Regenerator Matrix Research Articles

Numerical study on heat transfer characteristics of regenerator based on a simplified geometry

The heat transfer characteristics of regenerator in regenerative coolers such as pulse tube and Stirling coolers is important. Various methodologies of characterizing the Nusselt number between the regenerator matrix and working fluid have been established and applied. However, most of the existing formulas are based on the study of steady flow or oscillating flow with low pressure ratios at above ambient temperature. In this paper, a tube model with finite wall thickness was constructed to numerically simulate simplified #400 SS mesh and packed HoCu2 sphere, with the aim of investigating the Nusselt number in regenerators under various flow conditions, including different Valensi numbers and temperature ranges. The results provide more evidence to support that within the operating conditions, including Valensi numbers and pressure ratios typically used in coolers, the Nusselt number of oscillating flow and steady flow are similar. Additionally, a heat transfer deterioration effect is observed below 40 K, which is related to the heat capacity ratio between the solid matrix and working fluid. Based on these findings, the study emphasizes the importance of further investigating the heat transfer characteristics of oscillating flow at low temperatures.

Manifestation of improvement in regenerator performance of a low and high-frequency pulse tube cryocooler using layered pattern

Pulse tube cryocoolers (PTCs) have wide applications such as space and military equipment, cooling superconducting coils, magnetic resonance imaging, cryopumps, etc. In a cryocooler, the regenerator plays a vital role to achieve low temperature by periodically storing and discharging refrigeration produced at the pulse tube cold end. This paper presents the optimization of the regenerator as a layered pattern using open-source software, REGEN 3.3 wherein multiple sizes of Stainless Steel (SS) mesh are used as regenerator material. A rigorous parametric study is conducted having uniform regenerator mesh size throughout the regenerator space as well as with layered configuration of different sizes of SS wire mesh as regenerator material. Parameters such as operating frequency, mass flow rate, and phase angle are also varied to analyze the Coefficient of Performance (COP) of the PTC. To optimize the multi-layer regenerator, an algorithm is provided, and based on the outcome of the optimization process, it is recommended to use the multi-layer configuration of SS wire mesh that provided significantly better performance as compared to the use of a uniform regenerator matrix material throughout the regenerator space. Additionally, it is also found through this study that there exists an optimum multi-layer combination of the regenerator for any configuration of the PTC that can be identified using the algorithmic procedure followed in this paper. The optimized layer patterns for the PTC are also reported in the paper. By the use of a 2-layer regenerator, COP increased by up to 10% over the single material regenerator. Whereas with a multi-layer regenerator, COP has increased by 9.86% to 5.21%. The algorithmic procedure followed in this paper can be conveniently used to optimize the layered pattern of the regenerator of a low-frequency as well as high-frequency PTC.

Numerical investigation of alpha Stirling engine performance based on ideal and actual adiabatic analysis

This article discusses in detail the adiabatic models investigations of alpha Stirling engine with study the influence of performance factors; adiabatic analysis is a crucially effective method because it is close to the real and practical engines when compared to isothermal analysis. The numerical model was created using MATLAB software, an extremely useful tool for solving equations. The study includes two adiabatic analysis models: the ideal model, which considers heat transfer is the duty of the heater and cooler when the regenerator is ideal, and the simple model, which considers the loss and the transfer of heat between the regenerator matrix and the working fluid.

Design and multi-objective optimization of a new annular constructal bifurcation Stirling regenerator using response surface methodology

