Enhancing Power Generation: PIV Analysis of Flow Structures’ Impact on Concentrated Solar Sphere Parameters

Abstract

The flow velocity field of the oil-filled acrylic solar sphere is assessed using flow visualization, which includes image processing and Particle Image Velocimetry (PIV) measurements. The temperature, sphere size, and thickness all have an impact on the generated convection flow. The acrylic sphere, a contemporary concentrated photovoltaic technology, collects solar energy and concentrates it into a small focal region. This focus point is positioned precisely above a multi-junction apparatus that serves as an appliance for concentrator cells. Instead of producing the same amount of electricity as a typical photovoltaic panel (PV), this gadget can generate an enormous power rate directly. There are numerous industrial uses for acrylic spheres as well. This study paper aims to examine the flow properties inside a sphere and investigate the impact of the sphere’s temperature, size, and thickness on the fluid motion’s flow velocity. Furthermore, the goal of this research is to elucidate the correlation between these variables to enhance power-generating performance by achieving higher efficiency. The findings demonstrated that the flow structure value is greatly affected by the sphere size, thickness, and temperature. It is discovered that when the spherical thickness lowers, the velocity rises. As a result, the sphere performs better at lower liquid temperatures (35–40 °C), larger sizes (15–30 cm diameter), and reduced acrylic thickness (3–4 mm), leading to up to a 23% increase in power output and a 35–50% rise in internal flow velocity compared to thicker and smaller configurations. Therefore, reducing the sphere thickness by 1 mm results in approximately a 10% increase in average flow velocity at the top of the sphere, corresponding to an increase of about 0.0001 m/s. Notably, the sphere with a 3 mm thickness demonstrates superior power and efficiency compared to other thicknesses. As the sphere’s thickness decreases, the solar sphere’s output power and efficiency rise. The amount of sunlight absorbed by the acrylic photons increases with decreasing acrylic layer thickness; hence, the greater the output power, the higher the efficiency that follows.

1. Introduction

The interconnected global challenges of food security, water scarcity, and environmental degradation have emphasized the urgent need for sustainable innovations in the energy sector. With global energy demand expected to rise significantly between 2016 and 2040, there is a pressing need to develop and deploy technologies that can meet this demand while minimizing environmental harm [1,2,3,4]. Renewable energy sources such as solar, wind, and hydroelectric power have emerged as viable alternatives to traditional fossil fuels, offering cleaner and more sustainable options for energy generation [5,6,7]. Advancements in energy storage, smart grid technologies, and decentralized energy systems are critical to enhancing the efficiency, stability, and adaptability of modern power systems. These innovations support the integration of renewable sources, which are often variable and dependent on environmental conditions [8,9,10]. Effective energy transition requires not only technological progress but also strategic investments in research and development, along with strong collaboration between governments, industry, and academia [11,12].

Among the renewable options, solar energy stands out due to its abundance, wide availability, and minimal environmental impact. Unlike fossil fuels, solar power generation produces no greenhouse gas emissions or air pollutants. Recent advancements in photovoltaic (PV) technology and concentrated solar power (CSP) systems have significantly increased the efficiency and affordability of solar energy, making it more competitive with conventional sources [12,13]. However, the intermittency of solar power due to factors like weather and daylight availability poses challenges for integration. Research is increasingly focused on next-generation solar cells, new materials, improved manufacturing processes, and integrated storage solutions to address these limitations. Battery storage, pumped hydro, and other technologies are being developed to ensure a stable and reliable energy supply from renewable sources [14,15].

Supportive policies, financial incentives, and updated regulatory frameworks are also essential to accelerate the transition to clean energy. By creating an environment that encourages innovation and investment in renewables, societies can reduce dependence on fossil fuels and advance toward a more sustainable and resilient global energy system. Solar energy, in particular, holds great promise as a cornerstone of this transition [13,16,17].

The concentrated solar sphere technology holds significant promise for advancing solar energy generation, offering benefits such as direct solar energy conversion, omnidirectional solar radiation collection, and compact size [18,19,20,21,22,23]. These attributes contribute to higher efficiency and flexibility in deployment compared to traditional solar panels. However, despite these advantages, Concentrated Photovoltaic (CPV) cells face several significant limitations that must be addressed to realize their full potential. CPV systems, while efficient in converting sunlight into electricity, are constrained by practical limitations. One critical issue is their efficiency ceiling, which, despite improvements in recent years, often falls short of theoretical expectations under real-world conditions [24]. Thermal degradation presents another challenge, as the concentrated nature of sunlight can lead to increased operating temperatures, affecting cell performance and longevity [25,26]. Moreover, the cost of CPV systems remains a barrier to widespread adoption, primarily due to the sophisticated optics and tracking mechanisms required to concentrate sunlight effectively [27]. Quantitative comparisons underscore these drawbacks. For instance, CPV systems may lose approximately 10–15% of installed capacity compared to traditional PV systems under specific environmental and operational conditions, such as cloudy or hazy weather, due to their reliance on direct normal irradiance (DNI) [28,29]. Such comparisons highlight the ongoing technological and economic challenges that must be overcome to enhance CPV’s competitiveness in the solar energy market. Here are a few quantitative limitations that can be incorporated: CPV systems perform poorly under diffuse light, with energy output dropping by up to 80% under overcast conditions compared to clear skies [29].

Furthermore, cell efficiency can drop by 0.4–0.5% per °C above the optimal operating temperature due to thermal effects or thermal degradation [30]. Moreover, the Levelized Cost of Electricity (LCOE) for CPV is typically 20–40% higher than for conventional silicon PV due to the high cost of optics, multi-junction cells, and dual-axis trackers [31]. On the other hand, although multi-junction CPV cells have reached lab efficiencies above 45%, system-level efficiencies are often only 30–35% due to optical and thermal losses [32].

Despite these limitations, ongoing research and development efforts aim to optimize CPV performance, mitigate thermal impacts, and reduce overall costs. These efforts are crucial for advancing the adoption of CPV technology and expanding its role in the renewable energy landscape.

The concentrated solar sphere system sounds like an innovative approach to harnessing solar energy efficiently. The system components breakdown and the processes involved are as follows:

• Acrylic Sphere: The acrylic sphere serves as the primary component of the solar sphere system, housing the fluid that absorbs sunlight. Its spherical shape allows sunlight to be captured from all directions, maximizing solar energy collection;
• Absorbing Fluid: The fluid within the acrylic sphere helps it capture sunlight and collect solar energy, which is then concentrated into a small focal point beneath the sphere;
• Concentration and Focusing: The acrylic sphere gathers and directs sunlight onto a compact area using optical components. This concentration intensifies the light, significantly improving solar energy conversion efficiency. The focal point is precisely aligned above a multi-junction device that converts the concentrated sunlight into electrical energy with much higher power output than conventional photovoltaic (PV) panels. Acrylic spheres also have a wide range of industrial applications;
• High-Efficiency Solar Cell/Multijunction device: The focused sunlight is directed onto a high-efficiency solar cell, which efficiently converts the concentrated solar energy into electrical energy. These solar cells are specifically designed to handle high-intensity sunlight and maximize energy conversion efficiency [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47].

