Introduction

Unmanned Aerial Vehicles (UAVs), commonly known as drones, have revolutionized various industries because of their versatility and adaptability. From aerial photography and surveillance to search and rescue operations and environmental monitoring, drones have found application in a diverse range of fields that demand special maneuvering capabilities1,2,3,4,5,6. The effectiveness of UAVs in performing complex tasks is strongly dependent on their aerodynamic performance, which is largely determined by the airfoil profiles of their wings7.

This study focused on the aerodynamic analysis of three National Advisory Committee for Aeronautics (NACA) airfoil profiles: NACA 2412, NACA 4415, and NACA 0012. These profiles have been widely adopted owing to their well-documented aerodynamic properties and ease of implementation in computational studies8,9,10,11,12,13,14. The selection of an appropriate airfoil is crucial for optimizing UAV performance in applications that require agile maneuvering, such as indoor navigation, urban environment operations, and precision agriculture15.

Our study employed computational fluid dynamics (CFD) and XFOIL simulations to comprehensively analyze the airfoil performance under various conditions. CFD simulations offer detailed insights into the flow characteristics and pressure distributions16, whereas XFOIL provides a computationally efficient method for preliminary analysis17. Furthermore, we developed a hybrid artificial neural network (ANN)-Genetic Algorithm (GA) model to optimize the design parameters of the selected airfoil, such as the angle of attack (AOA) and Reynolds number, to maximize the lift-to-drag ratio.

This study builds on previous research on airfoil design and UAV applications. Obradovic et al.18 focused on morphing wing configurations for enhanced maneuverability. Ali et al.19 conducted a comparative analysis of NACA profiles for power generation. However, our study is unique in its focus on the specific requirements of drones that require special maneuvering capabilities. Factors such as agility, flight stability, and efficiency in diverse operational environments were considered.

Recent advancements in machine-learning techniques have demonstrated promising results for airfoil design optimization. For instance, Teimour et al.20 demonstrated the effectiveness of machine learning and surrogate modelling for airfoil aerodynamic performance. Wu et al.21 employed a GA coupled with a deep neural network to optimize the airfoil shapes for improved performance. The proposed hybrid ANN-GA approach builds upon these developments, combining the predictive power of neural networks with the optimization capabilities of GAs.

The context of drones requiring special maneuvering results in unique constraints and considerations in terms of the UAV design. As reported by Sun et. al.22, factors such as the control surface effectiveness, stability derivatives, and aerodynamic moments are critical for the successful implementation of highly maneuverable UAVs. This study addressed these issues by focusing on airfoil designs capable of enhancing lift-to-drag ratios and providing favorable stability characteristics under various operating conditions.

Highly maneuverable drones find application in a vast and rapidly expanding range of fields. In urban environments, UAVs can be used for infrastructure inspection, traffic monitoring, and emergency response23. In agriculture, they enable precision farming through detailed crop monitoring and targeted interventions24. In case of search and rescue operations, agile drones can navigate complex terrain and provide critical support in time-sensitive situations25. Further, in environmental research, maneuverable drones facilitate close-range observations of wildlife and ecosystems without causing significant disturbances26.

This study aimed to provide valuable insights into the field of UAV design for applications that require special maneuvering capabilities. By optimizing airfoil designs to enhance the aerodynamic performance, we sought to improve the overall efficiency, agility, and versatility of drones across various industries. The integration of advanced computational methods, machine learning techniques, and practical considerations for highly maneuverable UAVs presents a novel approach for addressing the evolving challenges in drone technology and its wide-ranging applications.

Airfoil selection

The selection of an appropriate airfoil is crucial for designing an efficient UAV wing, particularly for applications that require special maneuvering capabilities. In this study, we selected three specific airfoil profiles from the NACA series: NACA 2412, NACA 0012, and NACA 4415, as shown in Fig. 1.

The NACA 2412 airfoil exhibits good aerodynamic performance under various operating conditions, providing a balance between lift generation and drag minimization27. This balance is particularly important for UAVs that must maintain their efficiency over long distances and under varying flight conditions. Its moderate camber (2% at 40% chord) and maximum thickness (12% at 30% chord) contribute to its versatility, rendering it suitable for various UAV applications28.

