Hostname: page-component-669899f699-7tmb6 Total loading time: 0 Render date: 2025-04-26T11:25:47.077Z Has data issue: false hasContentIssue false

Self-adaptive turbulence eddy simulation for complex flows on a high-order finite differencing PHengLEI-HyOrder solver

Published online by Cambridge University Press:  04 April 2025

W. Wu
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China State Key Laboratory of Aerodynamics, Mianyang 621000, People’s Republic of China
N. Xie
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, People’s Republic of China
Y. Min*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, People’s Republic of China
X. Han*
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China
Y. Ma
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, People’s Republic of China
Z. Yan
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, People’s Republic of China
*
Corresponding authors: Y. Min and X. Han; Emails: minyb@126.com; xshan@nuaa.edu.cn
Corresponding authors: Y. Min and X. Han; Emails: minyb@126.com; xshan@nuaa.edu.cn

Abstract

Turbulent flow widely exists in the aerospace field, and it is still challenging to realise the accurate prediction in the numerical simulation. To realise the high-fidelity numerical simulation of compressible turbulent flow, a high-order accurate self-adaptive turbulence eddy simulation (SATES) method is developed on the PHengLEI-HyOrder open-source solver, combining with the high-order accurate weighted compact nonlinear schemes (WCNS). The compressible flow in the subsonic and transonic is numerically simulated, including some typical cases, such as subsonic flow past a circular cylinder and flow past a square cylinder, high-lift configuration DLR-F11, transonic flow around a circular cylinder. The results predicted by the current high-order accurate SATES are in good agreement with the available experimental and numerical data. The present numerical method can also accurately capture the interactions between shock waves and turbulence while accurately simulating flow separation, shear layer instability and large-scale vortex shedding. The results obtained show that the current high-order accurate SATES simulations based on PHengLEI-HyOrder solver can accurately simulate complex turbulent flows with high reliability.

