Investigation of the Engine Combustion Network Spray a Characteristics using Eulerian and Lagrangian Models

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Investigation of the Engine Combustion Network Spray a Characteristics using Eulerian and Lagrangian Models

Item Type Conference Paper

Authors Liu, Xinlei;Al-lehaibi, Moaz;Im, Hong G.

Citation Liu, X., Allehaibi, M., & Im, H. G. (2022). Investigation of the Engine Combustion Network Spray a Characteristics using Eulerian and Lagrangian Models. SAE Technical Paper Series. https://

doi.org/10.4271/2022-01-0507 Eprint version Post-print

DOI 10.4271/2022-01-0507

Publisher SAE International

Rights Archived with thanks to SAE International Download date 2024-01-26 17:22:47

Link to Item http://hdl.handle.net/10754/676402

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2022-01-0507

Investigation of the Engine Combustion Network Spray A Characteristics using Eulerian and Lagrangian Models

Xinlei Liu

King Abdullah University of Science and Technology

Moaz Al-lehaibi

Umm Al-Qura University; King Abdullah University of Science and Technology

Hong G. Im

King Abdullah University of Science and Technology

Abstract

This work presents a numerical study of the Spray A (n-dodecane) characteristics using Eulerian and Lagrangian models in a finite- volume framework. The standard k- turbulence model was applied for the spray simulations. For Eulerian simulations, the X-ray measured injector geometries from the Engine Combustion Network (ECN) were employed. The High-Resolution Interface Capturing (HRIC) scheme coupled with a cavitation model was utilized to track the fluid-gas interface. Simulations under both the cool and hot ambient conditions were performed. The effects of various grid sizes, turbulence constants, nozzle geometries, and initial gas volume within the injector sac on the modeling results were evaluated. As indicated by the Eulerian simulation results, no cavitation was observed for the Spray A injector; a minimum mesh size of 15.6 m could achieve a reasonably convergent criterion; the nominal nozzle geometry predicted similar results to the X-ray measured nozzle geometry. For both the Eulerian and Lagrangian simulations, the higher C1 value of the turbulence model resulted in the lower turbulent kinetic energy, longer jet penetration, and spray cone angle.

Since the Eulerian-Lagrangian coupled method has the advantage over spray distribution at the nozzle exit, it predicted a significantly better near-nozzle mixture distribution compared to the conventional Lagrangian model at a non-vaporizing condition. By employing an initial gas volume fraction of 30% within the injector sac as recommended by the Engine Combustion Network committee, the Eulerian-Lagrangian coupled method could well reproduce the experimental rate of injection profile, fuel mixture distributions, and spray penetrations at a vaporizing condition. Furthermore, the higher injection pressure promoted the vapor penetration, but it had limited effects on the liquid penetration owing to the competitive relationship between the higher spray momentum and evaporation rate. The higher ambient temperature reduced the liquid penetration for the higher evaporation rate, but it had limited effects on the vapor penetration since the spray momentum and ambient density were kept unchanged.

Introduction

The internal combustion engine (ICE) will continue to play a significant role in human society for the next few decades.

Especially, for areas such as heavy-duty transportation, power plant,

and agriculture, ICEs are still irreplaceable. In these areas, a direct injection compression ignition (DICI) engine is preferred owing to the higher thermal efficiency compared to its counterpart, the spark- ignition engine. However, due to the diffusion combustion process, DICI engines face the issues of soot and NOx emissions. To fulfill the more stringent fuel economy and emission regulations, high injection pressures have been used as an efficient solution. Currently, with the more advanced technology, it is possible to adopt an ultra- high injection pressure up to 3000 bar and even to 5000 bar [1]. The investigations show that high injection pressure can effectively improve the soot-NOx trade-off relationship, which helps to relieve the dependence of engine after-treatment systems [2].

DICI combustion involves a series of complicated processes, including the internal nozzle flow, spray breakup and atomization, air-fuel mixing, and turbulent combustion processes. Especially when using a multiple-injection strategy with short injection intervals, flow physics will be much more complicated. At such a high injection pressure, liquid compressibility must be considered [3]. Besides, high velocities within the injector channels can lead to phase change and cavitation, which has a significant impact on the spray breakup process [4]. Therefore, to get concise control of the spray-combustion process, we need to get an in-depth understanding of the internal and near-nozzle flow patterns both experimentally and numerically.

