1

1. INTRODUCTION

1.1 Cryocoolers

Cryocoolers are small refrigerators that can reach cryogenic temperatures and provide

refrigeration in the temperature below 120 K. The use of Cryocoolers has been propelled

by many necessities of modern day applications such as adequate refrigeration at specified

temperature with low power input, long lifetime, reliable and maintenance free operation

with minimum vibration and noise, compactness, and lightweight. The requirements

imposed in each of these applications have been difficult to meet and have been the impetus

for considerable research in the field of Cryocoolers for the past forty years.

Typical applications of Cryocoolers are:

Liquefaction of gases such as nitrogen, oxygen, hydrogen, helium,

natural gas

Cooling of super-conducting magnets

Cooling of infra-red sensors for missile guidance

Cryo vacuum pumps

SQUID magnetometers

Gamma ray sensors for monitoring nuclear activity

Cooling of high temperature superconductors and semiconductors

Cryosurgery

Preservation of biological materials, blood, biological specimens etc.

1.2 Classification of Cryocoolers

Cryocoolers are classified into two types based on the type of heat exchanger used:

(1) Recuperative cryocoolers and

(2) Regenerative cryocoolers.

2

Recuperative types, as shown in figure 1.1, utilize continuous flow of the refrigerant in one

direction, analogous to a DC electrical system. As a result, the compressor and expander

must have inlet and outlet valves to control the flow direction, unless rotary or turbine

compressor or expanders are used. The recuperative heat exchangers have two or more

separate flow channels. The performance of the recuperative cryocoolers is dependent on

the properties of the working fluids used. Also, the maximum exergy loss in most

cryocoolers occurs in the compressor. The main advantage of DC cryocoolers, however, is

that they can be scaled to any size (up to few MW of refrigeration).

Fig.1.1 Schematic of Recuperative Cryocoolers

Regenerative types, as shown in figure 1.2, the refrigerant undergoes an oscillating flow or

an oscillating pressure analogous to an AC electrical system. The compressor and the

pressure oscillator for the regenerative cycles need no inlet or outlet valves. The

regenerator has only one flow channel, and the heat is stored for a half cycle in the

regenerator matrix, which must have a high heat capacity. The performance of the

regenerative type cryocoolers is dependent on the phase difference between the pressure

and mass flow rate phasors. Helium is the refrigerant of choice for most regenerative type

3

cryocoolers. The main disadvantage with regenerative type cryocoolers is that they cannot

be scaled to large sizes like the recuperative cryocoolers.

Fig. 1.2 Schematic of Regenerative Cryocoolers

4

2. Pulse tube Cryocoolers

2.1 Pulse Tube Cryocooler

The pulse tube refrigerator (PTR) or pulse tube cryocooler is a developing technology

that emerged largely in the early 1980s with a series of other innovations in the broader

field of thermoacoustics. In contrast with other cryocoolers (e.g. Stirling cryocooler

and Gifford-McMahon cooler), this cryocooler can be made without moving parts in

the low temperature part of the device, making the cooler suitable for a wide variety of

applications.

2.2 Uses

Pulse tube cryocoolers are used in industrial applications such as semiconductor

fabrication and in military applications such as for the cooling of infrared sensors. Pulse

tubes are also being developed for cooling of astronomical detectors where liquid

cryogens are typically used, such as the Atacama Cosmology Telescope or the Qubic

experiment (an interferometer for cosmology studies). PTR's are used as precoolers of

dilution refrigerators. Pulse tubes will be particularly useful in space-based telescopes

where it is not possible to replenish the cryogens as they are depleted. It has also been

suggested that pulse tubes could be used to liquefy oxygen on Mars.

2.3 Types of pulse-tube refrigerators

For getting the cooling, the source of the pressure variations is unimportant. PTR's for

temperatures below 20 K usually operate at frequencies of 1 to 2 Hz and with pressure

variations from 10 to 25 bar. The swept volume of the compressor would be very high

(up to one liter and more). Therefore the compressor is uncoupled from the cooler. A

system of valves (usually a rotating valve) alternatingly connects the high-pressure and

the low-pressure side of the compressor to the hot end of the regenerator. As the high-

temperature part of this type of PTR is the same as of GM-coolers this type of PTR is

5

called a GM-type PTR. The gas flows through the valves are accompanied by losses

which are absent in the Stirling-type PTR. PTR's can be classified according to their

shape. If the regenerator and the tube are in line (as in Fig.1) we talk about a linear

PTR. The disadvantage of the linear PTR is that the cold spot is in the middle of the

cooler. For many applications it is preferable that the cooling is produced at the end of

the cooler. By bending the PTR we get a U-shaped cooler. Both hot ends can be

mounted on the flange of the vacuum chamber at room temperature. This is the most

common shape of PTR's. For some applications it is preferable to have a cylindrical

geometry. In that case the PTR can be constructed in a coaxial way so that the

regenerator becomes a ring-shaped space surrounding the tube.

