Effects of the heat transfer fluid velocity on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study

A numerical study of the effects of the thermal fluid velocity on the storage characteristics of a cylindrical latent heat energy storage system (LHESS) was conducted. Due to the low thermal conductivity of phase change materials (PCMs) used in LHESS, fins were added to the system to increase the rate of heat transfer and charging. Finite elements were used to implement the developed numerical method needed to study and solve for the phase change heat transfer (melting of PCM) encountered in a LHESS during charging. The effective heat capacity method was applied in order to account for the large amount of latent energy stored during melting of the PCM and the moving interface between the solid and liquid phases. The effects of the heat transfer fluid (HTF) velocity on the melting rate of the PCM were studied for configurations having between 0 and 18 fins. Results show that the overall heat transfer rate to the PCM increases with an increase in the HTF velocity. However, the effect of the HTF velocity was observed to be small in configurations having very few fins, owing to the large residual thermal resistance offered by the PCM. However, the effect of the HTF velocity becomes more pronounced with addition of fins; since the thermal resistance on the PCM side of the LHESS is significantly reduce by the large number of fins in the system.     

Shell-and-tube type latent heat thermal energy storage: numerical analysis and comparison with experiments

The melting process of industrial grade paraffin wax inside a shell-and-tube storage is analyzed by means of numerical simulation and experimental results. For this purpose, the enthalpy porosity method is extended by a continuous liquid fraction function. The extended method is tested using results gained from a gallium melt test inside a rectangular enclosure.     

Experiments on thermal characteristics of a natural circulation loop with latent heat energy storage under cyclic pulsed heat load

 An experimental investigation has been made of thermal characteristics of a rectangular, annular single-phase natural circulation loop with the inner tube filled with a solid–liquid phase change material (PCM) under cyclic pulsating heat load. A rectangular, annular loop of 150 cm in height and 75 cm in width was constructed with an annular gap of 0.6 cm, within which water was filled. The inner tube of the annular loop was filled with a PCM (n-Eicosene) or air. Under the cyclic pulsating heat load, temperature field within the water-filled annular loop with PCM- or air-filled inner tube was found to evolve into a steady periodic variation for the range of parameters considered. The water temperature and/or its fluctuating amplitude along the heated or cooled sections of the loop with the PCM-filled inner tube were found to be markedly lower than those measured in the loop with the air-filled inner tube under the identical conditions. On the other hand, along the insulated sections of the loop a somewhat minute difference in temporal variations of the water temperatures exists between the loops with PCM- and air-filled inner tube. In addition, at the outer wall along the cooled section, a time-periodic variation of temperature was detected in synchronizing with the pulsating heat load. Parametric effects of varying amplitude and time-period of the pulsating heat input, as well as of varying the inlet coolant temperature of the cooling jacket were investigated. Received on 30 June 2000 The authors are grateful for the support for this study from National Science Council of Republic of China in Taiwan under the Project Nos. NSC87-2212-E006-054 and NSC88-2212-E006-022.     

3D numerical simulation on fluid flow and heat transfer characteristics in multistage heat exchanger with slit fins

In this paper, a numerical investigation is performed for three-stage heat exchangers with plain plate fins and slit fins respectively, with a three-dimensional laminar conjugated model. The tubes are arranged in a staggered way, and heat conduction in fins is considered. In order to save the computer resource and speed up the numerical simulation, the numerical modeling is carried out stage by stage. In order to avoid the large pressure drop penalty in enhancing heat transfer, a slit fin is presented with the strip arrangement of “front coarse and rear dense” along the flow direction. The numerical simulation shows that, compared to the plain plate fin heat exchanger, the increase in the heat transfer in the slit fin heat exchanger is higher than that of the pressure drop, which proves the excellent performance of this slit fin. The fluid flow and heat transfer performance along the stages is also provided.     

