Numerical analysis on pressure drop and heat transfer performance of mesh regenerators used in cryocoolers

An anisotropic porous media model for mesh regenerator used in pulse tube refrigerator (PTR) is established. Formulas for permeability and Forchheimer coefficient are derived which include the effects of regenerator configuration and geometric parameters, oscillating flow, operating frequency, cryogenic temperature. Then, the fluid flow and heat transfer performances of mesh regenerator are numerically investigated under different mesh geometric parameters and material properties. The results indicate that the cooling power of the PTR increases with the increases of specific heat capacity and density of the regenerator mesh material, and decreases with the increases of penetration depth and thermal conductivity ratio (a). The cooling power at a = 0.1 is 0.5-2.0 W higher than that at a = 1. Optimizing the filling scale of different mesh configurations (such as 75% #200 twill and 25% #250 twill) and adopting multi segments regenerator with stainless steel meshes at the cold end can enhance the regenerator’s efficiency and achieve better heat transfer performance.     

Wave-shaping of pulse tube cryocooler components for improved performance

The method of wave-shaping acoustic resonators is applied to an inertance type cryogenic pulse tube refrigerator (IPTR) to improve its performance. A detailed time-dependent axisymmetric experimentally validated computational fluid dynamic (CFD) model of the PTR is used to predict its performance. The continuity, momentum and energy equations are solved for both the refrigerant gas (helium) and the porous media regions (the regenerator and the three heat-exchangers) in the PTR. An improved representation of heat transfer in the porous media is achieved by employing a thermal non-equilibrium model to couple the gas and solid (porous media) energy equations. The wave-shaped regenerator and pulse tube studied have cone geometries and the effects of different cone angles and the orientation (nozzle v/s diffuser mode) on the system performance are investigated. The resultant spatio-temporal pressure, temperature and velocity fields in the regenerator and pulse tube components are evaluated. The performance of these wave-shaped PTRs is compared to the performance of a non wave-shaped system with cylindrical components. Better cooling is predicted for the cryocooler using wave-shaped components oriented in the diffuser mode.     

Numerical analysis of an OPTR: Optimization for space applications

A numerical study is reported here for the investigation of the flow and heat transfer processes in a co-axial type single stage orifice type pulse tube refrigerator (OPTR). The OPTR is driven by a cyclically moving piston at one end of the system with helium as the working fluid. The regenerator and the various heat exchangers are modeled as porous media and a thermal non-equilibrium model is applied in these regions. The simulations reveal interesting steady-periodic flow patterns that develop in the pulse tube due to the fluctuations caused by the piston and the presence of the inertance tube. When the secondary flow patterns are well-developed, they help isolate the cold and hot ends of the pulse tube and create a thermal buffer zone at the center of the pulse tube, enhancing the performance of the OPTR.     

Investigation on the internal thermal link of pulse tube refrigerators

Within a pulse tube refrigerator (PTR) in coaxial configuration the pulse tube is located inside the regenerator matrix in axial direction. An internal thermal contact between these two main components of the coldfinger occurs. The experimental investigation of the direction and the quantity of transferred heat is in focus of this paper. Intermediate cooling of the regenerator by the corresponding part of its own pulse tube can improve the cooling performance of a PTR. Therefore, a well-adapted geometrical arrangement between the pulse tube and the regenerator is essential, considering the temperature distribution inside the coldfinger. We deduce design parameters to optimise the configuration of coaxial PTRs.     

Computational fluid dynamics simulations of an orifice type pulse tube refrigerator: Effects of operating frequency

A numerical study is reported here for the investigation of the fundamental flow and heat transfer processes found in an orifice type pulse tube refrigerator (OPTR). The OPTR is driven by a cyclically moving piston at one end of the system with helium as the working fluid. The regenerator and the various heat exchangers are modeled as porous media and a thermal non-equilibrium model is applied in these regions. The system is studied for different operating frequencies of the driver piston. The simulations reveal interesting steady-periodic flow patterns that develop in the pulse tube due to the fluctuations caused by the piston and the presence of the inertance tube. The predicted secondary-flow recirculation patterns in the pulse tube are found to affect the OPTR performance. When the secondary-flow patterns are well-developed, they help isolate the cold and hot ends of the pulse tube and create a thermal buffer zone at the center of the pulse tube, enhancing the performance of the OPTR.     

