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Phase shift between gas velocity and pressure in an orifice pulse tube
J. Daligault, J. Domblides, C. Dodray, G. Pelfrene
To cite this version:
J. Daligault, J. Domblides, C. Dodray, G. Pelfrene. Phase shift between gas velocity and pres- sure in an orifice pulse tube. Journal de Physique III, EDP Sciences, 1994, 4 (4), pp.659-662.
�10.1051/jp3:1994155�. �jpa-00249134�
Classification Physic-s Abstracts
07.20M 47.60
Phase shift between gas
velocity
and pressure in an orifice pulsetube
J. Daligault, J. P. Dimblides, C. Dodray and G. Pelfrene
Laboratoire du froid, CNAM, 292 rue Saint-Martin, 75141Paris Cedex 03, France (Received15 July 1993, ret,ised 8 October 1993, accepted 15 November J993)
Abstract. In order to investigate how the phase shift between pressure P (t and velocity of gas v (t affects the net refrigeration power of an orifice pulse tube, we have recorded at the cold end of the regenerator, when the temperature is constant at 173 K and 259 K, the net refrigeration power
and the two signals of dynamic pressure and velocity of gas. The phase shift is computed from FFT of the two signals. If
we maintain the amplitude of pressure AP
=
(P
~~~
P~,~) constant, the net refrigeration power varies as a function of the phase shift between pressure and velocity of gas.
Introduction.
With the modifications proposed by Mikulin [I] and Zhu [2] the orifice pulse tube, originally suggested by Gifford and Longsworth [3], is now, especially for space applications, a very
attractive cryocooler with good performances, and no cold moving part.
Because their theories were not fully confirmed by their experiments tile analytical model
proposed by Storch and Radebaugh [4] and later modified by Basks et al. [5], is inadequate to find an optimum design of the refrigerator [6] ; in order to overcome this difficulty, it is necessary to measure some important parameters such as pressure, temperature, and gas
velocity in different points of the tube, especially at the cold end of the regenerator [7].
With this experimental set-up shown in figure I we report on phase shift measurements between pressure and gas velocity.
Description of the experimental set-up.
The pressure oscillation is generated by a dry valveless compressor with a 500 cm3 sweep volume operating at 7 Hz. All components of the tube are manufactured in stainless steel tube with 0.2 mm wall thickness. The flange B~ supports a piezorestive pressure transducer and a hot wire anemometry system using two platinum wires 15 ~Lm in diameter it gives us the
shape of gas velocity.
Some characteristics of the experimental set-up are given here after
. heat exchanger El : 50 tubes of copper ID I mm, 80 mm length ; water cooled
. regenator it is made of three parts
JOURNAL DE PHYSIQUE III T 4 N'4 APRIL 1994 2s
660 JOURNAL DE PHYSIQUE III N° 4
first part : 40 mm ID, 85 mm length, filled with 620-180 mesh phosphor bronze screen disks
second part : 150 mm length, ID 30 mm, filled with the same screen third part is 50 mm length, filled with lead balls of 1.3 mm.
. heat exchanger E~: 52 mm length, 119 tubes of copper ID 1.8 mm soldered in a copper block on which the resistance R~~ is fixed ;
. tube 600 mm length, ID 20 mm
. heat exchanger E~. 185 mm length, 58 tubes of copper ID I mm, water cooled ;
. tank : RI
"
6 500 cm~ R~
= 7 200 cm~.
Experimental procedure.
For all the experiences the average pressure is held constant. In a first experience, for various
opening of the needle valve Vi, valve V~ being closed, and valve V~ opened we adjust, with the electric power dissiped in the resistance R~~, the temperature at the cold end of the
regenerator (T
=
173 K curve a and T
=
259 K curve b).
The instantaneous signals of pressure and gas velocity are displayed on a digital
oscilloscope, and recorded on a computer the phase shift is easily achieved from FFT of the two signals.
The compressor is a machine with constant volumetric flow opening the valve
Vj modified the amplitude of pressure in the tube to overcome this difficulty, in a second
experience, we maintain constant AP
= (P~~~ P~,~) in the tube (curve al and bl), with ballast R~ and the valves V~ and V~.
Results.
On curves (a) and (b) respectively for T
=
173 K and T
=
259 K, the net refrigeration power
increases when phase shift decreases, with a maximum of 50 w situated around 35° on
curve (a), and 105 w around 35° on curve (b) ; beyong this point, a parameter (AP becomes
preponderant in the determination of the refrigeration power.
Opening valve Vj results in a decrease of the amplitude of pressure in the tube, because the increase of mass flow in the ballast Rj increases pressure drop in the regenerator. When
AP
= (P~~~ -P~,~) is constant (curve aj and bj) the maximum of refrigeration power
observed on curve (a and b) vanishes, and the net refrigeration power increases when the phase
shift between pressure and velocity of gas decreases.
Conclusion.
According to Radebaugh [8] and Zhu Shaowei [2] an enthalpy flow from the cold end to the hot end of the tube is produced, and can be expressed as
C
~A T
(H)
=
P (t) V (t) dt
R T
o
where : C~ =
specific heat of the fluid A
= cross sectional area of the tube R
=
the gas
constant ; V (t) = Vo cos (wt + 4 ) velocity of gas P (t) = Po cos wt pressure and
r =
period of the cycle. This equation shows that (H) is maximum when the phase shift between V (t and P (t is minimum ; it is what we have shown experimentally by elitriinating
the influence of pressure drop in the regenerator.
valve Vi
Heat
Water
Vacuum
Tank Et
iauie
' Heat
R,eb
Reienerator ( screens)
(lead ball)
Water
heat Et
~~~~Rg Needle valve V4
Needle valve
Compressor
Fig. I. Schematic diagram.
662 JOURNAL DE PHYSIQUE III N° 4
a
e
o
Fig. 2. Net refrigeration power versus phase shift dl. curves a T =173 K aj T =173 K and P
= Cte b T
= 259 K bj T
=
259 K and P
= Cte.
References
Ii Mikulin E. I., Tarasov A. A. and Shkrebyonock M-P-, Low temperature expansion pulse tube, Adv.
Cryo. Eng. 29 (1984) 629-636.
[2] Zhu Shaowei, Wu Peiyi and Chen Zhongqi, Double inlet pulse tube refrigerators : an important improvement, Cryogenic-s 30 (1990) 514-520.
[3] W. E. Gifford and Longsworth R. C., Pulse tube refrigerator, Trans. ASME serie B 86 (1964) 264- 268.
[41 Storch P. J. and Radebaugh R., Development and experimental test of an analytical model of orifice
pulse tube refrigerator, Adv. Cryo. Eng. 33 (1988) 851-859.
[5] Baks M. J. A., Hirschberg A., Van der Ceelen B. J. and Gijsman H. M., Experimental verification of an analytical model for orifice pulse tube refrigerator, Cryogenics 30 (1990) 947-951.
[6] David M., Marechal J. C. and Encrenaz P., Measurements of instantaneous gas velocity and temperature in a pulse tube refrigerator, Adv. Cryo. Eng. part B 37 (1992) 939-946.
j7] Domblides J. P., Daligault J. and Veyssie J. J., Etude expdrimentale d'un r6frigdrateur du type tube h impulsions avec double injection et orifice, Proceedings of the 18'h intemational congress of
refrigeration Montr6al Qu£bec vol.1 (1991) pp. 159-161.
j8] Radebauhh R., Zimmerman J., Smith D. R. and Louie B., A comparison of three types of pulse refrigerators new method for reaching 60 K, Adv. Cryo. Eng. 31 (1986) 779-789.
