ILASS Americas, 2 th Annual Conference on Liquid Atomization and Spray Systems, Chicago, IL, May 27 Method to Specify Fuel Injection Profiles for Diesel Engine Exhaust Aftertreatment Simulations Using Fuel Spray Measurements J. E. McCarthy, Jr. Eaton Corporation 2621 Northwestern Highway Southfield, MI 4876 Abstract The goal of this work is to develop a method for simulating fuel and exhaust mixing in diesel engine exhaust aftertreatment systems using standard spray measurement techniques. The method is used to support the development of Eaton s aftertreatment program consisting of a low pressure diesel injector, fuel-exhaust mixing elements, diesel fuel reformer, lean NOx trap (LNT), diesel particulate filter (DPF) and selective catalytic reduction (SCR) catalysts. Fuel is injected into the exhaust tailpipe in a transient fashion covering a multitude of fuel injection rates to provide uniform and fully vaporized sprays at the inlet of the fuel reformer catalyst. Although fuel sprays are quite complex and difficult to model, low pressure diesel sprays are characterized using spray diagnostic equipment such that a representative spray profile is injected into the simulation directly at the nozzle exit; thus, eliminating the need to simulate fuel break-up. The spray profile is defined using probability density functions independent of the fuel injection rate resulting in a simple input file for the simulation. The drop size distribution is characterized in terms of a volume probability density function while the spray pattern is described in terms of a volume flux probability density function. The fuel mass flow rate is a user input in order to evaluate a variety of fuel injection profiles. The simulation is used to compare fuel injection systems, optimize mixing elements and guide experimental configurations.
Introduction Eaton is developing an advanced exhaust aftertreatment system using a fuel dosing system, mixing elements, fuel reformer, lean NOx trap (LNT), diesel particulate filter (DPF) and selective catalytic reduction (SCR) catalysts arranged in series for both on- and off- highway diesel engines to meet the upcoming emissions regulations [1]. A sample configuration is shown in Fig. 1. This system utilizes a fuel reformer to generate hydrogen (H 2 ) and carbon monoxide (CO). These reductants are used to regenerate and desulfate the LNT catalyst. NOx emissions are reduced using the combination of the LNT and SCR catalysts. During LNT regeneration, ammonia is intentionally released from the LNT and that ammonia is stored on the downstream SCR catalyst to further reduce NOx that passed through the LNT catalyst. This approach converts the drawbacks of the single leg LNT approach (low conversion during regeneration and NH 3 slip) into an advantage while remaining independent of any urea infrastructure since diesel fuel is the only reductant. Eaton has developed an aftertreatment simulation to understand the effects of fuel dosing on the fuel vapor concentration at the inlet to the fuel reformer. The simulation required a method to specify the fuel spray along with mixing elements to mix and vaporize the fuel drops upstream of the fuel reformer. Many fueldosing systems have been evaluated and an innovative method to specify the fuel distribution has been developed. Two commercially available dosing systems were chosen for the paper discussion. These were chosen to show that sprays could be measured using different spray diagnostic tools; yet, identical spray input files could be derived even though different types of instruments were used to characterize the spray. The methodology involves measuring fuel spray characteristics and specifying the spray input file based upon probability density functions (PDFs) that are independent of fuel flow rate. This method allows for a single input file that maintains the spray integrity over all fuel injection flow rates. This model has been implemented in the Fluent Version 6.3 CFD code, which is a commercially available software tool. The input files include a volume PDF to specify the drop size distribution and a volume flux PDF to specify the spray pattern. Other input files include the exhaust mass flux, exhaust temperature, fuel mass flow rate and drop velocity of the nozzle exit. The simulation model has been qualitatively validated with experimental measurements of catalyst temperature and reformate (i.e., H 2 and CO) production. The goal of the CFD model is to predict the inlet fuel vapor concentration to the fuel reformer while the chemical reactions of the fuel vapor on the fuel reformer catalyst are not modeled. Hence, only a qualitative comparison of reformer outlet temperatures could be performed as it relates to the inlet fuel vapor concentration. In general, the fuel reformer will react with the fuel vapor more efficiently when the fuel vapor concentration on the inlet to the reformer is more uniform. A short comparison of fuel vapor concentration is presented. Non-intrusive spray diagnostic equipment (i.e., laser based) was used to characterize the sprays. The fuel spray from the first dosing system, which will be referred to as spray A, was characterized using a Malvern Particle Sizer, En Urga SETscan optical Spray Patternator and spray visualization equipment. The Malvern Particle Sizer will be referred to as the Malvern throughout the paper. Likewise, the SETscan optical spray patternator will be referred to as the SETscan. The fuel spray from the second dosing system described