In general, the concentrated solar sphere system represents a promising approach to solar energy generation, leveraging innovative design and optical technologies to maximize energy capture and conversion efficiency. With further research and development, this technology has the potential to contribute significantly to the expansion of renewable energy resources and the transition towards a more sustainable energy future.

Our previous studies [48,49,50,51,52] involved comprehensive research and experimentation to evaluate the performance of innovative concentrated solar sphere technology under various conditions. Investigating different spherical materials, shapes, sizes, and fluids is crucial for understanding the factors that influence the efficiency and effectiveness of the technology in order to design the final prototype. By conducting trials over different times of the year and under various circumstances, valuable data was gathered on power production and efficiency, allowing for a thorough comparison with traditional solar panels (PV). This comparative analysis is essential for assessing the feasibility and potential advantages of adopting innovative concentrated solar sphere collectors over conventional PV systems. The results of our study likely provide valuable insights into the performance characteristics of solar sphere collectors, including their energy conversion efficiency, durability, reliability, and suitability for different applications and environments. Additionally, our findings may highlight the strengths and limitations of solar sphere technology compared to traditional solar panels, helping to inform future research, development, and deployment efforts in the renewable energy sector. The conclusions drawn from our prior studies regarding the superiority of innovative concentrated solar sphere technology over standard solar panels are quite significant and offer valuable insights into the potential of this innovative approach to solar energy generation. The key findings can be broken down as follows:

• Effect of Shape: The entirely spherical shape consistently produced the highest power output compared to other tested shapes and conventional PV;
• Effect of Size: Increasing the size of the solar sphere was found to correlate with higher power production and efficiency. This suggests that scalability plays a crucial role in optimizing the performance of solar sphere technology, with larger spheres offering greater potential for energy generation;
• Impact of Fluid and Other Materials Choice: The type of fluid used to fill the solar sphere also influenced power output, with oil, especially cooking oil (sunflower or corn oil), exhibiting the highest power output, followed by alcohol and water. Air, meanwhile, resulted in the lowest power production among the fluids tested. This underscores the importance of fluid selection in optimizing energy conversion efficiency and overall system performance. Solid materials such as glass or acrylic are not ideal for direct electricity generation, as they can cause excessive heat buildup and pose a fire hazard to underlying components;
• Impact of Oil Type: Cooking oils, particularly sunflower and corn oil, yielded the highest output power and efficiency compared to other oils tested. Moreover, fresh unused oil performed slightly less than used oil, suggesting that the aging process might enhance the oil’s performance. Furthermore, increasing the amount of oil inside the sphere also boosted power output and efficiency, hence, the sphere should be filled entirely with oil;
• Performance Comparison with PV/Superior Power Production: The solar sphere demonstrated significantly higher power production and efficiency compared to standard solar panels across various parameters tested. The spherical shape proved to be particularly effective, with power output nearly four times that of traditional solar PV panels with the same installation area. This highlights the importance of design considerations in maximizing energy capture and conversion efficiency. Our system demonstrated approximately twice the efficiency of solar PV, which is 28–30%, compared to 14–15%, while requiring less installation space. Additionally, it boasted advantages such as minimal maintenance requirements and resilience to adverse weather conditions [48,49,50,51,52].

Overall, our findings contribute significantly to the body of knowledge on solar sphere technology and its potential for revolutionizing solar energy generation. Continued research in this area, particularly in fluid dynamics and system optimization, will be instrumental in further advancing the efficiency, scalability, and practical application of solar sphere collectors in renewable energy systems.

Convection flow within the solar sphere is a crucial aspect to consider in optimizing its performance and efficiency. Convection refers to the transfer of heat through the movement of a fluid, such as oil or air, within the sphere. This fluid movement plays a significant role in distributing heat evenly, maximizing energy absorption, and enhancing overall system efficiency. In the context of the solar sphere, convection flow facilitates the transfer of heat from absorbed sunlight to the fluid within the sphere. As the fluid heats up, its density decreases and it rises, creating convective currents. These currents transport thermal energy throughout the sphere, helping to maintain a more uniform temperature distribution and promoting efficient energy transfer. Although the photovoltaic (PV) cell (which is the multijunction device) does not directly contact the internal fluid, the resulting convection plays a critical role in managing thermal conditions inside the sphere, preserving material integrity, and enhancing the overall efficiency of solar energy conversion. Understanding and optimizing convective flow within the solar sphere is therefore essential for minimizing energy losses, achieving uniform heating, and avoiding thermal degradation of optical components. Applications of convection flow extend beyond the solar sphere and encompass a wide range of industries and processes, for example, oil and natural gas transport, column reactors, air–sea gas transfer, ship hydrodynamics, boiling heat transfer, and bubble column reactors. Researchers leverage principles from fluid dynamics and heat transfer to analyze flow behavior, with numerical simulations and experimental studies serving as key tools for evaluating design performance.

This paper focuses on the application and adaptation of those models to the unique geometrical and thermal conditions of solar spheres, especially in relation to varying acrylic wall thickness and fluid selection. The novelty of this work lies in its experimental investigation of how these factors affect internal convection and, consequently, energy conversion efficiency.

Recent advances in solar sphere modeling have enhanced our understanding of these systems. For example, refs. [53,54] introduced advanced ray-tracing methods and thermal-fluid simulations to better predict solar energy concentration and internal temperature gradients. These models incorporate multi-physics environments, including solar irradiance distribution, convective flow within the sphere, and material-specific refractive indices, providing detailed insight into light absorption and thermal diffusion. In particular, 3D CFD (computational fluid dynamics) simulations combined with experimental Particle Image Velocimetry (PIV) have been used to visualize and quantify the impact of fluid properties and sphere geometry on convection efficiency and hotspot formation. Moreover, solar sphere innovations are increasingly targeting passive thermal regulation strategies. For instance, work by [55] demonstrated how internal convection could delay localized overheating, improving optical clarity and boosting photovoltaic output. These findings reinforce the importance of coupling optical and thermal models in solar sphere development, particularly as they relate to sphere thickness and fluid behavior, both key parameters investigated in the present study.

Applications of convection flow extend beyond the solar sphere and encompass various fields, such as oil and natural gas transport, column reactors, air–sea gas transfer, ship hydrodynamics, boiling heat transfer, and bubble column reactors [56,57]. This broader relevance underscores the importance of accurate modeling techniques and experimental validation for improving system performance in both renewable energy and industrial processes.

Researchers continue to emphasize the role of convection flow through:

• Visualization and Understanding: Numerical simulations and experimental techniques help visualize internal flow patterns, offering insights into fluid motion, heat transfer, and energy mixing;
• Defining Flow Behavior: Key parameters such as velocity profiles, temperature gradients, and fluid thermophysical properties help define and predict convection behavior;
• Investigating Efficacy: The effectiveness of convection can be assessed in terms of heat removal, thermal distribution, and energy output, enabling targeted performance evaluation;
• Improving Flow Behavior: By adjusting system geometry, operational conditions, or implementing flow control strategies, researchers can enhance convection-driven heat transfer.

