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Modeling Soot Formation in Turbulent Jet Flames at Atmospheric and High-Pressure Conditions May Yen, Vinicio Magi, and John Abraham Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b01946 • Publication Date (Web): 25 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018

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Modeling Soot Formation in Turbulent Jet Flames at Atmospheric and High-Pressure Conditions May Yen†, Vinicio Magi‡, and John Abraham*,†, ∆ †

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 ‡ School of Engineering, University of Basilicata, Potenza 85100, Italy ∆ Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182

* Corresponding author: [email protected]

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Abstract Simulations of soot in an atmospheric turbulent jet flame and in high-pressure turbulent diesel jets are presented. A kinetic soot model and a semi-empirical soot model are employed for predicting soot in the atmospheric jet flame. Consistent with results published in the literature, this work shows that the kinetic model predicts the location of the maximum soot volume fraction to lie considerably upstream of the measured maximum soot volume fraction. Furthermore, the radial spreading and axial penetration are lesser than in the measurements. The semi-empirical model is able to predict the location of the maximum within 20%, but the lower radial spreading and axial penetration persist suggesting potential deficiencies in predicted soot oxidation. The semi-empirical model is applied to simulate soot in diesel jets and shown to predict the measured location of the soot and effect of changes in operating conditions well. Keywords Modeling soot in turbulent flames, kinetic soot model, semi-empirical soot models, soot in diesel jets

1. Introduction Soot emissions from combustion applications, including transportation, are harmful to human health1 and a contributing factor to climate change.2 Sources of soot include diesel engines, and the burning of agricultural waste and biomass. Diesel engines, while advantageous due to their higher energy efficiency and durability compared to spark-ignited engines, are a major contributor of soot emissions leading regulatory agencies to impose stringent limits on them. These limits have been met with a combination of strategies, including exhaust after-treatment devices and in-cylinder modifications.3-5 The assessment of low-polluting strategies and technologies can be achieved through engine parametric studies in experimental campaigns, but doing so is expensive and time consuming. As the cost of designing advanced engines grows, the need for data-driven design has become critical as the benchmarks for performance and emissions continue to rise. Multidimensional models are widely utilized in the engine design process.68

Computational models that accurately predict the physics in engines can have a significant impact on

engine design. The accuracy of such models depends, however, on the understanding of the physics and the accuracy of the sub-models, e.g. for soot formation. In the case of soot, the challenge is that the physics and chemistry of soot formation is not well understood at a fundamental level. Furthermore, predictions are sensitive to gas-phase chemistry predictions, turbulence/chemistry interactions, radiation and turbulence/radiation interactions. There is significant effort under way to address these limitations. This 2 ACS Paragon Plus Environment

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work adopts existing models and assesses their ability to predict soot in atmospheric and high-presssure (diesel) turbulent jets. The first part of this work reports on the modeling of an atmospheric turbulent jet flame. Modeling the atmospheric jet removes the uncertainty associated with chemical kinetics at high pressures in diesel jets. There have been several experimental and modeling studies of soot distribution in such flames, starting with pioneering studies about 30 years ago9-12, and progressing to more recent studies.13-21 Advances in laser diagnostics and other measurement techniques13-15 and the dramatic increase in computational power have led to the generation of measured data which were not possible 30 years ago and the use of more sophisticated models21-26, including the application of the models to problems of engineering interest.24, 26 Nevertheless, progress in improving the understanding of the mechanisms of soot formation in turbulent flames and its modeling has been slow as evident from the proceedings of the International Sooting Flames Workshop that are held biennially.27 In fact, the simpler models for soot formation/oxidation, can do just as well or better than the more sophisticated ones. The experimental work of interest, under atmospheric pressure conditions, in this work is that of Köhler et al.13 Ethylene was injected at a bulk velocity of 44 m/s from a steel pipe with an inner diameter of 2 mm into air with co-flow of 0.29 m/s at atmospheric conditions which results in a Reynolds number of 10,000. There have been several prior simulations of this jet flame. The results from the prior work will be reviewed in the next section. The section that follows will describe the computational model. Results will then be presented and discussed. This section will also present results from an application of the semiempirical model which showed promise in atmospheric turbulent jets to diesel jets. The paper will end with summary and conclusions. 2. Prior Simulations of the Turbulent Flame Simulations of the turbulent jet flame of ref 13 have been carried out by several research groups. Reference 13 itself presents results from simulations of the measured flame using an incompressible Reynolds-Averaged Navier-Stokes (RANS) solver by employing a 43-species mechanism for the gas phase chemistry combined with a reduced PAH chemistry sub-model that had been reported earlier.16, 17 The soot model uses a sectional method with 25 sections where soot nucleates upon reaching a size of 800 amu. Radiation was modeled using an optically thin approximation. Turbulence was modeled using the standard k-ε model and turbulence/chemistry interactions modeled using a presumed-PDF approach with a Gaussian-PDF for temperature and a β-PDF for species mass fraction. Figure 1 shows the value of the soot volume fraction fv along the jet centerline from the measurements and the simulation of ref 13 as well 3 ACS Paragon Plus Environment

