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SAE TECHNICALPAPER SERIES 2004-01-0530

Optimization of Injection Rate Shape UsingActive Control of Fuel Injection

Harmit Juneja, Youngchul Ra and Rolf D. ReitzEngine Research Center, University of Wisconsin-Madison

Reprinted From: Diesel Fuel Injection and Sprays 2004(SP-1824)

2004 SAE World CongressDetroit, MichiganMarch 8-11, 2004

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2004-01-0530

Optimization of Injection Rate Shape Using Active Control of Fuel Injection

Harmit Juneja, Youngchul Ra and Rolf D. Reitz Engine Research Center, University of Wisconsin-Madison

Copyright © 2004 SAE International

ABSTRACT

The effect of injection rate shape on spray evolution and emission characteristics is investigated and a methodology for active control of fuel injection is proposed. Extensive validation of advanced vaporization and primary jet breakup models was performed with experimental data before studying the effects of systematic changes of injection rate shape. Excellent agreement with the experiments was obtained for liquid and vapor penetration lengths, over a broad range of gas densities and temperatures. Also the predicted flame lift-off lengths of reacting diesel fuel sprays were in good agreement with the experiments. After the validation of the models, well-defined rate shapes were used to study the effect of injection rate shape on liquid and vapor penetration, flame lift-off lengths and emission characteristics. A consistent trend was observed over the entire range of densities and temperatures, which lead to the conclusion that the fuel distribution can be controlled by modifying the injection rate shape. Since it is believed that the NOx and soot emissions are substantially affected by the equivalence ratio distribution of the gas mixture prior to the combustion, the variation of fuel distribution via the modification of injection rate shape offers a useful way of emission control. From the knowledge gained by this study, a control approach was devised to maintain the local equivalence ratios below a certain level using active control of fuel injection, thus preventing soot formation.

INTRODUCTION

BACKGROUND - Due to their relative simplicity, low capital cost, high power density and high efficiency characteristics, diesel engines enjoy widespread popularity for use as prime movers. However, the diesel engine suffers from relatively high nitrogen oxide (NOx) and particulate matter emissions. In order to improve air quality, legislation on emissions from mobile sources has tightened considerably over the last decade. As emission regulations for heavy-duty diesel engines become stricter, engine manufacturers are increasingly challenged to find methods of reducing emissions without compromising the performance, reliability and

fuel economy that make the diesel engine an obvious choice in a variety of applications.

Modifying the diesel combustion process so as not to produce pollutants is thus very desirable. This is not a simple task since the intermittent, transient spray combustion process of diesel fuel is an extremely complex phenomenon. To precisely control such a complex process, it is necessary to have detailed knowledge of how this spray combustion occurs.

Until recently, little detail was known about the processes inside the cylinder and many descriptions of diesel combustion were based on a number of unproved assumptions. In 1997, a new conceptual model, based on results from various optical diagnostic tools, was presented by Dec [1]. This conceptual model together with work by Naber and Siebers [2-7] on spray penetration, dispersion, vaporization, flame lift-off and an “idealized” spray model have furnished the engine developer with a framework for interpreting experimental measurements. These studies also guide the development of numerical modeling and provide a base for calculations of spray combustion.

The fundamental background for the high emissions of NOx and soot from diesel engines, despite their overall lean operation, is the fuel heterogeneity in the combustion chamber. This fuel heterogeneity stems from the procedure used to introduce the fuel into the hot high-pressure atmosphere when the piston is near top dead center (TDC). Diesel fuel autoignites readily when heated, and the mixing between fuel and air is thus very limited before combustion sets in. This creates a mixing-controlled combustion situation with very hot combustion zones where the fuel and oxygen meet. The production of NOx is favored due to its strong dependence on gas temperature. Fuel rich regions are encountered in the central parts of the reacting fuel spray and these promote the formation of soot.

This heterogeneous spray combustion process of the diesel engine is highly dependent on the fuel injection parameters. Modifying the injection rate-shape offers a great deal of flexibility in terms of controlling the amount of fuel available for mixing and combustion. In addition,

modifying the injection rate changes the momentum of the spray, which can either enhance or reduce the fuel/air mixing rate. Though little research has been performed regarding the effect of injection rate shape on spray evolution [8,9], the primary focus has been on the application of optimization techniques to split injections that are useful to improve overall performance. The effect of the shape of an individual injection pulse is not well understood and it is important to study the effect of the rate shape on spray and combustion phenomena.

To understand the overall effect of the injection rate shape, it is necessary to study its influence on individual phenomenon such as drop breakup, coalescence and vaporization. In order to ensure the reliability of computational models, spray processes such as breakup, collision and vaporization must be modeled accurately and validated extensively with experimental data.

OBJECTIVE

The objective was to study the effectiveness of the injection rate-shape as a means of controlling diesel spray combustion. It is a purely computational study, which uses the capabilities of the KIVA code [12] to investigate injection rate-shape effects on spray liquid and vapor penetrations, and the flame lift-off lengths of sprays over a wide range of ambient gas density and temperature. In addition the influence of rate-shape on NOX and soot emissions was studied. The role of fuel-air mixing upstream of the flame lift-off length has been identified as a very important parameter which affects the soot formation [5]. Different injection rate-shapes were investigated and the advantages of one rate-shape over the other are explained in terms of factors such as liquid and vapor penetration and fuel/air mixing upstream of the flame lift-of length.

Another goal of the project was to validate the KIVA-3V code [12], with improved sub models for droplet vaporization [13] and primary jet breakup [14] and with the use of a detailed chemical kinetics mechanism to describe combustion. These advanced models capture the physics of droplet vaporization and atomization in an accurate manner and provide increased confidence in the computational results.

