Control volume based modelling of compressible flow in reciprocating machines

An approach to modelling unsteady compressible flow that is primarily one dimensional is presented. The approach was developed for creating distributed models of machines with reciprocating pistons but it is not limited to this application. The approach is based on the integral form of the unsteady conservation laws for mass, energy, and momentum applied to a staggered mesh consisting of two overlapping strings of control volumes. Loss mechanisms can be included directly in the governing equations of models by including them as terms in the conservation laws. Heat transfer, flow friction, and multidimensional effects must be calculated using empirical correlations; correlations for steady state flow can be used as an approximation. A transformation that assumes ideal gas is presented for transforming equations for masses and energies in control volumes into the corresponding pressures and temperatures to improve the scaling of variables and to simplify initial conditions. Artificial dissipation for dissipating unwanted acoustic phenomena is discussed, and an asymmetric interpolation method with filtering properties for minimising numerical diffusion without introducing non physical oscillations is presented. The capabilities of the modelling approach are illustrated with a solution to a Stirling engine model that provides results in good agreement with experimental data. Keywords: Simulation, compressible flow, one dimensional, control volume.