There have been many optical measurements conducted to quantify the spray features including spray penetrations [5], velocity fields [6], and fuel mixture distributions [7] et al., which provide significant insights into the middle- and far-field spray behavior. However, it is still a challenge to directly measure the mixture distribution in the near-nozzle region, where the liquid jet core is extremely dense and optically impenetrable [8]. Owing to the highly penetrative property of X-rays, Powell et al. [9] proposed to use the X-ray radiography method to quantitatively measure the near-field density. X-rays can also be used to measure the internal injector geometry and internal flow details, which provide a valuable dataset for numerical investigations [10].

Owing to the low computational cost, the Eulerian-Lagrangian approach has been widely used for spray modeling in ICEs [4, 11].

This modeling approach describes the liquid phase using a Lagrangian scheme but describes the gas phase using an Eulerian scheme. Due to the simplification, several additional sub-models

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including parcel initialization, spray breakup, droplet collision, and evaporation are needed to well predict the spray development process [4]. However, this approach usually needs a rate of injection (ROI) profile as the input and several sub-module parameters need to be tuned to provide reasonable predictions. It does not consider the in- nozzle effects on the spray development process and the prediction of dense spray in the near-nozzle region may not be accurate enough [12].

The Eulerian method has seen great progress in the past two decades, and various methods to track the liquid-gas interface such as Level- Set [13] and Volume of Fluid (VOF) [14] have been proposed. There have been many research works using this kind of method to study the near-nozzle and far-field spray features, which validates its ability to precisely capture the major spray parameters, such as fuel mixture distribution, spray penetration, velocity field, and Sauter Mean Diameter [8, 15, 16]. However, a very fine mesh is required for this method to explicitly capture the liquid-gas interface, which will consume more computational resources compared to the conventional Eulerian-Lagrangian approach.

Therefore, a combined Eulerian to Lagrangian approach would be preferred to reduce the computational cost while maintaining the ability to capture the near-nozzle spray feature [17]. To achieve this, the internal nozzle flow simulation using the Eulerian method is conducted first and then the three-dimensional (3D) result around the nozzle exit is used as the inlet boundary condition for the following Lagrangian simulation [18]. Unlike the conventional Lagrangian method, the Eulerian-Lagrangian coupled method does not need a ROI profile as input. Since time scales and mesh qualities for the Eulerian and conventional Lagrangian spray calculations are very different, the Eulerian-Lagrangian coupled case can just adopt an intermediate time step but use a similar coarser mesh as the conventional Lagrangian case, which significantly saves the computational resources [17].

This work is organized as follows. First, the experimental data of Spray A (n-dodecane) from the Engine Combustion Network (ECN) and the modeling setup are briefly introduced. Second, Eulerian simulations are performed and validated against the X-ray measured data. The effects of different grid sizes, turbulence constants, and nozzle geometries on the prediction results are evaluated. Next, a comparative study using the Eulerian, Eulerian-Lagrangian coupled, and conventional Lagrangian models is performed. Finally, the Eulerian-Lagrangian coupled model is employed for the prediction of spray-penetration and mixture distribution at a vaporizing condition.

Evaluation of the effects of injection pressure and ambient temperature on the spray development was also conducted.

Conclusions are summarized in the last section.

Experimental Data and Computational Setup Experimental Data

Experimental data at both the cold non-vaporizing and hot vaporizing conditions are used for numerical validations. Two series of single- nozzle Spray A injectors are adopted, 210675 and 210677. Table 1 lists the primary experimental conditions and injector parameters.

Note that for both injectors the nominal diameter is 90 m. However, due to the manufacturing defects, detailed internal geometries for these two injectors are different. As seen in Table 1, injector 210677 has a slightly smaller nozzle diameter but a larger K factor than injector 210675. K factor is defined as the difference between the

inlet and exit diameters divided by 10, ((dinlet-dexit)/m). This factor will give an indication of the divergence and convergence of the nozzle.

Table 1. Experimental conditions and injector specification.