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as other simulation studies that will be discussed below. The simulation of ref 13 predicts the maximum soot volume fraction fv to occur at a height of about 12 cm above the burner whereas the measured maximum is at a height of about 30 cm. The simulated maximum over-predicts the measured maximum by about 20%. The radial distribution of fv from the measurement and several simulations, in an axial plane located at 21.3 cm above the burner is shown in Figure 2. A distinct feature is the narrower spreading of the simulated soot compared to the measurements. Chittipotula et al.18 presented results from simulations of this jet flame using a RANS framework with the k-ε turbulence model and a 36-species mechanism to model chemistry. Radiation was modeled using an optically thin assumption. Soot was modeled using a semi-empirical model. As Figure 1 shows, the soot volume fraction reaches its maximum value about 20 cm above the burner height whereas the measured maximum is at 30 cm. This is an improvement over the simulated results of ref 13. The predicted maximum value is, however, about twice the measured maximum. Furthermore, the soot appears to penetrate farther axially than in the measurements.

Figure 1. Soot volume fraction along jet centerline from measurement (symbol) and simulations (lines). Busupally and De19 also simulated soot in this flame using a semi-empirical model. Their semiempirical model differs from that of Chittipotula et al.18 in the oxidation sub-model and the model 4 ACS Paragon Plus Environment

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constants. A steady laminar flamelet library was employed to generate chemical source terms with a chemical mechanism that has 82 species and 1450 reactions. Radiation was modeled using a non-gray assumption. The predicted soot volume fraction is shown in Figures 1 and 2. The predicted maximum centerline soot volume fraction is about 50% higher than the measured maximum.a As in the work of ref 18, the maximum is situated about 20 cm above the burner compared to about 30 cm in the measurements. The penetration of the soot is noticeably less than in the measurements. Consistent with the results of ref 13, the predicted radial spread is noticeably narrower than in the measurements.

Figure 2. Measured (symbol) and simulated (lines) radial soot volume fraction, fv, in an axial plane 21.3 cm above the burner. Eberle et al.20 simulated soot in the flame using a kinetic soot model similar to the one used in ref 10, but soot surface growth was modeled using the sub-model of Appel et al.21 Furthermore, soot oxidation by OH was modified so that the collision efficiency of OH is reduced at low temperatures28 and also when temperatures are higher than 2000 K.29 Radiation was modeled using an optically thin approximation. Figure 1 and Figure 2 show the simulated fv along the jet centerline and in the radial direction in an axial plane 21.3 cm above the burner, respectively. It is expected that reducing the oxidation rates will increase soot volume fraction and also cause it to penetrate farther. Not surprisingly, the axial location of the 5 ACS Paragon Plus Environment

