Aerodynamic optimisation of flat-upper-surface wing

Abstract

Purpose

The paper aims to optimise several concepts of the flat-upper-surface wing that could install the largest possible number of photovoltaic cells and test them in flight. A wing ideal flat upper surface was necessary to provide the same lighting conditions for each tested cell.

Design/methodology/approach

The optimised wings were built based on a developed family of airfoils having 75% of their upper surface flat. Within the developed parametric model of the wings, the design parameters described the spanwise distribution of base airfoils. Maximisation of the endurance factor was assumed as the main objective. The aerodynamic properties of optimised wings were evaluated using a panel method coupled with boundary layer analysis.

Findings

The paper proves that it is possible to design wings with 75% of their upper surface perfectly flat, which are also characterised by good aerodynamic properties.

Practical implications

The research conducted will allow designing an experimental unmanned aerial vehicle dedicated to investigating the properties of electrical propulsion systems at various altitudes. Data obtained in these investigations will help in the development of future generations of electric-propulsion aircraft.

Originality/value

The innovative wings, developed within the research are unique due to their unusual geometric and aerodynamic properties. They have 75% of their upper surface perfectly flat. That makes them ideal for testing various photovoltaic cells in flight. The biggest challenge was to design the wings so that their specific geometric features did not impair their aerodynamic properties. The paper proves that this challenge has been fully overcome.

Citation

Stalewski, W., Bugała, P. and Galinski, C. (2025), "Aerodynamic optimisation of flat-upper-surface wing", Aircraft Engineering and Aerospace Technology, Vol. 97 No. 1, pp. 87-107. https://doi.org/10.1108/AEAT-03-2024-0088

Nomenclature

Symbols

C

= airfoil chord;

C_D

= drag coefficient;

C_L

= lift coefficient;

C_L1.5/C_D

= endurance factor;

C_Lmax

= maximum lift coefficient;

C_m

= pitching moment coefficient;

C_P

= pressure coefficient;

Ma

= Mach number;

Re

= Reynolds number;

S

= distance measured along the wing span;

X_sep

= chordwise position of flow-separation beginning;

α

= angle of attack; and

ϕ

= the angle of the geometric twist of an airfoil.

Definitions, acronyms and abbreviations

BFGS

= Broyden–Fletcher–Goldfarb–Shanno (algorithm);

ISA

= International Standard Atmosphere;

MAC

= mean aerodynamic chord;

MTOW

= maximum takeoff weight;

SL

= sea level;

UAV

= unmanned aerial vehicle; and

URANS

= unsteady Reynolds-averaged Navier–Stokes.

Introduction

In 2019, aviation was responsible for only 2.3% of greenhouse gas emissions (Ficca et al., 2023). However, this 2.3% means 0.918 gigatonnes of CO₂ emitted that year. Annual CO₂ emissions will probably further grow with the rapid growth of commercial air traffic. For example, it is expected that US commercial aviation traffic may grow by 2.0% per annum till 2050 (Jensen et al., 2023). It should also be remembered that pollution caused by aviation is more dangerous than the one caused by other sectors of the economy because greenhouse gasses are emitted high above the ground, including the stratosphere. Moreover, it also generates very strong local pollution near the airports (Glowacki et al., 2021).

On the other hand, flying always requires energy efficiency; therefore, more efficient airplanes (Marino and Sabatini, 2014; IATA, 2024) and flight procedures (Antczak et al., 2021; Carmona et al., 2024) have been and are being proposed and introduced systematically resulting in fuel consumption and CO₂ emissions reductions. As a result, CO₂ emissions growth is usually smaller than traffic growth. For example, passenger traffic in the US grew by 89% between 1991 and 2019. At the same time, fuel use grew only by 27% (Jensen et al., 2023). However, this is not enough. More environmentally friendly aviation is requested by authorities all over the world (ACARE, 2022; European Commission, 2019; FAA, 2021; ICAO, 2019). Unfortunately, the improvement of traditional designs provides only incremental reduction of fuel consumption and greenhouse gas emissions. For example, a change of −1.5% per annum in CO₂ emission intensity was observed in the US between 2000 and 2019 (Jensen et al., 2023). Therefore, breakthrough solutions have to be introduced, starting with more electric airplanes (Rosero et al., 2007), going to airplanes with fuel cells or fully electric propulsion systems (Marianowski et al., 2017), sometimes supplied with solar energy (Amos, 2010; Czarnocki et al., 2019; Desantes et al., 2022; Gibbs, 2018; Ross, 2008). The last idea is interesting because of natural zero emissions during the flight and reduced overall CO₂ footprint. Unfortunately, designers are facing serious barriers, making the task of electric fight difficult. One of the most important problems is the lack of information on the real characteristics of expensive devices that could be used in propulsion systems. Usually, their published characteristics were obtained in laboratory conditions at sea level or on the laboratory level where a particular device was created. On the other hand, application in a real airplane requires information on real characteristics at different altitudes. Traditionally influence of the altitude was carefully studied in the case of internal combustion engines because of the amount of oxygen available in the ambient atmosphere at various altitudes for burning the fuel. All-electric propulsions do not burn any fuel and, therefore, they seem to be insensitive to altitude (Orkisz and Kuźniar, 2020). Unfortunately, the assumption of electric propulsion insensitivity to altitude results in a paradoxical conclusion. Constant power allows airplanes to fly faster at higher altitudes, which is also necessary to generate enough lift to balance the weight. On the other hand, the speed of sound decreases with altitude. Therefore, propeller-driven electric airplanes should fly with transonic airspeeds, at some altitudes, which seems unlikely. In reality, electric propulsion systems are exposed to the variation of pressure, temperature, radiation intensity and spectrum when altitude grows.

