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A1 11 02577752

NBS TECHNICAL NOTE 1301

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards
M he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

J^ Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials Science and Engineering

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

coordinates the system with measurement systems of other nations and

furnishes essential services leading to accurate and uniform physical and

chemical measurement throughout the Nation's scientific community, in- dustry, and commerce; provides advisory and research services to other Government agencies; conducts physical and chemical research; develops,

produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

• Basic Standards^

• Radiation Research

• Chemical Physics

• Analytical Chemistry

The National Engineering Laboratory

Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops

and proposes new engineering practices; and develops and improves

mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

Applied Mathematics

Electronics and Electrical Engineering-^

Manufacturing Engineering

Building Technology

Fire Research

Chemical EngineeringThe Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

Programming Science and

Technology

Computer Systems

Engineering

The Institute for Materials Science and Engineering

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information fundamental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Institute consists of the following Divisions:

Ceramics

Fracture and Deformation ^ Polymers

Metallurgy

Reactor Radiation

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address

Gaithersburg, MD 20899. -Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
NBS

RESEARCH

INFORMATION CENTER Measurements of the Efficiency and ^^^

Refrigeration Power of Pulse-Tube ^^o.^^ot

Refrigerators Mf^c

Steffen Herrmann

Ray Radebaugh

Chemical Engineering Science Division

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Supported by

NASA Ames Research Center

Moffett Field, California 94035

e.

^'•-imo**"'^

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued September 1986
National Bureau of Standards Technical Note 1301

Natl. Bur. Stand. (U.S.), Tech Note 1301, 52 pages (Sept. 1986)

CODEN:NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1986

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402
Contents

Page

1

.

Introduction 2

2. Analysis 4

3. Test Apparatus 8

4. General Description of the Experiments 13

5. Experiments 14

5.1 Pulse Tube I F = 3 Hz 14

5.2 Pulse Tube I F=6 Hz 17

5.3 Pulse Tube I F=9.5 Hz 21

5.4 Pulse Tube I F = 11.5 Hz 25

5.5 Summary for Pulse Tube I 29

5.6 Pulse Tube II 32

5.7 Summary for Pulse Tube II 37

5.8 Pulse Tube III 38

5.9 Summary for Pulse Tube III 42

6. Comparison and Discussion of the Three Pulse Tubes 43

7. Conclusions 45

8. Acknowledgments 45

9. References 46

Measurements of the Efficiency and Refrigeration Power

of Pulse-Tube Refrigerators *

Steffen Herrmann and Ray Radebaugh

Chemical Engineering Science Division

National Bureau of Standards

Boulder, Colorado

Pulse-tube or thermoacoustic refrigerators have the potential for high

reliability since they require only one moving part —an oscillating piston or diaphragm at room temperature.

If a tube is closed at one end and connected to a pressure wave generator at the open end, and if the phase angle between mass flow and pressure is shifted from

90°, then refrigeration occurs at the open end. The shift in phase angle can be

realized by thermal relaxation between the gas and the tube walls or by an orifice

at the closed end. A low temperature of 60 K using helium gas in a one stage

orifice pulse tube has been achieved at NBS. This report describes the first

measurements of the efficiency, refrigeration power, and refrigeration power per unit mass flow, for three pulse-tube refrigerators. Three tube sizes, differing in length and diameter, were studied over a frequency range of 3 to 11.5 Hz. Cooling

efficiencies as high as 90? of the Carnot efficiency were obtained when compressor

and regenerator losses are neglected. With the optimum orifice setting, gross

refrigeration powers of 1M W were measured at a temperature of 100 K in a tube of

12.7 mm diameter and 240 mm length at a pulse frequency of 6 Hz. The influence of

pulse frequency, orifice setting, diameter, and length of tube are discussed in relation to some theoretical understanding of pulse-tube behavior.

Key words: cryocooler; cryogenics; efficiency; pulse-tube refrigerator;

refrigeration power; refrigerator; regenerative refrigerator.

Work funded by NASA Ames Research Center, Moffett Field, CA 9M035
1 . Introduction

The lack of reliability in small cryocoolers is a problem that has been studied for many

years. One approach to increased reliability is the elimination of some of the moving parts

in a mechanical refrigerator. Stirling refrigerators have only two moving parts —the

compressor piston and the displacer. In 1963 Gifford and Longsworth [1] discovered a new refrigeration technique which eliminates the displacer from the Stirling refrigerator. They

called it pulse-tube refrigeration, but we refer to it here as the "basic" pulse tube. Under

Gifford's direction [2-5], basic pulse-tube refrigeration was advanced to the point where a temperature of 124 K was achieved with one stage, and of 79 K with two stages [4]. A single-stage unit with the warm end at 65 K achieved 30 K [4].

The principle of operation, as given by Gifford and coworkers [1-5] and by Lechner and

Ackerraann [6], is qualitatively simple. The basic pulse tube, shown in Figure 1, is closed

at the top end, where a good heat-transfer surface must exist between the working gas (helium

is best) and the surroundings, in order to dissipate heat. The bottom, open, end also has a good heat transfer surface to absorb heat from its surroundings. The open end is connected

to a pressure-wave generator (in our case a compressor) via a regenerator. During the

compression part of the cycle any element of gas in the pulse tube moves toward the closed

end and at the same time experiences a temperature rise due to adiabatic compression. At that time the pressure is at its highest value. During the maximum in the pressure wave the

gas is cooled somewhat by heat transfer to the tube walls. In the expansion part of the

cycle the same element of gas moves toward the open end of the pulse tube and experiences

cooling due to adiabatic expansion. During the pressure minimum the gas is warmed by heat

transfer from the tube walls. The net result of cycling the pressure in this manner is a "shuttle" heat transfer process in which each element of gas transfers heat toward the closed

end of the pulse tube. The heat pumping mechanism described here requires that the thermal

contact between the gas and tube be Imperfect, so that the compression and expansion

processes are somewhere between isothermal and adiabatic. The best intermediate heat

transfer generally occurs when the product of pulse frequency and thermal relaxation time

between the gas and the tube walls is approximately unity.

The early work on this type of refrigerator was done using a valved compressor and a rotary valve to switch the pulse tube alternately between the high and low pressure sides of

the compressor; the pressure wave was approximately a square wave. Such a technique lowers

the overall efficiency since no work is recovered in the expansion process. However the

actual refrigeration process is relatively efficient because of the short times for

compression and expansion, and the long times for heat transfer at the pressure plateaus.

The lowest temperature of 124 K was achieved in 196? by Longsworth [4] with a pulse tube

19 mm in diameter by 318 mm long. The high and low pressures were 2.38 MPa and 0.56 MPa,

respectively, for a pressure ratio of 4.25, at a pulse frequency of 0.67 Hz. At the low

temperature limit of 124 K, a gross heat pumping rate of 5 W was obtained which was totally

consumed by loss terms such as conduction and regenerator ineffectiveness.

Also in 1967, Gifford and Kyanka [5] used a valveless compressor to recover work in the

expansion process and increase overall efficiency. The pressure wave in that case was sinusoidal. The pressure ratio used was 4.2 and a low temperature limit of 165 K was achieved in one stage. The pulse tube consisted of a bundle of four stainless steel tubes,

each having a diameter of 6.35 mm and a length of 102 mm. The peak pressure was 2.17 MPa and

the minimum pressure was 0.52 MPa at a frequency of 6.2 Hz. They estimated that the work

input for the same cooling power was approximately ^0% of a system with a valved compressor.

In 1984 Mikulin, et al. [7] installed an orifice at the top of the pulse tube to allow

some gas to pass into a large reservoir volume. This type of configuration is called the

"orifice pulse tube." Although the original work of Mikulin et al. [7] placed the orifice

just below the Isothermal section, our version of this modification placed the orifice above

this section (Fig. 2). They applied the pressure wave by the use of valves and used air as

the working gas even though the Joule-Thompson effect is not used as a cooling mechanism in

the orifice. They were able to obtain a low temperature of 105 K using a pulse tube 10 mm in

diameter by 450 mm long with maximum and minimum pressures of 0.4 MPa and 0.2 MPa at a frequency of 15 Hz. The net refrigeration capacity at approximately 120 K was 10 W. It is not clear from their report what fraction of gas passed through the orifice.
A low temperature of 50 K was achieved in our laboratory using helium gas with our version of the orifice pulse tube [8]. The tube was 12.7 mm in diameter by 237 mm long and

operated at a frequency of 9 Hz with a valveless compressor.

Measurements of the efficiency of these pulse tube refrigerators have not previously

been made. Also, no measurements exist on the refrigeration capacity per unit mass flow.

Such a quantity is needed to design the compressor and regenerator for a particular

pulse-tube refrigerator. The purpose of this work is to provide measured values of the

efficiency and refrigeration per unit mass flow for both the "basic" and "orifice" pulse

tubes.

