A non-linear flow model based on flow translation and its application in the mechanism analysis of water inrush through collapse pillar

Water inrush through karst collapse pillar is one of the great disasters which threaten coal mine safety pro-duction. In this paper,a three field coupled non-linear flow model was built based on the essentially flow translation, from laminar flow in aquifer to turbulence flow in tunnel,in the process of collapse pillar water inrush. And then,the model that couples the Darcy laminar,Forchheimer flow and N-S turbulence flow was applied in the numerical simula-tion analysis of Luotuoshan Coal Mine “3·1” collapse pillar water inrush incident from coal seam floor. The results show that,with the increase of water inrush flow,the Forchheimer flow in karst collapse pillar is firstly controlled by viscous resistance,and then affected by both viscous resistance and inertial resistance,and finally controlled by inertial resistance. Therefore,collapse pillar water inrush is the dynamic process of flow transition gradual to mutation. It fur-ther indicates that Forchheimer equation applied to describe the high non-linear laminar flow can reflect the intermediate state of the flow translation from the laminar flow in aquifer to turbulence flow in tunnel,and also can reveal the es-sence of the three flow translation of the water inrush through karst collapse pillar.