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Using Lagrangian coherent structures (LCSs), the mass transport process of large-scale coherent structures in a buoyant jet diffusion flame is studied numerically to gain a key understanding of combustion instability. First, the reacting flow fields of the jet diffusion flame are numerically simulated for two cases, a stable case without considering the buoyancy effect and an unstable case that includes the buoyancy effect corresponding to combustion instability. In particular, large-scale Kelvin-Helmholtz instability (KHI) vortex structures outside the flame surface are captured in the unstable case. Then, the ridges in finite-time Lyapunov exponent (FTLE) fields that sketch the distinct regions in the reacting flow field are extracted as LCSs. The mass transport process is studied by comparing the distribution of LCSs with reaction fields. The flame surface is found to coincide with the attracting LCSs, which separate the fuel and air on opposite sides of the flame surface. In contrast, the reaction products, including species and reaction heat, are confined in the boundaries consisting of repelling LCSs on the inner and outer sides of the flame surface. Finally, the evolution of LCSs is tracked to analyze the generation of KHI vortices and species transport in the jet diffusion flame. With the aid of LCSs, it is found that there exist some saddle-type flow features separating the distinct flow structures into several regions, and the jet fuel and airflow enter into the separated regions from different open boundaries. Importantly, the attracting LCSs in the separated regions then bulge outwards, forming KHI vortices as the attracting LCSs further stretch and fold. Furthermore, the vortices continue moving upwards while species flow from repelling LCSs to attracting LCSs, leading to mixing. These results show that attracting and repelling LCSs can act as the flame surface and the mass and energy transport boundary of the reaction products, respectively. In summary, the work presented can provide a new method in combustion controlling to estimate the location of the flame surface and the transport boundaries of species from the velocity field, by using LCSs. [ABSTRACT FROM AUTHOR]

Abstract The mass transport and lift enhancement in flows over the NACA0015 airfoil with a synthetic jet (SJ) are studied numerically using Lagrangian coherent structures (LCSs). Trajectories of synthetic particles belonging to 9 different groups in a vicinity of the airfoil are tracked to analyze the transport. The influence of mass transport on the aerodynamic performance of the airfoil and on the surface pressure coefficient distribution is studied. The difference in transport properties for the airfoil with and without the SJ is analyzed to understand the reasons of the lift enhancement. The results show that the LCSs could be successfully used to describe transport and mixing in the complex flows in the blowing and suction phases. More, the fluid originating in the upper reaches is continuously sucked out of the flow field in the suction phase, then the jet injected by the jet slot moves to the lower reaches of the jet slot in the blowing phase. Compared with the original airfoil, the controlled airfoil could bring about the fluid adhering to the surface moving constantly and the lift coefficient improved apparently, whether in the suction or blowing phase. Resulting from the SJ, the high momentum fluid is injected into the flow field near the airfoil. Therefore, the boundary layer separation point of the airfoil is pushed downstream, and the area of the flow separation zone is greatly reduced. Generally, utilizing LCS to study mass transport process can provide a new perspective for the study of the SJ. [ABSTRACT FROM AUTHOR]

The evolution of vortex structure and mass transport process during dynamic stall of the two-dimensional pitching NACA0012 airfoil are studied in detail, using Lagrangian coherent structures (LCSs), and the nature of dynamic stall is given from viewpoint of nonlinear dynamics. First, the numerical method with SST k − ω turbulence model is used to simulate the flow field around the pitching oscillation airfoil. Then, the Lagrangian-averaged vorticity deviation (LAVD) method is used to analyze the formation and evolution of vortex structure during dynamic stall. Further, the circulation development process of the primary leading edge vortex (LEV) is studied, with comparison between LAVD method with Q criterion. Finally, the dynamic behaviors, such as the mass transport and evolution of flow structure during the process of dynamic stall, are analyzed in depth by using LCSs, and the fluctuation of lift coefficient and the dynamic stall are investigated from the viewpoint of nonlinear dynamics. The results show that the evolution of vortex structure and mass transport are closely related to the fluctuation of lift coefficient during the dynamic stall, and the low-pressure region formed by vortices and the complex mass transport and mixing process on the suction surface of the airfoil are the main reasons for the high lift during the dynamic stall process. In particular, the primary LEV, which can be accurately identified and tracked by LAVD method, plays a very important role in lift enhancement, and the primary LEV and the secondary LEV form and grow in turn by the intermittent feeding process of shear layer. Additionally, the fluid particles in front of the leading edge of the airfoil enter the LEV through a special mass transport channel, which is textured by LCSs and opened and closed intermittently. More importantly, the saddle point of LCSs is an important component of vortex boundary, and its dynamic behaviors represent the behaviors of vortex. The first separation of saddle point from the shear layer at leading edge indicate the separation of primary LEV from the suction surface of the airfoil, and the occurrence of dynamic stall. The second separation of saddle point from the shear layer at leading edge indicate that primary LEV begins to leave the upper region of the airfoil, corresponding to a sharp drop in lift coefficient. Generally, compared to the traditional visualization techniques, the Lagrangian analysis based on LCSs and LAVD can provide a deeper insight into the dynamics of the vortex in flow field around pitching oscillation airfoil and the dynamic mechanism of dynamic stall. [ABSTRACT FROM AUTHOR]