Piston

Regenerator

Piston

Heat

Exchanger

Pulse Tube

Heat

Exchanger

Regenerator

Reservoir

Volume

Qf

Throttle Valve

Heat

Exchanger —Qh

Pulse Tube —Qc

Heat

Exchanger

Fig. 1 Schematic diagram of the basic

pulse-tube refrigerator

Fig. 2 Schematic diagram of the orifice

pulse-tube refrigerator
2. Analysis

Unified explanations of the pulse tube as well as of the Stirling refrigerator, based on enthalpy flow, are given here which provide a basis for comparing different types of pulse

tubes with each other and with other refrigerators. For steady- flow recuperative systems,

such as the Joule-Thompson refrigerator, the enthalpy flow analysis is simple and has always

been used. The enthalpy flow in regenerative systems, such as the Stirling and pulse-tube

systems, is more complex because of the oscillation. The enthalpy flow H for an ideal gas in any region of an open system is

H = mh = mc T, (1 )

where m is the mass flow rate through the region, h is the specific enthalpy, Cp

is the specific heat at constant pressure, which for an ideal gas is constant, and T is the

temperature. For an oscillating flow the time average of the enthalpy flow over one period

is

<H> = Cp/T m T dt. (2)

According to the first law of thermodynamics the average heat flow rate^<Q> into a region is related to the change in enthalpy flow through that region A<H> and to

the average work rate <W> produced in the region, by

<Q> = A<H> + <W>. (3)

For a pulse tube, equation (2) cannot be used directly but T may be determined from the

pressure P by use of the equation of state for an ideal gas:

T = P/Rp. (M)

Thus an alternative and often more useful equation for the enthalpy flow becomes, using (2)

and (4),

<H> = c A /Rt J u P dt (5) PS o

where m has been replaced by pAgU, and where Ag is the cross-sectional area perpendicular to the gas flow direction and u is the gas velocity. Since both eqs (2) and

(5) are cyclic integrals, only the dynamic temperature T^j and pressure P^j need be used in

those equations. Consider a sinusoidal pressure wave, P|j, with amplitude P(jq superimposed on

the average pressure P in a pulse tube

Pd = Pdo sin ut (6)

This leads to a flow velocity u, mass flow rate m, and dynamic temperature T^,

given by

u = UoSin((ot + (j)), (7)
m = m sin((jjt + 6)

(8)

Td = TcJoSin(ut + a) (9)

where ij), 9, and a are the phase angles by which each of these waves leads the pressure wave.

The assumption of sinusoidal behavior follows from the assumption that (P(j/P) and (T^j/T) are both small compared to unity. The integrals in eqs. (2) and (5) are of the form

I = (K/t) sin(a)t)sin(a)t + 6)dt, (10)

o

(K = constant terms) which becomes

I = (K/2)cos 6 . (11 )

Thus, <H> is a maximum when u and P|j (eq. 5) or m and T^j (eq. 7) are in

phase (6=0) and is zero when the phase angle between them is Tr/2.

We now consider three ranges of heat transfer between the gas and the walls. For adiabatic conditions (wTt>>1 )4>=''r/2, e=iT/2, a=0, and from eq. (5) <H>=0. For isothermal conditions (u)Tt<<l )T(j=0 and from eq. (2) <H>=0. For intermediate

conditions (a)Tt=1)i 9 and 4) are less than •n-/2 and a becomes nonzero. The phase angle between

m and T^j then is less than it/2, so by eqs. (2) and (11) <H> is nonzero.

The enthalpy flow as a function of position is shown in Figure 3 for the basic pulse

tube. A positive <H> means the enthalpy flow is to the right. The enthalpy flow

at the left (cold) end of the pulse tube is initially greater than that on the right (hot)

end because m is greater there, whereas T^ is the same on both ends. The abrupt changes in

<H> at the pulse tube boundaries give rise to heat flow terms according to eq. (3), since no work crosses the rigid boundary. If the net heat input at the left end is less than Q^,

that end of the pulse tube cools until equilibrium is reached. At that time <H> will become

constant for all x within the wt^^I region and heat flows occur only at the boundaries. A first-law analysis shows that Qq = % at equilibrium, which means that a measurement of Qh gives the gross refrigeration power of the pulse tube.

The basic pulse tube relies on heat transfer to the walls to bring about a phase angle

between u and P(j different from it/2. In the orifice pulse tube the orifice at the warm end

is the phase shifting mechanism between u and P(j, by analogy to an RC electrical circuit. Heat transfer along the walls is still possible with the orifice pulse tube, but we have

found that the amount of heat transferred there should be less than that in the basic pulse

tube for best results. Therefore the orifice pulse tube works better at higher frequencies

than the basic pulse tube, for tubes of the same diameter.
Basic Pulse Tube

(JJT^«^

Regenerator

curt«l (JJT^«1

Heat

Exchanger

X

Fig. 3 Enthalpy Flow in the basic pulse-tube refrigerator

The enthalpy flow analysis is easily extended to the Stirling refrigerator (Fig. 4).

Because a)Tt<<1 in the regenerator section, <H>=0. The sections on each end of the regenerator can have any value of <H> in practice. If coTt>>1 (adiabatic), the movement of the

piston causes a phase shift between u and P^j away from ir/2 to a phase angle of approximately

zero. The enthalpy flow according to eqs. (5) and (11) is then a maximum and heat flows occur at the discontinuities in <H> at each end of the regenerator. The term <H> goes to zero at the boundary with the piston which means the First Law in eq. (3) is satisfied by balancing A<H> with the work flow <W>. If a)Tt<<1 (Isothermal) in the

sections between the regenerator and the pistons, the enthalpy flow is zero. The energy

balance at the piston boundary is then satisfied by having <Q> = <W> at the boundary.

The similarity between the Stirling refrigerator and the pulse tube refrigerators is now evident when the cold piston or displacer is viewed simply as a mean of shifting the phase

between the velocity and pressure waves, just as intermediate heat transfer or flow through

an orifice causes such a phase shift in the pulse tubes. However, a phase shift of as much

as ir/2 cannot be reached in the pulse tubes except in some asymptotic fashion where Tcj->0 or

m->"».

Some quantitative comparisons between the pulse tube refrigerator and the Stirling

refrigerator will be given later.
Stirling Refrigerator

CUTt » 1 CJTt « 1 CJTt »

1

<H>|

^Regenerator |

w,

Fig. 4 Enthalpy flow in the Stirling refrigerator
3. Test Apparatus

The pulse-tube test apparatus provides a means for measuring the relevant parameters for

calculating efficiency, refrigeration power and mass flow. Photographs of the apparatus are given in Figure 5 and Figure 6. Also a schematic diagram of the system is given in Figure 7. The pulse tube test apparatus is surrounded by a radiation shield held at 77 K by the use of

liquid nitrogen. In addition, a vacuum of 10"^ Pa (10~^ torr) is maintained throughout the

whole test appar^atus.

Fig. 5 Photograph of the pulse-tube refrigerator test apparatus showing the

reservoir volume and orifice

Fig. 6 Photograph of the pulse-tube

refrigerator test apparatus showing

the pulse-tube, the regenerator,

and the two isothermalizers
Regenerator

s o t h e r m a I i z e r #1

Isothermalizer

#2

Reservoir

Volume

HoO

S)c mJocAP

^AT=0

m m

Cryostat

Top

Pulse

Tube

FillVent

,1

Ng gas

LN.

Radiation

Shield

Fig. 7 Schematic diagram of the test apparatus

Previous measurements of the pulse tube behavior were made in systems where the

regenerator loss was mixed with the refrigeration effect. In an attempt to separate the

regenerator loss term from the intrinsic refrigeration, paired isothermalizers have been

employed here: isothermalizer #1 is adjacent to the regenerator, and #2 is next to the pulsetube. The isothermalizers have excellent heat transfer between the working gas and the body

of the isothermalizer and a high heat capacity to eliminate temperature oscillation at the

working frequency. The two isothermalizers are thermally isolated from each other; but if

they are maintained at the same temperature by external means, the cooling power required by

the y/1 isothermalizer should equal the regenerator loss, and the heat input to isothermalizer

#2 should equal the intrinsic refrigeration power of the pulse tube. The natural tendency is

for #1 isothermalizer to be warmer than #2 isothermalizer when no cooling from the boil-off

nitrogen vapor is provided to the ih isothermalizer. Cooling of the #1 isothermalizer was
balanced by increased heating required by the #2 isothermalizer . The heat flow to the

cooling water at the top end of the pulse tube was not affected since the total gross heat

input to the cold end was not changed when cooling was provided to the #1 isothermalizer.

However, it was found that the two isothermalizers could not be maintained at the same temperature. V/ith no cooling temperature differences were around 7 K. With the maximum

cooling power available the difference was reduced to only about H K and the heat input to the #2 isothermalizer was then much greater than the heat rejected at the hot end. This

behavior is not understood at present, so the measurements reported have used the heat

rejected at the hot end as a measure of the gross refrigeration power.