NACA 0012, which is a symmetric airfoil with a thickness of 12% of the chord length, offers structural advantages and low pitching moments, thereby contributing to the flight stability of the UAV29. Its symmetrical profile results in zero lift at a zero AOA, which can be beneficial for certain flight phases. In addition, it exhibits good stall characteristics, which can be advantageous for UAVs operating under unpredictable weather conditions. The simplicity of NACA 0012 also makes it easy to manufacture, potentially reducing production costs30.

The NACA 4415 airfoil, which is characterized by a moderate camber (4% at 40% chord) and a thickness-to-chord ratio of 15%, exhibits a high lift-to-drag ratio28. This property is particularly advantageous because it can potentially improve flight efficiency and endurance, thereby facilitating longer mission ranges or increased payload capacity. The NACA 4415 also exhibits desirable stall characteristics, enhancing the UAV’s flight stability and controllability27. Further, it exhibits a higher maximum thickness compared with the other two profiles and may consequently offer additional structural benefits and internal volume for the payload or fuel.

By analyzing and comparing the aerodynamic performances of these NACA airfoils, we aimed to identify the most suitable configuration to maximize lift, minimize drag, and enhance the overall flight efficiency. This study considered various performance metrics, including the lift and drag coefficients, lift-to-drag ratios, and stall characteristics, for various angles of attack and Reynolds numbers relevant to typical UAV operations7.

Fig. 1
figure 1

Airfoil profiles considered for the UAV design.

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Preliminary analysis using XFOIL

XFOIL (v 6.99), developed by Drela at MIT, is a widely used computational tool for analyzing and predicting the aerodynamic properties of airfoils17. It combines the principles of CFD and potential flow theory to provide efficient and reasonably accurate results for subsonic airfoils. The popularity of XFOIL in the aerospace industry and academia is attributable to its ability to rapidly generate performance predictions. This renders it an invaluable tool for preliminary design and optimization studies.

The core methodology of XFOIL involves numerically solving two-dimensional, steady-state, incompressible flow equations around an airfoil using a panel method coupled with an integral boundary layer formulation. This process involves the discretization of the airfoil surface into panels, calculation of the inviscid flow field using a linear-vorticity stream function panel method, coupling of the inviscid solution with a two-equation integral boundary layer formulation, and the iterative adjustment of the circulation around each panel to satisfy the boundary conditions. This approach facilitates XFOIL in predicting aerodynamic behavior over various angles of attack and Reynolds numbers with remarkable computational efficiency31.

XFOIL offers several advantages for preliminary airfoil analysis, including rapid computation times compared with full Navier-Stokes CFD simulations, reasonably accurate predictions for attached flow conditions, ability to handle a wide range of Reynolds numbers, and integrated and inverse design capabilities. However, it is crucial to understand the limitations of XFOIL. The software assumes inviscid flow, neglects the effects of viscosity and turbulence, and has limited accuracy in predicting the separated flow and post-stall behavior. Further, it is restricted to two-dimensional, incompressible, and steady-state flow conditions and may overpredict the maximum lift coefficient and underpredict the drag in certain cases. Despite these limitations, XFOIL remains a valuable tool for initial airfoil assessment and optimization32.

In this study, we utilized XFOIL as a preliminary analysis tool to evaluate the aerodynamic characteristics of the selected NACA airfoils (2412, 0012, and 4415). The analysis was conducted for various angles of attack (− \(5^{\circ }\) to \(15^{\circ }\)) and at three specific Reynolds numbers: 200,000, 500,000, and 800,000. These Reynolds numbers were chosen to represent a range of operating conditions typical of small-to medium-sized UAVs, thereby covering various flight speeds and altitudes15. For each airfoil and Reynolds number combination, XFOIL was used to generate data on the lift coefficient (\(C_L\)), drag coefficient (\(C_D\)), moment coefficient (\(C_m\)), lift-to-drag ratio (\(C_L/C_D\)), pressure distribution along the airfoil surface, and boundary layer parameters.

CFD analysis

CFD simulations were conducted using ANSYS Fluent 2022 R2 to complement the preliminary analysis performed using XFOIL and achieve a more comprehensive understanding of the aerodynamic behavior of the selected NACA airfoils. This advanced numerical approach facilitates a detailed investigation of the flow field around the airfoils, thus providing insights that are crucial for optimizing UAV performance, particularly for designs that require special maneuvering capabilities. Geometric data files for the NACA 2412, 0012, and 4415 airfoil profiles were retrieved from the Airfoil Data Site of the University of Illinois at Urbana-Champaign (UIUC). Consequently, the computational domain was created as a C-grid topology, extending 20 chord lengths upstream and downstream of the airfoil and 15 chord lengths in the vertical direction to ensure the accurate capture of far-field conditions33.