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maximum value of soot volume fraction is in better agreement than the results from Köhler et al.13 The soot also penetrates farther. Figure 2 shows that the radial spread is not affected by the changes. This same soot model, however, predicted laminar non-smoking flames to be smoking.20 The fact that it cannot predict the non-smoking/smoking transition in laminar flames suggests that this model cannot be applied to a wide range of flames without first addressing the under-predicted oxidation under laminar conditions. This brief review highlights the enormous challenges in modelling soot even in atmospheric flames. Sub-models and constants vary considerably in the literature even for kinetic models. In general, prior simulations have not been able to predict the measured results well. Common features of the results above are that the predicted soot is generally located upstream of the measured soot. In all simulations, the radial spread of the soot is noticeably lower than in the measurements. The next section will describe the computational model employed in this work and results will be presented in the subsequent section. 3. The Computational Model An axisymmetric RANS model is employed for the simulations.30 This model has been employed extensively in prior work. Turbulence is modeled using the standard k-ε model.31 Soot is modeled using two approaches: a kinetic model21 and a semi-empirical model described below. The kinetic model represents the formation of poly-aromatic hydrocarbons (PAHs) with additional models to account for surface growth and oxidation. An unsteady flamelet progress variable (UFPV) model for turbulence/chemistry interactions is employed.30,32 Details of the specific model employed in this work are given in ref 30. In brief, the energy and species transport equations in an unsteady flamelet are solved, and the chemical source terms obtained from that solution are tabulated as a function of the independent variables of mixture fraction, scalar dissipation rate, and a progress variable. These source terms are then employed in the RANS simulations where the average source terms are obtained by convolving the instantaneous source terms from tabulated values with probability density functions for the independent variables. The GRI Mech3.033 is employed to model the kinetics of ethylene oxidation. The semi-empirical model is described by the following equations:34 𝑑𝜌𝑌𝑠 𝑑𝑡 𝑑𝜌𝑁𝑠 𝑑𝑡

+ ∇ ∙ (𝜌𝑣𝑌𝑠 ) = ∇ ∙ (𝜌𝐷𝑠 ∇𝑌𝑠 ) + 𝛼𝑛𝑢𝑐 + 𝛼𝑠𝑢𝑟 − 𝛼𝑂2 − 𝛼𝑂𝐻 ,

(1)

+ ∇ ∙ (𝜌𝑣𝑁𝑠 ) = ∇ ∙ (𝜌𝐷𝑠 ∇𝑁𝑠 ) + 𝛽𝑛𝑢𝑐 − 𝛽𝑐𝑜𝑎𝑔 ,

(2)

where Ys is the local mass fraction of the soot and Ns is the soot number density. Empirical models for inception, surface growth, oxidation via O2, and oxidation via OH are represented by the source terms 6 ACS Paragon Plus Environment

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𝛼𝑛𝑢𝑐 , 𝛼𝑠𝑢𝑟 , 𝛼𝑂2 , 𝛼𝑂𝐻 , respectively, in eq 1. Inception and coagulation in eq 2 are modeled by source terms 𝛽𝑛𝑢𝑐 and 𝛽𝑐𝑜𝑎𝑔 . Since the model was first proposed in ref 34, several formulations of the sub-models which appear on the right-hand-side of eqs 1 and 2 have appeared in the literature. At this point, there is no consensus on one semi-empirical model. The specific model employed in this work has been extensively assessed in laminar sooting flames.35 Following ref 28, 𝛼𝑛𝑢𝑐 is modelled as 𝛼𝑛𝑢𝑐 = 3.4 𝑀𝑠 exp (−

7548

) [𝐶2 𝐻2 ][𝑘𝑔 𝑚−3 𝑠 −1 ],

𝑇

(3)

where [𝐶2 𝐻2 ] is the molar concentration of acetylene and 𝑀𝑠 is the molecular weight of carbon. The soot nuclei grow via adsorption of carbon, i.e. 𝛼𝑠𝑢𝑟 = 12𝑀𝑠 exp (−

6038

) 𝐴𝑠 [𝐶2 𝐻2 ] [𝑘𝑔 𝑚−3 𝑠 −1 ],

𝑇

(4) 6 2/3

where 𝐴𝑠 is the surface area of soot per unit volume defined as 𝐴𝑠 = 𝜋𝜌 (𝜋)

−2/3 2/3 1/3 𝑌𝑠 𝑁𝑠 .

𝜌𝑠

The

oxidation rate by O2 is modeled using the widely-used formulation of Nagle and Strickland-Constable.36 OH oxidation is modeled using the model proposed by Fenimore and Jones:37 1

1

1

𝛼𝑂𝐻 = 1.63𝑒4 𝐴𝑠 𝜑𝑂𝐻 𝑃𝑂42 𝑃𝐻22 𝑂 𝑇 −2 e−

19023 T

,

(5)

where Pi is the partial pressure of species i and 𝜑𝑂𝐻 is the collision efficiency which is assumed to have a value of 0.2 in this work.28 The source terms for the soot number density in eq (2) are modeled as28 𝛽𝑛𝑢𝑐 = 𝐶

