2 ANSYS Multiphysics Analysis Mesh and solve for resonant frequency of vacuumUse surface EM results to calculate surface heat loadsMesh and solve for temperature distribution in copperUse temperature distribution as structural load for thermal expansionMesh and solve for structural displacements of copperMorph vacuum to fit inside newly displaced copper cavityf = 324MHzΔf ~ 100kHZΔf/f ~ 1x10-4Mesh not good enough?
3 Slater Perturbation Theorem Electric and magnetic fields rearrange in a deformed cavity∴ Resonant frequency of cavity varies when its boundary surfaces moveEnergy change due to deformed boundaryStored energy of entire cavity vacuum
4 Fill this copper volume with a vacuum body Use vacuum to solve for resonant frequencyUse copper to solve for temperature and structural distributions
5 Magnetic fieldBoundary mesh elementsElectric fieldSurface heat losses
7 Predictions for 200kW input RF power: Temperature rise ~1500 °C Simulation in ANSYSCold Model TestsTemperature Rise / C1515.6Frequency Shift / kHZ-78-89Max Temperature = 37 °CPredictions for 200kW input RF power:Temperature rise ~1500 °CFrequency Shift ~ 3 MHZ(but irrelevant for molten copper!)Max Structural Deformation = 0.3 mm
8 Cooling Pipe Flow Requirements For P = 200 kW and ΔT = 40 °CNeed mass flow of 1.19 kg s-1(If split over 4 pipes, need 0.3 kg s-1 per pipe)If we allow a flow velocity of 5 ms-1,need pipe diameter of ~ 9 mmFor 1m long pipes,required pressure drop ~0.3 Bar
9 Cooling Pipe Heat Transfer Can get Heat Transfer Coefficientof ~ W m-2 K-1
10 Proposed Pipe Positioning Applied HTC = W m-2 K-1