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.     

Mathematical Modeling of Cross-Flow Tube Heat Exchangers With a Complex Flow Arrangement

The general principles of mathematical modeling of heat transfer in cross-flow tube heat exchangers with complex flow arrangements that allow the simulation of multipass heat exchangers with many tube rows are presented. The finite-volume method is used to solve the system of differential equations for temperature of the both fluids and the tube wall with appropriate boundary conditions. A numerical model of a multipass steam superheater with 12 passes is presented. The convection and radiation heat transfer on the flue gas side are accounted for. In addition, the deposit layer is assumed to cover the outer surface of the tubes. Comparing the computed and measured steam temperature increase over the entire superheater allows for determining the thermal resistance of the deposits layer on the outer surface of the superheater. The developed modeling technique can especially be used for modeling tube heat exchangers when detailed information on the tube wall temperature distribution is needed.     

Finite element analysis of shell and tube heat exchanger

A finite element model to predict temperature distribution in heat exchangers is reported. The model can be effectively used to analyse and design the heat exchangers with complex flow arrangements for which no regular design procedure is available. Illustrations are provided to explain the application of the method for the analysis of shell and tube heat exchangers.     

Performance investigation of plain and finned tube evaporatively cooled heat exchangers

The performance of two evaporatively cooled heat exchangers is investigated under similar operating conditions of air flow rates and inlet hot water temperatures. The heat exchangers are plain and plate-finned circular tube types which occupy the same volume. Spray water, which is circulated in a closed circuit, is injected onto the exposed surfaces of the tubes and fins. The contact between air and spray water results in evaporative heat transfer. The tubes are copper, 10 mm o.d. The finned configuration is constructed by introducing 0.5 mm thick copper plates between the tubes, with a total area ratio of four. A substantial increase in heat transfer takes place for the plate-finned tubes. The increase is 92–140% for air velocities from 1.66 to 3.57 m s⁻¹. A model is used to calculate the thermal performance of the plain and finned tubes assuming a constant spray water temperature in the heat exchanger. The wet-finned surfaces show low fin efficiency compared with dry surfaces. An energy index defined as the ratio of volumetric thermal conductance to air pressure drop per unit length is found to be close for the two heat exchangers. This reveals higher thermal utilisation of the occupied volume by the finned tubes with the same energy index.     

A study on the thermal contact conductance in fin–tube heat exchangers with 7 mm tube

The thermal contact resistance has been frequently neglected in the process of design of heat exchangers because of the difficulty of measurement and the lack of accurate data. However, the thermal contact resistance is one of principal parameters in heat transfer mechanism of fin–tube heat exchangers. The objective of the present study is to investigate new factors such as fin types and manufacturing types of the tube affecting the thermal contact conductance and to find a correlation between the thermal contact conductance and the effective factors in fin–tube heat exchangers with 7 mm tube. The thermal contact conductances in the 22 heat exchangers with 7 mm tube have been investigated through the experimental–numerical method. A numerical scheme has been employed to calculate the thermal contact conductance and the portion of thermal resistances using the experimental data. As a result, the thermal contact conductance has been evaluated quantitatively, and a new correlation including the influence of new factors such as fin types and manufacturing types of the tube has been developed in the fin–tube heat exchanger with 7 mm tube. Also, the portion of each thermal resistance has been evaluated in each case.     

Simple method for estimation of effectiveness in one tube pass and one shell pass counter-flow heat exchangers

In one tube pass and one shell pass counter-flow heat exchangers, when both streams change temperature by different amounts, the effectiveness is defined as the temperature change for the stream with lower capacity divided by the maximum possible change and the effectiveness depends on the number of transfer units and the thermal capacity ratio. In this paper, an attempt has been made to formulate a simple-to-use method which is easier than existing approaches, less complicated and with fewer computations for accurate and rapid estimation of effectiveness in one tube pass and one shell pass counter-flow heat exchangers as a function of number of transfer units and the thermal capacity ratio. The proposed method permits estimating the exit temperature for a one tube pass and one shell pass counter-flow heat exchanger without a trial-and-error calculation. The average absolute deviations between the reported data and the proposed correlations are found to be less than 2% demonstrating the excellent performance of proposed correlation. The tool developed in this study can be of immense practical value for engineers and scientists to have a quick check on the effectiveness in one tube pass and one shell pass counter-flow heat exchangers at various conditions without opting for any experimental measurements. In particular, practice engineers would find the predictive tool to be user-friendly with transparent calculations involving no complex expressions.     

