Rotating inner ring / Normal-tangential boundary

[jeroenr]

I'm doing a simple test-case on rotating boundaries in context of the Navier-Stokes solver. The long-term goal is to analyse the heat transfer in mechanical seals.

The ring is a fluid body with internal diameter of 60mm, outer diameter of 80mm and height of 10mm. Since the ring was modelled in mm, I've put "Coordinate Scaling = 0.001" in the simulation section. The normal-tangential coordinate system was used to simulate the motion of the inner boundary. Some experimenting was needed to find the right variable to use (Velocity 3 = 20 in Boundary Condition 3).



After some trials and tweaking I was happy the solution converged. But looking at the results I see some strange things, which I cannot exactly understand. I think I'm missing something, because the direction of the tangential velocity seems to turn around at a random point in the circumference:

Code: Select all

Header
  CHECK KEYWORDS Warn
  Mesh DB "." "."
  Include Path ""
  Results Directory ""
End

Simulation
  Max Output Level = 5
  Coordinate System = Cartesian
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Steady state
  Steady State Max Iterations = 1
  Output Intervals = 1
  Timestepping Method = BDF
  BDF Order = 1
  Solver Input File = case.sif
  Post File = case.ep
Coordinate Scaling = 0.001
End

Constants
  Gravity(4) = 0 -1 0 9.82
  Stefan Boltzmann = 5.67e-08
  Permittivity of Vacuum = 8.8542e-12
  Boltzmann Constant = 1.3807e-23
  Unit Charge = 1.602e-19
End

Body 1
  Target Bodies(1) = 1
  Name = "Body 1"
  Equation = 1
  Material = 1
End

Solver 1
  Equation = Navier-Stokes
  Procedure = "FlowSolve" "FlowSolver"
  Variable = Flow Solution[Velocity:3 Pressure:1]
  Exec Solver = Always
  Stabilize = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Nonlinear System Convergence Tolerance = 1.0e-9
  Nonlinear System Max Iterations = 20
  Nonlinear System Newton After Iterations = 8
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 0.5
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStab
  Linear System Max Iterations = 80
  Linear System Convergence Tolerance = 1.0e-11
  Linear System Preconditioning = ILU2
  Linear System ILUT Tolerance = 1.0e-5
  Linear System Abort Not Converged = False
  Linear System Residual Output = 1
  Linear System Precondition Recompute = 1
End

Equation 1
  Name = "Navier-Stokes Eq"
  Active Solvers(1) = 1
End

Material 1
  Name = "Oil, olive (25 C)"
  Viscosity = 0.06
  Heat expansion Coefficient = 0.72e-3
  Heat Conductivity = 0.17
  Sound speed = 1430.0
  Heat Capacity = 1970.0
  Density = 800.0
End

Boundary Condition 1
  Target Boundaries(1) = 1
  Name = "Outflow"
  Velocity 1 = 0
  Velocity 2 = 0
  External Pressure = 100000
End

Boundary Condition 2
  Target Boundaries(1) = 2
  Name = "No-slip wall"
  Noslip wall BC = True
End

Boundary Condition 3
  Target Boundaries(1) = 3
  Name = "RotatingWall"
  Velocity 3 = 20
  Velocity 1 = 0
  Velocity 2 = 0
  Normal-Tangential Velocity = True
End

Boundary Condition 4
  Target Boundaries(1) = 6
  Name = "Inflow"
  Velocity 1 = 0
  Velocity 2 = 0
  External Pressure = 110000
End

Could anyone explain why the tangential velocity turn around, while it should all be pointing in the same direction around the circumference? Is this the wrong way to set up the boundaries for this problem?

[raback]

Hi

When you go to N-T coordinate system here is the problem: the tangential components are not uniquely defined. The normal component is always well defined. Particularly in 3D the two tangential vectors are not. Usually this is not a problem since we usually want to fix the normal component. Unfortunately in your case this is not therefore easily applicable.

However, you do already know all components. So why not use something like (assuming rotating aroun z-axis):

Code: Select all

  $Omega=1.23 ! angular velocity
  Velocity 1 = Variable Coordinate 2
    Real MATC "-Omega*tx"
  Velocity 2 = Variable Coordinate 1
    Real MATC "Omega*tx"
  Velocity 3 = 0.0

As in test case $ELMERSRC/fem/tests/RotatingFlow. This case may be a little bit confusing as within one command file it includes fixed and rotating coordinate system to ensure consistancy.

-Peter

[jeroenr]

Peter,

Thank you for the (very fast) response. I'll try your solution as soon as I get the Windows laptop back (not mine, but running all the GUI and Post stuff). My own PC runs Linux and I still haven't been able to build all Elmer components from source, but that's another topic.

Regards,
Jeroen

[raback]

Hi,

You might use a fresh Ubuntu VM that is optimized for Elmer, see
http://www.nic.funet.fi/pub/sci/physics ... in/Vmware/
It also includes working compilation scripts for all the stuff.

-Peter