Convection of particle thermals

The motion induced by particle thermals (a cloud of heavy particles released into an otherwise stagnant fluid) has been investigated by a three-dimensional numerical model. The model formulation is based on the governing equations for the conservation of mass, momentum and density excess, assuming the discrete particles can be represented by a continuous field of density difference with a specified settling velocity, and the Boussinesq approximation is valid. A mixing length model is used to represent the induced turbulence because of the existence of a well-defined length scale (the cloud size). A sensitivity analysis on the model parameters has been performed and suitable values of the parameters are identified and used in the subsequent model simulation. The model simulation results reveal an inverse relationship between the rate of spreading of the cloud and the settling velocity, and show that the frontal velocity approaches the settling velocity in the ultimate stage. These findings are supported by physical experiments.