Second law based modeling to optimum design of high capacity pulse tube refrigerators

The optimum design of a high capacity double inlet pulse tube refrigerator based on second law of thermodynamics has been presented in this paper. Second law is applied to calculate the work loss in the regenerator and to optimize the cryocooler performance. To investigate the behavior of the pulse tube refrigerator, mass and energy balance equations are applied to several control volumes of the cryocooler cycle. A complete system of conservation equations is employed to solve the regenerator analytically. The proposed model reports the cooling capacity of 110 W at 80 K cold end temperature at frequency of 50 Hz, orifice conductance of 0.4 and double inlet coefficient of 0.6, with 2.4 kW net power delivered to the gas. In this case, the entropy generation in the gas phase is dominant which is contributing more than 85% of the total lost work in the regenerator. The optimum thermal efficiency of 99.1% was achieved at a proper mesh number. However, the second law efficiency is reported to have an inverse behavior at this mesh number.     

A novel coupled VM-PT cryocooler operating at liquid helium temperature

This paper presents experimental results on a novel two-stage gas-coupled VM-PT cryocooler, which is a one-stage VM cooler coupled a pulse tube cooler. In order to reach temperatures below the critical point of helium-4, a one-stage coaxial pulse tube cryocooler was gas-coupled on the cold end of the former VM cryocooler. The low temperature inertance tube and room temperature gas reservoir were used as phase shifters. The influence of room temperature double-inlet was first investigated, and the results showed that it added excessive heat loss. Then the inertance tube, regenerator and the length of the pulse tube were researched experimentally. Especially, the DC flow, whose function is similar to the double-orifice, was experimentally studied, and shown to contribute about 0.2 K for the no-load temperature. The minimum no-load temperature of 4.4 K was obtained with a pressure ratio near 1.5, working frequency of 2.2 Hz, and average pressure of 1.73 MPa.     

A two-stage Stirling-type pulse tube cryocooler with a cold inertance tube

A thermally coupled two-stage Stirling-type pulse tube cryocooler (PTC) with inertance tubes as phase shifters has been designed, manufactured and tested. In order to obtain a larger phase shift at the low acoustic power of about 2.0 W, a cold inertance tube as well as a cold reservoir for the second stage, precooled by the cold end of the first stage, was introduced into the system. The transmission line model was used to calculate the phase shift produced by the cold inertance tube. Effect of regenerator material, geometry and charging pressure on the performance of the second stage of the two-stage PTC was investigated based on the well known regenerator model REGEN. Experimental results of the two-stage PTC were carried out with an emphasis on the performance of the second stage. A lowest cooling temperature of 23.7 K and 0.50 W at 33.9 K were obtained with an input electric power of 150.0 W and an operating frequency of 40 Hz.     

CFD modeling and experimental verification of a single-stage coaxial Stirling-type pulse tube cryocooler without either double-inlet or multi-bypass operating at 30–35 K using mixed stainless steel mesh regenerator matrices

This paper presents the CFD modeling and experimental verifications of a single-stage inertance tube coaxial Stirling-type pulse tube cryocooler operating at 30–35 K using mixed stainless steel mesh regenerator matrices without either double-inlet or multi-bypass. A two-dimensional axis-symmetric CFD model with the thermal non-equilibrium mode is developed to simulate the internal process, and the underlying mechanism of significantly reducing the regenerator losses with mixed matrices is discussed in detail based on the given six cases. The modeling also indicates that the combination of the given different mesh segments can be optimized to achieve the highest cooling efficiency or the largest exergy ratio, and then the verification experiments are conducted in which the satisfactory agreements between simulated and tested results are observed. The experiments achieve a no-load temperature of 27.2 K and the cooling power of 0.78 W at 35 K, or 0.29 W at 30 K, with an input electric power of 220 W and a reject temperature of 300 K.     

