STUDIES ON PHASE SHIFTINGMECHANISM IN A PULSE TUBECRYOCOOLER (PTC)
26th International Cryogenic Engineering Conference
ICEC26 – ICMC 2016
8-O-1B-2
COMPRESSOR REGENERATOR DISPLACER
STIRLING CRYOCOOLER
COMPRESSOR REGENERATOR PT, IT, RESERVOIR
PULSE TUBE CRYOCOOLER
Padmanabhan
Gurudath C S
Srikanth Thota
Basavaraj S A
Dr.Ambirajan A
Dinesh Kumar
Prof. Venkatarathnam G
Table of Contents
INTRODUCTION
OBJECTIVE
THEORY
EXPERIMENTAL SET – UP
RESULTS AND DISCUSSION
CONCLUSION
FUTURE WORK
Cryocoolers : Devices that generate temperatures in the cryogenicrange i.e. from near absolute zero to 120K.
Broadly classified as -
1.Steady state type cryocoolers
Flow is unidirectional
Comparable to DC electrical systems
Performance depends on properties of the working fluid
2. Periodic type cryocoolers
Flow is oscillatory
Comparable to AC electrical systems
Performance depends upon the phase angle between Pressurepulse (voltage) and mass flow (current)
Introduction
1
Pulse Tube Cryocoolers (PTC) are of the periodic flow type havingdifferent configurations of a passive cold head encompassing differenttypes of phase shifting mechanisms to attain optimum performance
2
Objective
To study the phase shifting characteristics of an Inertance type phaseshifter on the performance of the PTC.
To obtain an optimum phase angle between the mass flow anddynamic pressure at the PT cold end that results in the largestpossible heat lift from this unit.
Develop a Theoretical model using Phasor Analysis and TransmissionLine Model (TLM) for different mass flow and arrive at values ofoptimum frequency and phase angles.
Compare the experimental data from the PTC for differentconfigurations of the Inertance tube/reservoir at various frequenciesand charge pressures.
These studies were carried out to characterise an existing cryocoolerand design an optimised phase shifter with the aim of improving theperformance with respect to specific power input.
PHASOR ANALYSIS
Phasor representation
3
Where Qc = Gross refrigerating power
Governing equations –
P = P0 + P1 cos (t)
T = T0 + T1 cos (t). (Sinusoidal variation)
Applying conservation of mass condition :
Yields equation connecting the cold and hot end flows as –
Thus, is given by the vectorial addition of the 1st
and 2nd term which are at an angle of (/2) to each other.
INERTANCE PULSE TUBE CRYOCOOLER (IPTC)
Using the Inertance tube both leading and lagging phase angle are obtained byvarying the r, l & c of the Inertance tube and capacitance of the reservoir.
The Orifice PTC gives only lagging phase angles i.e. pressure lagging mass flow.
PressurePhasor
PressurePhasor
Pressurephasor
Compr
Pulse
Tube
Res
Reg
Inertance tube
Compr
Pulse
Tube
Res
Reg
Orifice
4
Res
Compr
Pulse
Tube
Real axis
P
Inertance tube
Imaginary axis
r,h
r,c
•Phase angle is zero at the centerof the regenerator
•Mass flow rate is minimum for agiven heat load.
•Regenerator losses are at aminimum, resulting in maximumperformance of the system.
• Obtaining maximum cooling forgiven flow rate is the primeobjective of the phase shiftingcircuit .
Inertance Pulse Tube Cryocooler (IPTC)
5
Electrical Parameter
Resistance (r)
Inductance(l)
Capacitance(c)
Capacitance (Cr)
Reservoir
Equivalent Fluid parameter(per unit length)
TRANSMISSION LINE MODEL
Governing Equations
Electrical Parameter
Equivalent Fluid parameter
Impedance (Z)
Z = E /I
E = Voltage
I = current
Impedance (Zm)
= /
= Pressure amplitude
= mass flow rate
6
r
c
Cr
Z -INDUCTIVE
Z - CAPACITIVE
Solution to this pair of simultaneous differential equation yields the compleximpedance of a terminated transmission line of length Le
Where, impedance of the compliant load ; characteristic impedance
|Zm| is the amplitude of the complex impedance at the inlet to the Inertance tube i.e.at the Pulse Tube / Inertance tube interface. θz is the angle by which leads .
