Numerical simulation of a two‐stage pulse tube refrigerator based on adiabatic model

Cryocoolers are devices that are capable of achieving and maintaining cryogenic temperatures for a number of applications such as high‐energy physics, cooling of superconducting magnets, sensors, high‐vacuum production, cryotronics, cryonics, and so on. All the above applications need coolers with high reliability, efficiency, low maintenance, and low cost. The absence of moving parts at the cryogenic temperatures makes the pulse tube (PT) coolers quite suitable for the above applications. In spite of considerable developments in the area of PT cryocoolers, many of the fundamental processes responsible for the cold production are not fully understood. In this work, we present the results of numerical simulations of two‐stage pulse tube refrigerators (PTR) using adiabatic flow of gas through the pulse tube system. A two‐stage PTR is the improved version of single‐stage system to achieve temperature close to 4 K. Assuming adiabatic gas flow through PTs, the algebraic equations for pressure, mass flow, and volumes at different locations have been derived and solved by a MATLAB based program. Using the above, the performance of PTR has been optimized for different operational parameters. The cooling powers predicted by the model have been compared with the experimental data, and they are in good agreement with each other.     

Theoretical modeling and experimental verifications of the single-compressor-driven three-stage Stirling-type pulse tube cryocooler

This paper establishes a theoretical model of the single-compressor-driven (SCD) three-stage Stirling-type pulse tube cryocooler (SPTC) and conducts experimental verifications. The main differences between the SCD type and the multi-compressor-driven (MCD) crycooler are analyzed, such as the distribution of the input acoustic power in each stage and the optimization of the operating parameters, in which both advantages and difficulties of the former are stressed. The effects of the dynamic temperatures are considered to improve the accuracy of the simulation at very low temperatures, and a specific simulation example aiming at 10 K is given in which quantitative analyses are provided. A SCD three-stage SPTC is developed based on the theoretical analyses and with a total input acoustic power of 371.58 W, which reaches a no-load temperature of 8.82 K and can simultaneously achieve the cooling capacities of 2.4 W at 70 K, 0.17 W at 25 K, and 0.05 W at 10 K. The performance of the SCD three-stage SPTC is slightly poorer than that of its MCD counterpart developed in the same laboratory, but the advantages of lightweight and compactness make the former more attractive to practical applications.     

混合工质脉管制冷机性能的数值模拟

开发了适用于混合工质的脉管制冷机的计算程序，利用此程序对应用混合工质提高脉管制冷机的制冷性能进行了研究，发现当混合工质采用氦气和氢气，且处于合适的配比下，可以进一步改进脉管制冷机的制冷性能，给出了当混合工质最佳配比时，脉管制冷机内热力参数的瞬时变化及一周期的循环参数，用该计算程序可以获得混合工质脉管制冷机内复杂过程的详细信息，为制冷机设计和改进提供依据。     

Exergy destruction in the double inlet pulse tube cryocooler (DIPTC): A parametric study

In this paper the exergy analysis of a double inlet pulse tube cryocooler (DIPTC) has been performed. The pulsating mass flow has been modelled by a sinusoidal approximation using phasor analysis. The corresponding values were used to find out the average exergy flow through and exergy destructions in various components. The effect of different parameters on the exergy flow and exergy destruction has been studied over a large range of parameters. The parameters considered here are frequency, cold end temperature, valve coefficients of orifice valve and double inlet (DI) valve, system average pressure and initial phase angle of compressor outlet pressure. A higher sensitivity of the losses in a DIPTC system is observed with operating frequency and initial phase angle of compressor pressure within some specific range of these parameters. It was observed that for a DIPTC system there is a critical cold end temperature below which the losses are significant and also there exists a critical frequency below which there will practically be no cooling. It was found that the losses in the DIPTC are more sensitive to the orifice valve opening in comparison to the DI valve opening. A Grassmann diagram has also been constructed for the DIPTC. Copyright © 2009 John Wiley & Sons, Ltd.     

First and second law analysis of pulse tube refrigerator

The first and second law of thermodynamics was used to analyze the orifice type and the double-inlet type of pulse tube refrigerator (PTR). Detailed dynamic characteristics of the thermodynamics, flow and heat transfer processes in the PTR were revealed, including the dynamic pressure variations, transient gas temperature, mass flow rate in the PTR. The exergy loss method was used to analyze each component in the PTR for the first time, and the performance coefficients of all components of PTR have been obtained. It was found that the performance coefficient of the double-inlet PTR was 0.108, 9% higher than that of the orifice PTR. The analysis also showed that the exergy efficiency of the double-inlet PTR was 29.95%, significantly higher than that of the orifice PTR (25.04%). In addition, it was found that the exergy losses in the regenerator and orifice were substantially larger than in other components of the PTR system. The optimal design of these two key components is, therefore, essential for the further improvement of the PTR performance.     

