Lagrangian visualization of mixing enhancement induced by finite-time stretching in compressible vortex interaction
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R E G UL A R P A P E R
Zhonghua Zheng • Zhouqin Fan • Zi’ang Wang • Bin Yu • Bin Zhang • Miaosheng He
Lagrangian visualization of mixing enhancement induced by finite-time stretching in compressible vortex interaction Received: 19 November 2019 / Revised: 1 March 2020 / Accepted: 19 August 2020 Ó The Visualization Society of Japan 2020
Abstract The investigation of the coupling relationship between mixing enhancement and convective stretching bears practical and scientific significance. In this paper, Lagrangian perspective is adopted for compressible vortex interaction visualization to emphasize the effect of inner flow dynamics other than the vorticity structure on mixing performance. Transport characteristics of the flow are studied through a blob of passive particles. The results demonstrate that Lagrangian coherent structures are faithfully tracked throughout the moving of particles, and the blob initially arranged upon the ridge of Lagrangian coherent structures exhibits efficient stretching. In this sense, the physical meaning of Lagrangian coherent structure as a material barrier and maximum stretching direction is highlighted. On this basis, mixing characteristics are investigated through the introduction of helium concentration blob considering viscous diffusion. Characterized by high growth rate of mixing and low mixing time, mixing enhancement is achieved with the aid of significant stretching directly reflected by high average finite-time Lyapunov exponent in the region of blob deposition, offering an optimal strategy for fluid mixing. Keywords Lagrangian visualization Vortex interaction Mixing Fluid stretching
1 Introduction The interaction of two co-rotating vortices is a type of fundamental flow which has given rise to numerous numerical and experimental research for its extensive application background in external (Rossow 1977) and internal (Maddalena et al. 2014) flows. A body of studies contributed to determining the onset condition of vortex merging. Saffman and Szeto (1980) remarked the critical aspect ratio of vortex pair to be 0.315, above which the equilibrium state would be broken down. Melander et al. (1988) numerically determined that the critical ratio was 0.326. Meunier et al. (2002) experimentally and analytically demonstrated that the critical ratio was in the range of 0:220:24, and this value was independent of the vorticity profile if the core radius was defined using the angular momentum. Their results were confirmed by Cerretelli’s experiment (Williamson 2003) and Le Dizes’s numerical computation (Dizes and Verga 2002).
Z. Zheng Z. Fan Science and Technology on Scramjet Laboratory, China Aerodynamics Research and Development Center (CARDC), Mianyang, People’s Republic of China Z. Wang B. Yu B. Zhang (&) M. He (&) School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, People’s Republic of China E-mail: [email protected] M. He E-mail: [email protected]
Z. Zheng et al.
As for the physics of vortex merging, Melander et al. (1
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