Approximate analytical model for PCM solidification in a rectangular finned container with convective cooling boundaries

Thermal energy storage units that utilize latent heat storage materials have received increased attention in the recent years because of their relatively large heat storage capacities and isothermal behavior during charging and discharging. In this study, an analytical approach is presented for the prediction of temperature during the solidification in a two-dimensional rectangular latent heat storage using a phase change material (PCM) with internal plate fins. The basic energy equation is formulated accounting for the presence of a heat thermal fluid (HTF) on the walls. A two-dimensional numerical model is developed based on the enthalpy method to predict the distribution temperature of the fin and solid–liquid interface in storage. Results from the analytical solution and numerical model show a good agreement. The developed analytical model estimates satisfactorily the solidification time of PCM in storage, which is useful in the design of PCM-based thermal energy storages and cooling systems.     

AA-CAES系统释能过程运行特性分析

为了研究释能过程中膨胀机运行特性对先进绝热压缩空气储能(AA-CAES)系统性能的影响,提出3种膨胀机运行方式:定压运行、定滑运行和滑压运行,并建立AA-CAES系统热力学模型。使用数值计算的方法,对比3种方式的系统性能差异,并分析关键参数对采用不同方式的系统性能的影响。计算结果表明:基本运行参数相同时,膨胀机采用滑压运行时储能效率和储能密度最大;适当调整储气压比差值,可改善3种方式的系统性能;存在最佳换热器效能使得3种运行方式的储能效率最大;膨胀机效率下降系数对定滑方式的影响最大;3种方式的稳定间隔时间较接近,对流换热系数增加到一定值时,不存在稳定间隔时间。     

Combined Experimental and Numerical Study for a Multiple-Microchannel Heat Transfer System

Multiple microchannel heat sinks for potential use for heat removal from localized thermal sources such as electronic chips are studied experimentally and numerically to characterize their thermal performance. An approach based on combined experimental and numerical modeling is presented. The numerical simulation is driven by experimental data, which are obtained concurrently, to obtain realistic, accurate, and validated numerical models. The ultimate goal is to design and optimize such thermal systems.

The experimental setup was established and liquid flow in the multiple microchannels was studied under different flow rates and heat influx. The temperature variation versus time was recorded by thermocouples, from which the time needed to reach steady state was determined. The measured temperatures under steady-state conditions were compared with those from three-dimensional steady-state numerical simulations for the same boundary and initial conditions. The experimental data were employed for the validation of the numerical model. In case of significant discrepancy, the numerical model was improved, starting initially with a relatively simple model. Fairly good agreement between the experimental and simulation results was finally obtained, indicating the main considerations for an accurate model. The numerical model also served to provide inputs that could be employed to improve and modify the experimental arrangement.

The main focus of this work is on the combined experimental and numerical approach to model and simulate thermal systems, such as the one considered here, particularly in regions where additional transport mechanisms are important. Consequently, low flow rates are employed to consider other transport mechanisms and make this combined experimental-numerical approach useful for design and optimization.     

Three-dimensional transient cooling simulations of a portable electronic device using PCM (phase change materials) in multi-fin heat sink

Transient three-dimensional heat transfer numerical simulations were conducted to investigate a hybrid PCM (phase change materials) based multi-fin heat sink. Numerical computation was conducted with different amounts of fins (0 fin, 3 fins and 6 fins), various heating power level (2 W, 3 W and 4 W), different orientation tests (vertical/horizontal/slanted), and charge and discharge modes. Calculating time step (0.03 s, 0.05 s, and 0.07 s) size was discussed for transient accuracy as well. The theoretical model developed is validated by comparing numerical predictions with the available experimental data in the literature. The results showed that the transient surface temperatures are predicted with a maximum discrepancy within 10.2%. The operation temperature can be controlled well by the attendance of phase change material and the longer melting time can be conducted by using a multi-fin hybrid heat sink respectively.     