The ultimate objective of this work is to utilize the improved knowledge of injection effects to develop a feedback control based approach to reduce NOX and soot emissions through active control of fuel injection. For this purpose in-cylinder equivalence ratio feedback control was explored. It has been well established that soot forms in regions with equivalence ratios ranging from two to four [1] and NOX forms in regions that are close to stoichiometric [15]. If the local equivalence ratios in the cylinder are maintained below a value of two, substantial reduction in soot formation can be realized. In order to achieve emissions reduction, injection pulse width modulation is used as a tool in this study, coupled with a feedback control approach. Fuel is

injected in pulses and the amount of fuel vapor above a certain equivalence ratio is monitored during the injection event. A simple PD (proportional-derivative) control algorithm is devised which uses this information as an input to calculate the optimum dwell time between successive injection pulses. As a result, better fuel-air mixing is achieved resulting in lower equivalence ratio regions within the cylinder and hence lower soot formation. Varying the injection rate-shape directly affects the formation of soot as the fuel distribution is altered. However, the effect on NOX is indirect, since it depends on the temperature field and temporal history inside the cylinder.

CFD MODELS

In the present work, the KIVA-3V Release 2 code [12] was modified with improved models for atomization and vaporization and applied to simulate spray evolution under well characterized diesel-engine-like conditions.

A one-dimensional primary break-up model [14] that is computationally effective as well as comprehensive enough to account for the effects of aerodynamics, liquid properties and nozzle flows was employed. This model uses the concept of “blobs”, and, takes advantage of the benefits of Lagrangian and Eulerian methods. The blobs are tracked by the Lagrangian method while the break-up of each blob is calculated by a Eulerian method. For the secondary and further break-up processes, a Kelvin Helmholtz (KH) – Rayleigh Taylor (RT) hybrid model [20] was used.

A droplet collision model based on the stochastic particle method [12] was used, in which collision frequency is used to calculate the probability that a drop in one parcel will undergo a collision with a drop in another parcel, assuming all drops in each parcel behave in the same manner.

An advanced unsteady vaporization model [13] was used to predict the evaporation process of a spray more realistically. In this model, an unsteady internal heat flux model, a new model for the determination of the droplet surface temperature, and an equation to calculate the external heat flux with the inter-diffusion of fuel vapor and the surrounding gas taken into account, were incorporated. Also, this model considers droplet temperature ranges from flash-boiling conditions to normal evaporation.

MODEL VALIDATION

Model validation was one of the preliminary goals of this study. Accordingly, the KIVA3V code [12] was validated, with improved sub models for droplet vaporization [13] and primary jet breakup [14], and with the use of a detailed chemical kinetics mechanism to describe combustion [18]. The first step was to validate the models in an inert environment by comparing the computed spray liquid and vapor penetration lengths with experimental data [3,16]. For the reacting cases, the

flame lift-off lengths were compared to the available experimental results [5] over a wide range of density and temperature. Liquid and vapor penetrations and flame lift-off lengths were chosen as validation parameters, because they are relatively easy to measure and they reflect the major observable characteristics of spray evolution and combustion. The spray calculations were conducted using a 2-D axisymmetric mesh, as shown in Fig. 1. The grid size was 1mm in the radial direction and 2 mm in the axial direction. Beale and Reitz [20] suggested a 1x1 mm grid, but it was observed that a resolution of 2 mm in the axial direction did not affect the results and the difference was less than 5%. The injector was located at the top left cell of the mesh and the spray was injected downward along the axis.

Fuels Experiment : DF2 Simulation : Tetradecane

Ambient Gas Density (kg/m3) 7.3 , 14.8, 30.2, 59

Ambient Gas Temperature (K) 700, 850, 1000, 1300

Orifice Diameter 246 mµ Nozzle L/D ratio 4.2 Discharge Coefficient 0.8 Injection Pressure 136 MPa Fuel Temperature 438 K Injection Duration 4 ms

Table 1 Operating conditions considered for comparison of liquid penetration length results [3].

Figure 1 2-D axisymmetric mesh for spray calculation. 0 1 2 3 4

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Figure 2 Injection rate shape used in the computation of liquid penetration length. The rate shape is similar to the top hat profile used in the experiment [3].

Liquid Penetration Length

The computed liquid penetration length of sprays was compared with the experimental results of Siebers [3]. The operating conditions considered in the computations are summarized in Table 1. The fuel injector used in the experiment was a prototype, electronically controlled, common-rail, solenoid activated injector designed by Detroit Diesel Corporation. The injection rate shape employed has a very rapid start and end of injection with a constant injection rate during the injection (i.e., a “top hat” profile) as shown in Fig. 2.

In the conventional spray breakup model (Kelvin Helmholtz model), a breakup length is assumed which prevents droplets within a certain distance from the injector tip, from being subject to secondary breakup. However, in the new breakup model every droplet is subject to secondary breakup, irrespective of its distance from the injector tip. Using the standard model constants resulted in excessive breakup and, consequently, smaller drop sizes, resulting is shorter liquid penetration lengths. A value of 0.2 was used for the adjustable RT model constant C3 (cnst3rt in KIVA) to increase the time between breakup events, resulting in larger child droplets and hence longer liquid penetration lengths. The results are shown in Fig. 3. It is seen that use of the unsteady vaporization model and the new primary jet breakup model results in good agreement between the measured and computed data.

The computations were carried out using a nozzle discharge coefficient of 0.8, consistent with the experimental data. In this study, the liquid length was determined as the distance from the injector tip to the point where the mass of the liquid phase accumulated from the injector tip is greater than 95 % of total liquid phase at that time.

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Figure 3 Liquid penetration as a function of gas temperature for different ambient gas densities, using version 3. The fuel, injection pressure and orifice diameter are DF2, 135 MPa and 0.246 mm, respectively. The filled and hollow symbols represent measured and computed data, respectively.

