Comparative Study of CFD Solvers in the Aerodynamic Analysis of a Miniature Unmanned Aerial Vehicle ^†

Abstract

This study is part of a research program at the Military University of Technology aimed at creating a tool to support light aircraft design at the conceptual stage. The project seeks to develop a method for optimizing a conceptual model of a small manned or unmanned aircraft based on specific mission requirements and aerodynamics. Recognizing the need for a reliable CFD analysis tool in this process, the focus was placed on investigating popular tools utilizing panel methods.

1. Introduction

This paper presents numerical studies in computational fluid dynamics (CFD) to analyze the aerodynamic properties of the miniature unmanned aerial vehicle (UAV) called “Rybitwa” (Figure 1), designed at the Military University of Technology in Warsaw, whose design parameters are presented in

Table 1. Design parameters of the analyzed UAV.

Wingspan	3.35	[m]
Length	1.83	[m]
Take-off weight	11	[kg]
Maximum speed	140	[km/h]
Ceiling	500	[m]
Endurance	1	[h]
Propulsion	Electric, 2.5	[kW]
Configuration	High-wing layout with T-tail	-
Launch/landing	Hand launch/parachute + skid recovery	-

. The research compared open-source (panel methods) software (XFLR5 ver. 6.62, OpenVSP ver. 3.45.4) and commercial (finite volume method—FVM) software (Fluent ver. 2024R1). The study estimated lift and drag coefficients and basic aerodynamic properties. The results were analyzed for accuracy and efficiency, identifying the strengths and weaknesses of each solution to inform the choice of CFD tools for future aerodynamic optimization of unmanned aerial systems.

The research presented in this article was developed as part of a university project aimed at creating a smart and efficient method for optimal parametric modeling of the aerodynamic body of a manned (or unmanned) aircraft with established mission requirements. A progressively developed model of the airframe’s external geometry would be tailored to the functional requirements of a given aircraft type, while simultaneously being optimized to achieve the best possible aerodynamic properties and, consequently, the most favorable values or specific performance parameters. The ultimately developed algorithm for shaping the aircraft’s aerodynamic body is demonstrated in Figure 2. Three design stages are visible, each representing a different stage of project development. In the first stage, the so-called prototype model 1 is developed through adaptation to mission requirements, statistical analysis, and the selection of basic design parameters (basic geometric dimensions, characteristic mass characteristics, fuselage, wing, and tail shapes). In the second stage, following the distribution of equipment, installations, and onboard cargo masses, prototype model 2 is developed. The total model aircraft mass in any mission configuration should not exceed the imposed maximum value. At the same time, the desired mass balance must be ensured and the minimum stability criterion must be met. Finally, in the final third stage, the aircraft geometry is refined to achieve optimal aerodynamic properties and the best possible performance qualities.

2. Method of the Study

The unmanned reconnaissance aircraft “Rybitwa” is a miniature, remotely controlled unmanned aerial vehicle (mini-UAV) developed at the Military University of Technology (Warsaw, PL). It is characterized by a slender fuselage, large wingspan, and an underslung tubular payload pod housing electronic equipment such as a daylight and a thermal imaging camera. The aircraft is capable of fully autonomous flight along a pre-programmed route, including autonomous take-off, landing, and loitering. It can remain airborne for up to 50–60 min and operate within a range of approximately 12 km from the ground control station. For numerical analysis purposes, the CAD model was developed using Siemens NX software ver. 1847 (Figure 3). The modeling approach employs a simplified dimension parameterization method, utilizing semi-interactive control forms to define dimensions and functional relationships, bypassing direct drawing (Figure 4).

The aerodynamics of the Rybitwa UAV aircraft were analyzed using Ansys Fluent, XFLR5, and OpenVSP software. Fluent is commercial software included in the Ansys package. The solution to the flow problem is obtained by simulating the laws of mass conservation, momentum conservation, and energy conservation (Navier–Stokes equations). For incompressible, isothermal, constant-viscosity flows, the Navier–Stokes equations can be simplified to the following ones [1,2,3,4]:

$$\nabla ·\overrightarrow{V}=0$$

(1)

$$\varrho \left[{\displaystyle \frac{\partial u}{\partial t}}+\nabla ·\left(\overrightarrow{V}u\right)\right]=-{\displaystyle \frac{\partial p}{\partial x}}+\mu {\nabla }^{2}u+F_{b,x}$$

(2)

$$\varrho \left[{\displaystyle \frac{\partial v}{\partial t}}+\nabla ·\left(\overrightarrow{V}v\right)\right]=-{\displaystyle \frac{\partial p}{\partial y}}+\mu {\nabla }^{2}v+F_{b,y}$$

(3)

$$\varrho \left[{\displaystyle \frac{\partial w}{\partial t}}+\nabla ·\left(\overrightarrow{V}w\right)\right]=-{\displaystyle \frac{\partial p}{\partial z}}+\mu {\nabla }^{2}w+F_{b,z}$$

(4)

The incompressible Navier–Stokes equations provide a reasonable model for flows of liquids and gases at relatively low speeds. The simplifications for the incompressible Navier–Stokes equations introduce the following singularities:

−

Continuity equation does not involve density (density is constant);

−

Viscosity μ is assumed constant;

−

No energy equation is required for isothermal flow;

−

If flow is not isothermal, the energy equation is decoupled from the other equations if the density, viscosity and thermal properties are constant.

