Computer Fluid Dynamics Assessment of an Active Ventilated Façade Integrating Distributed MPPT and Battery

A numerical model was developed to investigate the airflow and temperature distributions of a ventilated façade based on the experiments carried out at CNR-ITAE.

The numerical model was implemented in the multi-physics Finite Volume Code Ansys Fluent. The simulated prototype consists of a PV panel mounted above a layer of insulation separated by an air channel. A heat source (battery and dc/dc) has been simulated within the air cavity.

A schematic of the model is shown in Figure 1(a).

The PV panel used in the performed module consists of a lower sheet of tempered prismatic glass (dimensions 680 x 680 mm x 3 mm), a layer of EVA 0.5 mm (vinyl acetate that undergoes temperature turns into inert adhesive), matrix of photovoltaic cells 0.2 mm, a layer of EVA0.5 mm and a sheet of tempered prismatic glass dimensions 680×680 mm×3 mm. A schematic of the PV's layers is shown in Figure 1 (b).

The air channel thickness is 20 cm [10]. On the other side of the air channel, typical construction materials made up the wall. The EVA and the PV cells are thin (compared with other computational domains) so the temperature difference across the EVA and PV cells is negligible. Therefore, the EVA sheets and PV cells are treated as a single domain for the heat transfer simulation. A similar approach was used by Nizetic et al. [11].

Fixed on the insulation there are two casings 18 cm×14 cm×4 cm containing a battery, an integrated MPPT and bidirectional battery charger (dc/dc). The battery 116 mm×106 mm×22 mm has nominal capacity 23 Ah and nominal voltage 2.3 V. The diode  (Shottky), consisting of metal-semiconductor junctions, has a slope resistance r 8.8 mΩ. The battery and the diode are available on the market and the data is reported in the manufacturers’ datasheets. The casings are closed to protect the battery and the electrodes of the diode from dust and moisture. As a result, generated heat by Joule effect is not well dissipated. Since both battery and diode dissipate heat is important to assess whether the surface temperatures reached are compatible with the maximum temperatures that can be combined with the materials of which the casing is made.

figure_1.png

Figure 1. (a) Schematic of the model and (b) schematic of the PV panel layers

In Table 1 e Table 2 each material physical properties including density ρ, thermal conductivity λ and specific heat capacity (Cp) are specified [12].

Table 1. Properties of PV module layers

Table 2. Properties of Box and Insulation materials

Utilizing these dimensions and properties a numerical 2D model was created with temperature dependent air properties. The boundary conditions on the outside of the PV panel included the measured solar radiation as a heat flux and convective heat transfer due to the wind. Volumetric heat absorption was applied to the PV cells layer. A similar approach was used by in [19]. Volumetric heat generation was applied to the heat sources (casings) within the air cavity. In the inner wall a convective condition is imposed. The external surface of the insulation was fixed at T = 26 °C.

The thickness of the PV panel (7 mm) is small relative to his width and height (680 mm×680 mm) so it’s reasonable to assume that conduction occurs exclusively in the direction orthogonal to the surface of the panel. In this study the radiative heat transfer is neglected [20].

The air velocity and the air temperature were measured experimentally and used as inputs for the air inlet in the model. The air velocity and direction have a random character so it is not easy to predict its action. To design the wind effects the mean values for velocity and direction are used.

For the air outlet a pressure outlet boundary condition was imposed because outlet was provided to be free flow. A schematic of the boundary conditions is shown in Figure 2.

figure_2.png

Figure 2. Schematic of the boundary conditions

To estimate the volumetric heat dissipation of the dc-dc ($q_d$) and battery $q_b$ have been made the following assumptions:

$q_d=(1-η_d)P_{pv}$ (1)

$q_b=(η_d)(1-q_b)P_{pv}$  (2)

where $P_{pv}$ is the power of the PV panel (W), $η_d$ and $η_b$ are the efficiency of the diode and battery, respectively.

