A non-linear flow model for the flow behavior of water inrush induced by the karst collapse column.

Water inrush induced by the karst collapse column (KCC) is a great threat to coal mine safety. In this study, a non-linear flow model that couples three flow types is built based on flow transition from laminar flow in the aquifer to turbulent flow in the mine roadways during the process of water inrush induced by KCC. The proposed model couples Darcy flow, Forchheimer flow, and turbulent flow, and is then used to simulate the flow behavior of water inrush induced by KCC. In particular, the "3.1" water inrush incident from the coal seam floor in the Luotuoshan coal mine, China, is numerically investigated. The numerical results show that with the increase of the inrush flow rate, Forchheimer flow in the water inrush channel is first controlled by viscous resistance, then affected by both viscous resistance and inertial resistance, and finally controlled by inertial resistance. Therefore, water inrush induced by KCC is a dynamic process with a transition from laminar to turbulent. The Forchheimer equation proved to be applicable in describing the high-velocity non-linear flow, and can also reflect the intermediate state of the flow translation from laminar flow in the aquifer to turbulent flow in the roadway during the water inrush process.