Sherwood number correlation for nuclear graphite gasification at high temperature

Gasification of nuclear graphite in the unlikely event of massive air ingress in High-Temperature and Very-High Temperature gas-cooled Reactors is a safety concern, requiring accurate and reliable predictions of the erosion rate of the external surface and within volume pores. At low temperature, gasification occurs within the open pores gradually degrading the mechanical strength of graphite components. Gasification shifts gradually to the external surface with increasing temperature. At high temperatures, although the rates of chemical reactions increase exponentially with temperature, they are limited by the oxygen diffusion to the external surface. A semi-empirical Sh correlation is developed to calculate the oxygen diffusion velocity. It is based on an extensive database of reported measurements of the convective heat transfer coefficient for heated wires and cylinders in air, water and paraffin oil flows at 0.006 ≤ Re ≤ 2.42 × 10⁵ and 0.068 ≤ Pr ≤ 35.2 and the mass transfer coefficient at 4.8 ≤ Re ≤ 10⁴ and Sc = 0.609 and 1300–2000. The database also includes reported values of the averaged Sh for gasification of a cylinder of V483T nuclear grade graphite (300 mm long and 200 mm in dia.) at 1141–1393 K in ascending cross-flow of nitrogen gas containing 5 vol.% oxygen at 533 ≤ Re ≤ 1660. The Sh correlation is within ±8% of the compiled 807 data points and applicable to both internal and external parallel and cross-flow conditions. When implemented in a chemical-reaction kinetics model, the calculated gasification rates are consistent with reported measurements for different size specimens of nuclear graphite grades NBG-18, NBG-25, IG-11, IG-110 and IG-430 at intermediate and high temperatures in atmospheric air (0.08 ≤ Re ≤ 30).