Rotorcraft Airfoil Performance in Martian Environment

Abstract

In 2021, the Ingenuity helicopter performed the inaugural flight on Mars, heralding a new epoch of exploration. However, the aerodynamics on Mars present unique challenges not found on Earth, such as low chord-based Reynolds number flows, which pose significant hurdles for future missions. The Ingenuity’s design incorporated a Reynolds number of approximately 20,000, dictated by the rotor’s dimensions. This paper investigates the implications of flows at a Reynolds number of 50,000, conducting a comparative analysis with those at 20,000 Re. The objective is to evaluate the feasibility of using larger rotor dimensions or extended airfoil chord lengths. An increase in the Reynolds number alters the size and position of Laminar Separation Bubbles (LSBs) on the airfoil, significantly impacting performance. This study leverages previous research on the structure and dynamics of LSBs to examine the flow around a cambered plate with 6% camber and 1% thickness in Martian conditions. This paper details the methods and mesh used for analysis, assesses airfoil performance, and provides a thorough explanation of the results obtained.

1. Introduction

Over the recent sixty years, interest and enthusiasm in space exploration, particularly on Mars, have increased dramatically. The crowning achievement in this field was realised by the Ingenuity helicopter in 2021, which executed the first flight on the Red Planet, ushering in a new era of planetary exploration. Rotorcrafts, like the Ingenuity helicopter, offer a quicker and more adaptable method for exploration compared to rovers, which are significantly affected by ground features. However, flying vehicles must contend with the atmospheric conditions of their environment, and the Martian atmosphere presents considerable challenges for aerodynamic design. Ingenuity employed two coaxial counter-rotating rotors, featuring a custom-developed airfoil (clf5605), which operated at speeds up to 2800 RPM and a maximum Reynolds number of 1.8 × 10⁴ [1].

Given the limited rotor dimensions mandated for the mission, the low atmospheric density on Mars results in low chord-based Reynolds numbers, predisposing the boundary layer to separation. In many cases, particularly within the Reynolds number range of 50,000 ≤ Re ≤ 100,000 [2], this phenomenon leads to a transition to turbulent flow with subsequent reattachment, thus inducing the formation of Laminar Separation Bubbles (LSBs). The initial studies on low chord-based Reynolds number flows date back to the 1960s when Schmitz identified a critical Reynolds number that drastically alters airfoil performance [3]. This critical value was later confirmed by Mueller [4] and McMasters [5], delineating three regions that describe the flow behaviour relative to the Reynolds number, as shown in Figure 1: subcritical (Re < 1 $\times {10}^5$), critical (Re = 1 $\times {10}^5$), and supercritical (Re > 1 $\times {10}^5$). Unlike conventional aircraft wings, which are in the supercritical region and indicate turbulent flow and boundary layer separation at high angles of attack, low Reynolds numbers typically result in laminar flow which tends to separate and may reattach under specific conditions to form a LSB. The formation of the bubble is influenced not only by the Reynolds number but also by the airfoil’s geometry, turbulence intensity, and the angle of attack [6,7]. The impact of the bubble on airfoil performance is generally detrimental, but the extent depends on the bubble’s location and size. Two types of bubbles are identified based on their length relative to the airfoil chord: short and long. Short bubbles, covering less than one per cent of the chord, do not significantly alter the pressure distribution [7]. In contrast, long bubbles cover a substantial part of the chord, significantly altering the pressure distribution and the resultant forces [8]. Studies have indicated that short bubbles typically form near the airfoil tip, and an increase in the angle of attack coupled with a decrease in the Reynolds number can cause the bubble to ‘burst’ [8,9]. This bursting may result in the formation of a long separation bubble (LoSB) or an unattached shear layer [8]. Additionally, a LoSB can develop at low Reynolds numbers, affecting the airfoil’s performance and stalling behaviour [10,11]. Understanding the characteristics of LoSBs is crucial for predicting their impact on airfoil performance. This knowledge is essential for selecting appropriate airfoils for specific applications, such as Mars rotorcrafts. Moreover, awareness of potential performance losses, such as a decrease in the lift coefficient or an increase in the drag coefficient, can assist in the selection or development of techniques to mitigate these effects.