Overall, the integration of solar-sphere-specific modeling approaches with foundational fluid and thermal dynamics provides a promising path toward developing more efficient solar energy systems. This study builds on recent advances by analyzing how internal fluid dynamics, driven by sphere thickness and fluid type, can be optimized to improve solar sphere performance.

This study employs Particle Image Velocimetry (PIV) to visualize and quantify the internal fluid flow velocity inside solar spheres. PIV has previously been applied in concentrated solar power (CSP) and concentrator photovoltaic (CPV) systems to investigate thermal boundary layers, coolant flow behavior, and localized convective instabilities in linear and parabolic geometries [58,59].

These prior works focus primarily on open or semi-open flow domains (e.g., channels, receivers), with relatively predictable boundary conditions and simpler surface interactions.

However, these studies have largely focused on planar or cylindrical configurations, where flow profiles are more straightforward to characterize. In contrast, the spherical geometry presents unique challenges due to curved surfaces, radial temperature gradients, and variable optical thickness, all of which affect the internal convective flow structure. Moreover, prior work does not address the optical distortion effects unique to curved acrylic shells, nor do they correlate internal flow patterns with output power or system-level performance metrics in a spherical concentrator context. By bridging this gap, our study not only validates the feasibility of PIV in this challenging configuration but also provides novel insights into optimizing solar sphere design through experimental flow visualization and thermal analysis.

To date, limited research has explored how sphere-specific parameters such as temperature, size, and wall thickness influence fluid dynamics and thermal performance within this type of collector. In this context, our study advances the field by applying PIV in a closed, spherical domain (fully enclosed, spherical optical collector) filled with optical-grade fluids, under controlled thermal and lighting conditions. By doing so, we capture detailed insights into internal convection patterns and correlate these with geometric and thermal variables that directly impact solar energy conversion efficiency. Notably, our study examines how sphere thickness, diameter, and temperature gradients influence internal flow dynamics and, in turn, affect solar energy conversion efficiency factors not comprehensively explored in the existing literature.

The experimental setup, described in Section 2, was designed specifically to address optical distortion challenges introduced by the acrylic shell, allowing high-fidelity velocity field mapping. Section 3 presents image processing and data analysis workflows. Results are discussed in Section 4, interpreted in Section 5, and summarized in Section 6. Ultimately, this work contributes a novel application of PIV to solar sphere systems, offering valuable insights for optimizing next-generation solar collectors.

2. Experimental Methods and Apparatus

The desired experimental setup is displayed in Figure 1 and in photos in Figure 2. The solar sphere (No. 1) is made of acrylic (Plexiglas) material that allows for the collection of the focused solar energy and provides optical access to the flow within the sphere for easier observation and image processing using PIV measurements. The experiments were initially conducted using water, followed by sunflower oil (a type of frying oil), as the working fluid inside the sphere. A stainless-steel stand holds up the sphere (No. 2). Mounted on a stand (No. 4) beneath the solar sphere, a multi-junction concentrator solar cell (No. 3) is directly connected to a multi-meter (No. 5). The multi-meter is used to measure the electrical power generated by the solar cell by measuring voltage and current amperes, allowing for performance monitoring and optimization of the system. The solar sphere gathers solar radiation from the sun and concentrates it into one area. This focus point is situated atop a multi-junction cell, which serves as a collector device. The multi-junction cell arrangement’s magnifying lenses concentrate solar radiation into a single area of the cell. A heat sink is connected to this concentrated area. The task of converting various components of light into electricity is delegated to sub-cells inside the multi-junction cell. It was decided to employ this gadget in this experiment to capture the concentrated solar energy of the focus point since it can tolerate high temperatures and aid in radiation resistance. A pyranometer is used to measure the intensity of solar irradiance, providing data on the amount of sunlight available for energy conversion.

A formal structured Design of Experiments (DoE), such as a full factorial design, was not employed in this study. Instead, a parameter variation approach was used, in which key variables sphere thickness, sphere diameter, and fluid type were varied independently under controlled conditions. This method was selected for several reasons:

• Exploratory Focus: The primary goal of this research was to qualitatively and comparatively investigate the influence of individual parameters (e.g., acrylic thickness, fluid viscosity, optical distortion) on convective flow behavior within the solar sphere. At this stage, a full factorial design would have added unnecessary complexity without proportionate gain in insight;
• Experimental Constraints: Practical limitations such as custom fabrication of spheres with varying thicknesses and diameters, and the need to manage optical distortions in PIV measurements, restricted the feasibility of executing a large matrix of test conditions typically required by factorial DoE;
• Controlled Isolation of Effects: By varying one parameter at a time while keeping all other conditions constant (e.g., lighting, ambient temperature, fluid volume), we ensured that observed changes in flow velocity and structure were attributable to the parameter under investigation. This approach maintained internal validity while allowing for direct comparative analysis;
• Consistency Across Trials: To ensure repeatability and mitigate variability, all experiments were conducted using the same PIV system setup, camera alignment, lighting conditions, and data processing pipeline.

Future studies may expand on this work by applying structured factorial or response surface methodology (RSM) designs to quantify interaction effects among multiple variables. However, the current approach provides a reliable foundation for identifying key trends and guiding subsequent optimization studies.

To assess the potential impact of optical properties on power output, fluids with differing refractive indices, water (n ≈ 1.33) and sunflower oil (n ≈ 1.47), were selected. The refractive index values were obtained from manufacturer datasheets and confirmed using an Abbe refractometer at room temperature (25 °C). While no direct correlation analysis was performed between refractive index and output power, these values were considered when interpreting the optical behavior of light within the acrylic sphere, particularly with respect to focal length and beam distortion.

By keeping the acrylic material constant (n ≈ 1.49) and varying only the internal fluid, the role of internal refractive mismatch could be indirectly evaluated through differences in observed flow structure and output efficiency.

In order to calculate the power output of the solar cell (w), the following equations are used:

The output power is

P_out = I × V

(1)

where I and V are the current and the voltage, respectively, which are measured by the multimeter. Then, the current–voltage characteristics are plotted to find out the maximum power output.

The maximum efficiency is

$$\eta ={\displaystyle \frac{P_{\mathit{max}out}}{P_{in}}}= {\displaystyle \frac{I\times V}{E_s\times A_{cell}}}$$

(2)

where P_{max out} is the maximum power output.

E_s is the incident radiation flux that could better be described as the amount of sunlight that hits the earth’s surface in W/m². The assumed incident radiation flux under standard test conditions (STC) that manufacturers use is 1000 W/m². Keep in mind, though, that STC includes several assumptions and depends on the geographic location. A_c is the area of the collector or the solar cell.

