Pulsed Power Engineering Engineering SimulationsJune 13 - 17, 2011 3 Pulsed Power Engineering...
Transcript of Pulsed Power Engineering Engineering SimulationsJune 13 - 17, 2011 3 Pulsed Power Engineering...
Pulsed Power EngineeringEngineering Simulations
June 13-17, 2011
Craig Burkhart & Mark KempPower Conversion Department
SLAC National Accelerator Laboratory
June 13 - 17, 2011 2
Engineering Simulations in Pulsed Power Systems• Uses of engineering simulation• Tools• Typical methodology• Analytical estimates of electric field
USPAS Pulsed Power Engineering Burkhart & Kemp
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Pulsed Power Engineering Simulations
• Differential equations govern many processes of interest to pulsed power engineers.
– Ex. Heat flow, stress/strain, electric and magnetic field intensities• Simulations provide a straightforward method to solve these equations for
complex geometries and non-linear conditions.• Some Types of Simulations Used
– Finite Element Method (FEM)• Very common method; used for transient and non-linear problems
– Boundary Value Method (BVM)• Good for odd aspect-ratio problems with open spaces; quick simulation times
– Particle in Cell (PIC)• For particle trajectory problems and plasma simulation
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Types of Simulations
• Electrostatic/Magnetostatic– Electro, Maxwell 2D (free)/3D, Quickfield
• Multi-physics– ANSYS, ATILA (free)
• Capacitance/Inductance Solvers– FastHenry (free), FastCap (free)
• Electromagentic Solver– HFSS, Singula
• Particle-in-Cell– XOOPIC (free), LSP
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Electric Field Stress
CAD Drawing ofWater Capacitor
(azimuthally symmetric)
Electric FieldMagnitude Plots
Open Space
Along a Measurement Line
• What is the electric field stress for a certain geometry and voltage?• Shown is a rotationally symmetric capacitor.
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Electric Field Grading• Where should field shapers be placed to evenly grade the electric field along an
insulator?• Field response to geometry changes can be modeled.
Floating Conductors in aGas Discharge Switch
Equipotentials Electric Field Vectors
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Capacitance Matrices• Many electrostatic codes can generate a matrix of capacitance values from element
values to each other.• These values can be exported to circuit codes for transient simulations.
Effective CapacitanceBetween Isolated conductors
Simulation-Generated Capacitance Matrix
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Inductance Matrices
CAD Drawing
SimplifiedRepresentation
InductanceMatrix
• Simplified representations are in many time necessary and appropriate for simulating complex geometries.
• Self- and mutual- inductance matrices can be generated.
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PIC Cathode Design
• Some PIC codes can self-consistently model E&M systems.
• Above is a cathode design showing the effect of external fields and self-fields from electrons.
-200 kV -200 kV+300VGround
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Multi-Physics Design• In some cases, several systems interact. E.g.
mechanical, electrical, and thermal.
• For example, left is a simulation of a piezoelectric transformer. Coupled mechanical and electrical systems are simulated.
• ANSYS and ATILA (free) are two codes available.
Groundedelectrode +1kV
~35 kV
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Typical Work Flow
• Create Geometry– Through external CAD program– Through included CAD program– By manually entering text coordinates
• Define Boundaries and Sources– Ex. Force on a surface, voltage on a conductor, or charge in a volume.
• Define Solution Type• Create Mesh• Simulate• Post-Process
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Typical Workflow
• A complex geometry is created in a CAD program
• Can be 2D or 3D depending on the software and the nature of the problem
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Typical Workflow• The specific area of interest
is imported to the simulation software.
• Excitations and boundary conditions are set.
• Simulation settings are entered.
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Typical Workflow
• Once a problem has a converged solution, results can be viewed.
• Many programs have the option to view results in a post-processor program or export for processing elsewhere.
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Estimating Electric Fields
R
r
Concentric Spheres
EM =VR
r(R − r)
f =Rr
Rr
= 2
EM =2Vr
=4VR
EM = VR
r lnRr
f =
Rr
−1
ln Rr
Rr
= e
EM =Vr
=VeR
Concentric Cylinders(symbols as for concentric spheres)
Maximum Stress ( EM)
f =maximum stress
mean stress
Optimum ratio Rr
and correspondingmaximum stress
Maximum Stress ( EM)
f =maximum stress
mean stress
EM = VX
f ≅ V2r
for Xr
>>1
f =
Xr
+1+Xr
+1
2
+ 8
4≅ X
2r for X
r>>1
r
r
XD
Equal Spheres
Equal parallel Cylinders(symbols as for equal spheres
EM =V D2 − 4r 2( )
2r D − 2r( )ln D2r
+ D2r
2
−1
EM ≅V
2r lnDr
if D >> 2r
f =
Xr
2
+ 4 Xr
2ln X2r
+1 + 12
Xr
2
+ 4 Xr
f ≅X
2r lnXr
if Xr
>> 4
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Estimating Electric Fields
Dependence of the ratio on electrode geometry for concentric cylinders and spheres (calculated from stress table) and for cylinder surrounded by a torus.
f =maximum stress
mean stress
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Estimating Electric Fields
Dependence of the ratio on electrode geometry for separate spheres and separate cylinders (calculated from stress table) and sphere-plane and cylinder-plane assemblies
f =maximum stress
mean stress
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Control of High Stress Points
(triple point)
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