Characterization of the temporal evolution of the particle clustering in radiation-induced turbulence

In the context of particles laden flow, we explore a regime in which turbulence is sustained solely by the radiative energy absorbed by the dispersed phase. Under such conditions, the non-uniformities in particle distribution produce local temperature fluctuations. In response, the resulting buoyancy induced vortical fluid motions alter the particles concentration. From numerical simulations it has been shown that the feedback loop between the local particle concentration, the temperature fluctuations and the convective motion can create and sustain turbulence in a wide range of parameters, whose key parameter is the particle response time. In particular the temperature variance as well as the turbulent kinetic energy present a sharp peak for maximum particle clustering. The time scales of the temperature and momentum forcing are therefore highly influenced by the ``clusters life time.'' We employed a method that enables to track the temporal evolution of clusters and detect the clusters merging and splitting. This approach uses the Voronoi tessellation of the particle positions (and the connectivity of its cells) to detect the clusters. By introducing a cluster-cluster correlation we construct a random graph representative of the cluster temporal evolution.