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3d_vector_flowbox

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{  3D_VECTOR_FLOWBOX.PDE

 

 This is a modification of the example 3D_FLOWBOX.PDE to use vector variables.

 

 This problem demonstrates the use of FlexPDE in 3D fluid flow.  It shows the flow of

 fluid through a plenum box with a circular inlet at the bottom and an offset circular

 outlet at the top. The inlet pressure is arbitrarily set at 0.05 units.

 

 The problem runs in two stages, first as a massless fluid to get an initial pressure

 and velocity distribution in a linear system, and then with momentum terms included.

 

 Adaptive mesh refinement is turned off for speed in demonstration.  In a real application,

 regridding could be used to better resolve the flow past the corners of the ducts.

 

 The solution uses a "penalty pressure", in which the pressure variable is used merely

 to guarantee mass conservation.

 

}

title '3D flow through a plenum'

coordinates

 cartesian3

variables

 v(1e-6) = vector(vx,vy,vz)

 p

select

 ngrid=20

 stages=2

 regrid=off                  

definitions

 long = 2

 wide = 1

 high = 1/2

 xin = -1   yin = 0

 xout = 1   yout = 0

 rc = 0.5

 duct = 0.2

 dens=staged(0,1) { fluid density }

 visc= 0.01       { fluid viscosity }

 vm=magnitude(v)

 div_v = dx(vx) + dy(vy) + dz(vz)

 PENALTY = 1e4*visc/high^2

 Pin = 0.05

 Pout = 0

INITIAL VALUES

 v = vector(0,0,0)

 p=Pin+(Pout-Pin)*(z+high+duct)/(2*high+2*duct)

EQUATIONS

 v:    dens*dot(v,grad(v)) + grad(p) - visc*div(grad(v)) = 0

 p:    div(grad(p)) = PENALTY*div_v

extrusion z = -high-duct,-high,high,high+duct

boundaries

  Region 1   { plenum box }

      surface 2 value(v) = vector(0,0,0) natural(p)=0

      surface 3 value(v) = vector(0,0,0) natural(p)=0

      layer 1 void

      layer 3 void

      start(-long,-wide)

          value(v) = vector(0,0,0) natural(p)=0   { fix all side values }

        line to (long,-wide)

          to (long,wide)

          to (-long,wide)

          to close

  limited Region 2   { input hole }

    layer 1

    surface 1 natural(v) = vector(0,0,0) value(p)=Pin     { input duct opening }

    start(xin,yin-rc)

          layer 1   value(v) = vector(0,0,0) natural(p)=0 { duct sidewall drag }

      arc(center=xin,yin) angle=360

  limited Region 3   { exit hole }

    layer 3

    surface 4 natural(v) = vector(0,0,0) value(p)=Pout   { output duct opening }

    start(xout,yout-rc)

          layer 3   value(v) = vector(0,0,0) natural(p)=0 { duct sidewall drag }

      arc(center=xout,yout) angle=360

monitors

  contour(vx) on x=0 report dens report pin

  contour(vx) on y=0 report dens report pin

  contour(vz) on y=0 report dens report pin

  vector(vx,vz)on y=0 report dens report pin

  contour(vx) on z=0 report dens report pin

  contour(vy) on z=0 report dens report pin

  contour(vz) on z=0 report dens report pin

  vector(vx,vy)on z=0 report dens report pin

  contour(p)   on y=0 report dens report pin

plots

  contour(vx) on x=0 report dens report pin

  contour(vx) on y=0 report dens report pin

  contour(vz) on y=0 report dens report pin

  vector(vx,vz)on y=0 report dens report pin

  contour(vx) on z=0 report dens report pin

  contour(vy) on z=0 report dens report pin

  contour(vz) on z=0 report dens report pin

  vector(vx,vy)on z=0 report dens report pin

  contour(p)   on y=0 report dens report pin

end

 


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