In aerospace applications, airfoil analysis is conducted using computational methods, such as numerical modelling, alongside experimental techniques like wind tunnel experiments. These approaches provide a comprehensive understanding of airfoil behaviours by combining theoretical simulations with practical observations. Numerous studies have been undertaken to capture LSBs and understand their characteristics. Direct Numerical Simulations (DNSs) represent the sole method capable of truly capturing the complexity of LSBs, albeit at the cost of substantial computational resources and time. Koning et al. [12] uses unsteady laminar Navier–Stokes simulations, showing an alternative to DNS for resolving bubble dynamics. Alternatives such as models based on the Reynolds-Averaged Navier–Stokes (RANS) equations and Large Eddy Simulation (LES) approaches show promise [2,13]. LES simulations yield more detailed flow results than those obtained through RANS methods [14,15], including airfoils and cambered plates. In this work, we have opted to use the model developed by Menter et al. [16], the Transition SST model ($\gamma -R{e}_{\theta }$), focusing on airfoil performance rather than the precision of the model. Previous studies have demonstrated the model’s reasonable accuracy in predicting transition flows [17,18,19,20].

This analysis concentrates on the performance changes of a cambered plate with 6% camber and 1% thickness under two different Reynolds number flows, specifically 20,000 and 50,000. This type of airfoil is selected as it is an ideal candidate for these flows [21]. The simulations are conducted using the commercially available modelling environment ANSYS Fluent 2020 R2. Although experimental validation is not feasible, the results are considered reliable based on previous studies that utilised similar methods to model LSBs [22] and the convergence of the residuals. This paper aims to analyse a cambered plate in the Martian environment with the same maximum speed considered for Ingenuity, but at a higher Reynolds number, to assess the potential benefits of increasing the rotor’s dimensions. This article is organised as follows: Section 2 details the methodology, mesh, and boundary conditions used. Section 3 describes the general characteristics and effects of LSBs, along with a summary of prevention methods, and the impacts of the angle of attack and the Reynolds number. Section 4 presents the results of the simulations with a necessary discussion. Finally, Section 5 provides this paper’s conclusions.

2. Methods

2.1. The Martian Atmosphere

Mars’ environment poses significant aerodynamic challenges for the operation of a rotorcraft, with an atmosphere markedly different from Earth’s. The most conspicuous atmospheric differences are the lower density (0.017 $\mathrm{kg}/{\mathrm{m}}^3$), low temperatures (averaging 223.20 $\mathrm{K}$), and a predominantly CO₂-based composition. Generally, the low density significantly impacts the airfoil’s ability to generate lift and drag, and thus its overall performance. Low-Re fluid diminishes lift generation, affecting the pressure disparity between the upper and lower surfaces. It also leads to a reduction in drag in dimensional terms due to less resistance encountered by the airfoil moving through the fluid. Additionally, the stall characteristics of the airfoil are altered: the separation behaviour of the flow is modified, leading to a change in the critical angle of attack.

The typical flows for a rotorcraft on Mars are characterised by a low chord-based Reynolds number (10³–10⁴) [1], caused by the rarefied atmosphere and the dimensional limitations of the rotor. These types of flow result in reduced airfoil performance, leading to a decrease in lift force; the lower acceleration of gravity (3.71 $\mathrm{m}/{\mathrm{s}}^2$) partially offsets this loss in performance. Furthermore, the operation of a Mars rotorcraft is constrained by the lower speed of sound compared to Earth, which is induced by the composition and temperature of the atmosphere.

Table 1. Atmospheric conditions for Earth and Mars [23].

	Earth	Mars
Density [$\mathrm{kg}/{\mathrm{m}}^3$]	1.225	0.017
Temperature [$\mathrm{K}$]	288.20	223.20
Dynamic Viscosity [Pa·s]	1.750·10−5	1.130·10−5
Static Pressure, [$\mathrm{kPa}$]	101.30	0.72
Speed of sound [$\mathrm{m}/\mathrm{s}$]	340.35	233.13

shows some of the characteristics of the Martian atmosphere [23].

2.2. Computational Approach

2.2.1. Turbulence and Transition Modelling

Flow is analysed using the commercial software ANSYS Fluent 2020 R2, which employs a cell-centred pressure-based approach within the fluid domain. The primary equations governing the analysis are the continuity equation and the Reynolds Averaged Navier–Stokes (RANS) equations.