Resonance condition in the phase shifting circuit is defined as the frequency at whichthe imaginary part of the complex impedance goes to zero .
7
EXPERIMENTAL SET – UP
SCHEMATIC OF EXPERIMENTAL
SET-UP
ColdHead
Compressor
Phase
shifter
Detector I/F
8
RESULTS AND DISCUSSIONS
Length
0.6
1.0
1.5
2.0
0.05
2.28
-8.42
-67.37
-85.0
0.1
3.32
5.75
-33.15
-77.5
0.25
2.73
13.73
21.43
-18.15
0.5
-1.76
15.25
36.17
46.52
1.0
-18.99
11.82
40.57
59.47
1.5
-36.25
3.95
39.6
61.2
1.75
-41.22
-1.3
38.08
61.1
2.0
-43.8
-7.36
35.9
60.5
Phase Angle variation with Inertance Tube Geometry – TLM model.
Length
0.6
1.0
1.5
2.0
0.05
0.82
-3.54
-44.9
-78.1
0.1
0.87
2.27
-15.2
-61.8
0.25
-2
5.05
9.02
-7.8
0.5
-12.9
3.48
16
23.3
1.0
-38.7
-6.86
16.1
34
1.5
-45.8
-22.2
10.8
34.5
1.75
-45.4
-29.4
6.7
33.4
2.0
-44.7
-35.2
1.9
31.5
Test case -1 : m = 0.35 g/s
Test case -2: m = 1.05 g/s
To achieve a phase angle of > 300 at inertance inlet, tube sizes with ID around2mm are necessary, for mass flow in the range of 0.35 g/s to 0.5 g/s.
9
The primary data needed for constructing the phasor diagrams needed forarriving at the phase relationships, is the mass flow rate from thecompressor and that at the inertance tube inlet.
I.Mass flow rate measurements at compressor outlet
Compressor
Reservoir
P1
P2
Schematic of mass flow measurement
Uncertainty analysis show - 2.7% error for mass flow leaving the compressor and
1.4% error for mass flow entering the reservoir.
10
The mass flow into the Reservoir is given by
where, = time derivative of pressure, Vr = reservoir volume
and Tr = reservoir temperature
Sl. no
Inertance tube
Frequency -Hz
Mass flowIT entry g/s
Ph. AngleTLM (deg)
Pr. Ampl(bar)
Temp
(K)
ID (mm)
Length (m)
Exptl Opt
TLM
1
1.76
4.5
54
58
0.043
56.7
1.09
151
2.
1.76
4.0
59
65
0.055
59.9
1.14
132
3.
1.76
3.5
64
74
0.072
64.2
1.12
116
4.
1.76
3.0
71
86
0.091
67.2
1.14
103
5.
1.76
2.75
76
94
0.095
69.5
1.12
98
6.
1.12
2.0
64*
124
0.096
49.1
1.096
119
7.
1.12
1.75
64*
141
0.113
47.4
1.103
130
8.
1.12
1.5
64*
165
0.125
46.8
1.034
141
The lowest temperature achieved (at zero applied heat load): 151K to 98K.
Phase difference varies from 56.70 to 69.50 and mass flow from 0.043 to0.095 g/s
The results clearly show that the performance of the refrigerator iscritically dependent on the configuration of the inertance tube.
The lowest temperature achieved with all configurations is close to thenatural frequencies calculated by the model.
11
The operating frequency of the compressor was varied from 44 to 76 Hz and pressurefrom 18 to 28 bar. Reservoir volume constant at 100 cm3 .
An optimum frequency (fo) exists for each inertance tube/reservoircombination.
The cryotip temperature (at fo) decreases with an increase in the naturalfrequency of the inertance tube/reservoir and increase in chargepressure
Frequency and Temperature variation
Pressure and Temperature variation
12
Tube ID: 1.76mm
Operating experimental frequency is the frequency at which lowesttemperature is obtained for a given configuration
Operating frequency fo is always lower than the natural frequency
Calculated vs Optimum Experimental frequency.
Correlation between Calculated andOptimum frequency
13
Tube ID 1.76mm
An experimental approach to measure this natural frequency was explored.
There exists a clear minima in the piston amplitude for fixed inertance tubeinlet pressure amplitude.
TLM predicts a natural frequency that is 10 Hz higher than the experimentalvalue.
