糖心原创

Project description

Coffee filters, water filters, oil pipelines lined with wax and sewer pipes all block up in a similar way. Small particles carried by the flow stick to the walls, pile up, form arches across a narrow gap, and finally seal it. At that moment something odd happens mathematically. A second ago the deposit was part of a moving fluid. Now it is a solid plug holding back the pressure, with no flow through it at all. Most models fake this by making the fluid extremely thick, so the flow never quite stops. This project does it properly. The particles follow a familiar advection-diffusion equation. When the deposit reaches its packing limit, keeping it still becomes a constraint, enforced with a Lagrange multiplier just as in constrained optimisation, and that multiplier turns out to be the stress inside the clog. You will analyse simple versions of this switch and simulate complete clogging in OpenFOAM with a solver already under development, asking when a clog forms, when it bursts, and why some blockages open and shut over and over, like a sticking valve.