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho u_i\right)=0$$

(1)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho u_i\right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho u_i{u}_j\right)=-{\displaystyle \frac{\partial p}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\mu \left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}-{\displaystyle \frac{2}{3}}{\delta }_{ij}{\displaystyle \frac{\partial u_i}{\partial x_j}}\right)\right]+{\displaystyle \frac{\partial }{\partial x_j}}\left(-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right).$$

(2)

The turbulence modelling within this approach necessitates accurate modelling of the Reynolds stresses ($-\rho \overline{u_i^{\prime }{u}_j^{\prime }}$) to close the system of equations, which are achieved by the chosen turbulence model. The selected model for this analysis is the $\gamma -R{e}_{\theta }$ turbulence model, which integrates the SST $k-\omega$ model with two additional equations: one for intermittency and one for the momentum thickness Reynolds number. Proposed by Menter et al. [16] in 2002, this model is a modification of the $k-\omega$ SST model designed to more effectively describe transitional flows. The transport equations differ from those in the $k-\omega$ model due to alterations in the production term, dissipation term, and blending factor. The production of turbulent kinetic energy is influenced by the turbulent intermittency $\gamma$, which reflects the local state of the flow. If $\gamma =0$, the flow is locally laminar, whereas $\gamma =1$ indicates a fully turbulent flow. The value of $\gamma$ tempers the production of turbulent kinetic energy in areas where the boundary layer is laminar or transitional and scales the model to the $k-\omega$ SST in fully turbulent conditions. The dissipation term is modified to $D_{k}min(max(\gamma ,0.1),1)$, meaning that if $\gamma =0$, the dissipation drops to 10% of its turbulent value, and with $\gamma =1$, the model reverts to the $k-\omega$ turbulence model, as anticipated. It is crucial to note that the 0.1 limiter ensures the dissipation term never falls to zero, maintaining some level of turbulence damping by the wall, even when the flow is entirely laminar. The transport equations for kinetic energy (k) and the specific turbulence dissipation rate ($\omega$) are thus defined.

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+\nabla ·\left(\rho \mathit{U}k\right)=\nabla ·\left[\left(\mu +{\displaystyle \frac{{\mu }_T}{{\sigma }_k}}\right)\nabla k\right]+\gamma P_k-D_k\min \left[\left(\max \right(\gamma ,0.1),1\right]),$$

(3)

$${\displaystyle \frac{\partial \left(\rho \omega \right)}{\partial t}}+\nabla ·\left(\rho \mathit{U}\omega \right)=\nabla ·\left[\left(\mu +{\displaystyle \frac{{\mu }_T}{{\sigma }_k}}\right)\nabla \omega \right]+{\displaystyle \frac{\gamma }{{\nu }_T}}{P}_k-\beta \rho {\omega }^2+2(1-F_1){\displaystyle \frac{\rho {\sigma }_{\omega 2}}{\omega }}\nabla k:\nabla \omega .$$

(4)

The blending factor, also present in the $k-\omega$ SST model, determines whether the problem is locally addressed using the $k-ϵ$ or $k-\omega$ model. In the Transition SST model, this factor is adjusted to prevent inadvertent switches between the models [24]. The inclusion of intermittency necessitates a new equation to calculate this function, thus introducing an additional transport equation for $\gamma$ that needs to be solved. This equation reads

$${\displaystyle \frac{\partial \left(\rho \gamma \right)}{\partial t}}+\nabla ·\left(\rho \mathit{U}\gamma \right)=\nabla ·\left[\left(\mu +{\displaystyle \frac{{\mu }_T}{{\sigma }_{\gamma }}}\right)\nabla \gamma \right]+P_{\gamma }-D_{\gamma },$$

(5)

where the production term $P_{\gamma }$ governs the length of the transition region, whereas the dissipation term $D_{\gamma }$ facilitates the re-laminarisation of the boundary layer by dissipating intermittency fluctuations under appropriate conditions. The production of intermittency is dependent on the Reynolds number, which is calculated relative to momentum thickness $\theta$. This distance represents a theoretical length that the velocity profile must be displaced by to ensure that the velocity profiles maintain the same momentum, such that

$$\theta ={\int }_0^{\infty }{\displaystyle \frac{\rho U}{{\rho }_{\infty }{U}_{\infty }}}\left(1-{\displaystyle \frac{U}{U_{\infty }}}\right)dy.$$