The irreversible losses such as the flow loss and axial heat conduction loss in traditional porous regenerators have limited the specific power and thermal efficiency of Stirling engines to a great degree. Thereby, the objective of this paper is to design and optimize a novel annular constructal bifurcation regenerator for diminishing the flow and axial heat conduction losses in the regenerator based on constructal concept and response surface methodology. First, the bifurcation type structure units with an inclined angle to the flow direction and the layered approach were applied to construct the regenerator matrix. Thereafter, the numerical simulations were employed to investigate the gas flow and heat transfer characteristics of the constructal bifurcation regenerator. Based on the numerical data, the quadratic polynomial regression models between the geometric parameters and the regenerator performance were established using response surface methodology, and the specific effects of the geometric dimensions were analyzed via 2-D and 3-D response surface plots. Subsequently, a multi-objective optimization was conducted to minimize the flow resistance and maximize the heat transfer rate by genetic algorithm. A most eclectic solution with the global friction factor f = 3.478 and the number of heat transfer units NTU = 1.135 was selected from the optimal Pareto front. Finally, the overall performance of the constructal bifurcation regenerator was compared with that of the porous regenerator and the parallel geometry regenerator. The results indicate that a low flow resistance, low axial heat conduction, and high thermal performance are obtained by the constructal bifurcation regenerator. Therefore, it is reasonable to conclude that the annular constructal bifurcation regenerator achieves a high comprehensive performance, with the potential to improve the performance of Stirling engines. The findings of this paper may provide some new ideas and guidelines for the design and optimization of the regenerator structures.

The effect of internal leakage of air streams on effectiveness of the fixed-bed regenerator for fast switching cycle of its operation: mathematical model and numerical simulations

The paper describes an original mathematical model of heat and mass transfer for a fixed bed regenerator used to determine the effect of internal airflow leakage on heat exchanger efficiency. First, the build and operating principles of a fixed-bed heat exchanger were discussed. The presence of internal leakage was shown along with a proposed solution for its elimination. Then, a mathematical model based on a modified ε-NTU method for numerical simulation and analysis of coupled heat and mass transfer in a fixed-bed heat exchanger was presented. The model was supplemented with an additional detailed submodel designed to determine frost surface temperature and frost growth analysis. Initial numerical simulations of the operation of the model were performed for low outdoor air temperature conditions. Different zones of heat and mass transfer within the regenerator matrix were distinguished. The presence of accumulated frost area and its influence on the course of heat and mass transfer processes was revealed. In addition, the presence of a relative humidity limit curve associated with a mass balance deficiency conditioning the occurrence of frost accumulation was established.

Comparative Study on Performance of Regenerator for Miniature Pulse Tube Cryocooler with Metal Matrix Materials at Ultra High Frequencies

A Miniature Pulse Tube Cryocooler (MPTC) is the first selection for the cooling of IR sensors, infrared detectors, etc. in space technology. The regenerator is one of the key components to operate an MPTC at high efficiency. The objective of this study is to explore the possibilities of the different matrices as regenerator filler materials for MPTC operating at ultra-high frequencies. REGEN 3.3 is one of the best software available for the design and optimization of cryocooler regenerators. We have used REGEN 3.3 for numerical simulations of the three different regenerator matrix materials viz. stainless steel wire mesh screen (SS 635#), brass wire mesh screen (500#) and copper wire mesh screen (500#) at the hot end and cold end temperatures of 300[Formula: see text]K and 80[Formula: see text]K for COP, cooling power, total power losses and pressure losses, at an ultra-high frequency of 100[Formula: see text]Hz and 200[Formula: see text]Hz. The simulation results depict that the regenerator using stainless steel mesh screen shows better results than that of the brass mesh screen and copper mesh screen at 100[Formula: see text]Hz. However, the performance of brass mesh screen and copper mesh screen performs better than the stainless steel at 200[Formula: see text]Hz. Therefore, the proposed matrix materials can be used as regenerator materials for the MPTC at ultra-high frequencies with better performances.

A Class of Reduced-Order Regenerator Models

We present a novel class of reduced-order regenerator models that is based on Endoreversible Thermodynamics. The models rest upon the idea of an internally reversible (perfect) regenerator, even though they are not limited to the reversible description. In these models, the temperatures of the working gas that alternately streams out on the regenerator’s hot and cold sides are defined as functions of the state of the regenerator matrix. The matrix is assumed to feature a linear spatial temperature distribution. Thus, the matrix has only two degrees of freedom that can, for example, be identified with its energy and entropy content. The dynamics of the regenerator is correspondingly expressed in terms of balance equations for energy and entropy. Internal irreversibilities of the regenerator can be accounted for by introducing source terms to the entropy balance equation. Compared to continuum or nodal regenerator models, the number of degrees of freedom and numerical effort are reduced considerably. As will be shown, instead of the obvious choice of variables energy and entropy, if convenient, a different pair of variables can be used to specify the state of the regenerator matrix and formulate the regenerator’s dynamics. In total, we will discuss three variants of this endoreversible regenerator model, which we will refer to as ES, EE, and EEn-regenerator models.

