A Numerical Study of Instantaneous Heat Transfer During Compression and Expansion in Piston-Cylinder Geometry

Abstract

Abstract A numerical analysis of the flow and heat transfer in gas springs is presented. A gas spring is a volume of gas with constant mass confined by a moving piston inside a valveless cylinder. Repeated compression and expansion of the gas in the cylinder causes it to heat up. Although there is a heat transfer to and from the gas at different times during a cycle, there is a net flow of heat out of the gas which is equal in magnitude and opposite in direction to the net work done per cycle on the gas. The net work is not recoverable and is called the hysteresis loss. Furthermore, during compression and expansion the in-cylinder heat transfer is out of phase with the bulk gas-wall temperature difference and the conventional Newton’s law is not applicable. Instead of being proportional to bulk gas-wall temperature difference the heat transfer should also depend on the time derivative of the bulk gas temperature. An understanding of the in-cylinder heat transfer is essential in modeling compressors, internal combustion engines and other reciprocating machines. Gas springing is a starting point in constructing correlations for heat transfer during compression and expansion, and in the present paper the unsteady compressible axisymmetric flow inside the cylinder was modeled using a moving coordinate system and a finite volume methodology. Results for instantaneous temperature, pressure and heat flux are presented and discussed. The existing phase difference between the heat transfer and the gas-wall temperature difference is explored. Available correlations are compared with the numerical results showing that the time variation of the bulk gas temperature plays an important role in the heat transfer, this effect tend to decrease as both the crank shaft speed and the volume ratio increase.