Unfortunately, the effects of these phenomena are not widely published. Therefore, there is a need to investigate them thoroughly. It seems like the application of small, inexpensive unmanned aerial vehicles (UAVs) is the best way to explore them (Galinski, 2018). Taking into consideration the required small size of the vehicle combined with a need to investigate various solar cells, including rigid ones, it seems like the vehicle should be equipped with a rectangular wing, as flat as possible on the upper side (Galiński et al., 2020). In the case of rigid cells, flatness is obvious. In the case of elastic cells, it should be remembered that they tolerate their deformation in only one direction, and because of the expected large bending deflection of a high aspect ratio wing, this direction has to be oriented along the wing span leading to the need for a flat-upper-surface airfoil. A suitable airfoil was already designed (Galiński et al., 2020), exhibiting satisfactory performance. Further increase of performance, necessary to fly high, may be obtained by lift distribution optimisation along the wing span. Due to the rectangular planform, lift force distribution along the wing span has to be optimised through an appropriate definition of the aerodynamic and geometric twist of the wing. This paper shows the results of the attempt to design such a wing. A few of them were presented during the 13th EASN Conference in Salerno in 2023. Here, we publish them for the first time.

Subject and goals of the research

The presented research is part of a research-and-development project aiming at designing, building and flying inexpensive UAVs being flying laboratories dedicated to investigating the effect of flight altitude on the performance of electric-propulsion components. Among others, the project is focused on investigations of the performance of various types of photovoltaic cells in flight at different altitudes. Such investigations need equal exposure conditions for all investigated photocells. This can be achieved by designing UAV aircraft with a wing with a flat upper surface, where the photocells can be placed on. The research discussed in the paper focuses on the optimal design of such wings, and the main goals of the research are:

• to develop an effective and efficient methodology for the design and optimisation of flat-upper-surface wings; and

• to design and optimise flat-upper-surface wings intended for selected concepts of fixed-wing light UAVs using the developed methodology.

Considered configurations of the unmanned aerial vehicle

In the presented research, three concepts of fixed-wing UAVs have been considered.

Concept “S170”

The first concept, presented in Figure 1, is a high-aspect-ratio-rectangular-wing very small UAV, equipped with a single, tractor propeller. In Figure 1, the black areas on the wing correspond to the assumed flat surfaces where photocells can be placed. The main features of the concept “S170” of flat-upper-surface-wing UAV are presented in Table 1.

Concept “S340”

The second concept, presented in Figure 2, is a moderate-aspect-ratio-rectangular-wing light UAV, equipped with a single, tractor propeller. It is larger than the previous UAV (concept “S170”), and in this case, the number of photocells is twice as large as in the case of the previous concept. Similarly, the flat surfaces where photocells can be placed are marked in black in Figure 2. The main features of the concept “S340” of flat-upper-surface-wing UAV are presented in Table 2.

Concept “J170”

The third concept, presented in Figure 3, is a joined-wing light UAV equipped with a single pusher propeller. The proposed concept is based on Prandtl (1924), Cahill and Stead (1954), Zimmer (1978), Airkraft Sunny (2024), Mamla and Galiński (2009) and Galiński et al. (2017). The front and back parts have a taper ratio of 1 and are forward-swept and backward-swept, respectively. In Figure 3, the black areas on the wing correspond to the assumed flat surfaces, where photocells can be placed. The main features of the concept “J170” of flat-upper-surface-joined-wing UAV are presented in Table 3. The joined-wing concept is the most rigid compared to the formerly presented concepts, which is an advantage because of expected problems with flatter. However, it is probably difficult, though not impossible, to avoid the shadows cast by the upper wing onto the lower wing.

Research methodology

The process of design and optimisation of the flat-upper-surface wings intended for the three concepts of UAV consisted of two main stages. The initial stage concerned the design of a family of flat-uppers-surface airfoils. Within this scope, a single-parameter family of airfoils was developed, where the parameter was the angle of geometric twist of the airfoil, which could take on any real values in the range from −4.5° to 0.0°. Based on this airfoil family, a series of flat-upper-surface wings, intended for the three mentioned UAV concepts, has been designed and optimised, using the original, in-house methodology. In general, the process of wing design and optimisation consisted of searching for optimal smooth distribution along the wing span, the airfoils from the WS-FUS-X.X family. As a base criterion of optimisation, the maximisation of the endurance factor (C_L^1.5/C_D) of aircraft was selected (Torenbeek and Wittenberg, 2009; Stinton, 2001). This was not a typical selection, resulting from the specific mission requirements of the designed aircraft. Usually, the lift-to-drag ratio (C_L/C_D) is used as an objective function, since it influences the range of the airplane. The mission of the currently designed UAV assumes climbing to the maximum possible altitude to measure the properties of the propulsion system in a wide range of altitudes. In the current legal environment [European Commission Delegated Regulation (EU), 2019/945, European Commission Implementing Regulation (EU), 2019/947], a mission of that kind has to be performed in constrained air space, reserved by local aeronautical authorities for this mission. This means that UAVs will probably climb, circling in quite constrained space. In this case, range is not important at all. Instead, the climb rate is critical because it will allow experimenting in the widest range of altitudes. On the other hand, the climb rate is influenced by the endurance factor, not by lift to drag ratio.

Flat-upper-surface-airfoil family

The design and optimisation of the flat-upper-surface airfoil one-parametric family was conducted using the following tools:

• CODA4W – an original and very useful in-house code supporting airfoil design. The tool was successfully used in several aeronautical engineering research works (Stalewski, 2015; Stalewski and Zalewski, 2020). The software has several useful modules responsible for precise controlling of the smoothness of the designed airfoil shapes as well as a simple analysis of flow around the designed airfoils.

