Abstract
The paper describes the numerical methods and the associated parallel computing code ‘Gerbera’ designed to analyse the aerodynamics and tonal noise of arbitrary aircraft propeller systems. The capabilities, robustness and accuracy of ‘Gerbera’ are demonstrated on a series of validation and verification studies, including single propellers, distributed propellers, and contra-rotating open rotor. The correct calculation of the propeller thrust characteristics and the main noise harmonics, including quite ‘subtle’ interaction effects, is shown. The presented scalability tests confirm good speed-up up to thousands of CPU cores.
Acknowledgment
We thank the authors of the publication [28] for providing the calculation results, as well as V. O. Eremenko, R. V Akinshin and E. V. Streltsov for assistance in constructing the calculation meshes. Validation experiments were conducted on the basis of the TsAGI ‘AC-2 Anechoic chamber with flow’ upgraded with the financial support of the Ministry of Science and Higher Education of the Russian Federation. The research was carried out using the infrastructure of the Shared Research Facilities ‘High Performance Computing and Big Data’ (CKP ‘Informatics’) of Federal Research Center ‘Computer Science and Control’ of the Russian Academy of Sciences (www.frccsc.ru) and Supercomputing center of Peter the Great Saint-Petersburg Polytechnic University (www.spbstu.ru).
References
[1] I. Abalakin, P. Bakhvalov, V. Bobkov, A. Duben, A. Gorobets, T. Kozubskaya, P. Rodionov, and N. Zhdanova, NOISEtte CFD&CAA supercomputer code for research and applications. Supercomputing Frontiers and Innovations 11 (2024), No. 2, 78–101.10.14529/jsfi240206Search in Google Scholar
[2] A. F. Antoniadis, D. Drikakis, P. S. Farmakis, L. Fu, I. Kokkinakis, P. A. S. F. Silva, X. Nogueira, M. Skote, V. Titarev, and P. Tsoutsanis, UCNS3D: An open-source high-order finite-volume unstructured CFD solver. Computer Physics Communications 279 (2022), 108453.10.1016/j.cpc.2022.108453Search in Google Scholar
[3] G. N. Barakos, T. Fitzgibbon, A. N. Kusyumov, S. A. Kusyumov, and S. S. Mikhailov, CFD simulation of helicopter rotor flow based on unsteady actuator disk model. Chinese Journal of Aeronautics 3 (2020), No. 9, 2313–2328.10.1016/j.cja.2020.03.021Search in Google Scholar
[4] T. J. Barth and P. O. Frederickson, Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. In: AIAA paper No. 90-0013, 28th Aerospace Sciences Meeting 1990.10.2514/6.1990-13Search in Google Scholar
[5] D. V. Blokhintsev, Acoustics of Nonuniform Moving Media. Second Edition. Nauka, Moscow, 1981 (in Russian).Search in Google Scholar
[6] W. Boscheri and M. Dumbser, A direct Arbitrary-Lagrangian–Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D. Journal of Computational Physics 84 (2014), No. 2, 484–523.10.1016/j.jcp.2014.06.059Search in Google Scholar
[7] W. Boscheri, R. Loubère, and M. Dumbser, Direct Arbitrary-Lagrangian–Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws. Journal of Computational Physics 292 (2015), 56–87.10.1016/j.jcp.2015.03.015Search in Google Scholar
[8] S. Bosnyakov, I. Kursakov, A. Lysenkov, S. Matyash, S. Mikhailov, V. Vlasenko, and J. Quest, Computational tools for supporting the testing of civil aircraft configurations in wind tunnels. Journal of Progress in Aerospace Sciences 44 (2008), 67–120.10.1016/j.paerosci.2007.10.003Search in Google Scholar
[9] Y. Colin, B. Caruelle, and A. B. Parry, Computational strategy for predicting CROR noise at low-speed, Part III: Investigation of noise radiation with the Ffowcs-Williams Hawkings analogy. In: AIAA Paper, AIAA-2012-2223 2012.10.2514/6.2012-2223Search in Google Scholar