2

𝑚𝑖𝑛

𝑁𝐴 𝑟𝑛𝑢𝑐 , 1

𝛽𝑐𝑜𝑎𝑔 =

(6) 1

1 6𝑀 6 6𝜅𝑇 2 2𝐶𝑎 ( 𝜋𝜌𝑠 ) ( 𝜌 ) [𝐶 (𝑠)]6 [𝜌𝑁𝑠 ]11/6 𝑠 𝑠

,

(7)

where 𝐶𝑚𝑖𝑛 is minimum number of carbon atoms in a soot particle, assumed to have a value of 100, and [𝐶(𝑠)] is [ρYs/Ms]. 𝐶𝑎 is an agglomeration rate constant. Values of 0 – 9 have been employed for this constant in the literature. To be consistent with the selection of the model from ref 28, the value of 0 is employed. 𝑁𝐴 is the Avogadro number and 𝜅 is the Boltzman constant. 7 ACS Paragon Plus Environment

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Radiation is modeled using an optically thin approximation term38, 39, i.e., 𝑞𝑟𝑎𝑑 = 𝑞𝑠𝑜𝑜𝑡 + 𝑞𝑔𝑎𝑠 = −𝜀𝑠 (𝑇) ∗ 4𝜎 𝑇 4 − 𝑘𝑝 ∗ 4𝜎𝑇 4 ,

(8)

where 𝑞𝑟𝑎𝑑 is radiated energy per unit volume with Planck mean absorption coefficients, kp, for CO, CO2, and H2O calculated based on the statistically narrow band model.40 The symbol σ is the Stefan-Boltzmann constant and 𝜀𝑠 (𝑇) = 𝑘𝑠 ∗ 𝑓𝑣 ∗ 𝑇, where the value of 4𝜎𝑘𝑠 = 3.37 x 10-10 following ref 39. The modeling of radiation is critical in these sooting turbulent diffusion flames, e.g. Kent and Honnery10 found that neglecting radiation results in predicted temperatures that are up to 300 K higher. Notice that when the kinetic model is employed, the PAH soot mechanism requires input on the species concentration of various species. When the semi-empirical model is employed, the solution of the soot transport equations requires information about C2H2 and OH concentrations only. The semiempirical model described above has been successfully employed to predict soot distribution in a set of laminar flames35 which has motivated its extension to turbulent flames.

4. Results and Discussion Results will now be presented from simulations of the Köhler et al.13 turbulent ethylene jet flame. Figure 3 shows the mean axial velocity contours from the measurements and simulations. The velocity and temperature results are within 1% of each other when the kinetic and semi-empirical models are employed, and so only the set of computed results when the semi-empirical model is employed are shown. The measured results were obtained by averaging 200 PIV datasets. Notice that the measured results are available until an axial distance of about 28 cm. The contour plot in Figure 3 shows that measured and computed results agree quite well although higher velocities are noticeable at downstream axial locations in the measurements. It is also apparent that the simulations over-predict the jet spreading which is a wellknown problem when using k-ε turbulence models to simulate round jets. While k-ε turbulence models can accurately predict turbulence in wall bounded and 2D plane jet flows, its application to round jets typically results in spreading rates being over-predicted.40-44 This can impact results. In prior work,31, 42-44 modifications to the constants employed in the standard k-ε model, as well as in the formulation of the terms in the model, have been proposed, but none of the suggestions are universal and they have not been assessed in turbulent reacting jets. In fact, all the references cited in Section 1 employ the standard k-ε model.


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Figure 3. Contours of mean axial velocity for (a) measured and (b) computed turbulent ethylene jet flame. Figure 4 shows the centerline mean axial velocity from the measurements, the simulation of Köhler et al.13 and the current work. The measured results and the computed centerline mean axial velocities from this work agree within 15% with the prior work, with the agreement between 2 and 12.5 cm being within 10%. The greater differences at the jet exit can be explained by the fact that in the current simulation a uniform injection velocity of 44 m/s is assumed whereas the measured centerline mean axial velocity at the burner exit is 47.7 m/s which is larger than the bulk mean injection velocity of 44 m/s. Figure 5 shows the mean axial velocity as a function of radial distance from the measurements, in symbols, and from the simulations, in lines, at axial distances of 6.3, 11.3, 21.3, and 36.3 cm. At an axial distance of 6.3 cm, the centerline velocity is under-predicted and radial spreading is over-predicted. This difference persists, and 9 ACS Paragon Plus Environment

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becomes more apparent, at 11.3 and 21.3 cm. There is better agreement at 36.3 cm. These results are consistent with a simulated jet that is spreading faster than the measured jet as explained earlier.

