In recent years, the integration of photovoltaic systems with agricultural practices, commonly referred to as photovoltaic agriculture, has gained significant attention as a sustainable approach to land use. This synergy allows for simultaneous electricity generation and crop production, optimizing resource utilization. However, a critical challenge arises during summer months when temperatures under solar panels can soar to extreme levels, adversely affecting both the efficiency of the photovoltaic modules and the growth of underlying crops. High temperatures not only reduce the power conversion efficiency of solar panels but also create a hostile environment for plants, leading to issues such as reduced pollination and yield. To address this, spray cooling technology has been proposed as an effective method to mitigate heat accumulation under photovoltaic arrays. This study employs computational fluid dynamics (CFD) using Fluent software to simulate the thermal environment under solar panels with spray cooling, aiming to evaluate its effectiveness and provide insights for practical applications in photovoltaic agriculture.
The geometric model for this simulation is based on a typical photovoltaic agricultural project, representing a standard configuration of solar panels arranged in arrays. The model consists of multiple rows of photovoltaic modules, each measuring 2279 mm in length, 1134 mm in width, and 30 mm in thickness. The arrays are spaced 2 meters apart to allow for agricultural activities and airflow. The overall domain spans 96 meters by 20 meters, with the solar panels mounted at an angle of 16 degrees and a minimum height of 2.5 meters above the ground to accommodate crop growth. This setup mimics real-world conditions where photovoltaic systems are deployed over agricultural land, ensuring that the simulation reflects practical scenarios. The model incorporates a three-row array structure to capture the interplay between adjacent panels and the surrounding environment.
In the numerical simulation, the fluid flow and heat transfer under the photovoltaic arrays are modeled using the Euler-Lagrange approach for multiphase flows. The gas phase (air) is treated as a continuous medium, while the liquid phase (water droplets from spray) is modeled as discrete particles. This method allows for accurate tracking of droplet trajectories and their interactions with the air. The governing equations include the Navier-Stokes equations for fluid motion and energy equations for heat transfer. For the discrete phase, the motion of droplets is described by Newton’s second law, accounting for forces such as drag, gravity, and buoyancy. The drag force on a droplet can be expressed as:
$$ F_D = \frac{1}{2} C_D \rho_g A_p |u_g – u_p| (u_g – u_p) $$
where \( F_D \) is the drag force, \( C_D \) is the drag coefficient, \( \rho_g \) is the gas density, \( A_p \) is the projected area of the droplet, \( u_g \) is the gas velocity, and \( u_p \) is the droplet velocity. The acceleration of droplets is computed using:
$$ \frac{du_p}{dt} = \frac{F_D}{m_p} + g + F_{\text{other}} $$
Here, \( m_p \) is the mass of the droplet, \( g \) is gravitational acceleration, and \( F_{\text{other}} \) includes additional forces like lift and wall interactions. The turbulence in the gas phase is modeled using the standard k-ε model, which solves for turbulent kinetic energy k and its dissipation rate ε:
$$ \frac{\partial (\rho k)}{\partial t} + \nabla \cdot (\rho k u) = \nabla \cdot \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \nabla k \right] + P_k – \rho \epsilon $$
$$ \frac{\partial (\rho \epsilon)}{\partial t} + \nabla \cdot (\rho \epsilon u) = \nabla \cdot \left[ \left( \mu + \frac{\mu_t}{\sigma_\epsilon} \right) \nabla \epsilon \right] + C_{1\epsilon} \frac{\epsilon}{k} P_k – C_{2\epsilon} \rho \frac{\epsilon^2}{k} $$
where \( \mu \) is the dynamic viscosity, \( \mu_t \) is the turbulent viscosity, \( \sigma_k \) and \( \sigma_\epsilon \) are model constants, and \( P_k \) is the production of turbulent kinetic energy. For radiation heat transfer, the radiative transfer equation (RTE) is employed to account for solar radiation and thermal emissions:
$$ \frac{dI}{ds} = -k_s I + k_a B(T) $$
In this equation, \( I \) represents the radiation intensity, \( s \) is the path length, \( k_s \) is the scattering coefficient, \( k_a \) is the absorption coefficient, and \( B(T) \) is the blackbody radiation intensity at temperature \( T \). The discrete ordinates (DO) method is used to solve the RTE, considering the directional dependence of radiation. Additionally, species transport models are incorporated to simulate the evaporation of water droplets and the resulting humidity changes. The mass conservation for water vapor is given by:
$$ \frac{\partial (\rho Y_v)}{\partial t} + \nabla \cdot (\rho Y_v u) = \nabla \cdot (\rho D_v \nabla Y_v) + S_v $$
where \( Y_v \) is the mass fraction of water vapor, \( D_v \) is the diffusion coefficient, and \( S_v \) is the source term due to evaporation. The energy equation accounts for latent heat effects during phase change:
$$ \rho c_p \frac{\partial T}{\partial t} + \rho c_p u \cdot \nabla T = \nabla \cdot (k \nabla T) – \Delta h_v S_v $$
Here, \( c_p \) is the specific heat capacity, \( k \) is the thermal conductivity, and \( \Delta h_v \) is the latent heat of vaporization. Boundary conditions include no-slip walls for the solar panels and ground, with specified heat fluxes to represent solar irradiation. The spray injection is modeled as a conical mist with droplet size distributions based on nozzle characteristics, typically ranging from 10 to 100 micrometers in diameter. The initial conditions assume ambient temperatures of 40°C to 50°C, representative of summer conditions in photovoltaic agriculture settings.
