Experimental and Numerical Investigation of the Effect of PCM Mass on Thermal Storage Capacity, Heat Retention, and Discharge Performance of Parabolic Trough Collector

2.1 Experimental

The experiments were conducted in Kirkuk, Iraq, located at approximately 35° N and 45° E. Data were collected from 8:00 AM to 8:00 AM the following day.

2.2 Experiment conditions

The experiments were performed in Kirkuk city, Iraq (≈ 35° N 45° E), and data collection was done from 8 am to 8 am of each subsequent day. Experiments were performed in real outdoor climatic conditions during April in Kirkuk, Iraq. Testing began with the 10 kg PCM case, and then the 20 and finally the 30 kg cases were sequentially tested in the same storage tank and system configuration. The HTF flow rate was kept constant at 1 L/min for all tests.

Because the experiments were performed outdoors, solar radiation and ambient temperature varied naturally during the test period; therefore, these parameters were recorded for each experimental run to account for climatic variations when interpreting the effect of PCM mass. The detailed operating and climatic conditions are presented in Table 1.

Table 1. The operating and climatic conditions in the current experiments

2.3 Experimental setup

The experimental system comprised a PTC, a PCM storage unit with a helical-coil heat exchanger, a pump, a flow meter, a water storage tank, and an Arduino-based data acquisition system, as shown schematically in Figure 1(a) and photographically in Figure 1(b). Water was used as the HTF. Table 2 describes the main specifications of the experimental rig.

Table 2. Main specifications of the experimental system

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Figure 1. Experimental parabolic trough collector–phase change material (PTC–PCM) thermal energy storage system: (a) schematic diagram, (b) photograph of the fabricated experimental setup

2.4 Phase change material storage unit

The cylinder-shaped thermal energy storage unit was integrated with the PCM to improve the PTC system's thermal energy storage capacity. This thermal energy storage tank was fabricated using steel due to its mechanical strength and durability. Its height was 40 cm, while the outer diameter was 40 cm. Paraffin wax was chosen as the PCM owing to its high latent heat storage capacity, stability, compatibility, and suitable melting point for the production of domestic hot-water. Some of the main characteristics of the PCM utilized are presented in Table 3. The 30 kg PCM mass was adopted as the full nominal PCM charge of the fabricated storage unit. Accordingly, 10 and 20 kg were selected to represent approximately one-third and two-thirds of this nominal capacity, respectively. These three loading levels provided low, intermediate, and full PCM quantities while maintaining the same storage-tank geometry, double-helical-coil configuration, PCM type, and operating conditions. This selection enabled isolation of the effect of PCM mass and provided a practical basis for evaluating the trade-off among thermal storage capacity, thermal response, and heat-supply duration. The HTF circulated through a double-helical copper-coil heat exchanger embedded in the PCM storage tank, as shown in Figure 2. This arrangement was chosen due to its higher heat-transfer characteristics and better temperature distribution than the straight tubes [23]. The tank was thermally insulated to minimize heat losses. K-type thermocouples connected to MAX6675 modules monitored the water temperatures at the PTC inlet and outlet, the absorber-tube surface temperature, the coil inlet and outlet temperatures, the PCM temperature at different locations within the storage unit, and the storage-tank inlet temperature, as indicated in Figure 2.

Table 3. Thermophysical properties of paraffin wax used as phase change material (PCM) [24]

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Figure 2. Schematic diagram of the phase change material (PCM) thermal energy storage unit with thermocouple locations

2.5 Thermal energy analysis

The theoretical amount of heat stored in the PCM was calculated using Eq. (1).

$\begin{gathered}Q_{\text {stored}}=m_{\text {pcm}}\left[c p_{\text {pcm}, s}\left(T_m-T_i\right)+H_{\text {pcm}}\right.\left.+c p_{\text {pcml}}\left(T_f-T_m\right)\right]\end{gathered}$       (1)

where, $m_{p c m}$ is the PCM mass, $H_{p c m}$ is the latent heat of fusion, $T_i, T_m$, and $T_f$ are the initial, melting, and final temperatures, respectively, and $c p_{p c m, s}$ and $c p_{p c m l}$ are the are the specific heat capacities of the solid and liquid PCM, respectively. Sensible heat was evaluated over the temperature range of 18–64 ℃. The rate of heat supply or extraction for the HTF [23] was calculated using Eq. (2):

$Q F=\dot{m}_{H T F} C_{P, H T F} \Delta T_F$       (2)

The total energy supplied or recovered by the HTF during charging and discharging was calculated using Eq. (3):

$Q f t=\sum \Delta t \times Q f$        (3)

where, $\dot{m}$ is the HTF mass flow rate, $C_{P, H T F}$ is the specific heat capacity of the HTF, and $\Delta T_F$ is the temperature difference between the HTF inlet and outlet.

