Numerical modelling of Fanno flows in micro channels: a quasi-static application to air vents for plastic moulding

The flow in micro air vents, as those used in the plastic moulding industry, can be assimilated to a Fanno flow. Even though Fanno theory is well-established, its outcome strongly depends on the correct assessment of the friction factor term. Yet, friction factor evaluation is not straightforward since traditional fluid-dynamics formulas fail to account for the compressibility effects and are only valid when low Mach numbers are attained, which is often not the case. A numerical model implementing the non-isoentropic compressible Fanno flow theory is presented. A friction factor correlation is proposed, based on the results of a large set of CFD simulations used for calibrating the numerical model. The model is then used for characterizing micro air vent geometries under different operating stagnation pressures and temperatures. The vents characterization is finally employed for the quasi-static assessment of the mass flow rate through the vents, and of the air pressure in the mould during a typical moulding process.