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Solid particulate mass and number from ducted fuel injection in an optically accessible diesel engine in skip-fired operation

International Journal of Engine Research

Wilmer, Brady M.; Nilsen, Christopher W.; Biles, Drummond E.; Mueller, Charles J.; Northrop, William F.

Ducted fuel injection (DFI) is a novel combustion strategy that has been shown to significantly attenuate soot formation in diesel engines. While previous studies have used optical diagnostics and optical filter smoke number methods to show that DFI reduces in-cylinder soot formation and engine-out soot emissions, respectively, this is the first study to measure solid particle number (PN) emissions in addition to particle mass (PM). Furthermore, this study quantitatively evaluates the use of transient particle instruments for measuring particles from skip-fired operation in an optical single cylinder research engine (SCRE). Engine-out PN was measured using an engine exhaust particle sizer following a catalytic stripper, and PM was measured using a photoacoustic analyzer. The study improves on earlier preliminary emissions studies by clearly showing that DFI reduces overall PM by 76%–79% and PN for particles larger than 23 nm by 77% relative to conventional diesel combustion at a 1200-rpm, 13.3-bar gross indicated mean effective pressure operating condition. The degree of engine-out PM reduction with DFI was similar across both particulate measurement instruments used in the work. Through the use of bimodal distribution fitting, DFI was also shown to reduce the geometric mean diameter of accumulation mode particles by 26%, similar to the effects of increased injection pressure in conventional diesel combustion systems. This work clearly shows the significant solid particulate matter reductions enabled by DFI while also demonstrating that engine-out PN can be accurately measured from an optical SCRE operating in a skip-fired mode. Based on these results, it is believed that DFI has the potential to enable fuel savings when implemented in multi-cylinder engines, both by lowering the required frequency of active diesel particulate filter regeneration, and by reducing the backpressure imposed by exhaust filtration systems.

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Oxygenated Fuel Blending Effects in a Mixing-Controlled Compression-Ignition Engine Equipped with Ducted Fuel Injection [Slides]

Biles, Drummond E.; Mueller, Charles J.; Nilsen, Christopher W.; Wilmer, Brady W.

Continued creation of harmful emissions such as NOx and soot from compression-ignition engines utilizing mixing-controlled combustion systems (i.e., diesel engines) remains a problem and is the subject of on-going research. The inherently high efficiency, relatively low cost, and numerous other desirable attributes of such engines, coupled with a widely supported infrastructure, motivates their continued advancement. Recently, a scientifically distinct and mechanically simple technology called ducted fuel injection (DFI) has shown a robust ability to allow such engines to operate with simultaneously low engine-out soot and NOx emissions when it is employed with simulated exhaust-gas recirculation. To better understand the property ranges of sustainable, oxygenated-fuel blending stocks that will most improve engine performance, two oxygenated blendstocks were separately blended with a commercial diesel base fuel and tested within a heavy-duty diesel optical engine equipped with a four-duct DFI configuration. Conventional and crank-angle-resolved optical diagnostics were used to elucidate the effects of fuel ignition quality, oxygenate molecular structure, and overall oxygen content on engine performance.

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Effects of fuel oxygenation and ducted fuel injection on the performance of a mixing-controlled compression-ignition optical engine with a two-orifice fuel injector

Applications in Energy and Combustion Science

Mueller, Charles J.; Nilsen, Christopher W.; Biles, Drummond E.; Yraguen, Boni F.

This paper describes results from an optical-engine investigation of oxygenated fuel effects on ducted fuel injection (DFI) relative to conventional diesel combustion (CDC). Three fuels were tested: a baseline, non-oxygenated No. 2 emissions certification diesel (denoted CFB), and two blends containing potential renewable oxygenates. The first oxygenated blend contained 25 vol% methyl decanoate in CFB (denoted MD25), and the second contained 25 vol% tri-propylene glycol mono-methyl ether in CFB (denoted T25). Whereas DFI and fuel oxygenation primarily curtail soot emissions, intake-oxygen mole fractions of 21% and 16% were employed to explore the potential additional beneficial impact of dilution on engine-out emissions of nitrogen oxides (NOx). It was found that DFI with an oxygenated fuel can attenuate soot incandescence by ~100X (~10X from DFI and an additional ~10X from fuel oxygenation) relative to CDC with conventional diesel fuel, regardless of dilution level and without large effects on other emissions or efficiency. This breaks the soot/NOx trade-off with dilution, enabling simultaneous reductions in both soot and NOx emissions, even with conventional diesel fuel. Significant cyclic variability in soot incandescence for both CDC and DFI suggests that additional improvements in engine-out soot emissions may be possible via improved control of in-cylinder mixture formation and evolution.

