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Cyclorotor flow: I let a video rendering of a three-dimensional computational fluid dynamics simulation do most of the explanation

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The video shows the rendering of a hovering three-dimensional barebone cyclorotor computational fluid dynamics simulation after 14 initial rotor revolutions.

What is shown:
00:08 - Relative atmospheric pressure on the blades, the effects of the major dynamic stall event are mostly seen shortly after 270°. Most of the thrust is generated by pressure and one can see that the bottom passage has the strongest contribution.
00:45 - The coefficient of friction on the blade, considering that the blade rotates and oscillates, identifies in yellow positions where the relative velocity between blade and fluid goes to zero and indicates likelihood for detached flow. Once again, the position shortly after 270° shows the strongest action, because of dynamic stall.
01:08 - The velocity LIC lines in the rotating rotor reference frame (rotating but not locally oscillating) on the first layer of cells above the blade give another, more global, view of the dynamic stall action and the vortices that are created by the blade.
01:33 - The lambda2 contour surfaces show these vortices, such has the horseshoe vortex which detaches from the blade around angle 360° and the tip vortices of the blades. The lambda2 surfaces in the first 1 cm above the blade are cut out from the rendering to allow better visualization of the blade's coefficient of friction.
02:04 - The same lambda2 surfaces are now colored by the vorticity projected on the non-oscillating orbital blade path to highlight the direction of the vortices, in particular the tip vortices which have a different direction of rotation on the top passage as in the bottom one, because of the combination direction of motion of the blade and the thrust it generates.
02:36 - The sensitivity of the lambda2 surfaces is extended to identify the large turbulent structures that leave the upper blades and travel through the rotor. The pressure bubbles shown on the rearwards half the blades correlate with the magnitude of the generated thrust and also indicate that the large eddies coming from the upper blade have little influence on the lower passage. The LIC lines indicate the path of the flow inside the vortices identified by the lambda2 surfaces and the color indicates the radial distance from the center of the rotor, to ease understanding of motion of the turbulent structures traveling through the rotor.
03:16 - The arrows now allow identifying the inflow and wake generated by the rotor. Their size is scaled according to the square root of the velocity vector magnitude and they are shown for any velocity magnitude above 5 cm/s, thus allowing to identifying the zone of influence of the rotor. Although the arrows are filtered out near the blades, some local irregularities are seen and correspond to the flow response to the passage of a blade. Because of the small aspect ratio and the absence of endplates or side disks, the inflow is highly three-dimensional and the flow leaving the rotor forms, contrary to what is usually seen in 2D simulations, a rather wide wake. The arrows also highlight the acceleration of the flow through the rotor and also the marked difference of velocity between the upper and lower passages of the blades.
04:10 - The side view of the wake further pictures that air flows into the rotor from all sides and also in the middle of the rotor, thus between the two blade passages, while the wake remains rather bidimensional. As expected the flow is also curved through the rotor, thus bending the wake towards the positive x-direction.

Geometry: Blade chord is 15 cm and aspect ratio is 2; rotor radius is 50 cm. The motion function is given at the beginning of the video. A YouTube video demonstrates the cyclorotor mechanism.

CFD model: Turbulence is implemented using the unsteady Reynolds-averaged Navier-Stokes method with a k-ω SST turbulence model with a fully resolved wall using a first grid cell thickness of 6.6 μm. The v2012 pimpleFoam solver is used and the grid has pill-shaped moving mesh zones which contain the blades and which are coupled to a rotating background mesh through the AMI interface method. No symmetry is used and the complete mesh has 20.5 million cells. Second order schemes in both time and space are used.

Computational aspects: The simulation was run on the Hawk supercomputer of the High Performance Computing Center Stuttgart (HLRS) using 2048 processes on 32 nodes, taking approximately 6 seconds per timestep, each covering 0.5 degrees of rotation, thus leading to a maximum Courant number varying between 160 and 200.

Acknowledgments: This simulation was conducted at the Institute of Aerodynamics and Gas Dynamics of the University of Stuttgart for the A Novel and Simple Aircraft Requiring Minimal Power to Hover and is financed by the Humboldt Research Fellowship for postdoctoral researchers. Free open-source software used: FreeCAD and naca4gen and GNU Octave for the blade profile, OpenFOAM for the simulation, and ParaView and Python for post-processing.

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