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Diffstat (limited to 'typst/main.typ')
| -rw-r--r-- | typst/main.typ | 30 |
1 files changed, 28 insertions, 2 deletions
diff --git a/typst/main.typ b/typst/main.typ index 4de29dc..f389c9c 100644 --- a/typst/main.typ +++ b/typst/main.typ @@ -170,6 +170,30 @@ These forces diverge the smaller $h$ becomes. This is due to the viscous stress increasing on small films of fluid which then in turn dominate the interaction. +== Volume Averaged Navier-Stokes(VANS) + +For the suspension of multiple particles Laurez et al suggests the use of a volume averaged Navier-Stokes equation where +the a porostiy field $epsilon$ is introduced and defined as + +#math.equation( + block:true, +$ epsilon = +{ + cases( + 1", if the cell is occupied by fluids only", + (0,1)", if the cell is occupied by a fluid-solid aggregate or interface", + 0", if the cell is occupied by solids only." + ) + $ +) + +The mass balance equation for the fluid phase then reads + +#math.equation( +block:true + +) + == Clogging of porous structures Modifying a poiseulle channel flow by narrowing the channel we can observe mainly three different ways how the porosity is reduced. @@ -183,7 +207,7 @@ effect is disregarded due to the scale of the problem and accumulation of partic #figure( image("narrow_channel.png"), -caption: [One example geometry from Laurez@laurez2025bridging describing] +caption: [One example geometry from Laurez@laurez2025bridging describing the general narrow setup] ) With the narrow throat diameter $D$ and the pore radius $d_p$ the clogging probability starts to occur spuriously around @@ -241,4 +265,6 @@ To couple a particle dynamics system two major approaches exist within Lattice B The Immersed Boundary Method(IBM)@Peskin_2002 and the Homogenized Lattice-Boltzmann-Method(HLBM)@KRAUSE2017HLBM. The IBM approach is managed by calculating the coupling based on Lagrangian nodes from the point of view of the particles, requiring the recovery of the macroscopic variables and also distributing the force back. -While the approach by HLBM incorporates most the of the +While the approach by HLBM incorporates most the of the coupling into the collision modell. +The key difference between those two being that the coupling in IBM happens from the point of view of the cell while +the exchange in HLBM happens from the cell grids. There are key similarities to VANS due to the identical model of fluid averaging. |