Fuels

Experiment : n-dodecane doped with naphthalene(9%) and TMPD(1%) Simulation : Dodecane

Ambient Gas Density 7.5 kg/m3 and 15 kg/m3 Ambient Gas Temperature 800, 1000 and 1200 K

Orifice Diameter 158 mµ Nozzle Discharge Coefficient 0.7

Injection Pressure 90 MPa Fuel Temperature 298 K Injection Duration 1.4 ms

Table 2 Operating conditions considered for comparison of vapor penetration length results [16].

Figure 4 Vapor penetration as a function of time at an ambient gas density of 7.5 kg/m3. The values in the legend correspond to ambient temperature.

Vapor Penetration Length

The constants and models were optimized to give the best predictions of the liquid penetration length. Thus, it was of interest to verify that the vapor penetration results were also correct. In the computations, the vapor penetration was measured as the distance along the spray axis, from the injector tip to the point where the fuel vapor mass fraction is 0.001. The experiments of Kim and Ghandi [16] provide vapor penetration lengths for the desired range of interest. The experiments used an exciplex laser induced fluorescence technique with TMPD(Tetra-methyl-p-phenilene-diamine)/naphthalene doped into the fuel, to quantitatively determine the vapor phase concentration.

Table 2 summarizes the operating conditions for which the models were validated. The computations were carried out using a nozzle discharge coefficient of 0.7, estimated with the method of Sarre et al. [19].

located in the right place when combustion occurs.

Flame Lift-Off Length

The flame that is stabilized on a high injection pressure DI diesel spray under quiescent conditions is located some distance downstream of the fuel injector. The distance from the injector to the location of stabilization is referred to as the flame “ lift-off ” length. The position of the lift-off length in diesel sprays is determined by premixing of the injected fuel and the entrained air upstream of the lift-off length. There is growing evidence to suggest a strong link between the fuel-air mixing upstream of the lift-off length and soot formation [5, 10].

Figures 4 and 5 compare the vapor penetration length measurements of Kim and Ghandi [16] to the computed results for gas densities of 7.5 and 15 kg/m3 respectively. The present predictions are seen to agree well with the experimental measurements. The model predicts the correct magnitudes, as well as the correct rate of penetration. This implies that the correct gas flow field and fuel-air mixing rates are calculated. It also implies that when the model is applied to engine simulations, the combustible fuel-air mixture will be

Figure 5 Vapor penetration as a function of time at an ambient gas density of 15 kg/m3. The values in the legend correspond to ambient temperature.

Figure 6 Flame lift-off length determined by means of temperature and OH radical concentration at 6.0 ms after start of injection (ASI). Ambient gas density – 14.8 kg/m3, Ambient temperature – 900 K.

Fuels Experiment : DF2 Simulation : Tetradecane

Ambient Gas Density (kg/m3) 14.8 and 30.2

Ambient Gas Temperature (K) 900, 1000 and 1100

Orifice Diameter 180 mµ Nozzle Discharge Coefficient 0.77

Nozzle L/D ratio 4.2 Injection Pressure 138 MPa Fuel Temperature 438 K Injection Duration 6 ms

In the previous section, the validation of models in inert environments was carried out by comparing the liquid and vapor penetration lengths with experimental data. Under inert conditions the predictions were shown to be acceptably accurate, but a reacting environment poses a more important test for models to be used in engine combustion applications. As discussed in the previous paragraph, flame lift-off is an important parameter for diesel combustion. Also, extensive data is available in the literature [5-7], for comparison with computational results. Therefore, flame lift-off length was chosen as a parameter for validation of models in a reacting environment. In this case, along with the improved spray and vaporization models, the KIVA3V code was coupled with the CHEMKIN code with a 62-species skeletal chemistry mechanism for n-heptane fuel. This mechanism was modified from the 40-species mechanism of Ref. [17] by adding NOx reactions.

Table 3 Operating conditions considered for comparison of flame lift-off length results [5].

performed are summarized in Table 3. Research on lifted, turbulent diffusion flames shows that stoichiometric or near stoichiometric combustion occurs at the flame stabilization location, i.e., at the lift-off length [5]. Because the energetic reactions in stoichiometric combustion form excited state species, including excited OH radicals, the measurement of the distribution of OH radicals by chemiluminescence provides an excellent marker of the high heat release regions, such as the stoichiometric combustion region at the lift-off length. As was done in the experiments, the first location from the injector tip in the axial direction that showed a maximum OH radical amount was selected to indicate the lift-off length location of the flame in the numerical simulations. This observation was confirmed by monitoring the temperature distribution, which also indicates the most upstream location of combustion, as shown in Fig. 6.

Fig. 7 shows the predicted temperature distribution of a reacting spray at an ambient gas density of 30 kg/m3 and an ambient temperature of 900K. The flame lift-off length is marked with a white vertical line in the temperature distribution. This corresponds to the data point represented by the inverted triangle on the lift-off length vs. ambient temperature plot shown in Fig. 8 for various densities. Fig. 8 also shows the experimental results of Siebers [5]. Other conditions for which the simulations were carried out (see Table 3) are shown by the triangle data points on the same plot. As can be seen, excellent agreement was obtained between the measured and computed flame lift-off trends for all cases considered in the present study.

The operating conditions for which the simulations were

Figure 7 Predicted flame lift-off length for an ambient gas density = 30 kg/m3 ,T = 900K).

0.00.0

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Figure 9 Typical injection rate shape of the Caterpillar HI90 diesel injector and a simpler triangular representation.

can be appropriately approximated using three parameters, i.e., the injection duration, τd, the timing of peak velocity, τp, and the absolute value of the peak velocity, Vp.

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Figure 8 Measure(triangles) flame liftemperature (K) for kg/m3.

