Stirling Type Research Articles

Design, Heat Leakage Analysis and Stirling Cryocooler Option of Stirling-type Lyophilizer

Background: Based on referring to the relevant patents, it was found that the traditional lyophilizer refrigeration system has the disadvantages of large volume and high power consumption. Meanwhile, considering the context of advocating low carbon emission and environmental protection, the use of energy-saving refrigeration technology and the use of non-fluorine and harmless refrigerants are the trends of future development. Objective: In order to solve the traditional lyophilizer problems and enhance the lyophilizer reliability, the paper designs a Stirling-type lyophilizer with a working temperature of -70°C. Methods: Stirling cooling has the advantages of ultra-low refrigeration temperature and high cooling speed. Based on the above advantages, combining the characteristics of the lyophilization box, a Stirling- type lyophilizer with a capacity of 0.120 m3 and a shelf area of 0.4 m2 is designed. The Stirlingtype lyophilizer refrigeration system structure is analyzed. The flat plate heat pipe to transfer the cold is used. The rigid polyurethane as the insulation material of the lyophilization box is studied. The heat leakage calculation method of the lyophilization box is given. Results: Stirling cryocooler is selected based on the lyophilization box heat leakage. The experimental test of the Stirling cryocooler is conducted. The feasibility of the design is verified. The Stirling cryocooler, with a charging pressure of 2.9 MPa and an operating frequency of 68 Hz, could achieve -87.057°C within 24 min. The lowest refrigeration temperature could be maintained at - 100.286°C after 97 min. The cooling capacity obtained is 40.0 W at an input power of 99.2 W, and the COP is 0.403. Conclusion: Stirling refrigeration technology is suitable for use in lyophilizer and Stirling refrigeration technology improves the robustness of the lyophilizer refrigeration system.

Study on the regenerative performance of pressed stainless-steel wire screens used in a pulse tube refrigerator working around 20 K

Stirling type pulse tube refrigerators (SPTR) have been widely used in many fields because of their advantages of low vibration, long service life and high reliability. As one of the main regenerative materials of SPTR, the conventional stainless-steel (SS) wire screen, has large regenerative heat loss below 20 K due to its decreased volumetric heat capacity at low temperatures. Especially when working at high frequency above 50 Hz, the SPTR can hardly reach 20 K with conventional SS wire screen for its aggravated heat loss. In this work, a post-processed SS wire screen, i.e. the pressed SS wire screen is used as the regenerative material to improve the cooling performance of SPTR working below 20 K. Compared to the original one, the pressed SS wire screen can be thinner, so that more of them can be filled in the regenerator to increase the total volume heat capacity. Through Sage simulation and thermodynamic analysis, the cooling performance of pressed SS wire screen, conventional SS wire screen, HoCu2 and Er3Ni are compared and studied. The internal mechanism of reducing the loss of a regenerator by pressed SS wire screen is explained. Experiment shows that a no-load temperature of 19.19 K can be obtained with an electric power of about 450 W and a frequency of 51 Hz when pressed screen is used. Compared with the conventional SS wire screen, the pressed SS wire screen can reduce the no-load temperature from 20.67 K to 19.19 K, which is proved to be effective in improving the performance of SPTR at liquid hydrogen temperatures.

Energy conversion efficiency improvement of a Stirling type PTR for dual temperature cooling by adopting two active work-recovery phase shifters

Deep space exploration is required to solve the problem of energy acquisition and efficient utilization. Improving energy conversion efficiency is vital to this issue. The Stirling type pulse tube refrigerators (PTR) that work in dual temperature zones play a pivotal role in the field of space detection, and the phase shifter of PTR profoundly affects the conversion efficiency of the exergy to cooling capacity. However, the typical phase shifter causes the acoustic power at the hot end of the cold finger to be dissipated into the form of heat, limiting energy efficiency. With the intention of improving the energy conversion efficiency in the PTR, a novel type of active phase shifter with work recovery on a dual temperature zone PTR is proposed and investigated in this article. Based on the pulse tube refrigerator with two separated cold fingers, inertance tubes with reservoirs, active piston phase shifters, and active work-recovery piston phase shifters have been comparatively investigated. While the refrigerator adopts active work-recovery piston phase shifters, a relative Carnot efficiency of 15.5% is obtained in the 35 K and 85 K temperature zones, which is the highest efficiency ever achieved in these temperature areas.

