Numerical simulation of subsonic flow around oscillating airfoil based on the Navier–Stokes equations

ABSTRACT

Unsteady Reynolds-averaged Navier–Stokes equations of an incompressible fluid are used to numerically simulate the flow around an oscillating airfoil. A comparison is made between two differential one-equation turbulence models SA and SALSA on the problems of subcritical and supercritical turbulent incompressible flow around an oscillating NACA 0015 airfoil. The numerical algorithm utilized for solving the governing equations is founded upon a three-layer implicit scheme, which exhibits second-order integration accuracy in time, third order of upwind approximation of convective terms, and second-order symmetric approximation of the diffusion terms. Pressure and velocity field coupling is achieved through the implementation of the artificial compressibility approach, which is employed for the computation of unsteady problems. The system of initial equations is numerically integrated using the control volume method. The resulting system of algebraic equations has been solved by the GMRES method with ILU(k) preconditioning. The obtained instantaneous streamlines, vorticity contours, and hysteresis curves of unsteady airfoil aerodynamic loads are analyzed for cases of weak (${\alpha }_0=4^{°}$), developed (${\alpha }_0={11}^{°}$) and massive (${\alpha }_0={15}^{°}$) flow separation at Reynolds number $Re=1.95\times {10}^6$. In the case of weak flow separation, the values of the lift coefficient obtained using the SA and SALSA models differ from the experimental data by 10% and 5%, respectively. With a developed separation, these values are already equal to 10–20% for the SA model and 6–8% for the SALSA model. The average values of the lift coefficient, which are obtained using the SA and SALSA models, in the case of massive flow separation, differ from the experimental data by 50–60% and 10–15%, respectively. Comparing the calculation results with both known experimental and calculated data demonstrates that in flows with developed and massive flow separation, which are characterized by unsteady effects in turbulence, the SALSA turbulence model performs better than other tested models. The aerodynamic coefficients obtained with the SALSA turbulence model are in 10–15% better agreement with experimental data than those obtained with other turbulence models.

KEYWORDS:

• Subsonic Flow
• Oscillating airfoil
• RANS
• CFD
• Numerical simulations

Disclosure statement

The authors declare no conflict of interest.

Author contribution

Conceptualization, D. R.; methodology, D. R., O. P., and K.P.-P.; software, S. M.; and D. R.; validation, S. M., U.F.-G., and K.P.-P.; formal analysis, D. R., O. P., and K.P.-P.; investigation, K.P.-P. and O. P.; resources, U.F.-G.; data curation, U.F.-G.; writing – original draft preparation, U.F.-G and K.P.-P.; writing – review and editing, U.F.-G., K.P.-P., and S. M.; visualization, O. P.; supervision, U.F.-G.; project administration, U.F.-G.;. All authors have read and agreed to the published version of the manuscript.

Additional information

Funding

No external funding was applied to this study.

Notes on contributors

Dmytro. Redchyts

Dmytro Redchyts received the B.Sc. and M.Sc. degrees in Design and Manufacture of Rocket-Space Aircraft in 2000 and 2001, respectively and the Ph.D. degree in the Mechanics of Liquid, Gas and Plasma from the Dnipropetrovsk National University, Dnipropetrovsk, Ukraine, in 2007. He received the doctor of physical and mathematical sciences degree in the Mechanics of Liquid, Gas and Plasma from the Institute of Hydromechanics of the National Academy of Sciences of Ukraine (NASU), Kyiv, Ukraine in 2020. Since 2004, he has been working at the Institute of Transport Systems and Technologies of the NASU, Dnipro, Ukraine. His research interests include wind turbines aerodynamics, flow control with plasma actuators, aerodynamics of ground transportation, laser powder bed fusion, computational fluid dynamics, and development of CFD software.

Unai Fernandez-Gamiz

Unai Fernandez-Gamiz received the B.Sc. and M.Sc. degrees in mechanical engineering from the University of the Basque Country, Vitoria-Gasteiz, Spain, in 1999 and 2004, respectively, and the Ph.D. degree in the Mechanical Engineering, Fluids and Aeronautics from the UPC-Barcelona, Barcelona, Spain, in 2013. Since 2008, he has been a Full Lecturer with the Department of Energy Engineering, University of the Basque Country, Vitoria-Gasteiz, Spain. His research interests include renewable energy sources, flow control devices and applied computational fluids dynamics methods. Oleg Polevoy

Oleg Polevoy

Oleg Polevoy received the M.Sc. degree in fluid dynamics and the Ph.D. degree in mechanics of liquid, gas and plasma from the Dnepropetrovsk State University, Ukraine, in 1983 and 2012, respectively. Since 2003, he has been a Research Scientist with the Department of Dynamics and Strength of New Kinds of Transport, Institute of Transport Systems and Technologies of the National Academy of Sciences of Ukraine. His research interests include computational fluid dynamics, flow visualization, aerodynamics of ground transportation, flow separation control, development of CFD software.

Svitlana Moiseienko

Svitlana Moiseienko received the M.Sc. degree in Pedagogy and methods of secondary education, physics and fundamentals of informatics from the Kherson State Pedagogical University, Kherson, Ukraine, in 1999 and the Ph.D. degree in the Applied geometry, engineering graphics from the Kyiv National University of Construction and Architecture, Ukraine, in 2007. Since 2008, she has been working at the Kherson National Technical University, Kherson, Ukraine. Her research interests include wind turbines aerodynamics, computational fluid dynamics, mathematical, geometric and probabilistic modeling in the problems of recovering harmonic functions, development of numerical methods and algorithms based on finite element and Monte Carlo method.

Koldo Portal-Porras

Koldo Portal-Porras received the B.Sc. degree in Mechanical Engineering and B.Sc. degree in Industrial Electronics and Automation Engineering from the University of the Basque Country, Vitoria-Gasteiz, Spain, in 2020 and 2021, respectively, and the M.Sc. degree in Sustainable Energy Engineering from the same university in 2022. Since 2020 he has been a researcher in the Department of Energy Engineering, University of the Basque Country, Vitoria-Gasteiz, Spain. His research interests include computational fluids dynamics and deep learning.