• INVDES – an in-house code solving the inverse-airfoil-design problem. The software enables the design of the shape of the airfoil for which the static-pressure distribution is as close as possible to the required pressure distribution, defined by the user. The software has proven its reliability in several research projects (Stalewski, 2015; Stalewski and Zalewski, 2020).

• XFLR-5 (Drella et al., 2012) – a commonly used code for aerodynamic analysis of airfoils and wings in low-speed conditions. The program is widely recognised as one of the best in model-scale aerodynamics. For a given Reynolds and Mach number, the software determines all basic aerodynamic characteristics of the airfoil, including evaluating the maximum lift coefficient.

Using the above tools, the process involved designing a series of flat-upper-surface base airfoils differing from each other in the degree of camber of the mean line, i.e. in the level of lowering the airfoil nose, which corresponded to different levels of geometric twist of the airfoil. The optimisation process aimed at maximising the endurance factor (C_L^1.5/C_D) and minimising the drag coefficient of the airfoil for the design lift coefficient value, which ranged from 0.0 for the non-cambered airfoil to 1.6 for the airfoil with the most cambered mean line.

The final result of this stage was the airfoil family WS-FUS-X.X. All airfoils in this family have a perfectly flat upper surface in the range from 25% of the chord to the trailing edge. In general, the mathematical model of the WS-FUS-X.X family includes an infinite number of airfoils, indexed by the twist angle ϕ defined in Figure 4. As seen, ϕ is an angle between the x-axis and the airfoil chord – the line connecting the nose of an airfoil and the central point of the trailing edge. If the nose lies under the x-axis, the twist angle is negative. In the defined WS-FUS-X.X family, the twist angle can take any real value in the range from −4.5 to 0.0.

Mathematically, the WS-FUS-X.X family corresponds to a smooth surface spread on the base airfoils listed in Table 4.

The table highlights the WS-FUS-2.5 airfoil because this airfoil was a subject of earlier studies (Galiński et al., 2020), and in the presented research, it became the starting point for developing the entire WS-FUS-X.X airfoil family. The base airfoils were designed and optimised manually and independently, one after one, using the tools itemised above. Shapes of the base airfoils are presented in Figures 5 and 6.

The aerodynamic characteristics of base airfoils WS-FUS-X.X, calculated using the XFLR-5 software, are shown in Figure 7 where the dependencies: lift coefficient (C_L) vs drag coefficient (C_D) and endurance factor (C_L^1.5/C_D) vs lift coefficient (C_L), are presented. All the presented results were obtained for flow conditions defined by Reynolds number 290950 and Mach number 0.074, which were predicted as typical flow conditions for the designed wings.

Methodology of design and optimisation of flat-upper-surface wings

The parametric design and optimisation of several flat-upper-surface wings was carried out using the parametric design methodology, which was successfully used in many design works (Rokicki et al., 2009; Stalewski and Zoltak, 2011; Stalewski and Zoltak, 2012; Stalewski and Zoltak, 2014a; Stalewski and Zoltak, 2014a, 2014b; Stalewski, 2015; Stalewski and Zalewski, 2020). The general scheme of this methodology, adapted to the specificity of the task that is the subject of the paper, is shown in Figure 8. The design process is managed by the designer, who can be either a human being or computer code. In the first case, an experienced engineer interactively designs sequential variants of the designed object and manages optimisation cycles. In automatic mode, the designer is optimisation code. When solving a real engineering and design problem, both approaches – interactive and automatic – are useful. An interactively designed product can be used as a starting variant for numerical optimisation. On the other hand, the interactive mode can also be useful for making final adjustments to the results of automatic optimisation.

In the presented methodology, the numerical optimisation can be implemented using two independent methods, which were developed as internal codes by the author of the paper. The first method is the multi-objective genetic algorithm (Stalewski and Zoltak, 2012) – which is especially useful in multi-objective optimisation problems. The alternative optimisation method is the BFGS algorithm (Nocedal and Wright, 2006), which is an iterative, gradient-based method for solving non-linear problems with simple constraints. The BFGS algorithm has proven to have good performance even for non-smooth optimisations and is, therefore, one of the most popular members of quasi-Newton methods, i.e. methods close to the classical Newton method.

In the presented approach, it was assumed that the objective function would be single-valued and would express the so-called endurance factor – the ratio C_L^1.5/C_D, where C_L is the lift coefficient and C_D is the drag coefficient of the wing. The optimisation task, in this case, consisted of searching for a wing with the highest possible endurance factor, determined in flight conditions when the lift force is balancing the aircraft weight. The optimal solution to the optimisation problem defined in such a way should ensure the longest possible flight or largest climb rate of UAV equipped with the optimised wing.

The above definition of the optimisation task influenced that the design and optimisation process was carried out mainly based on an interactive design approach, with a successive search of the design parameter space. However, after determining the “nearly” optimal wing in this way, a more precise search for the optimal solution was conducted using the BFGS method. In this case, the number of unknown design parameters was usually reduced, while the rest of the design parameters were frozen. This reduction of the sought (unknown) design parameters allowed for conducting much more effective numerical optimisation. For example, in the case of the joined-wing concept, only the optimal values of design parameters describing the geometric twist of the side wing were sought, while the rest of the design parameters were frozen. In this way, the optimal distribution of side wing twist distribution was determined, which would be quite difficult using interactive designing.

