This work reports on the derivation of simplified but accurate models to describe gas flow through a bore-piston ring contact in reciprocating machines like compressors or IC engines. On the basis of the aperture field of a contact deduced from real measurements carried out on an expanding ring in a bore, a scale analysis on the complete compressible flow model is performed, assuming ideal gas law. It is shown that the flow can be treated as stationary and three distinct flow regimes can be identified (namely incompressible, compressible creeping, and compressible inertial regimes). Three dimensionless parameters characterizing these regimes are identified. While for the two former regimes, classical analytical Poiseuille type of models are derived, an Oseen approximation is further employed for the latter, yielding a quasi-analytical solution. The models are successfully compared to direct numerical simulations (DNS) of the complete initial set of balance equations in their steady form performed on an aperture field of sinusoidal shape. These simplified models are of particular practical interest since they allow an accurate gas flow-rate estimate through a real contact using the aperture field as the geometrical input datum, together with the thermodynamic conditions (pressure and temperature). This represents an enormous advantage as DNS is still very challenging in practice due to the extremely small value of the contact aperture to contact length ratio.

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.