Figure 4. Measured and computed mean centerline axial velocity as a function of Height Above Burner (HAB).

Figure 5. Comparison of mean axial velocity from measurements (symbols) and simulations (lines) as a function of radial distance at several axial distances. 10 ACS Paragon Plus Environment

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The measured and computed temperature along the centerline and radially in three axial planes are shown in Figures 6 and 7, respectively. Agreement between the measured and computed results is within 5% upstream of about 7.5 cm above the burner. Computed mean centerline temperature is under-predicted by about 15% from a distance of about 7.5 cm above the burner to about 25 cm above the burner. From 25 to 32 cm, computed and measured results agree within 5%. The maximum measured mean centerline temperature of 1951 K is reached at a distance of about 34 cm above the burner whereas the predicted temperature of 2130 K is at a distance of about 37 cm. Figure 7 shows the mean temperature profiles in axial planes of 6.3, 11.3, and 21.3 cm. Notice that the measured results are only available close to the axis. The largest disagreement is in the plane at 11.3 cm and is about 10%. The predicted results are, however, within the experimental error reported in ref 13.

Figure 6. Measured (symbol) and predicted (line) centerline temperature as a function of height above burner (HAB).


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Figure 7. Measured (symbol) and predicted (lines) temperature in axial planes at (a) 6.3 cm, (b) 11.3 cm, and (c) 21.3 cm.

Figure 8 shows measured (a) and simulated (b,c) contours of soot in the jet. Results obtained with the kinetic (b) and semi-empirical (c) models are shown. The results with the kinetic model show features that are similar to those seen in ref 13, i.e. the maximum value of soot volume fraction is located upstream and the radial spread narrower compared to the measured results. Note that the narrower spread of the soot is in spite of the greater spreading of the simulated jet. With the semi-empirical model, there is noticeable improvement in the location of the soot compared to the results with the kinetic model. Figure 9 shows the soot volume fraction along the jet centerline with the two models. The results predicted with the kinetics model show its maximum value at about 12 cm above the burner. This is similar to the predicted result of Köhler et al.13 with their kinetic model as seen in Figure 1. The maximum values predicted in this work are, however, noticeably lower than in the measurements. The results with the semi-empirical model are in better agreement with the measurements with the maximum predicted value at about 25 cm compared to 30 cm in the measured results. Furthermore, the maximum values themselves agree within 5%. This may be just fortuitous as no attempt was made to match the data quantitatively. Figure 10 shows the soot volume fraction in the radial direction in three axial planes, respectively, with the semi-empirical model. These results confirm the improved agreement with semi-empirical model, relative to the kinetic model results and prior work that was discussed earlier but the persistent under-prediction of soot spreading remain a challenge. The simulated results are still concentrated closer to the axis and with an axial bound of 15 and 35 cm as shown in Figure 8.


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Figure 8. Soot volume fraction contours; (a) measured, ref 10, (b) kinetic model, and (c) semi-empirical model.

Figure 9. Centerline mean soot volume fraction from measurements (symbol) and simulations (lines).


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Figure 10. Mean soot volume fraction in the radial direction from measurements (symbol) and simulations (lines) in three axial planes.

It is worth understanding the reasons for the differences in spreading and penetration. One possible reason can be differences in oxidation. If the oxidation rate in the simulations is significantly higher, that can explain the shorter penetration and narrower spreading. Figure 11 shows the contours of the measured (on the left) and computed (on the right) OH in the flame. An average of 1000 2D OH PLIF measurements are shown on the left side of the figure with the signal intensity scaled and presented in arbitrary units (a.u.). The location of the OH matches well. The OH PLIF indicates that the measured flame lift-off height is 2.35 cm whereas the computed lift-off height is about 2 cm. What is noticeably different between the images is that there is region of high OH concentration in the simulations at all heights whereas there is a decrease in the OH concentration with increasing height above the burner in the measurements. This can affect oxidation with the oxidation being higher in the simulations than in the measurements. Radial profiles of the scaled measured OH PLIF signal and the computed OH mass fraction for axial distances of 3, 11.3, and 35 cm are shown in Figure 12. They are generally in reasonable agreement in terms of radial location. The higher predicted OH concentration can also be on account of higher entrainment of air in the computed jets on account of the known deficiency of the k-ε model in predicting greater radial spread 14 ACS Paragon Plus Environment

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than in measurements. Note that the same lower spreading and shorter penetration of the soot is also predicted by LES models25-27 which can predict the jet itself with greater accuracy than the k-ε model. This suggests that the deficiency of the k-ε model may not be primary cause of the reduced soot spreading and penetration.

