October 27, 2023 - by Santina Russo

Welcome to the skies of Mars! Imagine a helicopter flying in air with a density of less than one percent of the atmospheric density here on Earth. To be able to lift off in this thin atmosphere, the Martian helicopter Ingenuity must be extremely light. Weighing only 1.8 kilograms, it features two rotors that turn in opposite directions with 1.2-metre-long airfoils that rotate ten times faster than a similar helicopter on Earth.

Ingenuity has proven a major success: It was the very first machine to fly on another planet, and since its first test flight in April 2021, it has completed more than 60 flights — impressing its developers and operators at NASA’s Jet Propulsion Laboratory, who were initially only hoping for five.

By now, NASA’s Mars helicopter Ingenuity has completed over 50 flights, exceeding initial expectation many times over. In its furthest flight to date, the lightweight rotorcraft covered 700 metres in a bit more than 2.5 minutes. (Video: NASA/JPL-Caltech/ASU/MSSS)

However, Ingenuity does not carry any scientific equipment and is not able to retrieve samples, for example from peaks and craters that the Mars rover can’t reach, because the weight requirements to perform such useful tasks would be too high. “Flying a helicopter on another planet is an absolutely amazing achievement,” says Peter Vincent, professor of computational fluid dynamics in the Department of Aeronautics at Imperial College London. “The next step is to design helicopters that can fly longer and further and carry loads with them to assist in scientific work.” One of the limiting factors to achieve this, explains Vincent, are the rotor blade airfoils, which need to be optimized for flying in the thin atmospheric conditions on Mars. To overcome this hurdle, Vincent and his team recently conducted simulations on CSCS’s supercomputer “Piz Daint”.

Adapting to the thin Martian atmosphere 

Compared to Earth, the atmospheric pressure on our red neighbouring planet is lower, and its atmosphere contains a much higher share of CO2. Also, the air temperature is lower, as is the speed of sound. All of this means that the Reynolds number — an important determinant of how unsteady and turbulent a flow is — is generally much lower on Mars compared to Earth. “In fact, the Reynolds number of a running helicopter rotor on Mars can be compared with that of a flying insect here on Earth,” illustrates Vincent. Furthermore, the Mach number, which is the ratio of a flow’s velocity to the speed of sound, is rather high on Mars because of the low speed of sound. These are conditions that just don’t exist here on Earth.

Nevertheless, Martian conditions can be investigated — specifically in the Mars Wind Tunnel at Tohoku University in Japan, a unique facility capable of mimicking the atmosphere of the red planet. As experiments at the site have shown, airfoils optimal for flight on Mars likely possess a different shape than airfoils on Earth: Instead of the conventional curved cross-section shape that somewhat mimics the shape of a bird’s wings, novel shapes based on triangles, thin cambered plates, and even corrugated concepts based on the profile of dragonfly wings are explored. These dragonfly wing profiles shed specific vortices off the tips of their zigzag features to create lift, and they do this at low Reynolds numbers — exactly what is needed for flight on Mars.

A way to optimize the design 

Vincent’s team has now thoroughly analysed the flow over triangular airfoils derived from this principle and optimized the airfoils’ profile. To study the type of temporary and unsteady vortex-dominated flow off these airfoils, the scientists used a software called PyFR, which is being developed at Imperial College London and Texas A&M University. This was necessary since the algorithms conventionally used for flow simulations, namely Reynolds-Averaged Navier Stokes (RANS) or unsteady Reynolds-Averaged Navier Stokes algorithms (URANS), have trouble with this kind of unsteady vortex flow, as Vincent explains. With PyFR however, the scientists were able to solve the relevant physics.

In a first step, Vincent’s team simulated experiments done in the Tohoku University wind tunnel on a reference triangular airfoil, and they were able to match the outcome of the experiments. “So consequently, we started to think about how we could start to optimize the airfoils’ design,” recounts Vincent. To this end, he and his team went on to combine their new software with a so-called genetic algorithm that mimicked a sort of natural evolution of the airfoils and varied their cross-section shape. Within certain parameters that kept the triangular concept intact, the scientists analysed multiple cross-section shape designs in hundreds of simulations. “Such a project involving many individual 3D direct numerical simulations could not have been done without a powerful supercomputer like ‘Piz Daint’ and a seamless integration of hardware and software,” states Lidia Caros, the PhD student in Vincent’s team who undertook the simulations.

How to maximize lift 

The team’s simulations illustrated how the triangular airfoils generate lift by creating a large vortex, somewhat trapped, above the surface from the tip to the apex of the cross-section shape. “A vortex has lower pressure inside it than the air all around,” Caros explains. This lower pressure at the top surface draws the airfoil upwards, creating lift.

In addition, the analysis as well as the genetic optimization of the design demonstrated how lift could be maximized. Simply put, the larger the top surface area of the airfoil and the more substantial the vortex being formed and trapped there, the larger the lift. “At the same time, the trailing edge behind the apex must not be too blunt and steep, since the vortex forming there has a negative effect,” Caros says, explaining that it draws the airfoil backwards and slows it down, creating drag.

Found: a set of optimal shapes 

Since this was a multi-objective optimization to simultaneously find airfoils with high lift and low drag, the result is not one single ideal shape, but a set of optimized shapes featuring the most favourable properties — that is to say, shapes with the most favourable combinations of increased lift and reduced drag. 

“There is still much to be explored,” says group head Peter Vincent. For instance, in this work, the angle of attack, meaning the angle that the airfoil makes with the oncoming air flow, was fixed at 12 degrees. Going forward, Vincent and his team plan to include the angle of attack as a design variable to be optimized as well. Also, this work produced an optimized set of shapes for a cross-section near the hub of the rotor, but further out towards the tips of the rotors, other shapes might be optimal. On the way to building a helicopter that can further explore Mars as well as help to answer scientific questions, there are still many possibilities to explore.

Image above: An Artist’s impression of NASA’s Mars helicopter Ingenuity next to the Perseverance Mars rover. The rotorcraft measures around half a meter in height and weighs less than two kilograms. To be able to lift off in the thin atmosphere on Mars, its airfoils rotate ten times faster than is usual on Earth. (Image: Wikimedia commons, NASA/JPL-Caltech)


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