If the total amount of fuel injected is maintained constant when the injection rate shape is varied, the area under the injection rate profile would be the same for all possible variations of the rate shapes.

14.8 kg/m3

NON-REACTING SPRAY CASES

The computations were conducted using the KIVA code

INJECTION RATE

With confidence inthe validations of rmodels as describeeffect of injection combustion charact

Fig. 9 shows a typithe Caterpillar HI90[16] and its simpletriangular form. As c

30 kg/m3

950 1000 1050 1100

mbient Gas Temperature (K)

d (open squares) and computed t-off length (mm) vs. ambient gas ambient gas densities of 14.8 and 30

and the numerical grid shown in Fig. 1. Four different well-defined rate shapes were employed to study the effect of injection rate shape on the spray evolution under non-reacting conditions, as shown in Fig. 10. Three of them are triangular in shape (ROI 1,2 and 3), and the other has a top-hat (constant velocity) shape. In order to inject the same amount of fuel, the velocity of the top-hat shape was set to be equal to half of the peak velocity reached by the triangular shapes. ROI 1 represents a rapidly rising and slowly falling injection velocity profile, while ROI 3 represents a slowly rising and rapidly falling injection velocity profile. In ROI2, the rising and falling rates of the velocity are symmetric. The duration of injection was chosen to be 1.4 ms for all cases. The operating conditions considered are listed in Table4.

-SHAPE EFFECTS

the modeling accuracy affirmed by eacting and non-reacting cases, the d earlier, were applied to study the rate shape on spray evolution and eristics.

The location of the liquid and vapor tip penetration lengths was determined from the liquid and vapor mass distributions as described in the previous section. A consistent trend in the predicted liquid and vapor penetration lengths was observed as the different injection velocity histories influenced the breakup, coalescence and vaporization characteristics of the sprays, as described next.

cal measured injection rate shape for injector used by Kim and Ghandi r representation obtained using a an be seen, the actual rate shape

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

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Figure 10 Injection rate shapes considered for sprays in a non-reacting environment.

Fuel Dodecane

Ambient Gas Density 7.5 kg/m3 and 15 kg/m3

Ambient Gas Temperature 1200 and 1000 K for 7.5 and 15 kg/m3 respectively.

Orifice Diameter 158 mµ Nozzle Discharge Coefficient 0.7 Injection Pressure 90 MPa Fuel Temperature 298 K Injection Duration 1.4 ms

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

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Figure 11 Liquid penetration vs. time for low-density conditions (7.5 kg/m3) using the injection rate shapes shown in Fig.10.

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Figure 12 Liquid penetration length vs. time for high-density conditions (15 kg/m3) using injection rate shapes shown in Fig. 10.

Table 4 Operating conditions considered for investigating the effect of injection rate shape on liquid and vapor penetration lengths for a vaporizing dodecane spray in an inert environment.

Figures 11 and 12 show the predicted liquid penetration lengths for the investigated rate shapes under low gas density (7.5 kg/m3) and high gas density (15 kg/m3) conditions, respectively. By comparison with Fig. 10, it can be seen that the location of the highest peak of the liquid length is closely coupled with the timing of the peak injection velocity in each case.

As the timing of the peak injection velocity is retarded, it takes longer to reach the maximum liquid penetration length, and the liquid penetrates further from the nozzle. The reason for the existence of a peak in the liquid penetration length and the differences in the peak values can be explained as follows.

vaporization. When droplets are injected during the rising part of the injection rate shape, the later injected drops catch up with the earlier injected ones after a time interval that is a function of the two injection timings of interest (the catch-up effect). This creates a closely spaced group of spray droplets and this favors increase in the collision frequency, and, consequently, increases the probability of coalescence among droplets, which produces bigger droplets. Bigger droplets have higher momentum and penetrate further. On the contrary, when droplets are injected during the falling part of the

There are distinctive characteristics of the rising and falling parts of the rate shapes (ROI1~ROI3). Consider first, a simple case that assumes no break-up and no

injection rate shape, the later injected drops tend not to catch up with the earlier injected drops, and the distance between the spray droplets increases with time (the scattering effect). This tends to decrease collision and coalescence frequencies, and hence drop sizes, and hence the tip penetration rate is reduced.

As far as break-up and vaporization are concerned, the injection velocity of the spray drops plays a key role in these processes too [21]. Higher injection velocities lead to faster break-up and hence more vaporization due to the small drop sizes. Also, because the mean size of child droplets after break-up decreases as the droplet velocity increases [20], the momentum as well as the life-time of the individual vaporizing droplets decreases. Therefore, additional liquid penetration becomes substantially shortened. This causes the peak liquid penetration to decrease as the rising slope of the triangular rate shapes increases (see e.g. ROI3 → ROI1). Once the coalesced spray, which experienced the catch-up effect vaporizes completely, the following spray droplets which experience less collision and coalescence by the arguments mentioned above, penetrate shorter distances and the liquid penetration curve falls.

Figures 13 and 14 show the corresponding variation of vapor penetration length with time for the different injection rate shapes (shown in Figure 10) under low density (7.5 kg/m3) and high density (15 kg/m3) conditions, respectively. It can be observed that the slope of the rising part of the rate shapes governs the initial slope of the vapor penetration length curve. Also, the different rate shapes, the asymptotic vapor penetration lengths become almost equal regardless of

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Figure 13 Vapor penetration length vs. time for the different injection rate shapes shown in Fig. 10. (Density = 7.5 kg/m3, T=1200K).

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Figure 14 Vapor penetration length vs. time for the different injection rate shapes shown in Fig. 10. (Density = 15 kg/m3, T=1000K).

the timing of the peak injection velocity after a sufficient time, for cases where the peak velocities are same. Since the velocity of the top-hat rate shape case was half that of the triangular shapes, the vapor penetration of the top-hat case at 2.0 ms is shorter than those of the triangular shapes, though its initial slope is the highest of all the cases. These differences are due to differences in the total injected momentum of the sprays, which are higher for the triangular sprays.