in this paper, which will be referred to as spray B, was characterized using a phase Doppler particle analyzer (PDPA). Since different equipment was used, the data needed to be manipulated to provide a valid comparison and develop a consistent input file to the simulation. Three measurement tools were used to characterize spray A while a multitude of measurements from a single instrument were required to characterize spray B. Spray A was characterized using the MPS, SETscan and spray photography, which are quick measurements that provide information of the entire spray. Spray B was characterized using the PDPA, which is a point measurement. In order to resolve spray B, a multitude of measurements across the spray were required. These measurements were required to develop an input file for the CFD simulation. A short description of the measurement devices is provided. The measurement equipment used to characterize spray A is described briefly. Fig. 2 shows the setup for the Malvern that was used to obtain the drop size distribution of the spray. The spray is traversed across the Malvern laser source at a constant velocity to obtain a drop size distribution that is representative of the entire spray [2]. Fig. 3 shows the SETscan optical patternator that was used to characterize the spray profile. Measurements using the Malvern and SETscan were made at various distances downstream of the nozzle over a range of mass flow rates to determine where atomization was complete. Additional measurements were made with the Malvern to understand the radial drop size variation. Fig. 4 shows a spray visualization photograph that was used to evaluate the spray cone angle.
The measurement equipment used to characterize the spray B is described. Fig. 5 shows the setup using the PDPA for spray B. The PDPA is a point measurement that measures drop size, drop velocity, volume flux and size-velocity correlation passing through that point. This point can also be referred to as a probe volume formed from the crossing of laser fringes. Integration of a multitude of these measurements is required to characterize the spray. The volume flux measurements were used to determine the spray cone angle of spray B. Calibration fluid was used to characterize both of the sprays. The calibration fluid chosen was universal calibration fluid (i.e., Viscor) that has similar properties to diesel fuel as shown in Table 1. This calibration fluid is commonly used in the spray and diesel calibration industry. It was used since it is less flammable and provides more consistent fluid properties. The two dosing systems used to create sprays A and B had flow ranges of approximately 4 to 4 grams per minute (gpm) per injector. These systems had injection supply pressures in the range of 5 to 8 bar. Exhaust pipes having pipe diameters of 3.5 to 5. inches were modeled in the simulation. The injectors were positioned to inject the fuel along the exhaust streamline. Sprays were injected in straight pipe with the injector positioned at an inclined angle. Injection into elbow pipes were also modeled. Approach An approach was developed to transform spray measurements from aftertreatment diesel fuel injectors into a non-dimensional form that could be modeled in a CFD code that computes mixing liquid fuel with diesel engine exhaust. The methodology includes measuring the diesel sprays at a distance far enough downstream that atomization is complete, yet, still within a reasonable length that could be injected in an exhaust tailpipe. These measurements were used to develop a mathematical spray profile such that fuel was injected into the simulation at the nozzle exit (i.e., near the exhaust pipe wall) with initial trajectories specified according to the spray cone angle. As a result, atomization was not modeled in the CFD code; rather, it was specified apriori. Additionally, all drops are assumed to be injected at the same drop velocity since the atomized drop size distribution is injected at the nozzle exit. Centerline and radial drop size measurements were made at specific locations downstream of the nozzle to determine where atomization was complete. It was found that atomization was complete and the spray was fully developed within 5 inches of the nozzle for both dosing systems independent of fuel flow rate. All data comparisons are made at 5 inches downstream of the nozzle. This data was transformed to create an input file for the CFD simulation for sprays A and B such that the drops were injected into the simulation at the nozzle. The goal of this project was to develop a method that allows the spray to be characterized in relatively simple terms such that it could be readily used to analyze different mixing configurations and optimize the fuelvapor concentration at the inlet to the fuel reformer. Precise fuel-exhaust mixing near the nozzle was not the goal; rather, accurate representations of the fuel vapor concentration through the mixing sections and at the inlet to the fuel reformer was desired. An important criterion was to make the spray characterization independent of injector mass flow rate since the Eaton fuel reformer requires variable fuel flow rates. For instance, a lower fuel rate is required to warm-up the reformer followed by a higher rate to consume the exhaust oxygen and an even higher rate for rich fuel-to-exhaust ratios to produce reformate. Reformate is formed by converting hydrocarbons to more reactive species including H 2 and CO. The paper describes that the spray can be