Injector serial # 210675 210677

Exit diameter (m) 89.4 84

K factor 1.3 1.8

Ambient temperature (K) 303 900 Ambient pressure (MPa) 2.0 6.05 Injection pressure (MPa) 155 152.7 Injection duration (ms) 1.54 1.54

Injection mass (mg) 3.72 3.46

Discharge coefficient 0.9 0.89

Fuel temperature (K) 343 373

Ambient oxygen content

(vol. %) 0.0 0.0

X-ray measured projected density, liquid and vapor penetrations, and mixture distributions experimental data from the ECN website [19]

have been used for numerical validations. The Argonne National Laboratory employed X-ray radiography to quantify the fuel mass density in the near-nozzle field. Average data from many injections during the steady-state were measured at various radial and axial positions [20]. Note that owing to the asymmetric nozzle geometry, the measured projected densities on two planes, i.e. the XY and XZ planes, are different. Figure 1 shows the schematic of the injector orientation. On the other hand, Sandia National Laboratory employed the Mie-scatter, schlieren imaging, and Rayleigh scattering

techniques [21, 22] to measure the liquid and vapor penetrations and mixture distributions, respectively. These measured data provide a significant basis for the following numerical validations.

Figure 1. Schematic definition for the spray A injector orientation.

Turbulence Model

The CONVERGE code [18] was used for three-dimensional computational fluid dynamics (3D CFD) numerical study. The standard k- turbulence model is used to model turbulence, which is typically applied for round-jet simulations [3, 4]. To solve the turbulent viscosity, two additional transport equations are needed, including the turbulent energy transport equation and the dissipation of turbulent kinetic energy (𝜀) transport equation.

To capture the in- and near-nozzle spray details, Eulerian simulations are performed by using the VOF method [23]. In this method, the gas and liquid fuel are considered as a single compressible fluid mixture, and the void fraction (𝛼_𝑙 is used to represent the volume fraction of liquid, which is defined as

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Page 3 of 12 𝛼𝑙=_𝑌 ^𝑌^𝑙^⁄^𝜌^𝑙

𝑙⁄ +𝑌𝜌_𝑙 _𝑔⁄𝜌_𝑔 (1)

𝑌 and 𝜌 represent the mass fraction and density, respectively. As shown in equation (6), the cell is filled with pure liquid when 𝛼_𝑙= 1 and with pure gas when 𝛼_𝑙= 0. The mixture transport properties are calculated as averages of the single-phase values. For example, the mixture density, viscosity, and conductivity in each cell are defined as

𝜌 = 𝜌𝑙𝛼𝑙+ 𝜌𝑔(1 − 𝛼𝑙) (2) 𝜇 = 𝜇_𝑙𝛼_𝑙+ 𝜇_𝑔(1 − 𝛼_𝑙) (3) 𝑘 = 𝑘_𝑙𝛼_𝑙+ 𝑘_𝑔(1 − 𝛼_𝑙) (4) respectively. Following equation (6), 𝛼_𝑙 is calculated using the individual species mass fraction for each species, which are transported according to the species conservation equation

𝜕𝜌̅𝑌̃_𝑘

𝜕𝑡 +^𝜕𝜌^̅𝑢^̃𝑌^𝑖^̃^𝑘

𝜕𝑥_𝑖 = ^𝜕

𝜕𝑥_𝑖(𝜌̅𝐷^𝜕𝑌^̃^𝑘

𝜕𝑥_𝑖) + 𝑆̃_𝑘   

𝑌_𝑘 is the mass fraction of species k, 𝐷 is the mass diffusion coefficient, and 𝑆𝑘 is the source term due to evaporation, respectively.

A high-resolution interface capturing (HRIC) scheme has been employed to capture the gas and liquid interface position [24]. A cavitation model based on the flash boiling hypothesis of Shield et al.

[25] is implemented, and a homogenous relaxation model [26] is used to predict the mass exchange between the liquid and vapor. Details of the related models are available in [18].

