Flame–spray interaction and combustion features in split-injection spray flames under diesel engine-like conditions

Combustion and Flame 210 (2019) 204–221

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Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame

Flame–spray interaction and combustion features in split-injection spray flames under diesel engine-like conditions Wanhui Zhao a, Haiqiao Wei a, Ming Jia b, Zhen Lu c, Kai H Luo d, Rui Chen a,e, Lei Zhou a,∗ a

State Key Laboratory of Engines, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, China School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China c Clean Combustion Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia d Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom e Department of Aeronautical and Automotive Engineering, Loughborough University, LE11 3TU, United Kingdom b

a r t i c l e

i n f o

Article history: Received 12 March 2019 Revised 22 August 2019 Accepted 23 August 2019

Keywords: Split -injection Ignition Flame–spray interaction Flame structure CEMA

a b s t r a c t In compression ignition engines, split-injection strategy has shown great benefits in reducing pollutant emissions and improving combustion efficiency. Spray–flame interaction involving in split injections is significantly complex, which affects the ignition process and even pollutant emissions. Therefore, the objective of this study is to investigate how the flame–spray interaction affects the subsequent ignition process and combustion features in split injections under diesel engine-like conditions. In this work, large eddy simulation coupled with a 54-species mechanism for split injections of n-dodecane is performed to study the effect of injection duration and dwell times (DTs) on spray–flame interactions and the ignition mechanism. The numerical model gives a reasonable agreement with the experiments in terms of the vapor penetration length, ignition delay times, mixture fraction distributions and the flame structures. The present study revealed that combustion for split injections is a multi-stage process and the ignition processes for the first and second injections are controlled by different mechanisms, namely autoignition for the first injection, and the accelerating ignition for the second injection due to the intermediate species and heating effect formed in the first injection. Moreover, the increase in dwell time between individual injections reduces the subsequently promoting ignition effect for the second injection and thus weakens the interacting process between the two injections. Consumption of the fuel in the first injection leads to a temperature increase and production of different species, which in turn accelerates the ignition of the second injection. Finally, the competition between the local flow timescale and chemical timescale is investigated based on the chemical explosive mode analysis (CEMA) methods. A balance between reaction and mixing processes dominates the combustion of the quasi-steady spray in the second injection with a short DT. However, the flame is controlled by autoignition when a longer DT is used. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Increasing concern about energy security and environmental pollution has promoted the development of advanced combustion strategies, such as homogeneous charge compression ignition (HCCI), partially premixed compression ignition (PCCI), and reactivity controlled compression ignition (RCCI) [1–3]. These strategies have shown great potential of achieving high efficiency while keeping the harmful emissions low. Multiple-injection technology has been a practically feasible technique in both conventional and advanced combustion strategies by balancing low emissions and

∗

Corresponding author. E-mail address: [email protected] (L. Zhou).

high power output [2,4]. The main parameters involved in multiple injections include the pilot injection timing (PIT), pilot injection ratio, dwell time, main injecting timing, and injection duration. These parameters have great influence on both the torque output and the pollutant emissions. Using either too early a PIT or too late a PIT, the pollutant emissions, including NOx and particulate, and the engine performance can be deteriorated [5]. Pilot injection can be used to reduce the fuel/air mixing of the main injection, which can lessen the NOx , CO and UHC emissions [6]. The proportion of fuel mass injected in the pilot and main injections are crucial in organizing the split-injection strategies. The fuel/air stratification [7] and the subsequent heat release process [8] will be influenced by the injection ratio or duration. Multiple injections show a strong interaction between the previously injected combusting jet and the upcoming cold spray,

https://doi.org/10.1016/j.combustflame.2019.08.031 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

W. Zhao, H. Wei and M. Jia et al. / Combustion and Flame 210 (2019) 204–221

Nomenclature

α ɛ k

λe e τf Jω

ω

Cμ Cɛ Tign Tamb Tmax Tmean Z

species number dissipation rate turbulent kinetic energy the largest non-zero eigenvalue of the Jacobian matrix the logarithmic form of λe the integral time scale the Jacobian of the chemical source term the chemical source term =0.067, model constant =0.916, model constant the ignition temperature the initial ambient gas temperature the maximum temperature the mean temperature the mixture fraction

and this interaction has a great influence on the ignition process and pollutant emissions for split injections [9,10]. Since the mixing and combustion processes of individual injections are strongly influenced by the gas flow and compression effect, recently, researchers paid more attention to the combustion of multiple injections in a constant volume combustion vessel [9–12]. Luminosity/chemiluminescence images showed that the two injections strongly interact with each other, thus further affecting the ignition and pollutant emissions. Skeen et al. [12] performed double injections at different ambient temperatures with an injection pressure of 150 MPa. Shorter ignition delays (IDs) were observed for the second injection because of the entrainment of hightemperature gases and intermediate species from the combustion of the first injection. The increase in the pressure and local temperature created favorable conditions for the second injection to ignite earlier [13]. Owing to the fuel-richer ignition and the interaction between the two consecutive fuel injection events, higher soot emission was observed for double injections compared with the single one [14]. Moiz and co-workers [9,10,15] performed both experimental and numerical studies to investigate the ignition and quasi-steady combustion process, as well as soot production under diesel engine-like conditions. The results show that by decreasing the initial temperature to 800 K, the production of soot in the first injection was negligible. Hasse and co-workers [16,17] applied the representative interactive flamelet (RIF) model for multiple injections. Lim et al. [18] extended the RIF model and only applied the 2-dimensional flamelet equations near the stoichiometric region, finding that the ignition delay for the second injection was closely related to the time when the vapor from the second injection starts to come into contact with the radicals generated in the first injection. Blomberg et al. [19] compared the combustion process of split injections using a conditional moment closure model (CMC) within the Reynold-Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES) methods, and concluded that the combustion recession at an initial temperature of 900 K could be captured by the LES approach, but not for RANS. The effect of the first injection has been investigated both experimentally and numerically [10–12]. Ignition of the second injection is attributed to different mechanisms. Combustion of the fuel/air mixture formed in the first injection creates a hightemperature environment with different kinds of intermediate species. The temperature rise in the combustion chamber accelerates the appearance of autoignition of the second injection. In addition, the first injection leaves residual flames behind. Once the second injection penetrates into the reaction regions, it can be ig-