The lowest temperature, reached with single-stage PTR's, is just above 10 K. [14]

However, one PTR can be used to precool the other. The hot end of the second tube is

connected to room temperature and not to the cold end of the first stage. In this clever

way it is avoided that the heat, released at the hot end of the second tube, is a load on

the first stage. In applications the first stage also operates as a temperature-anchoring

platform for e.g. shield cooling of superconducting-magnet cryostats. Matsubara and

Gao were the first to cool below 4K with a three-stage PTR. [15].

2.4 Analysis Of Pulse Tube Refrigerators

Enthalpy and Entropy Flow Model

The refrigeration power of the OPTR is derived using the First and Second Laws of

Thermodynamics for an open system. Because of the oscillating flow the expressions

are simplified if averages over one cycle are made. Even though the time-averaged

mass flow rate is zero, other time-averaged quantities, such as enthalpy flow, entropy

flow, etc., will have nonzero values in general. We define positive flow to be in the

direction from the compressor to the orifice. The First Law balance for the cold section

is shown in Figure 3. No work is extracted from the cold end, so the heat absorbed

under steady state conditions at the cold end is given by

Qc= H –H

r --- (1)

6

Where, H is the time-averaged enthalpy flow in the pulse tube,

Hr is the time-averaged enthalpy flow in the regenerator, which is zero for a

perfect regenerator and an ideal gas.

The maximum, or gross, refrigeration power is simply the enthalpy flow in the pulse

tube, with the enthalpy flow in the regenerator being considered a loss. Combining the

First and Second Laws for a steady-state oscillating system gives the time-averaged

enthalpy flow at any location as

H=PdV+T

0S ----- (2)

Where,

Pd is the dynamic pressure,

V is the volume flow rate,

T0 is the average temperature of the gas at the location of interest,

S is the time-averaged entropy flow.

The first term on the right hand side of Eq. (2) represents the potential of the gas to do

reversible work in reference to the average pressure P0 if an isothermal expansion process

occurred at T0 in the gas at that location. Since it is not an actual thermodynamic work

term, it is sometimes referred to as the hydrodynamic work flow, hydrodynamic power, or

acoustic power. Equation (2) shows that the acoustic power can be expressed as an

availability or energy flow with the reference state being P0 and T0. The specific

availability or energy is given as h – T0s. Processes within the pulse tube in the ideal case

are adiabatic and reversible. In this case entropy remains constant throughout the cycle,

which gives

S = 0 (ideal case) ---- (3)

Equations (1) and (2) are very general and apply to any oscillating thermodynamic system,

even if the flow and pressure are not sinusoidal functions of time. If they are sinusoidal,

the acoustic power can be written as

Pd V=0.5*P

1 V

1 Cosθ

7

=0.5*RT0m

1*(P

1/P

0) ---- (4)

Where,

P1 is the amplitude of the sinusoidal pressure oscillation,

V1 is the amplitude of the sinusoidal volume flow rate,

θ is the phase angle between the flow and the pressure,

R is the gas constant per unit mass,

m1 is the amplitude of the sinusoidal mass flow rate.