Investigation on hydrodynamic characteristics of a Stirling regenerator matrix using porous media approach: a CFD study

In this study, hydrodynamic characteristics of a Stirling regenerator matrix are predicted by porous medium based modeling. A regenerator is designed to be used in the beta type Stirling engine. CFD analysis of the designed regenerator is performed by the ANSYS Fluent software with porous media model. The flow properties in porous media are generally approximated by Forchheimer or Ergun flow regime. The equation of the Forchheimer flow model consists of two-term: viscous loss and the inertial loss. The viscous resistance and inertial resistance factors of the porous medium to be used in CFD analysis is determined from published experimental results for a regenerator made by stainless steel with the porosity of 70 %. The CFD simulation are validated by comparing the calculated the velocity distributions at the exit of the regenerator with results of previously published paper. By using both resistance factors, pressure drops, and friction factors of the regenerator matrix are calculated via CFD analysis. The friction results are interpolated to generate a correlation equation that can be able to calculate the pressure drops in the flow direction of the regenerator and to use in future numerical simulations.

Study of oscillating flows through a novel constructal bifurcation Stirling regenerator

High flow resistance in conventional porous regenerators has been an important factor for limiting the overall performance of Stirling engines. Herein, a novel constructal bifurcation regenerator based on constructal concept was developed to reduce the flow resistance in the Stirling regenerator. First, the pressure drop and transient conjugate heat transfer characteristics of oscillating flows through the constructal bifurcation regenerator with various geometrical parameters were investigated by the CFD approach. The results showed that the fluid flow and heat transfer between the acceleration and deceleration phases, as well as the discharge and suction phases, were varied significantly. These differences should be resulted from the local acceleration effect, the formation of eddies in the acceleration phase, and different windward surfaces generated by the regenerator matrix to the fluid in the discharge and suction phases. Additionally, the flow characteristics between the oscillating and steady flows were compared and the local acceleration effect was proven to be the main cause of the difference between them. Then the three-parameters correlation equations of friction factor and Nusselt number for each structure and four master correlation equations with geometrical parameter dependence were built to predict the regenerator performance. Thereafter, the constructal bifurcation regenerators were converted to equivalent porous media, and thus the main porous parameters were obtained for the full Stirling engine simulation in the next studies. Finally, the friction factor and Nusselt number of the constructal bifurcation regenerator were compared with those of other commonly used regenerators. It showed that the constructal bifurcation regenerator had a low flow resistance and moderate heat transfer, thus obtaining a high comprehensive performance. The superior comprehensive performance of the regenerator makes it possible to improve the performance of Stirling engines.

Numerical and experimental investigation on the effect of regenerator mesh size on performance of the traveling wave thermoacoustic-stirling heat engine

Traveling wave thermoacoustic-Stirling heat engine is a unique device that is used to convert heat energy to acoustic work. In this article, the thermoacoustic engine is modeled, manufactured and tested. The cyclic analysis is used to carry out the numerical analysis based on the Stirling cycle of the engine. This analysis has considered for study the physical property and characteristics of the regenerator matrix. The traveling acoustic wave produced from the prototype is measured using an audio-speaker as a linear alternator for extracting electrical power from acoustic power. The size and geometry of the regenerator mesh is defines the thermal penetration depth, pressure drop due to it, dead volume across the matrix and acoustic power produced. Hence, there is a need to optimize the mesh size for a given mesh material to maximize the power generated from the engine. The engine has tested with five combinations of mesh sizes. The results of the numerical analysis has shown that 50.1 W power is produced and the tested engine has developed 44.9 W electric-power with the thermal efficiency of 8.3% respectively for 304 wire mesh of SS having mesh size of 60 strands/inch. The results obtained from the numerical analysis and the experiments performed are presented in this paper.

