In the most elementary treatment of plane-wave reflection at the open end of a duct system, it is often assumed that the ends are pressure nodes. This implies that pressure is assumed as a constant at the open end termination and that steady flow boundary condition is supposed as instantaneously established. While this simplifying assumption seems reasonable, it does not consider any radiation of acoustic energy from the duct into the surrounding free space; hence, an error in the estimation of the effects of the flow on the acoustical response of an open-end duct occurs. If radiation is accounted, a complicated three-dimensional wave pattern near the duct end is established, which tends to readjust the exit pressure to its steady-flow level. This adjustment process is continually modified by further incident waves, so that the effective instantaneous boundary conditions which determine the reflected waves depend on the flow history.
In this work, a theoretical model to compute the reflected wave on the flow history is proposed. The model has been implemented as a boundary condition in a 1D thermo-fluid dynamic code for internal combustion engine simulation and it has been validated over a set of measurements, that were carried out on an experimental test rig for a variety of engine-like flow conditions.