Equations (1-3) can be combined to give the maximum or gross refrigeration power in

terms of acoustic power as

Qmax

=Pd

V ---- (5)

This simple expression is a very general expression and applies to the Stirling and Gifford-

McMahon refrigerators as well. In those two refrigerators the acoustic work is converted

to actual expansion work by the moving displacer. That work is easily measured by finding

the area of the PV diagram. In the case of the pulse tube refrigerator there is no moving

displacer to extract the work or to measure a PV diagram. Thus, the volume or mass flow

rate must be measured by some flow meter to determine the acoustic power. Such

measurements are difficult to perform inside the pulse tube without disturbing the flow

and, hence, the refrigeration power. Because there is no heat exchange to the outside along

a well-insulated pulse tube, the First Law shows that the time-averaged enthalpy flow

through the pulse tube is constant from one end to the other. Then, according to Eq. (2) the

acoustic power remains constant as long as there are no losses along the pulse tube to

generate entropy. The instantaneous flow rate through the orifice is easily determined by

measuring the small pressure oscillation in the reservoir and using the ideal-gas law to find

the instantaneous mass flow rate. The instantaneous pressure is easily measured in the

warm end of the pulse tube, and the product of it and the volume flow is integrated

according to Eq. (5) to find the acoustic power. The enthalpy flow model pertaining to the

8

ideal OPTR and leading to Eqs. (4) and (5) was discussed as early as 1986 by Radebaugh

and refined over the next few years.

Pulse Tube Losses and Figure of Merit

In an actual pulse tube refrigerator there will be losses in both the regenerator and in the

pulse tube. These losses can be subtracted from the gross refrigeration power to find the

net refrigeration power. The regenerator loss caused by Hr is usually the largest loss, and

it can be calculated accurately only by complex numerical analysis programs, such as

REGEN3.1 developed by NIST. The other significant loss is that associated with

generation of entropy inside the pulse tube from such effects as (a) instantaneous heat

transfer between the gas and the tube wall, (b) mixing of the hot and cold gas segments

because of turbulence, (c) acoustic streaming or circulation of the gas within the pulse tube

brought about by the oscillating pressure and gas interactions with the wall, and (d) end-

effect losses associated with a transition from an adiabatic volume to an isothermal volume.

The time-averaged entropy flows associated with (b), (c), and (d) are always negative, that

is, flow from pulse tube to compressor. The entropy flow associated with (a) is negative at

cryogenic temperatures, where the critical temperature gradient has been exceeded, but is

positive at higher temperatures, where the temperature gradient is less than the critical

value. Thermo acoustic models of pulse tube refrigerators, developed between 1988 and

1995, calculate the entropy flow associated with (a), but no models have been sufficiently

developed yet to calculate the entropy flows associated with (b) and (c). Because these

entropy flows in the pulse tube are negative, the enthalpy flow, and, hence, the refrigeration

power will be less than the acoustic power according to Eq. (2). For an ideal gas the pulse

tube figure of merit is defined as:

FOM=H/PdV ---- (6)

Measured values for FOM range from about 0.55 to 0.85 in small pulse tubes to as high as

0.96 in very large pulse tubes where acoustic streaming was eliminated with a light taper.

These values of FOM are then used as empirical factors in calculations of pulse tube

performance.

9

Effect of Phase between Flow and Pressure

Equation (4) shows that for a given pressure amplitude and acoustic power, the mass flow

amplitude is minimized for θ = 0. Such a phase occurs at the orifice, that is, the flow is in

phase with the pressure. However, because of the volume associated with the pulse tube,

the flow at the cold end of the pulse tube then leads the pressure by approximately 30° in

a correctly sized pulse tube. The gas volume in the regenerator will cause the flow at the

warm end of the regenerator to lead the pressure even further, for example, by 50 to 60°.

With this large phase difference the amplitude of mass flow at the warm end of the

regenerator must be quite large to transmit a given acoustic power through the regenerator.

This large amplitude of mass flow leads to large pressure drops as well as to poor heat

exchange in the regenerator. These losses are minimized when the amplitude averaged

throughout the regenerator is minimized. This occurs when the flow at the cold end lags

the pressure and flow at the warm end leads the pressure. A 30° lag at the cold end is the

approximate optimum. To achieve this phase angle requires that the flow at the warm end

of the pulse tube be shifted away from its normal 0° phase angle to about –50 to -60°. In

the last few years two different mechanisms have been developed to cause a beneficial

phase shift between the flow and the pressure at the warm end of the pulse tube.