The major loss term in these experiments are the regenerator conduction and the

regenerator Ineffectiveness. By using the liquid nitrogen boil-off gas to cool the bottom of

the regenerator when the pulse tube was not operating, it was found that the regenerator

conduction could be represented to within ±20? by 2.5(W) - 0.0086(W/K)*T. At 100 K the

conduction is then 1.6 W. Theoretical calculations based on curves of effectiveness vs. heat

transfer units in Kays in London [9] for the regenerator ineffectiveness gave an equation to represent the regenerator loss term for 6 Hz and a mass flow of 2g/s by 15(W) - 0.05(W/K)*T.

At 100 K the regenerator loss is then 10.4 W.

During this work experiments were done with three different pulse tubes, all of type 304

stainless steel. Dimensions of these tubes are given in the next section.

For good heat transfer the ends of the pulse tube were made of copper containing a few

layers of copper screen to provide a large surface for the heat transfer. The volume of each

of the isothermal ends was about ^0% of the pulse tube volume

The orifice consisted of a 15-turn needle valve and the reservoir volume above the

orifice was approximately 1L. The valve flow coefficient Cy for 1 or more turns is given by

-2.025E-10(m*s*/K)+2.825E-10(m*s*/K)*turns. The regenerator was a stainless steel tube 19 mm

in diameter by 127 mm long filled with 1050 discs of 150 mesh phosphor bronze screen.

For all pulse tubes the losses due to conduction along the steel tube length were

smaller than ^% and could be neglected.

The refrigeration power of the pulse tube was determined by measuring the electrical

power input to isothermalizer #2, as well as the mass flow rate, m, and the AT of

the cooling water flowing around the hot end of the pulse tube. The water measurement gives

the gross refrigeration power, since Qc=Qh ^^ equilibrium.

All absolute temperatures were measured by commercial diode thermometers which are accurate to ± 1 K. The temperature difference between isothermalizer #1 and #2 and the

temperature rise of the cooling water were measured with copper-constantan thermocouples.

The mass flow rate at the cold end of the pulse tube, mp^^, was determined

from measurements of the pressure drop across the laminar flow element of isothermalizer #2.

The construction of the isothermalizer is shown in Figure 8. For laminar flow of an ideal

gas the mass flow rate is given by

mpt=CKPptAPl/TcR (12)

where Cj^ is a flow coefficient, APj is the pressure drop across the laminar flow channel in

-the isothermalizer, Pp^ is the pressure in the pulse tube, R is the ideal gas constant and T^

is the temperature at the cold end of the pulse tube. The coefficient C^ was determined in a separate experiment where helium gas flowed continuously at room temperature through the

isothermalizer and a calibrated hot-wire flow meter. The variation of Cj( was less than 10? over a factor of ten in flow rate. There was a directional dependence of about 10-20? in the

flow coefficient. Laminar flow occurs in the isothermalizer for flow less than about 2.5 g/s.

The largest average mass flow rates were about 2.9 g/s for the largest volume pulse tube at 9.5 Hz frequency and at 80 K. Peak values were somewhat higher, although the same flow

coefficient was used to calculate m in all cases since the flow rate was less than

10
Pressure' Taps

100 mm

25 mm

^Annular Gaps

(178 fjLtn thick)

Ng Boil-off Gas

Fig. 8 Design diagram of the isothermalizer

2.5 g/s for most other situations. In the experiments the mass conservation law was used to calculate an exact ratio for forward and reverse flow coefficients in every measurement.

A variable reluctance pressure transducer of 50 kPa full scale was used to measure APj.

The cavity volume on each side of the diaphragm is about 0.07 cm^. The transducer was mounted on the side of the isothermalizer to keep the length of 1.5 mm diameter pressure

lines to a minimum to allow for fast response times. To determine if both cavities of the

transducer respond equally to a rapidly changing pressure, the isothermalizer was capped off

at the bottom end so very little mass flow would occur during pressure oscillations. Careful

adjustments of lengths of 1.5 mm diameter pressure taps were required to balance the

transducer for zero mass flow.

Since the pressure transducer is at the temperature of the isothermalizer, the

temperature dependence of the transducer sensitivity was measured in a separate experiment

but found to vary by less than ^3% between 300 K and 77 K. Because of the uncertainty of

other measured parameters, we decided to ignore the variation of transducer sensitivity with

temperature. However, the zero setting on the transducer changed with temperature more rapidly and it was necessary to stop the compressor momentarily and adjust the zero setting

for each new temperature.

The pulse tube pressure Pp^^ was measured with an absolute pressure transducer of the

variable reluctance type attached to the top end of the pulse tube. A similar transducer was installed next to the compressor to observe the pressure P^ at that point in the system.

The mass flow through the orifice was determined by measuring the pressure variation in

the reservoir volume with a piezoresisti ve pressure transducer. The mass flow rate through

the orifice averaged over one-half period is then calculated by

<mn> = 2Amr,/T = 2Vv.APr./TRT. (13)

where t is the cycle period, Vp is the reservoir volume, APf. is the difference between the

maximum and minimum pressure in the reservoir, AmQ is the change of mass of the gas, R is the

gas constant, and Tq is the reservoir temperature.

The compressor used to operate the pulse tube apparatus is quite large (-7 kw motor) to allow for volume throughout the versatile control panel. Measurement of electrical power

input to the compressor motor is then not a fair comparison with other systems that are better matched to the capacity of the compressor. The best method of comparing the

efficiency of the pulse tube refrigerator with other pulse tubes and with other refrigeration

techniques is to consider the efficiency of only the cooling process and neglect losses

11
associated with the regenerator and the compressor. The ideal thermodynamic work input to drive the pulse tube is determined from measured mp^ and Ppj^. The instantaneous mass within an ideal compressor with no dead volume between it and the cold end of the pulse tube

is given by

f'.

m (t) = J m (t) dt. (14)

Applying the equation of state for an ideal gas again we can calculate the volume variation

V(t) of the ideal compressor

Vpt(t) = mpt(t).R.To/Ppt(t) (15)

For a closed cycle the work input is

W = fPdV (16)

By using Ppt(t) and Vpt(t) the equation becomes

f-^ dV (t)

^c = J V^'^

-^ ' ''' ^''^

o

"^

which is the work input over one cycle. To obtain the average work input rate we multiply

this by the frequency,

W = W -f (18)

c

The average mass flow <mp^> is given by

<rn ^> = 2f(m ^ - m ^ . ) = 2fAm ^ (19) pt ptmax ptmin pt ,

The thermodynamic efficiency ri of the various types of pulse tube refrigerators is used for

cycle comparisons. This efficiency considers only the basic refrigeration element and

neglects regenerator and compression losses. The efficiency relative to Carnot is expressed

as

n = Q(T -T )/WT (20)

o c c

where Tq is the ambient temperature, T^ the temperature of the cold end of the pulse tube,

Q is the refrigeration power, and W is the work input.

The quantities Pq, Ppt, Pr» s"^ "^pt were measured with a digital oscilloscope with

12 bit resolution and recorded on floppy disc. A program was written for the digital

oscilloscope which carried out all the calculations In eqs. 12-20.

Measurements of pressures could be made to within ±25^ but due to uncertainties in

calibration of the laminar flow element the uncertainty of the mass flow is about ±15$.

Measurements of the refrigeration power are accurate to about ±55^. The efficiency

calculations use the refrigeration power and mass flow data therefore the inaccuracy of these

values will be about the same as mass flow Inaccuracy.

12
4. General Description of the Experiments

All experiments were done with the same equipment so that the results can be compared

without any restrictions. The only part changed in the apparatus was the pulse tube.

However for each pulse tube the same design for the bottom and top was used to guarantee

equal heat transfer at the ends of each tube.

Each pulse tube was constructed from type SO^i stainless steel to keep the losses due to conduction along the tube as low as possible. These losses were less than ]% and could be

neglected. The sizes and corresponding numbers for the three pulse tubes are listed here.

Pulse tube I Pulse tube II Pulse tube III

240mm length, 12.7mm O.D.

2il0mm length, 6.4mm O.D. 120mm length, 12.7mm O.D.

0.51 mm wall

0.30 mm wall

0.51 mm wall,

The most exhaustive experiments were done with pulse tube I to study all the general

properties of the pulse tubes. Pulse tube II was used to demonstrate the influence of the

cross-sectional area on refrigeration power and efficiency. Pulse tube III was one half the

length of pulse tube I in order to investigate the dependence of refrigeration power and

efficiency on length.

An average pressure of approximately 1 MPa and a pressure ratio of 2.6 was used for

measurements of each pulse tube. The value of 1 MPa seemed to be the best pressure and the

pressure ratio of 2.6 was the maximum that could be achieved with the available compressor.

Helium gas was used for all runs. The frequency range varied from 3 Hz to 11.5 Hz. It was

not feasible to go to hi^er frequencies with the existing compressor because of excess

vibrations.