Analytical treatment of counterflow pulse-tube refrigerators

In our laboratory we work an a new type of pulse-tube refrigerator. A complete set of relations is derived for the operation of counterflow pulse-tube refrigerators. The input parameters depend on the working fluid, the geometries of the pulse tube and the counterflow heat exchanger, and the compressor characteristics. The calculated molar flow in the heat exchanger agree within 5% with the measured value. The calculated and experimental lowest temperature and the temperature difference between the hot and cold gas in the heat exchanger agree within 10%. This larger difference is caused by difference between the modelled and real heat exchanger.     

The experimental investigation of a pulse tube refrigerator with a ‘L’ type pulse tube and two orifice valves

In order to simplify the structure of the cold end of the pulse tube refrigerator (PTR) and have a better utilization of the cold energy of the system, a single stage four-valve pulse tube refrigerator (FVPTR) with a ‘L’ type pulse tube structure and two orifice valves at the hot end of pulse tube has been constructed. Verification experiments show that a two-orifice valve structure gives different adjustments to the gas flow rate of the hot end of the pulse tube than that of the one-orifice valve structure, a lowest temperature of 72 K was obtained at a frequency of 2.5 Hz under a system average pressure of 1.6 MPa with 200 mesh bronze screens as regenerator material, 20 mesh copper screens as stuffing material of heat exchanger. Due to the difficulty in manufacturing the thin ‘L’ type pulse tube, the wall thickness of the pulse tube in the experiment is relatively bigger than that of the ordinary pulse tube, which resulted in relatively big system loss and affected the minimum temperature of the system to a certain degree.     

A new tapered regenerator used for pulse tube refrigerator and its optimization

The results of numerical simulation and theoretical analysis of the local heat transfer coefficient and the average remaining gas mass with the length of a uniform cross-sectional regenerator are presented in this paper. It was found that there are some serious thermodynamic limitations in the uniform cross-sectional regenerator and thus the efficiency of the regenerator can not fully exert. In order to further reduce the loss of the regenerator and improve the heat transfer of the cold end, the authors bring forward a design principle: the variation trend of the cross-section of the regenerator will be consistent with the direction of the temperature gradient, and introduce two kinds of tapered regenerators including convergent and divergent in order to improve the performance of the pulse tube refrigerator. Two models were introduced with governing equations to simulate two kinds of pulse tube refrigerators with tapered regenerator. The simulation results showed that there exist an optimum cone angle for tapered regenerator. When the cone angle is close to a certain value, the pulse tube refrigerator with convergent type regenerator can improve the performance which means increasing the cooling power, decreasing the working power, and eliminating the DC-flow rate. But the divergent type regenerator deteriorates the performance. In order to further validate the feasibility of this structural design, based on the enthalpy flow theory, the mechanism of the improvement of the performance of a PTR with tapered regenerator is systemically analyzed.     

Three-dimensional analysis for liquid hydrogen in a cryogenic storage tank with heat pipe–pump system

This paper presents a study on fluid flow and heat transfer of liquid hydrogen in a zero boil-off cryogenic storage tank in a microgravity environment. The storage tank is equipped with an active cooling system consisting of a heat pipe and a pump–nozzle unit. The pump collects cryogen at its inlet and discharges it through its nozzle onto the evaporator section of the heat pipe in order to prevent the cryogen from boiling off due to the heat leaking through the tank wall from the surroundings. A three-dimensional (3-D) finite element model is employed in a set of numerical simulations to solve for velocity and temperature fields of liquid hydrogen in steady state. Complex structures of 3-D velocity and temperature distributions determined from the model are presented. Simulations with an axisymmetric model were also performed for comparison. Parametric study results from both models predict that as the speed of the cryogenic fluid discharged from the nozzle increases, the mean or bulk cryogenic fluid speed increases linearly and the maximum temperature within the cryogenic fluid decreases.     