A structured mesh was generated using ANSYS ICEM CFD, with particular attention paid to the boundary-layer region. A comprehensive grid-independence study was conducted to ensure the accuracy and reliability of the CFD results. Four mesh resolutions were investigated: coarse (50,000 elements), medium (100,000 elements), fine (150,000 elements), and very fine (200,000 elements). The lift and drag coefficients of the NACA 4415 airfoil at a \(5^{\circ }\) AOA and Re = 500,000 were computed for each mesh resolution. The results of the grid independence study are listed in Table 1.

Table 1 Grid independence study results.
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Based on the grid independence study, a fine mesh with 150,000 elements was selected for all subsequent simulations. This is because it provided a good balance between computational efficiency and accuracy. The relative difference in the lift and drag coefficients between the fine and very fine meshes was less than 0.1%. Thus, further refinement would not significantly improve the results.

The selected mesh comprised approximately 150,000 elements with a y+ value less than 1 to resolve the viscous sub-layer accurately. The final mesh configuration provided a balance between the computational efficiency and accuracy, as illustrated in Fig. 2.

The inlet boundary was set to a prescribed velocity of 20 m/s, which is representative of typical UAV operating speeds. This velocity corresponded to Reynolds numbers of approximately 200,000, 500,000, and 800,000 for chord lengths of 0.15, 0.375, and 0.6 m , respectively, covering a range of small to medium-sized UAV configurations. The outlet boundary was specified as the pressure outlet under atmospheric conditions. A no-slip wall condition was applied to the airfoil surface.

Turbulence effects were incorporated using the shear stress transport (SST) k − \(\omega\) turbulence model. This model provides accurate predictions of adverse pressure gradient flows and separations34. Two turbulence intensity levels, 1% and 5%, were investigated to assess the impact of free-stream turbulence on the airfoil performance. These levels represented the relatively calm and moderately turbulent atmospheric conditions typically encountered by UAVs, respectively.

The pressure-based coupled solver was utilized employing second-order upwind discretization schemes for momentum, turbulent kinetic energy, and specific dissipation rate. The SIMPLE algorithm was employed for pressure-velocity coupling. Simulations were conducted for angles of attack ranging from \(-5\) to \(15^{\circ }\) in \(2^{\circ }\) increments. For each configuration, the solution was initialized using a hybrid initialization method. The convergence was monitored based on several criteria, including residuals for continuity, momentum, and turbulence equations below 1e–6 m stable lift and drag coefficients with less than 0.1% variation over 1000 iterations, and a mass flow rate imbalance of less than 0.1% between the inlet and outlet. Here, 5000 iterations were performed for each case; typically, convergence was achieved within 3000–4000 iterations.

To ensure the reliability of the CFD results, a validation study was conducted based on comparisons of the CFD predictions with the experimental data available in the literature for the NACA 0012 airfoil at Re = 500,0009. In addition, the CFD results were compared with XFOIL predictions to assess the limitations and advantages of each method.

Fig. 2
figure 2

CFD mesh and boundary conditions for airfoil analysis.

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Development of ANN and hybrid ANN-GA models

Development of ANN model

A feed-forward backpropagation ANN model was developed to predict the lift-to-drag ratio (\(C_L/C_D\)). The functional relationship between the input and the output is expressed as Eq. (1).

$$\begin{aligned} \frac{C_L}{C_D} = f\bigg (\textit {AOA}, Re, C_{max}, C_{pos}, {th}\bigg ) \end{aligned}$$
(1)

where, \(C_L/C_D\) denotes the ratio of the lift coefficient (\(C_L\)) to the drag coefficient (\(C_D\)), AOA denotes the angle of attack, Re denotes the Reynolds number, \(C_{max}\) denotes the maximum camber, \(C_{pos}\) denotes the position of the maximum camber, and th denotes the thickness.

The ANN model comprised three layers: input, hidden, and output. The input layer included five neurons corresponding to the parameters AOA, Re, \(C_{max}\), \(C_{pos}\), and th, whereas the output layer contained a single neuron representing \(C_L/C_D\). This architecture was consistent with standard practices in ANN design for aerodynamic applications35. The training process begins with the initialization of the ANN model, where the input weights (\(W_I\)), output weights (\(W_O\)), and biases (\(W_B\)) were randomly generated from a uniform distribution, as recommended by Haykin36.