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Heavy-Duty Mixed-Controlled Compression Ignition: Fuel Effects and Ducted Fuel Injection

Mueller, Charles J.

This project is focused on developing advanced combustion strategies for mixing-controlled compression ignition (MCCI, i.e., diesel-cycle) engines that are synergistic with renewable and/or unconventional fuels in a manner that enhances domestic energy security, economic competitiveness, and environmental quality. During this reporting period, the two focus areas were ducted fuel injection (DFI) and surrogate diesel fuels.

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Ducted Fuel Injection vs. Free-Spray Injection: A Study of Mixing and Entrainment Effects Using Numerical Modeling

SAE International Journal of Engines

Nilsen, Christopher W.; Yraguen, Boni F.; Mueller, Charles J.; Genzale, Caroline; Delplanque, Jean P.

Diesel engines are an important technology for transportation of both people and goods. However, historically they have suffered a significant downside of high soot and nitrogen oxides (NOx) emissions. Recently, ducted fuel injection (DFI) has been demonstrated to attenuate soot formation in compression-ignition engines and combustion vessels by 50% to 100%. This allows for diesel engines to be run at low-NOx emissions that would have otherwise produced significantly more soot due to the soot/NOx tradeoff. Currently the root causes of this soot attenuation are not well understood. To be able to better optimize DFI for use across a variety of engines and conditions, it is important to understand clearly how it works. This study expands on the current understanding of DFI by using numerical modeling under nonreacting conditions to provide insights about the roles of entrainment and mixing that would have been much more challenging to obtain experimentally. This study found that DFI enhances charge gas entrainment upstream of the duct and blocks entrainment inside of the duct. Mixing is enhanced by the duct, which results in lower peak equivalence ratios at the exit of the duct.

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Ducted Fuel Injection versus Conventional Diesel Combustion: An Operating-Parameter Sensitivity Study Conducted in an Optical Engine with a Four-Orifice Fuel Injector

SAE International Journal of Engines

Nilsen, Christopher W.; Biles, Drummond E.; Yraguen, Boni F.; Mueller, Charles J.

Ducted fuel injection (DFI) has been shown to attenuate engine-out soot emissions from diesel engines. The concept is to inject fuel through a small tube within the combustion chamber to enable lower equivalence ratios at the autoignition zone, relative to conventional diesel combustion. Previous experiments have demonstrated that DFI enables significant soot attenuation relative to conventional diesel combustion for a small set of operating conditions at relatively low engine loads. This is the first study to compare DFI to conventional diesel combustion over a wide range of operating conditions and at higher loads (up to 8.5 bar gross indicated mean effective pressure) with a four-orifice fuel injector. This study compares DFI to conventional diesel combustion through sweeps of intake-oxygen mole fraction (XO2), injection duration, intake pressure, start of combustion (SOC) timing, fuel-injection pressure, and intake temperature. DFI is shown to curtail engine-out soot emissions at all tested conditions. Under certain conditions, DFI can attenuate engine-out soot by over a factor of 100. In addition to producing significantly lower engine-out soot emissions, DFI enables the engine to be operated at low-NOx conditions that are not feasible with conventional diesel combustion due to high soot emissions.

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Ducted fuel injection vs. Conventional diesel combustion: Extending the load range in an optical engine with a four-orifice fuel injector

SAE International Journal of Engines

Nilsen, Christopher W.; Biles, Drummond E.; Yraguen, Boni F.; Mueller, Charles J.

Ducted fuel injection (DFI) is a technique to attenuate soot formation in compression ignition engines relative to conventional diesel combustion (CDC). The concept is to inject fuel through a small tube inside the combustion chamber to reduce equivalence ratios in the autoignition zone relative to CDC. DFI has been studied at loads as high as 8.5 bar gross indicated mean effective pressure (IMEPg) and as low as 2.5 bar IMEPg using a four-orifice fuel injector. Across previous studies, DFI has been shown to attenuate soot emissions, increase NOx emissions (at constant charge dilution), and slightly decrease fuel conversion efficiencies for most tested points. This study expands on the previous work by testing 1.1 bar IMEPg (low-load/idle) conditions and 10 bar IMEPg (higher-load) conditions with the same four-orifice fuel injector, as well as examining potential causes of the degradations in NOx emissions and fuel conversion efficiencies. DFI and CDC are directly compared at each operating point in the study. At the low-load condition, the intake charge dilution was swept to elucidate the soot and NOx performance of DFI. The low-load range is important because it is the target of impending, more-stringent emissions regulations, and DFI is shown to be a potentially effective approach for helping to meet these regulations. The results also indicate that DFI likely has slightly decreased fuel conversion efficiencies relative to CDC. The increase in NOx emissions with DFI is likely due to longer charge gas residence times at higher temperatures, which arise from shorter combustion durations and advanced combustion phasing relative to CDC.