Development of a 20K two-stage Stirling type pulse tube cryocooler with pre-cooling inside second-stage pulse tube

Cryocoolers working in the liquid hydrogen temperature are important for applications such as cryo-pump, superconductor cooling and cryogenic electronics. This paper analyzes and compares the 20K gas-coupled two-stage Stirling type pulse tube cryocooler with and without pre-cooling. The pre-cooling uses some of the cooling power generated by the first stage cold head to pre-cool the middle of the second stage pulse tube. Given the same input acoustic power, the simulation results show that the cooling capacity of the second stage increase from 0.64 W to 2 W@20 K while the first stage available cooling capacity decrease from 5.84 W to 3 W@77 K when the pre-cooling is used. Meanwhile, the cryocooler relative Carnot Efficiency in terms of acoustic power increases from 10.3% to 14.6%.

Study on the Regenerative Performance of Pressed Stainless-Steel Wire Screens Used in a Stirling Type Pulse Tube Refrigerator Working at Liquid Hydrogen Temperatures

Study on the Regenerative Performance of Pressed Stainless-Steel Wire Screens Used in a Stirling Type Pulse Tube Refrigerator Working at Liquid Hydrogen Temperatures

A two-stage thermally-coupled pulse tube cryocooler working at 35 K for space application

The attainment and maintenance of a low temperature environment is essential for aerospace cryogenic detectors to achieve their required performance. Developing cryocoolers with features of high efficiency, compact structure, and long lifetime is the main challenge for cryogenic detector cooling. In this paper, a high efficiency thermally-coupled two-stage Stirling type pulse tube cryocooler working at 35 K for HgCdTe long wave infrared detector cooling is designed and tested. The thermally-coupled type avoids gas distribution at cold side which minimizes the inter-stage influence. The whole cryocooler is driven by one linear compressor which enables compact structure. The influence of operation frequency and mean pressure is studied by numerical calculation and experiments to determine the optimum operation condition. Acoustic impedance characteristics of both stages and the whole cold finger are also analyzed by comparing performance of cryocooler with different frequency, mean pressure and structure dimensions. The distributions of acoustic power and phase angle are presented to study the relation between impedance characteristic and the cooling performance. Impedance match between compressor and cold finger is also discussed by analyzing the efficiency of the linear compressor and the performance of cryocooler with different pulse tubes. Under optimum impedance match and operation condition of a working frequency of 39.2 Hz and a mean pressure of 2.45 MPa, the cryocooler provides a cooling power of 1 W at 35.1 K with an input electrical power of 150 W, which indicates a relative Carnot efficiency of 5%. This is a rather high efficiency for developed Stirling type multi-stage pulse tube cryocooler working at 35 K with only inertance tubes as phase shifter. The development of this cryocooler lays a solid base for the further optimization to realize a competitive candidate for aerospace cooling requirements.

Cooling performance improvement of a two-stage pulse tube cryocooler with Er-plated screen as regenerator material

• A new regenerator material called Er-plated screen was proposed. • Comparision between Er-plated screen and stainless steel screen were involved. • Pre-cooling temperature, no-load temperature and cooling capacity were experimentally studied. • A lowest temperature of 15.29K with 235W input can be achieved while using Er-plated screen. As one of the key component in the pulse tube cryocooler (PTC), a regenerator needs to reduce losses for performance improvement. Thus, a good regenerator material should have large volumetric specific heat capacity and heat exchange area with small flow resistance. At present, high-mesh stainless steel screen and magnetic materials such as Er 3 Ni are commonly used as regenerator materials in the low temperature range. However, with the cooling temperature decreasing to lower than about 20K, the volumetric specific heat capacity of stainless steel decreases significantly, increasing the irreversible heat transfer losses of the regenerator. This paper proposes a new regenerator material which coats a magnetic material (Er) with high volumetric heat capacity at low temperature on the surface of stainless steel screen. The two-stage Stirling type pulse tube cryocooler (SPTC) with Er-plated screen filled in the cold end of the second-stage regenerator is investigated. The cooling performance of the SPTC filling with stainless steel screen and Er-plated screen is compared numerically and experimentally. A no-load temperature of 14.95 K can be obtained with an electric power of W when Er-plated screen is used. The relative Carnot efficiency (rCOP) of the cryocooler with Er-plated screen at 20K is 3.32 %, which is higher than with stainless steel screen. Another interesting phenomenon found in the research is that the rCOP of the SPTC with Er-plated screen reverses to be lower than with stainless steel screen when the temperature exceeds 30 K.

