Klaus D. Timmerhaus

Steady Secondary Momentum and Enthalpy Streaming in the Pulse Tube Refrigerator

Our study investigates the steady secondary momentum and enthalpy streaming that occurs in the pulse tube refrigerator. The linearized mass, momentum and energy conservation laws that are described by N. Rott1 are applied to a pulse tube, with the phase and amplitude of the axial velocity boundary conditions treated as independent parameters. Heat transfer between the gas and the tube wall is included. Heat transfer is shown to affect enthalpy flow by modifying the dynamic temperature amplitude and the temperature phase angle of the gas. We also calculate the steady mass flow circulation due to Reynolds stresses in the pulse tube. The length scale of the circulation is shown to be of the order of the tube length. Mass flow circulation is a loss mechanism because it results in a direct convection of enthalpy between the cold and hot ends.

Energy Flows in an Orifice Pulse Tube Refrigerator

A technique which allows for the instantaneous measurements of mass flow rate and temperature in an orifice pulse tube refrigerator (OPTR) during actual operation has been developed recently. This paper presents the values of enthalpy, entropy, and work fluxes at the cold end of the pulse tube evaluated from these measurements. They are thermodynamically self consistent within 1%. An analytical model describing the operation of an OPTR was developed at the National Institute of Standards and Technology (NIST) in the late 1980’s. This model assumes adiabatic performance of the pulse tube and purely sinusoidal mass flow rates, temperature, and pressure oscillations in the OPTR. The experimentally measured enthalpy flux varies from 60% to 85% of that predicted by the adiabatic model. The experimental work reported, here also gives values for various phase relationships that are needed for some calculations with the analytical model.

Higher Order Pulse Tube Modeling

A linearized model of the pulse tube is computed to second order to study heat transfer and steady mass streaming. A two-dimensional anelastic approximation of the fluid equations is used as the basis for this analysis. Anelastic theory applies because pressure drops in the open tube of the pulse tube are negligible; it allows the equations to describe compression and expansion of the gas without mathematical formation of shocks. The calculated results are given as functions of the dimensionless numbers appropriate for oscillating compressible anelastic flows. These dimensionless numbers were previously described at the 1995 Cryogenic Engineering Conferencel.

Ultrasonic Atomization Studies

Atomization of selected fluids has been observed to occur in a capillary at various resonance heights of the standing ultrasonic wave in the fluid. The length of fogging has been observed to be a function of the voltage applied to the transducer producing the ultrasonic wave in the fluid. A theoretical analysis is given to explain the experimental results obtained.

An Experimental Investigation of the Individual Boiling and Condensing Heat-Transfer Coefficients for Hydrogen

The efficient design of low-temperature hydrogen heat exchangers requires detailed heat-transfer information relevant to temperature gradients, heatfluxes, surface conditions and geometry, materials of construction, flow rates, and other important variables. This investigation determined only the relationship between the individual film heat-transfer coefficients and the variables of temperature difference and heat flux for boiling and condensing hydrogen films on a smooth vertical tube surface. The boiling occurred on the outside surface while the condensing took place on the inside surface.

Experimental Verification of Stability Characteristics for Thermal Acoustic Oscillations in a Liquid Helium System

Thermal acoustic oscillations (TAOs) are frequently observed when a tube is inserted into a cryogenic system, particularly when filled with liquid helium. A step temperature profile along the length of the inserted tube has typically been assumed by previous researchers in the development of a theoretical model for such oscillations[3,4]. Such theoretical predictions, however, have shown relatively large errors when compared with the experimental verifications. In this study, thermal acoustic oscillation parameters (including oscillation pressure amplitude and frequency) and temperature profile along the length of the oscillation tube have been measured simultaneously to investigate the effect of temperature profile on the characteristics of TAOs. Relatively steep temperature profiles have been observed. In addition, stability characteristics for thermal acoustic oscillations in a liquid helium system with a continuous temperature profile along the length of the tube have been predicted as well as the oscillation effect of the length ratio between the warm and cold sections of the tube. The latter effect has been observed experimentally to be very sensitive to the stability characteristics of TAOs. Good agreement has been achieved between experimental results and theoretical predictions.

Measurement of the Performance of a Spiral Wound Polyimide Regenerator in a Pulse Tube Refrigerator

A regenerator for use in a pulse tube refrigerator has been constructed from a polyimide (polypyromellitimide or PPMI) whose small ratio of thermal conductivity to heat capacity make it a good candidate for a regenerator material in cryocoolers. The regenerator was fabricated using 25 μm thick photoresist strips bonded to a 50 μm thick sheet of PPMI. This composite sheet was wound in jelly-roll fashion around a mandrel and inserted into the regenerator housing. The photoresist strips, formed using a photolithographic technique, provided a 25 μm spacing for the axial flow of gas between each layer of PPMI. Ineffectiveness results are presented for this material under actual operating conditions in a pulse tube refrigerator and compared with a numerical model. The numerical model indicated that a polyimide regenerator would perform much better than one constructed of stainless steel screen, but the experimental results showed the opposite behavior. Measured values for the ineffectiveness were 0.003 for the stainless steel screen and 0.017 for the polyimide.

Properties of Cryogenic Fluids

The cryogenic region of most interest is characterized principally by five fluids: oxygen, nitrogen, neon, hydrogen, and helium. We do in fact speak of the “oxygen range” or the “hydrogen range.” Table 2.1 gives the normal (0.101 MPa or 1 atm) boiling temperature, the normal melting temperature, the critical temperature and pressure, and the normal latent heat of vaporization for these five cryogenic fluids and several other common cyrogens. Some of the important characteristics of the most widely used cryogenic liquids are discussed more specifically in the following paragraphs.

Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models

One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when described with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse diffusion effects, either parameter corrections must be obtained through experimentation, or solutions to the twodimensional differential fluid equations must be found.

Useful Scaling Parameters for the Pulse Tube

A set of dimensionless scaling parameters for use in correlating performance data for Pulse Tube Refrigerators is presented. The dimensionless groups result after scaling the mass and energy conservation equations, and the equation of motion for an axisymmetric, two-dimensional ideal gas system. Allowed are viscous effects and conduction heat transfer between the gas and the tube wall. The scaling procedure results in reducing the original 23 dimensional variables to a set of 11 dimensionless scaling groups. Dimensional analysis is used to verify that the 11 dimensionless groups obtained is the minimum number needed to describe the system. We also examine 6 limiting cases which progressively reduce the number of dimensionless groups from 11 to 3. The physical interpretation of the parameters are described, and their usefulness is outlined for understanding how heat transfer and mass streaming affect ideal enthalpy flow.