These results show that the fuel distribution (liquid and vapor) can be modified by changing the injection rate shape, which implies that combustion can also be modified to some extent by changing the injection rate shape.

REACTING SPRAY CASES

The effect of injection rate shape on the combustion characteristics of sprays under reacting conditions is discussed next. The three representative rate shapes considered are shown in Fig. 15. An injection duration of 6 ms was chosen for all cases. The operating conditions are summarized in Table 5.

Fig. 16 a) to i) show the temporal evolution of the predicted flames for the three different rate shapes. It can be observed that ignition takes place earliest in the case of the top-hat profile (at 1.2 ms ASI), whereas the longest ignition delay is seen in the case of the late peak case, ROI2 (at 2.0 ms ASI). However, the ranking of the ignition distance from the nozzle varied as, ROI2, top-hat and ROI1, with the location of ROI2 being the closest to the injector tip. This confirms that the air-fuel mixing details are greatly affected by the change of the

Fuel Tetradecane Ambient Gas Density 14.8 kg/m3 Ambient Gas Temperature 900 K Orifice Diameter 180 mµ Nozzle Discharge Coefficient 0.77 Nozzle L/D ratio 4.2 Injection Pressure 138 MPa Fuel Temperature 438 K Injection Duration 6 ms

Table 5 Operating conditions considered for investigating the effect of injection rate shape on flame evolution for a vaporizing tetradecane spray in a reacting environment.

0 1 2 3 4 5 60.0

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Figure 15 Injection rate shapes considered for sprays in a reacting environment.

Figure 16 a) – i) Temporal evolution of the flame temperature for the three different rate shapes of Fig. 15. From left to right : Top Hat, ROI 1 and ROI 2. Ambient gas density 14.8 kg/m3, Ambient temperature 900 K.

injection rate shape.

The injection velocity for ROI 1 is the highest earliest, hence the vapor cloud travels farthest and ignition takes place further downstream. However, due to its very low injection velocity initially, the tip of the vapor cloud for ROI 2 is very close to the liquid penetration length, and the ignition is predicted to take place just downstream of the liquid penetration length.

It is interesting that the direction of the evolution of the flame lift-off locations was observed to be different for these three cases. In the case of ROI2, the ignition took place very close to the injector and the flame stabilized at the ignition location very soon, while, in the case of ROI 1, ignition took place further downstream and then the flame traveled upwards towards the nozzle and finally stabilized. Since the injected fuel has more time to mix with the ambient air before entering the reaction zone for ROI 1, leaner mixtures are expected compared to ROI 2, for which the flame lift off length is very small and the injected fuel has insufficient time to mix with the ambient air. This has direct implications on the formation of soot and NOX, which is discussed in the next section.

Soot and NOX Formation

The current detailed kinetics mechanism does not consider soot models. However, acetylene is known to be a very important pre-cursor for soot formation [15], so it gives a good indication of the propensity and location of soot formation for each injection rate shape. Acetylene is available in the chemistry mechanism and thus it was monitored in the present study. Fig. 17 shows the predicted temporal histories of the amount of acetylene (C2H2) for the three injection rate shapes corresponding to the results given in the previous section.

In the case of ROI 2 (for most of the injection the injection velocities are on the rising part of the shape), the fuel droplets upstream of the flame lift-off location, which were injected at higher velocities (or a higher flow rate) than the earlier spray droplets, enter the reaction zones with the entrained air. But the insufficient mixing

Figure 18 Temporal history of NO for different injection rate shapes.

Figure 17 Temporal history of acetylene for the different injection rate shapes given in Fig. 15. Ambient gas density 14.8 kg/m3, temperature 900 K.

concept of reduced soot formation with a falling rate of injection has been discussed by Beck et al. [22] and Azetsu and Wakisaka [25].

times and oxidizer amounts result in high levels of soot production during the early period of the injection, which can be seen from the large predicted amounts of C2H2. However, as the injection velocities increase on the rising part of ROI 2, the entrainment of air is enhanced and this favors the later oxidation of the soot precursor species produced earlier.

ACTIVE CONTROL OF FUEL INJECTION

CONTROL FORMULATION

From the previous results, it can be concluded that spray evolution is changed effectively by modifying parameters that determine the injection rate-shape, i.e., injection duration, timing of peak injection velocity and absolute value of the peak velocity. It was also seen that injection rate-shape affects ignition characteristics and the temporal history of soot and NOx formation. This implies controllability of emissions by optimization of the injection rate shape.

On the contrary, in the case of ROI 1, because the high injection velocity occurs at the early stage of the injection, it entrains more air that mixes with the fuel vapor. Thus, the reactions following ignition result in lower soot precursor species formation rates. Another reason for the low formation of soot in the case of ROI 1 is that, once the air entrainment is sufficiently enhanced, the spray droplets injected at lower velocities (on the falling part of ROI 1) have enough residence time to mix with air before entering the reaction zones. Thus, it seems that ROI 1 offers a better method to control soot as it inhibits the formation of soot in the first place, though a fair amount of soot oxidation takes place towards the end of the injection for ROI2.

It has been well established that soot forms in regions with equivalence ratios ranging from two to four [1] and NOX forms in regions that are close to stoichiometric [15]. If the local equivalence ratios in the cylinder are maintained below a value of two, substantial reduction in soot formation can be realized. Varying the injection rate-shape directly affects the formation of soot as the fuel distribution is altered. However, the effect on NOX is indirect, since it depends on the temperature field and temporal history inside the cylinder.