Feasibility analysis of HoCu2 and Gd2O2S as regenerative materials around 4–20 K

• Sage indicates that Gd 2 O 2 S would result in temperature rise at 5.8 K. • Gd 2 O 2 S effects on the heat exchange and the axial heat conduction are analyzed. • Gd 2 O 2 S experimentally reduces the no-load temperature from 4.75 to 4.57 K. • Gd 2 O 2 S can improve the performance if the cooling temperature is below 6.1 K. Stirling type pulse tube refrigerators have great application potentials in terahertz detection, deep space mid/long infrared detection and so on. It is still hard for Stirling type pulse tube refrigerators to work at liquid helium temperatures efficiently. One of the reasons is the large regenerative heat loss under such low temperatures. In this paper, the cooling performance of the regenerative materials HoCu 2 and Gd 2 O 2 S at liquid helium temperatures are investigated. Focused on the heat exchange between gas and matrix and the axial heat conduction, Sage simulations indicate that with high specific heat capacity and high thermal conductivity, Gd 2 O 2 S is able to improve the regenerator performance when the temperature is below 5.6 K since the Gd 2 O 2 S’s specific heat capacity is higher than that of HoCu 2 at these temperatures. As the refrigeration temperature increases, the optimal length of Gd 2 O 2 S decreases and too much Gd 2 O 2 S may deteriorate the performance, even causing the temperature to rise slightly at the cold end. This is because heat is released from matrix to gas and the axial heat conduction decreases even to negative value, which causes an increase in temperature gradient in the Gd 2 O 2 S part. Experimental results verify that the no-load refrigeration temperature can decrease from 4.75 to 4.57 K with 5 mm Gd 2 O 2 S instead of pure HoCu 2 at the cold end, and the refrigeration temperatures at the cooling powers of 20 mW and 40 mW also decrease. Experiments show that Gd 2 O 2 S is capable of improving the performance when the refrigeration temperature is below 6.1 K, which agrees well with the findings from the simulations.

New Biparametric Families of Apostol-Frobenius-Euler Polynomials level-m

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-$m$. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials.

Numerical investigation of the potential efficiency of a cryogen-free VM type pulse tube cryocooler

The Vuilleumier (VM)-type pulse tube cryocooler is a novel kind of cryocooler used to obtain liquid helium temperature, which has been experimentally verified. However, the overall efficiency is not satisfying. Based on previous work on a low pressure ratio system, numerical investigations that explore the effect of high pressure ratios on cooling performance are presented in this paper. The research system is cryogen-free in which a Stirling type pulse tube cryocooler is used to provide the required cooling power for the thermal compressor and makes it adjustable for pre-cooling temperature to achieve optimum efficiency. First, after increasing the displacer swept volume to increase the pressure ratio, the dimensions of the main components were optimized with the lowest no-load temperature as the optimization target. Then the dependence of system performance on average pressure, displacer swept volume, frequency and cold HX temperature were studied considering the heat transfer temperature difference of the thermal bridge. Compared with the previous low efficiency under low pressure ratio, when the heat transfer temperature difference of the thermal bridge is 0 K, a higher relative Carrot efficiency of 1.29% and a cooling power of 250 mW at 4.2 K were predicted with an average pressure of 3 MPa, a frequency of 3 Hz and a pressure ratio of 1.67. Further optimization is underway.

Investigation of improving cool-down speed of Stirling type pulse tube cryocooler with ambient displacers

For a cryocooler, besides high efficiency at the working temperature, the cool-down speed is also important for some applications. Because of the difference in structure and operating mechanism, different cryocoolers have different characteristics for cool-down speed. This work introduces a Stirling type pulse tube cryocooler with ambient displacers which works in the liquid nitrogen temperature region. Strategies for improving the cool-down speed from room temperature to liquid nitrogen temperature have been investigated through simulation. The pulse tube cryocooler is designed to provide a nominal cooling power of 17.8 W at 77 K with 232.5 W of input electric power at 70 Hz. By fixing the maximum displacer movement in the simulation, the characteristics of how tuning the frequency around 70 Hz can change the cool-down speed without exceeding the allowable displacement of the piston and the current draw of the actual compressor are investigated. The strategy for tuning both the frequency and voltage turns out be effective in the beginning stage of the cool-down process with an improvement of the cooling power by about 15%-20%. The gain becomes less obvious as the cold head temperature drops. In conclusion, tuning both the frequency and voltage during the cool-down process helps the cold-head to reach its final temperature faster but the average gain is not as big as expected.