In the approach based on parametric optimisation, modules responsible for the parametric modelling of the designed product play a very important role. In the presented methodology, specialised, in-house PARADES software (Stalewski, 2011; Stalewski, 2012) was used for this purpose. The software was developed and successfully implemented in many applications. In general, software, for a given set of design parameters (series of real numbers), creates the virtual geometry of the designed object. The high-quality surface of the object is modelled using the NURBS (non-uniform rational B-splines) representation. Additionally, in the presented case, the software generates computational mesh – the input data for the panel method assessing the aerodynamic properties of the designed wing. Also, some geometric properties of the designed object (e.g. wing area, span, mean aerodynamic chord) can be directly calculated by the software and can then be used to evaluate geometric objectives and constraints. The software can work in both interactive and batch mode. Figure 9 presents the workspace of the PARADES software when working in interactive mode.

Using the PARADES software, the parametric models of several flat-upper-surface wings were built. In the assumed approach, the main design parameters described a distribution of the sectional twist of airfoils along the wing span. This means that, in fact, the design parameters described a spanwise, continuous distribution of airfoils (from the WS FUS X.X family), creating the smooth surface of the wing. In the case of the joined wing concept (“J170”), the front and back parts of the wing were parameterised in this manner independently. For the joined-wing concept, the spanwise distribution of the geometric twist of the vertical connecting part of the wing was parameterised, too. Based on the previous author’s experiences with joined-wing design, the in-house airfoil WST060 (of 6% relative thickness) was applied to the side-connecting part of the wing. Additionally, for the joined wing, the sweep angles of the front and back parts of the wing were assumed as additional design parameters.

The aerodynamic properties of designed wings were calculated by the use of PANEL3DBL in-house software which was a fully three-dimensional panel method coupled with two-dimensional boundary layer analysis (Stalewski and Sznajder, 2010). The PANEL3DBL software has repeatedly proven its credibility and reliability in optimisation problems similar to the one discussed here (Stalewski and Zoltak, 2011).

Results of conducted optimisations of flat-upper-surface wings

Concept “S170”

The design and optimisation process of a flat-upper-surface wing intended for the “S170” concept of UAV was conducted for the assumed parameters of wing presented in Table 1. The assumed flight speed was 7 m/s in SL ISA atmospheric conditions. The design point corresponded to the balanced flight of the UAV when the lift force is balancing the assumed MTOW of the UAV, i.e. MTOW = 1.5 kg. These assumptions led to the following definition of the highest-priority design point:

• Ma = 0.0206.

• Re = 80447.

• C_L = 0.96.

where Ma and Re are Mach and Reynolds numbers, respectively, and C_L is the design value of the lift coefficient. For the above flight conditions, the optimisation task was to design a flat-upper-surface wing having as highest possible endurance factor (C_L^1.5/C_D). As a reference wing for the design process, the wing BASELINE-S170 was assumed to be built entirely based on the WS-FUS-2.5 base airfoil, which was the subject of previously carried out research and design works (Galiński et al., 2020). Figure 10 compares the spanwise distribution of the geometric twist of the baseline wing and finally designed wing named WS-FUS-S170-A. As mentioned, the BASELINE-S170 has a constant geometric twist equal to −2.5 deg. In contrast, the finally designed wing has a piecewise linear/parabolic distribution of geometric twist (or airfoils from the family WS-FUS-X.X) ranging from −4.0 deg to −1.0 deg. Table 5 compares the basic aerodynamic properties of wings BASELINE-S170 and WS-FUS-S170-A, determined computationally, using the PANEL3DBL code.

One may conclude, that compared to the baseline, the optimised wing WS-FUS-S170-A is characterised by:

• 3.

  4% increase in endurance factor (C_L^1.5/C_D) in balanced-flight conditions (C_L = 0.96);

• 3.

  4% increase in aerodynamic efficiency (C_L/C_D) in balanced-flight conditions (C_L = 0.96); and

• 7.

  5% increase in maximum lift coefficient (C_{L max}).

Figure 11 presents the basic aerodynamic characteristics of wings BASELINE-S170 and WS-FUS-S170-A, calculated using the PANEL3DBL code. They are the endurance factor versus lift coefficient and lift coefficient versus drag coefficient, respectively. Both aerodynamic characteristics are more favourable for the wing WS-FUS-S170-A than for BASELINE-S170.

Figure 12 compares for both discussed wings the pitching moment coefficient (C_m) versus the lift coefficient (C_L), where the centre of the moment was typically localised in the plane of symmetry, at 25% of the MAC of the wing. The pitching moment is quite negative, which was expected for assumed camber values of applied airfoils. Further analysis of stability and control is completed for the complete aeroplane (with horizontal and vertical stabilizer). It is done with the help of methods presented in Goetzendorf-Grabowski (2023), Goetzendorf-Grabowski and Pobikrowska (2019), Goetzendorf-Grabowski (2017), Goetzendorf-Grabowski and Mieloszyk (2017a, 2017b), Goetzendorf-Grabowski and Figat (2016), Goetzendorf-Grabowski and Antoniewski (2016) and Goetzendorf-Grabowski et al. (2011). Due to the specificity and extensiveness of the research performed in this area, they will be presented in a separate paper.

Figures 13 and 14 present three-dimensional visualisations of pressure coefficient (C_P) distribution on the upper surfaces of wing BASELINE-S170 and WS-FUS-S170-A, respectively. By comparing the pressure coefficient distributions in selected cross-sections of both wings, it can be concluded that C_P distribution on the WS-FUS-S170-A wing is more favourable because of the lack of underpressure pikes at the wing leading edge (observed in the case of BASELINE-S170 wing), which favours the reduction of friction drag.

Figures 15 and 16 compare spanwise distributions of local lift (C_L) and drag (C_D) coefficients, respectively, for the baseline and optimised wing. Spanwise distributions of local C_L are very close to each other. Greater differences are visible in spanwise distributions of local C_D, where additionally, the inviscid and viscous components of total drag are compared. All presented results of aerodynamic calculations confirmed the good properties of the optimised WS-FUS-S170-A wing.

