Transient heat transfer model and verification for gas cylinder expansion

Expanding gas such as in a piston-cylinder configuration is of considerable interest in power cycles in determining work during the process. In general, there can be considerable energy lost during expansion by heat transfer to the cylinder walls. This is a rather complex heat transfer process despite the rather simply geometry as the gas goes through its state changes. Most existing models either ignore the transient process in particular, and/or are very dependent on empirical input based on expansion rates. This study examines the transient convective heat loss rate during free expansion of a piston/cylinder and develops a transient one dimensional model to capture the time dependent heat loss rate based on a proposed characteristic Peclet number. In addition, the Peclet number is shown to characterize the polytropic expansion of the gas based on experimental expansion data. Results demonstrate the robust nature of the model over a range of expansion initial conditions of pressure and density. The model well predicts the initial peak heat loss rate and subsequent decay without the need for empirical input constants.