Dust explosions in spherical vessels: Prediction of the pressure evolution and determination of the burning velocity and flame thickness

A well known limitation of the ’cube-root-law’ is that it becomes invalid when the flame thickness is significant with respect to the vessel radius. In the literature flame thicknesses in dust-air mixtures ranging from 15 to 80 centimeters have been reported [1], which exceed the radii of the 20-1itre sphere and the 1 m3 vessel. Therefore we have developed a model (the three zone model) for the pressure evolution of confined dust explosions in spherical vessels which takes the flame thickness into account. The pressure-time curves that are generated with this model show a good resemblance with those measured in practice. It is shown by numerical simulations that the maximum rate of pressure rise can be normalized with respect to the vessel volume as well as to the flame thickness and that the ’cube-root-law’ becomes inaccurate for relative flame thicknesses exceeding 1%. Furthermore, the actual burning velocity and the flame thickness during real dust explosions can be obtained by fitting the model to the experimental pressure-time curve