Modeling and effect of leakages on heat transfer performance of fixed matrix regenerators

The following undesired leakages are inherent in operation of fixed matrix regenerators: gas pressure leakages due to pressure difference such as leakages through the valves and through cracks in regenerator housing for very high temperature heat recovery, and carryover leakages from the hot gas to cold gas and vice versa. The objective of this paper is to present a methodology for evaluation of the leakages and to determine quantitatively the detrimental influence of pressure leakages on the regenerator heat transfer performance. In this respect, a drop (reduction) in actual regenerator heat transfer effectiveness due to various leakages is presented in the paper. The results clearly suggest that a drop in the effectiveness due to leakages can be significant and depends on the category of leakages. The flow leakages due to the cracks in the regenerator housing have the most impact on reducing the regenerator performance.     

Performance analysis of a closed regenerated Brayton heat pump with internal irreversibilities

This paper analyses the performance of a real heat pump plant via methods of entropy generation minimization or finite‐time thermodynamics. The analytical relations between heating load and pressure ratio, and between coefficient of performance (COP) and pressure ratio of real closed regenerated Brayton heat pump cycles coupled to constant‐ and variable‐temperature heat reservoirs are derived. In the analysis, the irreversibilities include heat transfer‐irreversible losses in the hot‐ and cold‐side heat exchangers and the regenerator, the non‐isentropic expansion and compression losses in the compressor and expander, and the pressure drop loss in the pipe and system. The optimal performance characteristics of the cycle may be obtained by optimizing the distribution of heat conductances or heat transfer surface areas among the two heat exchangers and the regenerator, and the matching between working fluid and the heat reservoirs. The influence of the effectiveness of regenerator, the effectiveness of hot‐ and cold‐side heat exchangers, the efficiencies of the expander and compressor, the pressure recovery coefficient and the temperature of the heat reservoirs on the heating load and COP of the cycle are illustrated by numerical examples. Published in 1999 by John Wiley & Sons, Ltd.     

Empirical estimation of regenerator efficiency for a low temperature differential Stirling engine

An experimental method of regenerator evaluation is proposed in this paper. The configuration of the experimental equipment used in the method is similar to that of an alpha-configuration Stirling engine with a phase angle of 180°. The temperature of the hot side heat exchanger is controlled by an electric heater, and the heat sink was room air. An air conditioner controlled the temperature of the room air. The temperature and pressure of the working fluid were measured during the piston motion. A #18 stainless steel mesh was used as a regenerator matrix for a low temperature differential Stirling engine (LTDSE). The regenerator efficiency can be calculated based on the measurement results. The product of the swept volume, the density of the working fluid, the specific heat and the difference in the working fluid temperatures between the hot side and the cold side is greater than the amount of the internal energy fluctuation. The reason for this is assumed to be the temperature fluctuation in the region between the two heat exchangers. The walls of the region are made of acrylic resin. The amount of the temperature fluctuation in the region is assumed to be uniform. The regenerator efficiency is calculated as a function of the temperature fluctuation in the region. The evaluation method does not require a fast-response thermocouple. The prediction of the regenerator efficiency is possible basted on some experimental results of same matrix. Polyurethane foam and #18 stainless steel mesh, layered parallel to the stream line of the working fluid, were each tested. These materials can realize a non-rectangular regenerator without the generation of waste. Non-rectangular regenerator includes regenerator that can be installed into narrow gaps. The regenerator efficiency of the stainless steel mesh layered parallel to the stream line of the working fluid was significantly less in comparison to that of the normal mesh layers. In the polyurethane foam case, a pressure loss was observed.     

Heat exchange between two coupled fixed beds by fluid flow

Heat exchange by forced fluid flow between two coupled fixed beds containing solids can be used to recover heat from hot products to cool input in many industrial processes. The heat exchange between the fixed beds is studied. Analytical solutions for the transient fluid and solid temperature distributions and heat recovery effectiveness are derived. The intra-particle transient temperature distributions are accounted for in the more accurate analysis and the results are compared to lumped analysis. It is shown that the heat recovery effectiveness reaches maximum at certain optimum time instant at which the fluid circulation should be stopped. Damping of cyclic oscillations in fluid temperature or concentration is considered and analytical solution for the damper is presented.     

