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

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 quasi-steady assumption is based on asymptotically constant Cd 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 Cd\u27s 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 Cd\u27s in the range of 0.25–0.60 with a similar square-edge orifice. The variation in Cdwas found to be correlated to two dimensionless variables, η and ξ, defined as the standard deviation of the pulsating pressure signal, σΔp, normalized by ρV¯2 role= presentation style= box-sizing: border-box; display: inline; line-height: normal; font-size: 20px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(62, 61, 64); font-family: Georgia, Times New Roman , Times, serif; position: relative; outline: 0px !important; \u3eρV¯¯¯¯2ρV¯2 and Δp¯ role= presentation style= box-sizing: border-box; display: inline; line-height: normal; font-size: 20px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(62, 61, 64); font-family: Georgia, Times New Roman , Times, serif; position: relative; outline: 0px !important; \u3eΔp¯¯¯¯¯¯¯Δp¯ across the orifice, respectively. The results suggest that many aspects of compressible pulsating flow through flow restrictions are yet to be understood

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

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 quasi-steady assumption is based on asymptotically constant Cd 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 Cd'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 Cd's in the range of 0.25–0.60 with a similar square-edge orifice. The variation in Cdwas found to be correlated to two dimensionless variables, η and ξ, defined as the standard deviation of the pulsating pressure signal, σΔp, normalized by ρV¯2 and Δp¯ across the orifice, respectively. The results suggest that many aspects of compressible pulsating flow through flow restrictions are yet to be understood

Nucleation-accumulation Mode Trade-off in Non-volatile Particle Emissions From a Small Non-road Small Diesel Engine

Small (\u3c 8 kW) non-road engines are a significant source of pollutants such as particle number (PN) emissions. Many small non-road engines do not have diesel particulate filters (DPFs). They are so designed that air–fuel ratio (AFR) can be adjusted to control visible diesel smoke and particulate matter (PM) resulting from larger accumulation mode particles. However, the effect of AFR variation on smaller nucleation mode nanoparticle emissions is not well understood. Several studies on larger engines have reported a trade-off between smaller and larger particles. In this study, AFR was independently varied over the entire engine map of a naturally aspirated (NA) non-road small diesel engine using forced induction (FI) of externally compressed air. AFR’s ranged from 57 to 239 compared to the design range of 23–92 for the engine, including unusually high AFR’s at full-load operation, not previously reported for conventional combustion. As expected, larger accumulation mode particles were lowered (up to 15 times) for FI operation. However, the smaller nucleation mode nanoparticles increased up to 15 times. Accumulation mode particles stopped decreasing above an AFR threshold while nucleation particles continuously increased. In-cylinder combustion analysis showed a slightly smaller ignition delay and higher burn rate for FI cases relative to NA operation. Much higher peak cylinder pressures were accompanied by much lower combustion and exhaust gas temperatures (EGT), due to higher in-cylinder mass during FI operation. Peak nucleation mode emissions were shown to be negatively correlated to EGT for all the data, collapsing on a single curve. This is consistent with some other studies reporting increased nucleation mode emissions (and higher accumulation mode particles) with decreased load, lower speed, lower EGR, advanced combustion phasing, and higher injection pressure, all of which reduce EGT. The nucleation-accumulation trade-off has been explained by the ‘adsorption hypothesis’ by some investigators. In the current work, an alternative/supplemental argument has been made for the possibility that lower cylinder temperatures during the late-burning phase (correlated to lower EGT) phase hampers oxidation of nucleation mode particles and increases nucleation mode emissions

An Investigation into the Accuracy of Orifice Based Flow Estimates for Pulsating Compressible Flows

Orifices, flow nozzles and arbitrarily shaped flow obstructing flow measurement devices are widely used to estimate EGR flow rates in engines, and also used to model flow restricting components like valves in engine analysis tools such as GT-Power. The standard assumptions about the flow discharge coefficient and its variation with Reynolds number are based on investigations of orifices across steady non-pulsating flows, widely reported in literature. In this work, the discharge coefficient for steady state pulsating flow as well as accelerating pulsating flow, commonly encountered during steady state and dynamic engine operation respectively, were investigated by installing an orifice on the exhaust side of a naturally aspirated diesel engine, while making reference flow measurements with a Laminar Flow Element on the intake side. ‘Snap Throttle’ tests were performed to accelerate the flow on the exhaust side with a sudden increase in exhaust gas temperature and accompanying decrease in density. Contrary to reported literature based on steady non-pulsating flow, a linear and directly proportional relationship between coefficient of discharge and Reynolds number was determined for steady state operation at Reynolds numbers exceeding 45,000. The coefficient of discharge changed by about 11% as the Reynolds number increased from approximately 45,000 to 103,000, corresponding to part load and full load steady state conditions at three engine speeds. Compressibility effects were observed to be important. During dynamic operation, the primary source of inaccuracy for the orifice based estimate was determined to be the slow temperature measurement rather than dynamic pressure waves corresponding to the acceleration of flow during the snap throttle event. Another objective of this work was to understand the role of factors other than the fuel-Oxygen ratio in the production of smoke spikes during dynamic operation. Such factors include injector dribbling/overflow caused by pulsations in the fuel injection system, wall impingement, lack of mixture preparation while the full load in-cylinder flow field is established, and the relatively low cylinder wall temperature during the initial period of full load operation. Engine opacity during the snap throttle event was observed to track the fuel-Oxygen ratio, suggesting that these factors were of secondary importance

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 (Cd) of flow nozzles/orifices is solely a function of Reynolds number (Re), and Cd 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 Cd 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 Cd 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 Cd. 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

