Passive scalar mixing induced by the formation of compressible vortex rings
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RESEARCH PAPER
Passive scalar mixing induced by the formation of compressible vortex rings Haiyan Lin1 · Yang Xiang1 · Hui Xu1 · Hong Liu1 · Bin Zhang1 Received: 15 June 2020 / Revised: 17 August 2020 / Accepted: 8 September 2020 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study aims to determine the relationship between the physical features of a compressible vortex and the mixing process. Such relationship is of significant importance to design combustors that can achieve optimal or most effective mixing. The passive scalar mixing induced by the formation of a canonical compressible vortex ring (CVR) generated at the end of a shock tube is investigated by using numerical simulation. In addition, the method of finite-time Lyapunov exponent (FTLE) field are detected to identify the region of CVR, as well as to analyze the passive scalar mixing during the CVR formation. As the CVR rolls up, the ambient fluid outside the shock tube is entrained into the ring. The entrainment fraction (the mass of entrained fluid to the total mass of CVR) is found to strongly depend on two features of CVRs. One is the compressibility of CVRs, which is characterized by the Mach number of the incident shock denoted by Mach number (Ma). The other is pinch-off of CVRs, which happens at a certain timescale with narrow range of 2–4. As Ma increases, the entrainment fraction of the leading CVR decreases linearly due to smaller vortex core and weaker radial diffusion of vorticity generated by larger compressibility. After CVRs pinch off, trailing vortices appear and show less effective at entrainment than the leading CVRs do. Moreover, the tendency of the rate of entrainment is examined. The results indicate that increasing compressibility and total fluid flux are in favor of the rate of entrainment but restrain the entrainment fraction of total jet. Keywords Vortex ring · Finite-time Lyapunov exponent (FTLE) · Entrainment · Pinch-off
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1 Introduction For the purpose of improving combustion efficiency or stabilizing combustion, a common approach goes to construct a coherent vortex structure. The formation and motion of vortex structure can induce efficient mixing that enables the reactions and combustion to occur at the molecular level [1]. Thus, understanding the effect of vortex on flow field and mixing process is critical to establish the connection between fluid dynamics and combustion. A lot of authors have investigated the mixing in vortex structure with relative small scale, such as the vortex formed in the shear layer [2, 3] and in turbulent flow [4–6]. However, when it comes to the vortex structure with large scale like a vortex ring generated by separated flow, most of the studies have focused
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Yang Xiang [email protected] J. C. Wu Center for Aerodynamics, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
on the incompressible situation. To our knowledge
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