Fig. 18 shows the corresponding temporal histories of the NOx formation for the three injection rate shapes. It is seen that, for times during the injection (e.g. before 5.0 ms), the lower heat release due to insufficient mixing of the fuel and air in the case of ROI2 forms very low levels of NOx, while the ROI1 case shows a steady increase of NOx formation because better mixing enhances the energy release reactions. However, as the oxidation reactions become more vigorous towards the end of injection for ROI2, the heat release rate increases rapidly, and thus the formation of NOx also increases rapidly.

In order to achieve this objective, an in-cylinder equivalence ratio feedback control approach was explored using a purely computational approach. The idea is to inject the fuel in pulses and control the duration between successive injection pulses based on monitoring the equivalence ratio and providing feedback from the cylinder. The concept is explained by means of the schematic shown in Fig. 19.

The above trends are consistent with earlier predictions of the effect of injection rate shape on emissions in engine computations by Mather and Reitz [11], and the

The fuel is injected in pulses of duration tp. After injection of fuel in the first pulse, the fuel vapor above a certain threshold equivalence ratio φo is monitored. The local

Figure 19 Schematic for active control of fuel injection. φo is the desired equivalence ratio.

Figure 20 Maximum Local Equivalence ratio vs Time for the rate shapes shown in Fig. 15 and the conditions listed in Table 5.

equivalence ratio (φ ) is traced in all the grid cells and the fuel vapor is categorized as being lean, flammable or rich based on the following criteria:

φ < 0.5 Lean vapor Mass

0.5 < φ < 2.0 Flammable Vapor Mass

inside the combustion chamber for the fuel injection control.

φ > 2.0 Rich Vapor Mass

The lean, flammable and rich vapor mass is then normalized by the total injected mass to obtain lean, flammable and rich vapor fractions respectively. The local equivalence ratio (φ ) information is then supplied to the control algorithm, which calculates the duration between successive injection pulses (td). φo is the reference value of the equivalence ratio (i.e., the set point). td is inversely proportional to the difference between the local equivalence ratio in the cells (φ ) and the reference equivalence ratio (φo). This poses a problem because the information contained in φ should be a good representation of the equivalence ratio distribution inside the entire combustion chamber. Initially, it was decided that the maximum value of the local equivalence ratio could be a good choice forφ, based on the assumption that maximum soot concentrations will be formed in the richest regions of the combustion chamber.

Fig. 21 shows the plot of rich vapor fraction (i.e., φ > 2.0) with time. The arrows in the figure indicate the time of ignition for the three rate shapes. It can be seen that the rich vapor fraction for the top hat rate shape is higher than that for ROI 1, which is consistent with the results shown in Fig. 17. It was observed that the amount of rich vapor mass at the time of ignition also affects the soot formation. As discussed earlier, the fuel-air mixing in the case of ROI 1 is much better at early times than that of ROI 2, resulting in leaner mixtures at the time of ignition, which leads to decreased amount of soot formation.

Figure 21 Rich vapor fraction vs Time for the rate shapes shown in Fig. 15 and the conditions listed in Table 5.

Simulations were carried out using the rate shapes shown in Fig. 15 for the same conditions as those listed in Table 5. A value of two was chosen for the reference equivalence ratio (φo), based on the hypothesis that as soot begins to form in regions with equivalence ratios greater than two [1]. Referring to Fig. 17, it is expected that the maximum local equivalence ratio will be the highest in the case of ROI2, followed by the top hat profile and finally ROI 1. Fig. 20 shows a plot of the maximum local equivalence ratio with time for the three different rate shapes, i.e., ROI 1, ROI 2 and the top hat. As expected, the maximum equivalence ratio levels in case of ROI 2 are much higher compared to those of ROI 1 and the top hat rate shape. But, by the same reasoning, the maximum local equivalence ratio in case of the top hat rate shape should be higher than ROI 1 as more soot is expected to be formed in that case (see Fig. 17). This shows that maximum local equivalence ratio alone is not sufficient to represent the conditions

From these results, it can be concluded that the rich vapor fraction and the maximum local equivalence ratio are the two important parameters which should be used in the control criteria to determine the duration between successive injection pulses (td). The control criteria is formulated as a proportional derivative (PD) type expression as :

Figure 22 Injection rate shapes for comparing the results of the control rate shape (solid line) with the baseline (dash-dot) and high injection velocity (dash) rate shape.

( )( )d p pde tt K e t K Ddt

= + (1)

( ) ( ) orich riche t f t f= − (2)

where Kp is the proportional gain and D is the damping constant. The first term on the right hand side of Eq. 1, is the proportional term and the second term is the derivative term. The error term at time t, i.e. e(t) is the difference between the rich vapor fraction at time t, frich(t), and the set point i.e. the reference rich vapor fraction, o

richf .

RESULTS

CONSTANT VOLUME BOMB SIMULATIONS Figures 23 and 24 show the temporal history of the amount of acetylene and NO formation respectively, for the three rate shapes shown in Fig. 22. It can be seen that in case of the controlled rate shape, the fuel has sufficient amount of time to mix with air during the dwells between injections which discourages the formation of rich regions inside the bomb, thereby reducing the soot precursor formation drastically compared to the baseline cases. Since the residence time in the case of the controlled rate shape (12 ms) is higher compared to the other two cases, the amount of NO formed is also higher.

In order to ascertain the efficacy of this approach, preliminary simulations were carried out for spray injections in a constant volume bomb. The grid used was the same as shown in Fig. 1, and the operating conditions are listed in Table 5. The baseline case corresponds to the top hat rate shape shown in Fig. 15. The injection velocity used in the case of the top hat profile was 386 m/s. The amount of fuel injected was constant for all the cases and the rate shape was determined by the control algorithm. A set point of 0.45 was chosen, which corresponds to a reference rich vapor fraction, f 0

rich = 45%. The duration of an individual injection pulse was chosen to be 0.4 ms (similar to the minimum injection duration attainable with current injection hardware [23]) and the magnitude of the injection velocity for the control case was 518 m/s. In order to quantify the effect of injection velocity another case with a top hat profile corresponding to an injection velocity of 662 m/s was simulated. The solid line in Fig. 22 shows the rate shape obtained using the control algorithm. The other two rate shapes corresponding to the baseline case (duration: 6ms) and high injection velocity case (duration: 3.5 ms) are also shown. The total injection duration of the controlled rate shape was approximately 12 ms, which is twice as long as the baseline top hat rate shape having a duration of 6 ms.

