Reseach article below tested various shapes and contours for Velocity stack design. The Elliptical profile was by far the best design.
Gordon P. Blair, Senior Associate, Prof Blair & Associates and
W. Melvin Cahoon, Senior Engineer-Specialist State in their article:
“While there is not much in it, the elliptical profile comes out as the
winner over the aerofoil profile. In the all-important pressure ratio
PR range up to 1.1 one can conclude that the best bellmouth has an
advantage in CD terms of some 3.5% over the simplest bellmouth.
In design terms, one can usefully conclude that “short and fat” is
best with an optimum length criterion L of one diameter De, and
an optimum entry diameter Di of some 2.13 times the exit diameter
De, and with an elliptical profile. Although the investigations are not
presented here, the corner radius Rc can be usefully designed as 0.08
times the entry diameter Di”
Below is the full article
http://www.profblairandassociates.com/pdfs/RET_Bellmouth_Sept.pdf