Measurements on the different pulse tubes were made at the following frequencies:

Pulse tube I Pulse tube II Pulse tube III

3 Hz, 6 Hz, 9.5 Hz, 11.5 Hz

3 Hz, 6 Hz, 9.5 Hz, 11.5 Hz

6 Hz, 9.5 Hz

The temperatures ranged from approximately 270 K to the lowest possible temperature for

the given frequency. Data were taken at different points throughout the entire temperature

range.

The time required to realize the lowest possible temperature was especially long for

pulse tube II because of its very small refrigeration power. Some runs took roughly 12 hours

in order to obtain all the required data for the given frequency.

Special care was taken to obtain all data only at steady state conditions.

In the following section the individual results for each pulse tube and each frequency

will be discussed. A summary of the most interesting and important results is given at the

end of this report.

13
Experiments

5.1 Pulse Tube I; F = 3 Hz

As Fig. 9 illustrates, the highest relative efficiency is approximately 90$ of Carnot

efficiency when the orifice is completely closed. In this case the orifice pulse tube is equivalent to the basic pulse tube. The more the orifice is opened the lower the efficiency.

1.0

0.8

0.6

O

z

S2 0.4

LL

ULU

0.2

PULSE TUBE I

p = 1 MPa

f = 3 Hz

A- turns

-0.5 turns

0-1 turn

X- 2 turns

O- 3 turns

80 120 160 200 240 280

TEMPERATURE, K

Fig. 9 Efficiency relative to Carnot vs temperature for pulse-tube I at 3 Hz

320

At a frequency of 3 Hz, our results indicate that an orifice opening of 1 turn gives

the best results for the refrigeration power in the interesting temperature range, as shown

in Fig. 10. The lowest temperature for this frequency of approximately 90 K was achieved

with this orifice setting. For a larger orifice opening the mass flow through the orifice

becomes too large. With an orifice opening of 3 turns, the mass flow through the orifice is

roughly equivalent to the mass flow into the pulse tube, as shown in Fig. 11. This means

that the orifice does not produce much phase shift for this case.

The mass flow into the pulse tube ranged from 0.4 g/s to 0.6 g/s depending on the

orifice setting. It varies little with temperature. The ratio of refrigeration power to mass flow rate is shown in Fig. 12.

14
32

S24

O

Q.

16

<

Lil O

UJ 8

80

PULSE TUBE I

_ ^ A- turns

X -0.5 turnsD- 1 turn

2 turns

3 turns

120 160 200 240 280

TEMPERATURE, K

Fig. 10 Refrigeration power vs temperature for pulse-tube I at 3 Hz

320

15
- PULSE TUBE I

p = 1 MPa

f = 3 Hz

o

•E

1-2

0.9

0.6

0.3

1—I

\—

r

80

"1—I—

I—I—I—I—I—I—

I—I

0-0,5 turns

n- 1 turn

A- 2 turns

X- 3 turns

J L J L J L J L 110 140 170 200 230 260

TEMPERATURE, K

Fig. 11 "lo/nipt ^s temperature for pulse-tube I at 3 Hz

290 320

16
56

48

40

o) 32

-»

•E -O 241—

16

PULSE TUBE I

p = 1 MPa

f = 3 Hz

A- turns

D- 0.5 turns O- 1 turn X- 2 turns

0-3 turns

180 210

TEMPERATURE, K

Fig. 12 Q/nipt vs temperature for pulse- tube I at 3 Hz

300

5.2 Pulse Tube I; F = 6 Hz

The lowest temperature recorded with this pulse tube (75 K) was accomplished with a frequency of 6 Hz and an orifice setting of 2 turns. It is at this frequency that the best

combination of low temperatures and large relative efficiencies are realized. (Fig. 13). An astonishing efficiency of almost 90$ Carnot was obtained with an orifice setting of 1 turn at

a temperature of about 120 K. However, the refrigeration power at this setting was too low

to bring about a further decrease in temperature. As Fig. 14 shows the highest refrigeration

power can be achieved either with 2 or 3 orifice turns, depending on the temperature range.

17
0.8

0.6

>-O

z

UJo

LLLL

UJ 0.4

0.2

80

PULSE TUBE I

p = 1 MPa

f = 6 Hz

D-O turns

O- 0.6 turns

0-1 turn

A- 2 turns

X - 3 turns

120 160 200 240 280

TEMPERATURE, K

Fig. 13 Efficiency relative to Carnot vs temperature for pulse-tube I at 6 Hz

320

18
60

UJ^ 48

O

Q.

2 36

z

O

H

<

CC

UJ2 24

m

cc 12

1—

r

PULSE TUBE I p= 1 MPa

f = 6 Hz

-1 \

I \ [- n- turns

O-0.5 turns

O- 1 turn

A' 2 turns

X - 3 turns

80

Fig.

110 140 170 200 230 260 290

TEMPERATURE, K

14 Refrigeration power vs temperature for pulse-tube I at 6 Hz

320

19
For the basic pulse tube (orifice closed) a frequency of 6 Hz is already too hi^ to get

sufficient heat transfer between the gas and the tube walls. The refrigeration power in this

case is too low to be useful.

As can be seen from Fig. 15 the ratio of mQ/mp^^ drops significantly below about

140 K and it falls into a reasonable range between 30^ and >^0% for 2- and 3-turn orifice

openings. This explains the peak values of the efficiencies for orifice settings.

0.8

0.1

PULSE TUBE I

1 J L 80 110 140 170 200 230 260

TEMPERATURE, K

Fig. 15 mQ/nip^ vs temperature for pulse- tube I at 6 Hz

290

The mass flow at a frequency of 6 Hz into the pulse tube is now more dependent on the

temperature than at the lower frequency and varies from approximately 1.9 g/s to 0.9 g/s. It

is found to be an approximately linear function of the temperature. The variation of the mass flow with the orifice setting is less than ^0%.

The values for the heat transport per unit mass flow Q/ta^^ are not significantly

different compared to values at the lower frequency of 3 Hz (Figs. 12 and 16).

20
60

48

O)

£

•O

-"3 6

24

12

1—I—

I—I—I—

I—^—I—

I—I—

r

PULSE TUBE I

p = 1 MPa

f = 6 Hz

80 1 10 140

Fig. 16 Q/nipt vs

170 200 230 260

TEMPEATURE, K

temperature for pulse-tube I at 6 Hz

290 320

Considering all the tested frequencies, 6 Hz appears to be the best for application with

this pulse tube size. By going to higher frequencies the refrigeration power is increased in

the higher temperature range (>120 K) but only at the expense of a lower relative efficiency.

Below 100 K the frequency of 5 Hz yields not only the best relative efficiency but also the

highest refrigeration power.

5.3 Pulse Tube I; F = 9.5 Hz

The frequency of 9.5 Hz yielded the lowest relative efficiencies for pulse tube I (Fig. 17). These efficiencies are less than half of the efficiencies at 6 Hz without

improving the refrigeration power (Fig. 18). The peak relative efficiency was only 3^% of

Carnot at a temperature of about 90 K and an orifice setting of 3 opening turns. In addition

the lowest possible temperature was about 5 K higher than the lowest temperature achieved

with a driving frequency of 6 Hz. However, relatively high refrigeration powers were achieved below 100 K making this frequency more useful for applications than the frequency of

3 Hz in spite of its much lower relative efficiency.

21
0.32

0.24

>-O

z

UJo

iZ 0.16

u.

LU

0.08

T

f

80

PULSE TUBE I p= 1 MPa

f = 9.6 Hz

A-0 turns

n-0.5 turns

0-1 turn

x-2 turns

0-3 turns

120 180 200 240 280

TEMPERATURE, K

Fig. 17 Efficiency relative to Carnot vs temperature for pulse-tube I at 9.5 Hz

320

22
64

56

HI 48

O

°- 40

32

7? 24

CC

Li] g

CC

ULU

QC 16

8

80

PULSE TUBE I p= 1 MPa

f = 9.5 Hz

A-0 turns

D-0.5 turns

0-1 turn

x-2 turns

0-3 turns

120 160 200 240 280

TEMPERATURE. K

Fig, 18 Refrigeration power vs temperature for pulse-tube I at 9.5 Hz

320

23
The mass flow into the pulse tube is increased significantly in comparison to the 6 Hz frequency and the dependence on the orifice setting is even less significant than for 6 Hz. The flow ranges from approximately 1.2 g/s at 265 K to 2, 9 g/s at 80 K and is approximately a linear function of the inverse temperature.

32 PULSE TUBE I

p = 1 MPa

f = 9.5 Hz

24

O) -iO

18 -

12 -

80 120

A- turns

n-0.5 turns

0-1 turn

x-2 turns

O- 3 turns

160 200 240

TEMPERATURE, K

Fig. 19 Q/nipt vs temperature for pulse-tube I at 9.5 Hz

280 320

, ^ The ratio of mass flowing through the orifice to mass flowing into the pulse tube,

mo/mpt, diminished and is only approximately 18? at 100 K (Fig. 20). This is the lowest

ratio recorded with pulse tube I and could be an explanation for the relatively poor

characteristics of this pulse tube at 9.5 Hz.

