A New Constant Pressure Model for N-Branch Junctions

Abstract

Branch junctions are very frequently found in the intake and exhaust systems of multi-cylinder engines and they represent some of the most complex boundary conditions for wave action models. This article deals with the way of modelling a junction of N branches. Firstly, a completely new view of the general problem is presented, stating the number of closing equations that are required to obtain a well-posed problem and what kind of equations they should be. Secondly, the constant pressure theory proposed by R. S. Benson is revised from this new standpoint, showing that besides the assumption that the pressure is the same at every branch end, a second set of closing equations has to be added to the global system, and how the selection of this set is arbitrary. Then two new approaches for this second set of closing equations are proposed, analysed and compared with Benson's original theory. Finally, one of them—the assumption that the total enthalpy for all the outgoing flows is the same—is proposed to close the problem, constituting with the constant pressure hypothesis a new constant pressure model for N-branch junctions.