described based upon two PDFs. First, the drop size distribution is characterized in terms of a volume PDF as a function of drop size that is shown to be independent of fuel flow rate. Second, the radial distribution of the spray, or the spray pattern, is defined based upon volume flux PDF as a function of the fuel spray angle. These distributions are calculated from the spray measurements downstream of nozzle and injected near the wall of the exhaust pipe. Secondary break-up and drop coalescence is neglected in this approach. Additionally, estimates of the drop velocity are required. Since the sprays were characterized downstream of the nozzle; yet, injected into the simulation starting at the nozzle outlet with it s initial trajectory specified according the spray angle, all drops are injected at the same velocity. This is a reasonable assumption since air-entrainment and interactions with the exhaust flow have not occurred. Method Overview The overall method includes specifying the fuel mass flow rate as a function of time coupled with the atomized volume PDF as a function of drop diameter and the volume flux PDF as a function of spray angle. The fuel mass flow rate, m f, is defined by the continuity equation where is the fuel density, v is the fuel velocity and As is the spray area. m f va s (1)
The fuel mass flux is the product of the fuel density and the velocity. The fuel velocity can be re-written as the fuel volume flux, V, having units of cc/s/cm 2. Volume flux is used since it is readily measured using spray measurement equipment. m f v V Both sprays were found to be axially symmetric. As a result, the spray area was transformed into a series of circular rings where is the spray angle, is the half cone angle and the area difference is the area of individual spray rings. A s A A 1 1 (2) (3) The model defines each spray ring to be circular having equal spray angle as opposed to equal areas. As a result, the outer most rings will have a larger area than the inner rings. The mass flow rate, m, for each circular ring is defined as follows. m V f A A 1 (4) The CFD input file requires the volume flux fraction for each circular ring to be defined as follows. V V f A A 1 This equation allows the volume flux to be specified at each spray angle; thus, simplifying the CFD input file. (5) In addition to specifying the fuel mass flow rate as a function of time, volume PDF as a function of drop size and volume flux PDF as a function of spray angle, the drop velocity needs to be specified. As discussed earlier, the atomized drop size distribution is measured downstream of the nozzle where atomization is complete. This profile is translated to the injector nozzle so that atomization does not need to be modeled. Spray Measurements for Spray A The first fuel dosing system was characterized using the combination of a Malvern, SETscan and spray visualization photographs [3]. This spray is referred to as spray A and a spray photograph was previously shown in Fig. 4. The atomization characteristics are reported in terms of a volume PDF to define the drop size distribution and the spray profile is reported in terms of a volume flux PDF as a function of spray angle. The atomization characteristics are reported in terms of a characteristic mean diameter using measurements from the Malvern. Sauter mean diameter (SMD) is an accepted mean diameter for analyzing sprays in the spray community [4]. It is representative of a mean diameter that has a volume to surface ratio that is equal to that of the entire spray. Fig. 6 shows the SMD of spray A as a function of fuel flow rate. The SMD is reported as an average value over the spray domain. It is an average value since the spray was traversed across the Malvern laser at constant velocity [2]. Spray A has been calibrated at a 6 bar gauge operating pressure while the results cover 5 to 7 bar with two different injectors. The influence of operating pressure and part-to-part variation on SMD is small. Additionally, SMD is affected only slightly by fuel flow rate. At flow rates between 2 and 5 gpm, the SMD is approximately 14 to 15 m. As fuel flow rates increases past 15 gpm, the SMD plateaus at approximately 17 m. Thus, it will be assumed that differences in SMD as a function of fuel flow rate are negligible to simplify the input file. Additional measurements were performed at specific locations from the centerline to understand radial effects on SMD. Radial SMD s were approximately equal to the average value, so only the average SMD s are reported. The drop size data was transformed into a universal parameter describing the volume fraction as a function of drop diameter. The volume fraction shows the amount of volume located at each drop diameter. A Rosin-Rammler distribution was fit to both dosing systems using two parameters indicative of the mean drop size diameter, X, and the drop size spread, q. This distribution is an accepted method in the spray industry to characterize spray drop size distributions [4]. The cumulative volume fraction, Q, is defined as where D is the drop size. q D Q 1 exp (6) X Fig. 7 shows the cumulative volume fraction for spray A at low and high flow rates (i.e., 12 and 35 gpm). Notice that the profile is independent of flow rate. This greatly simplifies the CFD input file since the same distribution can be used independent of fuel flow rate. A Rosin-Rammler distribution was fit to spray A having a mean diameter of 25 m and a spread of 1.8 such that it is independent of fuel flow rate.