Lagrangian Modeling

For both the conventional Lagrangian and Eulerian-Lagrangian coupled spray simulations, the Lagrangian-parcel Eulerian-fluid approach is employed for the spray modeling [27] and the Kelvin- Helmholtz Rayleigh-Taylor model without a breakup length is employed to model the spray-breakup process [28]. For the Eulerian- Lagrangian coupled simulation, an Eulerian VOF simulation was performed to determine the near-nozzle boundary conditions, which was used later for the Lagrangian simulation. In contrast, the conventional Lagrangian simulation would require the ROI profile to determine the transient mass flow rate.

Computational Meshes

The X-ray measured nozzle geometries for both the injectors 210675 and 210677 are used for the Eulerian simulations at non-vaporizing and vaporizing conditions, respectively. Note that a nominal nozzle geometry for injector 210675 is also used to further study the effect of different nozzle geometries on the spray prediction results. Figure 2 compares the original and nominal nozzle geometries of injector 210675. The nozzle geometry of injector 210677 is similar to 210675 and is not shown here. As seen in Figure 2(b), the nominal nozzle geometry has a smoother surface and the nozzle channel with a K factor of 0 is centered on the symmetry plane.

Figure 2. Schematics for the (a) original and (b) nominal nozzle geometries for injector 210675.

Figure 3 shows the computational meshes for the (a) Eulerian and (b) Lagrangian simulations using injectors 210675 and 210677,

respectively. Note that the computational mesh for the Eulerian simulation case using injector 210677 is similar to injector 210675 and is not shown here. Since the Eulerian simulation focuses primarily on the in- and near-nozzle spray flow details, a relatively small computational domain is employed, which has a cylindrical chamber with 20 mm diameter and 30 mm length starting from the nozzle exit. Besides, various fixed embedding scales are used and the finest mesh covers the whole internal nozzle geometry. For the Lagrangian simulation, a cylindrical mesh with a dimension of 108 × 108 × 108 mm is adopted and a fixed embedding scale of 4 is imposed downstream of the nozzle exit, which ensures a minimum mesh size of 64 m. The adaptive mesh refinement (AMR) model is activated with a maximum refined scale of 3, which is able to refine the mesh automatically. The previous grid-sensitivity studies have demonstrated that the current mesh setup for the Lagrangian simulation is able to achieve convergent results [29].

Figure 3. Computational meshes for the (a) Eulerian case using injector 210675 and (b) Lagrangian case using injector 210677.

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For the Eulerian simulations, ensembled-averaged needle lift profiles are employed to describe the motion of injector needles, as shown in Figure 4(a). All of the simulations start from a needle lift of 2 m, corresponding to about 0.2 ms for both injectors. Fixed pressure (1527 bar) and temperature (363 K) are specified as the inlet boundary conditions. Figure 4(b) compares the experimentally measured and simulation-use injection pressure profiles. No significant fluctuation is observed for the injection pressure during the injection process, so the use of fixed injection pressure is reasonable. On the other hand, for the conventional Lagrangian simulations, the CMT-recommended ROI profiles [19] are employed.

0.0 0.5 1.0 1.5 2.0

0 100 200 300 400 500

Needle lift [m]

Time ASOI [ms]

210675 210677

(a)

0.0 0.5 1.0 1.5 2.0

0 500 1000 1500 2000 2500

Injection pressure [bar]

Time ASOI [ms]

Measured Simulation

(b)

Figure 4. (a) Needle lift profiles for two injectors; (b) measured and simulation-use injection pressure profiles.

Mesh-sensitivity Study for Eulerian Simulations

A mesh sensitivity study is performed for the Eulerian simulations and various minimum mesh sizes ranging from 7.8, 15.6, 31.2, and 62.5 m are employed. For all the cases, a C1 of 1.62 is employed, similar to the recommended value of 1.60 by Pope [30]. Figure 5 compares the predicted axial velocity (Vx) with various mesh setups.

Vx demonstrates a growing trend with a finer mesh, which tends to be obvious as approaching the nozzle exit. Besides, the case with a minimum mesh size of 15.6 m is able to predict an overall similar result with the case with a minimum mesh size of 7.8 m, indicating that a reasonable mesh-convergent result is achieved.

