Study of Thermal Behavior of a Horizontal Two Fins Annular Tube Heat Exchanger with Melting Phase Change Material: Fins Orientation Effects

Currently, the fossil fuels satisfy high percentage of the total energy needs, and their direct impact on the climate is alarming. For this reason, research on renewable energies is currently a major focus of development [1-3].

Due to its main advantages of abundance and environmental cleanness, solar energy, as renewable energy, is a promising energy resource. However, solar energy intensity is unstable with different times, weathers, and seasons, which can limit the application of solar thermal system in some specific regions. The efficiency of the system and its reliability are strongly ensured by an adequate choice of a heat storage system which remains a major problem for the solar thermal system. Recently, thermal energy storage systems, especially latent heat thermal energy storage (LHTES) in phase change materials (PCMs), have gained a greater attention from the viewpoint of global environmental problems and the energy-efficiency improvement. PCMs, as thermally active materials, are increasingly used in different engineering fields, such as: heat and cold storage, thermal insulation of buildings, passive air conditioning, heat recovery, refrigeration, solar thermal collector, thermal regulation of systems ..., etc. [4-9].

Various numerical models have been developed over the years for the solution of the phase change problem. Such interested in thermal energy storage systems can be subdivided into two classes.

The first one is focused on the effect of system geometry and the numerical calculation techniques. Among these works:

Darzi et al. [10] studied the melting process of n-eicosane as PCM inside a cylindrical concentric and eccentric double pipe heat exchanger. They reported that the melting rate is approximately the same for concentric and eccentric model before 15 min and after this time the melting rate decreases in the concentric case.

Seddegh et al. [11] investigated the two-dimensional melting process of paraffin wax (RT 50) in the annulus of two concentric tubes and heat transfer fluid (HTF) in the tube. They reported that the horizontal energy storage system has better heat transfer performance, in particular during part-load energy charging; however, the thermal behavior does not show any significant difference in the horizontal and vertical energy storage units in the discharge process.

Hong et al. [12] considered the melting of paraffin wax in two dimensional rectangular cavity with partially thermally active walls. They revealed that inclination angle, aspect ratio and number of discrete heat source have a significant influence on the time for complete melting.

Fadl and Eames [13] used Lauric acid as PCM to study the effect of mushy zone parameter on melting fraction and heat transfer characteristics. They found that proper selection of the mushy zone constant is essential for the accurate prediction of heat transfer characteristics within a PCM, where smallest values give unrealistic predictions of the melt front development and higher values delayed prediction of melting in the PCM.

Bouteldja et al. [14] investigated the effect of the aspect ratio and Grashof number on the convection diffusion phenomena associated with solid liquid phase transition processes during PCM solidification within a rectangular cavity. They reported that the solidification phase change process depends considerably on the thermal and geometrical parameters of the system. Additionally, it is demonstrated that the physical approach based on a purely conductive model remains valid to cases of low values of Grashof number and aspect ratio.

The second class of works aims to improve the efficiency of thermal storage systems where several technical solutions have been adopted. It consists in increasing the heat exchanges within PCM fluids by the incorporation of fins, the addition of nanoparticles, the simultaneous use of fins and nanoparticles or a porous medium. The published works can be grouped according to the adopted technique. We distinguish:

For the PCM-fins case:

Mat et al. [15] simulated a two-dimensional melting process of the RT82 as a PCM in a triplex-tube heat exchanger. They concluded that the complete melting using a triplex-tube heat exchanger with internal-external fins with the longest length fin was reduced to 43.3% compared with the triplex tube without fins.

 Al-Abidi et al. [16] analyzed the effect of two dimensional heat transfer enhancement for a triplex tube heat exchanger by using internal and external fins to accelerate the melting rate of RT82 as a PCM. They indicated that the effect of fin thickness is small compared to the fin length and number of fins.

Eslamnezhad and Rahimi [17] investigated the enhancement of heat transfer method using rectangular fins to melt the RT82 as phase-change material in a triplex tube heat exchanger. The predicted numerical results show that the impact of fin location on melting is very important in triplex type heat exchangers and the best fin arrangement could improve the melting time by 17.9%.