To investigate the effects of the heat sources on the insulation the inner insulation has been divided in four zones as shown in Figure 3.

figure_3.png

Figure 3. Schematic of the thermal zones of the insulation

2.1 Mathematical model

The mathematical model for the prototype described in this paper can be divided into three main parts: electrical model fluid model and heat transfer model.

2.1.1 Electrical model

It is known that a solar cell is represented by an equivalent circuit composed of a current source, an anti-parallel diode (D), a shunt/parallel resistance (R_p) and a series resistance (R_s). A schematic equivalent circuit is shown in Figure 4.

It is widely acknowledged that the photovoltaic generator is neither a costant voltage source nor a current source.

The photovoltaic generator is modeled by the relationship between current and voltage. Based on the Shockley diode equation I is as followed [15]:

$I=I_{ph}-I_0(e^{\frac{V+IR_s}{V_t}}-1)-\frac{V+IR_s}{R_p}$  (3)

where $I_ph$ is the photo current (A), $I_0$ is the diode saturation current (A), $R_s$ is the series resistance (Ω), $R_p$  is the shunt/parallel resistance (Ω), $V_t$ is the diode thermal voltage (V).

figure_4.png

Figure 4. Equivalent circuit for a solar cell [15]

An example of I-V and P-V curves are shown in Figure 5.

figure_5.png

Figure 5. An example of the I-V and P-V curves [15]

When a PV module is directly coupled to a load, as shown in Figure 8, the PV module's operating point will be at the intersection of its I–V curve and the load line which is the I–V relationship of load In general, the optimal intersection occurs at one particular operating point, called Maximum Power Point (MPP). The location of the MPP in the I–V plane changes dynamically depending on irradiance and temperature [14]. In order to optimize a BIPV power generation the adoption of a distributed MPPT approach, using a dc-dc converter per each panel, is suggested in literature overcoming major drawbacks due to the effect of module mismatching and of partial shading of the BIPVs.

figure_6.png

Figure 6. PV coupled to a load [16]

2.1.2 Fluid model

Based on two-dimensional space rectangular coordinate system, the momentum equation, i.e., Navier-Stokes equation, is as followed:

$u_x\frac{\partial u_x}{\partial x}+u_y\frac{\partial u_y}{\partial y}=v(\frac{\partial^2 u_x}{\partial x^2}+\frac{\partial^2 u_x}{\partial x^2})-\frac{1}{ρ}\frac{\partial P}{\partial x}$ (4)

$u_x\frac{\partial u_x}{\partial x}+u_y\frac{\partial u_y}{\partial y}=v(\frac{\partial^2 u_x}{\partial x^2}+\frac{\partial^2 u_x}{\partial x^2})-\frac{1}{ρ}\frac{\partial P}{\partial y}-g$ (5)

where ρ is the fluid density (kg/m3), $u_x$ and $u_y$ are the x-velocity and the y-velocity (m/s), v is coefficient of kinematic viscosity (N s / m²), g is the gravity acceleration (kg m/s²).

2.1.3 Heat transfer model

The heat transfer is a consequence of the solar radiation on the PV modules is partly reflected by the tempered glass layers and partly absorbed by the solar cell layers. The solar energy absorbed by the solar cells is partly converted into direct current (DC) electricity and the absorbed remainder is dissipated as waste heat increasing operating temperature for the PV module. Higher temperature of unit has negative influence on PV panel's efficiency [6].

The energy balance equations are as followed [17-18]:

$u_x\frac{\partial T}{\partial x}+u_y\frac{\partial T}{\partial y}=\frac{λ}{ρC_p}(\frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial y^2})$  (6)

where λ is the thermal conductivity of each part (W/(m K) and C_p is the specific heat of each part (J/(Kg K)).

The waste heat stemming from the solar cell layers is conducted within the front and back tempered glass layers.