24
0.8

0.7

0.6

*- 0.5

Q.

PULSE TUBE I

p = 1 MPa

f = 9.5 Hz

A-1 turn

O- 2 turns

D- 3 turns

120 160 200 240 280

TEMPERATURE, K

Fig. 20 iTiQ/mpi; vs temperature for pulse-tube I at 9.5 Hz

320

5.4 Pulse Tube I; F = 11 .5 Hz

In comparison to the results for 9.5 Hz, the results achieved at 11.5 Hz are better. In relation to a frequency of 6 Hz the only advantage at this frequency is in the high

temperature range above 1 80 K, where there is a hi^er refrigeration power. Below this

temperature the refrigeration power is almost identical to the power produced with a driving

frequency of 6 Hz (Fig. 21) but can only be achieved with a much lower efficiency (Fig. 22).

The peak in the relative efficiency is approximately 4?? of Carnot at a temperature of around

120 K with an orifice setting of 3 turns. It is possible that some resonance phenomenon is

responsible for this relatively high efficiency because 11.5 Hz is nearly the first harmonic

of 6 Hz. Recall that a frequency of 6 Hz gave the overall best results for this pulse tube

and yielded a relative efficiency of 90/S of Carnot at 120 K.

25
90

80 -

70

PULSE TUBE I p = 1 MPa

f = 11.5 Hz

1

1

D- turns

O- 0.5 turns

O- 1 turn

A- 2 turns

X- 3 turns

Fig. 21

160 200 240

TEMPERATURE, K

Refrigeration power vs temperature for pulse-tube I at 11.5 Hz

320

26
0.8 -

0.6 -

>-O

z

UJ

m

0.2

1

1

' 1 1 1

1 1 1 1 1

D- turns

PULSE TUBE I

p = 1 MPa

f = 11.5 Hz

O- 0.5 turns

O- 1 turn

A- 2 turns

X- 3 turns

-

-

1 1 1 < 1 ^x -

80 120 160 200 240 280 320

TEMPEATURE, K

Fig. 22 Efficiency relative for Carnot vs temperature for pulse-tube I at 11.5 Hz

27
The lowest temperature obtained at this frequency was about 90 K, with an orifice

setting of 3 turns. It appears that by increasing the frequency the lowest possible

temperature is also increased. Unfortunately, it was impossible to run experiments with this

test apparatus at higher frequencies to study this phenomenon more exactly.

The mass flow into the pulse tube at a frequency of 11.5 Hz was between 1.5 g/s for

270 K and 2.3 g/s for 90 K. The relation between mass flow and temperature is absolutely

linear and almost no dependence on the orifice setting was exhibited, although the ratio of

mo/mpt increased significantly compared to the frequency of 9.5 Hz (Fig. 23). This can also be explained by the previously hypothesized resonance phenomenon.

0.4

0.3

0.2

0.1

80

PULSE TUBE I

p = 1 MPa

f = 11.5 Hz

120 160 200 240 280

TEMPERATURE, K

Fig. 23 mg/mpt vs temperature for pulse-tube I at 11.5 Hz

320

Because of the increased mass flow into the pulse tube and comparable refrigeration

power the curves for the refrigeration power per unit mass flow have their lowest value for

this frequency (Fig. 24). This is the only parameter which decreases with increasing

frequency.

28
40

\

^ rPULSE TUBE I

p = 1 MPa

D-0 turns

O-0.5 turns

0-1 turn

A- 2 turns

X - 3 turns

80 120 160 200 240 280

TEMPERTURE, K

Fig. 24 Q/nipt vs temperature for pulse-tube I at 11.5 Hz

32C

5.5 Summary for Pulse Tube I

The experiments described above for different frequencies reveal the importance of

choosing the right frequency in order to get the best results. Although many experiments

were done at various frequencies it is still not clear why some frequencies yield lower

values for the refrigeration power and the efficiency. Nevertheless, some other conclusions

can be formulated and some suggestions made in earlier works can be confirmed.

The basic pulse tube (closed orifice) works best at lower frequencies; however, at these

frequencies its refrigeration power is much lower than the power of an orifice pulse tube.

The basic pulse tube has the highest relative efficiency throughout its complete temperature

range. The lowest temperature achieved with the basic pulse tube in this work was roughly

190 K and is therefore much higher than temperatures achieved with the orifice pulse tube.

As already mentioned in an earlier work [8], the heat transport per unit mass flow for

each pulse tube is relatively low. This was confirmed by these experiments. Because the

massif low in the pulse tube does not depend on the orifice setting at the hi^er frequencies

the Q/mp^ value is especially low for the basic pulse tube. In the low temperature

range there is little variation in these values at the different frequencies.

For the orifice pulse tube 6 Hz was the best frequency of all those tested and the

lowest temperature of 75 K was achieved at 6 Hz. This tube yielded a low temperature of 60 K when run without the isothermalizers [8]. Operation of the orifice pulse tube at 6 Hz also

yielded the greatest efficiency values and the highest refrigeration power in the low

temperature range. A frequency of 11.5 Hz produced reasonable refrigeration power curves and

efficiencies but the efficiencies were smaller by a factor of two than those measured at 6 Hz. The good results at this frequency may be a result of a resonance phenomenon because 11.5 Hz

is almost the first harmonic of 6 Hz. The poorest results of all were measured between these

two frequencies, at 9.5 Hz. The hi^est ef f iciency^at this frequency was only 3^% of Carnot.

This frequency also yielded the lowest ratio of mQ/mp^, which may account for the low

refrigeration power and efficiency. The low mQ/mp^ ratio indicates that little phase

29
shifting by the orifice has occurred, and confirms the theory that for the orifice pulse tube

most of the phase shift is caused by the orifice and not by heat transfer along the tube

walls.

With increasing frequency the mass flow of gas into the pulse tube becomes more and more

a linear function of the temperature and is almost independent of the orifice setting at the

hi^er frequencies. However, it is difficult to see a relation between frequency and the

amount of mass flow. It seems that the mass flow is also affected by the resonance

phenomenon because the experiments yielded peak values for the mass flow at a frequency of

9.5 Hz. This frequency gave the hi^est mass flow rate at temperatures below 200 K.

To show the frequency-dependent properties of the pulse tubes, the relative efficiencies

at particular temperatures and orifice settings were plotted against frequency in Fig. 25 through 29. These plots clearly show the peak values of the efficiency at 6 Hz for the

orifice pulse tube and at 3 Hz for the basic pulse tube. These plots also illustrate that

choosing the right frequency is especially important for low temperatures, where most

applications would occur.

30
1.0

UJO.5

1 1 1 1 1 1 1 1 1 1 1 1 1 PULSE TUBE 1 -

orifice: turns

_

/ \2iOK -

/ 240 K An -

-// /18OK \\^^-~^ -

// 1 1/ 1 1 1 T ^^ 1 1 1 1

1 1 9 12 FREQUENCY, Hz

15 21

1 1 1 1 1 ]

1 1

1

1 1 1 1

' PULSE TUBE I -

1.0 orifice: 0.5 turns -

>-z

lU 150 K

-

tljO.S Z/^^^^^^^nN ^° ^ - / ^\ - / \

/ 240 K \ _

/ / 1 , 1 , 1 \ , 1 1 III 9 12 FREQUENCY, Hz

18 21

PULSE TUBE I

orifice: 1 turn

180 K

9 12 15 FREQUENCY, Hz

Fig. 25-29 Efficiency relative to Carnot

vs frequency for different

orifice settings

21

0.5

1 '

1 ' 1

1

1

1

1

1

1 '

~ PULSE TUBE I

-

orifice: 2 turns ~

: A 120 K

-

/ ^*^~—,^150 K

- /\

-180K

yJ^A, r 1

, 1 — 240 K

1 1 1 1 1

1.0 -

9 12 FREQUENCY, Hz

I ' \

' r

PULSE TUBE I

orifice: 3 turns.

120 K

240 K

9 12 FREQUENCY, Hz

18 21

21

The experiments demonstrated that in the lower temperature range smaller values are designed for the ratio of mass flow through the orifice to mass flow into the pulse tube. To achieve optimal results these values should be around 20?. At higher temperatures, values of

40iS or more ^ield the best results. In general, by choosing the optimal orifice setting the

ratio of mp/mp^ is automatically in the best range for the corresponding temperature.

31
5.6 Pulse Tube II

Before describing the experiments done with pulse tube II, preliminary suppositions

regarding pulse tube behavior are stated which describe the most important differences

between pulse tube I and pulse tube II.