逆流开式发生器内部的热、质传递规律

针对以太阳能加热的空气为携热介质，以LiBr溶液为工作介质的填料塔型开式发生器，建立热质传递数学模型。对2种系统结构形式进行比较，并分别研究太阳能集热板温度、液气比、环境相对湿度以及填料层高度对溶液再生的影响，以揭示此类发生器内热、质传递的规律，为产品开发、设计提供理论帮助。     

Multi-objective optimization of rotary regenerator using genetic algorithm

The rotary regenerator (heat wheel) is an important heat recovery equipment, which rotates between two cold and hot streams. The pressure drop and effectiveness of rotary regenerator are important parameters in optimal design of this equipment for industrial applications. For optimal design of such a system, it was thermally modeled using -NTU method to estimate its pressure drop and effectiveness. Frontal area, ratio of hot to cold frontal heat transfer area, matrix thickness, matrix rotational speed, matrix rod diameter and porosity were considered as design parameters. Then fast and elitist non-dominated sorting genetic algorithm (NSGA-II) method was applied to find the optimum values of design parameters. In the presented optimal design approach, the effectiveness and the total pressure drop are two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The sensitivity analysis of change in optimum effectiveness and pressure drop with change in design parameters of the regenerator was also performed and the results are reported.     

Nonequilibrium Gas Flow and Heat Transfer in a Heated Square Microcavity

The flow of a rarefied gas in a square enclosure with one wall at high temperature and the other three walls at the same low temperature is investigated. The flow, characterized by the reference Knudsen number and ratio of the cold over the hot temperatures, is simulated both deterministically, using the nonlinear Shakhov kinetic model, and stochastically, using the DSMC method. Excellent agreement between the two approaches is obtained. It is found that along the side walls the gas velocity, depending on the flow parameters, may be either from cold to hot or from hot to cold regions. Furthermore, it is confirmed that the average heat flux departing from the hot plate exhibits a nonmonotonic behavior with regard to the temperature ratio, deducing a maximum heat flux at a temperature ratio of about 0.3. The flow and heat transfer characteristics are explained by computing the ballistic and collision parts of the total bulk quantities and by investigating the contribution of each part to the overall solution.     

Thermodynamic analysis of a Stirling engine including dead volumes of hot space, cold space and regenerator

This paper provides a theoretical investigation on the thermodynamic analysis of a Stirling engine. An isothermal model is developed for an imperfect regeneration Stirling engine with dead volumes of hot space, cold space and regenerator that the regenerator effective temperature is an arithmetic mean of the heater and cooler temperature. Numerical simulation is performed and the effects of the regenerator effectiveness and dead volumes are studied. Results from this study indicate that the engine net work is affected by only the dead volumes while the heat input and engine efficiency are affected by both the regenerator effectiveness and dead volumes. The engine net work decreases with increasing dead volume. The heat input increases with increasing dead volume and decreasing regenerator effectiveness. The engine efficiency decreases with increasing dead volume and decreasing regenerator effectiveness.     

Performance Optimization of Co-current Gas-to-Gas Micro Heat Exchanger Considering Radiation

Optimization of a parallel flow gas-to-gas tubular micro heat exchanger with hot core and cold annulus fluid is numerically analyzed, considering the beneficial role of surface radiation. Operating and geometric parameters are varied for fixed overall mass flow rate and temperature of cold core fluid, to study the effects on the following performance parameters: heat transferred to annulus fluid, logarithmic mean temperature difference, effectiveness, and volumetric heat transfer coefficient. The micro heat exchanger is optimized for high heat transfer to annulus fluid and volumetric heat transfer coefficient, for different operating and geometric conditions. Optimization for high volumetric heat transfer coefficient maximizes the micro heat exchanger effectiveness, heat transferred and improves logarithmic mean temperature difference.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Heat Exchangers Design Under Variable Overall Heat Transfer Coefficient: Improved Analytical and Numerical Approaches

In typical heat exchanger design methods it is generally assumed that the overall heat transfer coefficient is constant and uniform; however, the heat transfer coefficients on the hot and cold sides of the heat exchanger may vary with flow Reynolds number, surface geometries, fluid thermophysical properties, and other factors. In this article we present simple analytical and numerical methods for calculating heat transfer area for data sets introduced earlier in the literature. For the analytical methods presented in the article, the variation in the overall heat transfer coefficient with the local hot and cold fluid temperature difference is expressed as a power-law model and as a general polynomial model. The procedure for calculating the heat transfer area with the power-law model is explained with respect to a simple closed-form solution, while the polynomial model can also provide an analytical solution that seems to be quite accurate for the data sets examined. It is also shown that a Chebyshev numerical integration scheme that requires four points compared to the Simpson method of three points is quite accurate (within 1% of the exact value).     