205

nited by the hot flame directly [11]. By increasing the dwell time, the combustion region moved far away from the second injection. As a result, the enhanced evaporation and mixing effects from the combustion of the first injection were restrained. A previous study [20] found that the entrainment of oxygen was influenced by the dwell time. By prolonging the interval between the pilot and main injections, entrainment of surrounding oxygen into the flame region was increased and the smoke emissions were reduced. Different conclusions were drawn in [21], in which an endoscopic visualization system was used to investigate the matching between the pilot and main injections with different pilot ratios and dwell times. Only the pilot injection with a small pilot ratio and short dwell time could obtain high thermal efficiency. However, very few studies have focused on the competing effect of the local flow and chemistry time scale in split injections with variations in injection duration and dwell time (DT). Investigation on the local spray–flame interaction is quite challenging due to the lack of detailed temperature and species spatial distributions in experiments. The dwell time between individual injections affects the spray–flame interaction, the subsequent ignition process, and even pollutant emissions. The objective of this study is to investigate how the flame–spray interaction affects the subsequent ignition process and combustion features in split injections under diesel engine-like conditions. The spray–flame interaction is also influenced by the injection parameters. For this purpose, the effect of variations in injection durations and dwell times on the interaction of constituting injections is further studied. The novel features of the present work are (1) to investigate the ignition process and mechanisms for individual injections; (2) to evaluate how the dwell time and the first injection duration (FID) affect the spray–flame interactions and the difference between the movement of the individual injections; and (3) to study the dominant factor controlling the autoignition and stabilization processes of the second spray. For this purpose, the important intermediate species and CEMA are introduced. Besides, combustion of the second injection is significantly influenced by the products and intermediate species from the first injection. Analysis of the effect of DT and FID may contribute to the organization of advanced combustion strategies. The remainder of this article is structured as follows. The numerical approach and experimental setup are briefly presented in Section 2. Section 3 gives the simulated results and discussions, and the conclusions are shown in Section 4. 2. Methodology 2.1. Experimental and numerical setup Spray experiments have been performed in a constant volume combustion chamber. The test cases are denoted as Spray A in the Engine Combustion Network (ECN) [22]. The fuel injection pressure is 150 MPa, and the fuel temperature is 363 K. The nominal orifice diameter of the injector is 90 μm. The ambient gas density is 22.8 kg/m3 . In the experiments from Skeen et al. [12], a double injection schedule (0.5 ms/0.5 dwell/0.5 ms) was employed at different temperatures. Moiz et al. [8,10] performed double injections with shorter first and longer second injection durations (0.3 ms /0.5 dwell/1.2 ms) to study soot production. Based on their works, double-injection strategies with short and long FIDs were studied at different dwell times. Injection parameters for the investigated cases can be found in Table 1. As advanced combustion strategies always work at low temperature or low oxygen concentration conditions, different injection strategies are adopted at a low initial temperature of 800 K under reacting conditions. The injected fuel mass for the split injections is the same as that in the previous studies [10,12].

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Table 1 Injection parameters. Case

Duration 1st (ms)

Dwell (ms)

Duration 2nd (ms)

L1 L2 L3 S1 S2 S3

0.5 0.5 0.5 0.3 0.3 0.3

0.5 1.0 1.5 0.5 1.0 1.5

0.5 0.5 0.5 1.2 1.2 1.2

2.2. Flow solver The numerical scheme of the employed program is based on the Arbitrary Lagrangian–Eulerian method with finite volume method [23]. For the continuum phase in LES, a third-order Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) [24] is implemented to obtain high order accuracy for the convection term. The MUSCL scheme showed good performance in predicting the non-reacting spray structures and ignition process for reacting jets, as discussed in our previous study [25]. To describe the effects of the filtered small scale turbulence, a k-equation subgrid turbulent kinetic energy model with Cμ = 0.067 and Cε = 0.916 [26] has been implemented, which is named as KIVALES code. The present KIVALES version is further extended to include the linear eddy model (denoted hereafter, as LES–LEM [26]). The LEM model offers a fundamentally different closure for the scalar fields within the context of LES. In LEM, subgrid turbulent mixing and molecular diffusion processes evolve concurrently in a onedimensional domain within each LES cell and the turbulent mixing is considered by a stochastic approach called triplet map [27]. No parameters are required to adjust to the LES–LEM method. In order to simulate the combustion process, parallel computation of the chemistry using the Message-Passing Interface (MPI) has been implemented into KIVALES code. MPI allows for chemistry to be calculated in parallel on several CPUs. This process is accomplished at each computational time step. Once combustion occurs and chemical kinetic calculations start, KIVALES transfers the temperature, pressure and compositions information from each LES cell to CHEMKIN, where chemical reactions are computed on a number of CPUs using decomposed uniform grids. It means that the chemical reactions are solved on LES cells based on the average composition, pressure and temperature information. A similar method has been applied for the simulation of non-premixed hydrogen jet flames by Zhou et al. [28]. In the present work, a skeletal mechanism including 54 species and 269 reactions [29] was used, which validated against shock tube data, jet stirred reactors and laminar premixed flames. And the skeletal mechanism shows very good accuracy over a wide range of conditions for the simulation of Spray A [30–32]. The discrete droplet model (DDM) [23] is applied for the discrete phase. The droplet particles were tracked by solving the droplet velocity, mass, and temperature equations using the Lagrangian method. The Kelvin–Helmholtz Rayleigh–Taylor (KH–RT) model [33] is used to predict the primary and secondary liquid breakup processes. And the O’Rourke [34] model is employed for the simulation of collision and coalescence. The interactions between liquid and gas phases are described through a two-way coupling, i.e. “gas-to-liquid” and “liquid-to-gas”. In “gas-to-liquid” coupling, the changes of the droplet velocity in the computation domain are attributed to the drag force Fi, d on droplet and they are calculated in terms of the relative velocity between the droplet and the gas. In the “liquid-to-gas” coupling, the effects of liquid motion on the gas phase are treated as the Lagrangian source terms in the Eulerian momentum equation. Note that in LES the subgrid dispersion velocity model [35] is employed to calculate the effects

of turbulent flows on droplets. Furthermore, the spray source term model [36] with a two-test filtering subgrid gas velocity treatment is used to deal with spray effects on the subgrid turbulent kinetic energy. Equations for spray modeling can be found in our previous study [25]. The present model can give a good agreement with the experiments with variations in injection strategies (single injection or split injection) and injection pressure. Validation of the present model including the penetration lengths for single and double injections, mixture fraction distributions, and flame structures is given in Appendix A. Moreover, results also show that the present model can give a reasonable prediction both for Spray A and Spray H. Detailed information can be found in Appendix A. 3. Results and discussion 3.1. Ignition process and ignition mechanisms 3.1.1. Ignition process for the first and second injections The previous study [10] showed that the dwell time has a great influence on soot formation. In this section, the autoignition process for the double injections with an FID of 0.5 ms is further analyzed, and meanwhile, the combustion process at different dwell times (DT) is mainly investigated. The temporal evolutions of key species in the temperature versus mixture fraction (Z) space are shown in Fig. 1, including formaldehyde (CH2 O) and hydroxyl (OH). It is noted that only points with Yα > 20% × Yαmax are shown in Fig. 1, where Yαmax is the maximum value of Yα . Distribution of CH2 O mass fraction in the T–Z space is given in Appendix B, where the information for all LES cells is shown. As mentioned above, autoignition for the first injection appears during the dwell time. Musculus and Kattke [37] found that a so-called ‘entrainment wave’ travels downstream through the jet at twice the initial jet penetration velocity after the end of the injection (EOI). An increase in mixing leads to fuel-lean mixtures in the transient jet. The entrainment wave has been shown to increase the entrainment after EOI by a factor three. Consistent with this conclusion, the present study illustrates that the entrainment of the mixing after the end of the first injection is improved, and thus fuel-rich regions are significantly reduced. The mixture fraction is less than 0.1 in the computational domain. However, it should be noted that autoignition is still initiated in the region where the mixture fraction is greater than stoichiometry. In addition, Fig. 1 also shows that OH and CH2 O are located at different places in the T–Z space. OH is mainly formed at high-temperature regions with stoichiometric mixture fraction (Zst), and CH2 O as one ignition precursor is distributed over a wider region in the mixture fraction space at low-temperature regions. Since the second injection starts at later times after the start of injection (ASOI) with a long DT, the first injection already moves further downstream. The effect of dwell time on the ignition of the second injection at different times after the start of the second injection (ASSI) is shown in Fig. 2. Key intermediate species, including OH and CH2 O, are plotted in the T–Z space at times relative to the start of the second injection. By increasing the DT, the second shot is injected into the combustion chamber under different conditions in terms of temperature and chemical compositions compared with the case with a short DT. For the case with DT = 0.5 ms, the second injection penetrates into intermediate products and experiences first-stage ignition with an advanced timing, as reported in the experimental study [12]. At 0.1 ms ASSI, CH2 O appears in the near-injector region, which is characterized by low temperature and different values of Z. At 0.2 ms ASSI, temperatures in the cells of fuel-rich regions increase to 1500 K approximately, indicating that the ignition process for the second injection is initiated very quickly. In a previous study, Gong et al. [38] studied the two-stage ignition process of Spray A from a