A numerical study of heat transfer during flow of melt in a cylindrical mould

A numerical analysis of transient heat transfer during the flow of a melt in a cylindrical mould is presented. The analysis includes thermal resistance at the melt-mould interface, and axial conduction inside both melt and mould. Energy equations are formulated in a domain that expands continuously due to the advance of the melt inside the empty mould, and solved by the finite difference method using a time-stepping procedure. Calculations are compared to existing analytic results. It is found that axial conduction in the melt can significantly influence the rate of heat loss from the flowing melt, and that analytic approximations, which neglect axial conduction, may give erroneous predictions for the rate of heat loss.     

Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins

Experiments were performed to determine the heat transfer and pressure drop characteristics in the entrance and fully developed regions of tubes with internal wave-like longitudinal fins. The test tube has a double-pipe structure, with the inner tube as an insertion. The wave-like fins are in the annulus and span its full width. Experiments were conducted for two cases: one with the inner tube blocked (no air flowing through it) and the other with the inner tube unblocked. The outer tube was electrically heated. Local and average heat transfer coefficients and friction factors were measured. The friction factor and Nusselt number correlations in the fully developed region were obtained in the Reynolds number range of 9×10² to 3.5×10³. It has been found that the wave-like fins enhance heat transfer significantly with the blocked case being superior. In addition, the in-tube heat transfer process is characterized by an earlier transition from laminar to turbulent flow and Reynolds number-dependent thermal entrance length. Received on 12 May 1998     

Effect of cavity aspect ratio on flow and heat transfer characteristics in pipes: a numerical study

Using the standard k–ε turbulence model, a two-dimensional turbulent pipe flow was simulated with and without square cavities. Effect of cavity aspect ratio on flow and heat transfer characteristics was investigated. Uncertainty was approximated through experimental validation and grid independence. The simulation revealed circulation inside the cavities. Cavity boundaries were shown to contribute significantly toward turbulence production. Cavity presence was shown to enhance overall heat transfer through the wall, while increasing pressure drop significantly across the pipe. It was predicted that cavities with higher aspect ratio enhance heat transfer more while increasing pressure drop.     

Three-dimensional numerical study of jet-in-crossflow characteristics at low Reynolds number

A numerical study of a square jet in a cross flow is carried out at a Reynolds number of 100. The flow field and heat transfer characteristic downstream of the jet have been explored by solving three-dimensional unsteady Navier–Stokes equations and energy equation using higher order spatial and temporal discretization. The projection of vortical structure on a plane is seen to give the component of vortex normal to the plane. Four combinations of velocity profile namely (1) uniform crossflow and uniform jet, (2) laminar boundary layer crossflow and uniform jet, (3) uniform crossflow and parabolic jet profile, and (4) laminar boundary layer crossflow and parabolic jet are compared at same phase to see their effect on the flow field and heat transfer characteristic. All the four cases are seen to exhibit unsteadiness but the jet with parabolic profile is seen to show stronger unsteadiness. The instantaneous vortical structures of all the cases at the same phase show that the structures are more complex for the jet with parabolic velocity profile. The temperature field is seen to be correlated with the vortical structures. Comparison of the time averaged flow field reveals that the jet penetration is the highest for the jet having parabolic profile and boundary layer crossflow. The adiabatic effectiveness is observed to be more for the jet with uniform velocity profile and uniform crossflow and was least for the jet with parabolic velocity profile and boundary layer crossflow.     

Nonstationary heat conduction in a half-space with an infinite number of cylindrical heat sources

The problem of nonstationary heat conduction is treated for a half-space containing an infinite number of cylindrical heat sources, and a boundary condition of the first kind at the surfaces. It is assumed that the radii of the sources are small in comparison with their spacing and the ordinate of the center.     