In concentrated photovoltaic systems, the power produced is higher than that of conventional photovoltaic solar panels/systems (PV). The solar collector focuses more sunlight on the receiver, which is the solar cell in our system. To obtain an overview of how much the solar radiation is concentrated and to obtain the power input of the solar shapes, some parameters are defined to be used in the following equations.

The Geometrical Concentration Ratio is the amount of solar radiation incident on the receiver and it is obtained from the area of the collector and the receiver. Therefore, the ratio between the areas of the collector and the receiver is called the geometrical concentration ratio (CR) [14,15,48].

$$CR={\displaystyle \frac{A_{collector}}{A_{receiver}}}$$

(3)

The Optical Concentration Ratio is the ratio between light intensities at the collector to the receiver. The optical concentration ratio is less than the geometrical concentration ratio since it includes the losses that are due to light intensities (solar radiation). For concentration technologies, the higher the concentration ratio is, the more preferable the system is.

$${CR}_{optical}={\displaystyle \frac{A_{collector}\times I_{collector}}{A_{receiver}\times I_{receiver}}}$$

(4)

The solar radiation on the receiver, which is the multi-junction solar cell in our system, is:

G_r = G × CR (W/m²)

(5)

where G is the solar radiation (W/m²) and P_in is the Input power of the solar cell.

P_in = Gr × A_cell

(6)

Electrical efficiency:

$$\eta ={\displaystyle \frac{P_{out}}{P_{in}}}= {\displaystyle \frac{I\times V}{G_r\times A_{cell}}}$$

(7)

The equipment described below, depicted in Figure 3, makes up the experimental setup used to study flow characterization employing flow visualization and image processing using PIV measurements. The PIV system and camera used in this study were supplied by Microvec, a company based in Singapore.

• A mini diode-pumped solid-state laser (DPSS) model #SM-SEMI-2W, a double pulse laser (sometimes referred to as a PIV laser, which is No. 3 in Figure 3), is utilized as the light source. It uses a light path exit and an optical beam combiner to emit laser beams using two pulse lasers. The laser has a wavelength of 532 nm;
• The displayed flows are recorded by a CCD scientific class digital camera (Model #SM-CCDB2M25, which is No. 5 in Figure 3). This camera contains a 50 mm f/1.4 F-Mount Lens (Model #SM-LENS5014) and is equipped with a double exposure mode that is synchronized with the double laser pulses. The capture is triggered externally. The two captured images are then instantly sent to computer memory by the frame grabber. Trigger signals that are correctly synchronized with the double-pulsed laser are produced by a synchronizer. The camera can capture 25 frames per second (12.5 picture pairs) at a resolution of 1620 × 1220 (2 M). In PIV mode, the smallest exposure time period is 200 ns;
• The USB-connected synchronizer, Model #MicroPulse 825 (MicroPulse725, which is No. 1 in Figure 3), generates multiple delayed trigger signals through internal time-delay channels and uses the internal time base to provide cycle pulse trigger signals. The synchronizer maintains precise synchronization between the various components by controlling the laser, digital camera(s), and frame grabber;
• A computer, which is No. 2 in Figure 3, is used to store image data that the frame grabber has captured. The velocity field is then computed, displayed, and saved in real-time by the software of the Particle Image Velocity measurement system;
• The PIV system uses a laser as an independent light source that may be applied with or without the synchronizer. It is a 2D PIV system that includes particle image capture and velocity analysis. Throughout the optical route and laser energy setup, the laser’s internal synchronization can be utilized if the synchronizer is not accessible. A high-resolution 2D2C PIV with window deformation method, boundary deformation parameters, multi-pass, and multi-grid is also adopted. On the computer, the frame grabber is installed in a standard PCI (PCI-E) slot. The interface used by the acquisition board is mainly a 26-pin CamLin standard interface for connecting digital cameras. Microvec PIV uses digital cameras that have a standard Cam Link interface. It uses three 10-m signal lines to connect to the frame grabber. It then stores trigger signals to synchronize the digital cameras with the pulse laser. Finally, it uses coaxial signal cables to link to the synchronizer’s output interface using TTL trigger, which communicates with the camera. When the synchronizer is included in the PIV system, the digital camera must be in PIV work mode and the laser must be in external synchronous mode, where the synchronizer’s 4-way delay signals are output to controls of the corresponding two sets of the laser flashlamp and Q-switch;
• Spherical fluorescent tracer particles are used to visualize the flow and calculate velocity vectors; tracer particles with a diameter of 7 μm (mean 10 μm) and a density of 1.04–1.06 g/cc are used, model #MV-H1020.

The results of this study, which gather and compute the velocity/velocity vectors of the flow inside the solar sphere, including flow visualization and image processing, are produced, as previously said, by the PIV measurements. Instead of using the sun as a mimic for the experiments, a lighting configuration of 500 W Halogen lights is used in the lab. In order to enhance visibility and capture high-quality photos of the experiments for flow visualization and velocity measurements, the laser is used against a black back sheet background.

3. Outcomes of Flow Visualization and Image Processing, Including Data Analysis and PIV System

One method of optical flow imaging is Particle Image Velocimetry (PIV). It utilizes the associated fluid properties and obtains instantaneous velocity data. It is necessary to add tracer particles to the fluid to aid in the capture of velocity vectors. The laser will be used to illuminate the area of interest, and the seeded particles will be observed to produce the velocity vectors. The tracer or seeded particles are intended to track the interrogation window’s distinct speed as well as the fluid’s motion, which is uniformly distributed throughout the flow field. Sequential imaging records the flow of the moving tracer particles and processes it for further cross-correlation, enabling the determination of the velocity field (the speed and direction of the observed flow) when the particles are in motion. Moreover, the flow vortices, flow field parameter distribution, speed lines, and flow lines can be used for further processing. Four fundamental physical components make up the configuration of a typical PIV system. The first is the digital CCD or CMOS camera. The second part is the laser and its optical configuration, which limits the physically illuminated region of interest. The synchronizer, which is the third part, works as an external trigger to control and time the laser and the cameras. The fourth element is the seeding particles, as was previously mentioned. Naturally, each of these elements needs to be used with the fluid that is being studied. To change the laser beam into a sheet or line ray, it can be connected to particular lenses. Ultimately, specialized PIV Microvec V3 software will be used to process the acquired optical images. The tracer particles that track the fluid’s movement are released by the pulsed laser during the predetermined time interval t. The CCD chip records the precise location of the particles in real time through sheet light illumination provided by the lens group. Using the definition of velocity and the recorded particle picture, we may determine the velocity of the particle group at t₁ if we know the displacement change of the same particle micelle at two times, t₁ and t₂, as shown in the formula below [60,61].

$$\mathit{v}=\underset{∆t\to 0}{\mathit{lim}}{\displaystyle \frac{∆s}{∆t}}$$

It is necessary to define the concept of the interpretation area before delving into the analysis of the acquired image. The speed is obtained by carrying out signal processing in the interpretation region, and it refers to a square picture of a given size in a specific location inside the image. Assume that at two distinct times, t₀ and t_0+t, the system records images 1 and 2 in Figure 4, locating two identically sized interpretation regions, f(m, n), in the same area of the image, where (m, n) represents the corresponding relative locations of f and g in images 1 and 2. As seen in Figure 4, processing f and g produces the proper displacement S of the interpretation region.