Performance of finned tube heat exchangers operating under frosting conditions

In this paper, the performance of flat plate finned tube heat exchangers operating under frosting conditions was investigated experimentally. Heat exchangers of single and multiple tube row(s) were tested to show the effects of various parameters on heat transfer performance. The parameters include temperature and relative humidity of air, flow rate of air, refrigerant temperature, fin pitch, and row number. The time variations of heat transfer rate, overall heat transfer coefficient, and pressure drop of heat exchangers presented.     

Computational modeling of heat transfer in magneto-non-Newtonian material in a circular tube with viscous and Joule heating

Numerous industrial and engineering systems, like, heat exchangers, chemical action reactors, geothermic systems, geological setups, and many others, involve convective heat transfer through a porous medium. The diffusion rate, drag force, and mechanical phenomenon are dealt with in the Darcy–Forchheimer model, and hence this model is vital to study the fluid flow and heat transport analysis. Therefore, numerical simulation of the Darcy–Forchheimer dynamics of a Casson material in a circular tube subjected to the energy losses due to the viscous heating and Joule dissipation mechanisms is performed. The novelty of the present investigation is to scrutinize the convective heat transport characteristics in a circular tube saturated with Darcy–Forchheimer porous matrix by utilizing the non-Newtonian Casson fluid. The flow occurs due to the elongation of the surface of a tube with a uniform heat-based source/sink. The similarity solution of the nonlinear problem was obtained using dimensionless similarity variables. The effects of operating parameters related to the flow phenomena are analyzed. Further, the friction factor and Nusselt number are also analyzed in detail. The present flow model ensures no flow reversal and acts as a coolant of the heated cylindrical surface; the existence of the magnetic field, as well as an inertial coefficient, acts as the momentum-breaking forces, whereas Casson fluidity builds it. The Joule heating phenomenon enhances the magnitude of temperature. The thermal field of the Casson fluid is higher at the surface of the circular pipe due to convective thermal conditions.     

Slip Boundary Conditions in Ballistic–Diffusive Heat Transport in Nanostructures

Ballistic–diffusive heat conduction, which is predominantly affected by boundaries and interfaces, will occur in nanostructures whose characteristic lengths are comparable to the phonon mean free path (MFP). Here, we demonstrated that interactions between phonons and boundaries (or interfaces) could lead to two kinds of slip boundary conditions in the ballistic–diffusive regime: boundary temperature jump and boundary heat flux slip. The phonon Boltzmann transport equation (BTE) with relaxation time approximation and the phonon tracing Monte Carlo (MC) method were used to investigate these two slip boundary conditions for the ballistic–diffusive heat conduction in nanofilms on a substrate. For cross-plane heat conduction where the boundary temperature jump is the dominant non-Fourier phenomenon, ballistic transport causes the temperature jumps and thus introduces a ballistic thermal resistance. Importantly, when considering the interface effect, the corresponding model was derived based on the phonon BTE and verified by comparing with the MC simulations. In addition, an interface–ballistic coupling effect was identified, which indicates inapplicability of the standard thermal resistance analysis. In contrast, for the in-plane case that is controlled by boundary heat flux slip, both phonon boundary scattering and perturbation of the phonon distribution function induced by the interface can cause heat flux slip, leading to a variation in in-plane thermal resistance. In addition, a model beyond the Fuchs-Sondheimer formula, which can address both the boundary scattering and the interface effects, was derived based on the phonon BTE. The good agreements with the MC simulations indicate its validity.     

Study on the design procedure for a multi-cool/heat tube system

The objective of this study is to contribute to widespread use of earth-to-air heat exchangers by proposing a design procedure. In this paper, it is discussed the design method when an earth-to-air heat exchanger system consists of multiple pipes with a close arrangement.A numerical model for this multi-cool/heat tube system was developed and it was verified by field measurements. With taking into account the thermal interference between tubes, the heat transfer performance was evaluated under various design conditions such as number of tubes, arrangement interval, air velocity and length, and soil properties. Based on these results, an estimation method for the heat transfer rate for the multi-cool/heat tube system is proposed.     