2.6 Uncertainty

Experimental uncertainty was evaluated for the measured temperature, flow rate, and solar irradiance. The uncertainty is calculated by Eq. (4):

$\begin{aligned} & U_R^2=\left[\left(\partial \mathrm{R} /\left(\partial \mathrm{x}_1\right) \Delta \mathrm{x}_1\right)^2+\left(\partial \mathrm{R} /\left(\partial \mathrm{x}_2\right) \Delta \mathrm{x}_2\right)^2\right. \left.+\ldots \ldots \ldots+\left(\partial \mathrm{R} /\left(\partial \mathrm{x}_{\mathrm{n}}\right) \Delta \mathrm{x}_{\mathrm{n}}\right)^2\right]\end{aligned}$       (4)

where, U_R is the combined uncertainty in the calculated result R, xi is the ith independent variable, Δ_xi is its associated uncertainty, and ∂R/∂xi represents the sensitivity of R to xi.

The uncertainty for the temperature difference was calculated by applying Eq. (5).

$\delta(\Delta T)=\sqrt{ }\left[(\delta \text {Tin})^2+(\delta \text {Tout})^2\right]$        (5)

where, δ(ΔTf) is the uncertainty in the HTF temperature difference, while $\delta \operatorname{Tin}$ and $\delta \operatorname{Tout}$ are the uncertainties associated with the inlet and outlet temperature measurements, respectively.

The calculated uncertainties were within acceptable experimental limits. Experimental uncertainty was evaluated for the measured temperature, flow rate, and solar irradiance, with uncertainties of ±2 ℃, ±0.1 L/min, and ±5%, respectively. The uncertainty in the calculated results was estimated using Eq. (4), where U_R represents the uncertainty in the calculated result R, and x denotes the independent variable. The uncertainty in the temperature difference was determined using Eq. (5). The calculated uncertainties were within acceptable experimental limits.

2.7 Numerical investigation

2.7.1 Computational geometry and mesh generation

The exact geometry of the experimental storage system unit is designed and built using the design modeler.

The fluid domain geometry consists of two geometric arrangements – one is a helical coil domain, and another is a PCM domain.

Additionally, thermal energy transfer occurs from the HTF (water) through two helical copper coils, which are arranged in a concentric arrangement—one large helical coil on the outside and one small helical coil inside. The helical radius of the inner coil (L1) is 150 mm, while that of the outer coil (L2) is 175 mm. The diameter (di) of each tube in the coils is 9 mm. Heat transfer begins with water entering the helical outer coil from the top and then flowing down along the helical path into the inner helical coil; finally, it exits from the inner helical coil at the top end of the tank. The series arrangement ensures the full temperature profile of the HTF interacts with the PCM across both the radial and axial extents of the storage vessel, as shown in Figure 3.

In order to make sure that the results obtained through numerical calculation do not depend on the grid used, the grid independence test was carried out on seven different meshes, with numbers varying from 1,110,000 to 3,100,000 cells. Outlet temperature was chosen as the criterion for the analysis. It was established that the fluctuation in temperature was insignificant starting from 2,500,000 cells. Thus, 2,500,000 cells were taken as the optimal mesh number, as shown in Figure 4.

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Figure 3. (a) Computational geometry of the phase change material (PCM) storage unit, (b) meshing of the numerical model

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Figure 4. Mesh sensitivity study

2.7.2 Boundary conditions

The HTF inlet was defined as a mass-flow inlet with a constant mass flow rate of 0.0167 kg/s, corresponding to the experimental flow rate of 1 L/min. The inlet temperature was specified as a time-dependent condition based on the experimentally measured PTC outlet temperature. The water outlet was set as a pressure outlet at 0 Pa gauge pressure. Because the storage tank was thermally insulated, its external walls were treated as adiabatic with zero heat flux (0 W/m²). The water–copper and copper–PCM interfaces were defined as coupled walls to allow heat transfer between the HTF, copper coil, and PCM without additional interfacial thermal resistance.

2.7.3 Governing equations

The CFD model solves the time-dependent, 3-D conservation equations of mass, momentum, and energy for incompressible laminar flow in the HTF domain, coupled with the enthalpy–porosity formulation for phase change. The thermophysical properties of the materials were treated as constant, except for the density variation associated with buoyancy, which was represented using the Boussinesq approximation. Therefore, natural convection in the molten PCM was included in the numerical model. The continuity equation for incompressible flow is calculated by Eq. (6):

$\frac{\partial u_{\mathrm{i}}}{\partial x_{\mathrm{i}}}=0$       (6)

The momentum equation, incorporating the Boussinesq buoyancy term and the Carman–Kozeny source term for the mushy zone, is calculated by Eq. (7):

$\begin{gathered}\rho\left(\frac{\partial u_i}{\partial t}+u_j \frac{\partial u_i}{\partial x_j}\right)=-\frac{\partial P}{\partial x_i}+\frac{\partial}{\partial x_i}\left[\mu\left(\frac{\partial u_i}{\partial x_i}\right)\right]+\rho g \beta\left(T-T_{r e f}\right) \delta_i^2+S_i\end{gathered}$      (7)

where, the source term Sᵢ is the Carman–Kozeny drag term used in the enthalpy–porosity method, Eq. (8):

$S_{\mathrm{i}}=-A_{\text {mush}} \cdot \frac{(1-\gamma)^2}{\left(\gamma^3+\varepsilon\right)} \cdot u_{\mathrm{i}}$       (8)

Here, γ ∈ [0, 1] is the liquid fraction, $A_{\text {mush}}$ is the mushy-zone constant [kg·m⁻³·s⁻¹], and ε equals 10⁻³, which is a small constant preventing division by zero.