Although the cumulative volume fraction was determined to characterize the spray, the derivative of this parameter is more useful to define the CFD input file since it is representative of the spray volume located at each drop size. This derivative is referred to as the volume PDF defined as: dq dd q D q q D D exp (7) X X Fig. 8 shows the volume PDF for Spray A. The spray volume is spread over many diameters ranging from 5 to 5 m while the majority of the volume is contained between diameters of 1 and 28 m. This parameter is useful to compare drop size distributions of different sprays. Spray A will be compared with spray B from a different type of aftertreatment fuel injector at the end of the paper. The SETscan optical patternator was used to provide definition of the spray profile. Fig. 9 shows the spray patternation data as a function of spray width and fuel flow rate. Notice that the spray width is nearly identical for all fuel flow rates as evidenced by K approaching zero around 6 mm from the centerline of the spray. The spray patternation metric is a variable called K, which is the surface area per unit volume of spray [3,5]. This parameter is not a straightforward metric to define the spray profile. A method is described along with appropriate assumptions based upon spray data to show that the spray volume flux profile is proportional to K. Furthermore, it will be shown that K can be normalized into a PDF such that it is independent of fuel flow rate. This data is used to define a volume flux PDF as a function of spray angle. This makes the spray input file simple so that various fuel mass flow rates can be specified as a function of time. A derivation of the approach follows. Mathematically, K is defined [5] as K D N D ( ) 4 2 2dD where N(D) is the number of drops per unit volume having units of (1/mm 3 ) and D is the drop size measured in mm. The integral is doubled since the scattering cross section is twice the area [6,7]. N(D) can be re-redefined as [6]: (8) where N t is the total number of drops per unit volume and F(D) is the fraction of drops having size D. Combining equations (8) and (9) yields: 2 K N t F( D) D dd 2 (1) The integral of eqn. (1) can be simplified by recognizing that it is equivalent to a characteristic mean diameter known as the area mean diameter, D 2 where n i is the number of drops of each drop size. 2 n D i i i D 2 2 F( D) D dd (11) n i i Combining eqns. (1) and (11) yields the relationship that K is proportional to the square of the area mean diameter. Solving for N t yields: 2 K N t D 2 (12) 2 2K N t (13) 2 D2 The area mean diameter, D 2, is related to the volume mean diameter, D 3, and the SMD (i.e., D 32 ) as follows: 3 2 2 3 n i D i n i D i n i D D i 3 i i i D2 * (14) n 3 i ni D n i D 32 i i i i Recognizing that the spray volume flux is related to the volume mean diameter, D 3, while the SMD (i.e., D 32 ) has already been characterized, combining eqns. (13) and (14) yields the following relationship. N t 2KD32 3 D3 (15) The next step is to solve for the volume flux entering the simulation domain [6]. N ( D ) N t F ( D ) (9) D V f 3 N ( D ) vdd Nt v F( D) D dd (16) 6 6 3