Concept “S340”

The design and optimisation process of a flat-upper-surface wing intended for the “S340” concept of UAV was conducted for the assumed parameters of wing presented in Table 2. The assumed flight speed was 7 m/s in SL ISA atmospheric conditions. The design point corresponded to the balanced flight of the UAV when the lift force is balancing the assumed MTOW of the UAV, i.e. MTOW = 4 kg. These assumptions led to the following definition of the highest-priority design point:

• Ma = 0.0206.

• Re = 160894.

• C_L = 0.96.

where Ma and Re are Mach and Reynolds numbers, respectively, and C_L is the design value of the lift coefficient.

For the above flight conditions, the optimisation task was to design a flat-upper-surface wing having as highest possible endurance factor (C_L^1.5/C_D). As a reference wing for the design process, the wing BASELINE-S340 was assumed to be built entirely based on the WS-FUS-S340-2.5 base airfoil, which was the subject of previously carried out research and design works (Galiński et al., 2020). The finally designed flat-upper-surface wing intended for the UAV concept “S340” was named WS-FUS-S340-B. Table 6 compares the basic aerodynamic properties of wings BASELINE-S340 and WS-FUS-S340-B, determined computationally, using the PANEL3DBL code. One may conclude, that compared to the baseline, the optimised wing WS-FUS-S340-B is characterised by:

• 3.

  8% increase in endurance factor (C_L^1.5/C_D) in balanced-flight conditions (C_L = 0.96);

• 3.

  7% increase in aerodynamic efficiency (C_L/C_D) in balanced-flight conditions (C_L = 0.96); and

• 2.

  4% increase in maximum lift coefficient (C_{L max}).

Figure 17 compares the spanwise distribution of geometric twist for the baseline wing and finally designed wing WS-FUS-S340-B. It is worth reminding, that the geometric twist, defines the shape of the wing cross-section at a given spanwise position. As mentioned, the BASELINE-S340 was entirely built based on WS-FUS-2.5 airfoil. In contrast, the finally designed wing has a quasi-parabolic distribution of geometric twist (or airfoils from the family WS-FUS-X.X) ranging from −3.14 deg to −0.5 deg.

Figure 18 presents the basic aerodynamic characteristics of wings BASELINE-S340 and WS-FUS-S340-B, calculated using the PANEL3DBL code. They are the endurance factor versus lift coefficient and lift coefficient versus drag coefficient, respectively. Both aerodynamic characteristics are more favourable for the wing WS-FUS-S340-B than for BASELINE-S340.

Figure 19 compares for both discussed wings the pitching moment coefficient (C_m) versus the lift coefficient (C_L), where the centre of the moment was typically localised in the plane of symmetry, at 25% of the MAC of the wing. The pitching moment is quite negative, which was expected for assumed camber values of applied airfoils. Further analysis of stability and control is completed for the complete aeroplane (with horizontal and vertical stabilizer). Due to the specificity and extensiveness of the research performed in this area, they will be presented in a separate paper.

Figures 20 and 21 present three-dimensional visualisations of pressure coefficient (C_P) distribution on the upper surfaces of wing BASELINE-S340 and WS-FUS-S340-B, respectively. By comparing the pressure coefficient distributions in selected cross-sections of both wings, it can be concluded that C_P distribution on the WS-FUS-S340-B wing is more favourable because of lower levels of underpressure pikes at the wing leading edge (compared to BASELINE-S340 wing), which favours the reduction of friction drag.

Figures 22 and 23 compare spanwise distributions of local lift (C_L) and drag (C_D) coefficients, respectively, for the baseline and optimised wing. Spanwise distributions of local C_L are very close to each other. Greater differences are visible in spanwise distributions of local C_D, where additionally, the inviscid and viscous components of total drag are compared. All presented results of aerodynamic calculations confirmed the good properties of the optimised WS-FUS-S340-B wing.

Analysis of boundary layer detachment

Based on the entire computational results presented in this paper, the UAV designers concluded that the most promising and suitable for further development concept of UAV would be the concept “S340” equipped with the wing WS-FUS-S340-B. Therefore, for this wing, the aerodynamic analyses were extended to a wider range of flight conditions and physical phenomena investigated. One such phenomenon is a separation of flow on the suction side of the wing, occurring at high angles of attack. This phenomenon plays a significant role in aircraft design, and it can substantially impact its performance and aerodynamic characteristics. Flow separation occurs when the boundary layer becomes unstable, and the flow loses contact with the wing surface. The effect of flow separation is a sudden increase in aerodynamic drag and a decrease in lift, which can result in undesirable effects such as reduced stability and controllability. In the worst case, an aircraft in a deep-stall state is prone to fall into spin, and recovery from such a state is very problematic for automatic control systems.

Based on the boundary layer analysis implemented in the PANEL3DBL code, it is possible to predict the development of the flow separation on the wing surface. If separation is present at a given spanwise position, the PANEL3D determines the chordwise position (X_sep) of the beginning of flow detachment.

Results of such analysis conducted for the wings BASELINE-S340 and WS-FUS-S340-B are presented in Figure 24. As one can see, for both wings, the development of flow detachment, with increasing angle of attack (α), is safe for the controllability of the UAV. In the case of wing WS-FUS-S340B at angle of attack α = 11.5 deg, there is no flow separation. The flow detachment occurs at an angle of attack of 12 deg, covering approximately 45% of the inner span of the wing. For the higher angles of attack, the spanwise range of flow detachment gradually progresses towards the wingtip.

