Numerical Simulations of Fluid Flow and Heat Transfer through Aluminum and Copper Metal Foam Heat Exchanger – A Comparative Study

Abstract

This article discusses about a numerical simulation of a metal foam heat exchanger system carried out by a commercial software. A metal foam layer is attached to the bottom of the heat exchanger to absorb heat from the exhaust hot gas leaving the system. Two types of metal foams with two different pores per inch (PPI) values are considered for heat transfer enhancement. Similarly, two different materials Aluminum and copper, that poses high thermal conductivity, metal foams are considered for the present numerical simulations. The heat exchanger system is simulated over a range of 6–30?m/s fluid velocity. The proposed simulations are compared with theoretical and experimental data available in the literature. The goal is to improve the thermal performance of the heat exchanger by decreasing the pressure drop and maximizing the heat transfer rate. Finally, it has been noticed that the velocity of the fluid decreases as PPI increases at the expense of its pressure drop. The copper metal foam gives a maximum increase of 4–10% heat transfer rate compared to aluminum metal foams for a fluid velocity of 30?m/s.     

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

泡沫铜强化石蜡相变蓄热特性的数值分析

通过构建泡沫金属内固液相变传热模型,对方腔蓄热单元中泡沫铜强化石蜡相变蓄热特性进行数值分析。数值模型采用考虑泡沫金属真实结构的等效导热系数通用模型,并兼顾石蜡在融化前后与金属骨架之间的热非平衡效应。通过求解模型得到方腔内石蜡固液界面演化规律与温度分布,进而对蓄热过程进行火用分析。结果表明:当前数值模型能较好地预测泡沫铜内固液相变传热;泡沫铜显著改善了石蜡相变的空间均匀性,减小了蓄热区温度梯度,使蓄热速率和火用效率得到有效提高。     

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity

A numerical study on natural convection heat transfer of cold water near 4 °C in a thick bottom walled cavity filled with a porous medium has been performed. It is assumed that the cavity is isothermally heated from the outside of the thick bottom wall and cooled from ceiling. The finite-difference method has been used to solve the governing partial differential equations of heat and fluid flow. Effects of thermal conductivity ratio, Rayleigh number and bottom wall thickness on heat transfer from the bottom to the ceiling have been studied. The heatline visualization technique has been used to demonstrate the path of heat transport through the enclosure. Moreover, streamlines and isotherms have been used to present fluid flow and temperature distributions. The obtained results show that multiple circulation cells are formed in the cavity and the local Nusselt numbers at the bottom wall and solid–fluid interface are highly affected by formed cells. The increase of Rayleigh number and thermal conductivity ratio increases heat transfer through the cavity. However, the increase of thickness of the bottom wall reduces the mean Nusselt number. Almost one-dimensional conduction heat transfer is observed in the solid bottom wall of the cavity.     

WALL HEAT CONDUCTION EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH A NON-DARCIAN POROUS MEDIUM

ABSTRACT

A numerical analysis has been made of the conjugate natural convection in a rectangular enclosure filled with a fluid-saturated porous medium and surrounded with four solid walls. The conductance of the walls is assumed to be much greater than that of the cavity filled with a porous medium. The main objective was to investigate the influences of the ratio of thermal conductivity of the wall to that of the fluid-porous matrix composite, the Darcy-modified Rayleigh number, the Prandtl number, and the aspect ratio. The streamlines and isotherms are presented; also, the local and average Nusselt numbers are presented along the interface between walls and cavity. A non-Darcian model was employed and the numerical method was SIMPLE-C. The numerical results indicate that the wall heat conduction effects decrease the heat transfer rate. When the wall heat conduction is considered, the greater the conductance of the solid walls surrounding the cavity, the greater is the rate of heat transfer.     

Fully developed forced convective heat transfer in an annulus partially filled with metallic foams: An analytical solution

An analytical solution for fully developed forced convective heat transfer in an annulus partially filled with metallic foam was proposed. The inner surface attached with an annular metallic foam layer was exposed to constant heat flux while the outer surface was adiabatic. In the metallic foam region, the Brinkman–Darcy equation was used to describe the fluid flow and the thermal non-equilibrium model was employed to establish the heat transfer equations. At the porous-fluid interface, no-slip coupling conditions were utilized to couple flow and heat transfer of the porous and open regions. A closed-form analytical solution was obtained for velocity and temperature profiles. The explicit form of friction factor and the Nusselt (Nu) number were also provided. The solutions were validated by two extreme cases: the empty annulus and the annulus fully filled with metallic foam. The effects of key parameters on friction factor, Nu number, and j/f^1/3 were examined. The relationship between flow heterogeneity and heat transfer was also discussed by introducing the flow heterogeneity coefficient. The porosity, pore density, and foam thickness for engineering applications were recommended. In the present analytical solution, a benchmark was also established for improving discretizing schemes in numerical works.     

