Theory would suggest that it doesnt matter (air does not get backed up unless its over mach one, infact below mach 0.3 its essentially incompresible which is nice). I would just test and see.
Any kind of fan clearance would help. The primary turbulence noise from a fan is caused by the central hub support hubs interacting with the fan. Hence fans should never have an even number of blades and support struts. By putting a big radiator by a fan your distrupting its airflow and causing this smae effect with it. I think support beam fan theoretical models for dBA are included in some of the BTX information on formfactors.org.
9-15 diameters sounds awfully high to me. This sounds alot like the time it takes a flow to gain a fully developed duct profile which is not what we are after. I cant think of any good rule off the top of my head but a "common sense" guess would probably be good. At home i have a derivation of a theoretical model of turbulence for a grid that might give a good approximation i'll see what that says
More sciency explanation of the model above
its a model of the turbulence produced by a square grid accordign to the K-e viscosity turbulence model. This is the basis of alot of the models for cfd. Its fairly exact so should give a good punt guess (5% if it was an exact model of the flow) for spacing for air flow coming through the rad to the fan. Assuming that it works for the reverse case (fan to rad) is more tricky. Since the outlet profile of the fan can be guessed you could discreatise that profile for each hole and do it like that taking the maximum turbulence distance.
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