Exergy transfer effectiveness on heat exchanger for finite pressure drop

In this paper, exergy transfer effectiveness is defined to describe the performance of heat exchangers operating above/below the surrounding temperature with/without finite pressure drop. It is discussed systemically that the effects of heat transfer units number, the ratio of the heat capacity of cold fluids to that of hot fluids and flow patterns on exergy transfer effectiveness of heat exchangers. Furthermore, the results of exergy transfer effectiveness with a finite pressure drop are compared with those without pressure drop when different objective media, such as ideal gas and incompressible liquid, etc. are applied. The detailed comparisons of the exergy transfer effectiveness with heat transfer effectiveness are also performed for the parallel flow, counter flow and cross flow heat exchangers operating above/below the surrounding temperature.     

新型旋流热风炉填充球蓄热室实验研究及效率分析

提出了向小型化，高效化改造热风炉的方案。建立了新型旋流式热风炉填充球蓄热室温度分布的混合扩散数学模型，通过模型的数值解讨论了影响蓄热室热效率和温度效率的主要因素，并通过实验检测验证了新型旋流式热风炉蓄热室能更好的满足数学模型的假设条件。     

Performance of Counterflow Microchannel Heat Exchangers Subjected to External Heat Transfer

This article analyzes the effect of external heat transfer on the thermal performance of counterflow microchannel heat exchangers. Equations for predicting the axial temperature and the effectiveness of both fluids as well as the heat transferred between the fluids, while operating under external heating or cooling conditions, are provided in this article. External heating may decrease and increase the effectiveness of the hot and cold fluids, respectively. External cooling may improve and degrade the effectiveness of the hot and cold fluids, respectively. For unbalanced flows, the thermal performance of the microchannel heat exchanger subjected to external heat transfer depends on the fluid with the lowest heat capacity. At a particular number of transfer units (NTU), the effectiveness of both the fluids increased with decrease in heat capacity ratio when the hot fluid had the lowest heat capacity. When the cold fluid had the lowest heat capacity, the effectiveness of both fluids increased with decrease in heat capacity ratio at low values of NTU but at high values of NTU the effectiveness increased with increase in heat capacity ratio. A term called the “performance factor” has been introduced in this article to assess the relative change in effectiveness due to external heat transfer.     

Unsteady thermal flow analysis in a heat regenerator with spherical particles

Heat regenerator occupied by regenerative materials improves thermal efficiency of regenerative combustion system through the recovery of sensible heat of exhaust gases. By using one-dimensional two-phase fluid dynamics model, the unsteady thermal flow of regenerator with spherical particles, were numerically analysed to evaluate the heat transfer and pressure drop and to suggest the parameter for designing heat regenerator. It takes about 7 h for the steady state in the thermal flow of regenerator, where heat absorption of regenerative particle is concurrent with heat desorption. The regenerative particle experiences small temperature fluctuation below 10 K during the reversing process. The thermal flow in heat regenerator varies with inlet velocity of exhaust gas and air, configuration of regenerator and diameter of regenerative particle. As the gas velocity increases with decreasing the cross-sectional area of the regenerator, the heat transfer between gas and particle enhances and pressure losses increase. As particle diameter decreases, the air is preheated higher and the exhaust gases are cooled lower with the increase of pressure losses. At the same exhaust gases temperature at the regenerator outlet, the regenerator length need to be linearly increased with inlet Reynolds number of exhaust gases. It is confirmed that inlet Reynolds number of exhaust gases should be introduced as a regenerator design parameter. Copyright © 2002 John Wiley & Sons, Ltd.     

Explicit Design of Balanced Regenerators

An explicit procedure for the design and sizing of balanced regenerators has been developed. A set of performance curves relating the thermal ratio, harmonic mean reduced length and period, and minimum cold fluid outlet temperature is presented. The specific characteristics of the regenerator's matrix including the heat transfer and pressure drop correlations are used to develop interrelations, represented by a set of three design curves, between these quantitites and the operating characteristics of the regenerator. The performance and design curves are used in the design procedure to determine the dimensions of the regenerator for the specified operating conditions.     