The relationship between the digital signal transfer function and the displacement vector, interpretation regions f and g, is shown in Figure 5 (the capital letters in the picture represent the lowercase Fourier transform). For image and correlation analysis. The method starts with a Fast Fourier Transform (FFT) correlator analysis of the images, which yields a 50% overlap of the 6464 Interrogation Areas (IAs). Next, the correlation peak is analyzed to provide the results of the last 1616-pixel questioning zone. This is found using the subpixel precise Gaussian curve-fitting method. One of the post-processing techniques in the TSI analysis program, the median procedure, is utilized to eliminate spurious vectors from velocity fields. The vectors have a rejection rate of about 3%. These rejected vectors are substituted with their neighbors using the Gaussian-weighted method [62].

The applied image processing finds the values of the flow velocity inside the spheres with diameters of 10 cm, 15 cm, and 30 cm, and for varying thicknesses of 3, 4, 5, 6, and 8 mm, using an average time of 10 µs consecutive frames (between two consecutive frames). Three separate temperature rates of 35, 40, and 45 °C are used for these tests. For each of these spheres or cases, the velocity is ascertained and subsequently estimated. The flow velocity estimate is computed at approximately 10,000 vectors in the flow photos during image processing. The entire sphere is used in velocity measurement tests. The temperature, voltage, and current amperes are measured for each example. Then, the output power is calculated.

To ensure reliable comparison across solar sphere configurations, a controlled experimental design was implemented to account for sphere diameter, wall thickness, and optical focal behavior. Acrylic spheres with outer diameters of 10 cm, 15 cm, and 30 cm were used, each tested with varying wall thicknesses of 3 mm, 4 mm, 5 mm, 6 mm, and 8 mm. For consistency, the internal volume of fluid was adjusted proportionally to sphere size, ensuring uniform thermal capacity and boundary conditions across tests. The focal length of each sphere, determined by the refractive index of the acrylic (n ≈ 1.49) and that of the working fluid (e.g., water, n ≈ 1.33; sunflower oil, n ≈ 1.47) was measured using a laser beam alignment method. The receiver or photovoltaic target was then precisely positioned at this focal region, normalizing the optical path for each test case and minimizing variation in solar concentration due to geometry.

Additionally, wall thickness was selected with consideration of the extinction coefficient of acrylic, which governs light attenuation through absorption and scattering. According to the Beer–Lambert Law, even low extinction coefficients (k ≈ 10⁻⁵ to 10⁻⁴ in the visible spectrum) can lead to measurable optical losses at greater material thicknesses [63,64]. Thinner spheres were expected to transmit more solar energy due to reduced scattering and reflection at curved interfaces. However, thicker walls were included in the study to examine trade-offs in structural integrity and their potential impact on convective behavior within the sphere. This comprehensive control of geometric and optical parameters allows for clear attribution of performance trends to design features such as sphere size and wall thickness.

The sphere with a diameter of 15 cm and a thickness of 8 mm is shown in Figure 6, while the experimental acrylic sphere with a diameter of 10 cm and a thickness of 4 mm, which is illuminated by a laser for flow visualization and additional image processing for velocity size calculation, is presented in Figure 7a,b as a sample of flow images.

4. Results

While general heat transfer models and convection principles are well-established, they form the theoretical foundation for analyzing heat transfer and fluid motion within closed domains like the solar sphere. These models define the primary governing equations relevant to convection behavior. Although the current study emphasizes qualitative observations and comparative experimental analysis, the established theoretical models support the interpretation of the observed convection phenomena:

• The Governing Equations for Incompressible Flow:

-

Continuity Equation (Mass Conservation):

∇⋅u = 0

where:

• u is the velocity vector field of the fluid;

-

Navier–Stokes Equation (Momentum Conservation):

ρ[(∂u/∂t) + (u⋅∇u)] = −∇p + μ∇²u + ρg

where:

• ρ: fluid density (kg/m³);
• u: Velocity vector field (m/s);
• t: Time (s);
• p: pressure (Pa);
• μ: dynamic viscosity (Pa·s);
• ∇²u: Viscous (diffusion) term—Laplacian of velocity;
• g: gravitational acceleration (m/s²);

2.

Energy Equation (Thermal Transport):

ρ_cp[(∂T/∂t) + ]u⋅∇T)] = k∇²T + Q

where:

• T: temperature (K);
• c_p: specific heat capacity at constant pressure (J/kg·K);
• k: thermal conductivity (W/m·K);
• ∇²T: Laplacian of temperature (conduction term);
• Q: Volumetric heat generation rate (W/m³), which may be zero if internal heat generation is neglected;

3.

Optical Concentration Ratio (C):

C = A_aperture/A_receiver

Used to describe how much sunlight is focused onto the photovoltaic area by the acrylic sphere. A higher concentration ratio can increase temperature and therefore convective activity within the sphere.

These models are widely used in computational fluid dynamics (CFD) and theoretical analysis to understand convective flow, temperature gradients, and heat transfer performance in solar thermal systems, including spherical geometries.

Figure 8 shows a PIV vector plot with an instantaneous velocity field (vectors sample) of the flow within the sphere of 15 cm diameter and 3 mm thickness at a temperature of 35 °C measured by PIV between the first frame and frame number 200 since the flow inside the sphere is quite sluggish. Figure 9 shows an example of the flow’s instantly dispersed velocity vector at a temperature of 35 °C, as determined by PIV between the first and 80th frames of a sphere with a diameter of 15 cm and a thickness of 5 mm. To enhance the clarity of the PIV results and avoid relying on raw screenshots, post-processing techniques, such as those available in Tecplot, were employed [65].

A sample of the instantly distributed velocity vector of the flow in a sphere with a diameter of 15 cm and a thickness of 8 mm, as determined by PIV between the first and 200th frames at a temperature of 35 °C, is represented in Figure 10. The flow visualization of vorticity of the flow in the sphere with a diameter of 10 cm and a thickness of 6 mm, as recorded by PIV between the first and 40th frames at a temperature of 45 °C, is illustrated in Figure 11.

These graphs demonstrate that the fluid velocity (particle velocity) near the top of the sphere is clearly higher than the seeded particle velocity in other parts of the fluid motion. The flow generated on the top of the sphere is thought to be an appropriate technique that helps in the detailed investigation of the flow regime during the flow motion from the bottom of the sphere to the top of the sphere because there are many different types of interactions between the liquid flow and the upper part of the inside wall of the sphere. Moreover, the top region’s liquid flow characteristic behaves differently from other flow zones. This is a result of the fluid flow on top reaching the upper wall and mirroring the downward direction in response. Because of this, the fluid flow is guided, reflected, and steered by the upper wall in this particular area while it is delayed in other areas of the spherical wall. In fact, there is a clear contact between the spherical wall and the fluid flow. Consequently, the data it provides helps to ascertain the downward entrainment flow. As a result, this study and the measurements that go along with it help to determine the entrainment flow in a downward direction. Additionally, this encourages research into the expression of relative velocity and how it reacts and behaves in relation to the surrounding liquid. A schematic diagram of this free convection flow is shown in Figure 12.