To ensure that the analyses of the development of detachment of the boundary layer on the wing, performed using the PANEL3DBL program, are reliable, the authors conducted analogous flow simulations in Ansys Fluent software (ANSYS Inc, 2019) – a URANS solver commonly used in aeronautical engineering. The computational mesh, necessary in this case to conduct CFD calculations, was generated using Ansys Fluent Meshing software. The hybrid mesh consisted of poly-hexahedral elements in regions far from the wing surface and prismatic elements within the boundary layer, satisfying the condition Y + ≤1. The total number of cells was approximately 1.2 million. The following settings and flow models were applied in the presented simulations:

• Energy equation: on.

• Turbulence model: the k-ω SST, due to its accuracy in predicting flow separation and adverse pressure gradients.

• Pressure-velocity coupling: the coupled algorithm.

• Spatial discretisation: second-order upwind schemes for momentum, turbulence kinetic energy and specific dissipation rate.

• Fluid properties: the ideal gas model of density and Sutherland model of viscosity.

The CFD calculations were conducted for Standard ISA SL conditions.

Figure 25 shows a pressure coefficient (C_P) distribution and flow detachment areas completed with pathlines visualisation to observe a separation at higher angles of attack. The pathlines have been set in limited integration time to most closely resemble the tufts visualisation used in a wind tunnel. This allows for areas, that would be missed in the case of detachment, to be shown. The visualisations also show areas of backflow, which is not always equivalent to a detachment. It can also indicate laminar bubbles forming. As one can see from Figure 25, the wingtips are free of flow separation despite the slightly unusual twist distribution along the wing span, especially in the wingtip area. The separation usually causes the vortices to appear along the flow stream, and because of that, usually, such vortices appear in pairs. Therefore, the beginning of detachment is visualised by such uneven pressure increase border in pressure distribution and the separation strips in reverse flow distribution. The results of flow-separation-development analysis, conducted using the advanced CFD code Ansys Fluent (Figure 25), comply in general with those obtained using the PANEL3DBL code (Figure 24). In both cases, for angle of attack α = 11 deg, the flow stays fully attached to the upper surface of the wing WS-FUS-S340-B. Also, in both cases, the flow separation appears at angles of attack 12 deg and higher, but it does not cover the wingtip zone, which is favourable from the point of view of UAV stability and controllability.

Concept “J170”

The design and optimisation process of a flat-upper-surface wing for the joined-wing concept “J170” was conducted for the assumed parameters of the wing presented in Table 3. The assumed flight speed was 7 m/s in SL ISA atmospheric conditions. The design point corresponded to the balanced flight of the UAV when the lift force is balancing the assumed MTOW of the UAV, i.e. MTOW = 3.5 kg. These assumptions led to the following definition of the highest-priority design point:

• Ma = 0.0206.

• Re = 80447.

• C_L = 1.12.

where Ma and Re are Mach and Reynolds numbers, respectively, and C_L is the design value of the lift coefficient. For the above flight conditions, the optimisation task was to design a flat-upper-surface joined wing having the highest possible endurance factor (C_L^1.5/C_D). As a reference wing for the design process, the wing BASELINE-J170 was designed. The front and back parts of this wing were built entirely based on the WS-FUS-2.5 base airfoil, which was the subject of previously carried out research and design works (Galiński et al., 2020). In the presented approach, the side connecting part of the joined wings was built based on the symmetric airfoil WST060 (of 6% relative thickness), formerly designed by the author for vertical connections of joined wings.

Figure 26 compares the spanwise distribution of the geometric twist of the baseline wing and the finally optimised joined wing named WS-FUS-J170-C. As mentioned, the BASELINE-J170 has a constant geometric twist of front and back wings, equal to −2.5 deg. The side-connecting part of this wing has a constant zero geometric twist. In contrast, the finally designed wing WS-FUS-J170-C has:

• constant geometric twist (−4 deg) of the front part of the wing;

• parabolic distribution of geometric twist, ranging from −4.0 deg to −2.5 in the back part of the wing; and

• linear distribution of geometric twist, ranging from −4.0 deg to −2.0 in a side part of the wing.

Table 7 compares the basic aerodynamic properties of wings BASELINE-J170 and WS-FUS-J170-C, determined computationally, using the PANEL3DBL code.

It may be concluded that compared to the baseline wing, the optimised wing WS-FUS-J170-C is characterised by:

• 5.

  6% increase in endurance factor (C_L^1.5/C_D) in balanced-flight conditions (C_L = 1.12); and

• 5.

  6% increase in aerodynamic efficiency (C_L/C_D) in balanced-flight conditions (C_L = 1.12).

Figure 27 presents the basic aerodynamic characteristics of wings BASELINE-J170 and WS-FUS-J170-C, calculated using the PANEL3DBL code. They are the endurance factor versus lift coefficient and lift coefficient versus drag coefficient, respectively. Both aerodynamic characteristics are more favourable for the wing WS-FUS-J170-C than for BASELINE-J170.

Figure 28 compares for both discussed wings the pitching moment coefficient (C_m) versus the lift coefficient (C_L), where the centre of the moment was localised in the plane of symmetry, at 25% of the MAC of the front wing. The pitching moment is quite negative, which was expected for assumed camber values of applied airfoils. Further analysis of stability and control is completed for the complete aeroplane (with horizontal and vertical stabilizer). Due to the specificity and extensiveness of the research performed in this area, they will be presented in a separate paper.

Figures 29 and 30 present three-dimensional visualisations of pressure coefficient (C_P) distribution on the upper surfaces of wing BASELINE-J170 and WS-FUS-J170C, respectively. By comparing the pressure coefficient distributions in selected cross-sections of both wings, it can be concluded that C_P distribution on the WS-FUS-J170-C wing is much more favourable because of the lack of underpressure pikes at the wing leading edge (observed in the case of BASELINE-J170 wing), which favours the reduction of friction drag. In the cross-section of the side-connecting part of the wing (Section No. 11), the C_P distribution for the case of wing WS-FUS-J170-C is also more favourable for the wing BASELINE-J170.