Modelling the thermal performance of earth-to-air heat exchangers

A new complete numerical model for the prediction of thermal performance of the earth-to-air heat exchangers is presented. The model describes the simultaneous heat and mass transfer inside the tube and into the soil accounting for the soil natural thermal stratification. The model is validated against an extensive set of experimental data and it is found accurate. The proposed algorithms are suitable for the calculation of the temperature and humidity variation of the circulating air and for the temperature and humidity distribution inside the ground. The presented model was developed within the TRNSYS environment and can be easily coupled with building or greenhouse simulation codes in order to describe the impact of the earth-to-air heat exchangers to indoor environments.     

Application of laser-based instrumentation for measurement of time-resolved temperature and velocity fields in the thermoacoustic system

This work aims to develop reliable laser-based measurement techniques to enable fundamental heat transfer and fluid flow studies in thermoacoustic systems. The challenge is to better understand the modes of energy transfer between the key components, such as stacks (or regenerators) and the hot and cold heat exchangers (located on two sides of the stack/regenerator structure), under the oscillatory flow conditions imposed by the acoustic field. The measurement methodologies adopted in this work include combined two-dimensional temperature and velocity field measurements using Planar Laser-Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV), respectively. These are investigated around the fins of a pair of mock-up heat exchangers placed side by side in a quarter-wavelength standing-wave acoustic resonator, to mimic the working conditions of a thermoacoustic system. The fins are kept at constant temperatures by means of resistive heating and water cooling, respectively. The velocity and temperature field distributions for 20 phases in the acoustic cycle have been obtained. The impact of the inertial, viscous and thermal effects on the time-dependent local temperature and velocity distributions is discussed. Mutual interaction between both fields is also shown. Future work towards obtaining useful heat transfer correlations in oscillatory conditions is outlined.     

Thermal stress analysis of eccentric tube receiver using concentrated solar radiation

In the parabolic trough concentrator with tube receiver system, the heat transfer fluid flowing through the tube receiver can induce high thermal stress and deflection. In this study, the eccentric tube receiver is introduced with the aim to reduce the thermal stresses of tube receiver. The ray-thermal-structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. During the sequential coupled numerical analyses, the concentrated heat flux distribution on the bottom half periphery of tube receiver is obtained by Monte-Carlo ray tracing method, and the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The temperature distributions and thermal stress fields are obtained by the CFD and FEA analyses, respectively. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated. It is recommended to adopt the eccentric tube receiver with optimum eccentricity and 90° oriented angle as tube receiver for the parabolic trough concentrator system to reduce the thermal stresses.     

Air side heat transfer characteristics of plate finned tube heat exchangers with slit fin configuration under wet conditions

An experimental study was performed on compact finned tube heat exchangers under wet conditions. Eight different finned tube heat exchangers having slit fins with hydrophilic coatings were tested. The effects of tube diameter, the number of tube rows, and inlet air relative humidity on air side heat transfer and pressure drop characteristics were investigated. Air side heat transfer coefficients were calculated using the log mean enthalpy difference method. The effects of the number of tube rows and the tube diameter on the Colburn j-factor and the f-factor were larger compared with those of the inlet air relative humidity. The Colburn j-factor and the f-factor of the single-row heat exchanger were larger than those of two- or three-row heat exchangers. The j-factor for the 5.30 mm tube diameter was compared with those for 7.35 mm and 9.95 mm tube diameters at 46% RH and was found to be 33% and 55% larger, respectively.     

Velocity distribution and vibration excitation in tube bundle heat exchangers

Design criteria for tube bundle heat exchangers, to avoid fluidelastic instability, are based on stability criteria for ideal bundles and uniform flow conditions along the tube length. In real heat exchangers, a non-uniform flow distribution is caused by inlet nozzles, impingement plates, baffles and bypass gaps. The calculation of the equivalent velocities, according to the extended stability equation of Connors, requires the knowledge of the mode shape and the assumption of a realistic velocity distribution in each flow section of the heat exchanger. It is the object of this investigation to derive simple correlations and recommendations, (1) for equivalent velocity distributions, based on partial constant velocities, and (2) for the calculation of the critical volume flow in practical design applications. With computational fluid dynamic (CFD) programs it is possible to calculate the velocity distribution in real tube bundles, and to determine the most endangered tube and thereby the critical volume flow. The paper moreover presents results and design equations for the inlet section of heat exchangers with variations of a broad range of geometrical parameters, e.g., tube pitch, shell diameter, nozzle diameter, span width, distance between nozzle exit and tube bundle.     