where V f is the fuel volume flux, and v is the drop velocity. Recognizing that D 3 is equivalent to the cube root of the integral in eqn. (16), 1 3 3 D 3 ( ) F D D dd (17) the volume flux is shown to be proportional to the cube root of D 3. (18) V 3 f N t v 6 D 3 Substituting N t from eqn. (15) into eqn. (18) reveals that the volume flux dependence on D 3 cancels out such that the volume flux is proportional to K, SMD and the spray velocity. KD 3 v D vd V 2 f 32 3 32 K (19) 3 D 6 3 3 It was previously shown that the effect of fuel flow rate on SMD is small, so SMD is assumed to be constant, which further simplifies the model. Additionally, the drops enter the CFD domain at the nozzle exit where the drop drag has not altered the drop velocity, so the initial drop velocity is assumed to be constant. As a result, the spray volume flux can be specified as only a function of K. This approach reduces a complicated problem to an simple solution by correlating the spray volume flux to the SETscan optical patternator parameter, K. The author recognized that normalizing K eliminates the dependence on fuel flow rate. Fig. 1 shows normalized K data in terms of a volume flux PDF as a function of spray angle at two flow rates of 12 and 35 gpm. The remaining fuel flow rates fall on this same volume flux PDF curve leaving the CFD input file independent of fuel flow rate. As a result, eqn. (19) reduces to vd V f 32 CK PDF 3 (2) where C is a flow rate constant and K PDF is normalized such that it is a PDF. Since all values are constant besides K PDF, volume flux is proportional to K PDF ; hence, the volume flux PDF,, is equal to K V f, PDF PDF. V f, PDF K PDF All parameters are defined for spray A including the dq volume PDF,, and the volume flux PDF, V PDF, dd while the desired fuel mass flow rate and the drop velocity remain user inputs to the model. Spray Measurements for Spray B PDPA measurements were used to acquire the spray data for spray B. The procedure for inputting spray data into the Eaton CFD simulation is more straightforward than using the combination of the Malvern, SETscan and spray visualization measurements; however, many more spray data points are required to assemble the CFD input file. (21) Spray measurements using a PDPA were made using a diesel fuel injection system that formed spray B. A photograph of spray B was previously shown in Fig. 5. The atomization characteristics are reported followed by profiles of the volume and volume flux PDFs that define the spray for the CFD simulation. The drop size measurements from the PDPA are reported in terms of a characteristic mean diameter. Consistent with spray A, the SMD was chosen as the characteristic mean drop size diameter. Fig. 11 shows the SMD of spray B at multiple radial locations from the centerline covering all four quadrants of the spray (i.e., measurement matrix forms a cross in the spray). Two fuel flow rates are reported including both low and high flow conditions of spray B (i.e., 1 and 38 gpm). Two diametrical passes are reported for each flow rate as a function of distance from the centerline of the spray. The centerline SMD measurements (i.e., zero location) are 5 m while the outer edges of the spray are 7 m. This indicates that there are generally smaller drops near the centerline while larger drops are at the outer edges. Fig. 12 shows the volume PDF for the dosing system B at various radial distances from the centerline along with the average profile. The profiles show that smaller drops exist at the centerline of the spray (i.e., R=) while larger drops tend toward the outer edge of the spray (i.e., R=1.25). Once again the outer edge of the spray is shown to have larger drops than the centerline. An average profile was obtained by weighting each radial distance profile of spray B by the spray volume flux. The average profile was used for the Eaton spray simulation. The profile is measured downstream of the nozzle; yet, injected into the simulation at the nozzle exit. Hence, the average profile is the only profile needed to define the spray input file.
