One size fits all ?

Every once in a while within the Bantam racing context, the subject of flow separation in exhaust pipe diffusers crops up, and the Honda/Bantam pipe discussion has prompted just such a question. Another interesting question posed was how are pipe diameters arrived at, or more precisely what are the relevant qualifying criteria.
The internal conditions of similar pipes operating at optimum performance on very different engines are not comparable, where the Honda is up around 13+bar bmep and the Bantam down at around 8bar.
According to some scientific publications for most practical applications a maximum angle of 7* produces little in the way of flow separation. Above this there is a gradual degradation of stability, so I guess that most Bantam race applications can be covered by those figures.
In reality the angle depends more on the expansion behaviour of the gas and its Mach number and Mach numbers a very temperature influenced. Gas expansion in the flow direction equates to higher particle velocity, with gas expansion perpendicular to this direction filling the whole cross section of the diffuser.
It is therefore, the ratio between these two expansions and their velocities, both of which are temperature sensitive, that fundamentally dictate the ideal shape of the diffuser, which will then be of a horn like profile. Both temperature and so gas particle quantity and velocity from an RS Honda engine are vastly higher than the modest Bantam so the same pipe cannot be said to be ideal for both! The hugely powerful,17bar bmep, Aprilia engine at its max rpm has a residual cylinder pressure of 11bar at exhaust port opening, that energy level will give one hell of a shove to the exhaust gas and pressure wave. The RS will be some way below that figure with the Bantam a long way back again!  
Professor Blair, with his much copied pipe formulas attempted to tie pipe design loosely to the bmep of various engine spec parameters and so included a horn factor to establish a suitable maximum diameter for differing performance specifications. By and large a very workable pipe can be calculated using the software he devised back in the 1980s.

The following short piece should have been included in the preceding post, but for some reason which I can`t explain, was overlooked when I typed the final draught for posting here on the Bantam site:

The frequency of the Helmholtz System consisting of crankcase volume, inlet duct diameter and length should be such that it resonates in step with a combination of exhaust system frequency and engine rpm.
As such it is probably the “holy grail” of engine tuning, and all might come together sweetly at some point in the rpm scale, but is invariably at the unintended rpm!
It is all associated with mass movement of mixture and not necessarily an expanding mixture volume or velocity, which in turn crucially affects density.
A bigger case volume lowers the Helmholtz frequency, a larger inlet duct diameter increases it, a longer duct length then decreases the frequency. A larger, maximum exhaust pipe diameter lowers the frequency, but, the gas expansion ratio decides a final diameter which leaves sufficient energy to adequately perform the later but important, plugging function. Each engine produces a finite energy level but in case of a Bantam race engine that is precious little, and should be acknowledged as such. So as one can see, going “big” is not always best!