Presented at the 

 11th International Cryocooler Conference 

June 20-22, 2000 

Keystone, Co

Vapor Precooling in a Pulse Tube Liquefier

E.D. Marquardt, Ray Radebaugh, and A.P. Peskin 

National Institute of Standards and Technology

Boulder, CO 80303 

ABSTRACT

Experiments were performed to study the effects of introducing vapor into a dewar where a

coaxial pulse tube refrigerator was used as a liquefier in the neck of the dewar. We were

concerned about how the introduction of vapor might impact the refrigeration load as the vapor 

barrier in the neck of the dewar is disturbed. Three experiments were performed where the input

power to the cooler was held constant and the nitrogen liquefaction rate was measured. The first

test introduced the vapor at the top of the dewar neck. Another introduced the vapor directly to

the cold head through a small tube, leaving the neck vapor barrier undisturbed. The third test

placed a heat exchanger partway down the regenerator where the vapor was pre-cooled before

being liquefied at the cold head. This experiment also left the neck vapor barrier undisturbed.

Compared to the test where the vapor was introduced directly to the cold head, the heat

exchanger test increased the liquefaction rate by 12.0%. The experiment where vapor was 

introduced at the top of the dewar increased the liquefaction rate by 17.2%. A computational

fluid dynamics model was constructed of the dewar neck and liquefier to show how the

regenerator outer wall acted as a pre-cooler to the incoming vapor steam, eliminating the need

for the heat exchanger.

INTRODUCTION

Liquefaction plants have always used some form of recuperative cryogenic refrigerator (i.e.

Joule-Thomson, Claude, or Brayton cycles) to provide the cooling. The reason for this is the

higher efficiencies that can be obtained with recuperative systems over regenerative systems (i.e. 

Stirling, pulse tube, or GM cycles) in larger scale cryogenic refrigerators. There is now increased 

interest in small to medium liquefaction plants (20 W to 1 kW refrigeration capacity) for local

cryogen liquefaction in the aerospace, military, and commercial sector. As refrigeration capacity

is reduced, regenerative systems become comparable with and then surpass recuperative systems 

in efficiency, making them attractive choices for small and medium scale liquefaction plants. 

One advantage of recuperative systems is the ability to continuously cool the vapor through 

the recuperative heat exchanger. An ideal regenerator cannot accept heat so the regenerative

systems must be multi-stage or remove all the heat at the lowest temperature, reducing

efficiency. It has been shown by Radebaugh et. al.

1

that non-ideal regenerators are able to accept

some heat at any point. We performed three experiments to determine whether this effect could 

be used to improve liquefaction efficiency of regenerative systems.
EXPERIMENTAL SETUP

Figure 1 shows the experimental setup with the pulse tube in the neck of a dewar. The pulse

tube was fully characterized2

 in a vacuum chamber so that refrigeration loads could be

determined from the input power. It had a nominal refrigeration capacity of 18.8 W at 90 K (20%

of Carnot) and produced 14.5 W at 77 K (19% of Carnot) with 223 W PV input power. Nitrogen

was used as the test fluid to be liquefied. In all experiments, the input PV power was held

constant at 223 W. The nitrogen mass flow rate was measured to hold the pressure in the dewar 

constant. 

In the first experiment, the nitrogen was introduced through a 1.5 mm tube directly to the

cold end. This did not allow the insulating gas in the neck of the dewar to be disturbed. The

second experiment introduced the nitrogen at the top of the dewar. The final experiment

introduced the nitrogen through a tube leading to a heat exchanger and then through another tube

leading directly to the cold end. The heat exchanger was clamped to the 50 mm long regenerator 

30 mm down from the warm end. It was a split design allowing it to be clamped anywhere along

the regenerator’s length. The contact thickness was 1.65 mm and the heat exchanger contained a

channel 25 cm long to insure adequate heat transfer between the fluid and heat exchanger. 

RESULTS

Figure 2 shows a typical cool down of the dewar with the inlet at the top of the dewar. The

temperature locations are shown in Figure 1. Under steady state operation, the temperature

profile in the neck of the dewar changes dramatically as the warm fluid flows passed the neck.

Figure 3 shows the wall temperature profiles in the dewar neck for both the cryocooler and the

dewar walls. The dewar wall temperatures were measured at the three positions shown in

Figure 1. Experiments 1 and 2 show linear temperature profiles, as expected, along the wall

Figure 1. Experimental setup. 
Figure 2. Typical cool down with fluid inlet at the top. Temperature locations are given in Fig 2. 

Table 1. Refrigeration power required for liquefaction.

