On the turbulent mean-flow at the leading edge of a swept wing

Due to the presence of a singularity in the governing three-dimensional (3D) momentum integral equation at the attachment line (AL) and numerical issues while marching immediately downstream, a numerical fix was previously imposed in the leading edge (LE) modelling of Airbus Callisto. This technique has been employed for half a century during the design and optimisation of transonic wings, but recent analysis on AL control for form drag reduction rose concerns about this previously accepted numerical fix. An experimental study was conducted to validate this LE approximation. Measurement of the boundary layer integral quantities immediately downstream of the AL showed considerable increment; therefore a modification to the 3D governing equation was suggested to remove the numerical fix in the LE modelling. Comparison with experimental measurements showed that the proposed numerical model is not only able to predict the flow within an agreement of ±5%, but it is also able to capture the non-monotonic behaviour in the development of the momentum thickness in the vicinity of the AL, not reported previously.