Effect of inlet flow maldistribution on the thermal performance of a three-fluid crossflow heat exchanger

This study investigates the effect of flow maldistribution on the thermal performance of a three-fluid crossflow heat exchanger by the numerical method. In the inlets of three fluid streams, this study considers four modes of flow nonuniformity arrangement by using three flow maldistribution models. According to the results of temperature fields, effectiveness and deterioration factor, this study discusses the deterioration or promotion due to the flow maldistribution in the heat exchanger. The results indicate that there is a best one in choice between the four maldistribution modes and the best flow maldistribution mode promotes the thermal performance of a three-fluid crossflow heat exchanger when NTU and heat capacity rate ratios are large.     

Numerical investigation of high temperature metal hydride water pumping system

I n the present work, a high temperature Metal Hydride Water Pumping System (MHWPS) equipped with a latent heat exchanger was investigated numerically. The operating concept of the pump was presented and the mathematical model of heat and mass transfer within the pump was established. We simulated the pump under different operating conditions using the alloy Mg₂Ni as a metal hydride and the KNO₃ as a Phase Change Material (PCM). The obtained results have shown that i) the developed numerical model is flexible and accurate in predicting the dynamic behavior of the pump ii) the numerical model without radiative heat transfer gives results with errors that can reach 38%, particularly for pumping time iii) the integration of the PCM provides a reduction in the pumping time of about 90% and an increase of the efficiency of the pump of about 7.6 times compared to the case without PCM which represents an improvement of 86% and iv) the Mg₂Ni alloy requires high temperature and a mass of PCM about 9 times larger than the case of LaNi₅ alloy to pump a volume 6.5 times greater than that pumped with LaNi₅.     

Study on phase change temperature distributions of composite PCMs in thermal energy storage systems

A one‐dimensional (1D) physical model is developed for latent heat thermal energy storage (TES) systems using composite phase change materials (PCMs) with different phase change temperature (PCT) distributions. By theoretical investigation under the assumption of neglecting the sensible heat, the optimum linear PCT distributions which are corresponding to minimum phase change time are derived. To verify the theoretical results of the optimum linear PCT distributions, the finite difference method is adopted to simulate the cyclical freezing and melting processes of composite PCMs. The numerical results in which the sensible heat is taken into account show that: (1) the optimum linear PCT distributions obtained from the theoretical analyses seem to be the optimum ones of composite PCMs in practical latent heat TES systems; (2) the phase change time of composite PCMs with the optimum linear PCT distributions used in practical latent heat TES systems can be decreased by as much as 25–40% by properly selecting the segmented numbers of composite PCMs as compared with that of PCMs of a single PCT. Copyright © 1999 John Wiley & Sons, Ltd.     

Thermal Performance Enhancement of Triplex Tube Latent Thermal Storage Using Fins-Nano-Phase Change Material Technique

Latent heat thermal energy storage (LHTES) systems using a phase change material (PCM) can reduce the heat-transfer rates during charging/discharging processes because of their inherently low thermal conductivity. In this study, heat-transfer enhancement using various configurations of longitudinal fins employing both a PCM and a nano-PCM in a large triplex-tube heat exchanger (TTHX) was numerically investigated via the Fluent 15 software. The results showed that the thermal conductivity of the pure PCM (0.2 W/m K) can be observably enhanced by dispersing 10% alumina (Al₂O₃) to 25%. Therefore, the melting time is reduced to 12%, 11%, and 17% for the internal, internal-external, and external fins, respectively, compared with the case of the PCM without nanoparticle. It is concluded that the model of external fins-nano-PCM embedded in a large TTHX is the most efficient model for achieving complete PCM melting in a short time (188 min), where improving the thermal performance to 14% and 11% compared with the TTHX with internal and internal-external fins-nano-PCM, respectively. The simulation results are validated and agree well with experimental results for the PCM and nano-PCM.     