Design and prototyping of a large capacity high frequency pulse tube

This document describes the design and the prototyping performed at CEA/SBT in partnership with AIR LIQUIDE of a high frequency large cooling power pulse tube. Driven at 58 Hz by a 7.5 kW flexure bearing pressure wave generator, this system provides a net heat lift of 210 W at 65 K. The phase shift is obtained by an inertance and a buffer volume. This type of cryogenic cooler can be used for on site gas liquefaction or drilling site and for high temperature superconductivity power device cooling (transmission lines, large generators, fault current limiters).In this paper, we focus on two essential points, the regenerator and the flow straightener. The regenerator is a key component for good performance of the pulse tube cooler. It must have a large thermal inertia, a low dead volume, a good heat transfer gas/matrix and at the same time, small pressure drop. In the present case and unlike typical moderate cooling power pulse tubes, the regenerator is very compact. However, the resulting conductive losses remain negligible compared to the cooling power targeted. The goal of the flow straightener is to avoid as much as possible any jet stream effect and to guarantee the uniformity of the velocity field at both ends of the pulse tube. Indeed multi-dimensional flow effects can significantly impact the performances of the machine.     

Stirling-type pulse tube refrigerator (PTR) with cold compression: Cold compressor,colder expander

This research paper focuses on the performance prediction and its validation via experimental investigation of a Stirling-type pulse tube refrigerator (PTR) equipped with a cold linear compressor. When the working gas is compressed at cryogenic temperature, the acoustic power (PV power) can be directly transmitted through the regenerator to the pulsating tube without experiencing unnecessary precooling process. The required PV power generated by the linear compressor, furthermore, can be significantly diminished due to the relatively small specific volume of the working gas at low temperature. The PTR can reach lower temperature efficiently with higher heat lift at the corresponding temperature than other typical single-stage Stirling-type PTRs. Utilizing a cryogenic reservoir as a warm end and regulating the entire operating temperature range of the PTR will enable a PTR to operate efficiently under space environment.In this research, the experimental validation as a proof of concept was carried out to demonstrate the capability of PTR operating between 80 K and 40 K. The linear compressor was submerged in a liquid nitrogen bath and the lowest temperature was measured as 38.5 K. The test results were analyzed to identify loss mechanisms with the simple numerical computation (linear model) which considers the dynamic characteristics of the cold linear compressor with thermo-hydraulic governing equations for each of sub components of the PTR. All the mass flows and pressure waves were assumed to be sinusoidal.     

The effect of thermal cycling in superplastic diffusion bonding of 2205 duplex stainless steel

In view of the requirement of large cold rolling deformation and bonding pressure in the conventional superplastic diffusion bonding of 2205 duplex stainless steel, a novel method of introducing thermal cycling into the process was proposed. During the thermal cycling process, due to the change of temperature, surface chemical activity of 2205 duplex stainless steel was improved, activity of atoms and grain boundaries were improved, and the recrystallized grains were refined. The shear bond strength of joint prepared in the mode of thermal cycling using specimens with the cold roll reduction of 60% was 15 MPa higher than that of conventional bonding using specimens with the cold roll reduction of 85%. Compared to the shear bond strength of 430 MPa under the specific pressure of 10 MPa after conventional bonding, shear bond strength of 623 MPa was obtained under the condition of T_max = 1000 °C, T_min = 900 °C, cycle number of heating and cooling N = 3, and specific pressure P = 5 MPa.     

Numerical analysis on performance and contaminated failures of the miniature split Stirling cryocooler

A mathematical model based on thermodynamic theory of variable mass is developed for the split Stirling refrigerator, in which, the whole machine is considered by one-dimensional approach while the processes in the regenerator are simulated by two-dimensional approach. First, the influence of the ideal frost layer distributions on the flow and heat transfer in the regenerator and the performance of the Stirling cryocooler are simulated. Then, the distribution of the contaminated water vapor and its coagulated and deposited process is qualitatively analyzed. Finally, the lifetime of the refrigerator is evaluated based on the calculated data. The results show that when the refrigerator is operated at uniform distribution of the water vapor partial pressure in the regenerator, the cooling capacity is reduced over 10% at about 631 h, and the power consumption of compressor is increased over 20% at about 1168 h. However, for the linear distribution of water vapor partial pressure, the refrigerator can work properly because the frost never reaches the criterion of failure. Also, it is found that when the Stirling cryocooler restarts after a shutdown, the cooling capacity is reduced by 10% once the frost mass is over 7.05 mg, and there is no cooling capacity once the frost mass reaches 41.2 mg.     