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Fig. 1. Ignition process for the first injection with an injection duration of 0.5 ms. The black dashed line represents the stoichiometric mixture fraction (Zst).

Fig. 2. Combustion process at different times after the start of the second injection (ASSI). Top: Case L1, DT = 0.5 ms, Middle: Case L2, DT = 1.0 ms, Bottom: Case L3, DT = 1.5 ms. The black dashed line represents the place of Zst.

single injection based on the development of several species. Following their study, the consumption of ketohydroperoxide (KET) and the formation of H2 O2 indicate the onset of the first-stage ignition. And the rapid decomposition of H2 O2 together with the formation of OH implies the onset of the second-stage ignition. Since the temperature for fuel is 363 K, fuel droplets evaporate during a very short time to form fuel/air mixture before they penetrate into high-temperature regions caused by the combustion in the first injection. Thus, during this time, fuel/air mixture needs to initiate the first-stage ignition with different intermediate species formed in the second spray. Consequently, the high-temperature ignition occurs quickly after the two injections starting to get contact. By increasing the dwell time, the combustion process has been sustained for a longer time, and consumption of fuel from the first injection is more complete at the time when the second injection starts. As a result, the effect of intermediate species on the ignition of second injection becomes minor. By increasing the DT, most of CO is converted to CO2 during the high-temperature ignition stage by CO+OH→CO2 +H [39]. Thus, more CO2 is formed

in the entire domain, and due to diffusion, CO2 is located in a wider region. The increase in the CO2 production and temperature generated by the first injection plays an important role. Production of CO2 delays the high-temperature ignition of the second injection, and on the contrary, the increased temperature promotes the ignition process. Once the cold second injection penetrates into the already burnt region, the fuel spray is surrounded by CO2 to prevent the high-temperature ignition. Moreover, due to the increased time before the first and second injections starting to interact with each other at a longer DT, ignition is prolonged for the second injection. For example, in the case with DT = 1.5 ms, both OH and CH2 O mass fractions are lower than 20% of the maximum value at 0.1 ms ASSI. The appearance of high-temperature products, for example OH, is delayed by increasing the dwell time. The tail of the first injection has moved further downstream, and thus more time is needed for the second injection to catch up with the tail of the first injection. After the two injections start to interact with each other, high-temperature reactions occur in the second spray quickly. It means that the fuel/air mixing for the

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W. Zhao, H. Wei and M. Jia et al. / Combustion and Flame 210 (2019) 204–221 Table 2 Ignition process for the homogeneous reactor.

Fig. 3. Comparisons of CH2 O mass fractions, axial velocities, and temperatures for the first and second injection spray heads (Case L1, DT = 0.5 ms).

second injection strongly depends on the interaction time before high-temperature ignition. Brands et al. [11] found in the chemiluminescence/luminosity images that the high-temperature reactions in the second injection start almost immediately when the two individual injections get into contact. Thus, they made a conclusion that the second injection is ignited directly by the combustion of the first injection. It is true for the case with a short DT. However, the combustion regions get cooler and more oxygen is entrained into the already burnt region by increasing the DT. Longer time is needed for the interaction between the first combusting spray and the second injection. Consequently, the prolonged interaction time and the entrainment of oxygen into the burnt region in the first injection lead to the improved mixing process with a long DT. As a result, the high-temperature kernels appear in fuel-leaner regions compared with a short DT (case L1). Moreover, distributions of OH in the T–Z space become very sparse at long DT, indicating that high-temperature reactions are weaker than that in the cases with short DT at the same time after injection. More time is needed for the two injections to interact with each other and the time when the second injection penetrates into the burning regions is also delayed at longer DT. Therefore, combustion in the first injection has a weak influence on the subsequent ignition process for the second injection during the early time after the start of injection. Fresh air enters into the low-density zone after the combustion of the first injection. As a result, the entrainment in the second injection at a long DT is improved with less fuel-rich regions compared to the case with a short DT. Thus, the improvement in the mixing process between fuel and air leads to a reduction in soot emission [10]. 3.1.2. Analysis of ignition mechanism To compare the flame development for the first and second injections, temporal evolutions of CH2 O mass fraction, axial velocity, and temperature profiles at the second spray tip are shown in Fig. 3. Lines without symbols represent the time interval after the start of the first injection (ASFI) and lines with symbols are the time interval ASSI. At the same time interval after the start of injection, autoignition for the first ignition has not occurred. The injected fuel is evaporating, and thus temperature at the spray tip is very low. It shows in Fig. 3 that the temperature increase at

T (K)

P (MPa)

O2 (%)