The training parameters are listed in Table 2. To prevent overfitting, the model was validated using a separate validation dataset. Error minimization was achieved through back-propagation, which is a technique widely used in ANN training owing to its efficiency and effectiveness37.

Table 2 Training parameters for developing the ANN model.
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The optimal number of neurons in the hidden layer was determined by increasing the neuron count incrementally until the minimum mean squared error (MSE) and maximum correlation coefficient (R) were obtained, as shown in Fig. 3. The optimal ANN architecture was established as 5-13-1.

Fig. 3
figure 3

Estimating the optimum number of neurons: (a) MSE versus Number of neurons in a hidden layer and (b) R versus Number of neurons in a hidden layer.

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The final values of \(W_I\), \(W_O\), and \(W_B\) are listed in Table 3, and the architecture of the developed ANN model is depicted in Fig. 4.

Table 3 Details of weights of input, output layers, and biases.
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Fig. 4
figure 4

Developed ANN model architecture.

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The developed ANN model was trained using a CFD dataset. The various statistical parameters of the inputs and output variables are illustrated in Table 4. Of the total 198 dataset, 70% was used for training, and 15% each was used to test and validate the ANN model, respectively, following the recommendations by Demuth et al.38.

Table 4 Data statistics of the CFD data used for ANN modeling.
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The data were normalized using Eq. (2) to train the ANN model. The resulting output was de-normalized using Eq. (3) to compare the results. This normalization process is crucial for improving the ANN’s learning efficiency and preventing the dominance of variables with larger magnitudes39.

$$\begin{aligned} x_{Ni}= & x_L + \frac{x_i - x_{min.}}{x_{max.} - x_{min.}}(x_U - x_L) \end{aligned}$$
(2)
$$\begin{aligned} x_{DNi}= & x_{min.} + \frac{x_{Ni} - x_L}{x_U - x_L}(x_{max.} - x_{min.}) \end{aligned}$$
(3)

where \(x_{Ni}\) is the normalized value of the \(i{\text {th}}\) observation, \(x_{DNi}\) is the de-normalized value of the \(i{\text {th}}\) observation, \(x_i\) is the \(i{\text {th}}\) observation in the dataset, \(x_U = 0.9\) and \(x_L = 0.1\) are the upper and lower limits of the normalized value of the data, respectively, and \(x_{min.}\) and \(x_{max.}\) are the minimum and maximum values of the datasets, respectively. The performance of the developed ANN model for predicting \(C_L/C_D\) was assessed by evaluating the statistical parameters, that is, the mean percentage error (MPE), MSE, and correlation coefficient (R), as shown in Eqs. (4)–(6), respectively.

$$\begin{aligned} MPE= & \frac{1}{n}\sum _{i=1}^{n}\left( \frac{O_i - P_i}{O_i}\right) \times 100 \end{aligned}$$
(4)
$$\begin{aligned} MSE= & \frac{1}{n}\sum _{i=1}^{n}(O_i - P_i)^2 \end{aligned}$$
(5)
$$\begin{aligned} R= & \frac{\sum _{i=1}^{n}(O_i - \bar{O})(P_i - \bar{P})}{\sqrt{\sum _{i=1}^{n}(O_i - \bar{O})^2\sum _{i=1}^{n}(P_i - \bar{P})^2}} \end{aligned}$$
(6)

where Oi and Pi are the observed and predicted values, respectively and \(\overline{O}\) and \(\overline{P}\) are the mean of observed and predicted values, respectively.

Development of hybrid ANN-GA model

The hybrid ANN-GA model integrated the predictive capabilities of ANNs with the optimization power of GAs to determine the optimal design parameters for airfoils. This approach leveraged the ability of ANN to model complex relationships between input parameters and aerodynamic performance, while utilizing the robust optimization techniques of GA to determine the optimal configuration.

Equation (1) indicates that the lift-to-drag ratio (\(C_L/C_D\)) is dependent on the airfoil parameters (\(C_{max}\), \(C_{pos}\), and th) and the flow parameters (AOA and Re). The hybrid ANN-GA model aimed to determine the optimal values of these parameters to maximize the \(C_L/C_D\) ratio. The optimization problem can be mathematically formulated as

$$\begin{aligned} \begin{aligned}&\text {Minimize} & f(x) = -(C_L/C_D) \\&\text {subject to} & x^L \le x \le x^U \end{aligned} \end{aligned}$$
(7)

where x represents the vector of independent variables, including AOA and Re, and \(x^L\) and \(x^U\) denote the lower and upper bounds of the vector x, respectively.