[10] M. Dumbser and M. Käser, Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J. Comput. Phys. 221 (2007), No. 2, 693–723.10.1016/j.jcp.2006.06.043Search in Google Scholar
[11] M. Dumbser, M. Käser, V. A. Titarev, and E. F. Toro, Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J. Comput. Phys. 226 (2007), 204–243.10.1016/j.jcp.2007.04.004Search in Google Scholar
[12] J. E. Ffowcs Williams and D. L. Hawkings, Sound generation by turbulence and surfaces in arbitrary motion. Philos. Trans. R. Soc. London, Ser. A 264 (1969), 321–342.10.1098/rsta.1969.0031Search in Google Scholar
[13] E. Gaburro, M. Dumbser, and M. J. Castro, Direct Arbitrary-Lagrangian–Eulerian finite volume schemes on moving nonconforming unstructured meshes. Computers and Fluids 159 (2017), 254–275.10.1016/j.compfluid.2017.09.022Search in Google Scholar
[14] A. V. Gorobets and A. P. Duben, Technology for supercomputer simulation of turbulent flows in the good new days of exascale computing. Supercomputing Frontiers and Innovation 8 (2021), No. 4, 4–10.10.14529/jsfi210401Search in Google Scholar
[15] S. Gottlieb and C.-W. Shu, Total variation diminishing Runge– Kutta schemes. Mathematics of Computation 67 (1998), No. 221, 73–85.10.1090/S0025-5718-98-00913-2Search in Google Scholar
[16] E. Greenwood, K. S. Brentner, R. F. Rau, and Z. F. T. Gan, Challenges and opportunities for low noise electric aircraft. International Journal of Aeroacoustics 21 (2022), No. 5-7, 315–381.10.1177/1475472X221107377Search in Google Scholar
[17] S. Guérin and D. Tormen, A contribution to the investigation of acoustic interferences in aircraft distributed propulsion. CEAS Aeronautical Journal 14 (2023), No. 4, 965–982.10.1007/s13272-023-00679-6Search in Google Scholar
[18] L. Gutin, On the sound field of a rotating propeller. Translated as NACA Technical Memorandum 1195 1948, pp. 1–21.Search in Google Scholar
[19] D. Han and G. N. Barakos, Loads transfer principles of coaxial helicopter rotors. Journal of the American Helicopter Society 68 (2023), No. 1, 012008.10.4050/JAHS.68.012008Search in Google Scholar
[20] A. Harten, P. D. Lax, and B. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 25 (1983), No. 1, 35–61.10.1137/1025002Search in Google Scholar
[21] C. W. Hirt, A. A. Amsden, and J. L. Cook, An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J. Comput. Phys. 14 (1974), 227–253.10.1016/0021-9991(74)90051-5Search in Google Scholar
[22] A. Jameson, Time-dependent calculations using multrigrid, with application to unsteady flows past airfoils and wings. AIAA paper 91-1596 1991.10.2514/6.1991-1596Search in Google Scholar
[23] A. Jameson and S. Yoon, Lower-upper implicit schemes with multiple grids for the Euler equations. AIAA Journal 25 (1987), No. 7, 929–935.10.2514/3.9724Search in Google Scholar
[24] M. J. Kingan and A. B. Parry, Time-domain analysis of contra-rotating propeller noise: Wake interaction with a downstream propeller blade. Journal of Fluid Mechanics 901 (2020), A21.10.1017/jfm.2020.504Search in Google Scholar
[25] V .P. Kolgan, Application of the minimum-derivative principle in the construction of finite-difference schemes for numerical analysis of discontinuous solutions in gas dynamics. Transactions of the Central Aerohydrodynamics Institute 3 (1972), No. 6, 68–77 (in Russian).Search in Google Scholar
[26] V. P. Kolgan, Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics. J. Comput. Phys. 230 (2011), No. 7, 2384–2390.10.1016/j.jcp.2010.12.033Search in Google Scholar
[27] V. F. Kopiev, V. A. Titarev, and I. V. Belyaev, Development of a methodology for propeller noise calculation on high-performance supercomputers. TsAGI Science Journal 45 (2014), No. 3-4, 293–327.10.1615/TsAGISciJ.2014011857Search in Google Scholar