The TLM results are based on a constant mass flow rate whereas in realitythe mass flow rate changes with the piston amplitude.
This requires further study.
14
Conclusions
The performance of a Pulse tube refrigerator is a strong function of thephase angle between the pressure and flow rate phasors
The cooling capacity of the refrigerator is highest when the compressorfrequency is close to the natural frequency of the inertance tube.
Higher natural frequency of the inertance tube higher the coolingcapacity or lower the temperature achieved.
The minima in temperature obtained in the PTC with respect tofrequency variation is directly correlated with the natural frequency,obtained from the mathematical model, of the PSM.
Higher the average pressure higher the cooling capacity, however thehighest pressure is limited by the presence of transition joints betweendissimilar metals in the refrigerator.
Importance of natural frequency and an experimental approach todetermine the same.
15
FURTHER SCOPE OF WORK
Study for natural frequency determination of compound Inertance tubesand subsequent cooling performance of the PTC with theseconfigurations to obtain lower temperatures.
As observed from the test results, improved performance is obtained athigher frequencies and pressures. Hence Design and realisation of a highfrequency PTC is envisaged.
16
THANK YOU….for your attention
References
[1]Ross, R.G., Jr and Green K.1997 Cryocoolers 9 Plenum Publishing
pp.885 - 8 94
[2]Chan CK, Ross RG Jr et al. 1999 Cryocoolers 10 Plenum Publishing
pp.139 -147
[3]Hoffman A. and Pan H. 1999 Cryogenics 39 pp.529-537
[4]Faculty, 2011 CEP Course Adv. in Cryocooler Tech., Dept of Mech. Engg
IIT-B Ch.1-4.
[5]Skilling, H.H., 1951 Electric Transmission Lines, McGraw-Hill, Chapter 1-4.
[6]Radebaugh R, Lewis M, Luo E, et.al. 2006 Adv. in Cryogenic Engg. 51
pp.59-67.
[7]Luo,E., Radebaugh R. and Lewis M., 2004 Adv. in Cryogenic Engg. 49pp.1485-1492.
[8]Schunk L.A., Experimental investigation and modeling of inertance tubes,MS Dissertation, University of Wisconsin-Madison, 2004, Chapter 4.
[9]Haizen Dang., 2012 Cryogenics 52 pp 205 – 211.
17
Compressor
Pulse Tube
CHX
HHX
Regenerator
After cooler
Orifice
Reservoir
Compressor
Pulse Tube
CHX
HHX
Regenerator
After cooler
Orifice
Reservoir
Double inlet valve
Compressor
Pulse Tube
CHX
HHX
Regenerator
After cooler
Inertancetube
Reservoir
OPTC
DIPTC
IPTC
PHASE SHIFTING MECHANISMS IN PULSE TUBE CRYOCOOLERS
Res
Compr
Pulse
Tube
Real axis
P
Inertance tube
r,h
r,c
Real axis
Imaginary axis
Imaginary axis
Phasor diagrams for two practical cases for the IPTC
P4
P1
P2
Compressor
PTC Coldhead
Cryotip
P3
T1
Inertance tube
Reservoir
Schematic of performance evaluation test set-up
P3
P1
Compressor
Reservoir
P2
Inertancetube
LVDT
Schematic of set-up for Natural frequency determination of phase shift circuit
III (e)Effect of change in Reservoir volume on phase angle
An order of magnitude change in the reservoir volumes do not change the phaseangles significantly.
The guideline for choosing the reservoir is that it should be at least 50 times thepulse tube volume to provide for sufficient capacitance.
II (c)Mathematical model results with frequency variation
Length = 4m
Higher diameter tubes have lower sensitivity to mass flow rate, reflected by thesame resonant frequency irrespective of the mass flow rate.
Frictional “resistance” occurs on the inner surface of the tube. Clearly the ratio ofperimeter to cross-sectional area decreases with an increase in diameter (i.e.D/[D2/4]=4/D).
Phase angles (calculated using TLM) are plotted as a function of frequency.
Minima in temperature occur at the frequency near the knee of the phase shiftcurve, for a given inertance tube / reservoir combination.
This seems physically plausible as the highest cooling is obtained when thepressure leads the mass flow rate by app. 60o
1.76mm; L =3.5m
1.76mm; L =2.75m