Performance improvement of a pulse tube cryocooler with a single compressor through cascade utilization of cold energy

The high-frequency pulse tube cryocooler (HPTC) has been attracting increasing and widespread attention in the field of cryogenic technology because of its compact structure, low vibration, and reliable operation. The gas-coupled HPTC, driven by a single compressor, is currently the simplest and most compact structure. For HPTCs operating below 20 K, in order to obtain the mW cooling capacity, hundreds or even thousands of watts of electrical power are consumed, where radiation heat leakage accounts for a large proportion of their cooling capacity. In this paper, based on SAGE10, a HPTC heat radiation calculation model was first established to study the effects of radiation heat leakage on apparent performance parameters (such as temperature and cooling capacity), and internal parameters (such as enthalpy flow and gas distribution) of the gas-coupled HPTC. An active thermal insulation method of cascade utilization of the cold energy of the system was proposed for the gas-coupled HPTC. Numerical simulations indicate that the reduction of external radiation heat leakage cannot only directly increase the net cooling power, but also decrease the internal gross losses and increase the mass and acoustic power in the lower-temperature section, which further enhances the refrigeration performance. The numerical calculation results were verified by experiments, and the test results showed that the no-load temperature of the developed cryocooler prototype decreased from 15.1 K to 6.4 K, and the relative Carnot efficiency at 15.5 K increased from 0.029% to 0.996% when substituting the proposed active method for the traditional passive method with multi-layer thermal insulation materials.     

Numerical simulations of transport processes in a pulse tube cryocooler: Effects of taper angle

A numerical model is developed for the prediction of the performance and transport characteristics in an orifice pulse tube refrigerator (OPTR). The OPTR is studied for a two specific geometries. In the first geometry (A), only the taper angle of the pulse tube is changed. In the second geometry (B), the taper angle of the pulse tube is varied along with the diameter of the hot heat-exchanger. The taper angle of the pulse tube is shown to have significant effects on the secondary streaming patterns observed in the pulse tube. Tapering the pulse tube improved the performance of the OPTR only for Geometry-B. In this case, suppression of velocity streaming is achieved in the warm end of the pulse tube.     

Thermodynamic optimization of a coiled tube heat exchanger under constant wall heat flux condition

In this paper the second law analysis of thermodynamic irreversibilities in a coiled tube heat exchanger has been carried out for both laminar and turbulent flow conditions. The expression for the scaled non-dimensional entropy generation rate for such a system is derived in terms of four dimensionless parameters: Prandtl number, heat exchanger duty parameter, Dean number and coil to tube diameter ratio. It has been observed that for a particular value of Prandtl number, Dean number and duty parameter, there exists an optimum diameter ratio where the entropy generation rate is minimum. It is also found that with increase in Dean number or Reynolds number, the optimum value of the diameter ratio decreases for a particular value of Prandtl number and heat exchanger duty parameter.     

Three-dimensional numerical simulation of the basic pulse tube refrigerator

A three-dimensional physical and numerical model of the basic pulse tube refrigerator (PTR) was developed. The compressible and oscillating fluid flow and heat transfer phenomenon in the pulse tube were numerically investigated using a self-developed code. Some cross-section average parameter variations such as velocity, temperature and pressure wave during one cycle were revealed. The variations of velocity and temperature distributions in the pulse tube were also analyzed in detail for further understanding of the working process and refrigeration mechanism of PTRs. __________ Translated from Journal of Engineering Thermophysics, 2006, 27(5): 737–740 [译自: 工程热物理学报]     

CFD simulation of a Gifford–McMahon type pulse tube refrigerator

Pulse tube refrigerator has the advantages of long life and low vibration over the conventional cryocoolers, such as Gifford–McMahon (GM) and Stirling coolers because of the absence of moving parts in low temperature. This paper performs a two-dimensional computational fluid dynamic (CFD) simulation of a Gifford–McMahon type double inlet pulse tube refrigerator (DIPTR), operating under a variety of thermal boundary conditions. A commercial Computational Fluid Dynamics (CFD) software package Fluent 6.1 is used to model the oscillating flow inside a pulse tube refrigerator. Helium is used as working fluid for the entire simulation. The simulated DIPTR consists of a transfer line, an after cooler, a regenerator, a pulse tube, a pair of heat exchangers for cold and hot end, an orifice valve with connecting pipe, a double inlet valve with connecting pipe and a reservoir. The simulation represents fully coupled systems operating in steady-periodic mode. The externally imposed boundary condition is sinusoidal pressure inlet by user defined function at one end of the tube and constant temperature or heat flux boundaries at the external walls of the hot end and cold-end heat exchangers. The general results, such as the cool down behaviors of the system, phase relation between mass flow rate and pressure at pulse tube section and the temperature profile along the wall of the cooler are presented.The simulation shows the minimum decrease in temperature at cold-end heat exchanger for a particular combination of cryocooler assembly. The CFD simulation results are compared with available experimental data. Comparisons show that there is a reasonable agreement between CFD simulation and experimental results.     