Experimental study of one-stage VM cryocooler operating below 8 K

The Vuilleumier (VM) refrigerator, known as heat driven refrigerator, is one kind of closed-cycle Stirling type regenerative refrigerator. The VM refrigerator with power being supplied by liquid nitrogen was proposed by Hogen and developed by Zhou, which shows great potential for development below 10 K. This paper describes the experimental development of a VM cryocooler operating below 8 K, which was achieved by using liquid nitrogen as a heat sink of middle cavity. The regenerator was optimized by using a part of metallic magnetic regenerator material Er₃Ni to replace the lead sphere and a no-load temperature of 7.8 K was obtained. Then all the lead spheres were replaced by Er_0.6Pr_0.4 material and a no-load temperature of 7.35 K was obtained, which is the lowest temperature for this kind of refrigerator reported so far. The cooling power at 10 K is about 500 mW with a pressure ratio near 1.6 and a charge pressure of 1.8 MPa. Especially, the magnetic material Er_0.6Pr_0.4 was found to be a potential substitution for the conventional lead.     

Pressure drop of slush nitrogen flow in converging–diverging pipes and corrugated pipes

Cryogenic slush fluids such as slush hydrogen and slush nitrogen are solid–liquid, two-phase fluids. As a functional thermal fluid, there are high expectations for use of slush fluids in various applications such as fuels for spacecraft engines, clean-energy fuels to improve the efficiency of transportation and storage, and as refrigerants for high-temperature superconducting equipment. Experimental flow tests were performed using slush nitrogen to elucidate pressure-drop characteristics of converging–diverging (C–D) pipes and corrugated pipes. In experimental results regarding pressure drop in two different types of C–D Pipes, i.e., a long-throated pipe and a short-throated pipe, each having an inner diameter of 15 mm, pressure drop for slush nitrogen in the long-throated pipe at a flow velocity of over 1.3 m/s increased by a maximum of 50–60% as compared to that for liquid nitrogen, while the increase was about 4 times as compared to slush nitrogen in the short-throated pipe. At a flow velocity of over 1.5 m/s in the short-throated pipe, pressure drop reduction became apparent, and it was confirmed that the decrease in pressure drop compared to liquid nitrogen was a maximum of 40–50%. In the case of two different types of corrugated pipes with an inner diameter of either 12 mm or 15 mm, a pressure-drop reduction was confirmed at a flow velocity of over 2 m/s, and reached a maximum value of 37% at 30 wt.% compared to liquid nitrogen. The greater the solid fractions, the smaller the pipe friction factor became, and the pipe friction factor at the same solid fraction showed a constant value regardless of the Reynolds number. From the observation of the solid particles’ behavior using a high-speed video camera and the PIV method, the pressure-drop reduction mechanisms for both C–D and corrugated pipes were demonstrated.     

Influence of the connecting tube at the cold end in a U-shaped pulse tube cryocooler

In some special applications, the pulse tube cryocooler must be designed as U-shape; however, the connecting tube at the cold end will influence the cooling performance. Although lots of U-shape pulse tubes have been developed, the mechanism of the influence of the connecting tube on the performance has not been well demonstrated. Based on thermoacoustic theory, this paper discusses the influence of the length and diameter of the connecting tube, transition structure, flow straightener, impedance of the inertance tube, etc. on the cooling performance. Primary experiments were carried out in two in-line shape pulse tube cryocoolers to verify the analysis. The two cryocoolers shared the same regenerator, heat exchangers, inertance tube and straightener, and the pulse tube, so the influence of these components could be eliminated. With the same electric power, the pulse tube cryocooler without connecting parts obtained 31 W cooling power at 77 K; meanwhile, the other pulse tube cryocooler with the connecting parts only obtained 27 W, so the connecting tube induced more than a 12.9% decrease on the cooling performance, which agrees with the calculation quite well.     

Pressure drop and heat transfer during two-phase flow vaporization of propane in horizontal smooth minichannels

This study examined the two-phase flow boiling pressure drop and heat transfer for propane, as a long term alternative refrigerant, in horizontal minichannels. The pressure drop and local heat transfer coefficients were obtained for heat fluxes ranging from 5–20 kW m^?2, mass fluxes ranging from 50–400 kg m^?2 s^?1, saturation temperatures of 10, 5 and 0 °C, and quality up to 1.0. The test section was made of stainless steel tubes with inner diameters of 1.5 mm and 3.0 mm, and lengths of 1000 mm and 2000 mm, respectively. The present study showed the effect of mass flux, heat flux, inner tube diameter and saturation temperature on pressure drop and heat transfer coefficient. The experimental results were compared against several existing pressure drop and heat transfer coefficient prediction methods. Because the study on evaporation with propane in minichannels was limited, new correlations of pressure drop and boiling heat transfer coefficient were developed in this present study.     