Effects of DC flow on a cryogen-free Vuilleumier type pulse tube cryocooler

Abstract DC flow may exist in a pulse tube cryocooler if a closed loop is formed by double inlet, etc. It has been found that, given the right amount and the right direction, DC flow may be favorable to the cooling performance of a PTC working at liquid hydrogen temperature and liquid helium temperature with Stirling type or G-M type PTC. In case of Vuilleumier type PTC, which is driven by a thermal compressor, none has been studied. In this paper, the effects of DC flow on a Vuilleumier type PTC working around 10 K have been studied through numerical analysis. In the simulation, the software SAGE is utilized to study the DC flow with a double-inlet module capable of adjusting the DC flow rate. The dependence of performance for thermal compressor on DC flow was firstly investigated. Then the influence of DC flow on the cooling performance was studied, including the cold end enthalpy, cooling capacity, expansion efficiency for pulse tube, etc. Main factors affecting the pulse tube expansion efficiency was distinguished. Finally, the operating parameters effects on cooling performance with varying DC flow rate were carried out. It is found that certain amount of DC flow is beneficial to the system performance with the optimum ratio between DC flow rate and AC flow rate amplitude lying within the approximate range from 0.05% to 0.08%.

On the Nielsen distribution

We introduce a two-parameter discrete distribution that may have a zero vertex and can be useful for modeling overdispersion. The discrete Nielsen distribution generalizes the Fisher logarithmic (i.e., logarithmic series) and Stirling type I distributions in the sense that both can be considered displacements of the Nielsen distribution. We provide a comprehensive account of the structural properties of the new discrete distribution. We also show that the Nielsen distribution is infinitely divisible. We discuss maximum likelihood estimation of the model parameters and provide a simple method to find them numerically. The usefulness of the proposed distribution is illustrated by means of three real data sets to prove its versatility in practical applications.

A Stirling type pulse tube cryocooler working at liquid hydrogen temperatures with a precooled transmission tube

Stirling type pulse tube cryocoolers (SPTCs) usually require multi-stage configuration for working below liquid hydrogen temperatures but their cooling efficiency is still poor at present. One of the main reasons is that their high-temperature part regenerators consume large amount of input pV power as isothermal components with large temperature drop. Theoretically, when there is a surplus cold source such as LN2 or LNG for precooling, the high-temperature part regenerator can be replaced by an empty tube with little pV power drop, which will increase the efficiency of the SPTC while recovering cold energy. In this paper, the SPTC with a precooled transmission tube instead of high-temperature part regenerator is proposed and studied. The hot end of the transmission tube was linked to the room-temperature compressor at ~300 K, while its cold end was connecting to the low-temperature part regenerator precooled to ~ 80 K by LN2. The heat transfer and pV power losses in the precooled transmission tubes under different sizes were calculated and analyzed. Experiments were carried out to verify the feasibility of the precooled transmission tube in a SPTC. Results show that the SPTC can work well with the precooled transmission tube. A no-load refrigeration temperature of 17.7 K and cooling capacity of 1.74 W at 25 K are obtained with a total input pV power of about 52.9 W. The hot end heat exchanger of the precooled transmission tube is found to be necessary for quickly stabilizing the cold end cooling temperature.

On r-Stirling Type Numbers of the First Kind

Some combinatorial properties of -Stirling numbers are proved. Moreover, two asymptotic formulas for -Stirling numbers of the first kind derived using different methods are discussed and corresponding asymptotic formulas for the -Stirling type numbers of the first kind are obtained as corollaries.

Development of Stirling-type pulse tube cryocooler

Stirling type pulse tube cryocoolers are very attractive for cooling of diverse application because it has it has several inherent advantages such as no moving part in the cold end, low manufacturing cost and long operation life. A moving magnet type linear motor of dual piston configuration is designed, and this compressor could be operated with the electric power of 100 W at the operating frequency of 50 Hz. A pulse tube cold finger with a double segmented inertance tube was designed for the desired cooling capacity. The coiled inertance tube was assembled inside the reservoir. In experiment, the pulse tube cryocooler is capable of providing the cooling capacity of 2.0 W at 80 K with power consumption of 99.1 W. Random and sinusoidal vibration tests have been conducted to evaluate their performance characteristics and structural integrity.