Figure 6 and Figure 7 compare the predicted transverse density profiles at different axial locations (a) 0.1 mm, (b) 2.0 mm, and (c) 4.0 mm on the XY and XZ planes at 0.5 ms ASOI, respectively. Note that the radial range is longer at a further downstream location, which indicates a wider spray periphery due to the intense gas-entrainment process. Owing to the asymmetric nozzle geometry, the peak values of the projected density profile on the XY plane tend to shift towards

the positive direction. However, the projected density profiles on the XZ plane always show a comparatively more symmetric feature.

At an axial location of 0.1 mm downstream of the nozzle exit, the cases with minimum mesh sizes of 7.8 and 15.6 m are both able to well reproduce the experimental result. This indicates that for the following one-way Lagrangian simulation, a minimum mesh size of 15.6 m is sufficient to capture the near-nozzle spray details. As a result, in the following subsections, the minimum mesh size of 15.6

m is employed to reduce computational expenses. However, with a further coarser mesh, a wider jet with a lower peak projected density is predicted. Note that all the cases tend to overpredict the fuel dispersion radially beyond 2 mm, which is also observed in Xue et al.’s work [4]. The discrepancies are probably owing to the overprediction of radial diffusion further downstream of the nozzle [4], which will be discussed in the following section.

1 2 3 4 5 6 7 8 9

200 300 400 500 600 700

7.8m 15.6m 31.2m 62.5m

Axial velocity [m/s]

Axial distance [mm]

Figure 5. Comparison of the predicted axial Vx with different minimum mesh sizes at 0.5 ms ASOI.

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0

20 40 60 80 (a)

Expt.

7.8m 15.6m 31.2m 62.5m

Projected density [g/mm2]

Radial distance [mm]

0.1mm

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

20 40 60 (b)

Expt.

7.8m 15.6m 31.2m 62.5m

2.0mm

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-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0

10 20 30

(c) Expt.

7.8m 15.6m 31.2m 62.5m

4.0mm

Figure 6. Predicted transverse density on the XY plane at different axial locations (a) 0.1 mm, (b) 2.0 mm, and (c) 4.0 mm.

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0

20 40 60 80 (a)

Expt.

7.8m 15.6m 31.2m 62.5m

0.1mm

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

20 40 60 (b)

Expt.

7.8m 15.6m 31.2m 62.5m

2.0mm

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0

10 20 30

(c) Expt.

7.8m 15.6m 31.2m 62.5m

4.0mm

Figure 7. Predicted transverse density on the XZ plane at different axial locations (a) 0.1 mm, (b) 2.0 mm, and (c) 4.0 mm.

Results and Discussions Non-vaporizing Condition

Effect of C1

For the round jet simulation, Pope [30] recommended a modification of the default C1 value (1.44) to a higher value, 1.60 for example, when using the standard k- turbulence model. In this subsection, a parametric study is performed to analyze the effect of different C1

values on spray prediction. Figure 8 compares the predicted

transverse density profiles on the XY plane with different C1 values.

The longer dense jet core and narrower downstream spray periphery are predicted with a higher C1 value. Various cases generate similar results near the nozzle exit (x = 0.1 mm), indicating that the adoption of different C1 values has a marginal effect on the predicted internal nozzle flow field. Note that a higher C1 value always yields a higher peak projected density but a narrower spray periphery, which is more obvious at a farther distance from the nozzle exit. Of the five cases, the case with C1 = 1.62 predicts the best result.

Note that in [30], Pope revealed that using the commonly used turbulence parameters (Cε1 =1.45), the velocity field in a two- dimensional plane jet could be calculated quite accurately, but large errors occur for axisymmetric jets, for example, a round jet.

Specifically, the spreading rate of the round jet is overestimated by about 40% [30]. Therefore, he proposed to utilize a higher Cε1 value (1.60). As a result, in this work, a Cε1 value of 1.62 is used for the Eulerian VOF simulations based on the parametric study, although it is slightly higher than the proposed value.

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0

20 40 60 80 (a)

Expt.

C_1=1.62 C_1=1.57 C_1=1.50 C_1=1.44

0.1mm

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

20 40 60 (b)

Expt.

C_1=1.62 C_1=1.57 C_1=1.50 C_1=1.44

2.0mm

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-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0

10 20 30

(c) Expt.