CFD study of heat transfer in Stirling engine regenerator

A three dimensional rhombic-drive beta-type Stirling engine is computationally studied with the utilization of ANSYS Fluent software. Research is mainly focused on the characteristics of heat transfer between the working fluid and the regenerator matrix. The regenerator is divided in several sections. The variation of gas and matrix temperature, as well as heat transfer during one cycle of the engine are presented and discussed. The fluctuation of fluid temperature is higher than that of the matrix, while fluid and matrix temperatures in each section are almost equal at the respective instances of flow reversal. Moreover, Nusselt number increases with Reynolds number by a linear trend. The derived correlation for Nusselt number is representative of the total engine cycle.Working gas and metal matrix temperature profile is linear in the biggest part of the regenerator, while at the regenerator ends it is approximated by a 2nd order polynomial equation. The spatial and temporal variation of temperature, as well as the heat transferred between gas and matrix is well approximated by derived equations that incorporate time and length as independent variables and can calculate the value of the studied quantities at a given time instance and a location in the regenerator. These findings can be used as input in a simple analytical model for the specific engine and improve the model outcomes.

A zero-dimensional, real gas model of an [formula omitted] Stirling engine

In the paper the authors present a zero-dimensional model of an alpha type Stirling engine and special consideration is paid to the problems of the evaluation of internal heat transfer between the heat exchange surfaces and the working fluid. Furthermore, a thermodynamic model of the engine, developed by the authors is shown. The model can be classified as zero-dimensional. Energy and mass conservation equations are written in a differential form, and solved for finite time steps for control volumes, that is the expansion cylinder, the compression cylinder, the regenerator, the regenerator matrix and the engine as a whole, which allows to transform the differential equations into a solvable system of algebraic equations. Unlike most models shown in literature, the one created by the authors evaluates the gas properties based on a real gas model. The impl ementation of a real gas model further helps to evaluate parameters such as viscosity and thermal conductivity of the gas, which is necessary for calculating the heat transfer coefficients. Those are calculated for each volume from known correlations, for a given moment in time. That is, the gas parameters needed are not evaluated as an average for the stroke, rather, they are calculated from instantaneous gas parameters and implemented as variables in the energy equations. The engine working fluid is atmospheric air. The influence of different heat transfer models on the predicted engine performance is shown in the form of engine characteristics for different models, based on variables such as pressure, and rotational. It can be shown, that further research into in-cylinder heat transfer is necessary, as the established models, when implemented into the Stirling engine, predict starkly different engine performance. Furthermore, non-physical results based on those models are shown.

A Computational Fluid Dynamics analysis of the influence of the regenerator on the performance of the cold Stirling engine at different working conditions

The paper presents a Computational Fluid Dynamics (CFD) model of the cold alpha-type Stirling engine. The developed mathematical model comprises of Unsteady Reynolds Averaged Navier-Stokes (URANS) set of equations, i.e. continuity, momentum and energy equations. Moreover, the developed mathematical model comprises a non-equilibrium description of the regenerator, by the introduction of the energy conservation equation for the regenerator matrix. It was implemented in the framework of commercial CFD software ANSYS Fluent. The work presents an in-depth analysis of the influence of the numerical mesh and applied turbulence model on the obtained results. The model was used to analyse the influence of the regenerator on the performance of the cold Stirling engine at different operating conditions. It appeared that on an average application of the regenerator increased the engine specific work by 10 J/kg and this increase is significantly higher at a high rotational speed of the engine. At the same time, the engine efficiency averagely was increased by 10 percent points and again this increase was significantly higher at higher rotational speeds of the engine. Especially, the influence of the heat source and sink temperatures on the engine operation were analysed. It appears that the lower are temperatures of a heat source and sink the more pronounced is the presence of the regenerator in the engine. Finally, the influence of the elementary parameters: particle diameter and porosity of the solid matrix which constitute the regenerator filling was investigated. It was shown that for the analysed engine the optimal value of the regenerator packing porosity equals about 0.72 it results in the specific area of the regenerator equal around 1675 m2/m3. Obtained results can be used to analyse the possibility of application of Stirling engines to recover low-temperature exergy of regasified Liquified Natural Gas (LNG), which for small regasification units can be alternative for commonly utilised Ambient Air Vaporizers (AAV) and it aside for regasification of LNG it could produce electric energy.

