Paper n. 2010-01-1051 Modeling of Pressure Wave Reflection from Open-Ends in I.C.E. Duct Systems F. Piscaglia, A. Montorfano, A. Onorati, G. Ferrari Dipartimento di Energia, Politecnico di Milano Copyright c  2010 Society of Automotive Engineers, Inc. ABSTRACT 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. INTRODUCTION The internal combustion engine is currently experiencing a significant evolution, mainly finalized to the optimization of performances and the reduction of fuel consumption and emissions. In the recent years, researchers focused their activity on the development and the application of advanced simulation models for the calculation of the thermo-fluid dynamic processes in I.C. engines; this choice was motivated by a strong interest towards efficient and reliable simulation models in the automotive research field. Commercial and research 1D and multi-D codes are widely applied during the design stage of a new engine, essentially to predict the unsteady flows in the intake and exhaust duct-systems and their consequent effect on engine volumetric efficiency, on the gas exchange process, on the characteristics of the thermodynamic cycle. During the last two decades, substantial research work lead to significant enhancements in several significant aspects in the 1D models, about: i) the numerical methods adopted for the solution of the conservation equations, ii) the boundary conditions required to represent complex components in duct-systems (multi-pipe junctions, EGR valve, silencers, turbochargers), iii) the transport of reacting chemical species to allow for emission conversion in catalytic reactors (TWC, DOC, DPF, SCR), iv) the quasi-D combustion models adopted to calculate the S.I. and C.I. combustion process and the related pollutant emissions. All these improvements have contributed to render 1D simulation models reliable, robust, accurate and computationally efficient. In this scenario, they are fundamental tools to shorten the development and the prototyping times, to understand in detail the phenomena and to guide the experimental activity towards promising configurations in terms of torque, power, fuel consumption, raw and tailpipe emissions. Despite of that, one fundamental boundary condition has not been studied with sufficient insight, even if it plays an important role in the non-linear modeling of one-dimensional pipe-systems: the tailpipe outlet. In this case, the simple assumption of constant ambient pressure established in the ”vena contracta” is universally adopted, to develop a simple quasi-steady boundary condition, as described in [1, 2]. For subsonic outflows from the open end of a duct-system, pressure is often considered as constant and equal to the ambient pressure (steady flow outlet b.c.). This assumption looks realistic with steady flows; conversely, when unsteady flows with propagation of finite amplitude pressure waves are involved, it has been experimentally proven that the pressure at the duct exit is not constant and it has significant oscillations. This affects the wave motion in the duct and the radiation of tailpipe pulse noise. The 1D modeling of the open end can be carried out in detail by the acoustic approach, which can be applied for pressure waves of small amplitude. In this case, a pressure reflection coefficient R [3, 4], defined by the ratio between the reflected and incident wave amplitudes, can correctly