Simplified model and lattice Boltzmann algorithm for microscale electro-osmotic flows and heat transfer

The extremely small length scale of the electric double layer (EDL) of electro-osmotic flows (EOF) in a microchannel makes it difficult to simulate such flows and associated thermal behaviors. A feasible solution to this problem is to neglect the details in the thin EDL and replace its effects on the bulk flow and heat transfer with effective velocity-slip and temperature-jump boundary conditions outside the EDL. In this paper, by carrying out a scale analysis on the fluid flow and heat transfer in the thin EDL, we analytically obtain the velocity and the temperature at the interface between the EDL and the bulk flow region. The Navier–Stokes equations and the conservation equation of energy, along with the interfacial velocity and temperature as the velocity-slip and temperature-jump boundary conditions, form a simple model for the electro-osmotic flows with thermal effects in a microchannel with a thin EDL. We use the double distribution function lattice Boltzmann algorithm to solve this model and found that numerical results are in good agreement with those by the conventional complete model with inclusion of the EDL, particularly for the cases when channel size is about 400 times larger than the Debye length. Moreover, we found that the present model can substantially reduce the computational time by four to five times of that using the conventional complete model. Therefore, the simplified model proposed in this work is an efficient tool for simulating electro-osmosis-based microfluidic systems.     

Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM

In this paper an improvement of the model CaRM (CApacity Resistance Model) is presented to consider the borehole thermal capacitance, both of the filling material of the borehole and of the heat carrier fluid inside the ground heat exchanger. Several models, numerical and analytical, are available in literature for short time step analyses of ground-coupled heat pump systems. According to the modelling for the surrounding ground, the new approach for the inside of the borehole is based on electrical analogy. In this study the double U-tube ground heat exchanger is analyzed. The new model has been validated by means of a commercial software based on the finite elements method as well as measurements of ground response test, using a suitable plant system. In this last comparison, the contribution of the thermal capacitance of the circulating fluid is investigated, since it is frequently neglected in short time step simulations. In both cases, there is agreement between the CaRM results and data from numerical simulations and measurements as well.     

Investigation of dynamic heat transfer process through coaxial heat exchangers in the ground

Recently, researchers are focussing on using ground coupled heat pump systems as a heat source or sink rather than air source heat pumps for HVAC needs due to the stable temperature and the high thermal inertia of the soil. The investment cost of these systems is too expensive therefore the precise thermal analysis, design and parameter optimization are essential. For an accurate design, the maximum of physical phenomena such as: axial effects, seasonal effects, underground water flow and BHE dynamic behaviour must be accounted for in order to reflect exactly the real physical situation. In the present paper thermal interferences are investigated under seasonal effects and a dynamic heat flux for a vertical coaxial borehole heat exchangers field. This enables to avoid thermal interferences by predicting efficient period of operation corresponding to the beginning of the studied phenomena (interferences) for a given separation distance between two boreholes. To reach this purpose, as a first step, a transient 2D Finite volume method (FVM) for a single borehole heat exchanger was built using MATLAB, which accounts for accurate axial and seasonal effects and a dynamic heat flux that is function of depth and time. This model has been validated against the Finite Line Source (FLS) analytical solution and good agreement between analytical and numerical methods has been obtained. Then the model has been extended to a quasi-3D model in order to investigate thermal interferences between two neighbouring boreholes. After 500 h and at the mid-point of the separating distance (1.5 m) where interferences are the strongest, the temperature is 50% (6.64 °C) lower than the case where there are no interferences.     

Review of mathematical investigation on the closed adsorption heat pump and cooling systems

A mathematical model of the closed adsorption heat pump and cooling systems is particularly used to assist in interpreting the observed phenomena, to design the system, to predict the trends, and to assist in optimization. In this paper, various mathematical models mainly analyzing the heat and mass transfer process of an adsorption bed in closed adsorption heat pump and cooling systems are reviewed and classified based on complexity, into three main groups: i.e. thermodynamic model; lumped parameters model; heat and mass transfer model. The major characteristics of different models and assumptions used are presented and discussed. Also, the numerical methods and validation of the models are summarized and significant results obtained through mathematical model are detailed. Although the models have evolved to a point where several features of the process can be predicted, more effort is required before the models can be applied to define actual operating conditions as well as to further investigate new closed adsorption cycles.     

