Flame shapes and burning rates of spherical fuel particles in a mixed convective environment

In this work, experimental and numerical investigations of spheres burning in a convective environment have been carried out. In the numerical simulations, transient axi-symmetric Navier–Stokes equations along with species and energy conservation equations are solved using a finite volume technique based on non-orthogonal semi-collocated grids. A global single step reaction involving two reactants, two products and one inert species together with an Arrhenius rate equation has been used to model kinetics. For the sake of comparison, an infinite rate chemistry model has also been attempted. The density of the mixture has been evaluated from ideal gas equation of state. Thermo-physical properties like thermal conductivity and viscosity have been evaluated using the Chapman–Enskog description of binary gas mixtures. Specific heats and species enthalpies have been evaluated using piece-wise polynomials of temperature. The burning of isolated spherical particles in a mixed convective environment at atmospheric pressure has been simulated for various particle sizes, free-stream velocities and ambient temperatures. The numerical predictions have been compared with experimental results obtained using the porous sphere technique and the agreement is found to be good. Correlations have been developed for the critical Reynolds number at which transition from the envelope to wake flame occurs and also for the mass burning rates at sub-critical or super-critical Reynolds number regimes. It is observed that, at higher ambient temperatures, transition to wake flame is delayed to a higher critical Reynolds number value. The infinite rate chemistry model predicts flame shapes and mass burning rates with reasonable accuracy in the sub-critical Reynolds number regime, but it fails to predict transition to wake flame shape. For analyzing transition phenomena, a finite rate chemistry model is required.