in this case at the moment when q=qm~=80W at the outlet from the TT of N1, temperature oscillations in the range 7 0 - 1 0 0 K were observed. Temperature
measurement
Measurement of the temperature distribution along the thermoacoustical element is one of preconditions for the possibility of numerical calculation, which is why it is of interest. However, measurement of temperature inside the TT turned out to be a complicated problem. Though a miniature crystal semiconductive transducer was used, its insertion, together with the conducting wires inside the TT, changed the oscillation intensity: anomalous strong oscillations were transformed into normal weak ones. Outlet temperature measurement from the cold end of the thermoacoustic tube turned out to be the most successful method. The transducer was installed 10 mm lower than the outlet. Under weak oscillations, harmonic temperature oscillations with a frequency equal to the pressure oscillation frequency and amplitude (0.02 K) were observed. Under anomalous strong oscillations the temperature of the oscillations turned out to be complex and non-harmonic:
Thermoacoustic oscillations in cryostats: A.G. Kuzmina In one of the tests, where q = 250 W, the cryostat was left in the open position, in order to observe the evolution of the resulting process. The results of this test, in the form of the relations of the wall temperature and oscillation amplitude to time, are illustrated in Figure 9. In this test the metal reducer was set up between the TT and the vacuum hose, its total length being 1000 ram: 100mm of D = 12 x 1 mm and 900mm of D = 12 × 0.3 ram. The transducers were mounted on the reducer: the first one at a distance of 50 ram, the second at a distance of 550 mm and the third at a distance of 950 mm from the point of connection of the reducer to the TT. It was characteristic that the greatest oscillation intensity was observed at the beginning, then there was a temporary drop, then another peak, followed by a gradual decrease in the oscillation intensity. The intensity decrease agrees with the theory which states that a sudden temperature jump is the most favourable condition for the existence of thermoacoustic oscillations,
a
10 8 6
4 I
b 12108-
Thermoacoustic
6-
I
I
200 h (ram)
I
300
Figure8 Temperature distribution along c r y o s t a t height w i t h (a) q = 25 W and (b) q = 2 5 0 W : 1, initially; 2, after TE operation w i t h gas discharge closed. - , Liquid helium level in STG-40
against a background of weak oscillations in the range 4.3 - 4 . 4 K, irregular peaks of = 4 . 8 K with a frequency of 1 - 2 Hz were observed. Furthermore, the character of the oscillations turned out to be complicated. A pulsing vapour bubble was formed at the end of the tube. Such a picture was observed with q = 50 W and Ap = 0.05 MPa, when operating with the gas discharge vent open. Similar measurements were carried out for more powerful oscillations, where q = 2 0 0 - 2 5 0 W and when the time of the pressure rise was measured from 0, 1 to 0.16 MPa. In this test, the lower transducer did not register any oscillation and the temperature was increasing smoothly, in accordance with the rising pressure. The transducers, located in the vapour phase, registered the temperature increase (the more intensive the oscillations the greater the temperature increase) (see Figure 8). This, at the same time as checking the heat inflow value by two methods, disproved the authors' initial assumption that anomalously greater heat inflows are connected with the carryover of drops into the drainage system. The temperature change on the warm end of the element was also of interest. Usually, for purposes of helium economy, the relations q(L), Ap(L) and ~(L) were recorded during the first 1 - 2 rain and, under strong oscillations, during the first 2 0 - 3 0 s after the oscillations had been generated. The temperature of the element warm end could not set, and an unsteady process proceeded, so that it was difficult to estimate the heat inflow from the outside.
in cryostat
neck
During the course of the tests, thermoacoustic oscillations were observed in the cryostat neck. Their intensity increased with increasing rate, which is why these oscillations reached a substantial value in the resonance areas. It was of interest to determine whether the resonance peaks in relations q(L) and Ap(L) were the result of the resonance of two oscillations: those in the thermoacoustic tube and in the cryostat neck.
4-
100
oscillations
300 --
3
200 ! w"
100
l
I
I
I
t
I
t (s)
0.12 EL v
0
.
1
0
0.08 I
20
I
40
I
60 t(s)
I
80
I
1oo
Figure 9 Change of oscillation amplitude and t e m p e r a t u r e on metal reducer surface w i t h time for specimen N8 w i t h qmax (1, 2 and 3 indicate the number of the transducer)
Cryogenics 1992 Vol 32, No 1
17
Thermoacoustic oscillations in cryostats: A.G, Kuzmina The oscillation frequency in the STG neck is 4 0 - 4 2 Hz. Numerous joint recordings of oscillations on one tape do not lead to the proposal of mutual influence of the two oscillations. There is, however, an indirect influence: with oscillation intensity rising in the TT, the gas flow rate increases and this causes an increase in oscillation intensity in the neck. The following factor was a determinant which ruled out the effect of the resonance of two oscillations: at the moment of the most intensive oscillations in the thermoacoustic tube the gas discharge in the neck was so great that the temperature in the top part decreased and the oscillations in the neck stopped completely. This did not influence the oscillation intensity in the thermoacoustic tube. It was shown by a special test, where the heater was used to create a vapour flow in the neck and the generated power was registered, that the thermoacoustic oscillations in the cryostat neck did not influence the quantity of evaporating helium.