Development and Experimental Investigations on Two Stage GM Type Pulse Tube Refrigerator for 20 K Applications

Because of the absence of any moving components at the cold region, low vibration and high reliability, two stage GM type pulse tube refrigerator (PTR) is nowadays preferred compared to conventional GM refrigerator for cooling of superconducting magnets, SQUIDs, and cryopumping applications. The second stage regenerative material plays an important role in achieving low temperature below 20 K. Leads balls with 0.2 mm to 0.4 mm average diameter was selected as second stage regenerator matrix material while 200 mesh of SS 304 material was filled in the first stage. A two stage GM type PTR was developed. A rotary valve was fabricated and the valve timing effects on cooling performance of PTR were also studied. The valve timings were varied by the different width of rotor slit forming the flow area with stator ports. The lowest no-load temperature of 18.52 K and cooling capacity of 7 W at 29.58 K were obtained with an optimum frequency of 1.6 Hz, charging pressure of 16.5 bar.

Design and development of porous regenerator for Stirling cryocooler using additive manufacturing

The performance of the Stirling cryocoolers essentially depends on the performance of the regenerator. The regenerator used in Stirling cycles has, essentially, having a high surface area and heat capacity leading to large heat transfers. Packed Metal wool, packed wire Mesh screen, randomly packed sphere, porous metal structure are some of the common types of regenerator matrix materials. Wire mesh based regenerators matrix material are common as it provides high heat transfer area with lower entropy generation rate. The paper study in detail the design and structural parameters of mesh type regenerators of Stirling cryocoolers. The work also involves the design, development and attempt to fabricate a prototype porous type Stirling Cryocooler regenerator with a porosity range of 69–71% using Direct Metal Laser Sintering (DMLS) techniques of additive manufacturing, which will enable to use it as a retrofit regenerator to the existing Stirling cycle based liquid nitrogen plants.

Numerical modeling and optimization of beta-type Stirling engine

Numerical modelling can significantly contribute to the performance enhancement and technological advancement of Stirling engines. In this paper, a practically feasible thermodynamic model was developed for beta type of Stirling engines with rhombic-drive mechanism. Quasi-steady flow approach was adopted to analyze the heat transfer and flow friction effects of the heater, cooler, and regenerator on the performance of engine. The numerical model predicts the output power and thermal efficiency while considering the pressure drop in heat exchangers and numerous power and thermal losses. A parametric study is utilized to investigate the impact of operating and geometric parameters on the power output and efficiency of the Stirling engine. A combination of optimized temperature ratio, swept volume, regenerator matrix porosity, phase angle, pressure and engine frequency are assessed. The optimized model is then compared and validated against the experimental data obtained from the General Motor’s prototype of GPU-3 Stirling engine. Substantial improvement on the performance of the engine is achieved by optimizing the operating and geometric parameters of the engine.