Fig. 13 shows the volume flux as a function of radial position for two fuel flow rates. Since the spray is axially symmetric, the spray volume fluxes from multiple quadrants of the spray are plotted in the figure. Volume flux curve fits for both fuel flow rates were established. Notice that the spray widths for both fuel flow rates are the same. Similar to spray A, showing that the spray width is independent of fuel flow rate is key to providing a simple input file to define the spray pattern. The curve fits from Fig. 13 were transformed to a function of spray angle instead of radial distance from the centerline and normalized to create a volume flux PDF. Fig. 14 shows the volume flux PDF as a function of spray angle. Notice that the volume flux PDFs for both fuel flow rates are nearly identical. The volume flux difference of approximately 1% near the centerline of the spray (i.e., spray angles less than 4 degrees) was neglected since the measured difference near the centerline is small and it simplifies the model. Hence, an average volume flux PDF curve was specified in the simulation to define the volume flux PDF such that it is independent of fuel flow rate. Spray Input File The spray input files for the volume and volume flux PDFs are described for the two sprays. Fig. 15 shows the volume fraction for each spray. The volume fraction was grouped into 1 m drop size bins so that the sprays could be compared easily. However, the simulations were conducted using 2 m drop size bins for spray A and 5 m drop size bins for spray B. The volume fraction for spray A was created using the volume PDF from Fig. 8 and grouped into 2 m drop size bins. This allowed the drop size profile to be specified by a simple input file consisting of 31 individual drop size bins. The Fluent code randomly injects drop size packets covering each drop size bin. A bin independence study was conducted using both 5 and 2 m bin sizes for spray A yielding nearly identical results. Hence, 2 m bins were chosen for future studies using spray A. Similar to spray A, the volume fraction for spray B was created from the average volume PDF profile from Fig. 12. The input file was grouped into 21 individual drop size bins having a bin size of 5 m. Spray B has a much smaller and tighter drop size distribution than spray A. It has a SMD of approximately 6 m while spray A has a SMD of approximately 16 m. Additionally, the majority of the spray volume for spray B is contained in drop sizes less than 1 m while only 18% of the volume for spray A is contained in drop sizes less than 1 m. Spray A also has 1% of the spray mass contained in drop sizes above 4 m. The volume flux fraction for both sprays is shown in Fig. 16. This figure represents the volume flux fraction for each circular spray ring. The spray ring was defined earlier in eqn. (3). The volume flux fraction for spray A was calculated from the volume flux PDF (i.e., K PDF ) as shown previously in Fig. 1 and put into circular spray areas represented by 1 degree spray angle bins. Likewise, the volume flux fraction for spray B was calculated from the volume flux PDF shown in Fig. 14. This data provides a simple input file. Additionally, the spray pattern can be compared. Spray A is wider than spray B having a 23 degree spray angle at 5 inches downstream of the nozzle while spray B has an 18 degree spray angle. The volume flux is similar near the centerline (i.e., out to a 5 degree spray angle. Between 5 and 15 degrees, spray B has more volume while spray A has more volume at the outer edge. Model Application A sample of CFD results are shown for both sprays having various system configurations. Fig. 17 shows spray A simulated in an exhaust pipe showing the fuel vapor concentration at the inlet to the fuel reformer. Equal vapor concentration contours are desired. The baseline configuration shows a poor fuel vapor concentration at the fuel reformer inlet, which would reduce both reformer efficiency and durability. Fig. 17 also shows an improved configuration having a more uniform fuel vapor concentration. However, further improvement is still warranted. The main problem with spray A is that the large drops take longer to vaporize in exhaust streams than smaller drops. Fig. 18 shows spray B simulated in an elbow pipe. The fuel vapor concentration for a baseline case shows that further improvement is required. An improved system configuration shows a nearly uniform fuel vapor concentration; thus, enabling a more fuel-efficient and durable reformer operation. Spray B has smaller drops than spray A that are more easily vaporized yielding a more uniform distribution. Conclusions An innovative approach was developed to make relatively quick spray measurements and transform the parameters into a simple input file that is independent of fuel flow rate. Two approaches using different measurement equipment were discussed. Measurements with either type of measurement system were accommodated and qualitative comparisons of the sprays were made. The first approach was to measure the drop size distribution with a Malvern, measure the spray pattern
