The relationship between external and internal flow in a porous body using the penalisation method

Stockpiles of organic porous materials such as biosolids, coal, compost and woodchips are susceptible to spontaneous combustion. Flow fields within such materials are induced by buoyant forces and external agents such as the wind. However, the external forces may vary on a time scale of seconds, whereas the heat, mass and momentum processes within the porous medium may occur over timescales days or months. It would be computationally prohibitive to resolve all of the timescales, hence in this paper mean external forces are coupled to the flow field within stockpiles of biosolids by means of a penalisation method. It has been determined that four variables have a profound influence of the flow fields within porous media These are the velocity of the wind, the permeability of the porous biosolids, the angle of repose of the medium and aspect ratio of the stockpile. Four distinct flow regimes within the stockpiles have been identified. A correlation has been developed to assist managers of stockpiles, which relates mean velocities within the four flow regimes with a Darcy and Reynolds number, the aspect ratio and angle of repose. The correlation is accurate for two of the four flow regions identified, but the error in predicting the two remaining regions is relatively large. However, this error is expected to have minimal impact on estimating the time for spontaneous combustion to occur.