Figure 11. Measured OH PLIF (left) in arbitrary units (a.u.) and computed (right) OH mass fraction.


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(a)

(b)

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(c)

Figure 12. Measured (------) OH PLIF signal in a.u. and computed (solid) OH mass fraction at axial distances of (a) 3 cm, (b) 11.3 cm, and (c) 35 cm.

The semi-empirical model was employed within the same modeling framework employed above to simulate soot in nine n-heptane diesel jets measured at Sandia National Laboratories (http://www.ca.sandia.gov/ECN). The measurements and simulations are made in constant volume chambers with injection and chamber conditions that reflect conditions in a diesel engine at top-deadcenter. Table 1 summarizes these conditions. The conditions reflect changes in the injection pressure (Pinj) (Case 2), chamber temperature (Tamb) (Cases 3, 4), chamber oxygen concentration (O2 %) (Cases 5-7), orifice diameter (dnoz) (Case 8), and in chamber density (Case 9). The numbers in bold in the Table indicate the changed parameter(s) with reference to the baseline Case 1. In ref 30, the measured lift-off heights for the jets have been predicted within 12%. Measured soot distribution is available for five of the sprays (Cases 1, 5 -7, 9). Table 1. Computational conditions for diesel jet. Parameters changed relative to Case 1 are in bold. ρamb

dnoz

Pinj

Pamb

(mm)

(MPa)

(bar)

1

0.1

150

42.66

1000

14.8

21

2

0.1

60

42.66

1000

14.8

21

3

0.1

150

55.45

1300

14.8

21

4

0.1

150

38.39

900

14.8

21

5

0.1

150

43.02

1000

14.8

15

Case

Tamb (K)

(kg/m3)

O2%


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6

0.1

150

43.20

1000

14.8

12

7

0.1

150

43.45

1000

14.8

8

8

0.18

140

42.66

1000

14.8

21

9

0.1

150

86.47

1000

30.0

15

The computational domain is a constant volume cylindrical chamber with a depth of 12 cm and radius of 5 cm. The domain is discretized with a stretched axisymmetric grid with 78 cells in the axial direction and 46 cells in the radial direction. Stretching achieves higher resolution near the injector in both the axial and radial directions. The minimum grid size is 0.6 by 0.05 mm for Case 1. Recall that the orifice radius is 0.05 mm for Case 1. Figure 13 shows the computational domain with the grid employed for Case 1. The diesel spray is modeled as a vapor jet injected with the same mass and momentum flow rate as the spray.41 This approximation is also made in ref 30.

Figure 13. Computational domain showing stretched grid. The same computational model that is described in Section 3 is employed for this part of the study. A skeletal mechanism45 of 44 species and 112 reactions is used to simulate n-heptane oxidation in the simulations. Recall that the results from these simulations are needed to provide C2H2 and OH concentrations for the semi-empirical model calculations. The temperature contours of the 9 cases of Table 1 are shown in Figure 14. Results are shown 2.5 ms after start of injection (ASI), by which time a steady 17 ACS Paragon Plus Environment

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lift-off height is achieved. The lift-off heights agree within 15% with measured values as shown in Table 2. It is important for the simulated lift-off heights to be in relatively close agreement with the measured lift-off heights because it has been suggested that the soot formation rate in the jet correlates with the mass entrained upstream of the flame lift-off height.30 It is reasonable to assume that the more the air entrained, the less the amount of soot formed. The temperature contours in Figure 14 are consistent with the understanding about diesel jet penetration and temperature variation as discussed in prior work.21 Lower injection pressure results in shorter penetration and less spreading (compare Cases 1 and 2). Higher chamber temperature results in higher flame temperature but shorter lift-off height which reduces entrained air (Cases 1 and 3) and vice-versa for lower chamber temperature (Cases 1 and 4). Lowering the chamber oxygen concentration (Cases 5, 6, and 7) reduces flame temperature. Increasing the nozzle diameter increases the momentum flow rate and penetration (compare Cases 1 and 8). The higher density of Case 9 relative to Case 5, results in shorter penetration.