Addition/%

700– 1300

5.25

10 10 10 10 10

No addition C12 H25 O2 /0.01; 0.05 CH2 O/0.1; 0.5 H2 O2 /0.1; 0.5 OH/0.01; 0.05

the second spray tip at 0.3 ms ASFI is small and the highest temperature at the inner side is below 10 0 0 K. However, at 0.3 ms ASSI, the maximum temperature at the inner head is more than 20 0 0 K, indicating the appearance of high-temperature reactions. Desantes et al. [40] pointed out that locations of the spray tip for the non-reacting and reacting sprays are very similar prior to ignition. However, once high-temperature reactions occur, the spray head is significantly accelerated due to gas expansion. Comparisons of the spray tip for the first and second injections illustrate the effect of combustion. Combustion occurs much earlier in the second injection, while the fuel droplets are still evaporating at the same time interval after the start of injection. The movement of the second spray head is quickly accelerated and the velocity is much higher. Therefore, the second spray head quickly deviates from the first one caused by the gas expansion after combustion. In addition, the second spray is injected into a higher-temperature environment with different intermediate species, and different mechanisms may dominate the ignition process for the first and second injections. For example, Fig. 3 also shows the difference in terms of CH2 O distributions ahead of the spray. High-temperature reactions appear much earlier, thus restricting the mixing time between fuel and air and leading to fuel-richer ignition. The decomposition of fuel molecule leads to high levels of CH2 O which can shorten the ignition delay times [41]. Our aim is to compare the effects of the temperature increase and the appearance of different intermediate species on the ignition process of the second spray since the different environment can contribute to the different ignition mechanisms which are further discussed below. Luong et al. [39] identified the key species during the combustion process of a primary reference fuel/air mixture based on the chemical explosive mode analysis. It is found that RO2 is one of the most important species in the low-temperature chemistry pathway. RO2 is formed by the oxidization of R radical which is produced by the H-atom abstraction from a fuel molecule. Between the first- and second-stage ignition, the low-temperature reactions are suppressed by the chain branching reaction H2 O2 + M  OH + OH + M. When the temperature rises above 10 0 0 K, H2 O2 decomposition exceeds its production. Then the formed OH pool significantly accelerates the overall reaction rate. Moreover, CH2 O, representing cool flame, and H2 O2 can also be used as ignition precursors. Thus, C12 H25 O2 (or known as RO2 ), CH2 O, H2 O2 , and OH are used to represent the main species formed ahead of the second spray. And the presence of these species on the subsequent ignition process is further studied. Different cases for a homogeneous reactor with C12 H25 O2 , CH2 O, H2 O2 , or OH additions are shown in Table 2. As a large amount of oxygen is consumed by the first injection, the effects of species addition on the ignition process at low oxygen concentration are investigated. The initial temperature for the homogeneous reactor is chosen based on Fig. 4, in which the temperature at the second spray tip is slightly increased at 0.1 ms ASSI. Meanwhile, as reported in [12], the pressure rise is very little. Therefore, the initial pressure for the cases shown in Table 2 is set to 5.25 MPa, equal to the initial pressure for the 3D constant volume combustion vessel. The predicted ignition delay times in the temperature versus equivalence ratio space without species addition are shown in Fig. 5 using CHEMKIN-Pro [42]. The

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Fig. 4. Predicted IDs at different temperatures and equivalence ratios without species addition.

predicted IDs with values of 0.1 ms and 1.0 ms imply the mixture with short and long IDs, as shown in Fig. 5. It shows that ndodecane exhibits a negative temperature coefficient (NTC) regime in the region with temperature ranging from 900 to 1100 K and equivalence ratio smaller than 2. At the regions with a temperature lower than 800 K, ID is longer than 2.0 ms at different equivalence ratios. To study the effect of those species including C12 H25 O2 , CH2 O, H2 O2 , and OH on the ignition process, comparisons of the IDs with different species addition are shown in Fig. 5. C12 H25 O2 is one of the key species in the low-temperature reactions through the O2 addition to the R radical. CH2 O can be used to mark the cool flame, H2 O2 is decomposed intensively once temperature increases over 10 0 0 K [39]. Comparing Fig. 4 and Fig. 5, it can be seen that ID is reduced in the low-temperature regions even by adding a small amount of C12 H25 O2 . At the regions with a temperature greater than 800 K, the effect of C12 H25 O2 addition on the ID is insignificant, especially for the fuel-rich mixtures. The appearance of C12 H25 O2 promotes the low-temperature chemistry, and the production and decomposition of ketohydroperoxide are also promoted [39]. Once the temperature rises above 10 0 0 K, the chain-branching reaction of H2 O2 plays the dominant role. C12 H25 O2 can be quickly consumed and its influence on the ignition process is very weak. In contrast, the addition of CH2 O mainly prolongs the autoignition timing for the mixture with a temperature lower than 950 K. Owing to CH2 O addition, the times when the ketohydroperoxide starts to form, and when the temperature starts to increase quickly are delayed. The maximum OC12 H23 OOH mole fraction is also reduced, indicating that the low-temperature reaction path is restrained with the addition of CH2 O. For the fuelrich mixture with a temperature above 1200 K, the effect of CH2 O addition on the ID is negligible. Similar to CH2 O addition, the existence of H2 O2 in the initial gas prolongs the ID at low initial temperatures. For the mixture with a temperature above 10 0 0 K, the decomposition of H2 O2 is promoted through the chain-branching reaction H2 O2 +M  OH + OH + M. The temperature rise appears earlier and a reduction in the ID is observed. In contrast, a previous study found that the addition of CH2 O and H2 O2 can significantly shorten the ignition process for methane/air mixture [41]. CH2 O and H2 O2 are the two of the most important species related to the explosive mode that case autoignition. However, they are two species built up during the first-stage of ignition for n-dodecane,

209

which exhibits a two-stage ignition process. Their promoting effect on the ignition process only occurs at a high temperature. As shown in Fig. 5(g) and (h), IDs are significantly reduced through the addition of OH, especially for the mixture with equivalence ratio greater than 1.5, and most of the mixture has an ID lower than 0.1 ms with 0.05% addition of OH. However, OH is mainly formed in high-temperature regions. The production of the amount of OH in the second spray still needs more time due to the limited mixing between fuel and air. After about 0.2–0.3 ms ASSI, high-temperature reactions appear in the first spray, where high concentration of OH is formed. Once the second spray catches up with the first one, a significant reduction in ID can be observed. Hence, it can be concluded based on Fig. 5 that the existence of CH2 O and H2 O2 prolongs the ID at low temperatures. Although the existence of C12 H25 O2 shortens the ID, this effect is very limited. The addition of OH significantly reduces the ID, especially for the fuel-rich mixture. In spray flames, amount of OH has formed quickly after the start of the second injection. Once the first and second injections get to interact with each other, the existence of OH in the first spray can ignite the second injection. Therefore, the second injection is ignited by the first one. Figure 6 illustrates the effect of the existence of two species on the ignition process and it shows that the addition of CH2 O with H2 O2 mainly prolongs the ignition process at a low temperature below 800 K over a wide range of equivalence ratio. It can be interpreted by that the existence of high levels of CH2 O together with H2 O2 suppresses the low-temperature reaction pathways, thus limiting the accumulation of heat before the second stage of ignition. In contrast, the existence of RO2 (or C12 H25 O2 ) significantly shortens the ignition delay for all mixtures by promoting the low-temperature reactions, i.e. the isomerization of RO2 to generate hydroperoxy alkyl, QOOH, and the second O2 addition reaction via QOOH + O2  O2 QOOH. It is found that the production and decomposition of ketohydroperoxide (KET) determine the overall rate of low-temperature combustion (LTC) [39]. 3.2. Effect of injection duration on combustion The injected fuel mass or injection duration for the first injection is of great importance to improve fuel stratification [7], optimize the combustion phasing [8], and reduce soot emission [43,44]. Therefore, in order to optimize the combustion process, the ignition process for double injections with different FIDs should be further analyzed in detail. Figure 7 shows the scatters in the temperature versus mixture fraction space with different dwell times at short FIDs (Cases S1–S3). Similar conclusion in terms of the ignition process can be found by increasing the DT with long and short FIDs. OH and CH2 O mass fractions are weaker at longer DTs. The fuel/air mixture in the first injection becomes leaner than that at a long FID at the autoignition timing due to the lack of fuel. Before the start of the second injection, the mixture becomes very lean. Thus, OH is mainly formed in fuel-lean regions. After the start of the second injection, the fuel-rich mixture is formed to support the production of CH2 O. Although CH2 O is found in fuel-lean regions, most of them are still formed in fuel-rich regions in the inner side of the second injection. It should be noted that compared to the cases with long FIDs, the second injection starts much earlier than the case with the same DT but a longer FID. The first injection has burned for a shorter time. Therefore, there are many cells with OH mass fraction greater than the 20% of the maximum value at 0.1 ms ASSI with DT = 1.5 ms. Then at 0.3 ms ASSI, combustion of the first injection is more complete. Thus, OH mass fraction is very weak. The appearance of OH mass fraction around Zst is again attributed to the combustion of the second injection. To further compare the combustion process with long and short FIDs, temporal evolutions of the mean temperature and apparent

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Fig. 5. Predicted IDs with different species addition.

