{ VECTOR_SWIRL.PDE
This is a modification of the example SWIRL.PDE to use vector variables.
}
TITLE 'Swirling cylindrical flow'
COORDINATES
ycylinder ('r','z')
VARIABLES
V(0.001) = vector(vr, vz, vt)
p(0.001) { pressure, with linear interpolation and minimum expected range }
DEFINITIONS
rad=0.01 { vial radius }
ht=0.035 { vial height }
dens=1000 { fluid density }
visc=0.001 { fluid viscosity }
vm=magnitude(V)
div_v= div(V) { velocity divergence }
PENALTY = 1e4*visc/rad^2 { the phony equation of state coefficient }
band = ht/20 { height of force band }
bf = 1000 { arbitrary body-force scaling }
f { stirbar force - assigned by region later }
rpm =staged(50,100,150) { several stirring speeds }
vimp = 2*pi*r*rpm/60 { impeller velocity }
vr0 = 0.2*vimp { arbitrary partition of stirring velocity }
vt0 = 1.0*vimp
vz0 = 0.3*vimp
V0 = vector(vr0, vz0, vt0)
mass_balance = div_v/integral(1)
INITIAL VALUES
vr=0
vz=0
vt=0
p=0
EQUATIONS
V: dens*dot(V,grad(V)) + grad(p) - visc*div(grad(V)) = F*(V0-V)
p: div(grad(p)) = penalty*div_v
BOUNDARIES
Region 'domain'
F=0
Start 'outer' (0,0)
{ mirror conditions on bottom boundary }
natural(vr)=0 natural(vt)=0 value(vz)=0 natural(p)=0 line to (rad,0)
{ no slip on sides (ie, velocity=0) }
value(vr)=0 value(vt)=0 value(vz)=0 natural(p)=0 line to (rad,ht)
{ zero pressure and no z-flow on top, but free vr and vt }
natural(vr)=0 natural(vt)=0 value(vz)=0 value(p)=0 line to (0,ht)
{ no radial or tangential velocity on spin axis }
value(vr)=0 value(vt)=0 natural(vz)=0 natural(p)=0 line to close
Region "impeller"
F=bf
Start(0,0) line to (0.9*rad,0) to (0.9*rad,band) to (0,band) to close
{ add a gridding feature to help resolve the shear layer at the wall }
Feature start(0.95*rad,0) line to (0.95*rad,ht)
MONITORS
contour(vr) as "Radial Velocity" report(rpm)
contour(vt) as "Swirling Velocity" report(rpm)
contour(vz) as "Axial Velocity" report(rpm)
elevation(vt,v0) from(0,0) to (rad,0) as "Impeller Velocity" report(rpm)
contour(p) as "Pressure"
vector(vr,vz) as "R-Z Flow"
PLOTS
contour(vr) as "Radial Velocity" report(rpm)
contour(vt) as "Swirling Velocity" report(rpm)
contour(vz) as "Axial Velocity" report(rpm)
contour(vm) as "Velocity Magnitude" report(rpm)
contour(p) as "Pressure" report(rpm)
vector(vr,vz) norm as "R-Z Flow" report(rpm)
contour(mass_balance) report(rpm)
elevation(vr) from (0,0) to (rad,0) as "Radial Velocity" report(rpm)
elevation(vt) from (0,0) to (rad,0) as "Swirling Velocity" report(rpm)
elevation(vz) from (0,0) to (rad,0) as "Axial Velocity" report(rpm)
elevation(vt,v0) from(0,0) to (rad,0) as "Impeller Velocity" report(rpm)
elevation(vm) from (0,0) to (rad,0) as "Velocity Magnitude" report(rpm)
elevation(vr) from (0,ht/2) to (rad,ht/2) as "Radial Velocity" report(rpm)
elevation(vt) from (0,ht/2) to (rad,ht/2) as "Swirling Velocity" report(rpm)
elevation(vz) from (0,ht/2) to (rad,ht/2) as "Axial Velocity" report(rpm)
elevation(vm) from (0,ht/2) to (rad,ht/2) as "Velocity Magnitude" report(rpm)
elevation(vr) from (0,0.9*ht) to (rad,0.9*ht) as "Radial Velocity" report(rpm)
elevation(vt) from (0,0.9*ht) to (rad,0.9*ht) as "Swirling Velocity" report(rpm)
elevation(vz) from (0,0.9*ht) to (rad,0.9*ht) as "Axial Velocity" report(rpm)
elevation(vm) from (0,0.9*ht) to (rad,0.9*ht) as "Velocity Magnitude" report(rpm)
elevation(vm) from (rad/2,0) to (rad/2,ht) as "Velocity Magnitude" report(rpm)
END