Measurement and Prediction of Discharge Coefficients in Highly Compressible Pulsating Flows to Improve EGR Flow Estimation and Modeling of Engine Flows

Abstract

An assumption of constant discharge coefficient (Cd) is often made when modeling highly compressible pulsating engine flows through valves or other restrictions. Similarly, orifices and flow nozzles used for real-time EGR flow estimation are often calibrated at a few steady-state points with one single constant Cd that minimizes the error over the selected points. This assumption is based on near constant Cd observed at high Reynolds number for steady flow. It has been shown in this work that this assumption is not reasonable for pulsating flow, particularly at large amplitudes and low flow rates. The discharge coefficient of a square-edged orifice placed in the exhaust stream of a diesel engine produced Cd’s varying between 0.60-0.90 for the resulting critical/near-critical flows. A novel pulsating flow measurement apparatus that allowed independent variation of pressure, flow rate and frequency and allowed reproducible measurements independent of transducer characteristics, produced Cd’s in the range of 0.25-0.60 with a similar square-edge orifice. The variation in Cd was characterized by two dimensionless variables that normalized the standard deviation of the pulsating signal with dynamic pressure and average differential pressure drop respectively. The results raise important questions that can potentially initiate fundamental work to fill the gap in the literature that exists for highly compressible pulsating flows.