(6)

The Reynolds number associated with this measure indicates the points at which fluctuations ($R{e}_{\theta ,c}$) and transitions ($R{e}_{\theta ,t}$) occur, both of which are empirically determined values. The method relies solely on local variables, and treating the transitional momentum thickness Reynolds number ${\overline{Re}}_{\theta ,t}$ as a scalar quantity leads to the derivation of the final necessary transport equation:

$${\displaystyle \frac{\partial \left(\rho {\overline{Re}}_{\theta ,t}\right)}{\partial t}}+\nabla ·\left(\rho \mathit{U}{\overline{Re}}_{\theta ,t}\right)=\nabla ·\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\theta ,t}}}\right)\nabla {\overline{Re}}_{\theta ,t}\right]+P_{\theta ,t}.$$

(7)

The $\gamma$-$R{e}_{\theta }$ model constitutes a four-equation turbulence model. The detailed workings of the model are elaborated upon in the work by Menter et al. [24]. Although Laminar Separation Bubbles typically represent a steady-state phenomenon, as demonstrated by Pauley et al. [25], the current work incorporates transient simulations to circumvent convergence issues with the model. As anticipated, the flow stabilizes shortly after varying the angle of attack, forming a bubble if conditions allow it to. Additionally, pressure–velocity coupling is managed using the coupled scheme, a pressure-based algorithm that provides a robust and efficient single-phase implementation [26]. Solution accuracy is further enhanced by the second-order accurate upwind scheme used for the spatial discretisation of all variables [26]. The adequacy of convergence for the simulation is monitored through the residuals of all variables, with particular attention to continuity, while the lift and drag coefficients are also closely supervised.

2.2.2. Computational Mesh

The flow around the cambered plate is analysed using a C-type computational mesh. The airfoil features a camber of 6% and a thickness of 1% along the entire chord. The mesh includes a semicircular frontier representing the inlet and a straight boundary as the outlet. The airfoil is positioned at a distance of 50c from all boundaries, as seen in Figure 2, and is tested at variable angles of attack. As illustrated, the mesh density is increased near the airfoil and in regions where the wake is expected to form. The height of the first cell adjacent to the airfoil surface is designed to ensure a minimum $y^{+}$ value (≤1), which is verified during each post-processing routine. Quadrilateral elements are chosen for their precision, efficiency in memory usage, and convergence benefits [27]. After preliminary evaluations on the number of elements required for meshing, discussed in Section 2.2.4, the final mesh utilised in this study comprises a total of 400,000 elements. This denser mesh near the airfoil and behind the trailing edge is crucial for capturing the flow’s critical characteristics.

2.2.3. Boundary Conditions

The boundary domain is divided into an inlet, an outlet, and horizontal components that are designated as inlet, outlet, or wall depending on the inclination of the flow, as illustrated in Figure 2. The inlet boundary condition is restricted to the velocity of the free stream, whilst the outlet is set to have a pressure equivalent to atmospheric pressure. Free-stream velocity is set to produce a chord-based Reynolds number of approximately 20,000 or 50,000, depending on the case analysed. The upper horizontal component acts as an inlet when the flow is negatively inclined and as an outlet when the flow is positively inclined. Conversely, the lower horizontal component behaves oppositely. They are both walls with no slip condition when the flow is horizontal. Owing to the choice of the turbulence model $\left(\gamma -R{e}_{\theta }\right)$, the essential specifications required at the inlet are intermittency, turbulent intensity (TI), and turbulent viscosity ratio, which are subsequently calculated throughout the domain using the equations of the model. All three of these values are empirical, and it is possible to ascertain the potential ranges for this type of study. The intermittency is set to 1, which is the value expected for external flows with a fully developed turbulent region [26]. According to Wang et al. [28], the effect of TI is significantly reduced for flows with low Re (Re $\approx {10}^4–3\times {10}^5$). Therefore, the value is set at the standard 0.082%, as utilised by Koning et al. [1] for Ingenuity’s rotor model analysis. The third parameter is chosen to be the turbulent viscosity ratio, which is convenient to use in low-turbulence cases, like external aerodynamics, where it is difficult to estimate the characteristic length scale, and it is typically found in the range $1<{\mu }_t/\mu <10$ [26]. The value does not significantly influence the results of the simulations; hence, it is maintained at the standard value of 10.