XFLR5 is a potential flow solver coupled with XFOIL results, using airfoil theory, the Vortex Lattice Method (VLM), and the 3D panel method to analyze wings and aircraft models at low Reynolds numbers. Due to the limitations of the panel method, the XFLR5 program solves the flow problem under the following assumptions: incompressible, non-vortex flow outside the boundary layer (potential), low Mach numbers (typically Ma < 0.3), small angles of attack (formally small disturbances), wings treated as thin lifting surfaces, without modeling thickness in Lifting Line Theory (LLT) and Vortex Lattice Method (VLM) models [4,5]. The idea behind the panel method included in XFLR5 is to determine the velocity from the potential gradient (5) in the flow described by Laplace’s Equation (6).

$$V=\nabla \mathsf{\Phi }$$

(5)

$${\nabla }^2\mathsf{\Phi }=0$$

(6)

VSPAero (ver. 3.45.4) is a potential flow solver developed at NASA Ames. It is designed to directly utilize OpenVSP geometry through DegenGeom, a “streamlined” representation of thin surfaces. The program performs calculations according to one of two available algorithms: the Vortex Lattice Method (VLM) for thin lifting surfaces and panel method for solid bodies and stronger interference [6,7]. In addition, it allows for the analysis of propellers/wind turbines according to the actuator disk model. VSPAero returns reasonable compliance with the RANS OVERFLOW code at a fraction of the computational cost (especially with the actuator disk model) [8].

3. Numerical Analyses Performed

The preliminary numerical flow analysis of the mini-UAV model was performed for the flight speed value V = 20 [m/s], which means it was in fact the design cruise speed Vc = 72 km/h. First, a CFD analysis was run using the model developed on the basis of the FVM. For this purpose, the CAD model of the mini-airplane was imported into the Ansys Fluent software. The developed mesh domain had a shape of a rectangular cuboid with base dimensions of 9 × 9 m and a height of 13 m. The virtual flow space consists of approximately 2.5 million aerodynamic elements, taking into account the gradually thinned elements situated in the boundary layer zone. The analysis was carried out for the Spalart–Allmaras turbulence model (vorticity-based), using the SIMPLE scheme and Green–Gauss cell-based method, and second order accuracy for the remaining parameters in spatial discretization. Figure 5 presents the distribution of streamlines for the analyzed case: freestream velocity V = Vc, real Reynolds number $Re$ = 467 × 10³ calculated for formerly mentioned $Vc$ and for the mean aerodynamic chord of the wing $c_{aer}$ = 350 mm.

For the purposes of analysis in the VSPAero panel program, a new CAD model was created in OpenVSP (Figure 6). In the applied model, the Vortex Lattice Method (VLM) was applied.

The second tool used for the fast CFD analyses was XFLR5 with VLM available. Figure 7 shows the results of the analyses performed using this program. In the calculated case, the wing discretization resulted in 702 panels, and the empennage surface consisted of 440 elements.

The fundamental aerodynamic characteristics obtained after analyzing the three described program models are displayed in Figure 8. As can be seen, the Cd(α) and Cl(α) dependence curves determined for the usable angle of attack ranges are relatively consistent. A slight but noticeable advantage of the Ansys Fluent spatial model is demonstrated by slightly more realistic values of the Cd and Cl coefficients. The Cd coefficients determined using the panel methods are slightly underestimated, while the Cl coefficients from both panel methods are slightly overestimated.

In order to assess the correctness of the created virtual flow mesh, the numerical results were compared with some experimental ones. The recently published paper [9] and the older report [10] also reveal measurement results from experimental tests of a scaled UAV model, which were performed in a wind tunnel located in the IAT FMAA MUT. Figure 9 shows the UAV scale model suspended in the duct of the wind tunnel.

The results of the tunnel tests published in the report [10] are presented in Figure 10. Due to the limited cross-sectional diameter of the tunnel, a model used for the measurements had dimensions reduced four times compared to the actual aircraft. For the identical flow velocity $V = Vc =$ 20 m/s but a four times reduced chord, the actual Reynolds number was also four times smaller than the one taken in previously described software simulations, i.e., $Re =$ 117 × 10⁵. Due to the lower Re number for the flow in the tunnel, the aerodynamic coefficients determined by the experimental method will show noticeable deviations from the coefficient values obtained from numerical methods.

4. Conclusions

The individual results of the analyses are consistent with each other in terms of the $C_D\left(\alpha \right)$ and $C_L\left(\alpha \right)$ characteristics obtained. In addition, all programs showed a disturbance in the AoA region of six for the C_L calculation case. As expected, the highest resistance coefficient was determined by Ansys Fluent, which is related to the simplified viscosity model in the flow around the solid. The $C_L\left(\alpha \right)$ graph shows the tendency of panel methods to shift the critical angle towards higher values. The $C_L$ coefficients determined by the FVM method are lower than those obtained by panel methods, which raises doubts. For example, ref. [11] shows that the results of the FVM method should be higher than those obtained by LLT or VLM. This inconsistency creates a need for further research on the tested CFD models.

For the purposes of developing a tool to support the optimal design of light aircraft, it can be concluded that the solver implemented in OpenVSP, i.e., VSPAero, appears to be a promising tool. The presented results show a high degree of similarity to those obtained using the FVM method, the accuracy of which has been compared with the expert method. Nevertheless, further research is needed to achieve high accuracy and to verify the correctness of the calculations over a wide range of Reynolds and Mach numbers.