with a SETscan optical patternator and determine spray cone angle with spray photography. The second approach was to use the PDPA for all measurements by characterizing the radial profile at a multitude of points within the spray. Both techniques have advantages and disadvantages. The first method is relatively quick, but requires fundamental calculations of the drop velocity at the nozzle. This method is preferred assuming that the equipment is available since the required parameters can be quickly measured. The second method is more labor intensive, but provides an assessment of the drop velocity throughout the spray. The paper showed that either method could be used. Regardless of the method, both create an equivalent input file that can be used for the simulation. This input file is also useful for comparing different sprays. Eaton has implemented this model in a Fluent CFD code and is using it to evaluate dosing systems, mixing elements and system configurations to provide a uniform fuel vapor concentration at the inlet face to the fuel reformer. The model allows for quick assessment of different injection and mixing systems to reduce the effort in experimentally determining the best solution. Eaton continues to use this model to improve system performance and has demonstrated substantial improvements in system efficiency as a result of the CFD effort. Acknowledgements I would like to acknowledge Professor Paul Sojka of Purdue University for participating in a research program to characterize diesel sprays and for his guidance in understanding the fundamental characteristics of the SETscan optical patternator. I would like to thank Dr. Yong Yi of ANSYS Fluent, Inc. and Ramu Ramamurthy of Eaton for implementing the spray in the Fluent CFD package. I appreciate the efforts of my Eaton teammates including Dr. David Ginter, Phil Wetzel, Milind Kulkarni and Ganesh Pandit for utilizing the CFD code to optimize the dosing and mixing system and Dmitry Shamis for his technical assistance. Finally, I appreciate the funding from the Eaton Aftertreatment Team for making this effort possible, especially Bill Taylor, Vishal Singh and Tom Stover for advocating this effort and securing the funding. 3. Sojka, P. E., Shu, F., Lee, A. and Muliadi, A., Research Contract Between Eaton Corporation and Purdue University for Spray Measurements, 25. 4. Lefebvre, A. H., Atomization and Sprays, Hemisphere, New York, 1989. 5. Lim, J., Sivathanu, Y., Narayanan, V. and Chang, S., Optical Patternation of a Water Spray Using Statistical Extinction Tomography, Atomization and Sprays, Vol. 13, pp. 27-43, 23. 6. Sojka, P. E., Personal consultation in August 26. 7. Sivathanu, Y., Personal consultation in August 26. Nomenclature A area d derivative indicator D drop diameter, m F(D) fraction of drops having size D K surface area per unit volume of spray (1/mm) m mass n number of drops N(D) number of drops per unit volume having size D (1/mm) q Rosin Rammler drop size spread Q cumulative volume fraction R radial distance from centerline SMD Sauter Mean Diameter v drop velocity V volume X Rosin Rammler mean diameter, m identifier for the half cone angle constant pi (3.1416) fuel density Subscripts f fuel t total i summation identifier r identifier referring to a spray ring 2 identifier for the surface mean diameter 3 identifier for the volume mean diameter 32 identifier for the Sauter Mean Diameter identifier for spray angle References 1. Hu, H., Reuter, J., Yan, J., and McCarthy, J., Jr., Advanced NOx Aftertreatment System And Controls For On-Highway Heavy Duty Diesel Engines, SAE 26-1-3552, 26. 2. McCarthy, J. E., Jr., Paint Transfer in Electrostatic Air Sprays, Ph.D. thesis, Purdue University, W. Lafayette, IN, 1995.
Fluid Property Diesel Fuel Universal Calibration Fluid-1 (Viscor) Density (g/cm 3 ).81 to.86.796 Surface Tension (N/m).24 to.3.28 Viscosity (kg/m-s) 2.2e-3 to 3.3e-3 2.8e-3 Table 1. Fuel Property Comparison Of Diesel Fuel and Universal Calibration Fluid [3]. Figure 1. Eaton Aftertreatment System (EAS) Layout. Traverse Atomizer Receiver Source Figure 2. Spray Measurement Setup Using the Malvern Particle Sizer [3].
Atomizer Laser sheet Array photodetector Figure 3. Spray Measurement Setup Using the En Urga Optical Patternator [3]. Figure 4. Spray Visualization Setup for Cone Angle Measurements (Half cone angle was 23+2 o ) [3]. Figure 5. Spray Measurements Using the Phase Doppler Particle Analyzer.
225 2 175 15 SMD, m 125 1 75 5 25 Spray A Measured 5 inches downstream of nozzle Injector 1, 5 bar Injector 1, 6 bar Injector 1, 7 bar Injector 2, 5 bar Injector 2, 6 bar Injector 2, 7 bar 5 1 15 2 25 3 35 4 45 fuel mass flow rate, gpm Figure 6. Sauter Mean Diameter Measurements for Spray A [3]. 1 Cumulative Volume Fraction (Q), m -1.9.8.7.6.5.4.3.2.1 1 2 3 4 5 6 Drop Diameter, m Spray A 12 gpm 3 gpm Rosin Rammler Fit Rosin Rammler Fit Q=1-exp(-(D/X) q ) X=25, q=1.8 Figure 7. Cumulative Volume Fraction for Spray A.
