Transcript Ion Source Modelling Progress Report

Coupled EM-Thermal-Structural
ANSYS Simulation of the
FETS 4 metre RFQ
Tuner & Coupler Ports
Vacuum Pump Flange
Designed to be
Fully Bolted
Together
Vanes
Vacuum Flange
Coolant Manifold
Water Baths
Milled Into Vanes
Tuner & Coupler Ports
Vane End
Water Bath
Shaped to
Follow Vane
Cut-Back
Vane Cut-Back
O-Ring Joint
to Mount to
End Wall
Requirements of Study
• Confirm resonant frequency is 324 MHz
• Use EM fields to calculate heat loads
• Confirm proposed cooling strategy ok
• Estimate coolant flow rates needed
• Calculate copper thermal displacements
• Estimate resonant frequency shift
ANSYS Coupled solver process
Resonant frequency:
High-frequency electromagnetic eigenmode solver
Surface heat flux:
Use macro to convert magnetic fields to thermal element loads
Temperature distribution:
Thermal solver
Vane and wall displacement:
Structural solver
Frequency shift:
Export results to MATLAB Slater perturbation algorithm
Model Geometry
(from Autodesk Inventor)
Simplified Geometry
Internal Space
‘Filled’ with
Vacuum Body
Water-Bath
Baffle Added
Simplifications made:
• Bolt Holes Removed
• Other Unnecessary Features Removed
• Sliced by Symmetry Planes
End Wall
Added
Mesh Optimization
• Depends on desired effect to be observed:
1) For frequency dependence on geometry,
enhance vacuum mesh in relevant regions
2) For surface losses/heat flux, need high
density mesh at copper-vacuum boundary
3) For accurate mechanical solutions, increase
mesh density in copper
• Coupled solvers need all three enhanced!
Mesh Optimization Examples
Resonant Frequency
and Q-factor Studies
Increased Surface Loss
Accuracy
Boundary Condition Regions
Transfer to ANSYS Classic
• Different ‘bodies’ are different mesh types
• Assign boundary condition to node groups
Resonant Frequency
Analysis
Eigenmode Solver
Surface H-Field Results
Eigenmode Solver
Magnetic Field Vector Results
H-Field flowing around
vane cut-backs
H-Field flowing past tuner
port and vacuum pump slots
Eigenmode Solver
Surface E-Field Results
Eigenmode Solver
Electric Field Vector Results
Quadrupole Mode
333.56 MHz
Dipole Modes
330.02 MHz
Why the Wrong Frequency?
• Poor Mesh Quality?
– Eigenmode solver very insensitive to mesh
• Eigenmode solver not as good as CST?
– Same (correct) frequency found for cold model
• Different tuner/coupler positions?
• Longer RFQ section?
• Effect of vane-tip to end-wall gap?
Frequency vs. Port Positions
Frequency vs. RFQ Length
Poisson Superfish result for
infinitely long RFQ = 338 MHz
End effects become
dominant in short 40cm
cold model (319 MHz)
∞
Frequency vs. End Wall Gap
Frequency vs. End Wall Angle
Re-sized RFQ for correct frequency
Note: set for slightly too high a frequency (326 MHz)
because Superfish assumes no features such as
couplers and vacuum pumping, which reduce the
frequency by 2 MHz. See slide 19.
Summary of Frequency Analysis
• Quad & Dipole modes remain well
separated by several MHz
• Resonant frequency increases with length,
asymptoting to 338 MHz Superfish result
• Quadrupole frequency of 400 cm RFQ is
~9 MHz shifted cf. 40 cm cold model
• Increase radius to 43.49mm for correct f
• Frequency and Q-value vary with end wall
geometry as measured on cold model
Temperature Distribution
Total Surface
Power Loss
Psolver 

surface
2
i
H
where:
 f 0 0


2
i
dAi
Heat Flux Per
Element
Preal  2
Fi 
Hi
Psolver 2
Psolver = Calculated total surface power (W)
ρ = Surface resistance (Ω)
H = Tangential magnetic field at surface (T)
dA = Area of surface mesh element (m2)
f = Cavity resonant frequency (Hz)
µ0 = permeability of free space (H m-1)
σ = Conductivity of cavity walls (S m-1)
F = Heat flux due to surface losses (W m-2)
Preal = Expected total surface power (W)
Convection Boundary Conditions
Heat Transfer
Coefficient (HTC)
/ W m-2 K-1
Thermal Solver Solution
Temperature / °C
Water-bath HTC = 3000 W m-2 K-1
Temperature vs. Input Power
Outer Wall
Vane Tip
Squirt Tubes
Squirt Tubes Inserted
Squirt Tube HTC: 0 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 1000 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 2000 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 3000 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 4000 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 5000 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 7500 Wm-2K-1
Input Power: 500 kW
Squirt Tubes Inserted
Squirt Tube HTC: 10000 Wm-2K-1
Input Power: 500 kW
Variation With Squirt Tube HTC
Water bath HTC: 1000 Wm-2K-1
Tuner, Coupler & Vacuum Port HTC: 3000 Wm-2K-1
Input Power: 500 kW
Summary of Thermal Analysis
• Majority of heat flux at vane cut-backs
• Tuner/Coupler and Vacuum flange cooling
more than adequate
• Large temperature gradient at vane tips
can be smoothed using squirt tubes
• Majority of heat removed by water baths
• Test required to assess flow rates and HTC
Structural Analysis
Boundary Conditions
• Temperature distribution applied as load
• Frictionless supports at symmetry planes
• End wall either longitudinally fixed or free
• Effect of air pressure untested yet
Structural Deformation
Longitudinal
Displacement / mm
Vane ends move toward end wall
by ~300 µm.
Vertical
Displacement / mm
Vanes move toward each other by ~30 µm.
Walls move outward by ~150 µm.
Von Mises Stress
200 MPa of stress in vane cutbacks
End Wall Movement Constraint
Fixed End Wall
Max Stress 196 MPa
Free End Wall
Max Stress 23.3 MPa
End Wall Movement Constraint
Fixed End Wall
Free End Wall
Frequency Shift
Import EM fields and boundary node
displacements into MATLAB.
Algorithm written to calculate frequency shift
using Slater perturbation equation:
 
0

Energy change due to
deformed boundary

Total stored energy in
cavity vacuum
E  0 H dV
2
2
f boundary

2
2
f0
  0 E  0 H dV

volume
Frequency Shift vs. Input Power
Frequency Shift
• Walls expand outward
• Vanes grow toward each other
• ∴ Little net transverse movement of vanes
• Vane tips grow longitudinally toward end
wall by ~100 µm
• Creates ~300 kHz frequency shift
Summary of Structural Analysis
• Compensating movement of walls outward
and vanes inward
• Largest temperature gradients (~60°C) and
thermal expansion (100µm) at vane ends
• Resulting frequency shift ~300 kHz
• Well within moveable tuner range
• Free wall reduces stress at vane cut-backs
Conclusion & Actions Required
• Sequential EM-Thermal-Structural analyses
allow comprehensive study of RFQ
• Full 4-metre RFQ has a higher frequency
– Increase transverse size to lower the frequency
• Cooling scheme seems ok
– Confirm flow rate needed for water baths
• Small deformations and frequency shift
– Use as perturbation in tracking codes