2.5 History of Pulse Tube Cryocoolers

W. E. Gifford and R. C. Longsworth, in 1960's, invented the so-called Basic Pulse Tube

Refrigerator. The modern PTR was invented by Mikulin by introducing orifice in Basic

pulse tube in 1984. He reached a temperature of 105 K. Soon after that, PTR’s became

better due to the invention of new variations. This is shown in figure, where the lowest

temperature for PTR’s is plotted as a function of time. At the moment, the lowest

temperature is below the boiling point of helium (4.2 K). Originally this was considered

to be impossible. For some time it looked as if it would be impossible to cool below

the lambda point of 4He (2.17 K), but the Low-Temperature group of the Eindhoven

University of Technology managed to cool to a temperature of 1.73 K by replacing the

10

usual 4He as refrigerant by its rare isotope 3He. Later this record was broken by the

Giessen Group that managed to get even below 1.3 K. In a collaboration between the

groups from Giessen and Eindhoven a temperature of 1.2 K was reached by combining

a PTR with a superfluid vortex cooler.

Fig. 2.1 The temperature of PTR’s over the years

2.6 Staging in pulse tube cryocoolers

There is lot of research has been done and going on recently. To obtain lower and lower

temperature, staging is an effective way. As we can see in cascade cycle, we use different

refrigeration cycles in series to obtain lower temperature. So the same concept can be

applied in cryocoolers.

Y. Matsubara and J.L. Gao did some research on staging pulse tube cryocooler. They did

their research in atomic energy research institute, Nihon University, japan. A novel

multiple staging configuration for the pulse tube refrigerator is described for increasing its

performance and simplicity. To decrease both the regenerator loss and pulse tube loss, a

regenerative tube was developed for operating the pulse tube from room temperature to

11

liquid helium temperature. With this configuration a lowest temperature of 3.6K and a

cooling capacity of 119mW at 4.9K were achieved by a three-stage pulse tube refrigerator.

The test results and refrigeration performance of this refrigerator are also presented.

Figure. 2.2 Previous configuration of multiple stage pulse tube refrigerator

Here is some of the configuration and data of three stage pulse tube cryocooler used in

their experiment.

Figure. 2.3 Operating condition of three stage pulse tube refrigerator

12

The below graph shows the cool-down of the three stages vs time. One interesting thing

to notice is that the temperature of each stage is decreasing as stages go ahead.

Figure: 2.4 cool-down process of three stages

Figure: 2.5 schematic of three stage pulse tube cryocooler

13

The cooling performance on the third stage is shown below. The cooling capacity decreases

as the cooling temperature is lowered.

Figure: 2.6 cooling performance of third stage in three stage pulse tube refrigerator

T. Nguyen, R. Colbert, D. Durand, C. Jaco, M. Michaelian, and E. Tward did research on

10K Pulse Tube Cooler. The 10K 3-stage pulse tube cooler incorporates a 3-stage pulse

tube cold head mounted directly on the compressor center plate. This integral configuration

allows all the heat to be rejected from the single compressor centerplate. A model of the 3-

stage cooler is shown in Figure. The 1st and 2nd stages use a parallel coaxial 2-stage cold

head very similar to the coaxial HCC variant cooler to precool the gas to approximately

40K. The 3rd stage is implemented through the addition of a third stage in a serial

configuration with the 2nd stage in a U-tube cold head configuration, mounted on the cold

block of the 2nd stage. The parallel configuration of the 1st and 2nd stages has the advantage

that there is minimal interference in the thermal performance of the two stages with the 1st

stage. These upper stages can also be independently changed depending on the cooling

requirement at that temperature on different projects.

14

Figure: 2.7 three stage high capacity cryocooler model

D. Durand, D. Adachi, D. Harvey, C. Jaco, M. Michaelian, T. Nguyen, M. Petach, and J.

Raab from Northrop Grumman Space Technology published a paper on Mid Infrared

Instrument (MIRI) Cooler Subsystem Design. The Cooler Subsystem for the Mid Infrared

Instrument (MIRI) of the James Webb Space Telescope (JWST) features a 6.2 K Joule-

Thomson (J-T) cooler precooled by a three-stage Pulse Tube (PT) cryocooler to provide

68 mW of cooling at the instrument’s Optical Bench Assembly (OBA). This paper shows

an important application of staged pulse tube cryocooler.