Figures 31 and 32 compare spanwise distributions of local lift (C_L) and drag (C_D) coefficients, respectively, for the baseline and optimised wing. In this case, the distance-along-a-wing-span parameter S means the arc length measured along the line 25% of the local wing chord (C). Spanwise distributions of local C_L show, that compared to the baseline joined wing, the optimised joined wing is characterised by more balanced local values of C_L on its front and back parts. The lower level of local values of C_L on the front part of the wing WS-FUS-J170-C results in lower local values of C_D, which is visible well in Figure 32.

Additionally, Figure 32 shows that the desirable effect of negative local total drag on the side part of the joined wing, is well visible in the case of wing WS-FUS-J170-C while in the case of the baseline wing, this effect is not visible at all. All presented results of aerodynamic calculations confirmed the good properties of the optimised wing WS-FUS-J170-C.

Conclusion

The paper proves the feasibility of designing wings with 75% of their upper surface perfectly flat, and that have quite good aerodynamic properties. The research aimed at the optimisation of flat-upper-surface wings that could install the largest possible number of photovoltaic cells requiring an ideal flat upper surface of the wing when there is a need to test them in uniform lighting conditions. Using the in-house methodology of optimising flat-upper-surface wings, three wings representing three different concepts of UAV were optimised. For all three considered concepts of flat-upper-surface wings, the optimisation process led to significant improvement of both the endurance factor (C_L^1.5/C_D) and aerodynamic efficiency (C_L/C_D). In the case of the high-aspect-ratio rectangular wing (concept “S170”), the improvement was 3.4% and 3.4% of the endurance factor and aerodynamic efficiency, respectively. In the case of the moderate-aspect-ratio rectangular wing (concept “S340”), it was 3.8% and 3.7%, respectively. And in the case of the joined wing (concept “J170”), it was 5.6% and 5.6%, respectively. Based on the entire geometric and aerodynamic properties of the optimised wings, the authors decided to recommend the optimised moderate-aspect-ratio rectangular wing WS-FUS-S340-B as the proposal of the wing that could be finally adapted in the designed UAV – flying laboratory for flight tests of different types of photovoltaic cells. This wing has excellent aerodynamic properties at the highest assumed maximum take-off weight. At the same time, this wing should have good structural properties (good stiffness) and also provide the largest flat surface for photovoltaic cells.

Figures

Figure 1

Concept “S170”: high-aspect-ratio-rectangular-wing very small UAV

Figure 2

Concept “S340”: moderate-aspect-ratio-rectangular-wing light UAV

Figure 3

Concept “J170”: joined-wing light UAV

Figure 4

Definition of the angle ϕ of the geometric twist of the flat-upper surface airfoil

Figure 5

Comparison of the shapes of the base airfoils defining the WS-FUS-X.X family

Figure 6

Base airfoils defining the family WS-FUS-X.X

Figure 7

Lift coefficient (C_L) vs drag coefficient (C_D) (left graph) and endurance factor (C_L^1.5/C_D) vs lift coefficient (C_L) (right graph) calculated for the base airfoils of the WS-FUS-X.X family

Figure 8

General scheme of the methodology of designing and optimisation upper-flat-surface wings

Figure 9

Workspace of the PARADES software, when working in interactive mode

Figure 10

Comparison of the spanwise distribution of geometric twist for baseline wing (BASELINE-S170) and the finally designed wing (WS-FUS-S170-A) intended for the “S170” UAV concept

Figure 11

Dependencies of endurance factor (C_L^1.5/C_D) vs lift coefficient (C_L) and lift coefficient (C_L) vs drag coefficient (C_D) determined computationally (PANE3DBL code) for the wings BASELINE-S170 and WS-FUS-S170-A

Figure 12

Dependencies of pitching moment coefficient (C_m) vs lift coefficient (C_L) determined computationally (PANE3DBL code) for the wings BASELINE-S170 and WS-FUS-S170-A

Figure 13

Pressure coefficient (C_P) distribution on the upper surface of BASELINE-S170 wing at balanced flight conditions (C_L = 0.96)

Figure 14

Pressure coefficient (C_P) distribution on the upper surface of WS-FUS-S170-A wing at balanced flight conditions (C_L = 0.96)

Figure 15

Spanwise distribution of local lift coefficient (C_L) on the baseline wing BASELINE-S170 and the optimised wing WS-FUS-S170-A, determined computationally (PANEL3DBL code) at balanced flight conditions (C_L = 0.96)

Figure 16

Spanwise distribution of local drag coefficient (C_D) on the baseline wing BASELINE-S170 and the optimised wing WS-FUS-S170-A, determined computationally (PANEL3DBL code) at balanced flight conditions (C_L = 0.96)

Figure 17

Comparison of the spanwise distribution of geometric twist for baseline wing (BASELINE-S340) and the finally designed wing (WS-FUS-S340-B) intended for the “S340” UAV concept

Figure 18

Dependencies of endurance factor (C_L^1.5/C_D) vs lift coefficient (C_L) and lift coefficient (C_L) vs drag coefficient (C_D) determined computationally (PANE3DBL code) for the wings BASELINE-S340 and WS-FUS-S340-B

Figure 19

Dependencies of pitching moment coefficient (C_m) vs lift coefficient (C_L) determined computationally (PANE3DBL code) for the wings BASELINE-S340 and WS-FUS-S340-B