Study of a 72 Hz high-capacity pulse tube cryocooler for space applications

Most infrared detectors work at low temperature, which enhances their detection sensitivity and visual field. Nowadays, the cryocoolers commonly used in space detectors are Stirling and pulse tube cryocoolers (PTCs). Compared with the Stirling cryocoolers, PTCs have no moving parts in the cold finger, resulting in low vibration and long lifetimes, and after decades of development, some PTCs already have comparable efficiencies to Stirling models. Thus, PTCs have been considered as ideal substitutes for Stirling cryocoolers in the future. In recent years, with the rapid progress of aerospace applications, the structure and the function of infrared detectors have become more complicated, requiring a higher cooling capacity. However, increasing cooling power always increases of the PTC’s weight, whereas many special aerospace applications have strict size and weight restrictions. As a result, miniaturization of high-capacity PTCs is required urgently in space applications. According to the Radebaugh’s research, increasing the operation frequency of PTCs can be an efficient way to minimize their size and mass because a high operating frequency can increase the energy density. Thus, many researchers and institutions at home and abroad have focused on the study of miniaturized PTCs, but most of the work is carried out on the PTCs used in space with cooling capacities under 5 W. Although some studies have been conducted on high-capacity miniature PTCs in China, none are designed for space applications. Thus, there is an urgent demand for miniaturized PTCs with cooling power above 10 W at 80 K. To minimize the sizes and weights of PTCs, the influences of the length of the regenerators, the charging pressure, and the regenerator matrix upon the operating frequency are presented. The results show that decreasing the volume of the regenerator, increasing the charge pressure, and decreasing the hydraulic diameter of the matrix are beneficial for promoting PTC efficiency with high operating frequency. On the basis of this optimization, 35-mm and 45-mm-length regenerators are designed and manufactured. Some systematic experiments are carried out using the newly designed PTCs. The experimental results also demonstrate that the length of the regenerator, charge pressure, and hydraulic diameter of the matrix significantly impact the efficiency of PTCs with high operating frequencies. Finally, a 72-Hz high-capacity coaxial-pulse-tube cryocooler is obtained with a cooling capacity of 12 W at 80 K and an input electrical power of 250 W. It achieves around 13.2% of the Carnot efficiency at 80 K, which is high compared with the same kind of PTCs. Benefiting from our mature techniques in space-PTC design, this PTC is easy to transform into an engineering model with little difference in efficiency. The success of the design of a 72-Hz PTC cold finger solves the critical problem of ministration and can provide some theoretical and experimental guidance for the design of miniaturized PTCs for space applications.

Material screening metrics and optimal performance of an active magnetic regenerator

A variety of metrics to rank the magnetocaloric materials can be found in the literature, but a quantitative assessment showing their efficacy has not been reported. A numerical model of an active magnetic regenerator cycle is used to assess the predictive ability of a set of material metrics. The performance of eight cases of known magnetocaloric material (including first order MnFeP1-xAsx and second order materials Gd, GdDy, Tb), and 15 cases of hypothetical materials are considered. Using a fixed regenerator matrix geometry, magnetic field, and flow waveforms, the maximum exergetic cooling power of each material is identified. Several material screening metrics such as relative cooling power (RCP) are tested and a linear correlation is found between maximum RCP and the maximum exergetic cooling power. The sensitivity of performance to variations in the hot side and cold side temperatures from the conditions giving maximum exergetic power are determined.

Experimental research on a 12.1 K gas-coupled two-stage high frequency pulse tube cryocooler

High frequency pulse tube cryocoolers (HFPTC) have been widely used in many fields like physics experimental research and aerospace, for no moving part in cold region, low vibration and long life. A gas-coupled two-stage high frequency pulse tube cryocooler with single compressor is introduced in this paper. In the first stage of the cryocooler, double-inlet and multi-bypass has been adopted as phase shifters. To get a better performance in phase shifting the reservoir and the inertance tube of the second stage has been located on the cold head of the first stage. With SS mesh screen as the regenerator of both stage, no-load temperature of 13.5K has been achieved. To improve the heat capacity of the regenerator of the second stage magnetic material Er3Ni has been employed in the second stage as regenerator matrix. With the charge pressure of 1.8MPa, input power of 260W and operating frequency of 23.5 Hz, the no-load temperature of 12.1K has been achieved.

Enhanced thermodynamic modelling of a gamma-type Stirling engine

Modelling can substantially contribute to the development of Stirling engines technology and help understanding the fundamental processes of the real cycle for further performance improvement. In the present work, an enhanced thermodynamic model for Gamma-type Stirling engine simulation was developed based on the reconfiguration of non-ideal adiabatic analysis. The developed model was validated against experimental measurements on Stirling engine prototype (ST05 CNC), available at University of Birmingham. Good agreement was found between the model and experiment in predicting the indicated power, shaft power and thermal efficiency at different operating conditions. A parametric study was carried out to investigate the effect of phase angle, gas type, regenerator matrix type and dead volume on engine performance. The feasibility of utilizing the stored cold energy of LN2 to maximize the shaft power was also presented. Results showed that shaft power can be significantly enhanced by 49% for helium and 35% for nitrogen when cooling temperature is lowered to −50°C while heating temperature remains constant at 650°C.