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Fig. 6. Predicted IDs with two species addition.

Fig. 7. Ignition process for the second injection with a short FID. Top: Case S1, DT = 0.5 ms, Middle: Case S2, DT = 1.0 ms, Bottom: Case S3, DT = 1.5 ms. The black dashed line represents the location of Zst.

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900

850

900 DT=0.5 DT=1.0 DT=1.5

Tmean (K)

DT=0.5 DT=1.0 DT=1.5

850

800

200000

200000

150000

150000

AHRR (J/s)

AHRR (J/s)

800

100000 50000 0

0

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Tmean (K)

212

100000 50000 0

0

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1

1.5 2 Time (ms)

2.5

3

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(b) FID= 0.3 ms

Fig. 8. Temporal evolutions of mean temperature (Tmean ) and apparent heat release rate (AHRR). (a) Solid: Case L1; dash: Case L2; dash dot: Case L3; (b) Solid: Case S1; dash: Case S2; dash dot: Case S3.

heat release rate (AHRR) are shown in Fig. 8. Due to the combustion of first and second injections, the mean temperature in the entire computational domain is increased. With the earlier start of the second injection, the time when the profiles of Tmean continue to increase occurs much earlier. What is more, there are mainly two peaks in the AHRR profiles. The first peak is due to the premixed combustion of the first injection, while the second one is related to the consumption of the fuel injected during the second injection. Moiz et al. [8] experimentally compared the overall heat-release process by using the same injection strategy with Cases L1 and S1 but at a low temperature of 750 K. It should be noted that the ignition delay time at such a low temperature is significantly prolonged. The injection strategy with either a long or a short duration for the first injection does not help in an early ignition. However, more fuel is consumed in the premixed regime by using a short FID but a long duration for the second injection due to the longer ignition delay. Hence, a higher peak value for the heat-release profile is observed. On the contrary, high-temperature ignition occurs during the dwell time for the case with long FIDs. More fuel is injected into the computational domain, leading to a higher peak value in AHRR profile for the first injection before 1.2 ms. For the cases with a short FID, fuel/air mixture becomes very lean before the wide consumption of fuel, and a low AHRR peak is observed due to the lack of fuel. And most of the heat is released after the start of the second injection during which more fuel is injected into the combustion chamber. By increasing the DT, the peak AHRR appears much later. A previous experimental study found that the increase in fuel mass injected during the first injection provides a beneficial thermal condition for soot formation [43]. Thus, both the first and second injections emit higher levels of total soot mass for the case with a longer FID at an initial temperature of 870 K. The overall concentration is a bit richer for the case with a long FID. The time when the second injection starts has a great influence on the formation of CH2 O and the evaporated fuel mass, as shown in Fig. 9. CH2 O is formed in a wide region in the first injection, which promotes the appearance of high-temperature reactions. Less fuel is injected into the chamber during the first injection, leading to a low peak value in the total CH2 O mass. Once the high-temperature kernels appear, consumption of CH2 O leads

to the decrease of CH2 O mass [45]. As shown in Fig. 9, at the time when fuel mass starts to decrease, CH2 O mass in the entire combustion chamber starts to increase, indicating that n-dodecane is mainly consumed by the cool flame in the first injection. Once the second injection begins, the increase of the accumulated CH2 O mass profiles is not as quick as that in the first injection, indicating that the cool flame is not as obvious as that in the first flame. Since the ignition delay for the second injection is reduced compared with that in the first injection, the injected fuel goes into the hightemperature regions quickly. The high-temperature environment promotes the evaporation of fuel droplets and the appearance of high-temperature reactions in the second injection. The consumption of fuel in high-temperature reactions plays a dominated role. To further show the effect of DT on the combustion process of n-dodecane spray flames, the distributions of temperatures, mass fractions of fuel and oxygen along the axial direction are shown in Fig. 10. It should be noted that profiles are extracted along the center line of z-axis. The high-temperature regions mainly represent the combustion region in the first spray. The flame length is longer for the case with a long DT characterized by a longer hightemperature region. Oxygen concentration in the high-temperature regions is also higher than that in the other two cases with short DTs. This is because that although the oxidizer is consumed by the combustion of the first injection, the reduction in density due to gas expansion leads to the entrainment of O2 from the ambient gas to support the oxidization of the fuel for the second injection. By comparing the cases with the same DT and different FIDs, the temperature at the flame front is reduced with short FIDs because of the over-mixing between fuel and air in the first injection, as shown in Fig. 10. The mixture becomes too lean, and the combustion temperature drops obviously. Comparisons of the flame structures at different dwell times are shown in Fig. 11. It shows that the flame tip has moved downstream freely with less time for the cases with short FIDs, and thus, the second spray head could catch up with the first flame much earlier compared to the cases with longer FIDs. The first and second flame heads have merged before 2.0 ms ASOI, but there is a small gap between the first and second flame heads for the case with DT = 0.5 ms, as shown in Fig. 11(a). By increasing the DT, the maximum temperature in the first flame is reduced at the same time

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0.08 0.06 0.04 0.02

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T (K)

DT=1.0

0

2000

Yi

0.2 0.2 0.1 0.1 0

0.3

DT=0.5 T (K)

DT=0.5

2000 2000

YiYi

TT (K) (K)

Fig. 9. Temporal evolutions of fuel and CH2 O mass. (a) Solid: Case L1; dash: Case L2; dash–dot: Case L3; (b) Solid: Case S1; dash: Case S2; dash–dot: Case S3.

2

4 6 Axial Distance (cm)

8

0 10

(b) FID= 0.3 ms

Fig. 10. Profiles of instantaneous T and Z along the center axis at 0.4 ms ASSI with long and short FIDs. (a) Solid: Case L1; dashed: Case L2; dash–dot: Case L3; (b) Solid: Case S1; dashed: Case S2; dash–dot: Case S3.

ASOI, and ignition of the second injection is delayed in the cases with longer DTs. 3.3. The stabilization mechanism for double injections 3.3.1. Analysis of penetration length Following the work by Maes et al. [46], we introduced intensity axial time (IXT) plots by radially integrating planar fields of OH, CH2 O, and C2 H2

Ixt,i = ∫ Y˜i (x, y, t )dy

with

i = OH, CH2 O, C2 H2 .