Reproducibility of results obtained As far as it was impossible to maintain a definite temperature profile, the reproducibility of the results in some cases was only satisfactory. Most of the questions arising from this work arose from the following scenario, however. The oscillation intensity, especially in the field of resonance peaks, depended on tube 'training'. With the initial mounting of a newly manufactured tube, generally only weak oscillations were observed. Repeated tests showed the anomalous oscillations, with the heat inflow continuing to increase in the region of peaks and reaching the ultimate stationary values after four or five tests. If the tube was kept for half a year or more between tests, it showed average intensity anomalous oscillations with the first new test.
Analysis of results It has been shown that in tubes, one end of which was
immersed in liquid helium with the other at room temperature, there were anomalous strong thermoacoustic oscillations, the amplitude of the pressure oscillations being more than 0.1 MPa. The heat inflow introduced by these oscillations can reach 250-300 W. The basic conditions for the onset of such oscillations a heat-insulated cold part and tube expansion in the heat supply zone - are quite characteristic of many cryogenic devices. One of the possible interpretations of the physical nature of these resonance thermoacoustic oscillations is dealt with in an asymmetric form of the pressure variation curve (Figure 10). Of the total period, =0.8 is spent on the pressure rise ('inhalation') and 0.2 on pressure drop ('expiration'). The 'inhalations' and 'expirations' of ordinary thermoacoustic oscillations are nearly equal in duration. 'Inhalation' at the beginning of resonance oscillations proceeds similarly to that for ordinary ones when liquid is present at the cold end, i.e. with a reduced speed. Meanwhile, 'expiration' almost exactly repeats the analogous process in ordinary oscillations in a gaseous medium, i.e. it proceeds rapidly. Calculations show that 'expiration' can take 0.2
18
Cryogenics 1992 Vol 32, No 1
0"20I
).104 D.. ).102 cf
~0.15
0.1
0.10
0.1
t (s)
0.2
Figure 10 Recording of pressure oscillations: p, pressure in TE; Pl,
pressure in STG-40
of the period only in the case of absolute absence of liquid in the TT. Evidently, some event takes place between the first part of the 'inhalation' and the beginning of 'expiration'. This leads to partial liquid evaporation and partial liquid retreat to the cryostat and induces a more sharp pressure rise in the warm portion of TE than at the beginning of the process. Such a short-term event could be the explosive boiling of helium. But explosive boiling is observed only with superheated liquids. Extrapolating known experimental results, the lifetime of liquid helium overheated by 0 . 2 5 - 0 . 3 K is =0.01 s. Can helium in the TT superheat? Yes, it can. This is possible not only due to heat exchange with the wall but also due to the velocity increase which lowers the pressure in the flow. Simple calculations show that for a frequency of 10 Hz and a liquid rise up to the middle of the TT (approximately the quantity of liquid evaporated at qmax, the flow velocity reaches 24 m s-~ and pressure inside the flow drops by 0.03 MPa, which corresponds to superheating by 0.3 K. Thus, we propose the following sequence of events. The process begins with drawing liquid into the TT as with ordinary tbermoacoustic oscillations, but continues more intensively because there is an expansion at the warm end that acts as a weakened spring. The presence of vacuum insulation on the TT helps to preserve the wall heat of the previous cycle which is necessary for liquid superheating. Having achieved a maximum velocity, liquid boils up, pressure in the tube grows and the resulting vapour-liquid mixture is pushed out of the TT in both directions. At the outlet to the warm tube part, most of the liquid evaporates and vapour is warmed up due to the heat of the walls. At the moment of the pressure peak measured at the TE warm end, there is no liquid in the TT and generated vapour is pushed back into the cryostat due to the pressure difference. If these processes stay exactly within the period typical for ordinary thermoacoustic oscillations in a liquid, a resonance peak - a highest oscillation intensity and a highest heat inleak - is observed. If this coincidence is not complete, the system itself begins to regulate the process, and alternating oscillations of different intensity are observed, which are typical for other cases of parametric resonance. To validate the suggested hypothesis several additional experiments were carried out. For TT N9 a
Thermoacoustic oscillations in cryostats: A.G. Kuzmina simultaneous pressure recording in the TE warm portion and in the cryostat vapour space was performed. If helium boiling takes place inside the TT, the pressure in the cryostat would start rising to reach P .... in the TT. The recorded results, shown in Figure 10, illustrate this. Now, for the same TT, in its joint with the reducer, a diffusor was set up, i.e. hydraulic resistance was reduced. In this case separate peaks of Ap = 0 . 2 0.25 MPa instead of Ap = 0 . 1 - 0 . 1 2 MPa were observed. This indicates that in the process of 'inhalation' the pressure in the TT rises more intensively than in the TE warm portion, i.e. boiling takes place inside the TT. All the main test results have been analysed and they do not seem to contradict the suggested physical model. The initial step of vessel hard wall 'work-down" is well
known in thermal physics. According to the present author's estimations, which need careful verification, in some cases the heat supply at the warm end was less than the heat inflow to the cold zone. Evidently, this can be explained by the fact that in the calculations the evaporation heat was specified for normal conditions, while in reality the conditions differed greatly from the normal.
References 1 Clement, J.R. and Gaffney, J. Thermal oscillations in low temperature apparatus Adv Cryog Eng (1953) 1 3 0 2 - 3 0 6 2 Banister, J.D. Spontaneous pressure oscillations in tube connecting liquid helium reservoirs Bull hit hzst R£fi'ig (1966) 5 127-134 3 Ya~ki, T., Tominaga, A. and Narahara, Y. Large heat transport due to spontaneous gas oscillations induced in a tube with steep temperature gradients l)'ans ASME: J Heat Tran~j~,r (1983) 105 8 8 9 - 8 9 4
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