Pengembangan Mesin Stirling Tipe Gamma Sebagai Tenaga Penggerak Kipas Angin

Mesin stirling adalah mesin kalor yang mengambil kalor dari luar silinder kerjanya. Penelitian inimemberikan tinjauan literatur tentang mesin stirling type gamma dengan berbagai macampengembangannya seperti sebagai penggerak kipas angin. Tujuan dari penelitian ini adalah dapatmengembangkan sebuah mesin stirling yang energi keluarannya minimal sebesar 45 Watt dengan kecepatanputar 1000 rpm, sehingga mesin ini bisa digunakan sebagai tenaga penggerak sebuah kipas angin.Pengembangan mesin ini menggunakan metoda teknik perancangan VDI 2221. Proses perancanganmendapatkan beberapa alternatif rancangan. Rancangan yang terpilih menggunakan mesin stirling typegamma dengan 3 buah sudu kipas. Setelah dilakukan pengujian, maka didapatkan kecepatan putarmaksimum yaitu 3153 rpm, kecepatan putar rata-rata 1798 rpm, dengan efisiensi teoritis sebesar 63 %dengan daya keluaran sebesar 140 Watt

Topological phase transition in quantum-heat-engine cycles

We explore signatures of a topological phase transition (TPT) in the work and efficiency of a quantum heat engine, which uses a single layer topological insulator, stanene, in an external electric field as a working substance. The magnitude of the electric field controls the trivial and topological insulator phases of the stanene. We investigate the effects of TPT in two types of thermodynamic cycles, with and without adiabatic stages. For the adiabatic case, we examine a quantum Otto cycle. We find that at the critical point of TPT both work and efficiency plots with respect to the strength of the electric field exhibit a kink. For a non-adiabatic case, we consider an idealized Stirling type cycle with two isothermal and two isoelectric processes. We find no signatures of the TPT unless a voltage bias is introduced to restrict the involved energy bands to the electronic manifold above the Fermi level. In this case, either above or below the critical point, both work and efficiency become zero depending on the relative magnitudes of the electric fields in the isoelectric stages.

Effects of DC flow on pulse tube cryocooler working at liquid hydrogen and liquid nitrogen temperatures

The direct current gas flow (DC flow), normally treated as a loss in the pulse tube cryocoolers (PTCs) in the past, has been found may be beneficial to the cooling performance of the PTC working at low temperatures recently. However, the reason why it can improve the cooling performance is still not clear enough. In order to reveal the working mechanism of the DC flow independently, simulation analysis and experiment verification are carried out on a two-stage Stirling type PTC without the double-inlet valve. Results indicate that in the second stage PTC working around 20 K, by introducing the DC flow with a positive direction from regenerator side to pulse tube side, the cooling performance will be improved due to the remarkable increase of the AC enthalpy flow in the pulse tube and the decrease of AC enthalpy flow in the regenerator. This is because with the help of positive DC flow, the temperature gradients in the pulse tube and the regenerator of the 20 K PTC are improved, i.e. the DC flow causes smaller heat losses in them. Nevertheless, the DC flow has no help on improving the cooling performance of the PTC working around 80 K. Simulation and experiment show consistency that with an optimized DC flow, the no-load refrigeration temperature of the second stage Stirling PTC drops 6–7 K, and the cooling capacity at 22 K increases about 1 W.

CFD study of heat transfer and pressure drop for oscillating flow in helical rectangular channel heat exchanger

The heat transfer and pressure drop under oscillatory condition in helical rectangular channel heat exchangers are numerically investigated by using uniform design method. The correlations of three models with different ratios of height to width are obtained. The results show that the channel with the largest ratio of length to width has a larger heat transfer rate and a lower friction factor. Then, the field synergy principle is used to analyze heat transfer enhancement of helical rectangular channel heat exchanger. Besides, the Performance Evaluation Criteria (PEC) method has been used to compare the thermal-hydraulic performances of helical rectangular channel heat exchanger with helically coiled tube heat exchanger. The results show that the helical rectangular channel heat exchanger has a better performance operating at high frequency and high velocity. So it is more suitable for the Stirling type machines. Finally, a helical rectangular channel heat exchanger was experimentally used in our thermal-compressor system to verify the present numerical result.