Numerical analysis of heat transfer and flow field around cross-flow heat exchanger tube with fouling

Fouling is one of the main problems of heat transfer which can be described as the accumulation on the heat exchanger tubes, i.e.; ash deposits on the heat exchanger unit of the boiler. A decrease in heat transfer rate by this deposition causes loss in system efficiency and leads to increasing in operating and maintenance costs. This problem concerns with the coupling among conduction heat transfer mode between solid of different types, conjugate heat transfer at the interface of solid and fluid, and the conduction/convection heat transfer mode in the fluid which can not be solved analytically. In this paper, fouling effect on heat transfer around a cylinder in cross flow has been studied numerically by using conjugate heat transfer approach. Unlike other numerical techniques in existing literatures, an unstructured control volume finite element method (CVFEM) has been developed in this present work. The study deals with laminar flow where the Reynolds number is limited in the range that the flow field over the cylinder is laminar and steady. We concern the fouling shape as an eccentric annulus with constant thermal properties. The local heat transfer coefficient, temperature distribution and mean heat transfer coefficient along the fouling surface are given for concentric and eccentric cases. From the results, we have found that the heat transfer rate of cross-flow heat exchanger depends on the eccentricity and thermal conductivity ratio between the fouling material and fluid. The effect of eccentric is dominant in the region near the front stagnation point due to high temperature and velocity gradients. The mean Nusselt number varies in asymptotic fashion with the thermal conductivity ratio. Fluid Prandtl number has a prominent effect on the distribution of local Nusselt number and the temperature along the fouling surface.     

Analysis of temperature gradient bifurcation in porous media – An exact solution

The phenomenon of temperature gradient bifurcation in a porous medium is analyzed by studying the convective heat transfer process within a channel filled with a porous medium, with internal heat generation. A local thermal non-equilibrium (LTNE) model is used to represent the energy transport within the porous medium. Exact solutions are derived for both the fluid and solid temperature distributions for two primary approaches (Models A and B) for the constant wall heat flux boundary condition. The Nusselt number for the fluid at the channel wall is also obtained. The effects of the pertinent parameters such as fluid and solid internal heat generations, Biot number and fluid to solid thermal conductivity ratio are discussed. It is shown that the internal heat generation in the solid phase is significant for the heat transfer characteristics. The validity of the one equation model is investigated by comparing the Nusselt number obtained from the LTNE model with that from the local thermal equilibrium (LTE) model. The results demonstrate the importance of utilizing the LTNE model in the present study. The phenomenon of temperature gradient bifurcation for the fluid and solid phases at the wall for Model A is established and demonstrated. In addition, the temperature distributions for Models A and B are compared. A numerical study for the constant temperature boundary condition was also carried out. It was established that the phenomenon of temperature gradient bifurcation for the fluid and solid phases for the constant temperature boundary condition can occur over a given axial region.     

Heat transfer performance analysis of a solar flat-plate collector with an integrated metal foam porous structure filled with paraffin

The analysis of energy storage process of a solar flat-plate collector with an integrated aluminum foam porous structure filled with paraffin as the phase-change medium is reported in this paper. The momentum conservation of liquid paraffin is modeled with Darcy’s law with the Brinkman–Forchheimer’s extension, while heat transfer between the metal foams and paraffin in solid and liquid phases is modeled with a two-temperature model. It is shown that the assumption of the local thermal equilibrium between the metal foams and paraffin invoked in previous studies is inappropriate in predicting the heat transfer behavior, whereas the two-temperature model proposed in this work without this assumption can more realistically predict the real-world phase-change heat transfer process in the solar collector. In particular, the numerical results indicate that the heat transfer performance can be significantly improved by using the aluminum foams filled with paraffin.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

Investigation of the effect of metal foam characteristics on the PCM melting performance in a latent heat thermal energy storage unit by pore-scale lattice Boltzmann modeling