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Using ducted fuel injection to attenuate or prevent soot formation in mixing-controlled combustion strategies for engine applications

Applied Energy

Gehmlich, Ryan K.; Mueller, Charles J.; Ruth, D.J.; Nilsen, C.W.; Skeen, Scott A.; Manin, J.

Ducted fuel injection is a strategy that can be used to enhance the fuel/charge-gas mixing within the combustion chamber of a direct-injection compression-ignition engine. The concept involves injecting the fuel through a small tube within the combustion chamber to make the most fuel-rich regions of the micture in the autoignition zone leaner relative to a conventional free-spray configuration (i.e., a fuel spray that is not surrounded by a duct). This study is a follow-on to initial proof-of-concept experiments that also were conducted in a constant-volume combustion vessel. While the initial natural luminosity imaging experiments demonstrated that ducted fuel injection lowers soot incandescence dramatically, this study adds a more quantitative diffuse back-illumination diagnostic to measure soot mass, as well as investigates the effects on performance of varying duct geometry (axial gap, length, diameter, and inlet and outlet shapes), ambient density, and charge-gas dilution level. The result is that ducted fuel injection is further proven to be effective at lowering soot by 35–100% across a wide range of operating conditions and geometries, and guidance is offered on geometric parameters that are most important for improving performance and facilitating packaging for engine applications.

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Conceptual Investigation of the Origins of Hydrocarbon Emissions from Mixing-Controlled, Compression-Ignition Combustion

SAE International Journal of Engines

Cheng, A.S.Ed; Mueller, Charles J.

Experiments conducted with a set of reference diesel fuels in an optically accessible, compression-ignition engine have revealed a strong correlation between hydrocarbon (HC) emissions and the flame lift-off length at the end of the premixed burn (EOPMB), with increasing HC emissions associated with longer lift-off lengths. The correlation is largely independent of fuel properties and charge-gas O2 mole fraction, but varies with fuel-injection pressure. A transient, one-dimensional jet model was used to investigate three separate mechanisms that could explain the observed impact of lift-off length on HC emissions. Each mechanism relies on the formation of mixtures that are too lean to support combustion, or “overlean.” First, overlean regions can be formed after the start of fuel injection but before the end of the premixed burn. Second, during the mixing-controlled burn phase, longer lift-off lengths could increase the mass of fuel in overlean regions near the radial edge of the spray cone. Third, after the end of injection, a region of increased entrainment and mixing upstream of the lift-off length could cause late-injected fuel to become overlean. The model revealed a correlation between the lift-off length at EOPMB and overlean regions from the mixing-controlled burn that closely matched experimentally observed trends. HC emissions associated with overlean regions produced either before the end of the premixed burn or after the end of injection did not correspond as well to the experimental observations.

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Ducted fuel injection: A new approach for lowering soot emissions from direct-injection engines

Applied Energy

Mueller, Charles J.; Nilsen, Christopher W.; Ruth, Daniel J.; Gehmlich, Ryan K.; Pickett, Lyle M.; Skeen, Scott A.

Designers of direct-injection compression-ignition engines use a variety of strategies to improve the fuel/charge-gas mixture within the combustion chamber for increased efficiency and reduced pollutant emissions. Strategies include the use of high fuel-injection pressures, multiple injections, small injector orifices, flow swirl, long-ignition-delay conditions, and oxygenated fuels. This is the first journal publication on a new mixing-enhancement strategy for emissions reduction: ducted fuel injection. The concept involves injecting fuel along the axis of a small cylindrical duct within the combustion chamber, to enhance the mixture in the autoignition zone relative to a conventional free-spray configuration (i.e., a fuel spray that is not surrounded by a duct). The results described herein, from initial proof-of-concept experiments conducted in a constant-volume combustion vessel, show dramatically lower soot incandescence from ducted fuel injection than from free sprays over a range of charge-gas conditions that are representative of those in modern direct-injection compression-ignition engines.