The energy equation is written in terms of total enthalpy H, Eq. (9):

$\frac{\partial(\rho H)}{\partial t}+\nabla \cdot(\rho u H)=\nabla \cdot(k \nabla T)$        (9)

Total enthalpy is decomposed into sensible and latent contributions, Eq. (10):

$H=h+\Delta H=\int c_p d T+\gamma L$       (10)

where, h is the sensible enthalpy, L is the latent heat of fusion, and γ is the liquid fraction defined by the piecewise linear relation, Eqs. (11)-(13):

$\gamma=0$ if $T<T_{\text {solidus}}$       (11)

$\gamma=\frac{\left(T-T_{\text {solidus}}\right)}{T_{\text {liquidus}}-T_{\text {solidus}}}$ if $T_{\text {solidus}} \leq T \leq T_{\text {liquidus}}$      (12)

$\gamma=1$ if $T>T_{\text {liquidus}}$       (13)

The mushy region for a pure PCM reduces to a melting point only, that is, $T_{\text {solidus}}=T_{\text {liquidus}}=T_m$, and a narrow temperature region can be defined for stability purposes. The model for solidification and melting in ANSYS Fluent is based on the formulation in the literature [25].

2.7.4 Solver configuration and numerical scheme

Pressure-based transient analysis was used in ANSYS Fluent for modeling the charging and discharging operations. A laminar flow model was adopted as a simplifying assumption for the present numerical analysis. Natural convection in the molten PCM was accounted for through the Boussinesq approximation with gravity enabled. The laminar formulation was retained to provide a consistent computational framework, while its possible influence on the predicted HTF-side heat transfer is acknowledged. The energy equation, along with an enthalpy-porosity-based solidification-melting model, was included for modeling the phase change phenomenon. Coupling of pressure and velocity fields was accomplished via the SIMPLE algorithm, and a second-order upwind scheme was used for the momentum and energy equations, as shown in Table 4.

Table 4. Numerical solver settings and discretization schemes used in ANSYS Fluent

The assumption of constant thermophysical properties represents a numerical simplification, since the properties of the HTF and PCM may vary with temperature.

This assumption may bring deviations in the forecast local temperature distribution, heat-transfer rate, and PCM melting behavior. Similarly, under conditions near the transitional regime, the laminar-flow assumption can impact predicted HTF-side convective heat transfer. However, all the assumptions for the numerical model were satisfied, since it replicates the experimental temperature behavior well by showing that the basic thermal response and phase-change characteristics of the present system are adequately described.

This study experimentally investigated the effect of PCM mass on the thermal performance of a PTC integrated with a PCM-based thermal energy storage unit under real outdoor climatic conditions in Kirkuk, Iraq. Three paraffin wax masses of 10, 20, and 30 kg were examined, while a three-dimensional transient CFD model was developed and validated for the 30 kg case. The following are the main findings:

• Integration of PCM thermal energy storage greatly enhanced hot-water availability after sunset. The system without PCM had an availability of useful hot-water for about 2 h after sunset, while the case with 30 kg of PCM extended this to approximately 8 h.
• Increasing the PCM mass produced greater thermal storage capacity of the system. The stored thermal energy (theoretical) also increased from 2782 kJ (for 10 kg of PCM) to 8094 kJ for the 30 kg case.
• The amount of thermal energy recovered increased with increasing PCM mass. The recovery ratio was 41.7% for the 10 kg, while for the 30 kg case, it increased to approximately 66.8%.
• Larger PCM mass resulted in a compromise between storage capacity and the response time to heating. The 10 kg case had a relatively lower thermal storage capacity and heat-supply duration than the 30 kg case while providing the fastest thermal response, whereas the 30 kg case offered very high thermal storage ability and maintained this effect for a much longer time at the cost of slower response. The 20 kg case was an intermediate situation.
• The 30 kg case CFD analysis identifies the primary heat-transfer and phase-change mechanisms, consistent with those derived from physical reasoning to explain the experiment.

According to the above, the right amount of PCM should be chosen depending on what is needed for the specific solar thermal application rather than simply maximizing this amount. A lower PCM mass may be preferred when faster thermal response, lower storage-space requirement, and lower PCM material demand are important, whereas a higher PCM mass is more suitable when greater storage capacity and extended post-sunset heat supply are required. The 20 kg case provides an intermediate balance between these characteristics. Therefore, the present results should be regarded as a comparative design assessment within the investigated PCM mass range rather than a formal economic or mathematical optimization.