Application of the time discontinuous Galerkin finite element method to heat wave simulation

This paper deals with the numerical simulation of heat wave propagation in the medium subjected to different kinds of heat source, particularly heat impulse. The discontinuous Galerkin finite element method (DGFEM) proposed for the stress wave propagation in solids [X.K. Li, D.M. Yao, R.W. Lewis, A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media. Int. J. Numer. Meth. Eng. 57 (2003) 1775–1800] is extended to numerically solve for the non-Fourier heat transport equation constructed according to the CV model [C. Cattaneo, A form of heat-conduction equation which eliminates the paradox of instantaneous propagation, Compute Rendus 247 (1958) 431–433; P. Vernotte, Les paradoxes de la theorie continue de l’equation de la chaleur, Compute Rendus 246 (1958) 3154–3155]. Temperature and its time-derivative are chosen as primitive variables defined at each FE node. The main distinct characteristic of the proposed DGFEM is that the specific P3–P1 interpolation approximation, which uses piecewise cubic (Hermite’s polynomial) and linear interpolations for both temperature and its time-derivative, respectively, in the time domain is particularly proposed. As a consequence the continuity of temperature at each discrete time instant is exactly ensured, whereas discontinuity of the time-derivative of temperature at discrete time levels remains. Numerical results illustrate good performance of the present method in the numerical simulation of heat wave propagation in eliminating spurious numerical oscillations and in providing more accurate solutions in the time domain.     

Numerical simulation of geothermal-PVT hybrid system with PCM storage tank

As the increase in greenhouse emissions, climate changes, and other irreversible repercussions stems from environmentally destructive energies such as fossil fuels, exploiting solar and geothermal energy as unlimited clean sources of energy in the renewable energy technologies can survive the planet earth, which is facing a catastrophe on a global scale. The main purpose of this research is to study Techno analysis of the combined ground source heat pump (GSHP) and photovoltaic thermal collectors (PVTs) with a “phase-change material” (PCM) storage tank to fulfill the energy demands of a residential building. In the first step of this study, in order to model the heat pump behavior in multi-usage operation modes (heating and cooling), a numerical transient simulation of a water-to-water GSHP, which includes a vertical U-type ground source heat exchanger (GSHX) and a variable speed drive (VSD) compressor, was conducted by developing a numerical code in Engineering Equation Solver software. To study the thermodynamic aspect of the hybrid system in terms of exergy and energy, a transient numerical simulation was accomplished using the TRNSYS program. Also, the impact of effective characteristics of ingredients such as areas of PVT panels and the volume of the storage tank of PCMs on the performance of the hybrid system are investigated. On top of that, the two types of the GSHP-PVT-PCMs and GSHP-PV from the energy and exergy points of view are compared. The obtained results demonstrate that the irreversibility of the solar modules of the GSHP-PVT-PCMs is 6.6% lower than that of the GSHP-PV. Furthermore, the calculation of the annual required load of the building for these two kinds of hybrid systems shows that the use of collectors in this combined system has reduced the total load of the building by 6.5%. The use of collectors in the GSHP-PVT-PCM gives rise to a difference in the value of solar factor (SF) of this system by 1.4% more than the one for the hybrid system without thermal collectors.     

Study on the transient characteristics of the sensor tube of a thermal mass flow meter

In the present work, a simple numerical model for transient heat transfer phenomena involving the sensor tube of a thermal mass flow meter (TMFM) is presented. In order to validate the proposed model, extensive experimental investigations are performed. Based on the results of the proposed model, the transient heat transfer mechanism in the sensor tube is explained. Finally, a correlation for predicting the response time of the sensor tube is presented. This correlation can estimate the response time of the sensor tube quantitatively with errors of less than 30%. By using the proposed correlation, physical meanings and characteristics of the response time of the sensor tube are presented.     