Experimental and numerical study on flow characteristics and heat transfer of an oscillating jet in a channel

A fluidic oscillator can produce self-induced and self-sustaining oscillating jet by fluid supply without moving parts. This device has attracted research interest in heat and mass transfer enhancement in recent years. In the current study, a double-feedback fluidic oscillator was numerically investigated based on three-dimensional unsteady Reynolds-averaged Navier-Stokes equations (3D-URANS) while the operating fluid is an incompressible flow. Then, the results were validated with experimental data by two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) and thermographic phosphor thermometry (TPT) for the velocity and temperature field, respectively. A grid sensitivity study was done by comparison of instantaneous and time-averaged flow fields. Additionally, the proper orthogonal decomposition (POD) method was used to find the phase information of the oscillating jet, and fast Fourier transform (FFT) analysis was used to find the frequency of the oscillating jet to validate the numerical results. The effect of the working fluid was also studied. Finally, in order to determine the effect of the Reynolds number on heat transfer enhancement, the Q-criterion was calculated to provide detailed insight into the oscillating mechanism. The results show that the non-dimensional frequency of oscillation is independent of either the working fluid or mass flow rate. Additionally, for a given fluid, increasing Re causes strong vortices and increases the frequency of oscillation. However, the convection heat transfer did not change significantly when varying the mass flow rate because the convection velocity of vortices increases as the mass flow rate is enhanced. A comparison with a free jet reveals that the oscillating jet in a channel is useful in terms of covering a larger area.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

Modeling of PCM-based enhanced latent heat storage systems using a phase-field-porous media approach

Continuum Mechanics and Thermodynamics - This paper introduces a numerical study of latent heat storage systems, based on phase-change materials (PCMs) with various heat transfer enhancement...     

Effect of porosity and the inlet heat transfer fluid temperature variation on the performance of cool thermal energy storage system

This paper discusses the results of numerical and experimental study of an encapsulated cool thermal energy storage system. The storage system is a cylindrical storage tank filled with phase change material encapsulated in spherical container, placed in a refrigeration loop. A simulation program was developed to evaluate the temperature histories of the heat transfer fluid and the phase change material at any axial location during the charging period. The present analysis aims at studying the influence of the inlet heat transfer fluid temperature and porosity on system performance. An experimental setup was designed and constructed to conduct the experiments. The results of the model were validated by comparison with experimental results of temperature profiles for different inlet heat transfer fluid temperatures and porosity. The results are in good agreement with the experimental results. The results reported are much useful for designing cool thermal energy storage systems.     

Determining modes and Grashof number in 2D turbulence: a numerical case study

We study how the number of numerically determining modes in the Navier–Stokes equations depends on the Grashof number. Consider the two-dimensional incompressible Navier–Stokes equations in a periodic domain with a fixed time-independent forcing function. We increase the Grashof number by rescaling the forcing and observe through numerical computation that the number of numerically determining modes stabilizes at some finite value as the Grashof number increases. This unexpected result implies that our theoretical understanding of continuous data assimilation is incomplete until an analytic proof which makes use of the non-linear term in the Navier–Stokes equations is found.      

Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli

The influence of various Prandtl numbers on the laminar convection flow between concentric and vertically eccentric cylinders is studied numerically. To overcome the difficulties associated with the complex physical domains a numerical transformation method is used to map this region on a rectangle. Although two independent computer programs which are based on different formulations of the governing equations were used, nearly identical results were obtained. Local heat transfer results are presented for a wide range of Rayleigh numbers for the first time. Local heat transfer rates are found to depend on the Prandtl number in addition to the Rayleigh number dependence.     

Numerical simulation for fin effect of a rectangular latent heat storage vessel packed with molten salt under heat release process

The present numerical study has dealt with the enhancement of latent heat Release by using plate type fins mounted on the vertical cooling surface in the rectangular vessel packed with molten salt as a latent heat storage material. It was found that the fin thickness and pitch exerted an influence on solidification heat transfer in a liquid layer of a nitric molten salt. The numerical results elucidated the flow pattern, velocity profile and heat transfer rate in the melted liquid layer.