20-50 K and 40-80 K pulse tube coolers: Two candidates for a low temperature cooling chain

Following its important cryogenics heritage for the European Space industry for both Ariane launcher and Orbital programs, Air Liquide - Advanced Technology Division (AL/DTA) is proposing different pulse tube cryocoolers all over the temperature range to answer the needs of earth observation and scientific missions.This paper presents recent performance improvement of the large heat lift 40-80 K pulse tube cooler (LPTC). Four units have been manufactured and tested. Three units are dedicated to lifetime testing in the framework of French Military Space Program (under CNES contract) and Meteosat Third Generation program (ESA contract). The batch performances are described and the product maturity is discussed in this paper.To lower the temperature range and to complete our cryogenic chain, we developed in partnership with CEA/INAC/SBT, a heat intercepted 20-50 K pulse tube cryocooler. This cooler has been developed in the framework of an ESA contract (ESA/ESTEC No 20497/0/NL/PA-20-50 K pulse tube cooler). A development phase has been performed to test and optimize different cold head architectures to reach the 300 mW@20 K specification. A no-load temperature of 12.5 K has been demonstrated on breadboard model. The outputs of the trade-off, the resulting design and the performances are described.In complement to the dilution cooler similar to the one developed for the PLANCK mission, those two pulse tube coolers are potential candidates for a very low temperature cooling chain. By optimizing the capabilities of the 20 K stage for low temperature operation (no-load in the range of 8 K) the coupling of the three independent stages becomes possible.     

Multi-dimensional flow effects in pulse tube refrigerators

Pulse tube cryocoolers are often modeled as one-dimensional flow fields. We examine the adequacy of this assumption in this study. Two entire inertance tube pulse tube refrigerator (ITPTR) systems operating under a variety of thermal boundary conditions are modeled using a computational fluid dynamics (CFD) code. Each simulated ITPTRs includes a compressor, an after cooler, a regenerator, a pulse tube, cold and hot heat exchangers, an inertance tube, and a reservoir, and the simulations represent fully coupled systems operating in steady-periodic mode. The objectives are to ascertain the suitability of CFD methods for ITPTRs, and examine the extent of multi-dimensional flow effects in various ITPTR components. The results confirm that CFD simulations are capable of elucidating complex periodic processes in ITPTRs. The results also show that one-dimensional modeling is appropriate only when all the components in the system have large length-to-diameter (L/D) ratios. Significant multi-dimensional flow effects occur at the vicinity of component-to-component junctions, and secondary-flow recirculation patterns develop when one or more components have relatively small L/D ratios. Parameters in need of experimental measurement are discussed.     

Parametric and internal study of the vortex tube using a CFD model

A computational fluid dynamics (CFD) model is used to investigate the energy separation mechanism and flow phenomena within a counter-flow vortex tube. A two-dimensional axi-symmetric CFD model has been developed that exhibits the general behavior expected from a vortex tube. The model results are compared to experimental data obtained from a laboratory vortex tube operated with room temperature compressed air. The CFD model is subsequently used to investigate the internal thermal-fluid processes that are responsible for the vortex tube's temperature separation behavior. The model shows that the vortex tube flow field can be divided into three regions that correspond to: flow that will eventually leave through the hot exit (hot flow region), flow that will eventually leave through the cold exit (cold flow region), and flow that is entrained within the device (re-circulating region). The underlying physical processes are studied by calculating the heat and work transfers through control surfaces defined by the streamlines that separate these regions. It was found that the energy separation exhibited by the vortex tube can be primarily explained by a work transfer caused by a torque produced by viscous shear acting on a rotating control surface that separates the cold flow region and the hot flow region. This work transfer is from the cold region to the hot region whereas the net heat transfer flows in the opposite direction and therefore tends to reduce the temperature separation effect. A parametric study of the effect of varying the diameter and length of the vortex tube is also presented.     

Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model

Nanofluids and helical tubes are among the best methods for heat transfer enhancement. In the present study, laminar, developing nanofluid flow in helical tube at constant wall temperature is investigated. The numerical simulation of Al₂O₃-water nanofluid with temperature dependent properties is performed using the two-phase mixture model by control volume method in order to study convective heat transfer and entropy generation. The numerical results is compared with three test cases including nanofluid forced convection in straight tube, velocity profile in curved tube and Nusselt number in helical tubes that good agreement for all cases is observed. Heat transfer coefficient in developing region inside a straight tube using mixture model shows a better prediction compared to the homogenous model. The effect of Reynolds number and nanoparticle volume fraction on flow and temperature fields, local and overall heat transfer coefficient, local entropy generation due to viscous dissipation and heat transfer, and the Bejan number is discussed in detail and compared with the base fluid. The results show that the nanofluid and the base fluid have almost the same axial velocity profile, but their temperature profile has significant difference in developing and fully developed region. Entropy generation ratio by nanofluid to the base fluid in each axial location along the coil length showed that the entropy generation is reduced by using nanofluid in at most length of the helical tube. Also, better heat transfer enhancement and entropy generation reduction can be achieved at low Reynolds number.     