The above figures can be used to present and summarize the full description of the flow process inside the sphere. Around the sphere center, where the movements are mainly caused inside the fluid due to the tendency of the higher temperature and lower density fluid to rise and the lower temperature and higher density fluid to sink with the effect of gravity, resulting in heat transfer, an equally harmonic convection flow pattern is produced. In addition, the fluid flow is shown to be regular and steady all the way around the center, except the area on the upper surface where it meets and reflects. The wall of the sphere directs the rising flow around the center, creating a substantial fluid flow formation toward the upper part of the sphere. The flow develops as follows: The upper top region of the sphere is reached at the maximum velocity for the upward flow momentum. The upward flow rapidly shifts from an upward direction to a downward direction as it is reflected downwards on the wall. Once two circular liquid currents have formed around the center and have elapsed for a certain period of time, those circular currents stimulate the sphere’s center by promoting circulation across all fluid layers.

The relationship between the fluid velocity and the sphere thickness of 10, 14, and 30 cm diameter, at various temperatures of 35, 40, and 45 °C, and with a sphere thickness of 3, 4, 5, 6, and 8 mm, is depicted in Figure 13, Figure 14 and Figure 15, respectively. The average velocity of the upper region beneath the wall surface is used to compute the fluid velocity due to the fact that the fluid interacts with the upper surface frequently in this more complex area.

The relationship between the output power for a 10 cm diameter sphere at a temperature of 35 °C and sphere thicknesses of 3, 4, 5, 6, and 8 mm is shown in Figure 16. The relationship between the efficiency of a 10 cm diameter sphere at a temperature of 35 °C and sphere thicknesses of 3, 4, 5, 6, and 8 mm is shown in Figure 17. Plotting of the current-voltage characteristics was performed independently for sphere thicknesses of 3, 4, 5, 6, and 8 mm. At the maximum power point, there is an optimal functioning point. Figure 16 shows the total values of these highest power spots. This figure makes it evident that utilizing thinner acrylic increases output power and efficiency.

Table 1. Experimental parameters and results summary.

Parameter	Value (SI Units)	Impact on Flow Velocity	Impact on Power Output
Temperature	35–40 °C	Increase	23% increase
Sphere Size	15–30 cm diameter	Increase	-
Sphere Thickness	3–4 mm	Increase	10% per 1 mm decrease
Flow Velocity	Up to 35–50% increase compared to baseline	-	-

summarizes all experimental parameters and results.

To summarize, the quantitative analysis of the PIV data yielded:

• Maximum flow velocities ranging from 0.0009 m/s to 0.0025 m/s depending on sphere geometry and temperature;
• Velocity gradients (∂u/∂y, ∂v/∂x) indicative of shear layers, particularly near the sphere boundaries;
• Turbulence intensity levels up to 12% in regions with high temperature differentials, especially near the apex of the sphere;
• Vorticity contours, showing structured rotational flow zones enhanced by thinner sphere walls and higher temperatures.

These flow features directly influence convective heat transfer, enhancing fluid mixing and energy transport toward the focal region. Higher velocity gradients and turbulence intensity correspond to increased thermal boundary layer disruption, leading to more efficient heat exchange. As a result, a thinner sphere (e.g., 3 mm) at moderate temperature (40 °C) exhibited both greater internal flow activity and higher power output, confirming the positive relationship between flow dynamics and energy conversion efficiency. These power values correlate with internal flow structures, suggesting that enhanced internal convection translates into measurable performance gains in concentrated solar energy systems.

Uncertainty Analysis and Experimental Reliability

To ensure the reliability of the PIV measurements and the robustness of observed flow trends, multiple sources of experimental uncertainty were identified, controlled, and quantified where possible.

The seeding density was optimized to maintain 5–15 tracer particles per interrogation window in accordance with PIV standards, avoiding both under-seeding and particle overlap. Laser sheet alignment was regularly verified using a calibration plate to maintain consistent illumination along the mid-plane of the sphere, minimizing distortion and out-of-plane effects.

High-resolution CCD imaging was employed to ensure that particle displacements ranged between 5–10 pixels, well within the dynamic range for accurate vector calculation. Sub-pixel interpolation and window deformation algorithms were used to minimize displacement errors, while standard vector validation routines filtered outliers to preserve coherent flow fields.

Although the flow was slow and predominantly laminar due to natural convection, frame separation (80 to 200 frames) was adjusted to optimize displacement without inducing motion blur. Importantly, repeated measurements under identical thermal and geometric conditions yielded highly consistent velocity vector fields and flow structures, indicating high repeatability.

To statistically validate the flow measurements, each experimental configuration was repeated at least three times, and standard deviations of the average velocity values were calculated and included as error bars in Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17. Across these experiments, the standard deviation for average velocity measurements in the upper wall region remained within ±5–8%, reflecting good measurement precision. In regions of higher temperature gradients, turbulence intensity reached up to 12%, contributing to larger but still manageable variability.

For the power and efficiency data shown in Figure 16 and Figure 17, repeated I–V measurements were conducted, and the standard deviation at each sphere thickness was plotted as vertical error bars. The results confirmed that thinner spheres (e.g., 3 mm) consistently produced higher power output and efficiency, with less than ±4% variation between repetitions, further supporting the observed trends.

While the primary aim of this study is to capture relative trends in flow and thermal performance rather than absolute values, the inclusion of error bars and statistical variation strengthens the validity of the results. These quantitative assessments confirm that the conclusions regarding the effects of sphere thickness, diameter, and temperature are statistically reliable and not due to random noise measurement.

While the present study successfully captures qualitative flow structures, particularly the intensified motion and directional changes near the top wall of the acrylic sphere using PIV, claims such as “flow reflection from the upper wall” and “downward entrainment development” would benefit from additional substantiation through theoretical modeling or Computational Fluid Dynamics (CFD) simulations. The observed behaviors, including flow reversal at the apex and formation of circular convection cells, are physically plausible and supported by experimental observations; however, CFD validation using laminar buoyant flow models (e.g., Boussinesq approximation) could provide detailed streamline plots and pressure/velocity distributions to confirm these mechanisms. Moreover, numerical simulations would allow for parametric studies at higher spatial and temporal resolution than what is possible experimentally. This would enable a deeper analysis of the boundary layer development near the top wall, entrainment dynamics, and localized thermal gradients driving convection. Integrating such computational validation in future work would reinforce the current findings and elevate the predictive power of the study by bridging experimental data with first-principles modeling. A complementary study is currently underway, focusing on CFD modeling using ANSYS Fluent (https://www.ansys.com/products/fluids/ansys-fluent, accessed on 11 June 2025), with the aim of providing a comprehensive simulation-based validation of the experimental observations presented here.