湿热地区波纹翅片管式表冷器的运行性能和调节能力研究

表冷器作为空调系统中空气的热湿处理设备在湿热地区应用广泛。然而,随着户式中央空调的发展,它与中小型冷水机的匹配及运行优化仍缺少指南。建立了某9排管空气-水逆流式波纹翅片管式表冷器的传热除湿数学模型。模拟结果分析表明:室外气象参数的影响显著,气温越高且露点温度越高,则其供冷和除湿能力显著提高;在广州和杭州六月份平均气象条件下,调节表冷器的供水温度、供水流速或管外风速,其供冷能力可分别在名义供冷能力的32%~95%以及45%~120%内调节,除湿能力也可相应随之得到调节;入口水温愈低,则变水量或变风量对表冷器供冷及除湿能力的调节作用范围越广;风速愈大且水流速度愈高,则变水温的调节作用范围越广;入口水温越低、风速越大或水流速度越大,则联合调节风量水量、水温水量或水温风量对其供冷和除湿能力的调节作用范围也越广。     

Numerical simulation of flow field and temperature separation in a vortex tube

A numerical analysis of flow field and temperature separation in a uni-flow vortex tube type is described. Effects of the turbulence modeling (k–ε model and ASM), numerical scheme (hybrid, upwind and second-order upwind) and grid density on calculation of energy separation in the vortex tube are also conducted. It is found that the calculated results are in reasonably good agreement with the experimental data for both the static and total temperatures; the use of the ASM improves slightly the accuracy of the predictions than that the k–ε model. It is also observed that larger temperature gradients appear in the outer regions close to the tube wall for the static temperatures and the separation effect or the difference of the total temperature is high in the core region near the inlet nozzle. The maximum total temperature in the field is visible at the axis location of x/D_o between 0.5 and 1.0 for the ASM.     

Two-dimensional numerical simulation and performance analysis of tapered pulse tube refrigerator

Numerical simulation of two-dimensional viscous compressible oscillating flow was carried out for the uniform cross-section and tapered pulse tubes. Based on the numerical results, it was found that for the taper pulse tube refrigerator, there was an optimum taper angle, with which the performance of a cryogenic refrigerator can be greatly improved. However, on the other hand, the results also demonstrated that when the taper angle becomes much larger than this optimum value, the cooling performance becomes weaker than that of the circular tube. We discussed the effect of the tapered pulse tube on the performance of pulse tube refrigerator based on an evaluation of the secondary flow in the pulse tube. It was found that in comparison with the uniform cross-section pulse tube, the magnitude of the secondary flow in the tapered pulse tube decreases while its distribution becomes less uniform, which explains why the performance of the tapered pulse tube can be improved compared with the uniform cross-section pulse tube.     

Economic optimization of shell and tube heat exchanger based on constructal theory

In this paper, the new approach of constructal theory has been employed to design shell and tube heat exchangers. Constructal theory is a new method for optimal design in engineering applications. The purpose of this paper is optimization of shell and tube heat exchangers by reduction of total cost of the exchanger using the constructal theory. The total cost of the heat exchanger is the sum of operational costs and capital costs. The overall heat transfer coefficient of the shell and tube heat exchanger is increased by the use of constructal theory. Therefore, the capital cost required for making the heat transfer surface is reduced. Moreover, the operational energy costs involving pumping in order to overcome frictional pressure loss are minimized in this method. Genetic algorithm is used to optimize the objective function which is a mathematical model for the cost of the shell and tube heat exchanger and is based on constructal theory. The results of this research represent more than 50% reduction in costs of the heat exchanger.     

Experimental and theoretical studies of a two-stage pulse tube cryocooler operating down to 3 K

The development of a two-stage Pulse Tube Cryocooler (PTC) which produces a no-load temperature of ～3 K and delivers a refrigeration power of ～250 mW at 5 K is reported in this work. The system uses stainless steel meshes along with lead (Pb) granules and combinations of Pb, Er₃Ni and HoCu₂ in layered structures as the first and second stage regenerator materials respectively. With Helium as a working fluid, the pressure oscillations are generated using a 6 kW water-cooled Helium compressor along with an indigenous rotary valve. Different configurations of pulse tube systems have been experimentally studied, by both varying the dimensions of pulse tubes and regenerators as well as the second stage regenerator material composition. The pulse tube Cryocooler has been numerically analyzed by using both the isothermal model and the model based on solving the energy equations. The predicted refrigeration powers as well as the temperature profiles have been compared with the experimental results for specific pulse tube configurations.     

