**2. Validation of the FLUENT model with the experimental case study by Lacroix**

Lacroix [26], conducted a series of experiments to study the heat transfer performance of the shell-and-tube thermal storage unit using PCM. The PCM installed on the shell side, while the Heat Transfer Fluid (HTF) flowing inside the tube. The effects of several thermal and geometric parameters on the heat process were investigated. The schematic diagram of the model is presented in **Figure 1**. The PCM fills the shell with the diameter of De, whereas the HTF flows through the tube with a diameter of Di. The PCM is commercially available material *n-Octadecane*. The thermophysical properties of the *n-Octadecane* are presented in **Table 1**.

**Figure 2** illustrates the test unit scheme. Two concentric tubes were used. The inner tube (Di = 12.7 mm, Do = 15.8 mm, and L = 1 m) is made of copper, and

**Figure 1.**

*Schematic representation of the test unit.*


#### **Table 1.**

*Thermo-physical properties of the* n-Octadecane *[27–29].*

**Figure 2.** *Experimental test unit.*

outside tube (Di = 25.8 mm, and L = 1 m) is made of Plexiglas. Thick pipe insulation (Rubates Armstrong Armflex II) was used to isolate the system. The space between two tubes was filled with *N-Octadecane as a PCM,* while water was used as an HTF. An electrical heater inside a tank was used to maintain the inlet temperature of the HTF. Then, the HTF was circulating inside the copper tube with the mass flow ranging from 0.03 to 0.07 kg/s. Three thermocouples were used to record the temperature inside the PCM at different locations. Further, two thermocouples being used to record the inlet and outlet temperature of the HTF. A data acquisition unit was used to record the thermocouples signals into a PC. Finally, the storage unit was positioned vertically to depress the natural convection effects on the heat transfer inside the system.

For the validation purpose, Lacroix's experiments were numerically restudied using the ANSYS FLUENT software. In the preliminary simulations, different grid sizes and time steps were carefully examined to obtain computational grid convergence. The computational grid was constructed using 282504 hexahedral elements and boundary layers were used surrounding the pipe. Transient simulations were run using the *k-epsilon* turbulence model and the time step used in calculations was set to 0.1 s. To study the phase change phenomena in the PCM, the solidification/ melting model was enabled. The first-order upwind spatial discretization and the pressure solver with the PRESTO algorithm for pressure–velocity coupling were selected to obtain a converged solution. Convergence criteria were established by setting the absolute residual values to 10�<sup>6</sup> for energy and 10�<sup>3</sup> for all other variables. Zero heat flux boundary conditions were set on all sides of the shell. The mass flow rate and temperature of the HTF were specified at the inlet of the copper pipe. The mathematical formulations for solving PCM related problems have been categorized [30] as fixed grid, variable grid, front-fixing, adaptive grid generation, and enthalpy methods. Two methods are used to analyse the heat transfer in solid-liquid PCMs. These are the temperature-based and enthalpy-based methods. In the former, temperature is considered to be a single dependent variable. The energy equations for both solid and liquid are formulated separately; and thus the solid-liquid interface positions can be tracked easily to achieve an accurate solution for the problem [31, 32].

An enthalpy-porosity method is used for modelling the solidification/melting process [33]. This technique is described in detail by Voller and Prakash [32, 34].

The energy conservation equation for this case is written as:

$$\frac{\partial}{\partial t}(\rho H) + \nabla.\left(\rho \overrightarrow{v} H\right) = \nabla.(k \nabla T) + \mathcal{S} \tag{1}$$

*CFD Model of Shell-and-Tube Latent Heat Thermal Storage Unit Using Paraffin as a PCM DOI: http://dx.doi.org/10.5772/intechopen.95847*

The enthalpy of the material is calculated as the sum of the sensible heat, *h*, and latent heat, *ΔH*:

$$H = h + \Delta H \tag{2}$$

The sensible heat is calculated as:

$$h = h\_{\rm ref} + \int\_{T\_{\rm rf}}^{T} c\_p dT \tag{3}$$

The latent heat is also calculated as:

$$
\Delta H = \beta\_l L \tag{4}
$$

The liquid fraction, *βl*, can be calculated as:

$$\begin{aligned} \beta\_l &= 0, when \ T < T\_{solid} \\ \beta\_l &= 1, when \ T > T\_{solid} \end{aligned} \tag{5}$$

$$\beta\_l = \frac{T - T\_{solid}}{T\_{liquid} - T\_{solid}} \quad \text{if } T\_{solid} < T < T\_{liquid}$$

