Direct Numerical Simulation of a Starting Rotor

Authors: Adam Peplinski, Ronith Stanly
(​Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden)
Eman Bagheri, Siavash Toosi
(​Institute of Fluid Mechanics (LSTM), Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Germany)
Philipp Schlatter
(​Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden; Institute of Fluid Mechanics (LSTM), Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Germany)
Niclas Jansson
(PDC Center for High Performance Computing, KTH Royal Institute of Technology, Stockholm, Sweden)
Timofey Mukha
(Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST),
Thuwal, Kingdom of Saudi Arabia)

Rotors play a major role in various applications including ventilation and propulsion systems such as in helicopters, drones, gas turbines, wind turbines and many more. This visualization of instantaneous vortical structures (identified by the criterion) shows complex turbulence emanating λ2 from a twisted drone rotor that is starting to rotate. Initially, a starting vortex is formed as a result of lift generation and shed as a connected vortex tube from the entire surface of the blade, which has a strong connection to the blade tip via the so-called tip vortex. Leading-edge separation occurs at span positions of high twist, followed by wave-induced breakdown to turbulence along the whole wing span. This turbulence then sheds as small-scale vortices into the wake and dissipates. Understanding the behaviour of these vortices from such complex blades and how they interact with the other blade is critical to design more efficient and potentially more silent propellers.

While open rotors provide a higher propulsive efficiency as compared to ducted rotors, they have a higher noise footprint. With the advent of electric propulsion for green aviation, open rotors which were popular in the 1970s are now making a comeback in order to deliver, for instance, more thrust per kW of electricity. Simulation tools are to be developed to study the physics of these complex rotor blades to reduce their noise, as well as to understand how the flow structures from them interact with their surroundings. This has applications in several contexts, such as public safety–as drones are operated in urban environments–or to enable a swift helicopter take-off from a ship deck.
Owing to the complexity of the blades and high computational cost, the current state of the art for rotor simulations is to simulate blades modelled using source terms or to use unsteady Reynolds-averaged Navier Stokes (uRANS) in the near field. This RANS approach may sometimes be coupled to higher fidelity simulation methods in the far field. These methods may not always provide a reliable picture of the near-blade flow physics and thereby can contribute to uncertainties in the flow and corresponding noise predictions. To this end, we perform a blade-resolved direct numerical simulation (DNS) of the starting flow around a highly twisted drone rotor using advanced simulation capabilities including Adaptive Mesh Refinement (AMR) and in-situ visualization added to the open-source high-order CFD solver Nek5000 [3]. In AMR, the initial conformal mesh of 158,000 spectral elements, in a rotating frame of reference at a tip-chord based Reynolds number , grows in time to refine the fine vortices that are generated and shed. With three 𝑅𝑒𝑐=15,000levels of refinement, the final non-conformal mesh in this video contains 1,385,000 spectral elements, each having 7th order polynomials in three dimensions.
This visualization of instantaneous vortical structures (identified by the vortex identification λ2 criterion) allows us to see complex flow phenomena such as the creation of starting vortices, leading-edge separation and how the starting vortex interacts with the other blade. Looking at the tips of the blades, a strong primary tip vortex is created, which is surrounded by smaller-scale vortices emanating from the blade surfaces. Thus, the tip vortices become unsteady themselves, while propagating along a helical path and slowly decaying. Leading-edge separation occurs at span positions of high twist, followed by flow separation at different chord positions from other radial sections of the blades. This results in wave-induced breakdown to turbulence along the whole wing span, shedding small-scale turbulence into the wake. High-order methods with low numerical dissipation and dispersion are particularly suited to capture the interaction of the multiscale features of turbulence, and the longer-time dynamics of the comparably weak tip vortices. As part of ongoing work, we are also studying the noise emitted by this rotor using Ffowcs Williams-Hawking acoustic analogy, driven by the sound sources on the blades.
The actual video was produced by remote rendering on the NHR-FAU cluster Fritz with Paraview 5.13, in 4K resolution. The frame rate was increased to 60 fps using the RIFE real-time flow estimator.

R​eferences:

[1] R. Stanly, E. Bagheri, A. Peplinski, A. Memmolo, S. Becker & P. Schlatter. Direct numerical simulations of a rotor at Re= 10000 and analysis of acoustic sources. The Platform for Advanced Scientific Computing (PASC), 26 - 28 June, 2023
[2] S. Toosi, A. Peplinski, P. Schlatter & R. Vinuesa. The impact of finite span and wing-tip vortices on a turbulent NACA0012 wing. Journal of Fluid Mechanics, 997, A68, 2024
[3] N. Offermans, D. Massaro, A. Peplinski & P. Schlatter. Error-driven adaptive mesh refinement for unsteady turbulent flows in spectral-element simulations. Computers & Fluids, 251, 105736, 2023

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