(1)

A similar method was also used in [47]. The intensity Ixt is a function of axial distance and time. The IXT contours clearly show some aspects of spray flames in terms of lift-off length, flame

height, and even internal flame structure [10]. The formation region of CH2 O marks the location of cool flame, and the main zone of OH formation indicates the high-temperature combustion region as well as the flame height. After rapid evaporation and turbulent mixing, the early low-temperature reactions are initiated in the radial periphery of the jet, producing various intermediate species and radicals, such as RO2 , CH2 O, and H2 O2 [48,49]. Consequently, the turbulent cool flame wave propagates from the initiation point to both upstream and downstream locations [50]. For the case with short dwell time (Case L1), CH2 O formation region moves to most upstream locations at the time around 1.0 ms. After that location of CH2 O formation region gets quasi-steady, as shown in Fig. 12. The low-temperature reactions in the first injection lead to temperature increase and formation of intermediate species and radi-

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Fig. 11. Temperature contours at different times ASOI. (a) Solid: Case L1; dash: Case L2; dash–dot: Case L3; (b) Solid: Case S1; dash: Case S2; dash–dot: Case S3.

cals. When the temperature is above 10 0 0 K, the production of OH radical through H2 O2 + M  OH + OH + M outweighs the decomposition rate [4], and thus, OH intensity starts to increase at the time roughly prior to 1.0 ms. Consequently, the rapid consumption of fuel/air mixture through high-temperature reactions elevates the temperature. Due to the reduction in mixing time and oxygen concentration, higher levels of C2 H2 are formed in the second injection. Moreover, combustion of the mixture also prevents fresh air from entering into the inner spray [51], thus further reducing the entrainment in the second injection. As reported in the experimental study by Skeen et al. [12], the first and second injections show strong spray–flame interaction, which is strongly influenced by gas temperature and density [52]. The spray heads of the first and second injections meet an absolutely different environment in terms of gas temperature, density, and oxygen concentration. The spray–flame interactions are strongly influenced by the dwell time from the first and second injections, as shown in Fig. 12. Combustion of the fuel injected during the first injection creates a low-density environment, which reduces the resistance ahead of the second spray. The decrease in the gas density leads to gas expansion, which accelerates the movement of the second injection. Thus, the second spray tip moves faster than the first one, as confirmed by the experimental study [12]. By increasing the time interval between the two injections, combustion of fuel is more complete. Less CH2 O and OH formation regions are overlapped in the two injections. It means that the influence of the previously injected spray on the combustion of the second one becomes less important. The spray–flame interaction of two injections is less aggressive by prolonging the injection timing for the second spray. The improvement in the entrainment causes less C2 H2 formation. 3.3.2. Chemical explosive mode analysis Chemical explosive mode analysis (CEMA) is employed for the study of the development of n-dodecane spray flame using different injection strategies. CEMA was shown to be robust diagnose of complex fields and it can be used to predict the important flame features, such as ignition, extinction, and flame fronts [53–56]. In this study, CEMA method is briefly summarized. The Jacobian of the chemical source term, Jω , in the governing equations can be used to account for the local chemical characteristics. Jω is calculated by Jω = ∂ ω/∂ y, where ω represents the chemical source term, and y is the vector of species concentration and temperature. A chemical explosive mode (CEM) is known as the state with Re(λe ) > 0 where λe is the largest non-zero eigenvalue of the Jacobian matrix. A large positive eigenvalue indicates an explosive mix-

ture, and autoignition is underway. While negative values for e mean the mixture already ignited. The transition of a CEM from explosive, i.e., Re(λe ) > 0, to non-explosive, i.e., Re(λe ) < 0, can be regarded as a flame front or flame surface [54,57]. CEMA focuses on the unique features of the CEM, which is derived from all of the species concentration, temperature and pressure information on each cell. While the computational singular perturbation (CSP) concept is only based on the slow dynamics of a specific scalar, such as temperature [58]. Different combustion modes under HCCI, RCCI and stratification charge compression ignition (SCCI) conditions have been investigated by Yoo and colleagues using direct numerical simulation (DNS) [39,59]. Results showed that the combustion mode depends on the temperature gradient, fuel concentration and fluctuations in temperature [59]. Higher n-heptane concentration favors deflagration and lower n-heptane concentration favors ignition front. And high temperature stratification favors flame propagation [60]. Those conclusions are mainly made based on premixed combustion. However, both premixed and nonpremixed combustion coexist in turbulent spray flames [61]. To further examine the nature of the flame, a local Damköhler number, Da, is shown in Fig. 13. Da is defined as:

Da = τ f × |λe |

(2)

where τ f represents the integral time scale, which is calculated by τ f = k/ε . Distributions of T, e , and Da for double injections are shown in Fig. 13 with a long FID, i.e. (a)–(c), and a short FID, i.e. (d)–(f). The horizontal dashed line represents the position of flame lift-off length (FLOL). It shows that two flame bases are located near the FLOL. The transition for e at the position of FLOL from a positive value to a negative value can also be observed in Fig. 13. For double injections, the FLOL is reduced, and combustion of the second injection could extend to the upstream regions with higher scalar dissipation rates where high-temperature kernels could not sustain for single injection [17]. It should be noted that CEM represents the reciprocal chemical time scale of a local mixture. The appearance of CEM implies that the corresponding mixture is explosive. In the upstream the flame surface regions, Re(λe ) > 0, indicating that the mixture is explosive and autoignition is likely to occur without significant loss in heat and radicals. The previous results from the 1-D laminar simulations showed that a Da diffusive limit existed, below which, combustion of the mixture was due to flame propagation without autoignition. Although the critical value of Da is changed with the fuel, it is in order of unity [39,62,63]. In the present work, for the cases with short DT, for example with DT = 0.5 ms, combustion of the first injection provides a high-temperature environment. Xu et al. [64]

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215

Fig. 12. Radially integrated intensity for OH, CH2 O, and C2 H2 with different dwell times. Top: case L1 (DT = 0.5 ms), middle: case L2 (DT = 1.0 ms), bottom: case L3 (DT = 1.5 ms).

defined different zones in spray flames based on the eigenvalue distributions, namely the post-ignition zone with a negative value of λe , the premixed reaction fronts with λe = 0, the pre-ignition zone with a positive value of λe , and the chemically inactive zone with λe around zero. They also concluded that in the pre-ignition zone turbulence-chemistry interaction (TCI) is insignificant and it can be treated by the well-mixed model. It means that the species fluctuations can be ignored. In our work, we mainly want to investigate the spray–flame interactions which mainly occur in the region very close to the pre-ignition zone. The results derived from the CEMA approach and calculated by mean value on each LES cell are still credible. The different zones can also be clearly seen in Fig. 13. Dark blue regions can be observed around the head of the second spray, indicating the already burnt region. At the regions upstream of the