5. Discussion

The experiments were initially conducted using water, followed by sunflower oil, as the working fluid inside the sphere. Both fluids exhibit temperature-dependent physical properties, particularly viscosity and density, which can significantly influence convection behavior. For example, the dynamic viscosity of sunflower oil decreases by approximately 40–50% as temperature increases from 25 °C to 45 °C, leading to a corresponding rise in flow velocity and convection strength. While such changes are notable, they affect all configurations proportionally and are therefore consistent across comparative experiments. The primary goal of this study is not to provide precise, absolute velocity values, but to investigate relative trends and flow patterns as influenced by parameters such as sphere temperature, size, and wall thickness. Thus, the observed flow behavior remains valid and meaningful, especially given that experimental conditions (lighting, fluid volume, ambient temperature) were carefully controlled for each measurement set. The consistency of these conditions ensures that the detected differences in flow structure can be attributed to the investigated parameters rather than uncontrolled thermal variations.

The illustrations show that as the velocity increases, the fluid flow approaches the upper spherical surface. Moreover, a comparison of the velocity vectors reveals that the velocity increases with decreasing spherical thickness. On the other hand, in the area of the sphere’s top surface, the average velocity of the 3 mm thickness sphere is almost 20 to 30% higher than that of the 5 mm thickness sphere, and the average velocity of the 5 mm thickness sphere is almost 25 to 35% higher than that of the 8 mm thickness sphere, and also the average velocity of the 3 mm thickness sphere is almost twice that of the 8 mm thickness sphere. As a result, we can say that lowering the thickness by 1 mm will increase the average velocity on the top of the sphere by about 10%, which is about 0.0001 m/s. Moreover, fluid velocity rises with temperature. Furthermore, the fluid velocity increases along with the sphere’s size. It is also known that the 3 mm thick sphere has a higher output power and efficiency than other sphere thicknesses. In addition to the thickness of the acrylic sphere, a critical consideration in this study is the optical refraction caused by the curved and relatively thick spherical wall. As laser light passes through the acrylic material, bending and distortion of the beam might occur due to differences in the refractive indices between air and acrylic. This refraction might affect the accuracy of optical measurements, particularly in Particle Image Velocimetry (PIV) applications, by altering the laser sheet alignment, intensity distribution, and ultimately, the reliability of velocity field data. Therefore, accounting for and minimizing these optical distortions is essential for ensuring the precision and validity of experimental results. However, while the refraction of laser light through the thick acrylic wall is an inherent optical concern, it does not critically affect the outcomes of this study. This is because the primary focus is on analyzing the qualitative flow patterns rather than extracting precise quantitative velocity data. The objective is to investigate the general relationship between flow behavior and parameters such as sphere temperature, size, and wall thickness. As long as the flow structures and trends remain visually consistent and distinguishable, minor optical distortions caused by refraction do not compromise the integrity or conclusions of the study. Moreover, consistent experimental conditions and camera positioning were maintained throughout all tests, ensuring comparability across different cases.

In actuality, the amount of solar radiation received is regulated and limited, decreasing as the thickness of this acrylic solar sphere increases. The output power is lower as a result. Therefore, the more electricity generated by the sun, the thinner the acrylic. Decreasing thickness results in increased power production and increased efficiency. Therefore, the more solar light that the acrylic sphere absorbs, the thinner the acrylic coating. As a result, efficiency increases with increasing output power.

While the present study was conducted under controlled and stable illumination conditions, variable solar insolation in real-world environments would influence both the thermal gradient and the strength of natural convection inside the sphere. Under lower insolation levels, the induced flow velocities and internal temperature differences would diminish, leading to reduced fluid motion and lower power output. However, the relative trends observed with respect to sphere thickness, size, and temperature would remain consistent, albeit with reduced magnitudes. Furthermore, thinner spheres, with lower thermal inertia, are expected to respond more dynamically to fluctuating solar input, potentially offering advantages under variable conditions. Future studies incorporating real-time solar irradiance monitoring or outdoor testing would be valuable to evaluate dynamic performance and validate the robustness of the observed trends

5.1. Influence of Sphere Thickness on Optical Performance

The thickness of the acrylic sphere plays a critical role not only in mechanical stability and internal convection flow but also in its optical performance, particularly in terms of light transmission, absorption, and scattering. One of the key material parameters influencing this behavior is the extinction coefficient (κ), which quantifies how strongly the acrylic material absorbs and attenuates light at a specific wavelength. According to the Beer–Lambert law, the intensity of light transmitted through a material of thickness d can be expressed as:

I = I₀ e^−αdI

where:

• I₀ is the incident light intensity;
• α = 4πκ/λ is the absorption coefficient;
• κ is the extinction coefficient;
• λ is the wavelength of the incident light.

As the wall thickness increases, more light is attenuated before reaching the focal point or internal fluid region, due to increased optical path length through the acrylic. This directly reduces the available solar flux for energy conversion, decreasing the power output and efficiency of the system. Thinner spheres, conversely, allow greater light transmission, enabling a higher photon flux density at the focus and improving the efficiency of energy capture and conversion.

For example, assuming κ ≈ 0.01 at a representative solar wavelength of 550 nm (green light), the absorption coefficient α\alpha becomes approximately 0.23 mm⁻¹. Applying this to two sphere wall thicknesses:

• For 8 mm:

I = I₀ e^−αdI = I₀ e^−0.23×8 ≈ 0.16 → 84% attenuation;

• For 3 mm:

I = I₀ e^−αdI = I₀ e^−0.23×3 ≈ 0.51 → 49% attenuation.

This means the 3 mm thick sphere transmits over three times more light than the 8 mm thick spheres. The greater transmitted intensity leads to higher internal fluid heating and stronger convection, directly contributing to improved energy capture and flow velocity, aligning with experimental results showing a ~23% gain in efficiency and up to 50% increase in peak flow velocity for thinner configurations.

While the reduction in acrylic sphere thickness to 3 mm results in significant optical and thermal performance improvements, this optimization introduces potential mechanical limitations. Thinner acrylic walls exhibit reduced structural strength and may be more susceptible to thermal deformation or mechanical failure, particularly under outdoor or dynamic loading conditions. Therefore, while 3 mm is suitable for controlled laboratory environments, practical deployment may require reinforcement or alternative materials with higher impact resistance. Future work should explore hybrid sphere designs that combine optical transparency with mechanical robustness to ensure reliability under real-world operating conditions.

5.2. Impact of Refraction and Focal Precision

Moreover, thicker acrylic walls introduce more pronounced refraction and distortion, particularly near the edges where light enters at oblique angles. These optical distortions can shift or blur the focal point, leading to less precise light concentration onto the photovoltaic receiver or fluid volume. This effect becomes more significant when the refractive index mismatch between acrylic and the fluid is large, or when the sphere’s curvature is steep (i.e., small radius).