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.     

CFD simulation and experimental validation of a GM type double inlet pulse tube refrigerator

Pulse tube refrigerator has the advantages of long life and low vibration over the conventional cryocoolers, such as GM and stirling coolers because of the absence of moving parts in low temperature. This paper performs a three-dimensional computational fluid dynamic (CFD) simulation of a GM type double inlet pulse tube refrigerator (DIPTR) vertically aligned, 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. The simulation represents fully coupled systems operating in steady-periodic mode. The externally imposed boundary conditions are 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 cold-end heat exchangers. The experimental method to evaluate the optimum parameters of DIPTR is difficult. On the other hand, developing a computer code for CFD analysis is equally complex. The objectives of the present investigations are to ascertain the suitability of CFD based commercial package, Fluent for study of energy and fluid flow in DIPTR and to validate the CFD simulation results with available experimental data. The general results, such as the cool down behaviours of the system, phase relation between mass flow rate and pressure at cold end, the temperature profile along the wall of the cooler and refrigeration load are presented for different boundary conditions of the system. The results confirm that CFD based Fluent simulations are capable of elucidating complex periodic processes in DIPTR. The results also show that there is an excellent agreement between CFD simulation results and experimental results.     

液氦温区双向进气型脉管制冷机的绝热模型

在考虑２０Ｋ以下温区氦流体热物性特点的基础上，本文建立了液氦温区脉管制冷机的经热模型，用以研究液氦温区双向进气型脉管制冷机的动态工作过程及其制冷机理，为开展液氦温区多级脉管制冷机的实验研究提供了理论依据。     

Cryogen-free cryostat for neutron scattering sample environment

Today all advanced neutron facilities maintain a fleet of Orange cryostats, or similar systems, to provide low temperature sample environment in neutron scattering experiments. However recent liquid helium cost increases, caused by global helium supply problems, have raised significant concern about the affordability of such cryostats. The ISIS facility is carrying out a development programme intended to substitute conventional cryostats with cryogen-free systems preferably based on pulse tube refrigerators. The main aim of the development is to create a cryogen-free system as a potential replacement for the conventional Orange cryostat. This paper describes the design and test results of a cryogen-free cryostat, based on a pulse tube refrigerator, with 50 mm diameter top-loading sample facilities for neutron scattering experiments. The sample temperature range is 1.45–300 K in the continuous flow regime. The cryostat may also be used with ultra-low temperature dilution refrigerator inserts.     

液氮温区同轴脉冲管制冷机的实验研究

脉冲管制冷机冷头朝上布置可以使制冷机与超导器件的耦合更方便 ,但对G -M型脉冲管制冷机 ,重力会对这种布置方式产生不利影响。对双向进气型脉冲管制冷机 ,直流和耦合传热会共同影响脉冲管制冷机的性能。介绍了液氮温区G -M型同轴脉冲管制冷机的实验结果 ,主要研究了蓄冷器温度分布和重力对脉冲管制冷机性能的影响     

开架式气化器竖直圆管内超临界氮换热实验研究

目前国内外对液化天然气(LNG)接收站的开架式气化器中超临界天然气的流动换热实验研究非常少,本文为了研究开架式气化器中竖直管内超临界流体的流动换热特性,搭建了竖直单管超临界流体换热实验平台。以液氮代替液化天然气,研究了氮入口压力、水温和水流量等不同参数对换热的影响。结果表明:在拟临界温度以下,表面传热系数随着压力的增大逐渐减小,但拟临界温度以后,这种趋势相反;当水流量足够大时,氮出口温度取决于管外水温而不是水侧流量。最后,基于实验数据拟合出了适用于竖直圆管内超临界低温流体流动换热的半经验关联式,关联式预测值和实验值的平均绝对偏差为8.42％,可以准确预测竖直加热管中超临界氮的表面传热系数。     

Transferts thermiques en écoulements oscillants laminaires incompressibles

Phenomena concerning the temperature variations and the heat transfer are studied in the specific case of oscillating flow with null mean velocity circulating between two infinite walls. A 1D model is established and the interesting scale parameters are deduced from theoretical equations. The particular case of an oscillating laminar flow for incompressible fluid is detailed in order to illustrate and to discuss the effects of thermal interactions between the fluid and walls. Influence of wall length comparatively to the fluid displacement is studied. Conclusions for designing thermal heat exchangers of Stirling engines or PTR are proposed.