Hydrogen redistribution in Zr-base cladding under gradients in temperature and stress

TL;DR

This work addresses hydrogen redistribution in zirconium-based nuclear fuel cladding under temperature and stress gradients, aiming to predict localized hydride formation that can embrittle cladding. It develops two physically based modeling frameworks: (i) a single-phase diffusion model incorporating a Soret term and Gaussian fluctuations to describe axial localization near interpellet gaps in BWR cladding, and (ii) a two-phase α+δ diffusion–mechanics model that captures dense hydrided rims under corrosion with hydrostatic-pressure feedback and phase-transform hysteresis. Axial simulations reveal a pronounced δ-hydride peak opposite cooler interpellet gaps, while rim simulations reproduce realistic rim width and density when the δ-phase hydrogen concentration is a significant fraction of the α-phase concentration; swelling effects provide only weak feedback. Together, the approaches avoid ad-hoc fixes, reproduce key experimental trends, and offer physically grounded tools for predicting hydrogen-induced embrittlement in Zr alloys under reactor operating conditions.

Abstract

Computational models are used here for simulating diffusion-controlled redistribution of hydrogen that is picked up by zirconium-base nuclear fuel cladding during light water reactor operation. Axial localization of hydrogen, leading to localized precipitation of zirconium hydrides at lower-temperature regions near interpellet gaps, is studied with a bespoke model, while radial diffusion, leading to formation of a densely hydrided rim subjacent to the waterside oxide layer, is studied with a more general model. The calculated results are compared with experimental observations and similar computational studies reported in the literature. The results underline the importance of hydrogen redistribution with regard to local embrittlement of the cladding tubes.

Figures (5)

• Figure 1: (a) Cladding tube inner surface temperature $T_i(z)$ close to the interpellet gap position at $z=0$. (b) Temperature distribution across the cladding, close to the interpellet gap.
• Figure 2: Calculated wall-averaged cladding hydrogen concentrations in the vicinity of the interpellet gap at two stages of hydrogen uptake $N_g(t)$. Hydrogen in $\alpha$-phase (left) and $\delta$-phase (right).
• Figure 3: Rod average LHGR (solid black line) and calculated temperature histories for the cladding metal inner (red dotted line) and outer (blue dashed line) surface, 2540 mm above BFC. The cladding temperature drops to $<300$ K at zero power conditions.
• Figure 4: (a) Observed (insert) end-of-life hydride distribution, 2540 mm above BFC, in comparison with calculated results for different values of parameter $c$. (b) Calculated hydrogen distributions at end-of-cycle (EOC) 1 to 5. Calculated EOC wall-average hydrogen concentrations are indicated in the legend.
• Figure 5: (a): Calculated hydrogen-induced local swelling and resulting change in hydrostatic pressure. (b): Calculated feedback effect on end-of life hydrogen distribution ($c= 0.90$ in the calculations).