CFD-driven surrogate-based multi-objective shape optimization of an elbow type draft tube

Draft tube is the part of Francis turbines which is used to both discharge water and recover kinetic energy at the exit of the runner. A design optimization study of an elbow type draft tube based on the combined use of Computational Fluid Dynamics (CFD), design of experiments, surrogate models and multi-objective optimization is presented in this study. The geometric variables that specify the shape of the draft tube are chosen as input variables for surrogate models and the pressure recovery factor and the head loss are selected as output responses. It is determined that, pressure recovery factor, which is the main performance parameter, can be increased by 4.3%, and head loss can be reduced by %20 compared to the initial CFD aided design. Pressure recovery factor, is represented with a second order polynomial regression model in terms of the geometrical parameters based on the optimization results. The verification of the model is also provided by comparison with CFD results for different draft tubes other than that are used in the development of the model. The model is verified using 30 different design points and it can predict the pressure recovery factor with an error of less than 8%. This model allows the fast and correct design and optimization of elbow type draft tubes, without the need for further CFD simulations.     

Numerical simulation of horizontal tube bundle falling film flow pattern transformation

It is important to study the falling-film pattern of a horizontal tube bundle in order to set up a heat and mass transfer model accurately. The falling-film pattern of a horizontal tube bundle is simulated in this paper. The technique is based on computational flow dynamics (CFD) for the two-phase flow of gas and water. The experimental results were used to validate the mathematical model. It indicates that the simulation results accord with experimental data well. The simulated results show that the flow pattern varies with different flow rates. Under the different flow rates, it observes the droplet, droplet-columnar, columnar, columnar-sheet and sheet flow patterns. The critical value is 0.0125 kg/s between droplet and columnar, and the critical value is 0.02 kg/s between columnar and sheet.     

Numerical simulation of hydrothermal behavior in a concentric curved annular tube

This study performs a numerical investigation of the steady‐state fully developed laminar flow and forced convection heat transfer characteristics in a concentric curved annular tube with two different curvature angles, a 90°‐bend annular tube and a U‐bend annular tube. A wide range of aspect ratios (r* = 0.1, 0.25, 0.5, and 0.75) and three curvature ratios (δ_c = 0.1, 0.2, and 0.5) were adopted in this study. The governing equations consisting of continuity, momentum, and energy equations are solved by considering the outer wall to be insulated (adiabatic), and a constant temperature is applied at the inner wall by using the finite‐volume method (FVM) to investigate the hydrothermal performance for these two different bend angles.Features of axial velocity contours, temperature patterns, and secondary flow streamlines at different cross‐sectional locations along the angular coordinate of curved annulus are observed with a Dean number range of (De = 32‐632). Additionally, the circumferential friction factor and averaged Nusselt number are obtained along the concentric curved annulus flow direction. The numerical results indicate that the normalized average Nusselt number and Performance Evaluation Criteria (PEC) increase with increasing De and curvature ratio for both curvature angles of concentric curved annular tube. Moreover, the normalized average Nusselt number, normalized friction factor‐Reynolds number product, and PEC increase with decreasing the aspect ratio because the annular gap between the surfaces of the inner and outer tubes (the boundaries of annulus) increases with decreasing aspect ratio. The hydrothermal performance of the concentric curved annular tube is higher than that of the straight annular tube attributed to the formation of secondary flows (Dean's vortices) in a cross‐sectional direction and the impact of the inner tube wall boundary. The value of PEC for both curvature angles of the curved annular tube at aspect ratio = 0.1 and De = 632 is approximately two‐fold of the straight annular tube under the same conditions while at aspect ratio = 0.75, it increases by nearly 80%.     

波壁管几何尺寸对流动与传热特性的影响

基于数值模拟的方法,分析在低雷诺数下波壁管波形变化对流体流动与传热特性的影响,并分析了相同功耗下波壁管的综合传热性能。结果表明:波幅和波长变化对波壁管传热均有影响,强化效果与波幅成正比,与波长成反比;当功耗相同时,小波幅的波壁管有较好的综合换热效果,大波幅的波壁管强化传热以较大能量消耗作为代价;雷诺数大于2 000时,增大波长能达到较好的综合换热效果。     

Monte-Carlo simulation and performance optimization for the cathode microstructure in a solid oxide fuel cell

A 3D micro-scale model is developed to simulate the transport and electrochemical reaction in a composite cathode. This model takes into account the details of the specific cathode microstructure such as random pore structure, active TPB (three phase boundary) site distribution, particle size and composition and their interrelationship to the charge transfer and mass transport processes. Especially, the pore structure and mass diffusion were incorporated into this model. Influence of the microsturcture parameters on the performance was investigated by numerical simulations.