Three-dimensional topology of turbulent premixed flame interaction

The topology of turbulent premixed flames is analysed using data from Direct Numerical Simulation (DNS), with emphasis on the statistical geometry of flame-flame interaction. A general method for obtaining the critical points of line, surface and volume fields is outlined, and the method is applied to isosurfaces of reaction progress variable in a DNS configuration involving a pair of freely-propagating hydrogen-air flames in a field of intense shear-generated turbulence. A complete set of possible flame-interaction topologies is derived using the eigenvalues of the scalar Hessian, and the topologies are parametrised using a pair of shape factors. The frequency of occurrence of each type of topology is evaluated from the DNS dataset for two different Damköhler numbers. Different types of flame-interaction topology are found to be favoured in various regions of the turbulent flame, and the physical significance of each interaction is discussed.