The Influence of Core Capacitance on the Dynamic Performance of a Single-Phase Natural Circulation Loop With End Heat Exchangers

The effect of wall-core capacitance of heat exchangers on the dynamic behavior of a natural circulation loop (NCL) with end heat exchangers is studied under various excitations such as step, ramp, exponential, and sinusoidal. The transient one-dimensional conservation equations are derived for loop fluid, hot and cold fluid streams, and wall core of both heat exchangers. The solution of a set of transient partial differential equations and one integro-differential equation for loop fluid circulation rate is achieved through a finite-element technique. Imposing the excitations to the inlet temperature of hot fluid, the effects of wall-core capacitance on the responses of outlet temperatures of both hot and cold fluid streams and flow rate of loop fluid are studied. Wall-core capacitance diminishes the initial transients and delays the inception of hot and cold fluids outlet temperature profiles as well as loop fluid flow profile. Further, it has the ability to bring even unstable system behavior with reverse flows into a stable system with steady loop flow rate through quickly decaying oscillations. System responses are also greatly influenced by boundary conditions such as hot and cold fluids flow rates and their inlet temperature excitations such as step, ramp, and exponential. As flow stability is an important subject for single-phase NCLs, a stability map is constructed and compared with zero wall-core capacitance. Inclusion of wall-core capacitance in the present study reveals the important fact that the stable state operating zone widens with the wall-core capacitance.     

TWO-DIMENSIONAL AND UNSTEADY NATURAL CONVECTION IN A HORIZONTAL ENCLOSURE WITH A SQUARE BODY

A two-dimensional solution for unsteady natural convection in an enclosure with a square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multidomain methodology is used to handle a square body located at the center of the computational domain. The physical model considered here is that a square body is located at the center between the bottom hot and top cold walls. To see the effects of the presence of a body on natural convection between the hot and cold walls, we considered the cases that the body maintains the adiabatic and isothermal thermal boundary conditions for different Rayleigh numbers varying in the range of 103 to 106. When the Rayleigh number is small, the flow and temperature distribution between the hot and cold walls shows a symmetrical and steady pattern. At the intermediate Rayleigh number, the fluid flow and temperature fields maintain the steady state but change their shape to the nonsymmetrical pattern. When the Rayleigh number is high, the flow and temperature fields become time dependent, and their time-averaged shapes approach the symmetric pattern again. The Rayleigh number for the fluid flow and temperature fields to become nonsymmetrical and time dependent depends on the thermal boundary conditions of a body. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls and at the body surfaces for different Rayleigh numbers and thermal boundary conditions are also presented to show the overall heat transfer characteristics in the system.     

Numerical prediction of the instantaneous regenerator and in-cylinder heat transfer of a stirling engine

The paper is concerned with the study of the effects of the in-cylinder and regenerator heat transfer characteristics of a single-acting opposed-piston Stirling engine, with heater and cooler both omitted, for which a simulation model has been developed. The engine thermodynamic cycle is divided into a number of time-steps, and a system of nonlinear ordinary differential equations, which describe the energy balances over the three basic control volumes (hot and cold cylinders and regenerator), is solved numerically. Empirical correlations are used to determine the instantaneous heat transfer coefficients in the regenerator (flow across a porous medium) and inside the cylinder space (gas confined in a cylindrical volume with a moving boundary). Numerical results from the model are presented.     

Simulation of gas species and temperature separation in the counter-flow Ranque–Hilsch vortex tube using the large eddy simulation technique

A computational fluid dynamic model is used to predict the species and temperature separation within a counter flow Ranque–Hilsch vortex tube. The large eddy simulation (LES) technique was employed for predicting the gas flow and temperature fields and the species mass fractions (nitrogen and helium) in the vortex tube. A vortex tube with a circumferential inlet stream of nitrogen–helium mixture and an axial (cold) outlet stream and a circumferential (hot) outlet stream was considered. The temporal evolutions of the axial, radial and azimuthal components of the velocity along with the temperature, pressure and mass density and species concentration fields within the vortex tube are simulated. Even though a large temperature separation was observed, only a very minimal gas separation occurred due to diffusion effects. Correlations between the fluctuating components of velocity, temperature and species mass fraction were calculated to understand the separation mechanism. The inner core flow was found to have large values of eddy heat flux and Reynold’s stresses. Simulations were carried out for varying amounts of cold outlet mass flow rates. Performance curves (temperature separation/gas separation versus cold outlet mass fraction) were obtained for a specific vortex tube with a given inlet mass flow rate.