Figure 5 illustrates a flowchart of the hybrid ANN-GA model, detailing the process of integrating the pre-developed ANN model with the GA optimization framework.

Fig. 5
figure 5

Flowchart of hybrid ANN-GA model.

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The process began by obtaining NACA airfoil data, which were used to generate an initial population size of 50 potential solutions. Each solution in the population is represented by a set of design parameters (AOA, Re, \(C_{max}\), \(C_{pos}\), th). The trained ANN model then computed the \(C_L/C_D\) ratio for each solution in the population.

The GA evaluated the fitness of each solution based on an objective function (Eq. 7). If the stopping criteria were not satisfied, the GA applied selection, crossover, and mutation operators to create a new generation of solutions. This process continued iteratively, with each generation ideally moving closer to the optimal solution.

The key GA operators employed in this hybrid model are as follows:

  • Elitism The preservation of the best solutions from each generation to ensure the quality of solutions does not degrade over time40.

  • Crossover The combination of genetic information from two parent solutions to create offspring, thereby promoting exploration of the solution space41.

  • Mutation The introduction of random changes to solutions, thereby aiding the maintenance of genetic diversity and avoiding premature convergence to local optima42.

The adopted genetic algorithm parameters include an elitism rate of 5%, a mutation rate of 15%, and a crossover approach with a crossover fraction of 0.8 using an intermediate crossover function. The hybrid ANN-GA model performed several iterations of this process until the stopping criteria were satisfied, which may include reaching the maximum number of generations or achieving the desired level of fitness. Upon completion, the model output the optimal design parameters that maximized the \(C_L/C_D\) ratio for a particular airfoil.

This hybrid approach combined the ability of ANN to rapidly evaluate the airfoil performance coupled with the capability of GA to efficiently search large, complex solution spaces. By leveraging the strengths of both techniques, the hybrid ANN-GA model provides a powerful tool for the optimization of airfoil designs for specific UAV applications, considering both geometric and flow parameters simultaneously43.

Results and discussion

Angle of attack versus \(C_L/C_D\)

Figure 6 illustrates the relationship between the AOA and the ratio of the lift to the drag coefficients (\(C_L/C_D\)) for three NACA airfoil profiles: NACA 2412, NACA 4415, and NACA 0012. Simulations were conducted using both CFD and XFOIL for Reynolds number (\(Re\)) values of 200,000, 500,000, and 800,000. The ratio \(C_L/C_D\) is a measure of aerodynamic efficiency. Higher values indicate better performance, which is a crucial requirement for achieving efficient flight characteristics for long-range missions.

Fig. 6
figure 6

Angle of attack versus \(C_L/C_D\) for NACA 2412, NACA 4415, and NACA 0012 profiles at different Reynolds numbers.

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For NACA 2412 and NACA 4415, the CL/CD ratio increased with the AOA, peaking at approximately AOA = \(6^\circ\) to \(10^\circ\) before decreasing as the stall angle approached. NACA 4415 consistently demonstrated higher CL/CD ratios than NACA 2412, indicating its superior performance. The enhanced performance of NACA 4415 is particularly beneficial as it directly translates to improved endurance for UAVs. A higher lift-to-drag ratio means less energy is required to maintain flight, allowing for longer flight times and the ability to survey larger areas per flight—critical for applications like precision agriculture and environmental monitoring. This also indirectly impacts payload capacity; with a more efficient airfoil, more of the available energy can be dedicated to carrying heavier payloads.

The symmetric NACA 0012 profile exhibited a lower CL/CD ratio than the cambered profiles, with the peak occurring at approximately AOA = \(4^\circ\) to \(6^\circ\). Although this profile may not offer the highest efficiency, its symmetric nature could provide stability advantages during certain flight phases, which could be valuable for UAVs that operate in diverse and potentially challenging environments that are often encountered in remote-area deliveries.

Increasing the Reynolds numbers resulted in higher CL/CD ratios for all the profiles, indicating improved aerodynamic efficiency. This is particularly relevant for medical supply delivery UAVs, as they may operate at various speeds and altitudes depending on the mission requirements.