2.2.4. Grid Independence Study

A grid independence study is conducted to confirm that the solutions obtained are independent of the mesh resolution. This study involves the flow of Re = 20,000 for five different total numbers of elements in the mesh, ranging from 100 k to 500 k. The investigation is undertaken at angles of attack of 0° and 5°, maintaining the same setup as the other simulations. The monitoring focuses on the drag coefficient and the distribution of the pressure coefficient to check for instabilities and possible differences that indicate the influence of the mesh on the results.

Table 2. Grid independence study (Re = 20,000).

Mesh Elements	Boundary Distance	CD 0°	CD 5°
100 k	50c	0.0270395	0.0373019
200 k	50c	0.0275159	0.0364775
300 k	50c	0.0278523	0.0354827
400 k	50c	0.0280134	0.0352006
500 k	50c	0.0279638	0.0351146
400 k	50c	0.0280134	0.0352006
700 k	100c	0.027888	0.0350659

presents the results of the grid independence study, demonstrating that the mesh with 400 k elements suffices to obtain conclusive results for both angles of attack. Indeed, increasing the mesh would result in a change of 0.2% for both 0° and 5°. Furthermore, comparing the pressure coefficient distribution for the meshes in Figure 3, it is possible to notice instabilities with a mesh of 300 k elements, which disappear with an increase in mesh density. Despite the dimensions used to create the mesh being selected to ensure that the results are not affected by the boundary domain, an additional study is undertaken to confirm this. Another C-type mesh with boundaries at 100c in all directions from the airfoil is generated. The angle of attack is maintained at 0° and 5°, with the drag coefficient again chosen as the monitored variable. The results, displayed in Table 2, show a negligible change of 0.4% in the drag coefficient at both 0° and 5°. In conclusion, a mesh with 400 k elements is chosen, with the airfoil positioned at a boundary distance of 50c.

3. Laminar Separation Bubbles

3.1. General Features and Effects

All LSBs, both short and long, exhibit the same general characteristics and structure, as depicted in Figure 4a, where three principal points are highlighted: S is the point of separation, T is the point of transition, and R is the point of reattachment. Additionally, two regions are of utmost importance:

• The bubble region, formed by the recirculating flow and bounded by the streamline ST′R, where the integrated mass flow is zero;
• The shear layer, which is the area between the bubble and the outer edge of the boundary layer, identified with S″T″R″.

The formation process of the bubble begins with separation, followed by the transition of the shear layer that is caused due to disturbances; finally, reattachment occurs, eliminating the reverse flow near the wall.

The two types of bubbles still exhibit some differences that alter their impact on the airfoil. LoSBs cover a larger portion of the airfoil surface, resulting in an extended region of trapped flow, causing the portion of zero pressure gradient and a larger recirculation zone. Figure 4b illustrates the effect of the LoSB on the suction region pressure distribution. The dotted line represents the theoretical prediction without considering the bubble’s formation, while the second line displays experimental results. Two crucial details are the flat portion, which represents the zero pressure gradient caused by the bubble, and the fully attached flow at the trailing edge [31]. The modification of the pressure distribution significantly affects the airfoil performance, particularly causing a slight increase in lift and a substantial increase in drag, resulting in a decrease in the overall lift-to-drag ratio. Additionally, the aerodynamic behaviour of the airfoil is influenced by the camber effect. In fact, the bubble’s thickness affects the airfoil’s geometry. An increase in the angle of attack leads to an increase in the thickness of the bubble [32], producing a greater camber effect at higher angles which benefits the creation of lift. Nonetheless, the associated gain in lift comes with higher drag, leading to a poor lift-to-drag ratio.