C_1=1.62 C_1=1.57 C_1=1.50 C_1=1.44

4.0mm

Figure 8. Predicted transverse density on the XY plane with different C1

values at various axial locations (a) 0.1 mm, (b) 2.0 mm, and (c) 4.0 mm.

Figure 9 compares the predicted distributions of Vx on the axis using various C1 values, respectively. Different cases predict a similar velocity at the near-nozzle region (x < 1.2 mm), which indicates that C1 has a more significant impact on the downstream gas-

entrainment process rather than the upstream dense liquid flow dynamics. Figure 10 further consolidates this assumption, which compares the predicted distributions of turbulent kinetic energy (TKE) using various C1 values. Note that a smaller C1 value results in an overall higher TKE around the spray periphery, which promotes the ambient gas-entrainment process, reduces the jet velocity, and widens the downstream spray periphery. This finding is in agreement with Pope’s work [30].

1 2 3 4 5 6 7 8 9

200 300 400 500 600

700 C_1=1.62

C_1=1.57 C_1=1.50 C_1=1.44

Axial distance [mm]

Figure 9. Comparison of the predicted axial Vx with different C1 values.

Figure 10. Predicted distributions of TKE on the XY plane at 0.5 ms ASOI with different C1 values.

Recall in section 2.2.5 that further downstream of the nozzle tip (> 2 mm), the predicted fuel mixture distribution has slight sensitivity to different mesh setups, which all predict the wider results compared to the experiment. From the results of this subsection, it is inferred that the overprediction of radial projected density at the far-field region is perhaps due to the overprediction of turbulent kinetic energy and underprediction of axial velocity, which eventually leads to the overprediction of radial diffusion. To improve the predictive performance, the current VOF module needs further improvement in the future.

Effect of Nozzle Geometry

This subsection intends to evaluate the impact of nozzle manufacturing defects on the Eulerian spray simulation. For this purpose, two different internal nozzle geometries are employed, including the X-ray measured one and the nominal one, as illustrated in Figure 2(a) and Figure 2(b), respectively. Note that a C1 value of 1.62 is adopted here. Figure 11 compares the predicted distributions of projected density on the XZ plane using two nozzle geometries.

Both cases demonstrate similar results. Figure 12 further compares the predicted transverse density on the XZ plane at different axial locations. Due to the axisymmetric and smoother nozzle structure, the comparatively more symmetric density profiles with higher peak values are predicted by the nominal case.

Figure 11. Predicted distributions of projected density on the XZ plane at 0.5 ms ASOI with different nozzle geometries. Axis unit: mm.

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20 40 60 80 (a)

Expt.

Ori Modified

0.1mm

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-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

20 40 60 (b)

Expt.

Ori Modified

2.0mm

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0

10 20 30

(c) Expt.

Ori Modified

4.0mm

Figure 12. Predicted transverse density on the XZ plane with two different nozzle geometries at various axial locations (a) 0.1 mm, (b) 2.0 mm, and (c) 4.0 mm.

1 2 3 4 5 6 7 8 9

200 300 400 500 600

700 Original

Norminal

Axial distance [mm]

Figure 13. Predicted distributions of Vx on axis with two different nozzle geometries. Axis unit: mm.

Prediction with Different Spray Models

In this subsection, an Eulerian-Lagrangian coupled simulation case is performed, for which the in-nozzle flow field results are mapped from the baseline Eulerian case. A conventional Lagrangian simulation is also performed as a counterpart. For both cases, the Lagrangian spray model parameters are employed from the previous works [31], which have been calibrated against the experimental results.

Figure 14 compares the experimental and predicted distributions of projected density on the XZ plane by three spray models. Note that the Eulerian-Lagrangian coupled model predicts a significantly better result compared to the conventional Lagrangian model, which generates a significantly more diffused and shorter dense jet core.

Figure 15 further compares the predicted transverse distributions of projected density at various axial locations. At the nozzle exit (x = 0.1 mm), the conventional Lagrangian model predicts a narrower density distribution. Further downstream of the nozzle exit, it predicts

a more diffused spray periphery. Discrepancies between these two Lagrangian models are not surprising, since for the Eulerian- Lagrangian coupled model the parcel details are directly mapped from the baseline Eulerian case, which is able to better reproduce the in- and near-nozzle spray details. However, for the conventional Lagrangian case, uniform parcel distribution and a pre-calculated ROI profile are employed, which consequently results in a larger discrepancy.