Latent heat thermal energy storage (LHTES) has many advantages such as high energy density and phase change at a nearly constant temperature compared with sensible thermal energy storage or chemical energy storage techniques. However, one of its major drawbacks is the low thermal conductivity of phase change materials (PCMs) which impedes the heat transfer efficiency. High thermal conductivity metal foams could be added into the LHTES to enhance the heat transfer speed. Under this case, the investigation of the effects of metal foam porosity and pore size on the melting process is essential for improving the heat storage capability of LHTES. In this article, a pore-scale modeling of melting process in a LHTES unit filled with metal foams is carried out by enthalpy-based multiple-relaxation-time lattice Boltzmann method. The quartet structure generation set is used to generate the morphology of metal foams. In addition, a Compute Unified Device Architecture (CUDA) Fortran code is developed in this work for executing highly parallel computation through graphics processing units. The melting process in the PCMs is investigated in terms of porosity, pore size, nonuniform metal foam, hot wall temperature, and initial subcooled temperature to optimize the design of LHTES filled with metal foams.     

Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)

In this paper the experimental investigation on the solid/liquid phase change (melting and solidification) processes have been carried out. Paraffin wax RT58 is used as phase change material (PCM), in which metal foams are embedded to enhance the heat transfer. During the melting process, the test samples are electrically heated on the bottom surface with a constant heat flux. The PCM with metal foams has been heated from the solid state to the pure liquid phase. The temperature differences between the heated wall and PCM have been analysed to examine the effects of heat flux and metal foam structure (pore size and relative density). Compared to the results of the pure PCM sample, the effect of metal foam on solid/liquid phase change heat transfer is very significant, particularly at the solid zone of PCMs. When the PCM starts melting, natural convection can improve the heat transfer performance, thereby reducing the temperature difference between the wall and PCM. The addition of metal foam can increase the overall heat transfer rate by 3-10 times (depending on the metal foam structures and materials) during the melting process (two-phase zone) and the pure liquid zone. The tests for investigating the solidification process under different cooling conditions (e.g. natural convection and forced convection) have been carried out. The results show that the use of metal foams can make the sample solidified much faster than pure PCM samples, evidenced by the solidification time being reduced by more than half. In addition, a two-dimensional numerical analysis has been carried out for heat transfer enhancement in PCMs by using metal foams, and the prediction results agree reasonably well with the experimental data.     

Role of heat pipes in improving the hydrogen charging rate in a metal hydride storage tank

Metal hydrides can store hydrogen at high volumetric efficiencies. As the process of charging hydrogen into a metal powder to form its hydride is exothermic, the heat released must be removed quickly to maintain a rapid charging rate. An effective heat removal method is to incorporate a heat exchanger such as a heat pipe within the metal hydride bed. In this paper, we describe a two-dimensional numerical study to predict the transient heat and mass transfer in a cylindrical metal hydride tank embedded with one or more heat pipes. Results from a parametric study of hydrogen storage efficiency are presented as a function of storage tank size, water jacket temperature and its convective heat transfer coefficient, and heat pipe radius and its convective heat transfer coefficient. The effect of enhancing the thermal conductivity of the metal hydride by adding aluminum foam is also investigated. The study reveals that the cooling water jacket temperature and the heat pipe's heat transfer coefficient are most influential in determining the heat removal rate. The addition of aluminum foam reduces the filling time as expected. For larger tanks, more than one heat pipe is necessary for rapid charging. It was found that using more heat pipes of smaller radii is better than using fewer heat pipes with larger radii. The optimal distribution of multiple heat pipes was also determined and it is shown that their relative position within the tank scales with the tank size.     

Review on thermal transport in high porosity cellular metal foams with open cells

Thermal transport in metal foams has received growing attention in both academic research and industrial applications. In this paper the recent research progress of thermal transport in metal foams has been reviewed. This paper aims to provide the comprehensive state-of-the-art knowledge and research results of thermal transport in open celled cellular metal foams, which covers the effective thermal conductivity, forced convection, natural convection, thermal radiation, pool boiling and flow boiling heat transfer, solid/liquid phase change heat transfer and catalytic reactor. The forced convection and thermal conductivity have been extensively investigated, while less research were performed on two-phase (boiling and solid/liquid phase change heat transfer) and thermal radiation in metal foams. Also most research still treats the metal foam as one type of effective continuous porous media, very few researchers investigated the detailed thermal behaviours at the pore level either by numerical or experimental approaches.     