Joybari et al. [18] considered the simultaneous charging and discharging (SCD) of phase change material using RT31 inside triplex tube heat exchanger. They reported that depending on the initial PCM condition, different final solid-liquid interfaces were found, and the pure conduction model could be applied just for the initially fully melted PCMs under SCD.

Xu et al. [19] examined the temperature field of cold storage truck and cold storage plate of phase change material melting where NaCl is used as phase change material. They showed that the melting rate can be significantly increased with rise of environment temperature and the time of latent heat storage discharge will be shorter.

Talukdar et al. [20] investigated the charging and discharging of LHTES system which is an evaporator tube inside a PCM (water) filling a rectangular box. They indicated that faster solidification, as well as a higher energy storage capacity and heat flux during melting is found for the PCM pack of 6.5 cm thickness with higher number of fins.

For the PCM-nanoparticles case:

Arıcı et al. [21] discussed the melting of paraffin wax enhanced with Al₂O₃ nanoparticles in a square enclosure with partially thermally active walls. They concluded that the heat energy stored by PCM can be enhanced by changing orientation of thermally active walls of the enclosure, dispersing nanoparticules or applying both simultaneously.

Iachachene et al. [22] inspected the melting of paraffin wax in trapezoidal cavity. Grapheme nanoparticles were added to the phase-change materials to improve the system's efficiency associated with the orientation effect. It was observed that both effects are beneficial for heat transfer enhancements in PCMs.

Chamkha et al [23] investigated the melting process of a nano-enhanced phase change material in a square cavity with a hot cylinder located in the middle of the cavity in the presence of both single and hybrid nanoparticles. The authors showed that the solid-liquid interface and the liquid fraction are significantly affected by the volume fraction of nanoparticles and the thermal conductivity parameter.

Boukani et al. [24] investigated the melting of the nano-PCM of n-octadecane paraffin dispersed with Cu nanoparticles in partially filled horizontal elliptical capsules with different aspect ratios (AR). They concluded that for a given AR, the presence of nanoparticles enhances the melting rate and decreases the volume change of NePCM as compared to the pure PCM case.

For the PCM-fins-nanoparticles case:

Abdulateef et al. [25] analyzed the performance of a PCM triplex-tube heat exchanger using a combination of fins-nanoparticles. The results show that the external triangular fins-nanoparticle model which has fins number (8), fins length (141 mm) and fins aspect ratio (18%) considered the most efficient to minimize the melting and solidification times.

Mahdi et al. [26] investigated the heat transfer enhancement applying longitudinal fins with nanoparticles with a view to achieving better energy recovery process in the triplex-tube TES system. They found that the application of fins alone shows better enhancement than using either nanoparticles alone or combination of fins and nanoparticles.

Keshteli and Sheikholeslami [27] studied the solidification of RT82 within a three-dimensional triplex tube. The authors investigated the impacts of using nanoparticles, fins, and the combination of both of them on thermal characteristics during solidification in an energy storage unit. They found that using both nanoparticles and fins simultaneously has a significant impact on freezing time.

For the PCM-porous medium case:

Sardari et al. [28] investigated the effect of a high conductivity porous medium for the copper foam LHTES system. They reported that the presence of a porous medium increases the heat transfer significantly, but the improvement in melting performance is strongly related to the system’s dimensions.

Huo et al. [29] employed the porous medium to enhance the heat transfer of the PCM. They investigated the effects of the Rayleigh number and porosity on the heat transfer process in battery thermal management (BTM). The results show that decreasing the porosity will accelerate the melting rate. When the porosities are 0.9, 0.8, 0.7, and 0.6, the total melting times are decreased by 23.7%, 43.3%, 58.0%, and 75.4%, compared with pure PCM.

Mehryan et al. [30] examined the melting process of a PCM inside an inclined compound enclosure partially filled with a porous medium. They showed that the rates of melting and heat transfer are enhanced as the thickness of the porous layer increases. The melting rate is the highest when the inclination angle of the enclosure is 45°. An increase in the wall thickness improves the melting rate.

Shahsavar et al. [31] performed a numerical investigation for evaluating the impact of porous medium and surface waviness on the melting and solidification of composite PCM in a vertical double-pipe LHTES. Their results indicated that the total melting and solidification time can be significantly reduced by up to 91.4% and 96.7% when using porous structures with high conductivity and wavy channel, respectively.