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Leaner Lifted-Flame Combustion Enabled by the Use of an Oxygenated Fuel in an Optical CI Engine

SAE International Journal of Engines

Gehmlich, Ryan K.; Dumitrescu, Cosmin E.; Wang, Yefu; Mueller, Charles J.

Leaner lifted-flame combustion (LLFC) is a mixing-controlled combustion strategy for compression-ignition (CI) engines that does not produce soot because the equivalence ratio at the lift-off length is less than or equal to approximately two. In addition to completely preventing soot formation, LLFC can simultaneously control emissions of nitrogen oxides because it is tolerant to the use of exhaust-gas recirculation for lowering in-cylinder temperatures. Experiments were conducted in a heavy-duty CI engine that has been modified to provide optical access to the combustion chamber, to study whether LLFC is facilitated by an oxygenated fuel blend (T50) comprising a 1:1 mixture by volume of tri-propylene glycol mono-methyl ether with an ultra-low-sulfur #2 diesel emissions-certification fuel (CFA). Results from the T50 experiments are compared against baseline results using the CFA fuel without the oxygenate. Experimental measurements include crank-angle-resolved natural luminosity and chemiluminescence imaging. Dilution effects were studied by adding nitrogen and carbon dioxide to the intake charge. Initial experiments with a 2-hole fuel-injector tip achieved LLFC at low loads with the T50 fuel, and elucidated the most important operating parameters necessary to achieve LLFC. The strategy was then extended to more moderate loads by employing a 6-hole injector tip, where lowering the intake-manifold temperature, reducing the coolant temperature, and retarding the start-ofcombustion timing resulted in sustained LLFC at both 21% and 16% intake-oxygen mole fractions at loads greater than 5 bar gross indicated mean effective pressure. In contrast to the results with T50, LLFC was not achieved under any of the test conditions with CFA.

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Investigation of a tripropylene-glycol monomethyl ether and diesel blend for soot-free combustion in an optical direct-injection diesel engine

Applied Thermal Engineering

Dumitrescu, Cosmin E.; Mueller, Charles J.; Kurtz, Eric

Natural luminosity and chemiluminescence imaging diagnostics were employed to investigate if a 50/50 blend by volume of tripropylene-glycol monomethyl ether (TPGME) and ultra-low sulfur #2 diesel certification fuel (CF) could enable leaner-lifted flame combustion (LLFC), a non-sooting mode of mixing-controlled combustion associated with equivalence ratios below approximately 2. The experiments were performed in a single-cylinder heavy-duty optical compression-ignition engine at three injection pressures and three dilution levels. Results indicate that TPGME addition effectively eliminated engine-out smoke emissions by curtailing soot production and/or increasing soot oxidation during and after the end of fuel injection. TPGME greatly reduced soot luminosity when compared with neat CF, but did not enable LLFC because the equivalence ratios at the lift-off length, φ(H), never reached the non-sooting limit and incandescence from hot soot within the combustion chambered remained visible. Concerning other engine-out emissions, injection pressure influenced the effects of TPGME addition on NOx emissions. HC and CO emissions were higher compared to the baseline fuel, likely due to the lower net heat of combustion of TPGME and the need to limit fuel-injection duration for valid optical measurements.

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Diesel Fuel Property Effects on In-Cylinder Liquid Penetration Length: Impact on Smoke Emissions and Equivalence Ratio Estimates at the Flame Lift-Off Length

Energy and Fuels

Dumitrescu, Cosmin E.; Polonowski, Christopher J.; Fisher, Brian T.; Lilik, Gregory K.; Mueller, Charles J.