In the air cavity the heat exchange with the back side tempered glass layer of the PV panel and the front side of the insulation is dominated by the conductive and radiative heat transfer. At the front and back surface the energy balance equations are the following [17,18]:

$\begin{cases} ρC_pdx\frac{\partial T}{\partial t}=α_{glass}G_{PV}A(1-η)-q^{rad}_{front}+q^{conv}_{front}\\ q^{rad}_{front}=\varepsilon _{glass}F\sigma(T^4_{sur}-T^4_{sky})\\ q^{conv}_{front}=h(T_{sur}-T_{amb}) \end{cases}$  (7)

$\begin{cases} ρC_pdx\frac{\partial T}{\partial t}=q^{rad}_{front}+q^{conv}_{front}\\ q^{rad}_{front}=\varepsilon _{glass}F\sigma(T^4_{back}-T^4_{groud})\\ q^{conv}_{front}=h(T_{back}-T_{amb}) \end{cases}$  (8)

where $α_{glass}$ is the absorptivity of the glass, $G_{PV}$ is the solar radiation on the PV module (W/m²), η is the efficiency of the PV panel (%), $q_{front}^{rad}$e$q_{front}^{conv}$ are the radiative and convective heat flux at the front of the PV (W/m²), $q^{rad}_{back}$ and $q^{conv}_{back}$ are the radiative and convective heat flux at the back of the PV (W/m²), $ε_{glass}$ is the emissivity of the glass, F is the view factor of PV surface, σ is the Stefan-Boltzmann constant, h is the natural convective rate (W/(m2K)), $T_{sur}$, $T_{sky}$, $T_{back}$, $T_{ground}$ and $T_{amb}$ are respectively the temperature of the front surface, the sky, the back surface, the ground and ambient temperature (°C). In this study α is set as 0.9 [19] and as 14 %.

The net solar radiation on PV front surface is given by:

$Q=α_{glass}G_{PV}A$  (9)

where A is the area of the PV panel (m²).

The part of the energy that is converted in heat is given by:

$Q=α_{glass}G_{PV}A(1-η)$ (10)

h is given by [19]:

$f_{free}=\frac{λ}{L}\{0.825+\frac{0.387Ra^{1/6}_L}{[1+(0.492/Pr)^{9/16}]^{8/27}}\}^2$ (11)

 $h_{forced}=\frac{λ}{L}(0.664Re^{1/2}{L}Pr^{1/3})$ (12)

where L is the height of PV panel (m), $R_{aL}$ is the Raleigh number, $R_{eL}$ is the Reynolds number and Pr is the Prandtl number.

$Re=\frac{ul}{v}$ (13)

$Pr=\frac{v}{α}$ (14)

where α is the thermal diffusivity (N s / m²)

$Ra_L=\frac{gβΔTL^3}{αv}$  (15)

where β is the thermal expansion coefficient (1/K), ΔT is the temperature difference between PV and insulation.

In the Fluent solver, RNG k-$\varepsilon$ model was selected in the Viscous Model and Enhanced Thermal Treatment was active in near-wall treatment. Environmental atmospheric pressure was defined as standard atmospheric pressure. Coupled algorithm was used in pressure-velocity coupling equation. Second Order Upwind was selected in momentum and energy equations. The simulations have been conducted in steady state conditions.

2.2   Lab test

Experimental tests have been performed in CNR-ITAE in Messina (Italy).

To evaluate the producibility of two distinct photovoltaic cell technologies that can be integrated into the hybrid module (PV / insulation / batteries) to cover the perimeter walls of a building the panels have been tested.

The two panels, one in polycrystalline silicon with a metal frame and the other one in polycrystalline silicon with a double staggered glass, were arranged vertically as shown in Figure 7.

figure_7.png

Figure 7. Installated PV panels to carry out producibilty measurements in a vertical plane

To carry out the characterization measurements, the panels were connected to the terminals of the low impedance circuit of an electronic direct current load (Chroma 63640-80-80, in Figure 2), consisting of 5 modules (400W per module).

The light radiation was measured on the plane of the modules through a calibrated photovoltaic cell. The global radiation (G) was measured through the pyranometer of a weather station located a short distance from the panels, but raised to avoid the shadowing of obstacles on the plane of the panels under test. In parallel, air temperatures were measured near the modules, and on the rear panel of each module.