Since the diameter of pulse tube II is only one-half the diameter of pulse tube I the cross sectional area is one-fourth that of pulse tube I. Therefore it was assumed that the

refrigeration power would be one- fourth that of pulse tube I. Also because of the larger

ratio of wall surface to cross sectional area a much lower efficiency is expected at the same

frequency. As a result of the diminished refrigeration power the temperature minima are expected to be greater than the low temperatures recorded with pulse tube I. No assumptions

were made concerning the optimal frequencies. It is now interesting to see how the

experimental results agree with the theoretical predictions.

For pulse tube II a frequency of 3 Hz was much too low. With the basic pulse tube our

test apparatus was not sensitive enough to measure any refrigeration power. Operation of the

orifice pulse tube also produced values too low to be considered reliable. Consequently no plots were made for this frequency. Therefore, it appears that a smaller diameter tube

requires hi^er frequencies in order to obtain reasonable results.

At a frequency of 6 Hz measurable data were achieved. The most conspicuous result was

the lowest achievable temperature of only 180 K with an orifice setting of 1.5 turns. Also,

the refrigeration power was very low in fact, far below the expected value for this frequency

(Fig. 30).

20

<10

LUg

m

DC

T

PULSE TUBE n

^ p = 1 MPa

POWER,

\

f = 6 Hz

5 -

J L 1

1 rO- turns

A- 0.5 turns

V- 1 turn

D- 1.5 turns

O- 2 turns

100 140 180 220 260 300

TEMPERATURE, K

Fig. 30 Refrigeration power vs temperature for pulse-tube II at 6 Hz

340

32
The peak of the relative efficiency was roughly ^H% of Carnot efficiency with a closed

orifice, at a very high temperature of 240 K. This efficiency is much lower than the

comparable value for pulse tube I (Fig. 31)-

0.16

0.12

>-O

z

yj

o

GIO.OS

Li. LU

0.04

PULSE TUBE n

p = 1 MPa

f = 6 Hz

O- turns

A- 0.5 turns

V- 1 turn

D - 1 .5 turns

O- 2 turns

100 140 180 220 260 300 340

TEMPERATURE. K

Fig. 31 Efficiency relative to Carnot vs temperature for pulse-tube II at 6 Hz

The mass flow ranged between 0.52 g/s for 270 K and 0.62 g/s for 180 K and did not depend on the orifice setting. Mass flow values varied with temperature in a linear fashion

and were approximately one-half of the comparable values from pulse tube I. Since the

refrigeration powers are less than one-fourth those of pulse tube I, the maximum Q/mp^^

values for pulse tube II drop to values of 12 J/g at 270 K and 3-2 J/g at 210 K at a frequency of 6 Hz and an orifice setting of 1.5 turns.

Since the values for the mass flow into pulse tube II were much lower, smaller orifice

openings caused higher values for mQ/mp^. The optimum adjustment for pulse tube II at a frequency of 6 Hz was 1.5 turns, which^gave a mo/mpt ratio of 0.51 at 270 K and 0.48 at

180 K. The temperature dependence of mQ/mp^ may be neglected for all orifice settings

since the measurements were performed only in the high temperature range. A two turn opening

gave a ratio of about 0.68 and 1 turn yielded a ratio of roughly 0.34, although total mass

flow into the pulse tube was not affected by the valve setting. Mass flow ratios were not measurable with a 0.5 orifice opening and orifice settings of more than two turns proved as useless since the mass flow into the orifice was too large.

A frequency of 9.5 Hz already produced an important improvement in comparison with the

frequency of 6 Hz. The refrigeration power was increased by almost a factor of two although

the efficiency decreased slightly. At a frequency of 9.5 Hz the refrigeration power was much

higher than the theoretical estimate of one quarter but the comparison is not very well

grounded since this frequency rendered a surprisingly low value for the refrigeration power

using pulse tube I (Fig. 32).

33
20

1 1 1 1

' 1

PULSE TUBE n

1 1 1 1 1 /

—

of

p = 1 MPa /

-

f = 9.5 Hz J r ^15

O

Z

o

/ 1-<10

cc

111 o

cc

— j^ /

t// O- turns

—

ULUCC 5 /^^^^ A- 0.5 turns

^

V- 1 turn

D- 1.5 turns

—

n 1,1,1 0-2 turns

1,1,

100

Fig. 32

140 180 220 260 300

TEMPERATURE, K

Refrigeration power vs temperature for pulse-tube II at 9.5 Hz

340

The peak of the relative efficiency was around 12? of Carnot a a temperature of 210 K (Fig. 33). It was achieved with an orifice setting of one turn whereas the basic pulse tube

(orifice closed) at this temperature yielded a value of only 10.5? of Carnot. The higher

refrigeration power allowed lower temperatures, and the lowest possible temperature for

9.5 Hz was 140 K with an orifice setting of 1.5 turns.

34
0.16

'

1

' 1 1 1

1 1 1 1 1

O- turns

PULSE TUBE n A -0.5 turns

p = 1 MPa V- 1 turn -

f = 9.5 Hz x^^^^

D-1.5 turns

0.12 — / \^ 0-2 turns —

EFFICIENCY ob00 — /^^ ^^

\

I

—

0.04 - % —

n 1

-

100 140 180 220 260

TEMPERATURE, K

300 340

Fig. 33 Efficiency relative to Carnot vs temperature for pulse-tube II at 9.5 Hz

The mass flow into the pulse tube at 9.5 Hz was more dependent on the orifice setting

and varied by about 10?. The mass flow ranged from 0.87 g/s at 270 K to 1 .2 g/s at 145 K. No useful relation regarding the mass flow values obtained with pulse tube I at 9.5 Hz could

be found.

The best ratio of mg/mp^ at a frequency of 9.5 Hz was slightly greater using pulse

tube II. This ratio was obtained with an orifice setting of 1.5 turns which delivered values

for iTiQ/mpt of 0.25 at 150 K to 210 K and 0.32 for the higher temperature range. Ratios

of 40^ or greater are too high to be considered reasonable for applications.

As the results demonstrate, the resonance phenomenon present at pulse tube I is not evident when using pulse tube II.

The highest values for refrigeration power and efficiency were obtained using pulse tube

II at a frequency of 11.5 Hz. These results support the theoretical proposition which

predicted optimum results at higher frequencies.

The peak of the relative efficiency was 3555 of Carnot at a temperature of 1 80 K and an orifice setting of 1.5 turns (Fig. 34). Also a relatively high value of 28? of Carnot was achieved for the basic pulse tube at a temperature of roughly 240 K.

35
0-4 h PULSE TUBE E

p = 1 MPa

f = 11.5 Hz

0.3

>-O

z

UJ50.2

u.HI

0.1

100

O- turns

A- 0.5 turns

V- 1 turn

D- 1.5 turns

O- 2 turns

140 300

Fig.

180 220 260

TEMPERATURE, K

34 Efficiency relative to Carnot vs temperature for pulse-tube II at 11.5 Hz

340

At this frequency the assumption that the refrigeration power of pulse tube II is about

one-fourth the power of pulse tube I was verified (Fig. 35). The frequency of 11.5 Hz yielded the highest refrigeration power for pulse tube II and the best result was obtained

with an orifice setting of 2 turns. Also the lowest temperature of 140 K was achieved with

this orifice setting.

36
20

LIJ O

Q.

<10

CC

LUo

cc 5

PULSE TUBE n

p = 1 MPa

f = 11.5 Hz

O- turns

A-0.5 turns

V-1 turn

D-1.5 turns

0-2 turns

100

Fig. 35

140 180 220 260 300

TEMPERATURE, K

Refrigeration power vs temperature for pulse-tube II at 11.5 Hz

340

The mass flow into the pulse tube was relatively independent of the orifice setting at this frequency and can be approximated by a linear function of the temperature. The mass

flow ranged from 1.0 g/s at 270 K to 1.4 g/s at 140 K. Analogous to previous frequencies no reasonable relation between the mass flow for pulse tube I and pulse tube II at the

equivalent frequencies can be established.

The optimum ratio for mass flow t?irough the orifice and mass flow into the pulse tube

was obtained with pulse tube II at a frequency of 11.5 Hz with an orifice setting of 2 turns. Values of 0.35 in the higher temperature range and 0.27 in the lower temperature range were

measured. These values are below the optimum values for pulse tube I.

5.7 Summary for Pulse Tube II

The experiments demonstrate that the relation between different pulse tube diameters is

not as simple and direct as assumed. Unfortunately no experiments could be performed above a frequency of 11.5 Hz due to apparatus limitations.

Therefore some interesting work can be done in the future using this pulse tube size

with higher frequencies. Nevertheless some conclusions concerning the influence of the

diameter on pulse tube behavior can already be formed.

For smaller pulse-tube diameters a higier frequency is necessary in order to get optimum

results. Also the basic pulse tube functions better at a higher frequency when a smaller

diameter is used.

The influence of irreversibilities is much greater for the smaller tube and therefore

much lower efficiency values can be achieved. In this work 11.5 Hz delivered the optimum

efficiency but it is possible that at higher frequencies this tube would be even more

efficient

.