[28] V. F. Kopiev, I. V. Belyaev, B. S. Zamtfort, Y. V. Medvedev, M. L. Shur, and A. K. Travin, Assessment of community noise for a medium-range airplane with open-rotor engines. Acoustical Physics 63 (2017), No. 6, 723–730.10.1134/S1063771017060069Search in Google Scholar
[29] V. F. Kopiev, N. N. Ostrikov, G. A. Faranosov, V. A. Titarev, S. L. Denisov, and R. V. Akinshin, On the mechanism of lateral asymmetry of noise emission from a propeller installed near a wing. Acoustical Physics 70 (2024), No. 5, 833–849.10.1134/S1063771024601729Search in Google Scholar
[30] A. S. Kozelkov, V. V. Kurulin, S. V. Lashkin, R. M. Shagaliev, and A. V. Yalozo, Investigation of supercomputer capabilities for the scalable numerical simulation of computational fluid dynamics problems in industrial applications. Computational Mathematics and Mathematical Physics 56 (2016), 1506–1516.10.1134/S0965542516080091Search in Google Scholar
[31] A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems. Monographs and Surveys in Pure and Applied Mathematics, Vol. 118. Chapman and Hall, 2002.10.1115/1.1470672Search in Google Scholar
[32] R. H. Lange, A review of advanced turboprop transport aircraft. Progress in Aerospace Sciences 23 (1986), No. 2, 151–166.10.1016/0376-0421(86)90003-5Search in Google Scholar
[33] L. A. Lazarev, V. A. Titarev, and A. Yu. Golubev, Framework optimization of a reinforced shell under the action of the propeller’s acoustic field. Acoustical Physics 68 (2022), No. 3, 282–288.10.1134/S1063771022030071Search in Google Scholar
[34] S. Le Bras, K. Kucukcoskun, D. A. Giraldo, and M. Roger, Aeroacoustic simulations of a pylon-mounted propeller configuration at low Reynolds number. In: AIAA-2024-3101 2024.10.2514/6.2024-3101Search in Google Scholar
[35] B. van Leer, Towards the ultimate conservative difference scheme V: a second order sequel to Godunov’s method. J. Comput. Phys. 32 (1979), 101–136.10.1016/0021-9991(79)90145-1Search in Google Scholar
[36] H. Luo, J. D. Baum, and R. Löhner, A fast, matrix-free implicit method for compressible flows on unstructured grids. Journal of Computational Physics 146 (1998), 664–690.10.1006/jcph.1998.6076Search in Google Scholar
[37] A. V. Lysenkov, The propeller optimization with the use of CFD. In: AIP Conference Proceedings, Novosibirsk vol. 2027. American Institute of Physics Inc., Novosibirsk, 2018, 030124.10.1063/1.5065218Search in Google Scholar
[38] B. Magliozzi, D. B. Hanson, and R. K. Amiet, Propeller and Propfan Noise. Aeroacoustics of Flight Vehicles. Theory and Practice. ASA/AIP, 1991.Search in Google Scholar
[39] A. A. Maslov, Simultaneous evaluation of the aerodynamic characteristics and sound field of a ducted propeller. Acoustical Physics 43 (1997), No. 2, 179–185.Search in Google Scholar
[40] I. S. Men’shov and Y. Nakamura, An implicit advection upwind splitting scheme for hypersonic air flows in thermochemical nonequilibrium. In: A Collection of Technical Papers of 6th Int. Symp. on CFD vol. 2. Lake Tahoe, Nevada, 1995, p. 815.Search in Google Scholar
[41] I. S. Men’shov and Y. Nakamura, On implicit Godunov’s method with exactly linearized numerical flux. Computers and Fluids 29 (2000), No. 6, 595–616.10.1016/S0045-7930(99)00020-1Search in Google Scholar
[42] F. B. Metzger, A review of propeller noise prediction methodology: 1919–1994. In: NASA CR 1995, 198156.Search in Google Scholar
[43] A. Najafi-Yazdi, G. A. Bres, and L. Mongeau, An acoustic analogy formulation for moving sources in uniformly moving media. Proc. Royal Soc. A 467 (2011), 144–165.10.1098/rspa.2010.0172Search in Google Scholar
[44] D. M. Nark, W. T. Jones, P. G. Buning, and J. M. Derlaga, High-lift propeller noise prediction for a distributed electric propulsion flight demonstrator. In: AIAA Paper, AIAA-2017-3713 2017.10.2514/6.2017-3713Search in Google Scholar