Volume Probability Density Function, m -1.35.3.25.2.15.1.5 Spray A (average profile at 5 inches downstream of nozzle) 1 2 3 4 5 6 Drop Diameter, m Figure 8. Volume Probability Density Function for Spray A. Surface Area Per Unit Volume of Spray (1/mm) 4 x 1-3 3.5 3 2.5 2 1.5 17.5gpm 35gpm 6gpm 9gpm 12gpm 15gpm 2gpm 3gpm 35gpm 1.5 1 2 3 4 5 6 7 Axial Location from Centerline, mm Figure 9. Spray Patternation Data, K, For Spray A [3].
K Probability Density Function, degree -1.14.12.1.8.6.4.2 same profile can be used independent of flow rate 35 gpm 12 gpm 5 1 15 2 25 spray angle, degrees Figure 1. K Probability Density Function for Spray A. Sauter Mean Diameter (SMD), m 2 18 16 14 12 1 8 6 4 2 Spray A Spray B 38 gpm 1 gpm -2-1.5-1 -.5.5 1 1.5 2 Distance from Centerline of Spray, inches Figure 11. Sauter Mean Diameter of Spray B.
Volume Probability Density Function, microns -1 Volume Probability Density Function, mm -1.45.4.35.3.25.2.15.1.5 Average Profile dq/dd=(q/d)(d/x) q (exp(-(d/x) q )) X=56.382, q=3.473 centerline Spray B at 38 gpm 5 inches downstream of nozzle 1 2 3 4 5 6 7 8 9 1 drop diameter (D), m Centerline (R=) R=.25 inches R=.5 inches R=.75 inches R=1. inches R=1.25 inches Average Profile outer edge of spray Figure 12. Volume Probability Density Function For Spray B At Multiple Radial Locations Along With An Average Profile Determined By Weighting Individual Profiles By The Spray Volume Flux. Volume Flux, cc/s/cm 2.16.14.12.1.8.6.4 38 gpm 1 gpm y =.172x 2 -.1127x +.1425.2 y = -.22x +.349.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Radial Distance From Centerline, inches Figure 13. Measurements of Volume Flux for Spray B.
Volume Flux Probability Density Function, degrees -1.12 38 gpm 1 gpm.1.8.6.4.2 4 8 12 16 2 spray angle, degrees Figure 14. Volume Flux Probability Density Function for Spray B. Volume Fraction.25.2.15.1 Spray B Volume Fraction plotted with 1 m bins for easy comparison. Bin sizes used in simulation: 2 m bins for Spray A 5 m bins for Spray B.5 3 6 9 12 15 18 21 24 27 Spray A Droplet Size, m 3 33 36 39 42 45 48 Figure 15. CFD Volume Fraction Input File For Sprays A and B. 51 54 57 6
Volume Flux Fraction For Each Spray Ring.9.8.7.6.5.4.3.2.1 Spray B 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 Spray Angle, Degrees One Degree Spray Angle Bins For Each Spray Spray A Figure 16. CFD Volume Flux Fraction At Each Angular Spray Ring for Sprays A and B exhaust flow Large droplets wet opposite wall, leading to lean and rich regions at the fuel reformer inlet Injector for Spray A Reduced wall wetting yielding increased vaporization and better mixing Wall wetting effects Baseline Fuel Vapor Concentration Improved Fuel Vapor Concentration Figure 17. CFD Fuel Vaporization Plot At Inlet to the Fuel Reformer for Spray A
Injectors for Spray B exhaust flow Small droplets can re-circulate in the injection boss leading to lean and rich regions at the fuel reformer inlet System improvements that reduce small droplet re-circulation resulting in better mixing Baseline Fuel Vapor Concentration Improved Fuel Vapor Concentration Figure 18. CFD Fuel Vaporization Plot At Inlet to the Fuel Reformer for Spray B