This assumption has also been questioned in related areas such as pulsatile pipe flow and the modeling of turbocharger performance related literature has been discussed. Based on the literature and current work, the quasi-static assumption appears to be the biggest source of error. The literature on pulsating flow resistance has historically focused on sources of error when applying steady-flow knowledge to unsteady flow situations.
This is followed by a review of the literature addressing C d measurement in pulsating flow. This allowed a systematic investigation of dimensionless groups that might be correlated with flow resistance.Ī brief theoretical/historical background of steady-flow C d and its direct application to pulsating flow is provided below. To separate causative factors, a pulsating flow apparatus was constructed in which each factor could be independently varied. The engine pulsation parameters were correlated, e.g., pulsation amplitude increased with flow rate. The five engine operating conditions in the preliminary work were expanded to 105 steady state data points for the current work. The current work was initiated as a result of these observations. Steady-flow C d′s are asymptotically constant beyond that Re. A preliminary study investigating the C dof a square-edged orifice installed in the exhaust stream of a diesel engine found that C dkept increasing with Reynold's numbers exceeding 10,000 for steady pulsating flow ( Brahma et al., 2014). The simplest way of investigating this possibility was to measure the discharge coefficient ( C d) of an orifice located in pulsating flow. These investigations suggested the possibility that the flow resistance of flow restrictions, assumed constant at high flow rates/Reynolds numbers, might be a variable for the highly compressible pulsating flows encountered within engines, dependent on the pulsating pattern. The ECM estimates were based on the flow resistance of the EGR valve, EGR flow measurement flow-nozzle, engine intake/exhaust valves and the plumbing of the air-handling system. The inaccurate estimation of in-cylinder Oxygen mass was responsible for the smoke/particulate matter spikes. While trying to determine the root cause of smoke spikes in electronically controlled diesel engines, previous work by the author and co-workers have found that the flow-nozzle based EGR flow estimate as well as the Volumetric Efficiency estimate can be significantly inaccurate during the turbocharger lag period ( Brahma, 2011, 2013, 2014). The results suggest that many aspects of compressible pulsating flow through flow restrictions are yet to be understood.īackground, Motivation, and Existing Literature The variation in C dwas found to be correlated to two dimensionless variables, η and ξ, defined as the standard deviation of the pulsating pressure signal, σ Δ p, normalized by ρ V ¯ 2 and Δ p ¯ across the orifice, respectively.
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 C d's in the range of 0.25–0.60 with a similar square-edge orifice. The discharge coefficient of a square-edged orifice placed in the exhaust stream of a diesel engine produced C d's varying between 0.60 and 0.90 for critical/near-critical flows. It has been shown in this work that this assumption is not accurate for pulsating flow, particularly at large amplitudes and low flow rates.
This quasi-steady assumption is based on asymptotically constant C d observed at high Reynolds number for steady (non-pulsating) flow. 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 C d that minimizes the error over the selected points.