A comparison between CFD and XFOIL results indicated that CFD provided more accurate results, while XFOIL offered quicker predictions. The results from CFD and XFOIL were consistent at lower AOA values. However, the discrepancies increased at higher angles and near stall, with XFOIL generally underestimating the CL/CD ratio.

The analysis indicated that NACA 4415 generated the highest CL/CD ratio, rendering it the most suitable airfoil of the three studied profiles. Its superior lift generation and efficiency characteristics facilitated an increased payload capacity and extended flight range.

As shown in Table 5, the approximate stall angles for NACA 2412, NACA 0012, and NACA 4415 are \(11^\circ\), \(7^\circ\), and greater than \(12^\circ\), respectively. These values correspond to the observed peaks in the CL/CD curves, beyond which the aerodynamic efficiency begins to decrease due to stall.

Table 5 Approximate stall angles from CFD simulations.
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Pressure contours analysis at critical angles of attack

Figure 7 presents the pressure contours obtained from the (CFD) simulations for NACA 2412, NACA 0012, and NACA 4415 airfoil profiles at four AOA: \(-\,5^\circ\), \(0^\circ\), \(5^\circ\), and \(12^\circ\). These pressure contours provided valuable insights into the aerodynamic behavior of each airfoil under different operating conditions.

Fig. 7
figure 7

Pressure contours from CFD simulations for NACA 2412, NACA 4415, and NACA 0012 profiles at various angles of attack (\(AOA = -\,5^\circ\), \(0^\circ\), \(5^\circ\), and \(12^\circ\)).

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At AOA = \(-\,5^\circ\), all three profiles exhibited a low-pressure region near the leading edge on the upper surface and a high-pressure region on the lower surface. The symmetric NACA 0012 profile showed a more uniform pressure distribution than the cambered NACA 2412 and NACA 4415 profiles, resulting in a lower lift generation at this negative angle of attack.

As the AOA increase to \(0^\circ\), the pressure distribution became more asymmetric for the cambered profiles. Lower and higher pressures were observed on the upper and lower surfaces, respectively, thereby contributing to the increased lift. The NACA 4415 profile, which had the highest camber, exhibited the most pronounced pressure difference, indicating a higher lift generation compared to the NACA 2412 and NACA 0012 profiles.

At AOA = \(5^\circ\), the low-pressure regions on the upper surface became more prominent for all three profiles, particularly near the leading edge. This resulted in a further increase in the lift. The NACA 4415 profile maintained the highest pressure difference, suggesting a superior lift performance at this AOA.

Finally, at AOA = \(12^\circ\), the pressure contours revealed the onset of the flow separation and stall characteristics. The NACA 2412 and NACA 0012 profiles exhibited signs of flow separation near the trailing edge, as indicated by the reduced pressure difference between the upper and lower surfaces. In contrast, the NACA 4415 profile maintained a more stable pressure distribution, suggesting a better performance at higher angles of attack before stalling. This delayed stall is crucial for control responsiveness. The more gradual stall behavior of the NACA 4415 allows for more predictable handling, especially at lower speeds and higher angles of attack often encountered during landing or when operating in gusty conditions.

Pressure contour analysis from CFD simulations highlighted the significance of computational methods in modern airfoil design and optimization. The ability of the NACA 4415 profile to maintain a more stable pressure distribution at higher angles of attack suggests that it would be the most suitable choice. This characteristic would enable the UAV to maintain efficiency and stability under various flight conditions, which is essential for missions involving varied terrain and weather conditions.

Analysis of streamline and velocity profiles

The streamline patterns and velocity profiles for the three airfoils, presented in Figs. 8 and 9, offered a comprehensive view of their aerodynamic behavior at AOAs of \(-\,5^{\circ }\), \(0^{\circ }\), and \(5^{\circ }\). Although the streamline patterns offered qualitative insights into flow behavior, the velocity profiles provided essential quantitative data on velocity magnitudes and gradients, thereby aiding in the identification of flow separation and high-velocity zones, which are critical for assessing aerodynamic performance. Combining both visualizations facilitated a more complete analysis of the efficiency of each airfoil.

Fig. 8
figure 8

Streamline patterns for NACA 2412, NACA 0012, and NACA 4415 airfoils at angles of attack of \(-\,5^{\circ }\), \(0^{\circ }\), and \(5^{\circ }\).

