Growing interest in larger scale pulse tubes has focused attention on optimizing their thermodynamic efficiency. For Stirling-type pulse tubes, the performance is governed by the phase difference between the pressure and mass flow, a characteristic that can be conveniently adjusted through the use of inertance tubes. In this paper we present a model in which the inertance tube is divided into a large number of increments; each increment is represented by a resistance, compliance, and inertance. This model can include local variations along the inertance tube and is capable of predicting pressure, mass flow rate, and the phase between these quantities at any location in the inertance tube as well as in the attached reservoir. The model is verified through careful comparison with those quantities that can be easily and reliably measured; these include the pressure variations along the length of the inertance tube and the mass flow rate into the reservoir. These experimental quantities are shown to be in good agreement with the model’s predictions over a wide range of operating conditions. Design charts are subsequently generated using the model and are presented for various operating conditions in order to facilitate the design of inertance tubes for pulse tube refrigerators. These design charts enable the pulse tube designer to select an inertance tube geometry that achieves a desired phase shift for a given level of acoustic power.

1.
Mikulin
,
E. I.
,
Tarasov
,
A. A.
, and
Shrebyonock
,
M. P.
, 1984, “
Low-Temperature Expansion Pulse Tube
,”
Adv. Cryog. Eng.
0065-2482,
29
, pp.
629
637
.
2.
Zhu
,
S.
,
Wu
,
P.
, and
Chen
,
Z.
, 1990, “
Double Inlet Pulse Tube Refrigerators: An Important Improvement
,”
Cryogenics
0011-2275,
30
, pp.
514
520
.
3.
Marquardt
,
E. D.
, and
Radebaugh
,
R.
, 2001, “
Pulse Tube Oxygen Liquefier
,”
Adv. Cryog. Eng.
0065-2482,
45
, pp.
457
464
.
4.
Kanao
,
K.
,
Watanabe
,
N.
, and
Kanazawa
,
Y.
, 1994, “
A Miniature Pulse Tube Refrigerator for Temperature Below 100K
,”
Cryogenics
0011-2275,
34
, (supplement) p.
167
.
5.
Gardner
,
D. L.
, and
Swift
,
G. W.
, 1997, “
Use of Inertance in Orifice Pulse Tube Refrigerators
,”
Cryogenics
0011-2275,
37
(
2
), pp.
117
121
.
6.
de Boer
,
P. C. T.
, 2002, “
Performance of the Inertance Pulse Tube
,”
Cryogenics
0011-2275,
42
, pp.
209
221
.
7.
Ju
,
Y. L.
,
He
,
G. Q.
,
Hou
,
Y. K.
,
Liang
,
J. T.
, and
Zhou
,
Y.
, 2003, “
Experimental Measurements of the Flow Resistance and Inductance of Inertance Tubes at High Acoustic Amplitudes
,”
Cryogenics
0011-2275,
43
, pp.
1
7
.
8.
Luo
,
E.
,
Radebaugh
,
R.
, and
Lewis
,
M.
, 2004, “
Inertance Tube Models and Their Experimental Verification
,”
Adv. Cryog. Eng.
0065-2482,
49
, pp.
1485
1492
.
9.
Incropera
,
F. P.
, and
DeWitt
,
D. P.
, 2002,
Introduction to Heat Transfer
, 4th Edition,
John Wiley and Sons
, New York.
10.
Klein
,
S. A.
, and
Alvarado
,
F. L.
, 2002, “
EES-Engineering Equation Solver
,” F-Chart Software.
You do not currently have access to this content.