Figure 14. Comparison of the experimental and predicted distributions of projected density on the XZ plane at 0.5 ms ASOI with different spray models. Axis unit: mm.

-0.15 -0.10 -0.050 0.00 0.05 0.10 0.15 60

120 180 (a)

Eulerian

One-way Lagrangian Lagrangian

0.1mm

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20 40 60 (b)

Eulerian

2.0mm

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-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0

10 20 30 40 50

Eulerian

(c) 4.0mm

Figure 15. Predicted transverse density on the XZ plane with different spray models at various axial locations (a) 0.1 mm, (b) 2.0 mm, and (c) 4.0 mm.

Vaporizing Condition

The Eulerian-Lagrangian coupled model predicts a better result compared to the conventional Lagrangian model and it consumes less computational resources than the Eulerian model. Therefore, in this subsection, the Eulerian-Lagrangian coupled model is employed for the spray simulation of injector 210677 at a vaporizing condition.

Note that the injector 210677 is employed here instead of 210675 is because only the former injector-related experimental data including spray penetrations and mixture distributions are available from the ECN website.

Effect of Initial Gas Volume within the Sac

Accurate estimation of the initial gas volume within the sac is important for the precise prediction of spray penetrations, which directly affects the spray dynamics during the nozzle-opening period.

Based on the recent optical observations [32], the ECN group [19]

recommends employing an initial gas volume fraction of 30% within the injector sac. To examine the effect of initial gas volume within the injector sac on the spray simulation, three different initial gas volume fractions (0%, 30%, and 100%) are tested and analyzed.

Figure 16 compares the measured, CMT-recommended, and predicted mass flow rates. Different initial gas volume fractions have a significant impact on the initial injection period (before 0.22 ms ASOI). But during the steady injection period, similar predicted mass flow rates are observed. Note that a lower initial gas volume results in an earlier abrupt injection event. Both the 0% gas case and the CMT recommended result demonstrate the earliest abrupt injection event. Comparatively, the 30% gas case yields the best match with the experiment.

To further clarify the internal flow dynamics with various initial gas volume fractions within the sac, Figure 17 compares the predicted distributions of liquid volume fraction and velocity at 50 s ASOI.

Compared to the other two cases, there is still a large amount of gas within the sac for the 100% gas case, which leads to the lower mixture density, velocity, and thus mass flow rate. The primary reason is that a large flow restriction is generated due to the high amount of gas within the sac. Note that at 50 s ASOI, the 30% gas case has almost discharged all of the gas within the nozzle.

Therefore, it predicts a similar mass flow rate with the 0% gas case.

Besides, similar to injector 210675 at the non-evaporating condition, no cavitation is observed for injector 210677 at the evaporating condition either.

0.0 0.1 0.2 0.3 0.4 0.5

0 1 2 3

Measured 0% gas 30% gas 100% gas ECN Recommended

Mass flow rate [kg/s]

Time ASOI [ms]

Figure 16. Comparison of the measured, recommended, and predicted mass flow rates.

Figure 17. Comparison of the predicted distributions of void volume and velocity at 50 s ASOI using initial gas volume fractions of (a) 100%, (b) 30%, and (c) 0%.

Predicted Liquid and Vapor Penetrations

In section 3.1.1, it is found that for the Eulerian spray simulation a C1 value of 1.62 yields a better prediction result. However, due to the differences between the Eulerian VOF and Lagrangian spray models, their optimal C1 values may be different. For the Lagrangian simulation, a high C1 value may lead to the overprediction of spray penetrations [33]. For example, in Nicholson et al.’s work [34], a C1

value of 1.58 of the standard k- turbulence model was recommended to reproduce the experimental penetrations and mixture distributions.

In this subsection, to further evaluate the effect of C1 on the prediction of the one-way Lagrangian spray model, two different C1

values of 1.62 and 1.57 are employed and compared. During simulations, an initial gas volume fraction of 30% within the sac is employed. The liquid and vapor penetration lengths are defined as the maximum axial distances from the nozzle tip to locations where 97%

of the liquid fuel mass fraction and 0.1% of the vapor fuel mass fraction are obtained, respectively.