The present numerical study investigated the heat transfer during PCM melting in a horizontal annular tube heat exchanger. Two geometrical models, based on horizontal and vertical fins, respectively, are considered. The effect of fins orientation on the melting process were developed and studied. Liquid fraction, streamlines and temperatures contours are illustrated. Heat flux and heat transfer coefficient are presented and compared.

The paper is structured as follows: Section 2 describes the physical model. Section 3 presents the mathematical formulation and numerical method used for the computation and the validation. The numerical results are discussed in Section 4. Finally, concluding remarks are presented in Section 5.

3.1 Assumptions

The mathematical formulation of the melting process of the PCM inside the annulus cylinder is expressed under the following assumptions:

The flow is Newtonian, two-dimensional, laminar, unsteady and incompressible. The viscous dissipation is negligible. Boussinesq approximation is applied for buoyancy effects. The superheat and the volume expansion due to phase change are negligible.

3.2 Mathematical modeling

The melting problem is formulated using the enthalpy porosity method [10]. Under the prescribed assumptions, the model equations expressed in Cartesian coordinates system are as follows:

Continuity equation:

$\frac{\partial \rho}{\partial t}+\frac{\partial(\rho u)}{\partial x}+\frac{\partial(\rho v)}{\partial y}=0$    (1)

x-momentum equation:

$\frac{\partial(\rho u)}{\partial t}+\frac{\partial(\rho u u)}{\partial x}+\frac{\partial(\rho u v)}{\partial y}=\frac{\partial}{\partial x}\left(\mu \frac{\partial u}{\partial x}\right)$

$+\frac{\partial}{\partial y}\left(\mu \frac{\partial u}{\partial y}\right)-\frac{\partial p}{\partial x}+\rho g_{x}+S_{x}$    (2)

y-momentum equation:

$\frac{\partial(\rho v)}{\partial t}+\frac{\partial(\rho v u)}{\partial x}+\frac{\partial(\rho v v)}{\partial y}=\frac{\partial}{\partial x}\left(\mu \frac{\partial v}{\partial x}\right)$

$+\frac{\partial}{\partial y}\left(\mu \frac{\partial v}{\partial y}\right)-\frac{\partial p}{\partial y}+\rho g_{y}+S_{y}$    (3)

Energy equation:

$\frac{\partial(\rho h)}{\partial t}+\frac{\partial(\rho u h)}{\partial x}+\frac{\partial(\rho v h)}{\partial y}+\frac{\partial(\rho \Delta H)}{\partial t}$

$=\frac{\partial}{\partial x}\left(k \frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(k \frac{\partial T}{\partial y}\right)$    (4)

In these equations, u is the x-axis velocity component, u the y-axis velocity component, r the PCM density, m the dynamic viscosity, p the pressure, g the gravitational acceleration and k the thermal conductivity. The quantity H is the enthalpy of a control volume subjected to phase change. It is equal to the sum of sensible heat enthalpy (h) and the latent heat enthalpy (DH), defined as:

$h=h_{\text {ref }}+\int_{T_{\text {ref }}}^{T} c_{p} d T$    (5)

$\Delta H=\phi L$    (6)

$H=h+\Delta H$    (7)

where, h_ref is the reference enthalpy at the reference temperature T_ref, c_p the specific heat, L the latent heat of the PCM. The reference temperature is generally chosen equal to liquidus temperature (T_liq) where melting PCM and consequently buoyancy effects are present.

In momentum equation, Boussinesq approximation was introduced to account for the natural convection process in the melted PCM [11]:

$\rho=\rho_{l}\left[1-\beta\left(T-T_{l}\right)\right]$    (8)

and the source term is expressed as:

$\left\{\begin{array}{l}S_{x}=-A(\phi) u \\ S_{y}=-A(\phi) \cup\end{array}\right.$    (9)

where, f is the ratio between the molten PCM volume and the total volume of PCM in a computational cell, respectively.