Figure 23 Temporal history of acetylene formation for the rate shapes shown in Fig. 22.

Note that, in order to avoid long periods of no injection, constraints could be applied to the control formulation to restrict the maximum duration between successive injection pulses. It is also important to impose a constraint on the minimum dwell between pulses to avoid very small (impractical) dwell durations and to allow a certain minimum time for mixing of the fuel which has already been injected.

Figure 24 Temporal history of NO formation for the rate shapes shown in Fig. 22.

% Load 25 Engine Speed (rpm) 821 Injection Timing (ATDC) -9 deg. Intake Air Pressure (kPa) 102.7 Intake Air Temperature (K) 387 EGR Rate (%) 48.34 Total amount of fuel injected (g) 0.05967 Injection Duration (CA deg) 5.5

Exhaust Pressure (kPa) 106.8 Exhaust Temperature (K) 598 Table 7 Operating conditions for the baseline case.

However, it can be observed from Fig. 24 that the rate of NO formation is (slope of NO vs Time curve) in case of the controlled rate shape is lower compared to the other two rate shapes. These results were deemed to be encouraging and the next step was to apply a similar active control of fuel injection approach under engine conditions, as discussed in the next section.

ENGINE SIMULATIONS

The simulations were performed for a Caterpillar 3401E single cylinder oil test engine. The fuel injector used was a production style Caterpillar electronic unit injector. The details of the engine and the injector are listed in Table 6. A low speed, low load case was chosen as the baseline. The operating conditions for the simulation are listed in Table 7.The experimental injection rate shape for the baseline case is shown in Fig. 25 [24]. It was approximated by a top hat type rate shape in the simulations with the same injection duration, i.e., 5.5 CA degrees.

Engine Type (4-valve) Caterpillar 3401 Single cylinder, DI

Bore x Stroke 137.2 mm x 165.1 mm Compression Ratio 16.1 : 1 Displacement 2.44 liters Combustion Chamber Quiescent Piston Mexican Hat Swirl Ratio (nominal) 1.0 Injector Type Common Rail Injector Number of Nozzle Holes 6 Nozzle Hole Diameter 0.259 mm

-10 -9 -8 -7 -6 -5 -4 -30

5

10

15

20

25

30

35

Fuel

Flo

w R

ate

(3*m

g/C

A)

Degree CA (ATDC)

Figure 25 Experimental injection rate-shape for the baseline case [24].

Figure 26 Amount of fuel injected (g) vs. CA (degree ATDC) for the baseline and control rate shapes.

Table 6 Configuration of the Caterpillar diesel engine.

very early injections can be employed. However, it is even more important that ignition takes place close to the TDC in order to obtain sufficient power from the engine.

fuel injected was kept constant. The injection pulse duration was set equal to 1 CA degrees (0.2 ms at 821 rpm), the minimum and maximum dwell between successive injection pulses was chosen to be 1.5 CA degrees (0.3 ms at 821 rpm) and 5 CA degrees (1 ms at 821 rpm) respectively. The set point or the reference rich vapor fraction was set equal to 0.4, i.e., 40%. Fig. 26 shows a plot of the amount of injected fuel with time for the baseline and the control cases.

Fig. 29 a) to h) show the equivalence ratio distribution within the combustion chamber for the baseline (left) and the controlled rate shape (right). The start of injection was –9 degrees ATDC for both cases and, as mentioned earlier, the ignition time for both cases was also the same i.e., approximately –3 degrees ATDC. Looking at the left hand side of Fig. 29 b) (continuous injection, baseline case) it can be seen that there is a substantial rich region within the chamber. However, for the controlled rate shape the second injection has just begun and in the meantime, fuel that was injected in the preceding pulses has had sufficient time for mixing and only a lean region remains in the chamber. A similar trend is observed throughout the injection (see Fig. 29 e). Fig. 29 c) and d) show the equivalence ratio distribution within the combustion chamber around the time of ignition. Due to insufficient mixing prior to ignition, there are more rich regions in the chamber for the baseline case compared to the controlled case. Also, in the controlled case, due to dwell between successive injection pulses, the injected fuel loses momentum as time progresses whereas in the baseline case, fresh fuel pushes the vapor cloud present in the chamber and it has sufficient momentum to climb the bowl and start moving towards the center of the bowl (see Fig. 29 f). But, due to insufficient momentum in case of the controlled rate shape, the reverse squish velocities are more than the flow velocities and the vapor cloud stays in the squish region, where conditions are much more favorable for oxidation of the soot precursor species (and soot), thus reducing the amount of soot formed. It is clear from Fig. 29 g) and h) that a large amount of soot precursor is concentrated towards the center of the bowl for the baseline case, whereas for the controlled case, it stays in the squish region and is oxidized in a short period of time.

The ignition time for both cases was the same, i.e., around -3 degrees ATDC. It can be observed from Fig. 27 that the rich vapor fraction in case of the controlled rate shape is much less compared to the baseline at the time of ignition. This reduces the amount of soot precursor formed as can be seen in Fig. 28, which shows the temporal history of acetylene for the two rate shapes. In order to achieve better mixing before ignition,

Figure 27 Rich vapor fraction vs. CA (degree ATDC) for the two rate shapes.