Figure 20

Pressure coefficient (C_P) distribution on the upper surface of BASELINE-S340 wing at balanced flight conditions (C_L = 0.96)

Figure 21

Pressure coefficient (C_P) distribution on the upper surface of WS-FUS-S340-B wing at balanced flight conditions (C_L = 0.96)

Figure 22

Spanwise distribution of local lift coefficient (C_L) on the baseline wing BASELINE-S340 and the optimised wing WS-FUS-S340-B, determined computationally (PANEL3DBL code) at balanced flight conditions (C_L = 0.96)

Figure 23

Spanwise distribution of local drag coefficient (C_D) on the baseline wing BASELINE-S340 and the optimised wing WS-FUS-S340-B, determined computationally (PANEL3DBL code) at balanced flight conditions (C_L = 0.96)

Figure 24

Flow separation development on the upper surface of BASELINE-S340 wing (upper graph) and optimised wing WS-FUS-S340-B (lower graph)

Figure 25

Pressure coefficient (C_P) distribution (left) and flow detachment areas (right) completed with pathlines for separation calculated using the Ansys Fluent code, for angles of attack α = 11, 12 and 13 deg

Figure 26

Comparison of the spanwise distribution of geometric twist for baseline wing (BASELINE-J170) and the finally designed wing (WS-FUS-J170-C) intended for the “J170” UAV concept

Figure 27

Dependencies of endurance factor (C_L^1.5/C_D) vs lift coefficient (C_L) and lift coefficient (C_L) vs drag coefficient (C_D) determined computationally (PANE3DBL code) for the wings BASELINE-J170 and WS-FUS-J170-C

Figure 28

Dependencies of pitching moment coefficient (C_m) vs lift coefficient (C_L) determined computationally (PANE3DBL code) for the wings BASELINE-J170 and WS-FUS-J170-C

Figure 29

Pressure coefficient (C_P) distribution on the upper surface of BASELINE-J170 wing at balanced flight conditions (C_L = 1.12)

Figure 30

Pressure coefficient (C_P) distribution on the upper surface of WS-FUS-J170-C wing at balanced flight conditions (C_L = 1.12)

Figure 31

Spanwise distribution of local lift coefficient (C_L) on the baseline wing BASELINE-J170 and the optimised wing WS-FUS-J170-C, determined computationally (PANEL3DBL code) at balanced flight conditions (C_L = 1.12)

Figure 32

Spanwise distribution of local drag coefficient (C_D) on the baseline wing BASELINE-J170 and the optimised wing WS-FUS-J170-C, determined computationally (PANEL3DBL code) at balanced flight conditions (C_L = 1.12)

Table 1

Main features of the concept “S170” of flat-upper-surface-wing UAV

Planform	Rectangular
Wing span	3 m
MAC	0.17 m
Reference area	0.51 m2
Aspect ratio	17.6
Taper ratio	1
Dihedral	6 deg
Number of solar cells	24
MTOW	1.5 kg
Estimated time to altitude 10 km	4 h
Maximum airspeed	12–17 m/s

Source: Table by authors

Table 2

Main features of the concept “S340” of flat-upper-surface-wing UAV

Planform	Rectangular
Wing span	4 m
MAC	0.34 m
Reference area	1.36 m2
Aspect ratio	11.8
Taper ratio	1
Dihedral	6 deg
Number of solar cells	64
MTOW	4 kg
Estimated time to altitude 10 km	4 h
Maximum airspeed	12–17 m/s

Source: Table by authors

Table 3

Main features of the concept “J170” of flat-upper-surface-joined-wing UAV

Planform	Swept airfoils in a rhombus arrangement
Wing span	3 m
MAC	0.17 m
Reference area	1.02 m2
Aspect ratio	17.6
Taper ratio	1
Vertical distance between front and back airfoil	0.25 m
Dihedral	6 deg
Number of solar cells	48
MTOW	3.5 kg
Estimated time to altitude 10 km	4 h
Maximum airspeed	12–17 m/s

Source: Table by authors

Table 4

Base airfoils defining the family WS-FUS-X.X

Base airfoil	Twist angle ϕ [deg]
WS-FUS-0.0	0.0
WS-FUS-0.5	−0.5
WS-FUS-1.0	−1.0
WS-FUS-1.5	−1.5
WS-FUS-2.0	−2.0
WS-FUS-2.5	−2.5
WS-FUS-3.0	−3.0
WS-FUS-3.5	−3.5
WS-FUS-4.0	−4.0
WS-FUS-4.5	−4.5

Source: Table by authors

Table 5

Comparison of main aerodynamic properties of wings BASELINE-S170 and WS-FUS-S170-A

Aerodynamic property	BASELINE-S170	WS-FUS-S170-A	Improvement (%)
CL1.5/CD @ CL = 0.96	24.203	25.025	3.4
CL/CD @ CL = 0.96	24.721	25.557	3.4
CL max	1.309	1.407	7.5

Source: Table by authors

Table 6

Comparison of main aerodynamic properties of wings BASELINE-S340 and WS-FUS-S340-B

Aerodynamic property	BASELINE-S340	WS-FUS-S340-B	Improvement (%)
CL1.5/CD @ CL = 0.96	22.045	22.874	3.8
CL/CD @ CL = 0.96	22.526	23.361	3.7
CL max	1.398	1.432	2.4

Source: Table by authors

Table 7

Comparison of main aerodynamic properties of wings BASELINE-J170 and WS-FUS-J170-C

Aerodynamic property	BASELINE-S170	WS-FUS-S170-A	Improvement (%)
CL1.5/CD @ CL = 1.12	19.323	20.407	5.6
CL/CD @ CL = 1.12	18.266	19.295	5.6

Source: Table by authors