Single-crystal superalloy turbine blades (TBs) fabricated using directional solidification are key components of aeroengines and gas turbines. Owing to thermal–solutal convection during solidification, such components are susceptible to flow-induced defects such as freckles and/or eutectic accumulation. The formation mechanisms of the above defects are well understood, but reliable theories or empirical laws are unavailable to guide the engineering production process as the thermal–solutal convection is sensitive to the alloy, Bridgeman furnace design, shape and internal structure of the TB, withdrawal parameters, etc. This study proposes a novel method to ‘digitally twin’ the directional solidification of the TB, i.e. to utilise a physically based numerical model to quantitatively simulate the solidification process, including freckle formation and eutectic accumulation. It includes two simulations: one for the global thermal field in the Bridgeman furnace, including the casting system, and the other for the flow and solidification within the casting component. The former is modelled using ProCAST, the latter is modelled using a volume-average-based multiphase solidification model, and both are coupled. To verify the digital twin concept, an actual industrial TB with slight geometrical modification (removal of the fins while maintaining the inner surface profile) was cast in a Bridgman furnace, and the as-solidified TB was inspected for freckles. An excellent agreement between the simulation and experimental results was obtained. Typically, an actual TB features a complex inner structure (fins) that connects the front and back blades with an average wall thickness of 1.5 mm. A fresh simulation was performed for the TB with inner fins. It was observed that the inner fins of the TB along with other process conditions, such as the shadowing effect of the furnace, play an important role in freckle formation. This study demonstrates the necessity of the digital twin in future TB production.