Analytical Modeling of Discharge Flow Dynamics in Scroll Compressors

The dynami~ cha~:-acteristics of scroll compresso~: operation have been demonstrated and analyzed in a number of papers over the past decade. This paper discusses the modeling methods used to describe the scroll ~ompressor discharge dynamics. Nume~:ous models are required to accurately represent this complex dynamic p~:-ocess. These include the differential mass continuity and polytropic compression equations for the scroll pockets during compression and discharge, the isentropic flow equation and geometric area open fo~: flow through the discharge port, and acoustic modeling techniques for p~:essure oscillations in the discha~:-ge manifold. The modeling approach is validated by comparison of the predicted compression and discharge pocket pressure-s with dynamic p~:essure measurements. NOMENCLATURE A Area CD Discharge coefficient fo~: flow gc Gravitational acceleration h Enthalpy of gas Imaginary number m Mass of gas H Number of discrete manifold sections m Mass flow rate of gas np Polytropic exponent N Number of frequency harmonics p Pressu~:-e Q Volume velocity 0 Rate of Heat transfer SOS Start of suction process SOC Start of 'closed' compression process SOD Start of discharge process EOD End of discharge p~:-ocess t Time T Transfer matrix u Inte~:nal energy of gas v Velod ty of gas V Rate of bounda.y vork z Elevation of gas Z Acoustic impedance e Crank angle, or orbit angle position of orbiting scroll Oensi ty of gas ~ Angular frequency 0 Fundamental angular frequency ~ Phase angle of mass flow rate and volume velocity harmonics ~ Phase angle of pressure pulsation harmonics Subscripts c Control volume, chamber D Discharge port do Downstream in,i Into control volume, manifold L Discharge line