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Fig. 9
figure 9

Velocity profiles for NACA 2412, NACA 0012, and NACA 4415 airfoils at angles of attack of \(-\,5^{\circ }\), \(0^{\circ }\), and \(5^{\circ }\). The colors represent velocity magnitude, with red indicating higher velocities and blue indicating lower velocities.

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Starting with NACA 2412, which is a moderately cambered airfoil, the streamline patterns exhibited a clear progression in the flow behavior with increase in the AOA. At \(-\,5^{\circ }\), flow separation was observed near the trailing edge on the lower surface, with compressed streamlines indicating higher velocity near this region. This was confirmed by the velocity profile, which showed relatively high velocities at the lower surface and lower velocities at the upper surface. At \(0^{\circ }\), the flow became smoother with a slight acceleration over the upper surface, as shown in both the streamline pattern and velocity profile. At \(5^{\circ }\), the upper surface experienced a significant increase in velocity, and the streamlines became denser and more compressed near the leading edge. The corresponding velocity profile exhibited a steep velocity gradient on the upper surface, indicating an increase in the lift. However, certain flow separation near the trailing edge revealed the onset of aerodynamic inefficiency at higher angles of attack.

NACA 0012, which is symmetric, exhibited more balanced streamline patterns and velocity distributions, particularly at \(0^{\circ }\). At \(-\,5^{\circ }\), the flow pattern mirrored that observed at \(5^{\circ }\), with similar regions of flow separation on the lower and upper surfaces at negative and positive angles, respectively. This symmetry was evident in the velocity profiles, which exhibited nearly identical velocity distributions at \(-\,5^{\circ }\) and \(5^{\circ }\), with the upper and lower surfaces exchanging roles based on the AOA. At \(0^{\circ }\), the flow remained perfectly symmetrical, with the velocity profile exhibiting uniformity over both surfaces. Although the flow appeared stable, the overall velocity gradients were less pronounced compared to the cambered profiles, indicating lower lift generation.

In contrast, NACA 4415, which is a highly cambered airfoil, exhibited the most dynamic changes in both the streamline patterns and velocity profiles. At \(-\,5^{\circ }\), a significant flow separation was observed on the lower surface, as indicated by the streamline patterns. In contrast, the upper surface experienced considerably lower velocities. This was confirmed in the velocity profile, where the lower surface exhibited higher-velocity regions, leading to greater drag. At \(0^{\circ }\), the streamline patterns revealed a considerably stronger acceleration over the upper surface compared to that in case of NACA 2412, with denser and more compressed streamlines. The velocity profile further corroborated this finding, exhibiting a steeper velocity gradient along the upper surface, which translated to an enhanced lift. At \(5^{\circ }\), the camber of the NACA 4415 created the most compressed streamlines and the highest velocity regions among all three airfoils. The velocity profile exhibited a sharp increase in the velocity on the upper surface, with a mild flow separation near the trailing edge. The combination of these factors rendered the NACA 4415 the best-performing airfoil for lift generation, particularly at positive AOAs.

Optimization results from hybrid ANN-GA model

The hybrid ANN-GA model was employed to optimize the design parameters, namely AOA and \(Re\), to maximize the \(C_L/C_D\) ratio of the selected airfoils. Figure 10 shows the variation in the maximum \(C_L/C_D\) values with \(Re\) and the corresponding optimum AOA for the three airfoils.

The results demonstrated that the maximum \(C_L/C_D\) values for NACA 4415 and NACA 2412 increased with increasing \(Re\). In contrast, for NACA 0012, the maximum \(C_L/C_D\) values decreased as \(Re\) increased. The optimum AOA for NACA 2412 initially decreased until \(Re\) reached 300,000, and then gradually increased and stabilized. For NACA 4415, the optimum AOA consistently increased with \(Re\), as shown in Fig. 11.

Fig. 10
figure 10

Variation in \(Re\) with (a) maximum \(C_L/C_D\), and (b) optimum AOA.

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Fig. 11
figure 11

Variation in \(Re\) with maximum \(C_L/C_D\) and optimum AOA for (a) NACA 2412, (b) NACA 4415, and (c) NACA 0012.

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A comparative analysis across the airfoils clearly indicated that NACA 4415 outperformed the others, achieving a maximum \(C_L/C_D\) ratio of 25.2206 at \(Re = 770,801.5732\), with an optimum AOA of \(11.1929^\circ\). NACA 2412 closely follows, with a maximum \(C_L/C_D\) ratio of 23.9295 at \(Re = 773,695.4585\) and an optimum AOA of \(8.6413^\circ\). Consequently, NACA 4415 was identified as a superior airfoil for UAV design based on its aerodynamic performance.

