Numerical simulation on the effect of latent heat thermal energy storage unit

Abstract

Keywords: Latent heat; Thermal storage; Phase change material PCM; Numerical simulation; Flow distribution

Introduction

Solar radiation is intermittent by its nature. Its total available value is seasonal and dependent on the meteorological conditions of the location. Thermal Energy Storage (TES) is necessary for effective utilization of such energy source, to meet demand on cloudy days and at night. TES, therefore, plays an important role in conserving thermal energy, leading to an improvement in the performance and reliability of a range of energy systems. The heat storage occurs in the form of latent heat, sensible heat, or both. Compared with other heat storage methods, advantages of latent heat storage materials are that heat storage and delivery occur in a narrow temperature interval corresponding to their phase transition temperature and significantly smaller volume change before and after phase transition process. 599

Analysis

applications. Rathod [5] was reported a detailed review for thermal stability of different groups of PCMs. The PCMs are categorized as organic (paraffins and non-paraffins), inorganic (salt hydrates and metallics) and eutectics (organic eutectics and inorganic eutectics). Further, a broad database of different PCMs is developed for which thermal cycling tests were carried out by different researchers and reported in the literature. Soares [6] provides a comprehensive review on previous studies related to the evaluation of how and where, PCMs are used in passive latent heat thermal energy storage systems, and how these construction solutions are related to building’s energy efficiency. It was concluded that PCM can contribute to increase indoor thermal comfort, reduce energy consumption and contribute for the reduction of CO2 emissions associated to heating and cooling. Selka et al. [7] was presented a 2D numerical study of using PCM a phase change material to improve thermal performance of building in Tlemcen city. A specific paraffin material was placed in brick wall to reduce the room temperature during a daytime. The numerical results show a significant temperature reduction inside the studied solar test room, about 6°C to 8°C and therefore, the energy consumption due to air conditioning is reduced which provides benefits to economic and environmental aspects. After, the same authors was presented a 2D model with a real size home composed of two-storey (ground and first floor spaces) separated by a slab, enveloped by a wall with rectangular section containing PCM [8]. The numerical results showed that the model can reduce the room temperature by about 6 to 7°C of temperature depending on the floor level (first floor spaces or ground floor spaces). Castel [9] was presented an experimental study of a PCM tank for cold storage applications. It was also demonstrated that coil in tank designs are effective at delivering a constant outlet temperature and effective heat transfer with large surface areas. Darzi [10] was simulated plate type PCM storage numerically used in free cooling system. Results showed that increasing the Stefan number causes the increase of the cooling power and the outlet air temperature. Omojaro [11] was reported an experimental and modeling results on the transient performance of a latent thermal energy storage (PCM) heat exchanger under simultaneous charging and discharging operation. The simultaneous operation mode stores lesser energy based on the temperature difference but has 13% higher thermal efficiency for the operation set time. The study presented by Charzat [12] was to develop and validate a simulation model for the heat storage units comprising compact storage module panels filled with PCMs. The study showed that latent heat storage offers certain advantages over sensible heat storage and it attracts more attention even in the areas where it was not considered in the past. The major objective of the present study is to investigate the effect of PCM on the performance of the latent heat thermal energy storage system for water heating applications. The effects of the PCM quantity, number of pass and fluid flow rate have been analyzed during charging and discharging processes.

Mathematical

System description TABLE 1. PHYSICAL PROPERTIES OF SP22A17 [13].

Parameters Density ρ [kg/m3] Heat capacity cp [J/Kg K] Conductivity λ [W/mK] Latent heat Lf [J/kg] Solidus temperature [K] Liquidus temperature [K] Viscosity µ [kg/ms] Thermal expansion [K-1] Reference temperature de Tref [K]

The physical model studied is a 2D exchanger filled with PCM (code SP22A17) from Rubitherm. This is a Hydrated Salt and Paraffin Wax Combination. A water tube passes through inside the PCM to store heat latent during sunny periods and recover it during deficit periods. The copper tube has a diameter of 14 mm and the thickness is assumed negligible. The geometric parameters of the model are shown in Fig.1. For the water tube, the radius of the outer arc is 48 mm and of the inner arc is 20 mm. The thermo-physical properties of SP22A17 are given in table (1). 10 14

FIG. 1. GEOMETRIC CONFIGURATIONS OF THE STUDIED PROBLEM [mm].