Application of high porosity metal foams as air-cooled heat exchangers to high heat load removal systems

A numerical study has been conducted to investigate the fluid flow and heat transfer of an air-cooled metal foam heat exchanger under the high speed laminar jet confined by two parallel walls for which the range of the Reynolds number is 600–1000. Two independent numerical solvers were used and cross-validated being a FORTRAN code and the commercially available software CFD-ACE. The effects of local thermal non-equilibrium, thermal dispersion, porosity, and pore density on the heat transfer augmentation are examined for different Reynolds numbers. Application of energy flux vectors, for convection visualization, is also illustrated for a more comprehensive analysis of the problem. Finally, the performance of the metal foam heat exchanger is compared to that of conventional finned design. It is observed that the heat removal rate can be greatly improved at almost no excess cost.     

物性参数对环形空间流动和传热影响的模拟研究

利用有限容积法,建立了环形空间内单相流体竖直向上流动过程中流动和传热的稳态模型。模型将环形空间内管设置为具有固定生热速率的发热体;流体与内管壁之间设置流动和传热边界层,以更精确的描述壁面位置流体与固体之间动量和热量的耦合传递过程。通过与常物性模型的对比,流体密度、导热系数和黏度随温度变化的变物性模型,在传热能力上具有一定的减少,流体与固体传热面之间的界面剪切力稍有下降。通过比较常物性模型和变物性模型的Re和Ri,结果表明,随着流体强制循环速度的加大,流体物性变化对流动和传热过程的影响逐渐减小。     

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.     

Heat Transfer Analysis for a Concentric Tube Heat Exchanger Including the Wall Axial Conduction

The effect of wall axial conduction on the heat transfer in a concentric tube heat exchanger is examined for the inner flow laminar flow regime. The procedure used for the current analysis combines the analytical solution for the inner fluid with a numerical approximation for the wall conduction and has the capability of handling the temperature variation for the outer fluid. Both parallel and counterflow cases are evaluated for the analysis, and results are presented in terms of the axial variations of fluids and wall temperatures. Effects of the heat capacity rate ratio of the fluids on the temperature variations and on the mean heat flux are also pointed out. The effect of the exchanger length is included for the analysis. It is concluded that the total heat transfer between the fluids is greatly influenced by the wall axial conduction for the counterflow arrangement and is not ignorable when the heat capacity rate ratio of fluids are smaller than unity.     

Numerical Simulation of Natural Convection in a Porous Cavity with Linearly Temperature Distributions Under the Local Thermal Nonequilibrium Condition

A numerical investigation of the natural convection heat transfer in a rectangular cavity filled with a heat-generating porous medium by adopting the local thermal nonequilibrium (LTNE) model is reported in this paper. The top and bottom walls of the enclosure are adiabatic, the left wall is linearly cooled, and the right wall is cooled by a linear or uniform temperature profile. The results show that the isotherms for the fluid and solid phases become similar with the increase of the interphase heat transfer coefficient H; the increasing heat transfer between the two phases brings their temperatures closer to each other and thus the solid and fluid phases are in a state of the thermal equilibrium at higher values of H. For case A, the interphase heat transfer coefficient has little influence on the heat transfer rate of the solid phase of the porous cavity and the heat transfer profile of the solid phase (Nu_sy) is symmetrical with respect to the center point of line Y = 0.5. For case B, the interphase heat transfer coefficient H has a significant effect on that at the right wall, and the total heat transfer of the heat-generating porous cavity is implemented by the right-side wall. The total heat transfer rate Q of case B is higher than that of case A at a high thermal conductivity ratio γ (γ = 1, 10).     

Analysis of coiled-tube heat exchangers to improve heat transfer rate with spirally corrugated wall

Steady heat transfer enhancement has been studied in helically coiled-tube heat exchangers. The outer side of the wall of the heat exchanger contains a helical corrugation which makes a helical rib on the inner side of the tube wall to induce additional swirling motion of fluid particles. Numerical calculations have been carried out to examine different geometrical parameters and the impact of flow and thermal boundary conditions for the heat transfer rate in laminar and transitional flow regimes. Calculated results have been compared to existing empirical formulas and experimental tests to investigate the validity of the numerical results in case of common helical tube heat exchanger and additionally results of the numerical computation of corrugated straight tubes for laminar and transition flow have been validated with experimental tests available in the literature. Comparison of the flow and temperature fields in case of common helical tube and the coil with spirally corrugated wall configuration are discussed. Heat exchanger coils with helically corrugated wall configuration show 80–100% increase for the inner side heat transfer rate due to the additionally developed swirling motion while the relative pressure drop is 10–600% larger compared to the common helically coiled heat exchangers. New empirical correlation has been proposed for the fully developed inner side heat transfer prediction in case of helically corrugated wall configuration.