Eurofer 97-W target thermal FEA modelling

1 Preamble

Modelling the transient heating of a W-Eurofer 97 target using Magnum-PSI’s 300W pulsed Nd:YAG laser (LASAG FLS352N).

2 Target materials, geometry & meshing

Targets consist of a tungsten (W) plasma-facing layer diffusion bonded to Eurofer 97 reduced activation ferritic/martensitic steel via field assisted sintering (FAST). The target geometry is 20x20xL_E97+L_W mm, where L_W, the thickness of the W layer, varies from 0.25 mm - 4 mm, and the thickness of the Eurofer 97 (L_E97) is a constant 3 mm. Target symmetry is exploited such that only a quarter of each target is modelled. For simplicity, stepped target edges and thermocouple holes are neglected.

Temperature-dependent material properties for ITER-grade tungsten were taken from ITER materials handbook [1]. Material properties for grade 304 steel from Simcentre 3D’s material library were employed as a substitute for Eurofer 97.

The Eurofer 97 domain was meshed into 4.5 × 10³ 10-node tetrahedral elements with a characteristic size of 1 mm. A mesh control was used to reduce element size closer to the W-Eurofer 97 interface to improve accuracy in this region. The tungsten layer was meshed into 10-node tetrahedral elements with a characteristic size of 0.25 mm. The number of elements in the tungsten domain depends on L_W and is approx. 3600 × L_W.

3 Assumptions & boundary conditions

Perfect thermal contact is assumed across the W-Eurofer 97 joints, and across the clamped joints between the Eurofer 97 domain and Magnum-PSI’s target holder assembly. The water-cooled target holder remains at a constant temperature of 21 °C throughout. The emissivity (ε) of the plasma-facing sandblasted W surface is assumed to be 0.3. The LASAG is assumed to have a circular Gaussian beam profile with a FWHM of 1.0 mm, and the transmission of it’s optical path to Magnum-PSI’s target holder is assumed to be 75% [2].

4 Initial conditions

A steady state H plasma will be used to impose a background thermal load on the target to raise it to reactor-relevant temperatures prior to transient exposure. This will aim to maintain the temperature of the W-Eurofer 97 interface at approx. 500 °C. The Gaussian profile of Magnum-PSI’s plasma column is presently neglected and a uniform thermal load is applied to the plasma-facing surface.

For a target with a 250 µm W layer, a steady state thermal load of 7.5 MW m ^-2 was found to yield a maximum surface temperature of 498 °C. The temperature at the W-Eurofer 97 interface was 484 °C. These steady state temperature profiles are employed as initial conditions for transient loading steps.

Steady state temperature profile through a target with a 0.25 mm W layer, exposed to a 7.5 W mm^-2 thermal load.

5 LASAG transient thermal loading

The LASAG will be operated in burst mode, so rather than modelling individual shots, the average heat flux (φ_q,LASAG) arising from a burst of of n identical laser shots is calculated and applied to the FEA model. Preliminary LASAG settings taken from prior experiment/DIFFER wiki (to check these are achieveable) were adjusted to give the desired ΔT for Eurofer 97 (500-956 °C).

# LASAG parameters
pulse_length <- 0.001 # 1.0 ms (not used)
pulse_energy <- 30 # J per pulse (emited, max. 60 J)
pulse_frequency <- 50 # Hz
pulse_number <- 25 # number of pulses per burst, n

# Target/beamline parameters 
target_emissivity <- 0.3 # surface emissivity 
spot_dia <- 1.7 # mm dia spot at the target surface (sigma-4 of a Gaussian with a 1mm FWHM)
transmission <- 0.75 # transmission %

# Calculate burst duration and spot area
burst_duration <- pulse_number*(1/pulse_frequency) # length of burst in seconds
spot_area <- pi*(spot_dia/2)^2 # mm^2 

#Calculate absorbed energy per burst, absorbed power, and average heat flux
burst_energy_abs <- pulse_energy*pulse_number*target_emissivity*transmission # absorbed energy per burst (J)
burst_power_abs <- burst_energy_abs/burst_duration # absorbed power (W)
burst_heatflux_abs <- burst_power_abs/spot_area # absorbed heat flux (W mm-2)

Each LASAG burst will deposit 168.75 J into the target over 0.5 s, yielding a total deposited power per burst of 0.3375 kW. Assuming a 1.7 dia. spot, the absorbed heat flux per burst will be 148.6914693 W mm^-2.

A 150 W mm^-2 thermal load applied to the model for 0.5 seconds yielded a maximum Eurofer 97 temperature of 954.33 °C and a maximum W surface temperature of 1315 °C. The temperature at the centre of the Eurofer 97 domain (i.e. thermocouple location, not shown) was estimated to be 355 °C.

Temperature vs time profiles of max. W and Eurofer 97 temperatures for a target with 0.25 mm W layer exposed to 150 W mm^-2 for 0.5 s

6 Todo

• Instead of LASAG heating, model the effects of pulsing Magnum-PSI’s power supplies (strikepoint sweeping)
• scan of W layer thicknesses (0.25 - 4 mm) vs W surface, W-steel interface temperature, TC temperature
• Analytical validation using 1D time-dep. heat transfer equation

Bibliography

[1]

’ITER Organisation’, “ITER material properties handbook v3.3.” 2013. doi: 10.1016/S0022-3115(96)00202-4.

[2]

J. A. G. van Kesteren, “The effect of ELM-like laser loading on deuterium retention in tungsten,” 2024, Accessed: Jan. 08, 2025. [Online]. Available: https://pure.tue.nl/ws/portalfiles/portal/342701467/1376969_-_Kesteren_J.A.G._van_-_MSc_thesis_Thesis_-_NF.pdf