Measurement and correlation of frictional pressure drop of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube

The objective of this paper is to investigate the effect of nanoparticle on the frictional pressure drop characteristics of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube, and to present a correlation for predicting the frictional pressure drop of refrigerant-based nanofluid. R113 refrigerant and CuO nanoparticle were used for preparing refrigerant-based nanofluid. Experimental conditions include mass fluxes from 100 to 200 kg m^?2 s^?1, heat fluxes from 3.08 to 6.16 kW m^?2, inlet vapor qualities from 0.2 to 0.7, and mass fractions of nanoparticles from 0 to 0.5 wt%. The experimental results show that the frictional pressured drop of refrigerant-based nanofluid increases with the increase of the mass fraction of nanoparticles, and the maximum enhancement of frictional pressure drop is 20.8% under above conditions. A frictional pressure drop correlation for refrigerant-based nanofluid is proposed, and the predictions agree with 92% of the experimental data within the deviation of ±15%.     

Pressure drop reduction and heat transfer deterioration of slush nitrogen in triangular and circular pipe flows

Slush fluids such as slush hydrogen and slush nitrogen are characterized by superior properties as functional thermal fluids due to their density and heat of fusion. In addition to allowing efficient hydrogen transport and storage, slush hydrogen can serve as a refrigerant for high-temperature superconducting (HTS) equipment using MgB₂, with the potential for synergistic effects. In this study, pressure drop reduction and heat transfer deterioration experiments were performed on slush nitrogen flowing in a horizontal triangular pipe with sides of 20 mm under the conditions of three different cross-sectional orientations. Experimental conditions consisted of flow velocity (0.3–4.2 m/s), solid fraction (0–25 wt.%), and heat flux (0, 10, and 20 kW/m²). Pressure drop reduction became apparent at flow velocities exceeding about 1.3–1.8 m/s, representing a maximum amount of reduction of 16–19% in comparison with liquid nitrogen, regardless of heating. Heat transfer deterioration was seen at flow velocities of over 1.2–1.8 m/s, for a maximum amount of deterioration of 13–16%. The authors of the current study compared the results for pressure drop reduction and heat transfer deterioration in triangular pipe with those obtained previously for circular and square pipes, clarifying differences in flow and heat transfer properties. Also, a correlation equation was obtained between the slush Reynolds number and the pipe friction factor, which is important in the estimation of pressure drop in unheated triangular pipe. Furthermore, a second correlation equation was derived between the modified slush Reynolds number and the pipe friction factor, enabling the integrated prediction of pressure drop in both unheated triangular and circular pipes.     

Experimental study of the influence of cold heat exchanger geometry on the performance of a co-axial pulse tube cooler

Improving the performance of the pulse tube cooler is one of the important objectives of the current studies. Besides the phase shifters and regenerators, heat exchangers also play an important role in determining the system efficiency and cooling capacity. A series of experiments on a 10 W @ 77 K class co-axial type pulse tube cooler with different cold heat exchanger geometries are presented in this paper. The cold heat exchangers are made from a copper block with radial slots, cut through using electrical discharge machining. Different slot widths varying from 0.12 mm to 0.4 mm and different slot numbers varying from around 20–60 are investigated, while the length of cold heat exchangers are kept the same. The cold heat exchanger geometry is classified into three groups, namely, constant heat transfer area, constant porosity and constant slot width. The study reveals that a large channel width of 0.4 mm (about ten times the thermal penetration depth of helium gas at 77 K, 100 Hz and 3.5 MPa) shows poor performance, the other results show complicated interaction effects between slot width and slot number. These systematic comparison experiments provide a useful reference for selecting a cold heat exchanger geometry in a practical cooler.     

Attractive performance of a Gifford–McMahon cryocooler by co-axial layout of regenerator materials

A novel filling method of regenerator materials, which we name a co-axial layout, is experimentally investigated. The 2nd stage regenerator of a Gifford–McMahon cryocooler was packed with 50% by volume of the co-axial layout (low temperature side) that consisted of 20% Gd₂O₂S and 30% HoCu₂ spheres. The warm temperature side was packed with 50% lead spheres as a single layer. The experimental results show that the cooling power of co-axial layout is almost the same as that of a three-layer layout, 20% Gd₂O₂S, 30% HoCu₂ and 50% lead, at temperatures between the ultimate low temperature (3.0 K) and 6 K. Moreover, at the temperatures above 10 K, the co-axial layout has 1.7–2.0 times the cooling power of the three-layer layout. Thus the co-axial layout produces a major improvement in cooling power. In this paper, the performance of five types of material assortments is discussed.     

