Summary
In experimental boundary layer studies, a flat plate with some shaped nose piece is generally used; this is often prone to flow separation at the junction. By analysing the development of a laminar boundary layer on a two-parameter family of nose shapes, it is found that a cubic super-ellipse of axis ratio 6 or higher is a reasonable optimum shape for avoiding separation on or due to such nose-pieces.
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References
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Narasimha, R., Prasad, S.N. Leading edge shape for flat plate boundary layer studies. Experiments in Fluids 17, 358–360 (1994). https://doi.org/10.1007/BF01874418
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DOI: https://doi.org/10.1007/BF01874418