The test was conducted in galvanostatic control mode with voltage scans in 0.5 V steps every 2 seconds (with 2 Hz sampling) from 34 V to 0 V. The maximum voltage, although lower than the theoretical OCV, was in any case sufficient (due to the vertical inclination of the photovoltaic modules) to measure zero current.  For each iterated cycle, peak power was detected. In Figure 8 is shown the production from PV modules in vertical installation when G is 265 (W/m²). Experimental data have been measured every two minutes, the entire experimental test has a total time of three hours, the inputs of the simulations are the average values estimated every ten minutes.

figure_8.png

Figure 8. Production from PV modules in vertical installation when G is 265 (W/m²)

As previously mentioned, the temperature of the rear side of the PV was measured during the tests and the temperature of the backsheet was simulated based on the mathematical model provided in 2.1.3 to evaluate its thermal performance.

In Figure 9 are shown the solar radiation and the temperatures profiles evaluated during the tests.

figure_9.png

Figure 9. Hourly profiles of the air and backsheet temperature and solar radiation

2.3   Model validation

The free convection of the PV panel without cavity to predict the temperature profile of the backside of the PV panel was simulated. Experimental data solar radiation, air temperature and air velocity were used as boundary conditions in the numerical model.

To avoid the mesh dependency program, a grid sensitive test was conducted and a mesh of about 130,000 elements has been used for the simulations. Increasing the number of elements will provide a more accurate solution but will also increase the computation resources required.

Figure 10 shows a comparison between the numerical results and the experimental data during a test of about three hours. The simulations were conducted in steady state conditions. Inputs data are the experimental data average every ten minutes. Overall the numerical data showed a good agreement with the experimental ones.

figure_10.png

Figure 10. Comparison between experimental and numerical data of the backsheet temperature of the PV panel

2.4   Results and discussion

Utilizing experimental data mentioned above, the air channel between the BV panel and the insulation was simulated layer to predict the temperature profile of the insulation without the heat sources. The temperature difference between PV and insulation generates buoyancy to push up the channel air and remove part of the heat by natural convection. A part of the heat energy will be transmitted into the indoor space by means of thermal conduction through the wall of the building. The outdoor air can flow into the air cavity generating force convection and removing the heat both the PV and the insulation. A mixed convection mechanism is generated within the air cavity. The results showed an increase of the backsheet temperature less than 1 °C. The PV panel simulated has a Voltage coefficient = 122 mV/°C and a Current coefficient = 4.36 mA/°C so the reduction of the efficiency of the PV panel is neglected.

In order to evaluate the effect inducted by the battery and the electronics due the heat generated the system has been simulated also taking it into account. The results show that an increase in both the backsheet temperature and insulation temperature in respect of the previous case. Figure 11 shows a comparison of the thermal profile of the backsheet without cavity, with cavity without heat sources and with cavity and heat sources. shows the thermal profile of the average temperature of the insulation with and without heat sources in the air cavity. The presence of the heat sources leads to a restriction in the convective heat exchange causing an increase in the temperature both the backsheet and the insulation. It is worth noting that, as expected, front surface temperature of the insulation increase in the area corresponding to the back side of the casings as shown in Figure 12.

figure_11.png

Figure 11. Backsheet temperature of the PV panel without cavity, with cavity without heat sources and with cavity and heat sources

figure_12.png

Figure 12. Insulation average temperature in the air cavity with and without the heat sources

In order to assess the temperature profiles along an entire day, a simulation has been run from 8:00 AM to 8:00 PM of 20^th June 2018. The data have been logged by a weather station located at CNR-ITAE.

Table 3. Data logged by a weather station located at CNR-ITAE

The assessment allows checking the temperatures throughout the system and in particular on the battery casing, results are reported in Figure 13 e Figure 14.

Comparing the data provided by the manufacturers the maximum temperature admitted by the diode (150 °C) is much higher than that of the battery (60 °C) so it’s crucial to fix the casings to facilitate the cooling of the battery.

figure_13.png

Figure 13. Thermal profiles during an entire day (from 8:00 AM to 8:00 PM)

figure_14.png

Figure 14. Surface temperature of the casing containing the battery during an entire day (from 8:00 AM to 8:00 PM)