37
The lowest possible temperature was much higher for this pulse tube. Only 140 K could

be achieved with a frequency of 11.5 Hz. It is also possible that lower temperatures can be

obtained by increasing the frequency.

The proposed relation between the refrigeration power for the two pulse tube diameters

could only be justified at 11.5 Hz. At this frequency the power of pulse tube II was roughly

one-fourth the power of pulse tube I at corresponding temperatures.

Because pulse tube II yielded optimum values at much higher frequencies than pulse

tube I the assumption was verified that within the orifice pulse tube only little heat could

be transferred between the tubing wall and the gas.

5.8 Pulse Tube III

As with pulse tube II, theoretical suppositions will be stated first, describing the

main properties of pulse tube III.

Pulse tube III had the same tube diameter as pulse tube I suggesting that optimum

results for pulse tube III might be obtained also at a frequency of 6 Hz. The length of

pulse tube III was one-half that of pulse tube I. Because a frequency of 3 Hz provided

relatively low refrigeration power, no experiments were administered for pulse tube III at this frequency. In addition the refrigeration power for pulse tube III was expected to be

slightly smaller than the power produced by pulse tube I. Since the length of this tube is

shorter than for the original pulse tube, the temperature gradient along the shorter tube

must be steeper in order to achieve the same minimum temperature. Therefore a higher minimum

temperature was expected. Furthermore the efficiency will probably be slightly lower than

for pulse tube I. In addition the experiments should also indicate whether the length or diameter has the greatest influence on the properties of the pulse tube.

The first run of pulse tube III was conducted at a frequency of 6 Hz. The results were

as expected. The lowest possible temperature was 110 K with an orifice setting of 2 turns.

The relative efficiency was astonishingly high using the basic pulse tube (orifice

closed). A value of almost 85/S of Carnot was achieved at a temperature of 220 K. With the

orifice pulse tube a value of 55^ of Carnot was obtained at a low temperature of 120 K with

an orifice setting of 1 turn (Fig. 36).

38
0.9

0.8

0.7

0.6

O0.6

z

UJ2 0.4

UJ 0.3

0.2

0.1

100

PULSE TUBE m

p = 1 MPa

f = 6 Hz

O- turns

-0.5 turns

0-1 turn

A-2 turns

X- 3 turns

140 180 220 260 300

TEMPERATURE, K

Fig. 36 Efficiency relative to Carnot vs temperature for pulse t^ube III at 6 Hz

340

The refrigeration power was approximately one half the power produced by pulse tube I at the same frequency (Fig. 37). Similar to the case with pulse tube I, the best result was obtained with 2 turns.

39
40

LUo

Q.

PULSE TUBE m

p = 1 MPa

f = 6 Hz

'

\

' O-O turns

D-0.5 turns0-1 turn

A-2 turns

x-3 turns

100 140 180 220 260 300

TEMPERATURE, K

Fig. 37 Refrigeration power vs temperature for pulse-tube III at 5 Hz

340

The mass flow into the pulse t tube I. The range extended from 0. with an orifice opening of 2 turns, was much more evident with this pul

155^ was observed between the basic

using the same orifice settings as ratio of mass flow through the orif

Therefore Figure 15 of pulse tube I transport per unit mass flow values

1 at equivalent temperatures.

ube was also lower for pulse tube III than with pulse

71 g/s at 270 K with a closed orifice to 1.05 g/s at 110 K The dependence of the mass flow on the orifice setting

se tube than with pulse tube I. A mass flow variation of

pulse tube and an orifice setting of 3 turns. However employed with pulse tube I, equivalent values for the

ice to mass flow into the pulse tube were recorded,

is also applicable for pulse tube III. The heat were about 20^ below the values obtained with pulse tube

The data acquired with pulse tube III at 6 Hz showed that all the theoretical estimates

were appropriate and a comparison between pulse tube I and pulse tube III is easier to realize than between pulse tube I and pulse tube II. The behavior of pulse tube III is similar

to the behavior of pulse tube I at this frequency. The second point of interest was to ascertain how the values for refrigeration power and efficiency change by going to a frequency of 9.5 Hz.

The results for pulse tube III at 9.5 Hz clearly show the expected drop of the relative

efficiency values compared to the values at 6 Hz (Fig. 38). The highest efficiency of 35!^ of

Carnot was obtained with an orifice setting of 2 turns at a temperature of 120 K. The basic

pulse tube yielded efficiency values below 20iJ of Carnot at all temperatures. The behavior

of the efficiency curves and refrigeration power for pulse tube III are qualitatively the same as those of pulse tube I.

40
100 140 180 220 260 300

TEMPERATURE, K

Fig. 38 Efficiency relative to Carnot vs temperature for pulse-tube III at 9.5 Hz

340

For both tube I and tube III, the refrigeration power increased in going from 6 Hz to 9.5 Hz. However the increase was more notable with pulse tube III. The optimum

refrigeration power for pulse-tube III at 9.5 Hz was obtained with an orifice setting of

three turns (Fig. 39).

41
40

LU^ 30

o

a.z

O

<

QC

UJO

QC

Li. UJ

QC

20

to

PULSE TUBE m

p = 1 MPa

f = 9.5 Hz

O-O turns

n-0.5 turns

O- 1 turn

A- 2 turns

X- 3 turns

_L 100 140 180 220 260 300

TEMPERATURE, K

Fig. 39 Refrigeration power vs temperature for pulse-tube III at 9.5 Hz

340

Contrary to pulse tube I the lowest temperature for pulse tube III was achieved with

9.5 Hz. It was possible to attain a minimum temperature of 105 K with both 2 and 3 turns.

The values

pulse tube I at mass flow ranges orifice setting

linear function

equivalent orif

guise tube III. Q/mpt values of

pulse tube III

for the mass flow into pulse tube III were slightly smaller than those of

low temperatures but were about the same in the high temperature range. The

from 1.2 g/s at 270 K to 1.9 g/s at 110 K. Since the dependence on the

is insignificant for this frequency the mass flow can be approximated by a of the temperature. Similarly to the case with a frequency of 6 Hz,

ice setting yielded the same values for mQ/mp^ using pulse tube I as with

Therefore Figure 20 is also suitable for pulse tube III. Since the

pulse tube I and pulse tube III correspond well, accurate values for

can also be obtained from Figure 19.

5.9 Summary for Pulse Tube III

The results confirmed the predicted behavior of pulse tube III and showed that the

behavior of pulse tube I and pulse tube III were qualitatively similar at each experimental

frequency. Therefore, it may be reasonable to predict behavior paralleling that of pulse

tube I for frequencies not measured with pulse tube III. Refrigeration power and efficiency

were lower for pulse tube III than for pulse tube I but exhibited the same dependence on the

frequency. The contrast in the efficiencies of the two pulse tubes is much less than the

difference in the refrigeration power. The refrigeration values produced by pulse tube III are one half those of pulse tube I. Also, behavior at the same orifice settings is roughly

equal for both tubes. The lowest possible temperature for pulse tube III is significantly

above the minimum temperature achieved with pulse tube I.

42
6. Comparison and Discussion of the Three Pulse Tubes

As expected, the best results among the three pulse tubes were acquired with pulse tube

I. This same pulse tube size was used at NBS in earlier work to achieve a record low

temperature of 60 K [8].

In these experiments, the lowest temperature achieved was 75 K at a frequency of 5 Hz.

A possible reason that 60 K could not be obtained is because of the isothermalizers in the test apparatus. These have a small but finite gas volume (2.7 cm^) and cause a pressure drop.

The most surprising phenomenon of pulse tube I was the frequency dependence. The pulse tube

I achieved the best results for efficiency, roughly 90? of Carnot, at a frequency of 6 Hz. By increasing the frequency up to 9.5 Hz the efficiency dropped significantly down to a peak

value of only 3^% of Carnot. Going to a higher frequency of 11.5 Hz, the efficiency increased to a peak value of about ^8% of Carnot. In contrast the refrigeration power increased steadily with increasing frequency for a temperature range above 120 K. As the

frequency was increased the orifice had to be opened more and more in order to achieve

optimum results. Therefore the basic pulse tube (closed orifice) worked best at the lowest

frequency of 3 Hz where it yielded a peak in relative efficiency of 90/J of Carnot. Also the

minimum temperature obtained with the basic pulse-tube was found at 3 Hz.

Examination of the data reveals that a reduction of the pulse tube diameter has more

influence on behavior than shortening the length. Results showed that a tube of smaller

diameter requires higher frequencies to operate most efficiently. The values for both

refrigeration power and efficiency were much lower for pulse tube II than they were for pulse

tube I. The peak value of efficiency using pulse tube II was achieved at a frequency of

11.5 Hz and was only about 35% of Carnot. It is possible that greater relative efficiencies

can be obtained at higher frequencies. The lowest temperature for pulse tube II was measured

at this frequency and was only 140 K. The refrigeration power for pulse tube II was largest

at 11.5 Hz. The ratio of refrigeration powers for pulse tube I to pulse tube II at this

frequency was nearly equivalent to the ratio of the cross sectional areas, although the mass

flow into pulse tube II was more than one-fourth the mass flow into pulse tube I for each

frequency setting.