Conservation of energy The thermodynamic properties of PCM are supposed to be independent of temperature. The theory of mixtures is used to define the physical properties in a two-phase domain through a volumetric liquid fraction f l , where 0 ≤ f l ≤ 1 . This gives ( l and s design the liquid and solid phases):

 ∂ 2u ∂ 2u   ∂u ∂u ∂u  ∂p  = − +u +ν + µ  2 + 2  + Su  ∂x ∂x ∂y  ∂x ∂y   ∂t 

To simulate the process of heat transfer with phase change, a single domain enthalpy method is used. The enthalpy of the material is defined as the sum of sensible heat h = c pT and

 ∂ 2v ∂ 2v   + ρgβ (T − Tref ) + Sv + µ +  ∂ 2 x ∂y 2   

∆H = fl Ls where Ls is the latent heat of solidification and

Where u the x-velocity component, v the y-velocity component, P the pressure, T the temperature, Tref the reference temperature, H the enthalpy, μ the dynamic viscosity, g the gravitational acceleration, β the thermal expansion coefficient. Darcy source term (Su and Sv) automatically ensures that the velocity in the fully solidified control volumes vanishes [14-15].

liquid fraction with value 1 representing liquid state and 0 for solid state. In general the local liquid fraction will depend on the nature of solidification. To simplify and focus subsequent discussions in the current work, the liquid fraction is taken to be a function of temperature alone. Different forms have been proposed for the relationship between the liquid fraction and the temperature. One of the simple forms is a linear relationship [14-15]:

Initial and boundary conditions: At the entrance of the channel a fixed mass flow (0.01 kg/s.) and temperature (313 K charged period and 293 K during discharged period) are imposed. At the exit, a fully developed flow is assumed by imposing a zero gradient of all variables:

The source term ST which embodies the latent heat of fusion can be derived to be

where Tℓ and Ts are, respectively, the liquidus and solidus temperature. The conservation of thermal energy in the process can be expressed in terms of temperature in the form [14-15]:  ∂T 2 ∂T 2   ∂T ∂T ∂T  + S  = λ  +u +v +  ∂x 2 ∂y 2  T ∂x ∂y   ∂t  

A is the porosity and ε is a small positive number introduced to avoid division by zero.

Momentum equation The momentum equation of the fluid flows is governed by the unsteady Navier-Stokes equations in the Boussinesq approximation. In order to consider the phase change, we utilize Darcy's source term for handling the fluid flow in the solidifying molten metal pool. With the assumption of the constant density, the momentum equation in the liquid saturated porous medium can be expressed as the following form

Results And Discussions

The commercial FLUENT 6.3.2 software package was used for solving the set of governing equations. The numerical method employed is based on the finite volume approach. Fluent provides flexibility in choosing discretization schemes for each governing equation. The discretized equations, along with the initial condition and boundary conditions, were solved using the segregated solution method. Using the segregated solver, the conservation of mass and momentum were solved sequentially and a pressure-correction equation was used to ensure the conservation of momentum and the conservation of mass (continuity equation). A second-order upwind discretization scheme was used for the momentum equation. These schemes ensured, in general, satisfactory accuracy, stability and convergence. SIMPLE algorithm was used for pressure-velocity coupling. The discretized equations are solved implicitly in sequence, starting with the pressure equation followed by the momentum equations, by the pressure correction equation, and finally by the energy equations. The convergence criterion was set equal to 10-4 for all parameters. Before the numerical analysis, the grid-independency of the exchanger system was simply checked using a different number of grids. The system was finally divided into 9271 nodes corresponding to 8727 cells in consideration of grid-independency and calculating efficiency. In order to validate the developed algorithm, the heat transfer in PCM storage with internal fins for a two-dimensional case is solved numerically and the results are compared with those obtained analytically [16]. Fig. 2 show the comparison between the evolutions of the solid–liquid interface during time obtained numerically and predicted analytically by [16]. A comparison shows that there is excellent correlation between the results. This underlines the good accuracy of the method proposed in this work.

the quantity of PCM was divided by two. Fig. 3 shows the effect of the PCM thickness on the liquid fraction evolution according to time during the storage phase. The blue color indicates the solid region (ƒℓ = 0) and the red one indicates the liquid region (ƒℓ = 1). During the storage phase, the initial temperature at all region is 293 K. At the entry, the temperature is fixed at 313 K with a mass flow of 0.01 kg/s. At t = 5 min, in the two configurations the fusion of the PCM starts in the vicinity of the entry which represents the thermal source of the exchanger. At t = 30 min, the fusion front reaches the bottom of the channel in the configurations (a) and (b). At t = 40 min, the fusion reaches 56% in the configuration (b) and 28% in the configuration (a). This percentage reaches 80% in the configuration (b) and 42% in the configuration (a) after 60 min. At t = 80 min, the fusion is complete in the configuration (b). In the configuration (a), the fusion reaches a percentage of 53%. At t = 60 min, the mass of the molten PCM reaches 12.77 and 12.24 kg in the configuration (a) and (b), respectively. Then, the increases of the PCM thickness (its quantity in the exchanger) do not influence considerably the storage speed (quantity of the PCM melted per second).