Figure 14. Temperature contours at 2.5 ms after start of injection (ASI) in the 9 jets of Table 1.


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Table 2. Computed and measured lift-off heights. Lift-off Height [cm] Case

Computed

Measured

%Difference

1

1.49

1.7

12.3

2

1.35

1.35

0.0

3

0.66

0.77

14.2

4

2.22

2.55

12.9

5

2.31

2.34

1.3

6

2.76

2.92

5.5

7

4.04

4.23

4.5

8

2.42

2.40

1.0

9

1.15

1.19

3.3

Figure 15 shows the soot volume fraction contours for the 9 cases of Table 1. Results are shown at 4 ms ASI because the soot distribution has reached a quasi-steady state within the domain by this time for all nine cases. Figure 16 shows the centerline soot volume fraction for the nine cases. When compared to Case 1, the peak soot volume fraction in Case 2, where the injection pressure is 60 MPa compared to 150 MPa in Case 1, is higher and the total mass of soot formed is greater. Decreasing the injection pressure decreases the injection momentum flow rate which, in turn, reduces mixing upstream of the lift-off height and beyond. The reduced mixing results in richer mixtures downstream and greater amount of soot. Liftoff height is a measure of this mixing and hence the correlation between the lift-off height and soot. In Case 3, the soot volume fraction is increased relative to Case 1. This behavior correlates with the understanding that there is less premixing upstream of the lift-off height since the height is shorter at the higher chamber temperature. Furthermore, the higher pressure of Case 3 relative to Case 1 can also be contributing to the higher soot levels. Prior work in laminar flames have shown that integrated soot in such flames increase with increasing pressure.46 The opposite behavior is observed in Case 4 where the lower chamber temperature relative to Case 1 results in a longer lift-off height, greater mixing upstream of the lift-off height, and less soot. In Case 5, where the oxygen concentration in the chamber is decreased to 15%, the lift-off height is longer than in Case 1 resulting in less soot. This trend is accentuated in Case 6 where the oxygen concentration 19 ACS Paragon Plus Environment

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is reduced to 12% and lift-off height increases farther. In fact, in Case 7, where the oxygen concentration is further reduced to 8%, no soot is observed for the range of values shown in the contour plot. It is important to point out that in Cases 3-7, the behavior can also be explained as resulting from reduced nucleation and surface growth. Consider Case 8 where the orifice diameter is increased by a factor of 1.8 relative to Case 1. This results in an increase by a factor of 3.24 in the injected mass of fuel at 4 ms ASI. The greater amount of fuel results in greater amount of soot. In Case 9, the chamber density is more than doubled compared to Case 5. In both cases, the chamber oxygen concentration is 15%. The increase in density results in a shorter lift-off height. This shorter lift-off height does not, however, mean that the entrained air upstream of the lift-off height is less compared to Case 5 because the air entrained is denser than in Case 1. The pressure in Case 9 is, however, greater than in Case 5 by a factor of two. This increase in pressure will result in an increase in the soot mass in the jet as pointed out above for Case 3 relative to Case 1.46

Figure 15. Computed soot volume fraction contours for 9 cases of Table 1 at 4 ms ASI.


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Figure 16. Computed centerline soot volume fraction for 9 cases of Table 1.

Measured results are available for five of the nine cases, i.e. Cases 1, 5, 6, 7, and 9. Recall that these are the cases which evaluate the effects of chamber oxygen concentration, and chamber density. It is interesting to compare the simulated and measured results. Figure 17 shows the contour plots of the simulated soot volume fractions of the five cases at 4 ms ASI on the top half of the images and the measured soot volume fraction on the bottom half of each image. Figure 18 shows the quantitative comparison of the soot volume fractions along the centerline of the jet. Notice that the left y-axis is for the measured results and right y-axis for the predicted results. Measurements were taken from a database maintained by the Engine Combustion Network (www.sandia.gov/ecn). The measured soot volume fraction contours were made by averaging LII images from 1.5 to 7 ms ASI and assigning quantitative levels using averaged line-of-sight extinction data. Note that measured data past an axial distance of 8.7 cm is unavailable for Case 5, Figure 17 (b), and Case 6, Figure 17 (c). Both measurements and computations show no soot for Case 7, Fig. 17 (d). Although the computed results are shown at 4 ms ASI rather than averaged over a period of time, it is known from the simulations that the soot volume fraction distribution is at quasi-steady state at this time. In general, the agreement between the measured and computed soot location is reasonable. The computed and measured soot starts to form and reach a maximum concentration at similar axial distances. In Case 21 ACS Paragon Plus Environment