Using Lagrangian Coherent Structures, the influences of synthetic jet parameters, namely, velocity and frequency, on lift at post-stall attack angle are studied in detail, from viewpoint of mass transport. First, the pressure coefficient distribution and the Lagrangian Coherent Structures evolution process of the non-controlled airfoil and the controlled airfoil, at a post-stall attack angle, are compared with each other through numerical simulation, and hence the influences of the mass transport process on the lift coefficient are discussed. Then, the mass transport process and its influences on the lift coefficient under different jet velocities and frequencies are analyzed further. As the conclusion, it can be drawn that there are mainly four routes to enhance the lift of airfoil at post-stall attack angle using synthetic jet, that is, (a) The synthetic jet can directly improve the fluid momentum of the boundary layer in the middle section of the suction surface; (b) The suction phase of the synthetic jet significantly reduces the pressure on the front section of the airfoil suction surface; (c) The synthetic jet could carry the high momentum fluid from the mainstream into the separation zone at the rear section of the airfoil, thus reducing the suction surface pressure of the rear section; (d) The tail vortex reduces the pressure on the suction surface of the airfoil tail. In particular, the jet parameters affect the lift coefficient by these four routes. Specifically, the fluid momenta of the boundary layer in both the front and middle sections of the suction surface are greatly increased with the jet velocity, and the contributions of the tail vortex and the high momentum fluid from the mainstream to the lift are reduced with the jet velocity. As for jet frequency, the contributions of the tail vortex and the high momentum fluid from the mainstream to the lift are reduced with the increase of jet frequency. [ABSTRACT FROM AUTHOR]

In this study, the Lagrangian coherent structures (LCSs) of the flow around two-dimensional airfoil with a plunging motion are numerically investigated, in order to reveal the physics of the unsteady aerodynamics in the flapping wings. The present study, in which only low Reynolds ( Re ) flows are considered, focuses on two typical unsteady flows at zero angle of attack, respectively induced by slow and fast plunging motions. To simulate such unsteady flows, the Characteristic Based Split (CBS) scheme combined with Arbitrary Lagrangian–Eulerian (ALE) framework are applied. After that, the LCSs are introduced to study the dynamic properties in the unsteady flow and by using the finite-time Lyapunov exponent (FTLE), the evolution of the vortex structures in the two distinct flow patterns are determined. By presenting the dynamic evolution of the Lagrangian behaviors, such as the formation and transport of the flow patterns, as well as the flow separation, it proves that LCSs can describe the Lagrangian dynamics properly. Moreover, during investigating the formation of leading-edge vortex (LEV), the time-dependent separation profile is found to play a major role. To be specific, within the slow plunging motion, the flow is rolled up to form a LEV downstream the separation point where the unstable manifold attaches. In contrast, within the fast plunging motion, a transfer barrier is generated upstream the leading edge, causing the LEV to form upstream the separation point. It is also found that by studying the dynamic behavior of the intersection between the unstable manifold and the stable manifold, the evolvement of the vortex structures, including the formation and the shedding of them, is more clear. Compared to the traditional visualization techniques, the Lagrangian analysis based on LCSs can provide a deeper insight into the dynamics of the vortex, which plays an important role in understanding the high performance of the unsteady flow induced by flapping wings. [ABSTRACT FROM AUTHOR]