Temperature (K) Enthalpy (J/g) Q1 (W) Q2 (W) Q3 (W) 

300 306.0 - - -

165 170.4 - - 4.86

Sat Liquid (77) -122.0 13.70 16.05 10.48 

within the experimental errors associated with the placement of the thermocouples. The dewar 

wall temperature in experiment 3, as shown in Figure 3, is interpolated from the measurements at

the three locations given in Figure 1. The cryocooler wall temperatures along the regenerator for

experiment 3 are derived from our theoretical model and are displayed to show the boundary

conditions the gas is exposed to as it travels to the cold head.

The dewar had a measured heat leak of 1.1 W. The enthalpy required to liquefy nitrogen at

0.1 MPa from 300 K is 428 J/g. This results in 7.13 W·min/g energy required for nitrogen

liquefaction from room temperature. The measured mass flow rates for the 3 experiments were

1.92, 2.25, and 2.15 g/min. Table 1 shows the refrigeration power required for the liquefaction 

given these mass flow rates. Q1, Q2, and Q3 represent the refrigeration load required for the

three different experiments respectively. 

Given the 1.1 W dewar heat leak and the 14.5 W of cooling power available, the energy

required for the case where nitrogen is directly applied to the cold head, Q1, agrees well with the

calculated value. The case using the mid-stage heat exchanger, Q3, shows that by accepting

some energy at a mid-point, we can increase the liquefaction rate by 12%. Our theoretical model1

predicts a 15% increase in the liquefaction rate. The case where nitrogen was introduced at the

top of the dewar shows that the regenerator continuously pre-cools the fluid since we only have

14.5 W of cooling power available and with the dewar heat leak, we would require 17.15 W if

heat was only absorbed at the cold head. We have increased the liquefaction rate by 17.2%

without using any special heat exchangers or flow channels. The model predicts a 23% increase

if the fluid is continuously pre-cooled by the regenerator.

The liquefier figure of merit, FOM, can be determined by

FOM W W

m T s h

W

  ideal



/



( )



,

0  (1) 
Figure 3. Temperature profile in the dewar neck. 

Table 2. Experimental results summary.

Experiment Liquefaction Rate (g/min) W elec (watts) Wideal (watts) FOM

1 1.92 262 24.61 0.094

2 2.25 262 28.84 0.110

3 2.15 262 27.56 0.105

where Wideal is the ideal work required for liquefaction, W is the actual work input, m is the

liquefaction rate, T0 is the ambient temperature, s is the entropy difference from ambient to

the saturated liquid state, and h is the enthalpy difference from ambient to the saturated liquid state.

Assuming the efficiency of the compressor,

 / W W PV elec , is 85%, the total electrical input

power is 262 W. Table 2 summaries the experimental results.

CFD MODELING

We have numerically modeled the best case where fluid enters at the top of the dewar and 

the cryocooler cold head is placed within the neck of the dewar. Using a commercial CFD 

package, we have determined the temperature profile and streamlines within the dewar neck

shown in Figure 4. These results show how the regenerator pre-cools the fluid before it reaches 

the cold head. The predicted fluid temperature along the regenerator closely matches the

regenerator wall temperature shown in Figure 3. 

To study the flow and temperature profiles inside the dewar neck, we used a finite element

numerical model. We used a 2-dimensional model, discretisizing the domain into 13,350 4-node

elements. Constrained temperatures were input as boundary conditions along the cryocooler

walls and at the fluid entrance. Adiabatic conditions were assumed for the outside walls of the

dewar. Compressible flow was modeled by assuming a Boussinesq equation of state for the

density. A function for the volume expansion was input for a range of densities for vapor and 

liquid states. Fluid properties were taken from the NIST12 database

3

for nitrogen. 
Figure 4. CFD results showing temperature contour and streamlines with in dewar neck. 

CONCLUSIONS 

We have shown that heat transfer to the regenerator can be used to improve liquefaction 

rates in regenerative cryocoolers with no special attention given to the fluid flow paths.

Improvements of 17.2% were shown over then case were all the liquefaction energy is removed 

at the cold head. Regenerative systems do not require any complex recuperative heat exchangers 

where a leak could cause mixing of the working fluid and liquefaction fluid.

REFERENCES

1. Radebaugh, R., Marquardt, E.D., Gary, J., and O'Gallagher, A., "Regenerator Behavior with 

Heat Input at Intermediate Temperatures," Cryocoolers 11, Plenum Publishers, New York 

(2000), in press.

2. Marquardt, E. and Radebaugh, R., "A Pulse Tube Oxygen Liquefier," Cryogenic 

Engineering Conference Vol. 45, Plenum Press, (1999), in press.

3. Lemmon, E.W., McLinden, M.O., Peskin, A.P., and Friend, D.G., Thermodynamic and 

Transport Properties of Pure Fluids and Mixtures (NIST12). NIST: Gaithersburg, MD.