The CORELLA (CORrosion Erosion test facility for Liquid Lead Alloy) facility allows corrosion erosion tests in molten lead alloys at controlled oxygen content and temperature under flowing conditions. Its exposure chamber consists of a cylindrical container, partially filled with the liquid metal. An inner rotating cylinder drives the liquid metal flow. The specimens of interest are fixed vertically inside the chamber such that the lead alloy flows around the specimens on both sides. In this numerical study, the turbulent flow of liquid lead–bismuth eutectic is solved for various specimen configurations, filling heights, and rotational speeds of the inner cylinder. Hereby, the deformation of the free liquid surface is taken into account using a rotationally symmetric approximation. Highly turbulent flow is found even for 200 rpm (revolutions per minute), the lowest rotational speed investigated. The velocity of the liquid metal along the specimens’ lateral surfaces reaches values up to 1.5 m/s for a rotational speed of 1200 rpm, the limit of experimentally stable conditions. Due to the sudden flow constrictions and expansions around the specimens, a much higher effect of the flow on corrosion erosion is expected than for simple pipe flow at the same bulk velocity.