The refrigeration power and especially efficiency of pulse tube III was better than

those for pulse tube II. A temperature of 110 K could be achieved with pulse tube III at a frequency of 9.5 Hz which sets the minimum temperature of pulse tube III less than that of

pulse-tube II. The behavior of pulse tube III at the various frequency settings was similar

to pulse tube I. The best values for efficiency were obtained at a frequency of 6 Hz,

yielding relative efficiency values of 55% of Carnot with optimum orifice setting and 82% of

Carnot with the basic pulse tube. The refrigeration powers delivered by pulse tube III are roughly half those of pulse tube I in the temperature range tested here. The mass flow into

the pulse tube was slightly less using pulse tube III than with pulse tube I. A direct

comparison of pulse tube II with pulse tube III is not useful because their behaviors at the

various frequencies are completely different.

P-V diagrams (Fig. 40) for pulse tube I and an ideal Stirling refrigerator point out the most important difference between these refrigerators. The flat shape illustrated in the

diagram of the pulse tube reveals its small power per unit mass in comparison to an ideal

Stirling refrigerator which has a much greater area of work input from the same size

compressor. From this diagram the difference between the orifice pulse tube and the basic

pulse tube can also be compared. Both diagrams of the pulse tubes were produced with pulse

tube I at a frequency of 6 Hz and a temperature of 210 K. For the orifice pulse tube the

orifice setting was 3 turns. The ideal Stirling refrigerator was calculated from a Schmidt

analysis [10].

43
1.91

0) Q.

Ill (T

CO(0m

GC

a.

0.80

p-V DIAGRAM

ideal isothermal Stirling

60.1

VOLUME, cm'^

Fig. 40 p-V-diagram for basic pulse tube, orifice pulse tube, and Stirling refrigerator

44
7. Conclusions

The experiments performed here gave detailed performance data for three different

orifice pulse tubes which incorporated the same basic design but were of different sizes.

The refrigeration power, efficiency, and refrigeration per unit mass flow measured in these

experiments were the first such results obtained on orifice pulse tubes, but they are by no means a complete set of measurements from which detailed modeling can be developed. They do serve as a guide to future work. The orifice pulse tube is more useful for future

applications than the basic pulse tube since its refrigeration power can be an order of

magnitude greater. Also much lower temperatures can be achieved with the orifice. The only

disadvantage in comparison to the basic pulse tube is the lower efficiency of the orifice

pulse tube.

The diameter of the pulse tube has the greatest influence on the characteristic behavior

of the refrigeration power and efficiency curves at various frequencies, whereas the length

of the tube plays only a subordinate role. Nevertheless, a change of either length or diameter has a substantial effect on the refrigeration power.

The optimum frequency of the larger diameter tube (12.7 mm) was 6 Hz whereas the optimum

frequency for the smaller diameter tube (6.M mm) could be above the highest tested frequency

of 11.5 Hz.

The most important results of this work are listed below:

The lowest temperature measured was 75 K, which was achieved with pulse tube I at a frequency of 6 Hz. The best frequency for the 12.7 mm diameter orifice pulse tube was 6 Hz, which gave the

highest efficiency values of almost 90^ of Carnot.

- The basic pulse tube also yielded an efficiency of 905^ of Carnot but at a frequency of

3 Hz.

- A decrease in the diameter of the tube degraded the efficiency and refrigeration power,

- Smaller diameter tubes work better at higher frequencies.

The refrigeration power is approximately proportional to the tube length.

The tube length has less influence on the efficiency than does the tube diameter

The optimum frequency is independent of the tube length.

- The optimum orifice setting depends on the diameter of the tube.

- The basic pulse tube works better at lower frequencies than the orifice type.

are: The primary advantages of any pulse-tube refrigerator over other refrigeration cycles

Only one moving component (at room temperature).

- Uses modest pressure and pressure ratios.

Possible to achieve temperature ratios of greater than four in one stage.

- Works with an ideal gas, which implies one fluid for all temperatures.

A large orifice will not collect impurities at the high temperature part of the cycle.

- Large refrigeration powers in the orifice type.

Good intrinsic efficiency.

Several stages can be operated form the same pressure wave generator.

The one disadvantage of a pulse tube is the low refrigeration rate per unit mass flow

which means better regenerators are required,

8. Acknowledgments

Construction of much of the apparatus was done by Dr. David R. Smith and is greatly

appreciated. We acknowledge the careful revising of this report by Mary P. Russell and Dr. David R. Smith.

45
9. References

[1 ] Gifford, W.E, and Longsworth, R.C., Pulse-tube refrigeration ASME paper No. 63-WA-290

presented at Winter Annual Meeting of the American Society of Mechanical Engineers,

Philadelphia, Pennsylvania (Nov. 17-22, 1963).

[2] Gifford, W.E. and Longsworth, R.C., Pulse tube refrigeration progress, "Advances in

Cryogenic Engineering", Vol. 10B, Plenum Press, New York (1965), p. 69.

[3] Gifford, W.E. and Longsworth, R.C., Surface heat pumping, "Advances in Cryogenic

Engineering", Vol. 11, Plenum Press, New York (1966), p. 171.

[4] Longsworth, R.C., An Experimental Investigation of pulse tube refrigeration heat pumping

rates, "Advances in Cryogenic Engineering", Vol. 12, Plenum Press, New York (1967), p. 608.

[5] Gifford, W.E. and Kyanka, G.H., Reversible pulse tube refrigeration, "Advances in

Cryogenic Engineering", Vol. 12, Plenum Press, New York (1967), p. 619.

[6] Lechner, R.A. and Ackermann, R.A., Concentric pulse tube analysis and design, "Advances

in Cryogenic Engineering", Vol. I8, Plenum Press, New York (1973), p. '<67.

[7] Mikulin, E.I., Tarasov, A. A. and Shkrebyonock, M.P., Low temperature expansion pulse

' tubes, "Advances in Cryogenic Engineering", Vol. 29, Plenum Press, New York, (1984), p. 629.

[8] Radebaugh, R., Zimermann, J., Smith, D.R., and Louie, B., "A Comparison of Three Types

of Pulse Tube Refrigerators: New Methods for Reaching 60 K", Advances in Cryogenic

Engineering, Vol. 31, Plenum Press, New York, (1986), p. 779.

[9] Kays, W.M., and London, A.L., Compact Heat Exchangers , 3i"d ed., McGraw-Hill Book Co., New York, (1984).

[10] Walker, G., Cryocoolers, Plenum Press, New York, (1983).

46
NBS-n4A IREV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN-1301

2. Performing Organ. Report No'. 3. Publication Date

September 1986

4. TITLE AND SUBTITLE

Measurements of the Efficiency and Refrigeration Power

of Pulse-Tube Refrigerators

5. AUTHOR(S)

Steffen Herrmann and Ray Radebaugh

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

NASA Ames Research Center

Moffett Field, CA 94035

10. SUPPLEMENTARY NOTES

\2Z\ Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual sunnmary of most significant information. If document includes a significant

bi bliograpl^y or literature survey, mention it herej

Pulse-tube or thermoacoustic refrigerators have the potential for high

reliability since they require only one moving part—an oscillating piston or diaphragm at room temperature.

If a tube is closed at one end and connected to a pressure wave generator at

the open end, and if the phase angle between mass flow and pressure is shifted from

90°, then refrigeration occurs at the open end. The shift in phase angle can be

realized by thermal relaxation between the gas and the tube walls or by an orifice

at the closed end. A low temperature of 60 K using helium gas in a one stage

orifice pulse tube has been achieved at NBS. This report describes the first

measurements of the efficiency, refrigeration power, and refrigeration power per

unit mass flow, for three pulse-tube refrigerators. Three tube sizes, differing in

length and diameter, were studied over a frequency range of 3 to 11.5 Hz. Cooling

efficiencies as high as 90% of the Carnot efficiency were obtained when compressor

and regenerator losses are neglected. With the optimum orifice setting, gross

refrigeration powers of 14 W were measured at a temperature of 100 K in a tube of

12.7 mm diameter and 240 mm length at a pulse frequency of 6 Hz. The influence of

pulse frequency, orifice setting, diameter, and length of tube are discussed in

relation to some theoretical understanding of pulse-tube behavior.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

cryocooler; cryogenics; efficiency; pulse-tube refrigerator; refrigeration power;

refrigerator; regenerative refrigerator.

13. AVAILABILITY

fX~| Unlimited

Q For Official Distribution. Do Not Release to NTIS

[X] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

1^31 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

52

15. Price

USCOMM-DC 6043-P80 U.S. GOVERNMENT PRINTING OFFICE: 1986-0-673-313/4535 2

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