5.3. Balancing Optical, Structural, and Thermal Constraints

Therefore, in selecting the optimal sphere thickness, a trade-off must be managed between optical transparency (governed by κ and thickness), structural integrity, and thermal and fluid dynamic performance.

Empirical results in this study support the theoretical expectation that thinner spheres (e.g., 3 mm) yield higher power output due to reduced optical losses and enhanced internal convection. These findings align with previous material optics studies [66,67], which emphasized the critical impact of material absorption and scattering on the optical performance of concentrator geometries.

5.4. Temperature Dependence of Fluid Properties

The experiments were initially conducted using water, followed by sunflower oil (a type of frying oil), as the working fluid inside the sphere. It is important to note that the physical properties of both fluids, particularly viscosity and density, are highly temperature-dependent. As temperature rises, viscosity typically decreases, leading to lower resistance to flow and more vigorous convection. These variations can significantly influence flow behavior, making thermal conditions a critical factor in the analysis of flow patterns and their relationship to geometric parameters.

Although fluid properties such as viscosity and density vary with temperature, this does not compromise the validity of the results in the context of this study. The objective is not to obtain precise quantitative velocity measurements, but rather to investigate general flow behavior and trends related to parameters such as sphere temperature, size, and wall thickness. Since the focus is on relative comparisons, the influence of temperature-dependent properties is consistent across cases. Moreover, experimental conditions were carefully controlled and kept consistent during each set of measurements, ensuring that observed variations in flow behavior are attributable to the investigated parameters rather than uncontrolled thermal effects.

5.5. Role of Convection in Thermal Regulation

Although the fluid inside the acrylic sphere does not directly contact the photovoltaic (PV) cell, convective flow still plays a vital role in thermal regulation, which indirectly influences power output. As sunlight is absorbed and concentrated within the sphere, the fluid absorbs a portion of this thermal energy, creating convective currents that help redistribute heat. This circulation delays local overheating at the focal point and helps maintain the operational temperature of the acrylic material and surrounding structure within an optimal range. By mitigating heat buildup and promoting a more uniform temperature distribution, the fluid convection supports the system’s thermal stability, thereby protecting the optical properties of the acrylic and improving the overall efficiency of light focusing and energy conversion. Furthermore, improved thermal management contributes to longer PV cell lifespan and better performance, even without direct contact with the fluid. Thus, convection within the sphere remains a crucial factor in enhancing power output efficiency through passive thermal regulation.

5.6. Explanation of Apparent Geometric Distortion in PIV Figures

The apparent distortion and non-typical round shape seen in Figure 8 and Figure 9 can be attributed to a combination of optical effects and experimental measurement limitations. One of the primary reasons for this visual distortion is related to the slow flow of velocities observed in many regions of the sphere, particularly under low-temperature conditions.

In fact, as the flow is slow in many parts of the sphere, especially near the bottom or outer edges, it was difficult to perform accurate PIV measurements in those regions. PIV relies on capturing particle motion over short time intervals, and when fluid movement is minimal, the displacement of tracer particles becomes too small to resolve effectively. As a result, these regions may appear incomplete or geometrically distorted in the final velocity vector fields.

Additionally, in some experiments (as in Figure 8 and Figure 10), the velocity vectors were extracted from image sequences between frames 1 to 200. This frame selection was optimized to capture flow development over time while avoiding noise or fluctuations present in the initial or final frames. However, because the flow remained relatively slow during this interval in some zones, the resulting vector field may lack detail or coverage in those areas. On top of that, optical refraction through the curved acrylic wall further contributes to the visual distortion. The acrylic sphere introduces the bending of light rays due to refractive index mismatches between air, acrylic, and the internal fluid (water or sunflower oil). This effect is particularly pronounced near the edges of the sphere, where light enters at oblique angles, leading to geometric distortion in the 2D images.

Furthermore, slight misalignment of the camera, lens distortion, and the projection of the 3D spherical geometry onto a 2D imaging plane can exaggerate the elongation or asymmetry seen in the visualizations.

Despite these limitations, the qualitative flow structures and comparative trends remain consistent and scientifically valid across all experiments. Therefore, while the images may not always show a perfectly round sphere, the conclusions drawn regarding the influence of thickness, temperature, and size on internal flow dynamics remain reliable and robust.

5.7. Flow Dynamics and Efficiency Optimization

Lastly, an investigation into the behavior of flow motion within the solar sphere was conducted in an effort to enhance power generation efficiency. The purpose of this study endeavor was to maximize the related efficiency by improving fluid flow performance, which is explained in this publication, by examining the impact of sphere thickness on fluid flow. The findings showed that the fluid velocity value and flow structure are significantly changed by the sphere’s thickness. Therefore, to improve the solar sphere’s effectiveness, a thinner sphere ought to be used.

6. Conclusions

This study systematically investigated the internal fluid dynamics of solar spheres using Particle Image Velocimetry (PIV) to understand how geometric and thermal parameters influence flow behavior and energy performance.

6.1. Key Findings

• Optimal Sphere Thickness: A 3 mm thick acrylic sphere demonstrated a 23% increase in efficiency compared to thicker configurations, attributed to enhanced solar transmittance and reduced optical losses;
• Temperature and Size Effects: Increased temperatures and larger sphere diameters significantly boosted internal flow velocities, highlighting temperature management and sphere size as critical factors in performance optimization;
• Velocity Distribution Patterns: Flow visualization revealed higher velocities near the upper internal surface, indicating that reduced sphere thickness intensifies convection and heat transport efficiency;
• Comparative Advantage Over CPV/CSP: Unlike traditional CPV/CSP systems requiring external tracking and mirrors, the solar sphere offers a compact, passive alternative. This study advances the field by integrating fluid dynamic analysis previously overlooked [68,69], providing a more complete thermal-fluidic characterization.

6.2. Design Recommendations

• Use 3–4 mm acrylic thickness for optimal balance between strength and optical efficiency;
• Employ sphere diameters ≥ 15 cm to promote strong internal convection;
• Maintain internal fluid temperatures around 35–45 °C to enhance flow without degrading materials;
• Select fluids with high thermal stability and optical compatibility (e.g., sunflower oil).

6.3. Novelty and Future Directions

This study presents a novel experimental investigation of internal flow dynamics in acrylic solar concentrator spheres using Particle Image Velocimetry (PIV). By systematically analyzing the effects of wall thickness, sphere diameter, and fluid temperature with sunflower oil as the working fluid, the research uniquely links optical transmission, buoyancy-driven convection, and energy conversion performance. The results reveal how geometric and thermal parameters jointly influence flow structures and efficiency, establishing a solid experimental foundation for future CFD validation and solar system optimization.

Additionally, this work offers a comprehensive thermal-fluidic characterization framework for solar spheres. Future research should explore advanced materials, integration of thermal energy storage, scalability, and economic feasibility to support the real-world implementation of solar concentrator technologies.