A Predictive Model for Gas Flow Through a Bore-Piston Ring Contact
We report on the derivation of a simplified but accurate model to describe gas flow through a bore-piston ring contact. This is achieved by making use of a scale analysis on the classical mass, momentum and energy equations assuming that the gas obeys ideal gas law. The main regime of interest for practical application in reciprocating machines, corresponding to the compressible flow with inertia is identified and is shown to be free of unsteady terms in the simplified flow equation. For this regime, a quasi analytical solution is further provided that allows the estimation of the axial gas flow rate through the contact. This predictive model is successfully compared to direct numerical simulations of the complete initial set of balance equations performed on a model aperture field of sinusoidal shape. This simplified quasi analytical solution is of particular practical interest since it allows an accurate gas flow rate estimate through a real contact using the aperture field as the only input datum which would not permit a tractable direct numerical simulation otherwise.