In this study, elastic scattering was employed to investigate diesel fuel property effects on the liquid length (i.e., the maximum extent of in-cylinder liquid-phase fuel penetration) using select research fuels: an ultralow-sulfur #2 diesel emissions-certification fuel (CF) and four of the Coordinating Research Council (CRC) Fuels for Advanced Combustion Engines (FACE) diesel fuels (F1, F2, F6, and F8). The experiments were performed in a single-cylinder heavy-duty optical compression-ignition engine under time-varying, noncombusting conditions to minimize the influence of chemical heat release on the liquid-length measurement. The FACE diesel fuel and CF liquid lengths under combusting conditions were also predicted using Siebers scaling law and pressure data from previous work using the same fuels at similar in-cylinder conditions. The objective was to observe if the liquid length under noncombusting or combusting conditions provides additional insights into the relationships among the main fuel properties (i.e., cetane number (CN), the 90 vol % distillation recovery temperature (T90), and aromatic content) and smoke emissions. Results suggest that liquid-length values are best correlated to fuel distillation characteristics measured with ASTM D2887 (simulated distillation method). This work also studied the relationship between liquid length and lift-off length, H (i.e., distance from the fuel-injector orifice exit to the position where the standing premixed autoignition zone stabilizes during mixing-controlled combustion). Two possible cases were identified based on the relative magnitudes of liquid length under combusting conditions (Lc) and H. The low-CN fuels are representative of the first case, Lc < H, in which the fuel is always fully vaporized at H. The high-CN fuels are mostly representative of the second case, Lc ≥ H, in which there is still liquid fuel at H. Lc ≥ H would suggest higher smoke emissions, but there is not enough evidence in this work to support a compounding effect of a longer liquid length on top of the aromatic-content effect on smoke emissions for fuels with similar CN, supporting previous findings in the literature that lift-off length plays a more important role than liquid-length on diesel combustion. At the same time, the experimental results suggest a decrease in the fuel-jet spreading angle, i.e., a decrease in the entrainment rate into the jet at and downstream of H, under combusting conditions, that is not accounted for in the model used to predict the values of ø(H). As a result, Lc may be of interest for accurate predictions of ø(H), especially for combustion strategies designed to lower in-cylinder soot by operating near or below the nonsooting ø(H)-value (i.e., ø(H) - 2).

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Analysis of the ducted fuel injection concept for compression-ignition engines

Nilsen, Christopher W.; Mueller, Charles J.

Ducted fuel injection (DFI) is a technique for lowering emissions (primarily soot emissions) from high-efficiency compression-ignition (CI) engines, as well as other devices employing the direct injection of fuel into a combustion chamber. The DFI concept was inspired by the cleaner burn that is created by premixing fuel and air in the tube of a Bunsen burner, which was created to reduce soot production common in burners of the period as stated by Kohn [American Chemical Society, 1949].

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The Visualization of Soot Late in the Diesel Combustion Process by Laser Induced Incandescence with a Vertical Laser Sheet

SAE International Journal of Engines

Lilik, Gregory K.; Mueller, Charles J.; Dumitrescu, Cosmin E.; Gehrke, Christopher R.

Although soot-formation processes in diesel engines have been well characterized during the mixing-controlled burn, little is known about the distribution of soot throughout the combustion chamber after the end of appreciable heat release during the expansion and exhaust strokes. Hence, the laser-induced incandescence (LII) diagnostic was developed to visualize the distribution of soot within an optically accessible single-cylinder direct-injection diesel engine during this period. The developed LII diagnostic is semi-quantitative; i.e., if certain conditions (listed in the Appendix) are true, it accurately captures spatial and temporal trends in the in-cylinder soot field. The diagnostic features a vertically oriented and vertically propagating laser sheet that can be translated across the combustion chamber, where “vertical” refers to a direction parallel to the axis of the cylinder bore. The diagnostic allows soot visualization in almost the entire region above the piston bowl late in the cycle (until the piston descends below the imaged field of view). It also enables estimation of the total in-cylinder soot mass as a function of crank angle. These attributes of the diagnostic allow it to provide unique insights into the production, oxidation, and distribution of soot within the combustion chamber. This manuscript reports on the development of the diagnostic and results from its initial application, in which 21-, 18-, and 16-mol% intake-oxygen conditions were examined.

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Investigation of methyl decanoate combustion in an optical direct-injection diesel engine

Energy and Fuels

Cheng, A.S.; Dumitrescu, Cosmin E.; Mueller, Charles J.