Beyond impacting the aerodynamic performance of the airfoil, LSBs pose a potential risk of dangerous dynamic structural loading [33] due to their instability and consequent design uncertainty. Bubbles are considered a parasitic phenomenon that should be avoided. Various methods to control or eliminate LSBs have been studied: the most effective ones induce a premature turbulent transition, making separation more difficult. Passive methods include carefully selecting the airfoil [34] or using mechanical tabulators upstream of the laminar separation point [35]. Despite turbulence generation occurring regardless of the need, which is not the ideal solution for most systems, active methods offer alternatives, such as vortex generators or deforming the airfoil surface to introduce the desired disturbances. These solutions allow for the possibility of being switched off to avoid generating disturbance. Such systems are more challenging to design since they are usually tuned for the optimum design point and do not accommodate off-design conditions. For a rotorcraft on Mars, it can be argued that active methods of preventing LSBs are not suitable given the continuous change of its features during flight, such as the angle of attack or velocity; similarly, passive methods introduce potential undesired turbulence, which could be detrimental to the flight. The best option would be to review the features affecting the formation of LSBs and, if possible, modify them. As mentioned previously, the formation and features of LSBs are intricately linked to the geometry of the profile, the turbulence intensity, the angle of attack, and the Reynolds number [2]. Since the turbulent intensity is determined by the environment and the profile was chosen for this study, only the effects of the angle of attack and Reynolds number are analysed in more detail.

3.2. Angle of Attack

The angle of attack significantly influences the formation and characteristics of the LSB [2] and is more closely associated with the geometry of the airfoil and turbulence intensity. By employing the skin friction coefficient and pressure coefficient, it is possible to identify significant changes in flow behaviour: laminar separation, transition onset, and turbulent reattachment. For standard geometries, an increase in the angle of attack results in earlier laminar separation, moving the bubble closer to the tip of the airfoil, and earlier turbulent reattachment suggests a reduction in the length of the bubble. However, these changes occur alongside an increase in the thickness of the bubble [32].

3.3. Effect of the Reynolds Number

It is well established that the Reynolds number influences the formation and characteristics of the LSB (see, e.g., the work by Winslow [2]). Choudhry et al. [22] demonstrate that the increase in the overall extent of the bubble and the significant shifts in the separation and reattachment point to an increase in the Reynolds number. The effects of this increase include a delay in the laminar separation, which is not pronounced at high angles of attack; an earlier reattachment of the turbulent shear layer, implying a reduction in the length of the bubble; and a delay in the turbulent separation, resulting in a diminished impact of the bubble on stall behaviour. In conclusion, an increase in the Reynolds number results in an enhancement of airfoil performance owing to the decreased size of the bubble and the increase itself. A shorter and less thick bubble implies a lesser impact on the pressure distribution and a reduced camber effect.

4. Results

The simulation results depicted in Figure 5 illustrate the velocity magnitude for various angles of attack in flows with a Reynolds number of 20,000. Below an angle of attack of 0°, localised separated boundary layers (LSBs) are discernible on the bottom surface of the airfoil. As the angle of attack increases, the separation point shifts towards the trailing edge of the airfoil’s top surface. At 5°, an LSB begins to form on the upper surface, altering the airfoil’s geometry and influencing the pressure distribution. Notably, bubbles form near the trailing edge, and an increase in the angle results in a change in bubble thickness. Similarly, the influence of a fluid with a Reynolds number of 50,000 around the cambered plate is shown in Figure 6. Analogous to the flow at a 20,000 Reynolds number, a bottom surface bubble forms up to a 0° angle of attack, while the top surface bubble forms at a 5° angle. It is noteworthy that, with an increase in the Reynolds number, the bubbles persist on the airfoil, albeit with reduced thickness, thereby diminishing their effect on performance.

Figure 7 illustrates the effect of the angle of attack on the bubble forming on the suction surface of the airfoil for both Reynolds number flows. Similarly, Figure 8 demonstrates the impact of the angle of attack on the bubble forming on the pressure surface of the airfoil for both flows. It is clear that an increase in the angle of attack causes the bubble to move closer to the tip of the airfoil and results in a shorter length. Although the delay in laminar separation is not clearly visible, probably due to the relatively small difference in the Reynolds number, Figure 7 and Figure 8 corroborate previous studies, showing a reduction in the size of the bubble with an increase in the Reynolds number. The increase in the length of the bubble at an angle of attack of 0° at a Reynolds number of 20,000 and 8° at a Reynolds number of 50,000 is considered to be connected to the model used. While this model can capture the presence of the bubble, it inaccurately predicts bubble reattachment when bubble bursting should occur. The unusual results observed at these two angles are evident in the skin friction coefficient distribution (Figure 9), where the coefficient distribution does not behave as expected when a bubble is present. Although this effect does not produce clearly false results for lift and drag, it is not acceptable for this type of simulation. Therefore, there is a need for a more reliable model that accurately captures LSBs at every step.