Analysis and prediction of transient opacity spikes using dimensional modeling

Dimensional modeling, GT-Power in particular, has been used for two related purposes—to quantify and understand the inaccuracies of transient engine flow estimates that cause transient smoke spikes and to improve empirical models of opacity or particulate matter used for engine calibration. It has been proposed by dimensional modeling that exhaust gas recirculation flow rate was significantly underestimated and volumetric efficiency was overestimated by the electronic control module during the turbocharger lag period of an electronically controlled heavy duty diesel engine. Factoring in cylinder-to-cylinder variation, it has been shown that the electronic control module estimated fuel–Oxygen ratio was lower than actual by up to 35% during the turbocharger lag period but within 2% of actual elsewhere, thus hindering fuel–Oxygen ratio limit–based smoke control. The dimensional modeling of transient flow was enabled with a new method of simulating transient data in which the manifold pressures and exhaust gas recirculation system flow resistance, characterized as a function of exhaust gas recirculation valve position at each measured transient data point, were replicated by quasi-static or transient simulation to predict engine flows. Dimensional modeling was also used to transform the engine operating parameter model input space to a more fundamental lower dimensional space so that a nearest neighbor approach could be used to predict smoke emissions. This new approach, intended for engine calibration and control modeling, was termed the “nonparametric reduced dimensionality” approach. It was used to predict federal test procedure cumulative particulate matter within 7% of measured value, based solely on steady-state training data. Very little correlation between the model inputs in the transformed space was observed as compared to the engine operating parameter space. This more uniform, smaller, shrunken model input space might explain how the nonparametric reduced dimensionality approach model could successfully predict federal test procedure emissions when roughly 40% of all transient points were classified as outliers as per the steady-state training data

Advantages and applications of transforming empirical model input space with dimensional models

Model-based calibration of steady-state engine operation is commonly performed with highly parameterized empirical models that are accurate but not very robust, particularly when predicting highly nonlinear responses such as diesel smoke emissions. To address this problem, and to boost the accuracy of more robust non-parametric methods to the same level, GT-Power was used to transform the empirical model input space into multiple input spaces that simplified the input-output relationship and improved the accuracy and robustness of smoke predictions made by three commonly used empirical modeling methods: Multivariate Regression, Neural Networks and the k-Nearest Neighbor method. The availability of multiple input spaces allowed the development of two committee techniques: a ‘Simple Committee’ technique that used averaged predictions from a set of 10 pre-selected input spaces chosen by the training data and the “Minimum Variance Committee” technique where the input spaces for each prediction were chosen on the basis of disagreement between the three modeling methods. This latter technique equalized the performance of the three modeling methods. The successively increasing improvements resulting from the use of a single best transformed input space (Best Combination Technique), Simple Committee Technique and Minimum Variance Committee Technique were verified with hypothesis testing. The transformed input spaces were also shown to improve outlier detection and to improve k-Nearest Neighbor performance when predicting dynamic emissions with steady-state training data. An unexpected finding was that the benefits of input space transformation were unaffected by changes in the hardware or the calibration of the underlying GT-Power model

Reduction of Transient Particulate Matter Spikes with Decision Tree Based Control

Decision trees have been proposed as a basis for modifying table based injection to reduce transient particulate spikes during the turbocharger lag period. It has been shown that decision trees can detect particulate spikes in real time. In well calibrated electronically controlled diesel engines these spikes are narrow and are encompassed by a wider NOx spike. Decision trees have been shown to pinpoint the exact location of measured opacity spikes in real time thus enabling targeted PM reduction with near zero NOx penalty. A calibrated dimensional model has been used to demonstrate the possible reduction of particulate matter with targeted injection pressure pulses. Post injection strategy optimized for near stoichiometric combustion has been shown to provide additional benefits. Empirical models have been used to calculate emission tradeoffs over the entire FTP cycle. An empirical model based transient calibration has been used to demonstrate that such targeted transient modifiers are more beneficial at lower engine-out NOx levels

An alternative derivation of second law results to better relate derivation to practical exergy analysis

A more general and physically intuitive alternative to the classical macroscopic derivation of second law results is proposed. Instead of using imaginary reversible processes occurring within heat engines that operate between infinite temperature reservoirs, the new derivation is applicable to any arbitrary control volume across which heat and/or work interactions occur. The arbitrary control volume is discretized into infinitesimally small elements. So-called ‘Interface Equations’ are developed at the interfaces of these elements, utilizing the second law statement that heat transfer occurs from higher to lower temperatures. Terms from the interface equations are then rearranged at each element to show that dS\u3edQ/T; all other second-law formulation follow from this result. The derivation allows reversible processes to be mathematically defined, which in turn, allows irreversibilities and entropy generation to be understood in terms of spatial non-uniformity of temperature distribution

Development of Dynamic Constraint Models for a Model Based Transient Calibration Process

Model based calibration has gained popularity in recent years as a method to optimize increasingly complex engine systems. However virtually all model based techniques are applied to steady state calibration. Transient calibration is by and large an emerging technology. An important piece of any transient calibration process is the ability to constrain the optimizer to treat the problem as a dynamic one and not as a quasi-static process. The optimized air-handling parameters corresponding to any instant of time must be achievable in a transient sense; this in turn depends on the trajectory of the same parameters over previous time instances. In this work dynamic constraint models have been proposed to translate commanded to actually achieved air-handling parameters. These models enable the optimization to be realistic in a transient sense. The air handling system has been treated as a linear second order system with PD control. Parameters for this second order system have been extracted from real transient data. The model has been shown to be the best choice relative to a list of appropriate candidates such as neural networks and first order models. The selected second order model was used in conjunction with transient emission models to predict emissions over the FTP cycle. It has been shown that emission predictions based on air-handing parameters predicted by the dynamic constraint model do not differ significantly from corresponding emissions based on measured air-handling parameters