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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Studies on Typical Stalls of Airfoil at Low Reynolds Number Using Lagrangian Coherent Structures

Discontinuity, Nonlinearity, and Complexity 14(3) (2025) 491--510 | DOI:10.5890/DNC.2025.09.004

Jiazhong Zhang$^1$, Yan Liu$^{2}$, Pengliang Wang$^{1}$, Ruidong Jia$^{1}$, Yongkang Wang$^{3}$, Jie Song$^{4}$

$^{1}$ School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, 710049, China

$^{2}$ School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

$^{3}$ Huaneng Xinjiang Energy Development Co., Ltd.Energy Branch, Urumqi 830017, China

$^{4}$ Huaneng Xinjiang Qinghe Wind Power Generation Co., Ltd, Qinghe 836200, China

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Abstract

There are a large number of complex nonlinear behaviors, such as separation bubble and mass transport, in the unsteady flow separation and complicated flows around airfoils at typical stalls under low Reynolds number, and the explanations for these nonlinear behaviors are still open problems. At present, the research on unsteady separated flow is mainly based on the Eulerian description. However, the descriptions and definitions of some complex unsteady flow phenomena in complicated separation flow and others are somewhat not general, because of the lack of temporal correlation and dynamic property in Eulerian description, and such situations have further influences on the flow control, as one of the current challenges in aerodynamics. In contrast, Lagrangian description methods are objective and could accurately describe and analyze the nonlinear dynamical behaviors, such as mass transport and mixture in flows. Therefore, an efficient Lagrangian analysis method is introduced in this work, to study the unsteady flow separation and the complicated flow around airfoil at typical stalls under low Reynolds number, with combination of theoretical analysis and numerical method. In particular, the evolution of separation bubble and the mass transport in complex unsteady flow separation can be captured and revealed by tracing the intrinsic Lagrangian coherent structures, and the controlling of unsteady flow separation can be analyzed in depth, with unsteady excitations. First of all, an efficient Lagrangian analysis method, combining the method of grid partition matching and automatic adjustment of integral time, is introduced to analyze the dynamic behaviors and to save computing time, due to that a large number of fluid particles need to be tracked in the process of Lagrangian coherent structures (LCSs) calculation. Then, the evolution of LCSs near the airfoil at low Reynolds number is analyzed in detail, using LCSs and Lobe dynamics based on nonlinear dynamics. In particular, the mass transport and transport channels between the flow separation bubble on the airfoil surface and the mainstream are described dynamically, and the relationship between the mass transport and the lift is investigated further. In addition, by comparing the intrinsic LCSs %and mass transports in the flow around airfoil at stall and the airfoil controlled by synthetic jet, it can be concluded that the unsteady excitation could modify or adjust the topology of flow structures near the airfoil, and then induces the mass transport to improve the aerodynamic performances. Furthermore, the flow control with unsteady excitation on the post-stall airfoil is studied numerically and theoretically, and the influences of the amplitude and frequency of unsteady excitation on the mass transport, in a targeted transport way, are explained with LCSs in depth. %It is found that there are mainly four routes in mass transport to enhance the lift of airfoil at post-stall attack angle using synthetic jet, and the jet parameters modify or adjust the aerodynamic performances through the four routes. In summary, with introduction of an efficient numerical analysis method of Lagrangian coherent structures and Lobe dynamics, the evolutions of flow structures, mass transports in separation flow and typical stalls of airfoils at low Reynolds number are studied in detail, gaining some key understandings and providing theoretical explanations for the flow separation and typical stalls of airfoils. Also, one reliable theoretical basis is paved for improving aerodynamic performances of airfoil using unsteady excitation.

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