[45] V. V. Pakhov, R. P. Stepanov, A. N. Kusyumov, B. S. Kritskii, and R. M. Mirgazov, Investigation of aerodynamic performance of a multipurpose medium lift helicopter with different rear fuselage geometries. Russian Aeronautics 64 (2021), No. 2, 248–255.10.3103/S1068799821020112Search in Google Scholar
[46] M. Quaglia, S. Moreau, M. Roger, and R. Fernando, A preliminary semi-empirical approach for CROR noise modeling. AIAA Paper AIAA-2016-2743, 2016.10.2514/6.2016-2743Search in Google Scholar
[47] F. Ricci, P. A. S. F. Silva, P. Tsoutsanis, and A. F. Antoniadis, Hovering rotor solutions by high-order methods on unstructured grids. Aerospace Science and Technology 97 (2020), 105648.10.1016/j.ast.2019.105648Search in Google Scholar
[48] V. V. Rusanov, Calculation of interaction of non-steady shock waves with obstacles. USSR J. Comput. Math. & Math. Phys. 1 (1961), No. 2, 304–320.10.1016/0041-5553(62)90062-9Search in Google Scholar
[49] V. F. Samokhin, Semiempirical method for estimating the noise of a propeller. Journal of Engineering Physics and Thermophysics 85 (2012), No. 5, 1157–1166.10.1007/s10891-012-0758-ySearch in Google Scholar
[50] C.-W. Shu, Total-variation-diminishing time discretizations. SIAM J. Scientific and Statistical Computing 9 (1998), 1073–1084.10.1137/0909073Search in Google Scholar
[51] M. Shur, M. Strelets, and A. Travin, High-order implicit multi-block Navier–Stokes code: Ten-years experience of application to RANS/DES/LES/DNS of turbulent flows. Invited lecture. In: 7th Symposium on Overset Composite Grids and Solution Technology. Huntington Beach, USA 2004.Search in Google Scholar
[52] P. A. S. F. Silva, P. Tsoutsanis, and A. F. Antoniadis, Simple multiple reference frame for high-order solution of hovering rotors with and without ground effect. Aerospace Science and Technology 111 (2021), 106518.10.1016/j.ast.2021.106518Search in Google Scholar
[53] P. A. S. F. Silva, P. Tsoutsanis, and A. F. Antoniadis, Numerical investigation of full helicopter with and without the ground effect. Aerospace Science and Technology 122 (2022), 107401.10.1016/j.ast.2022.107401Search in Google Scholar
[54] P. A. S. F. Silva, P. Tsoutsanis, J. R. P. Vaz, and M. M. Macias, A comprehensive CFD investigation of tip vortex trajectory in shrouded wind turbines using compressible rans solver. Energy 294 (2024), 130929.10.1016/j.energy.2024.130929Search in Google Scholar
[55] D. A. Smith, A. Filippone, and G. N. Barakos, Noise source analysis in counter-rotating open rotors. AIAA Journal 60 (2022), No. 3, 1783–1796.10.2514/1.J060886Search in Google Scholar
[56] P. R. Spalart, A. K. Travin, M. L. Shur, and M. Kh. Strelets, Initial noise predictions for open rotors using first principles. In: AIAA Paper, AIAA-2010-3793 2010.10.2514/6.2010-3793Search in Google Scholar
[57] T. Suzuki, P. R. Spalart, M. Shur, M. Strelets, and A. Travin, Unsteady simulations of a fan/outlet-guide-vane system: Broadband-noise computation. AIAA Journal 57 (2019), 14.10.2514/1.J058177Search in Google Scholar
[58] T. Suzuki, M. L. Shur, M. Kh. Strelets, and A. K. Travin, Potential amplification mechanism of rotor–stator-interaction noise via spiral-Poiseuille-flow instability. AIAA Journal 60 (2022), No. 4, 2441–2457.10.2514/1.J060400Search in Google Scholar
[59] N. I. Tillaeva, A generalization of the modified Godunov scheme to arbitrary unstructured meshes. Transactions of the Central Aero-hydrodynamics Institute 17 (1986), No. 2, 18–26 (in Russian).Search in Google Scholar
[60] V. A. Titarev, G. A. Faranosov, S. A. Chernyshev, and A. S. Batrakov, Numerical modeling of the influence of the relative positions of a propeller and pylon on turboprop aircraft noise. Acoustical Physics 64 (2018), No. 6, 760–773.10.1134/S1063771018060118Search in Google Scholar