FLOL, dark red regions are observed for the e contours, indicating a pre-ignition zone where the mixture is highly explosive. However, for the cases with short first injection durations, the increase in the dwell time leads to large differences in the distributions of e , which is calculated by

e = sign(Re(λe ) ) × log10 (max(1, Re(λe )) )

(3)

where ‘sign’ represents the sign function and Re(λe ) is the real part of the largest non-zero eigenvalue (λe ). Since there is less fuel injected into the chamber during the first injection, the mixture ahead of the second spray at 0.6 ms ASSI becomes very lean. The temperature there is also very low (below 10 0 0 K). The low temperature and lean mixture result in positive values of e . With the increase in DT, the mixture becomes much leaner and values of e at the regions ahead of the second spray decrease. Large Da in or-

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Fig. 13. Distributions of temperature (T), e and the Damköhler number (Da) with different dwell times at 0.6 ms ASSI. (a)–(c) cases L1–L3, (d)–(f) cases S1–S3. The horizontal dashed line represents the place of FLOL.

der of unity at the FLOL is mainly distributed in the inner side of the spray, implying that the reaction and mixing process counterbalance each other. It indicates that the stabilization of the second injection is controlled by flame propagation. For the case with a longer DT, the mean temperature ahead of the second spray get a bit cooler and it drops about 200 K. At the same time, more oxygen is entrained into the low-density regions after the combustion of the first injection. In return, the increase in oxygen concentration enhances the mixture reactivity. However, the influence of the combustion products from the first injection on the combustion of the second injection is reduced. No obvious flame front exists between the explosive and non-explosive mixture. As reported in the previous studies [62,63], Da > 1 indicates a dominant CEM state which is likely to induce actual autoignition. For the cases with long DTs, for example, DT = 1.5 ms, Da at the location approaching the FLOL is larger than unity, suggesting that the chemical reaction is much faster than the mixing. The chemical explosive process dominates the mixing, and thus, the mixture is autoigniting [65]. A similar phenomenon is also found in the lifted ethylene jet flame in highly-heated coflow using DNS [53,57], where highly explosive mixtures are located near the injector. By increasing the interval between the two injections, the combustion of the first injection is more completed. Therefore, the main influence from the first injection is that the temperature increase ahead of the second injection promotes the appearance of the explosive mixture, as shown in Fig. 13(c) and (f), where a high value of Da appears at the spray head of the second injection. 4. Conclusions In this work, combustion mechanisms of multiple injections are investigated using large eddy simulation (LES). A reduced mech-

anism including 54 species and 269 reactions for n-dodecane is used in this work. Analysis of the combustion process at different dwell times (DTs) and first injection durations show that the appearance of high-temperature kernels at long dwell time is delayed. This is because that the time when the second injection starts to come into contact with the combustion regions from the first injection is prolonged with a long DT. High-temperature reactions are initiated at fuel-rich regions for the first and second injections. Different ignition mechanisms are identified. Ignition of the first injection is controlled by autoignition, while the second injection is ignited by the first flame. The interactions between the two reacting sprays are also discussed. The velocity of the second spray tip is obviously accelerated by the first reacting spray with a short DT. For the case with a long DT, fuel and intermediate species are almost consumed completely before the second tip catches up with the first one. Besides, the chemical explosive mode analysis (CEMA) method is used to interpret the stabilization mechanism. For the case with a short DT, a balance between reaction and mixing occur simultaneously for the second injection, thus the flame is stabilized because of flame propagation. For the case with a long DT, large values of Da are obtained, indicating that the chemical explosive mode dominates the mixing and the flame is controlled by autoignition.

Acknowledgment The work is supported by National Natural Science Foundation of China (Grant Nos. 91741119, 51606133, and 91641203) and Marine Low-Speed Engine Project (Phase I). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1 (A).

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Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.combustflame.2019.08. 031. Appendix A. Model validation for non-reacting spray The present numerical model with the basic mesh shows a great advantage in predicting turbulent sprays with variations in fuel type (n-heptane or n-dodecane), injection pressure, and injection strategies (single injection or split injection). Except for the experimental settings, including ambient gas temperature, pressure, fuel type, and fuel mass, it does not need to adjust any other injection parameters in injection-related models. It means that the present model can give a good prediction over a wide range of conditions. Here, the performance of the present model in predicting n-dodecane spray flames (Spray A) and n-heptane spray flames is compared below. Appendix A.1. Mesh resolution

number for the basic and fine meshes is approximately 0.8 million and 1.6 million, respectively. The vapor penetration length is defined as the distance from the farthest location with 0.1% fuel mass fraction to the nozzle exit. It can be seen from Fig. A1 that the vapor penetration length from the basic mesh is slightly underestimated before 0.5 ms, and consequently, the computational results agree quite well with the experiments. During the early time (before 0.5 ms), the results from the fine mesh capture the vapor penetration length more accurately. However, an underestimation is observed in terms of the predicted results after 1.0 ms. Reduction in grid size can resolve more turbulent kinetic and the fuel jet becomes more wrinkle. At the same time, the predicted penetration length is also reduced [68]. Generally, the present model with the basic mesh can give a reasonable prediction of the vapor penetration length. Appendix A.2. Model validation for a single injection from the basic mesh The present model can also give a good agreement of a single injection of Spray A without the adjustment of spray model parameters. The predicted and measured vapor penetration lengths for single injection with variations in injection pressure are shown in Fig. A2. The experimental settings can be found in Table 3. The increase in injection pressure causes a higher gas velocity and turbulence levels because fuel droplets have a higher speed after injection. A higher injection pressure also provides fuel droplets with more momentum, thus enhancing the mixing process. It is shown in Fig. A2 that the predicted vapor penetration lengths agree very well with the experiments with different injection pressures. To further illustrate the performance of the numerical model, Fig. A3 compares the mixture fraction distributions from experiments and simulations at different locations. It is reported that prediction of mixture fraction distributions is challengeable and there are certain differences between the measured and predicted data even with a very fine mesh [69]. Overall, most of the predicted results agree well with the experiments.

10

10 Experiments Basic Fine

Penetration (cm)

8

Exp.50MPa Exp.100MPa Exp.150MPa Sim.50MPa Sim.100MPa Sim.150MPa

8

Penetration (cm)

The present model can give a good agreement of split injections of Spray A without the adjustment of spray model parameters. It should be noted that in our previous study [66], the simulated distributions of the mixture fraction at different times and locations by the present numerical methods were compared with the experimental results, and good agreements between the predicted and measured results were obtained. We have compared the vapor penetration length for an inert dodecane spray with the experimental data in our previous study [25]. The present numerical model coupled with the high-order MUSCL scheme can give a reasonable agreement with the experimental data. We have also examined the quality of the performed LES by comparing the results from different realizations [67]. Results calculated by the ratio of resolved and total turbulent kinetic energy (TKE) illustrated that high-levels of TKE could be resolved, especially at downstream positions. Although the turbulent fluctuations are not completely resolved, the numerical model does not change the main conclusion. To validate the numerical model, the predicted vapor penetration lengths from the basic mesh and a fine mesh under inert condition at an initial temperature of 900 K are compared with the experimental data from [12], as shown in Fig. A1. The total cells

217

6

4

6

2 4

0 2

0

0

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1 Time (ms)

1.5

2

Fig. A2. Vapor penetration comparisons from experiments and simulations with different pressures. Single-injection experiments from Pickett [22].