Thermal and electrical properties of magnetite filled polymers

By the addition of metal-oxide particles to plastics the electrical and thermal conductivity of polymers can be increased significantly. Such particle filled polymers can substitute metals and metal oxides in applications like radio frequency interference shielding. Furthermore, particle filled polymers with higher thermal conductivity than unfilled ones become more and more important in applications with decreasing geometric dimensions and increasing output of power, like in computer chips.Therefore, thermal and electrical properties of polypropylene and polyamide with metal-oxide particle filler (magnetite, Fe₃O₄) are investigated. Different particle sizes of magnetite and types of additives were added in various proportions to a standard polypropylene and polyamide in an extrusion process. Samples were prepared by injection molding to investigate thermal and electrical properties systematically.The thermal conductivity increases from 0.22 to 0.93 W/(m K) for a filler content of 44 vol% of magnetite, whereas the electrical resistivity decreases more than seven orders of magnitude from an insulator (0% of magnetite) to 10 kΩ m (47 vol% of magnetite).The experimental results of thermal and electrical conductivity were correlated to the amount and particle sizes of magnetite filler. Electrical resistivity shows a significant drop at the theoretical percolation threshold (∼0.33) and for filler contents exceeding 33 vol% the magnetite particles have point contacts and are surrounded by the polymer matrix.     

Investigation on phase shifting for a 4 K Stirling pulse tube cryocooler with He-3 as working fluid

He-3 is generally recognized for its ability to provide more excellent thermophysical performance than He-4, especially in the 4 K temperature range. However, this was not always the case in our preliminary experiments on a three-stage Stirling-type pulse tube cryocooler (SPTC). Our ongoing studies, as reported in this paper, demonstrate that the different working fluids also affect the performance through their phase shifting capability. This feature has been passed over in large part by researchers considering refrigerant substitution. Unlike previous theoretical analyses that focus primarily on regenerator losses, this report investigates the effects of the working fluid on the phase angle at the cold end in order to quantitatively reveal the relationship between the lowest attainable temperature and the cooling capacity. The analysis agrees well with our experimental results on a three-stage SPTC. While running with the operating parameters optimized for He-3, the lowest temperature of the SPTC decreased from 5.4 K down to 4.03 K. This is the lowest refrigeration temperature ever achieved with a three-stage SPTC.     

Study on a 10 W/90 K in-line pulse tube cryocooler

A Stirling-type in-line pulse tube cryocooler (PTC) has been designed, built and tested at Shanghai Institute of Technical Physics (SITP), Chinese Academy of Sciences. This PTC prototype can obtain a low-noise cooling capacity of more than 10 W at around 90 K cold head temperature and is used for cooling a space-borne infrared photo detector. In order to achieve a highly efficient PTC, a simplified numerical simulation model has been established for design and optimization. The simulation results of the regenerator, pulse tube and inertance tube are analyzed in detail. Besides, some key parameters of the PTC are listed in the paper. The PTC’s performances are tested at different operating frequencies from 42 Hz to 55 Hz and its reject temperature dependence is observed in the range of 290 K to 320 K. Furthermore, the map of the PTC’s performance characteristics is presented.     

Study on cold head structure of a 300 Hz thermoacoustically driven pulse tube cryocooler

High reliability, compact size and potentially high thermal efficiency make the high frequency thermoacoustically-driven pulse tube cryocooler quite promising for space use. With continuous efforts, the lowest temperature and the thermal efficiency of the coupled system have been greatly improved. So far, a cold head temperature below 60 K has been achieved on such kind of cryocooler with the operation frequency of around 300 Hz. To further improve the thermal efficiency and expedite its practical application, this work focuses on studying the influence of cold head structure on the system performance. Substantial numerical simulations were firstly carried out, which revealed that the cold head structure would greatly influence the cooling power and the thermal efficiency. To validate the predictions, a lot of experiments have been done. The experiments and calculations are in reasonable agreement. With 500 W heating power input into the engine, a no-load temperature of 63 K and a cooling power of 1.16 W at 80 K have been obtained with parallel-plate cold head, indicating encouraging improvement of the thermal efficiency.