in flow and out flow in a short duct

jane

I have a short duct with a small fan, the flow is sucted from atmosphere in the inlet by the fan, the pressure in the upstream of the fan is lower than atmospheric pressure by Bernoulli. Then the fluids experience a static pressure increase because of the work added by the fan, then eject out to atmospheric. Since the duct is very short, the flow will from a recirculation: Flow ejecting from exit recirculates to inlet. Does anybody have experience on this kind of flow? How is the static pressure distribution in the recirculation area? Suppose if I wanna increase the recirculation area, what should I do? Many thanks.