Fraction Evolution The During The Storage

Analytical 400 s Analytical 800 s Numerical 400 s Numerical 800 s

PHASE. Fig. 4 shows the effect the PCM thickness on the temperature evolution vs. time during the storage phase. At t = 5 min, the two exchangers configurations are still out service since the outlet water temperatures are 293.15 K in the configuration (a) and 293,53 K in the configuration (b). Advancing in time, water warms up more and the PCM starts to store heat. After 30 min, the outlet water temperature increase in the configuration (b) and reaches 295.60 K, whereas the configuration (a) still out service and outlet temperature is 293.24 K. Since the PCM quantity used in the configuration (b) is less important than in the configuration (a), the PCM absorbs more heat from water in the configuration (a) and the outlet

FIG.2. COMPARISON BETWEEN NUMERICAL AND ANALYTICAL POSITION OF SOLID–LIQUID INTERFACE.

Charging phase We propose to study the effect the PCM thickness (quantity) contained in the exchanger. In the configuration (b) 602

temperature increases less rapidly. The same phenomenon is observed during time and at t = 80 min, the outlet water temperature reaches 296.81 K in the configuration (b) and 294.50 K in the configuration (a). The increase of the PCM quantity used influences considerably the outlet water temperature where the reduction reaches 2.31°C during 80 min of storage phase (temperature reduction speed is 1.73 °C/h). Finally, we can say that the configuration (b) is more dynamic when the configuration (a) stores more heat. Then, the configuration (b) is more adapted in zones with low solar radiation and the configuration (a) with high solar radiation.

Liquid Fraction Evolution During The

FIG. 4. EFFECT OF THE PCM THICKNESS ON THE TEMPERATURE [K] EVOLUTION DURING THE STORAGE PHASE. The Fig. 5 shows the effect of the number of pass on the liquid fraction evolution vs. time during the storage phase. At t = 30 min, the PCM fusion percentage reaches 9.81% in the configuration (c) corresponding to 5.59 kg of PCM liquid mass. In the configuration (a), 21% of the PCM is molten offering

Liquid Fraction Evolution During The

STORAGE PHASE (a) 0.01 kg/s AND (d) 0.02 kg/s. The Fig. 7 shows the effect of water mass flow on the liquid fraction evolution vs. time during the storage phase. At t = 5 min, the fusion of the PCM starts near the entry in the two configurations. At t = 30 min, the fusion of the PCM reaches 38% in the configuration (d) corresponding to a PCM liquid mass of 11.6 kg. In the configuration (a) 21% of the PCM is molten offering 6.32 kg of PCM liquid. Thus, the fusion process is accelerated in the configuration (d). Percentage of the molten PCM reaches 71% in the configuration (d) and 42% in the configuration (a) after 60 min. At t = 135 min, fusion process is complete in the configuration (d) but 79% of fusion is reached in the configuration (a). Then, there is an improvement of almost 3.4 kg in molten PCM corresponding to a 510 kJ of thermal energy stored in latent heat form (an improvement of 226.66 kJ/h). Fig. 8 shows the effect of the water mass flow on the temperature evolution vs. time during the storage phase. At t = 5 min, the water temperature in the channel starts to warm up in the two configurations that still out service since the outlet water temperatures are 293.15 K and 293.24 K in the configuration (a) and (d), respectively. At t = 30 min, the outlet temperature increases in the configuration (d) and reaches 296.57 K, whereas the configuration (a) is still out service with an outlet temperature of 293.24 K. The same phenomenon is observed during the all storage period and at 135 min the

Discharging phase: The study of the discharging phase is started at the end of the charging (storage) phase.

FIG. 9. EVOLUTION OF SOLIDIFICATION PROCESS VS. TIME DURING DISCHARGING PHASE.

The Fig. 9 shows the evolution liquid fraction vs. time during discharging phase. At t = 315 min, a fixed temperature of 285 K is imposed at the entry of the channel with a mass flow of

Share and Cite