Figure: 2.8 MIRI Cooler Subsystem Block Diagram

15

Q. Cao, L.M. Qiu, Z.H. Gan, Y.B. Yu, X.Q. Zhi presented a paper on A Three-Stage

Stirling Pulse Tube Cryocooler Approaching 4 K. A three-stage Stirling PTC is proposed

to investigate the cooling mechanism at different temperature ranges. The three separated

stages operate at LN2, LH2, LHe temperatures, which are all important temperature ranges

for cryogenics. The thermal-coupled structure employs three thermal bridges to connect

these stages. Each thermal bridge is detachable, which is convenient for assembling. It also

allows for a straight forward independent calibration of its thermal resistance, which is

helpful for the energy analysis. A schematic view of the three stage is shown in Figure 2.9.

Figure: 2.9 Sketch of Proposed Three Stage PTC

A three-stage Stirling PTC of thermal-coupled type is designed, which aims to reach 4 K

and investigate the cooling and coupling mechanism for basic research. The experiment

test of the first and second stages shows a high performance, which is in good agreement

with the thermodynamic model.

16

Parameter 1st stage 2nd stage 3rd stage

Frequency (Hz) 40 30 30

Mean Pressure (MPa) 2.0 1.0 1.0

PV Input Power (W) 250 170 60

Bottom Temperature (K) 37 11 4.9

Cooling power 15W@80K 1.4W@20K 60mW@6K

Relative Carnot 16.5% 11.5% 4.9%

Required Precooling None 8W@90K 4.5W@90K

1.2W@20K

Table: Working parameter of the proposed three-stage PTC

2.7 Applications of Pulse Tube Refrigerators

MILITARY

(a) Infra-red sensors for missile guidance

(b) Infra-red sensors for satellite surveillance

ENVIRONMENTAL

(a) Infra-red sensors for atmospheric studies of ozone hole and greenhouse effects

(b) Infra-red sensors for pollution monitoring

COMMERCIAL

(a) High temperature super-conductors for mobile phone base stations

(b) Semi-conductors for high speed computers

(c) Super-conductors for voltage standards

MEDICAL

(a) Cooling of super-conductors for magnets for MRI scans

(b) SQUID magnetometers for heart and brain study

17

2.8 Conclusion

From the report we can conclude the following.

a) Pulse-tube cryocooler is very useful in space application.

b) Staging in pulse-tube reduces the cooling power in subsequent stages.

c) Staging in pulse tube cryocoolers decreases the temperature as stages

increases.

d) This type of cryocoolers cannot be scaled to meet different sizes.

e) Two stage pulse-tube cryocoolers are available commercially. Three stage

pulse tube cryocoolers are still in development phase.

18

3. References

1. http://en.wikipedia.org/wiki/Pulse_tube_refrigerator

2. D. Durand, R. Colbert, NGST Advanced Cryocooler Technology Development

Program (ACTDP) Cooler System

3. D. Durand, D. Adachi, D. Harvey, Mid Infrared Instrument (MIRI) Cooler

Subsystem Design

4. Akshat Agrawal, Abhishek Soni, Design and an Experimental Investigation of Two

Stage Pulse Tube Refrigerator, SSRG International Journal of Mechanical

Engineering (SSRG-IJME) – volume1 issue 4 August2014

5. Computational study of a 4 K two stage pulse tube cryo cooler with mixed Eulerian-

Langrangian method, Y.L. Ju, Cryogenics 41 (2001)

6. Novel configuration of three-stage pulse tube refrigerator for temperatures

below 4 K, Y. Matsubara and J.L. Gao, Cryogenics 34,4

7. High frequency two-stage pulse tube cryocooler with base temperature below 20

K, L.W. Yang , G. Thummes, Cryogenics 45 (2005) 155–159

8. Low capacity Cryogenic Refrigeration, G. Walker, E.R. Bingham, Clerendon press,

oxford 1994

9. 10K Pulse Tube Cooler, T. Nguyen, R. Colbert, D. Durand, C. Jaco, M. Michaelian,

and E. Tward Northrop Grumman Space Technology Redondo Beach, CA, USA

10. High Capacity Staged Pulse Tube, C. Jaco, T. Nguyen, D. Harvey, E. Tward,

NGST, Redondo Beach, Cryocoolers 13

11. Various volumes of Cryocoolers

12. www.cryomech.com

13. http://www.northropgrumman.com/Capabilities/HighEfficiencyCryocoolers/Page

s/default.aspx

14. A Three-Stage Stirling Pulse Tube Cryocooler Approaching 4 K, Q. Cao, L.M. Qiu,

Z.H. Gan, Y.B. Yu, X.Q. Zhi