Abstract
The flow topologies of compressible large-scale distorted flames are studied by means of the analysis of the invariants of the velocity gradient tensor (VGT). The results indicate that compressibility plays a minor role in the distorted flame zone. And the joint probability density function (p.d.f.) of the Q-R diagram appears as a teardrop shape, which is a universal feature of turbulence. Therefore, the distorted flame exhibits the characteristic of large-scale turbulence combustion, especially behind the reflected shock wave, while the p.d.f. of the QS⁎-QW diagram implies that the dissipation is enhanced in the compression and expansion regions, where it is higher than that when P=0. Furthermore, we identify that the flame evolution is dominated by rotation by means of a quantitative statistical study, and the SFS topology is the predominant flow pattern. Not surprisingly, negative dilatation could suppress the unstable topologies, whereas positive dilatation could suppress the stable topologies.
Highlights
To date, great effort has been made to study the flow topology of turbulent flows
It is found that the distribution peak of the P value locates near zero, which indicates the distorted flame behind the shock wave mainly behaves as an incompressible flow
The flow topologies and statistical properties of compressible large-scale distorted flame are studied using the invariants of the velocity gradient tensor (VGT), which is helpful to understand the intrinsic flow dynamics
Summary
Great effort has been made to study the flow topology of turbulent flows. The topological study is based on an analysis of the invariants of the velocity gradient tensor (VGT), which is inherently interesting and significant in the flow dynamics and mechanisms. Chacın et al [6] studied the velocity field of incompressible turbulent boundary layers and found that the joint probability density functions (p.d.f.s) of the Q-R diagram showed a trend towards a teardrop shape. The previous works mainly focused on the flow topology in incompressible flows wherein P is zero, and many meaningful results were obtained. Pirozzoli and Grasso [12] studied the influence of initial compressibility on flow topology in compressible isotropic turbulence and found that the p.d.f.s of the Q-R diagram exhibited a universal teardrop shape as in the incompressible case. Suman and Girimaji [14] found that the velocity gradient structure and flow topology were similar to incompressible turbulence when conditioned upon zero dilatation. The purpose is to reveal the underlying mechanism of a fluid element rotation and strain in the complicated large-scale flame deformation processes, which can help us to achieve an improved understanding of the complicated phenomena in compressible reactive flows
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