Modelling and Supercomputer Simulation of Hinged Rotor

Ilya V. Abalakin; Vladimir G. Bobkov; Tatiana K. Kozubskaya; Aleksey V. Lipatov

doi:10.14529/jsfi250106

Authors

Ilya V. Abalakin Keldysh Institute of Applied Mathematics, RAS, Moscow, Russian Federation https://orcid.org/0000-0002-4296-6802
Vladimir G. Bobkov Keldysh Institute of Applied Mathematics, RAS, Moscow, Russian Federation https://orcid.org/0000-0001-7020-1586
Tatiana K. Kozubskaya Keldysh Institute of Applied Mathematics, RAS, Moscow, Russian Federation https://orcid.org/0000-0002-9529-4093
Aleksey V. Lipatov Bauman Moscow State Technical University, Moscow, Russian Federation https://orcid.org/0009-0008-6370-3631

DOI:

https://doi.org/10.14529/jsfi250106

Keywords:

helicopter, rotor kinematics, cyclic control, flapping motion, taper stabilization, computational fluid dynamics, turbulent flows, unstructured mesh, mesh deformation, higher-accuracy method, CPU GPU

Abstract

The paper presents a computational technology of numerical simulation of turbulent flow over a hinged rotor on high-performance heterogeneous computer systems. A key part of the technology is the developed mathematical model describing the complex motions of triple-hinged rigid blades of a helicopter under the action of external and aerodynamic forces and its implementation using an original unstructured mesh-deformation algorithm. The mesh-deformation method exploits an auxiliary web-structured mesh with its elastic compression-expansion controlled by low-cost quasi-one-dimensional strand-based algorithms. The mechanics model is verified by solving the pendulum problems. To demonstrate the correctness of the developed techniques, the problems on taper stabilization and blade motion under cyclic control for model helicopter rotors are considered. All the presented computations are carried out using the code NOISEtte for solving aerodynamics and aeroacoustics problem. The code implements higher-accuracy methods of computational fluid dynamics on unstructured mixed-element meshes and operates with a high efficiency on modern supercomputers with arbitrary architectures including CPU cores and GPU accelerators.

References

MBDyn - Multi-Body Dynamics. https://www.mbdyn.org

Abalakin, I., Bakhvalov, P., Kozubskaya, T.: Edge-based reconstruction schemes for unstructured tetrahedral meshes. International Journal for Numerical Methods in Fluids 81(6), 331–356 (2016). https://doi.org/10.1002/fld.4187

Abalakin, I.A., Bobkov, V.G., Kozubskaya, T.K.: Numerical study of fuselage impact on acoustic characteristics of a helicopter rotor. Supercomputing Frontiers and Innovations 9(4), 100–113 (Dec 2022). https://doi.org/10.14529/jsfi220409

Abalakin, I.V., Bobkov, V.G., Kozubskaya, T.K., et al.: Numerical simulation of flow around rigid rotor in forward flight. Fluid Dynamics 55(4), 534–544 (Jul 2020). https://doi.org/10.1134/S0015462820040011

Abalakin, I.V., Bakhvalov, P.A., Bobkov, V.G., et al.: Noisette CFD&CAA supercomputer code for research and applications. Supercomputing Frontiers and Innovations 11(2), 78–101 (aug 2024). https://doi.org/10.14529/jsfi240206

Altmikus, A.R.M., Wagner, S., Beaumier, P., Servera, G.: A comparison: Weak versus strong modular coupling for trimmed aeroelastic rotor simulations. In: AHS International, 58th Annual Forum Proceedings. vol. 1, pp. 697–710 (2002), https://api.semanticscholar.org/CorpusID:125998085

Bakhvalov, P.A., Kozubskaya, T.K.: EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes. Computers and Fluids 157, 312–324 (2017). https://doi.org/10.1016/j.compfluid.2017.09.004

Bakhvalov, P.A., Kozubskaya, T.K., Rodionov, P.V.: EBR schemes with curvilinear reconstructions for hybrid meshes. Computers and Fluids 239(105352) (2022). https://doi.org/10.1016/j.compfluid.2022.105352