Type
Research Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Choi, H. and Moin, P. Grid-point requirements for large eddy simulation: Chapman’s estimates revisited, Phys. Fluids, 2012, 24, (1), p 011702.CrossRefGoogle Scholar
Smagorinsky, J. General circulation experiments with the primitive equations: 1, Basic Exp., 1963, 91, (99), pp 99165.Google Scholar
Germano, M., Piomelli, U., Moin, P. and Cabot, W.H. A dynamic subgrid-scale eddy viscosity model, Phys. Fluids A., 1991, 3, (7), pp 17601765.CrossRefGoogle Scholar
Nicoud, F. and Ducros, F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow. Turbul. Combust., 1999, 62, (3), pp 183200.CrossRefGoogle Scholar
Sagaut, P. and Deck, S. Large eddy simulation for aerodynamics: status and perspectives, Phil. Trans. R. Soc. A: Math. Phys. Eng. Sci., 2009, 367, pp 28492860.CrossRefGoogle Scholar
Zhiyin, Y. Large-eddy simulation: Past, present and the future, Chin. J. Aeronaut., 2015, 28, (1), pp 1124.CrossRefGoogle Scholar
Spalart, P., Jou, W.-H., Strelets, M. and Allmaras, S.R. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach, in First AFOSR International Conference on DNS/LES, Advances in DNS/LES, Liu, C. and Liu, Z.Z. (Eds), Greyden Press, Columbus, OH, 1997.Google Scholar
Chaouat, B. The state of the art of Hybrid RANS/LES modeling for the simulation of turbulent flows, Flow. Turbul. Combust., 2017, 99, (2), pp 279327.CrossRefGoogle ScholarPubMed
Heinz, S. A review of hybrid RANS-LES methods for turbulent flows: Concepts and applications, Prog. Aeronaut. Sci., 2020, 114, p 100597.CrossRefGoogle Scholar
Sagaut, P., Deck, S. and Terracol, M. Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press: UK, London, 2006.CrossRefGoogle Scholar
Menter, F., Hüppe, A., Matyushenko, A. and Kolmogorov, D. An overview of hybrid RANS–LES models developed for industrial CFD, Appl. Sci., 2021, 11, (6), p 2459.CrossRefGoogle Scholar
Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K. and Travin, A. A new version of detached-eddy simulation, resistant to ambiguous grid densities, Theor Comput Fluid Dyn., 2006, 20, (3), pp 181195.CrossRefGoogle Scholar
Shur, M.L., Spalart, P.R., Strelets, M.K. and Travin, A.K. A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities, Int. J. Heat Fluid Flow, 2008, 29, (6), pp 16381649.CrossRefGoogle Scholar
Gritskevich, M.S., Garbaruk, A.V., Schütze, J. and Menter, F.R. Development of DDES and IDDES formulations for the k-ω Shear stress transport model, Flow. Turbul. Combust., 2012, 88, (3), pp 431449.CrossRefGoogle Scholar
Menter, F., Kuntz, M. and Bender, R. A scale-adaptive simulation model for turbulent flow predictions, in 41st Aerospace Sciences Meeting and Exhibit, 6–9 January 2003, Reno, Nevada, AIAA Paper 2003-0767, 2003.CrossRefGoogle Scholar
Liu, N.-S. and Shih, T.-H. Turbulence modeling for very large-Eddy simulation, AIAA J., 2006, 44, (4), pp 687697.CrossRefGoogle Scholar
Hsieh, K.J., Lien, F.S. and Yee, E. Towards a unified turbulence simulation approach for wall-bounded flows, Flow. Turbul. Combust., 2009, 84, (2), pp 193218.CrossRefGoogle Scholar
Girimaji, S.S. Partially-averaged Navier-stokes model for turbulence: A reynolds-averaged Navier-stokes to direct numerical simulation bridging method, J. Appl. Mech., 2006, 73, (3), p 413.CrossRefGoogle Scholar
Speziale, C.G. Turbulence modeling for time-dependent RANS and VLES: A review, AIAA J., 1998, 36, (2), pp 173184.CrossRefGoogle Scholar
Zhang, H., Bachman, C.R. and Fasel, H. Application of a new methodology for simulations of complex turbulent flows, in Fluids 2000 Conference and Exhibit, Denver, CO, AIAA Paper 2000–2535, 2000.CrossRefGoogle Scholar
Han, X. and Krajnović, S. An efficient very large eddy simulation model for simulation of turbulent flow, Int. J. Numer. Methods Fluids, 2013, 71, (11), pp 13411360.CrossRefGoogle Scholar
Han, X. and Krajnović, S. Validation of a novel very large eddy simulation method for simulation of turbulent separated flow, Int. J. Numer. Methods Fluids, 2013, 73, (5), pp 436461.CrossRefGoogle Scholar
Kravchenko, A.G. and Moin, P. Numerical studies of flow over a circular cylinder at ReD=3900, Phys. Fluids, 2000, 12, (2), pp 403417.CrossRefGoogle Scholar
Mittal, R. and Moin, P. Suitability of upwind-biased finite difference schemes for large-Eddy simulation of turbulent flows, AIAA J., 1997, 35, (8), pp 14151417.CrossRefGoogle Scholar
Deng, X. and Zhang, H. Developing high-order weighted compact nonlinear schemes, J. Comput. Phys., 2000, 165, (1), pp 2244.CrossRefGoogle Scholar
Deng, X., Mao, M., Tu, G., Liu, H. and Zhang, H. Geometric conservation law and applications to high-order finite difference schemes with stationary grids, J. Comput. Phys., 2011, 230, (4), pp 11001115.CrossRefGoogle Scholar
Deng, X., Min, Y., Mao, M., Liu, H., Tu, G. and Zhang, H. Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids, J. Comput. Phys., 2013, 239, pp 90111.CrossRefGoogle Scholar
Deng, X., Mao, M., Tu, G., Zhang, H. and Zhang, Y. High-order and high accurate CFD methods and their applications for complex grid problems, Commun. Comput. Phys., 2012, 11, (4), pp 10811102.CrossRefGoogle Scholar
Deng, X., Mao, M., Tu, G., Zhang, Y. and Zhang, H. Extending weighted compact nonlinear schemes to complex grids with characteristic-based interface conditions, AIAA J., 2012, 48, (12), 28402851.CrossRefGoogle Scholar
Han, X. and Krajnović, S. Very-large-Eddy simulation based on k-ω model, AIAA J., 2015, 53, (4), pp 11031108.CrossRefGoogle Scholar
Xia, Z., Cheng, Z., Han, X., and Mao, J. VLES turbulence modelling for separated flow simulation with OpenFOAM, J. Wind Eng. Ind. Aerodyn., 2020, 198, p 104077.CrossRefGoogle Scholar
Pope, S.B. Turbulent Flows. Cambridge, UK: Cambridge University Press, 2000.Google Scholar
Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J., 1994, 32, (8), pp 15981605.CrossRefGoogle Scholar
Strelets, M. Detached eddy simulation of massively separated flows, in 39th Aerospace Sciences Meeting and Exhibit, Reno, AIAA paper 2001-0879, 2001.CrossRefGoogle Scholar
Wenchang, W., Han, X., Min, Y., Ma, Y. and Yan, Z. Weighted compact nonlinear scheme based on smooth scale separation for self-adaptive turbulence Eddy simulations, Phys. Fluids, 2024, 36, (7), p 076103.Google Scholar
Canuto, V.M. and Cheng, Y. Determination of the Smagorinsky–Lilly constant CS, Phys. Fluids, 1997, 9, (5), pp 13681378.CrossRefGoogle Scholar
Borges, R., Carmona, M., Costa, B. and Don, W.S. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys., 2008, 227, (6), pp 31913211.CrossRefGoogle Scholar
Parnaudeau, P., Carlier, J., Heitz, D. and Lamballais, E. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900, Phys. Fluids, 2008, 20, (8), p 085101.CrossRefGoogle Scholar
Lyn, D.A., Einav, S., Rodi, W. and Park, J.H. A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder, J. Fluid Mech., 1995, 304, pp 285319.CrossRefGoogle Scholar
Murthy, V.S. and Rose, W.C. Detailed measurements on a circular cylinder in cross flow, AIAA J., 1978, 16, pp 549550.CrossRefGoogle Scholar
Rodriguez, O. The circular cylinder in subsonic and transonic flow, AIAA J., 1984, 22, (12), pp 17131718.CrossRefGoogle Scholar
Rumsey, LC and Slotnick, JP Overview and summary of the second AIAA high-lift prediction workshop, J. Aircr., 2015, 52, (4), pp 10061025.CrossRefGoogle Scholar
Escobar, J.A., Suarez, C.A., Silva, C., López, O.D., Velandia, J.S. and Lara, C.A. Detached-Eddy simulation of a wide-body commercial aircraft in high-lift configuration, J. Aircr., 2015, 52, (4), pp 1112–1121.CrossRefGoogle Scholar