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1, measured and predicted soot start forming at an axial distance of 3.34 cm with the soot volume fraction increasing with axial distance albeit more slowly in the predictions than in the measurements initially but then faster until a maximum value is reached at axial distance of about 4.5 cm which is within 10% of the axial distance where the measured value reaches a maximum. While this may be fortuitous, the maximum values agree within 35% of each other. Table 3 shows the simulated and measured peak centerline soot volume fraction, computed and measured peak centerline soot volume fraction location and the difference between the computed and measured quantities. As the measured data beyond an axial location of 8.7 cm is unavailable for Case 6, it is assumed that the peak soot volume fraction is at 8.7 cm. The differences between the measured and computed peak centerline soot volume fraction does not exceed 50% which is within the typical difference between measured and computed results reported earlier for atmospheric conditions. The important point does not lie in the quantitative agreement, but in the fact that the changes in soot volume fraction are predicted correctly as the operating conditions are changed. Important differences between simulated and measured results are that the axial penetration and radial spread of the soot are noticeably higher in the measurements than in the computations. This behavior is consistent with the findings for atmospheric turbulent jets reported earlier and may suggest excessive oxidation as discussed then.


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Figure 17. Measured (bottom) and simulated (top) soot volume fraction contours for (a) Cases 1, (b) Case 5, (c) Case 6, (d) Case 7, and (e) Case 9.


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Figure 18. Measured and computed centerline soot volume fraction. Table 3. Simulated and measured peak soot volume fractions and their axial locations. peak soot volume fraction

measured Case [ppb]

peak soot volume fraction location

computed [ppb]

% difference

computed [cm]

measured [cm]

difference

1

1220

799

34.5

5.59

5.50

1.6%

5

750

388

48.3

7.23

7.34

1.5%

6

420

283

32.6

8.80

8.7

1.1%


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9

6880

4692

31.8

4.90

4.54

7.9%

5. Summary and Conclusion Kinetic and semi-empirical soot models are employed within a Reynolds-Averaged Navier-Stokes (RANS) computational framework to simulate a measured turbulent ethylene jet flame. Consistent with prior studies reported in the literature, the kinetic model predicts maximum soot value to lie upstream of the measured location. The radial spreading and axial penetration are also under-predicted. With the semiempirical soot model, the computed and measured peak soot volume fraction along the centerline agree within 10%, and the axial location of the peak soot volume fraction agree within 17%. But, the radial spreading and penetration are still under-predicted. This may be related to higher oxidation rates in the simulations. Overall, the predictions with the simpler semi-empirical modelling approach are in better agreement than prior results reported in the literature for the same measured flame. This model is applied to simulate soot distribution in five measured diesel sprays. The location of the maximum value of the soot volume fraction is predicted within 8% across the five sprays and the maximum value itself is predicted within 50%. While the agreement in predicted values is encouraging, the more important point is that the model correctly predicts changes in soot volume fraction and distribution as operating conditions are varied. It is shown that the model is able to predict measured features of the soot distribution better than the kinetic model employed in prior work for the same sprays. This work highlights the enormous challenges in predicting soot accurately in turbulent atmospheric and high-pressure jet flames. In general, the simpler semi-empirical model provide better predictions than the more detailed kinetic models. But, the understanding of soot formation in turbulent diffusion flames is far from complete are predicted results are sensitive to mode formulation as evident when comparing the results of this work with those of earlier studies.


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6. Acknowledgements The authors thank Dr. Klaus Peter at DLR, Germany, for providing the experimental data for the turbulent atmospheric flame. The authors thank the Reviewers of this paper for providing the references which discuss the dependence of soot formation on pressure, and several additional references on soot modeling in turbulent diffusion flames.

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