0

0.5

Time (ms)

1

1.5

Fig. A1. Comparisons between the predicted and measured vapor penetration lengths. Experimental data from Skeen et al. [12].

Table 3 Experimental settings. Fuel

Orifice diameter

Injection duration

Fuel temperature

n-dodecane

90 μm

1.5 ms

363 K

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Exp. Height=20 mm Exp. Height=30 mm Sim. Height=20 mm Sim. Height=30 mm

Mixture Fraction

0.15

0.1

0.05

0

0

0.2

0.4 0.6 Radius (cm)

0.8

1

Fig. A3. Comparisons of predicted and measured mixture fraction profiles at different locations (Pinj = 150 MPa). Single-injection experiments from Pickett [22].

Appendix A.3. Performance of the present model for the simulation of n-heptane spray flames The present model can give a good agreement of single injections of Spray H without the adjustment of spray model parameters. In our previous work [25,70,71], we have performed LES studies of n-heptane spray flames with the same basic mesh and spray models. Results show that the LES code gives a very good prediction of n-heptane spray flames in terms of the ignition delay times and flame lift-off lengths with the variations in initial gas temperatures, oxygen concentration, and densities. Moreover, we have compared the results including ignition delay times and flame lift-off lengths for n-heptane spray flames under high-density conditions. Except for the fuel type, initial temperature, oxygen concentration, and gas density, other parameters including the pa-

rameters for spray models and the subgrid model do not need to adjust. But the present model can still give a reasonable agreement with the experiments in terms of ID and FLOL, as shown in Fig. A4. Appendix A.4. Model validation for reacting spray To further validate the numerical model under reacting conditions, comparisons of experimental images from planar-laserinduced fluorescence (PLIF) and the schlieren images with the simulated results for the reacting sprays are shown in Fig. A5 at an initial temperature of 800 K to further show the performance of the present models. The experimental ID for the first injection is 0.88 ± 0.09 ms from the pressure profile. In this work, ID is

60

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Experiments Bolla_RANS_WSR Bolla_RANS_CMC Haworth_RANS_PDF Haworth_RANS_WSR Zhou_LES_WSR LES-LEM

0.8

Ignition Delay (ms)

Fig. A5. Comparisons of (a) modeled results with (b) PLIF and schlieren experimental images at an initial temperature of 800 K. Experimental data are from Skeen et al. [12].

0.4

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(b) Flame lift-off lengths

Fig. A4. Comparisons of the ignition delay times and flame lift-off lengths with the experimental data [70]. The initial temperature is 10 0 0 K and the initial density is 30.0 kg/m3 . Reprinted with permission from Zhao et al., [70].

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Table 4 LES studies of n-dodecane spray flames. WSR: Well-stirred Reactor; TFM: Tabulated Flamelet; FGM: Flamelet Generated Manifold; ADF: Approximated Diffusion Flamelet Model; mRIF: Multiple Representative Interactive Flamelets; FPV: Flamelet Progress Variable; MMC: Multiple Mapping Conditioning. Reference

Chemistry

Combustion model

Objectives

Gong et al. [38,76] Som et al. [77] Pei et al. [78,79]

103 species 68 species 103 species

WSR SAGE SAGE

Ameen et al. [80,81]

106 species

WSR

Kundu et al. [82] Wehrfritz and co-workers [49,69,73]

103 species 130 species 257 species

TFM FGM

Akkurt et al. [83] Davidovic et al. [84] Ma et al. [85] Hakim et al. [86,87] Doisneau et al. [88] Xu et al. [64]

54 species255 species 57 species 54 species 2-step 2-step 54 species

FGM, ADF mRIF WSR WSR WSR TFM, FPV

Moiz et al. [10]

54 species

WSR

Hadadpour et al. [44,89] Blomberg et al. [19]

54 species 54 species

PaSR CMC

Salehi et al. [74,90]

106 species

MMC

Ignition process and flame stabilization for a single injection Assessing computational efficiency Mesh resolution, ignition process, the realization to realization variations The realization to realization variations, azimuthal averaging for spray flames Low-temperature combustion process, model validation Spray flame structures, ignition process with different injection pressures, identification of different stages of ignition Performance of two combustion models, chemical mechanisms Ignition process, performance of combustion model Injection and auto-ignition processes Performance of a simple chemical kinetics model coupled with LES Two-phase flow formalisms, the performance of a new model Identification of different regions in spray flames, comparisons of combustion models Soot production in double injections with a short first injection duration Mixing process and combustion process in split injections, Performance of the CMC combustion model coupled with LES and RANS Performance of MMC–LES model, ignition process for single injection

defined as the time when the maximum temperature in the entire domain reaches the ignition temperature Tign , which is calculated by Tign = 0.5 ∗ (Tamb + Tmax ) [72]. Tamb is the initial ambient gas temperature, and Tmax is the maximum temperature during the quasi-steady state. The predicted ID is 0.895 ms for the first injection. The experimental images show the distributions of polycyclic aromatic hydrocarbons (PAH) and formaldehyde (CH2 O) molecules. However, for the simulation, PAH is not included in the chemical kinetic mechanism, and acetylene (C2 H2 ) is employed to represent the formation of soot. Therefore, CH2 O and C2 H2 are used to give a qualitative comparison with the experiments. At 890 μs, the second injection has not commenced yet. Strong PLIF signal appears in the firstly injected spray, and very a weak color appears in the schlieren image. Skeen et al. [48] pointed out that during the low-temperature ignition stage, when the local temperature is close to the ambient gas temperature, the gradient in the local refractive index is reduced, and a “softening” effect near the head of the spray is observed. Consistent with this conclusion, high levels of CH2 O appear at the reacting spray head in the predicted result, and the decrease in the gas density is very slight at 0.9 ms. At 1290 μs, high-temperature reactions occur in the spray, leading to significant reduction in gas density, as shown in the schlieren image. The simulated result overestimates the reacting spray head for the first injection, while the position of the second spray or the second spray head agrees well with the experiments. Recently, great efforts have been made for the simulation of n-dodecane by using LES. Table 4 gives a detailed review of the previously published works. For example, Wehrfritz and coworkers [49,69,73] implemented the Flamelet Generated Manifold (FGM) combustion model to study the ignition and combustion of Spray A and n-dodecane/methane dual fuel. Results from the FGM model coupled with the LES approach agree quite well with the experiments in terms of CH2 O formation regions and estimation of ignition delay times. The decrease in grid size can significantly increase the computational cost. Salehi et al. [74] used a hexahedral mesh with a total cell number of 0.6 million which is close to ours. Results showed that the predicted data agree well with the experiments over a wide range of conditions. Moreover, other published works of n-heptane spray flames with a similar mean mesh size can also provide further insight into the complex combustion process [75].

Fig. A6. Scatters of temperature versus mixture fraction colored by CH2 O mass fraction. The black dashed line represents the location of Zst.

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