Experimental investigation of shell and coiled tube heat exchangers using wilson plots

In this work, an experimental investigation was performed to study the shell and helically coiled tube heat exchangers. Three heat exchangers with different coil pitches and curvature ratios were tested for both parallel-flow and counter-flow configurations. All the required parameters like inlet and outlet temperatures of tube-side and shell-side fluids, flow rate of fluids, etc. were measured using appropriate instruments. Overall heat transfer coefficients of the heat exchangers were calculated using Wilson plots. Heat transfer coefficients of shell and tube sides were evaluated invoking the calculated overall heat transfer coefficients. The inner Nusselt numbers were compared to the values existed in open literature. Though the boundary conditions were different, a reasonable agreement was observed.     

Effect of electroplating on the thermal conductance of fin–tube interface

This paper presents the experimental results of thermal contact conductance, heat transfer and interfacial temperature drop of finned tube heat exchanger test specimens. The results were based on the measured temperatures at several locations on the test specimen so that the thermal contact conductance could be directly determined. Each test specimen was assembled by mechanically expanding seven tubes into a single fin. The geometry of the specimens was based on a commonly used model of heat exchangers. The specimens included one bare tube (non-coated) specimen and four electroplated tube specimens. The plating metals were zinc, tin, silver and gold. The thickness of the plating in each case was 5 μm.Experiments have been conducted in both vacuum and nitrogen. Maximum enhancement was obtained when the tube was coated with tin. This indicates that, although the thermal conductivity is important, the softness of the plating material also plays an important role in enhancing the thermal conductance of the interface. The presence of an interstitial gas such as nitrogen is beneficial for the heat transfer and the thermal contact conductance. It is also noted that the interfacial temperature drop alone does not fully reflect the efficiency of the heat exchanger.     

Numerical simulations of gas resonant oscillations in a closed tube using lattice Boltzmann method

Numerical studies are presented for gas resonant oscillations in a two-dimensional closed tube using the lattice Boltzmann method. A multi-distribution function model of thermal lattice Boltzmann method is adopted in this work. The oscillating flow of the gas is generated by a plane piston at one end, and reflected by the other closed end. Both isothermal and adiabatic walls of the closed tube are considered. Boundary treatments such as moving adiabatic boundary are given in detail. The time dependent velocity, density and temperature at various locations of the tube for various frequencies and wall boundary conditions are presented. Shock waves with resonant frequency or slightly off-resonant frequencies are numerically captured. From the simulation results, the gas flow and heat transfer characteristics obtained are consistent qualitatively with those from previous simulations using conventional numerical methods.     

A synthesis of fluid and thermal transport models for metal foam heat exchangers

Metal foam heat exchangers have considerable advantages in thermal management and heat recovery over several commercially available heat exchangers. In this work, the effects of micro structural metal foam properties, such as porosity, pore and fiber diameters, tortuosity, pore density, and relative density, on the heat exchanger performance are discussed. The pertinent correlations in the literature for flow and thermal transport in metal foam heat exchangers are categorized and investigated. Three main categories are synthesized. In the first category, the correlations for pressure drop and heat transfer coefficient based on the microstructural properties of the metal foam are given. In the second category, the correlations are specialized for metal foam tube heat exchangers. In the third category, correlations are specialized for metal foam channel heat exchangers. To investigate the performance of the foam filled heat exchangers in comparison with the plain ones, the required pumping power to overcome the pressure drop and heat transfer rate of foam filled and plain heat exchangers are studied and compared. A performance factor is introduced which includes the effects of both heat transfer rate and pressure drop after inclusion of the metal foam. The results indicate that the performance will be improved substantially when a metal foam is inserted in the tube/channel.     

Microtube gas flows with second-order slip flow and temperature jump boundary conditions

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, second-order boundary conditions assuming an effective mean free path model predict a lower slip velocity than a first-order model assuming a hard sphere mean free path model. Heat transfer effects associated with rarefied flow are reduced for the second-order model. The effect of the second-order terms is most significant at the upper limit of the slip regime. For airflow at standard conditions, the maximum second-order change to the Nusselt number is on the order of 15%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.