Numerical simulation of the performance of a solar-earth source heat pump system

Solar-earth source heat pump (SESHP) is a new type of energy saving air conditioner. In this paper, numerical simulation of the performance of a solar-earth source heat pump system (SESHPS) operated at alternate or combined mode is carried out respectively. The results indicate that a resuming-rate of 30–60% of the earth temperature near buried coil can be preferable when SESHPS is operated alternately at a period of 24 h, and the proportion of the operation time of solar-assisted heat pump (SAHP ) should be confined to 42–58%. When SESHPS is operated at combined modes 2, the energy-saving rate with and without heat storage water tank is 14.5% and 10.4%, respectively, compared with ground source heat pump (GSHP). As for the overall effect, the combined operation mode with water tank in which the heated water flows through the solar collector first and then through the buried coil is preferable. The results are significant for the engineering design, operation and management of SESHPS.     

Experimental Validation of Numerical Solutions Using the Explicit Green's Approach to Simulate Transient Heat Conduction in Multilayer Systems

This article presents an experimental validation of numerical solutions using the explicit Green's approach (ExGA) for transient heat conduction in multilayer systems. The ExGA is an efficient recurrence relationship for the temperature in the time domain, based on the Green's matrix, which allows explicit time marching with a larger time step than is required by other methods found in the literature without losing accuracy. The multilayer system used in the experimental validation is built by overlaying different materials. The systems were subjected to heat variations that were recorded over time using thermocouples, and these results were used for comparison.     

Direct numerical simulation of interphase heat and mass transfer in multicomponent vapour–liquid flows

A Volume-of-Fluid methodology for direct numerical simulation of interface dynamics and simultaneous interphase heat and mass transfer in systems with multiple chemical species is presented. This approach is broadly applicable to many industrially important applications, where coupled interphase heat and mass transfer occurs, including distillation. Volume-of-Fluid interface tracking allows investigation of systems with arbitrarily complex interface dynamics. Further, the present method incorporates the full interface species and energy jump conditions for vapour–liquid interphase heat and mass transfer, thus, making it applicable to systems with multiple phase changing species. The model was validated using the ethanol–water system for the cases of wetted-wall vapour–liquid contacting and vapour flow over a smooth, stationary liquid. Good agreement was observed between empirical correlations, experimental data and numerical predictions for vapour and liquid phase mass transfer coefficients. Direct numerical simulation of interphase heat and mass transfer offers the clear advantage of providing detailed information about local heat and mass transfer rates. This local information can be used to develop accurate heat and mass transfer models that may be integrated into large scale process simulation tools and used for equipment design and optimization.     

A three-dimensional thermo-poroelastic model for fracture response to injection/extraction in enhanced geothermal systems

Water injection in enhanced geothermal systems sets in motion coupled poro-thermo-chemo-mechanical processes that impact the reservoir dynamics and productivity. The variation of injectivity with time and the phenomenon of induced seismicity can be attributed to the interactions between these processes. In this paper, a three-dimensional transient numerical model is developed and used to simulate fluid injection into geothermal reservoirs. The approach couples fracture flow and heat transport to thermo-poroelastic deformation of the rock matrix via the displacement discontinuity (DD) method. The use of the boundary integral equations, for the pressure diffusion and heat conduction in the rock matrix, eliminates the need to discretize the infinite reservoir domain. The system of linear algebraic equations for the unknown displacement discontinuities, and fluid and heat sources are used in a finite element formulation for the fluid flow and heat transport in the fracture. This yields a system of equations which are solved to obtain the temperature, pressure, and aperture distributions within the fracture at every time step. In this way, the temporal variation of the fracture aperture and fluid pressure, caused by pressurization and thermo-poroelastic stresses, are determined. Numerical experiments using the model illustrate the feed-back between matrix dilation, shrinkage, and pressure in the fracture. It is observed that whereas the poroelastic effects dominate the early stage of injection pressure profile and the fracture aperture evolution, thermoelastic effects become dominant for large injection times.