$\left\{\begin{array}{l}\phi=0 \text { if } T \leq T_{\text {sol }} \\ \phi=\frac{T-T_{\text {sol }}}{T_{\text {liq }}-T_{\text {sol }}} \text { if } T_{\text {sol }} \prec T \prec T_{l i q} \\ \phi=1 \text { if } T \geq T_{l i q}\end{array}\right.$    (10)

and A is the porosity function, defined as [35]:

$A(\phi)=\frac{C(1-\phi)^{2}}{\phi^{3}+\varepsilon}$    (11)

C is a constant that reflect the mushy zone morphology. It describes how steeply the velocity is reduced to zero when the material solidifies. This constant is situated between 10⁴-10⁷, so 10⁵ is considered for this work [36]. ε is a small number (0.001) to prevent division by zero.

3.3 Initial and boundary conditions

In all three considered cases, the outer surface of the annulus heat exchanger is adiabatic. The PCM is initially solid and subcooled at 23℃. The inner wall temperature of cylinder and fins are fixed to 70℃. The impermeability and no-slip boundary conditions were applied at the annulus walls (u= u= 0).

3.4 Numerical procedure and validation

The numerical solution of the developed model was conducted using Ansys Fluent. It uses the finite volume method [37] and the enthalpy-porosity technique for modeling the solidification/melting process.

In this enthalpy approach, the liquid volume fraction in each control volume is calculated at each iteration. When the region is entirely solid, the porosity is zero and also the flow velocity in that zone also drops to zero. The transient discretization is based on the second order-upwind scheme. Semi-implicit pressure-linked equations (SIMPLE) algorithm was used for pressure-velocity coupling and PRESTO for pressure correction.

Three simulations of different time step sizes (0.1 s, 0.05 s, 0.01 s) were investigated (Figure 3), a time step of 0.05 s was finally selected to achieve the convergence criteria (10^-4), as 0.01s and 0.05s produce nearly same results.

in order to check mesh independency, the results of the instantaneous PCM mean temperature were obtained by different grid sizes for each model and presented in Table 2. The final grid resolution considered for each case was summurized in Table 3.

3.png

Figure 3. Time step optimization

Table 2. Grid size independency verification for the studied cases based on PCM mean temperature with 0.05 s time step

Table 3. Grid resolution used for each case.

First, experimental data from an earlier study [15] was used for validation of the melting process.

In the experiment the melting process was in a triplex-tube heat exchanger with internal and external fins to enhance the heat transfer. The HTF and PCM are water and paraffin RT82 (Rubitherm Technologies GmbH). Initial average temperature of the PCM was 27℃ with phase change temperature range of 77-85℃, whereas the HTF temperature was maintained at 90℃.

Figure 4 compares the simulated PCM average temperature with the experiment of a triplex tube heat exchanger. A good agreement can be seen from the comparison, which verifies the reliability of the numerical model for solving the phase change problem.

Additionally First, the numerical predictions are validated by comparison with numerical results from the literature [10]. Good agreement is obtained as can be seen on Figure 4 for melt fraction versus time.

4.png

Figure 4. Comparison of the numerical predictions with experimental data (Mat et al. [15]) and numerical results (Darzi et al. [10])

Heat transfer enhancement for an annular heat tube exchanger by using fins to accelerate the melting rate of n-eicosane as a PCM was investigated numerically.

For the numerical analysis, the enthalpy-porosity formulation was used for modeling combined convection-diffusion phase change; this method found the melting front within the PCM over time. The model predicts the effect of using metal fins to enhance the heat transfer and the effect of their orientation (horizontal and vertical case) on the thermal performance.

Different parameters including PCM average temperature, liquid fraction, heat flux and heat transfer coefficient were analyzed.

The numerical results of the melting process have shown that primary heat conduction is the dominant heat transfer mechanism. The thermal behavior at this stage does not show any significant difference in two cases. With the increase of melted region, natural convection becomes dominant and plays the key role for the melting process. The upward melted PCM motion greatly affected the upper half of the system. This, results in a faster melting progress at the top of the annulus compared to the bottom. In horizontal fins case, the fins block the heat moving to the top section and hence resist natural convection that occurs during the charging; hence such configuration was not helpful for the melting process.

By use of this experience and considering the fact that the PCM material in the lower part of the heat exchanger is the last part which melts, allocating fins to the lower half make the melting quicker and the heat transfer enhanced. Vertical fins have been introduced. This geometry has improved the melting time. The complete melting time using vertical fins orientation was reduced with a factor 2.5 compared to horizontal case.