Bakhvalov, P.A., Surnachev, M.D.: Method of averaged element splittings for diffusion terms discretization in vertex-centered framework. Journal of Computational Physics 450(110819), 110819 (2022). https://doi.org/10.1016/j.jcp.2021.110819

Bakhvalov, P.A., Vershkov, V.A.: Edge-based schemes on moving hybrid meshes in the NOISEtte code. Keldysh Inst. Appl. Math. Preprint 127 (2018). https://doi.org/10.20948/prepr-2018-127

Bobkov, V.G., Vershkov, V.A., Kozubskaya, T.K., Tsvetkova, V.O.: Deformation technique of unstructured mesh deformation to find the aerodynamic characteristics of bodies at small displacements. Mathematical Models and Computer Simulations 13(6), 986–1001 (Nov 2021). https://doi.org/10.1134/s2070048221060028

Gorobets, A., Bakhvalov, P.: Heterogeneous CPU+GPU parallelization for high-accuracy scale-resolving simulations of compressible turbulent flows on hybrid supercomputers. Computer Physics Communications 271, 108231 (Dec 2022). https://doi.org/10.1016/j.cpc.2021.108231

Gorobets, A.V., Duben, A.P.: Technology for supercomputer simulation of turbulent flows in the good new days of exascale computing. Supercomputing Frontiers and Innovations 8(4), 4–10 (Dec 2021). https://doi.org/10.14529/jsfi210401

Ilkko, J., Hoffren, J., Siikonen, T.: Simulation of a helicopter rotor flow. Journal of Structural Mechanics 43(3), 186–205 (2011). https://doi.org/10.1016/j.jcp.2021.110819

Jameson, A.: Numerical solution of the Euler equations for compressible inviscid fluids. In: Angard, F., et al. (eds.) Numerical methods for the Euler equations of Fluid Dynamics, pp. 199–245. SIAM (1985)

Johnson, W.: Rotorcraft aerodynamics models for a comprehensive analysis. In: Proceedings of the 54th Annual Forum of the American Helicopter Society. vol. 2, pp. 1184–1206. Curran Associates, American Helicopter Society International, Washington, D.C. (May 1998)

Kopiev, V.F., Zaytsev, M.Yu., Vorontsov, V.I., et al.: Helicopter noise in hover: Computational modelling and experimental validation. Acoustical Physics 63(6), 686–698 (Nov 2017). https://doi.org/10.1134/s1063771017060070

Lallemand, M.H.: Dissipative properties of Runge-Kutta schemes with upwind spatial approximation for the Euler equations, Research Report RR-1173, INRIA (1990), https://inria.hal.science/inria-00075385

Lipatov, A.V., Abalakin, I.V.: The hinged rotor mechanics. Keldysh Institute Preprints (8), 1–24 (2025), https://library.keldysh.ru/preprint.asp?id=2025-8

Steijl, R., Barakos, G., Badcock, K.: A framework for CFD analysis of helicopter rotors in hover and forward flight. International Journal for Numerical Methods in Fluids 51(8), 819–847 (Jan 2006). https://doi.org/10.1002/fld.1086

van der Ven, H., Boelens, O.J.: A framework for aeroealistic simulations of trimmed rotor systems in forward fight. In: European Rotorcraft Forum, Marseille, September 1416 (2004)

Voevodin, Vl., Antonov, A., Nikitenko, D., et al.: Supercomputer Lomonosov-2: Large scale, deep monitoring and fine analytics for the user community. Supercomput. Front. Innov. 6(2), 4–11 (2019). https://doi.org/10.14529/jsfi190201

Vorontsov, V.I., Faranosov, G.A., Karabasov, S.A., Zaitsev, M.Yu.: Comparison of the noise directivity pattern of the main rotor of a helicopter for flight and hover modes. Acoustical Physics 66(3), 303–312 (may 2020). https://doi.org/10.1134/s1063771020030082

Xu, L., Weng, Pf.: Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids. Applied Mathematics and Mechanics 32(12), 1565–1576 (Dec 2011). https://doi.org/10.1007/s10483-011-1523-6

Zhang, Z., Qian, Y.: Unsteady RANS/DES analysis of flow around helicopter rotor blades at forword flight conditions. Modern Physics Letters B 32(12n13), 1840015 (2018). https://doi.org/10.1142/S0217984918400158