AUTHOR=Brahma Indranil 

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

JOURNAL=Frontiers in Mechanical Engineering

VOLUME=5

YEAR=2019

URL=https://www.frontiersin.org/journals/mechanical-engineering/articles/10.3389/fmech.2019.00025

DOI=10.3389/fmech.2019.00025

ISSN=2297-3079

ABSTRACT=<p>An assumption of constant discharge coefficient (<italic>C</italic><sub><italic>d</italic></sub>) 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 <italic>C</italic><sub><italic>d</italic></sub> that minimizes the error over the selected points. This quasi-steady assumption is based on asymptotically constant <italic>C</italic><sub><italic>d</italic></sub> observed at high Reynolds number for steady (non-pulsating) flow. It has been shown in this work that this assumption is not accurate 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 <italic>C</italic><sub><italic>d</italic></sub>'s varying between 0.60 and 0.90 for 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 <italic>C</italic><sub><italic>d</italic></sub>'s in the range of 0.25–0.60 with a similar square-edge orifice. The variation in <italic>C</italic><sub><italic>d</italic></sub>was found to be correlated to two dimensionless variables, <italic><bold>η</bold></italic> and ξ, defined as the standard deviation of the pulsating pressure signal, σ<sub>Δ<italic>p</italic></sub>, normalized by <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi><mml:msup><mml:mrow><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mo accent="true">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mo>Δ</mml:mo><mml:mi>p</mml:mi></mml:mrow><mml:mo accent="true">¯</mml:mo></mml:mover></mml:math></inline-formula> across the orifice, respectively. The results suggest that many aspects of compressible pulsating flow through flow restrictions are yet to be understood.</p>