An optically accessible heavy-duty diesel engine was used to investigate the impact of methyl decanoate (MD) on combustion and emissions. Specific goals of the study were to produce experimental data for validating engine combustion models using MD (a biodiesel surrogate), as well as to determine if MD could enable soot-free leaner-lifted flame combustion (LLFC), a mode of mixing-controlled combustion associated with equivalence ratios below approximately 2. An ultralow sulfur diesel certification fuel (CF) was used as the baseline fuel, and experiments were conducted at two fuel-injection pressures with three levels of charge-gas dilution; start of combustion and duration of fuel injection were held constant. In addition to conventional pressure-based and engine-out emissions measurements, exhaust laser-induced incandescence, in-cylinder natural luminosity, and in-cylinder chemiluminescence diagnostics were used to provide detailed insight into combustion processes. Results indicate that MD effectively eliminated soot emissions but that soot formation still occurred in-cylinder, with equivalence ratios at the flame lift-off length in excess of approximately 3. Nevertheless, the oxygen content of MD sufficiently limited soot formation and promoted soot oxidation such that very little soot remained at exhaust-valve open. Nitrogen oxides (NOx) emissions for MD relative to CF showed different trends depending on fuel-injection pressure, with distinct fuel effects influencing NOx formation depending on engine operating condition. Hydrocarbon (HC) and CO emissions were higher for MD compared to CF and corresponded to lower fuel-conversion and combustion efficiencies. These differences were attributed to the lower-load conditions of MD, resulting from its lower energy density and the need to limit fuel-injection duration to obtain valid lift-off length measurements.

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Predictions of Transient Flame Lift-Off Length With Comparison to Single-Cylinder Optical Engine Experiments

Journal of Engineering for Gas Turbines and Power

Mueller, Charles J.

A state-of-the-art, grid-convergent simulation methodology was applied to three-dimensional calculations of a single-cylinder optical engine. A mesh resolution study on a sector-based version of the engine geometry further verified the RANS-based cell size recommendations previously presented by Senecal et al. (“Grid Convergent Spray Models for Internal Combustion Engine CFD Simulations,” ASME Paper No. ICEF2012-92043). Convergence of cylinder pressure, flame lift-off length, and emissions was achieved for an adaptive mesh refinement cell size of 0.35 mm. Furthermore, full geometry simulations, using mesh settings derived from the grid convergence study, resulted in excellent agreement with measurements of cylinder pressure, heat release rate, and NOx emissions. On the other hand, the full geometry simulations indicated that the flame lift-off length is not converged at 0.35 mm for jets not aligned with the computational mesh. Further simulations suggested that the flame lift-off lengths for both the nonaligned and aligned jets appear to be converged at 0.175 mm. With this increased mesh resolution, both the trends and magnitudes in flame lift-off length were well predicted with the current simulation methodology. Good agreement between the overall predicted flame behavior and the available chemiluminescence measurements was also achieved. Our present study indicates that cell size requirements for accurate prediction of full geometry flame lift-off lengths may be stricter than those for global combustion behavior. This may be important when accurate soot predictions are required.

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The quantification of mixture stoichiometry when fuel molecules contain oxidizer elements or oxidizer molecules contain fuel elements

Mueller, Charles J.

The accurate quantification and control of mixture stoichiometry is critical in many applications using new combustion strategies and fuels (e.g., homogeneous charge compression ignition, gasoline direct injection, and oxygenated fuels). The parameter typically used to quantify mixture stoichiometry (i.e., the proximity of a reactant mixture to its stoichiometric condition) is the equivalence ratio, /gf. The traditional definition of /gf is based on the relative amounts of fuel and oxidizer molecules in a mixture. This definition provides an accurate measure of mixture stoichiometry when the fuel molecule does not contain oxidizer elements and when the oxidizer molecule does not contain fuel elements. However, the traditional definition of /gf leads to problems when the fuel molecule contains an oxidizer element, as is the case when an oxygenated fuel is used, or once reactions have started and the fuel has begun to oxidize. The problems arise because an oxidizer element in a fuel molecule is counted as part of the fuel, even though it acts as an oxidizer. Similarly, if an oxidizer molecule contains fuel elements, the fuel elements in the oxidizer molecule are misleadingly lumped in with the oxidizer in the traditional definition of /gf. In either case, use of the traditional definition of /gf to quantify the mixture stoichiometry can lead to significant errors. This paper introduces the oxygen equivalence ratio, /gf/gV, a parameter that properly characterizes the instantaneous mixture stoichiometry for a broader class of reactant mixtures than does /gf. Because it is an instantaneous measure of mixture stoichiometry,/gf/gV can be used to track the time-evolution of stoichiometry as a reaction progresses. The relationship between /gf/gV and /gf is shown. Errors are involved when the traditional definition of /gf is used as a measure of mixture stoichiometry with fuels that contain oxidizer elements or oxidizers that contain fuel elements; /gf/gV is used to quantify these errors. Proper usage of /gf/gV is discussed, and /gf/gV is used to interpret results in a practical example.

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74 Results
74 Results