[61] E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver. Journal of Shock Waves 4 (1994), 25–34.10.1007/BF01414629Search in Google Scholar
[62] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. 3rd ed., Springer-Verlag, 2009.10.1007/b79761Search in Google Scholar
[63] E. F. Toro, Chapter 2 – The Riemann problem: Solvers and numerical fluxes. In: Handbook of Numerical Methods for Hyperbolic Problems Handbook of Numerical Analysis vol. 17 (Eds. R. Abgrall and C.-W. Shu). Elsevier, 2016, pp. 19–54.10.1016/bs.hna.2016.09.015Search in Google Scholar
[64] P. Tsoutsanis, V. A. Titarev, and D. Drikakis, WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions. J. Comput. Phys. 230 (2010), 1585–1601.10.1016/j.jcp.2010.11.023Search in Google Scholar
[65] V. O. Tsvetkova, I. V. Abalakin, V. G. Bobkov, N. S. Zhdanova, T. K. Kozubskaya, and L. N. Kudryavtseva, Simulation of the flow near a rotating propeller on adaptive unstructured meshes using the immersed boundary method. Mathematical Models and Computer Simulations 14 (2022), No. 2, 224–240.10.1134/S2070048222020168Search in Google Scholar
[66] H. van der Ven and J. J. W. van der Vegt, Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows, II: Efficient flux quadrature. J. Comput. Phys. 191 (2002), No. 41-42, 4747–4780.10.1016/S0045-7825(02)00403-6Search in Google Scholar
[67] V. Venkatakrishnan, On the accuracy of limiters and convergence to steady-state solutions. In: AIAA paper 93-0880, 31st Aerospace Science Meeting & Exhibit, January 11-14, 1993, Reno, NV 1993.10.2514/6.1993-880Search in Google Scholar
[68] R. Wickersheim, M. Keβler, and E. Krämer, Noise prediction of a distributed propulsion system using the actuator line method. AIAA Journal 62 (2024), No. 3, 1123–1135.10.2514/1.J063457Search in Google Scholar
[69] N. S. Zawodny, D. D. Zawodny, and D. M. Nark, Aerodynamic and acoustic interactions associated with inboard propeller-wing configurations. In: AIAA-2021-0714 2021.10.2514/6.2021-0714Search in Google Scholar
[70] T. Zhang, G. Qiao, D. A. Smith, G. N. Barakos, and A. Kusyumov, Parametric study of aerodynamic performance of equivalent ducted/un-ducted rotors. Aerospace Science and Technology 117 (2021), 106984.10.1016/j.ast.2021.106984Search in Google Scholar
[71] T. Zhang, G. N. Barakos, and Furqan, On the aerodynamic performance of redundant propellers for multi-rotor eVTOL in cruise. Aerospace Science and Technology 145 (2024), 108846.10.1016/j.ast.2023.108846Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A two-level parallelization algorithm for the direct simulation Monte Carlo method of problems of rarefied gas dynamics
- Conservative correction of the sequential noniterative scheme for reactive transport problems with minerals precipitation–dissolution and variable media properties
- Numerical solution of BVP for the incompressible Navier–Stokes equations at large Reynolds numbers
- Low-rank Monte Carlo method for aggregation kinetics with particle sources
- Numerical simulation of propeller aerodynamics and tonal noise using parallel code ‘Gerbera’
Articles in the same Issue
- Frontmatter
- A two-level parallelization algorithm for the direct simulation Monte Carlo method of problems of rarefied gas dynamics
- Conservative correction of the sequential noniterative scheme for reactive transport problems with minerals precipitation–dissolution and variable media properties
- Numerical solution of BVP for the incompressible Navier–Stokes equations at large Reynolds numbers
- Low-rank Monte Carlo method for aggregation kinetics with particle sources
- Numerical simulation of propeller aerodynamics and tonal noise using parallel code ‘Gerbera’