The simulation results reveal significant insights into the thermal behavior under photovoltaic arrays with spray cooling. Temperature contours at different time intervals illustrate the evolution of cooling effects. For instance, at the initial stage of spray activation (0.12 seconds), the temperature distribution shows localized cooling directly under the spray nozzles, with higher temperatures persisting at the edges of the solar panels. As the spray continues (0.24 seconds), the cooled area expands, leading to a more uniform temperature reduction across the domain. After sustained spraying, the entire region under the photovoltaic arrays exhibits lower temperatures, with the core areas showing the most pronounced cooling due to direct droplet impingement and evaporation.
To quantify these observations, key parameters such as temperature reduction, humidity increase, and droplet evaporation rates are analyzed. The following table summarizes the average temperature changes under different spray conditions over a simulation period of 60 seconds:
| Time (s) | Spray Flow Rate (kg/s) | Average Temperature Under Panels (°C) | Temperature Reduction (°C) | Relative Humidity Increase (%) |
|---|---|---|---|---|
| 0 | 0 | 50.0 | 0.0 | 0 |
| 0.12 | 0.05 | 47.5 | 2.5 | 15 |
| 0.24 | 0.10 | 45.0 | 5.0 | 25 |
| 60.0 | 0.10 | 42.5 | 7.5 | 35 |
This table demonstrates that higher spray flow rates lead to greater temperature reductions, but also result in increased humidity levels, which must be managed to avoid adverse effects on crops. The evaporation process is critical, as it absorbs latent heat, thereby cooling the surrounding air. The rate of evaporation for a droplet can be modeled using:
$$ \frac{dm_p}{dt} = – \pi d_p Sh D_v \rho_g \ln(1 + B_m) $$
where \( d_p \) is the droplet diameter, \( Sh \) is the Sherwood number, \( D_v \) is the diffusion coefficient of vapor in air, and \( B_m \) is the Spalding mass transfer number. The cooling efficiency \( \eta_c \) of the spray system can be defined as the ratio of heat removed to the energy input:
$$ \eta_c = \frac{\dot{m}_w \Delta h_v}{P_{\text{pump}} + \dot{m}_w c_p \Delta T} $$
Here, \( \dot{m}_w \) is the water mass flow rate, \( \Delta h_v \) is the latent heat of vaporization, \( P_{\text{pump}} \) is the pump power, and \( \Delta T \) is the temperature drop. For typical operating conditions, \( \eta_c \) ranges from 0.6 to 0.8, indicating effective heat removal. However, the interplay between cooling and humidity rise necessitates optimized control strategies. For example, intermittent spraying cycles (e.g., 1 minute on, 1 minute off) can maintain temperature reductions while minimizing excessive moisture buildup.
Further analysis involves sensitivity studies on parameters such as droplet size, spray angle, and environmental wind speed. The following equation relates the Nusselt number \( Nu \) for convective heat transfer to these factors:
$$ Nu = C Re^m Pr^n $$
where \( Re \) is the Reynolds number, \( Pr \) is the Prandtl number, and \( C, m, n \) are constants dependent on flow conditions. Smaller droplet sizes enhance evaporation rates but may require higher nozzle pressures, increasing energy consumption. A balance must be struck to achieve efficient cooling without overwhelming the system. Additionally, the arrangement of solar panels influences airflow patterns; for instance, closer spacing may reduce ventilation, exacerbating heat accumulation. The table below compares different photovoltaic array configurations and their impact on cooling effectiveness:
| Array Spacing (m) | Spray Nozzle Density (nozzles/m²) | Max Temperature Reduction (°C) | Cooling Uniformity Index | Energy Consumption (kWh) |
|---|---|---|---|---|
| 2.0 | 0.1 | 7.5 | 0.85 | 0.5 |
| 3.0 | 0.1 | 6.0 | 0.75 | 0.4 |
| 2.0 | 0.2 | 9.0 | 0.90 | 0.7 |
| 3.0 | 0.2 | 7.0 | 0.80 | 0.6 |
The cooling uniformity index is calculated as the ratio of the standard deviation of temperature to the mean temperature under the panels, with lower values indicating better uniformity. Results show that higher nozzle density and closer array spacing improve cooling performance but at the cost of increased energy use. This highlights the need for tailored designs in photovoltaic agriculture to balance agricultural needs with energy efficiency.
In terms of practical implementation, the spray cooling system involves components such as pumps, nozzles, and control units. The initial investment for a typical setup is approximately $8,000, covering a 4 kW spray host, high-pressure tubing, and fittings. Operational costs, including electricity and water, amount to around $110 per day for an 8-hour operation with intermittent cycling. While spray cooling is effective and relatively easy to install, its performance heavily depends on control algorithms that adjust spraying based on real-time temperature and humidity sensors. Advanced strategies, such as model predictive control (MPC), can optimize spraying schedules to maximize cooling while conserving resources. The overall benefits include enhanced photovoltaic efficiency—since solar panels operate better at lower temperatures—and improved crop yields due to a more favorable microclimate.
In conclusion, this simulation study demonstrates the potential of spray cooling to mitigate high temperatures under photovoltaic arrays in agricultural settings. The use of CFD models provides a detailed understanding of thermal dynamics, droplet behavior, and environmental interactions. Key findings indicate that spray cooling can reduce temperatures by up to 7.5°C under optimal conditions, with uniformity improvements as spraying duration increases. However, challenges such as humidity management and energy consumption require careful consideration. Future work should focus on developing intelligent control systems and exploring hybrid cooling methods to further enhance the sustainability of photovoltaic agriculture. This research lays a foundation for practical applications, contributing to the advancement of integrated energy and food production systems.