Figure 10 presents the airfoil’s performance metrics in terms of the lift coefficient, drag coefficient, lift-to-drag ratio, and drag polars, respectively. The deductions drawn from the velocity profiles are confirmed by the variation in the lift and drag coefficients with the increase in the angle of attack. The sudden increases in lift that are visible in the figures can be attributed to bubble formation and the resultant camber effect. This effect is mirrored by the behaviour of the drag coefficient, which exhibits a noticeable increase. As validated by the velocity profiles, performance at higher Reynolds numbers is superior, owing to reduced bubble thickness.

5. Conclusions

This paper presented numerical simulations of a cambered plate with 6% camber and 1% thickness, analysed within the Martian environment. This study aimed to investigate the impact of low chord-based Reynolds number flows, which pose a significant challenge for rotorcrafts operating on Mars. The efficiency of the airfoil was evaluated at Reynolds numbers of 20,000 and 50,000, focusing on the formation of Laminar Separation Bubbles on the airfoil surface, which greatly influence performance. Turbulence modelling was conducted using the Transition SST model.

The analysis reveals that using an airfoil with similar features to Ingenuity, which generated a flow with a Reynolds number of 20,000, does not yield optimal performance. Increasing rotor or airfoil dimensions to generate flows with a Reynolds number of 50,000 does not lead to substantial improvements either as LSBs are still present on the airfoil and performance gains are minimal. These conclusions are drawn from the plots of lift and drag coefficients, together with the lift-to-drag graph (Figure 10). Another result of the analysis is the formation of bubbles in the both suction and pressure surfaces of the airfoil, together with the changes in length and position due to changes in the angle of attack and Reynolds numbers. The fundamental importance of identifying an error in the model used for simulations highlights the need to explore more reliable models. However, the current model effectively captures the phenomenon of bubbles, providing valuable insights into their impact on airfoil performance. Therefore, the necessity for exploring alternative solutions for utilising flying vehicles on Mars is evident. Customised airfoil designs, based on a cambered plate, are considered essential to improve efficiency. To comprehensively understand the airfoil’s real-world performance, other aerodynamic challenges, such as the effect of dust accumulation on the airfoil and resulting geometric changes, need to be investigated further.

The simulations highlight critical insights into the aerodynamic performance of airfoils designed for Martian conditions, where this unique environment presents significant challenges not commonly encountered on Earth. The findings underscore the limitations of current airfoil designs in low Reynolds number flows, particularly the persistent presence of Laminar Separation Bubbles, which detrimentally affect the efficiency of lift generation. Despite attempts to enhance performance by scaling up airfoil dimensions to increase the Reynolds numbers, the results indicate that such measures alone are insufficient. The ongoing presence of LSBs at higher Reynolds numbers and their minimal impact on performance improvements suggest that more radical design changes or alternative solutions may be required. This includes the possibility of rethinking airfoil shapes or incorporating adaptive technologies that can respond to the dynamic Martian atmosphere. Moreover, this study opens up several avenues for further research. The effect of Martian dust on airfoil surfaces could significantly alter aerodynamics, necessitating studies into materials or coatings that mitigate dust accumulation. Additionally, exploring the implications of geometric changes caused by dust build-up could provide valuable data that could inform the design of more robust airfoil systems for Mars.

In conclusion, while this research marks a significant step towards understanding the aerodynamics of airfoils in Martian conditions, it also clearly delineates the complexities and challenges that need to be addressed. Advancements in design, materials, and perhaps even a fundamental re-evaluation of flight mechanics for Martian applications are essential to realise the potential of aerial vehicles in extraterrestrial environments. Further studies and innovative approaches are critical in developing airfoil technologies that can successfully navigate the unique demands of Mars.

Our key findings are summarised in the following bullet points:

• The low chord-based Reynolds number regime in the Martin atmosphere causes the formation of Laminar Separation Bubbles on the airfoil, which affect its performance;
• The increase in the Reynolds number from 20,000 to 50,000 has a small impact on performance;
• The model used provides a good representation of the formation of bubbles on the airfoil, but, in some cases, can capture a bubble incorrectly;
• Future works should aim to construct a more reliable model and focus on the other challenges posed by the Martian environment.