The optimization results from the hybrid ANN-GA model provide valuable insights regarding the optimal operating conditions for the selected airfoils. This can enable designers to make informed decisions and enhance the aerodynamic efficiency of medical supply delivery UAVs. Further, the integration of data-driven modeling and optimization techniques demonstrates the potential for further improvements in the airfoil design and selection for specific UAV applications.

Prediction accuracy of ANN model with CFD data

The developed ANN model was trained using the CFD dataset, and its performance was evaluated using MPE, MSE, and correlation coefficient (\(R\)), as listed in Table 6. Of the total dataset, 70% was used for training, whereas 15% each was used to test and validate the ANN model. The data were normalized using Eq. (2) and the results were de-normalized using Eq. (3). The performance of the ANN model was assessed through comparisons of the predicted values of \(C_L/C_D\) with the CFD data.

Table 6 Performance evaluation of the ANN model.
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The ANN model demonstrated high accuracy in terms of predicting the \(C_L/C_D\) values, with an overall \(R\) value of 0.9946. This indicated a strong correlation between the predicted and observed values. The close alignment of the predicted \(C_L/C_D\) values with the CFD data for different Reynolds numbers highlighted the effectiveness and practical applicability of the proposed ANN model.

Fig. 12
figure 12

Comparison of prediction accuracy of ANN model with the CFD data at (a) \(Re = 200,000\), (b) \(Re = 500,000\), (c) \(Re = 800,000\).

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Figure 12 presents a comparison of the prediction accuracy of the ANN model with that of the CFD data at Reynolds numbers of 200,000, 500,000, and 800,000. The close agreement between the predicted and CFD values across different Reynolds numbers demonstrated the robustness and reliability of the ANN model for predicting the aerodynamic performance.

Pressure contour analysis demonstrated the superior stability of NACA 4415 at high AOAs, which is a crucial feature of UAVs operating in diverse environments. The dual approach of CFD and XFOIL simulations ensured a comprehensive understanding of the airfoil performance under various conditions relevant to medical supply delivery missions.

The hybrid ANN-GA model identified the optimal values of the AOA and Reynolds number for maximizing the \(C_L/C_D\) ratio of the NACA 4415 airfoil, thereby providing valuable insights into the optimal operating conditions for the selected airfoil. Moreover, the integration of data-driven modeling and optimization techniques demonstrates the potential for further improvements in airfoil design and selection for specific UAV applications.

Conclusion

This study comprehensively analyzed NACA 2412, 4415, and 0012 airfoils using CFD, XFOIL simulations, and a hybrid ANN-GA model, targeting UAV applications demanding high maneuverability and aerodynamic efficiency. The analysis focused on optimizing airfoil performance for complex operational environments.

The results consistently demonstrated the superior performance of the NACA 4415 airfoil across a range of angles of attack and Reynolds numbers. NACA 4415 achieved the highest lift-to-drag ratio (CL/CD), establishing it as the most suitable candidate for UAV applications prioritizing enhanced flight endurance, stability, and payload efficiency. This superior CL/CD directly translates to longer flight times and greater area coverage, crucial for applications such as precision agriculture and environmental monitoring.

The hybrid ANN-GA model further refined the aerodynamic performance of NACA 4415 by identifying the optimal angle of attack (\(11.19^\circ\)) and Reynolds number (770,801) for maximizing the CL/CD ratio. Streamline and velocity profile analyses corroborated these findings, revealing favorable flow behavior for NACA 4415, characterized by delayed flow separation and improved control responsiveness. While NACA 2412 exhibited decent performance, NACA 0012 offered greater stability but lower lift.

The ANN model, trained using CFD data, achieved high prediction accuracy (R = 0.9946), underscoring the potential of machine learning techniques for predicting aerodynamic performance and optimizing UAV designs efficiently.

In conclusion, the NACA 4415 airfoil emerges as the optimal choice for UAVs operating in environments requiring both high maneuverability and aerodynamic efficiency. Its superior characteristics and increased payload capacity make it highly suitable for applications in precision agriculture, infrastructure inspection, and environmental monitoring. Future research should prioritize experimental validation to further refine airfoil selection and UAV design strategies, addressing limitations inherent in computational models.