The solid and liquid temperatures are also calculated as

$$T\_{solid} = T\_{melt} + \sum\_{solute} K\_i m\_i Y\_i \tag{6}$$

$$T\_{liquid} = T\_{melt} + \sum\_{s \text{solute}} m\_i Y\_i \tag{7}$$

The source term in the momentum equation can be written as [33]:

$$S = \frac{(1 - \beta)}{\left(\beta\_l^{\ 3} + \epsilon\right)} A\_{mush} \left(\overrightarrow{v} - \overrightarrow{v}\_p\right) \tag{8}$$

Due to Darcy's law damping terms as a source term are added to the momentum equation because of the effect of phase change on convection, whereas *ε* is a small constant number (0.001) used to prevent division by zero and *Amush* is the mushy zone constant. Values between 10<sup>4</sup> and 10<sup>7</sup> are recommended for most computations [33]. In the present study, the mushy zone was set to 10<sup>5</sup> . *v* ! *<sup>p</sup>* is the solid velocity due to pulling solidification materials out of the domain; and in the present study, pull velocities are not included in the solution and so *v* ! *<sup>p</sup>* is set to zero. More details about the numerical model can be found at [32].

The liquid velocity can be calculated by the following Equation [33]:

$$\overrightarrow{v}\_{liq} = \frac{\left(\overrightarrow{v} - \overrightarrow{v}\_p(\mathbf{1} - \beta\_l)\right)}{\beta\_l} \tag{9}$$

The validation of the CFD model was carried out by comparing numerical results from ANSYS FLUENT to experimental data obtained by Lacroix [26]. The comparison was carried out for three different cases during the melting process. These are for three different HTF inlet temperatures above the melting temperature of *n-Octadecane* by 5, 10 and 20 K*.* The HTF mass flow rate was maintained at a constant value of 0.0315 Kg/s. **Figures 3**-**5** show the temporal temperature variations in the experiment and CFD data at locations T1 (h = 0.51 m, r = 0.002 m) and T2 (h = 0.95 m, r = 0.001 m) inside the PCM. It is clearly shown that the predicted numerical results of the temperature follow the experimental trend in Lacroix [26]. The main discrepancies between the

**Figure 3.**

*The variation of the predicted and experimental temperature at locations T1 and T2 (Tin = Tm + 20 K), the mass flow rate = 0.0315 kg/s.*

**Figure 4.**

*The variation of the predicted and experimental temperature at locations T1 and T2 (Tin = Tm + 10 K), the mass flow rate = 0.0315 kg/s.*

**Figure 5.**

*The variation of the predicted and experimental temperature at locations T1 and T2 (Tin = Tm + 5 K), the mass flow rate = 0.0315 kg/s.*

*CFD Model of Shell-and-Tube Latent Heat Thermal Storage Unit Using Paraffin as a PCM DOI: http://dx.doi.org/10.5772/intechopen.95847*

numerical and experimental results can be attributed to the measurements uncertainties and the difference in the PCM physical properties in the solid and liquid phase. Furthermore, CFD numerical results on the evolution of the liquid fraction in the PCM were compared with calculations of Lacroix [26]. **Figure 6** shows the variation of molten volume fraction of the PCM in the test unit as a function of time. The outer diameter (*De*) of the storage unit is 22 mm, the inside tube diameter (*Di*) is 12.7 mm, and the storage length (*L*) is 1 m. The HTF mass flow rate in simulations ranges from 1.5 <sup>10</sup><sup>4</sup> to 1.5 <sup>10</sup><sup>2</sup> and the HTF inlet temperature was 20 K above the PCM melting temperature. It can be seen in **Figures 7**-**9**, the current CFD results

**Figure 6.**

*The CFD liquid fraction variation in time against the numerical liquid fraction from [26] at several mass flow rate.*

**Figure 7.**

*Temperature distribution in the PCM for (A) bottom section plane, (B) middle section plane, and (C) top section plane (Tin = 320 K, HTF mass flow rate = 0.0315Kg/s., the elapsed time is 350 sec).*

#### **Figure 8.**

*PCM temperature versus time at the different radial positions: R = 0.001, 0.002, and 0.004 m from the axis of the computational domain at y = 0.5 m,Tin = 320 K, HTF mass flow rate = 0.0315Kg/s.*

#### **Figure 9.**

*PCM temperature versus time along the axis (y = 0.05, 0.49, and 0.95 m) for the radial distances z = 0.001 and 0.004 m,Tin = 320 K, HTF mass flow rate = 0.0315Kg/s.*

are in a very good agreement with calculations of Lacroix [26]. In general, comparison of CFD results with results presented in Lacroix [26] demonstrated that the developed CFD model accurately describes processes taking place in the experimental test rig and therefore can be used with confidence for further transient heat transfer simulations in the shell-and-tube latent thermal storage unit.