Figure 28 Acetylene (mg) vs. CA (degree ATDC) for the two rate shapes.

Fig. 30 shows the temporal history of NO for the two rate shapes. By employing the controlled rate shape, a substantial reduction in soot precursor species as well as NOX can be achieved. However a penalty is imposed in the form of a lower peak combustion pressure and consequently less power obtained from the engine (see Fig. 31) because less fuel has been injected prior to ignition in the case of the control rate shape compared to the baseline.

For obtaining the controlled rate shape, the amount of

Figure 29 a) to h) Equivalence ratio distribution within the combustion chamber for the baseline (left) and the controlled rate shape (right).

Figure 30 NOx (g) vs. CA (degree ATDC) for the two rate shapes.

Figure 31 Average in-cylinder pressure (MPa) vs. CA (degree ATDC) for the two rate shapes.

SUMMARY AND CONCLUSIONS

A computational study was performed to explore the use of injection rate shape as a means of controlling combustion of diesel sprays and consequently reduce engine-out emissions. The KIVA3V code was employed to investigate injection rate-shape effects on spray liquid and vapor penetrations, and the flame lift-off lengths over a wide range of ambient gas density and temperature. In addition the influence of rate-shape on NOX and soot emissions was studied. Different injection rate-shapes were investigated and the advantages of one rate-shape over the other were explained in terms of factors such as liquid and vapor penetration and fuel/air mixing upstream of the flame lift-of length.

As a first step, the KIVA-3V code was validated, with improved sub models for droplet vaporization and primary jet breakup and with the use of a detailed chemical kinetics mechanism to describe combustion. These advanced models capture the physics of droplet vaporization and atomization in an accurate manner and provided increased confidence in the computational results. Initially, the models were validated in an inert environment by comparing the computed spray liquid and vapor penetration lengths with experimental data. For the reacting cases, the flame lift-off lengths were compared to the available experimental results over a wide range of density and temperature.

With confidence in the modeling accuracy affirmed by the validations of reacting and non-reacting cases, the models were applied to study the effect of injection rate shape on spray evolution and combustion characteristics. Simpler representations of actual rate shapes were defined using three parameters i.e., the injection duration, τd, the timing of peak velocity, τp, and the absolute value of the peak velocity, Vp. A consistent trend in the predicted liquid and vapor penetration lengths was observed as the different injection velocity histories influenced the breakup, coalescence and vaporization characteristics of the sprays. It was observed that the location of the highest peak of the liquid length is closely coupled with the timing of the peak injection. As the timing of the peak injection velocity was retarded, it took longer to reach the maximum liquid penetration length, and the liquid penetrated further from the nozzle. This was explained in terms of the catch-up and scattering effect depending on whether the droplets were injected on the rising or falling part of the injection rate-shape. Injection velocity plays a key role in the droplet vaporization and breakup processes due to its direct influence on the drop size. It was also observed that the rising part of the rate shape governs the initial slope of the vapor penetration length curve and the final value of the vapor penetration depends on the total injected momentum of the spray.

The effect of injection rate shape on the combustion characteristics of sprays was explored by monitoring the flame lift-off length of sprays. From this study, it was confirmed that the fuel-air mixing details are greatly affected by the change of the injection rate shape. As

injection velocities become higher, the vapor cloud travels further downstream, which increases fuel-air mixing upstream of the lift-off length location, leading to leaner mixtures and hence reduced soot formation. This was confirmed by monitoring the formation of acetylene for different rate shapes. Acetylene is known to be a very important pre-cursor for soot formation [15], so it gives a good indication of the propensity and location of soot formation.

From these studies, it was concluded that injection rate-shape affects ignition characteristics and the temporal history of soot and NOx formation, which implies controllability of emissions by optimization of the injection rate shape. In order to achieve this objective, an in-cylinder equivalence ratio feedback control approach was explored using a purely computational approach. Fuel was injected in pulses and duration between successive injection pulses was controlled based on monitoring the equivalence ratio and providing feedback from the cylinder. To calculate the dwell time between successive injection pulses, a control criterion was formulated as a proportional derivative type expression, which incorporates the effect of rich vapor fraction and the maximum equivalence ratio in the combustion chamber. In order to ascertain the efficacy of this approach, preliminary simulations were carried out for spray injections in a constant volume bomb. By employing such an injection rate shape, the fuel had sufficient amount of time to mix with air during the dwells between injections, which discouraged the formation of rich regions inside the bomb, thereby reducing the soot precursor formation drastically. These results were deemed to be encouraging and the next step was to apply a similar active control of fuel injection approach under engine conditions. Similar results were obtained under engine conditions and it was also observed that the spray loses momentum due to dwell between the injection pulses, which prevents the vapor cloud from climbing and moving towards the center of the bowl. As a result, the vapor cloud remains in the squish region, where conditions are favorable for oxidation, resulting in reduced amount of soot precursor (and soot) formation. Also, the composition of the mixture prior to ignition plays a key role in soot precursor formation. A leaner mixture prior to ignition curbs the amount of soot precursor and hence soot formation. Since fuel is injected very close to TDC (i.e., high temperature and pressure conditions), it is advisable to keep the injection pulses as small as possible in the beginning. Longer injection durations result in more fuel being injected leading to insufficient time for mixing and also once ignition takes place, the environment is deprived of oxygen and fresh injected fuel is surrounded by a mixture of rich products of combustion. Due to this reason, small injection durations (0.2 ms) were employed in the present engine study. This is small compared to the capability of the current injection hardware. However, this study offers a new way of looking at optimization of injection rate shape and motivates the development of advanced injection equipment in the future.

ACKNOWLEDGEMENTS

The authors would like to thank Department of Energy/ Sandia National Laboratories, Caterpillar Inc. and Ricardo Inc. for supporting this work.

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