Measurement and Characterization of Flow Resistance of Critical and Near Critical Pulsating Flow through an Orifice Located in the Exhaust Stream of a Diesel Engine

The quasi-steady assumption is often used to determine the flow resistance of highly compressible critical or near-critical (approaching sonic velocity) pulsating flows through engine valves, EGR system and other flow restrictions for modeling and control. The quasi-steady assumption utilizes steady (non-pulsating) flow results where the discharge coefficient (C_d) of flow nozzles/orifices is solely a function of Reynolds number (Re), and C_d is constant at high Re. There exists some literature addressing the flow resistance of incompressible pulsating flows and also for compressible steady flow, but virtually no literature for the highly compressible, critical/near-critical pulsating flow typical in engines. In this work, the C_d of a square edged orifice placed in the exhaust stream of a four-cylinder diesel engine was measured and found not to be a sole function of Re, but correlated to Re. The measured C_d never became constant, varying instead between 0.60-0.90 for Re ranging from 40,000 to 160,000. No single variable could explain the variation in C_d. Instead, the data was shown to reasonably fit a two-dimensional surface, created by a pair of non-dimensional variables. The standard deviation of the pulsating pressure signal was normalized by the dynamic pressure and either the upstream pressure (for critical data) or Δp (for non-critical data) to obtain these two variables. No criteria for classifying pulsating compressible flow as critical or not could be found in literature. In this work, flow was classified using the peak pressure ratio of the pulsating signal to calculate the Mach number using isentropic relations. The critical data was better predicted than the non-critical data and the non-critical data was better predicted when treated as critical. It is possible that pulsating flow might become critical earlier than corresponding steady flow due to acoustic effects. Classification of pulsating compressible flow as critical/non-critical is therefore shown to be an important yet unanswered research question.