Figure 18 shows the experimental and predicted spray penetrations using two different C1 values. Note that the C1 = 1.57 case yields significantly better agreement with the experimental result. Figure 19 compares the experimental and predicted fuel mass fraction profiles.

Compared to the C1 = 1.57 case, the C1 = 1.62 case predicts a significantly higher axial fuel mass fraction but a narrower spray periphery. To further clarify the results, Figure 20 compares the predicted distributions of fuel concentration, TKE, and Vx at 1.5 ms

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ASOI by the two cases. Similar to the previous Eulerian case, the case with a higher C1 value yields a lower TKE and thus a less intense gas-entrainment process, which consequently promotes the spray penetration but results in a narrower spray periphery.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0

20 40 60 80

Vapor penetration [mm]

Time ASOI [ms]

Expt.

C1=1.57 C1=1.62

Spray A 900 K 60.5 bar

0 20 40 60 80

Liquid penetration [mm]

Figure 18. Comparison of the experimental and predicted spray penetrations.

10 20 30 40 50

4 8 12 16 20

Mass fraction [%]

Expt.

C1=1.57 C1=1.62

(a)

0 2 4 6 8 10

0 4 8 12 16

Mass fraction [%]

25 45 mm Expt.

C1=1.57 C1=1.62

(b)

Figure 19. Comparison of the experimental and predicted (a) axial and (b) radial mass fraction profiles.

(a)

(b)

Figure 20. Comparison of the predicted distributions of fuel mass fraction, TKE, and Vx at 1.5 ms ASOI using (a) C1 = 1.57 and (b) C1 = 1.62. Axis unit: mm.

Effects of Injection Pressure and Ambient Temperature

In this subsection, evaluation of the effects of injection pressure and ambient temperature on the spray development process is conducted by using the Eulerian-Lagrangian coupled method. The previous case with an injection pressure (Pinj) of 1500 bar and an ambient

temperature (Tamb) of 900 K is taken as the baseline case. Three various injection pressures (1000, 1500, and 2000 bar) and ambient temperatures (300, 600, and 900 K) are simulated and compared.

Note that the ambient density is kept at about 22.8 kg/m³, so the ambient pressure is also adjusted accordingly with the change of ambient temperature.

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Figure 21 and Figure 22 compare the predicted distributions of void volume and velocity at 1.0 ms ASOI with various injection pressures and ambient temperatures, respectively. No cavitation (liquid volume fraction of about 1.0) is observed from these Eulerian simulation results. With the growth of injection pressure, the injection velocity is also increased. However, the change of ambient temperature has almost no effect on the internal flow pattern owing to the similar mass flow rate.

Figure 22. Comparison of the predicted distributions of void volume and velocity at 1.0 ms ASOI using various ambient temperatures. (a) 300 K; (b) 600 K; (c) 900 K. Pinj = 1500 bar.

Figure 23(a) and Figure 23(b) compare the predicted liquid and vapor penetrations under various (a) injection pressures and (b) ambient temperatures. Various injection pressures have a significant effect on the vapor penetration but the liquid penetration is almost not affected.

This finding is in agreement with the experiment conducted by Payri et al. [35]. Since the higher injection pressure leads to the higher momentum and energy of the spray, the tip is able to penetrate further downstream, which induces the higher vapor penetration. On the other hand, the liquid penetration is dominated by two factors (spray momentum and evaporation rate) simultaneously. At a higher injection pressure, the higher spray momentum will promote the growth of liquid penetration. The spray-air entrainment is also enhanced, which leads to faster evaporation and thus reduces the

liquid penetration. As a result, these two competitive factors result in similar liquid penetrations with various injection pressures.

It is shown in Figure 23(b) that the ambient temperature has a more significant effect on the liquid penetration than the injection pressure.

Note that at 300 K, the spray is under a non-evaporation condition, so the vapor penetration is not included. Different from the injection pressure study, the growth of ambient temperature has a limited effect on the vapor penetration but has a significant effect on the liquid penetration, in agreement with the finding by Paryi et al. [5].

Since the injection pressure (spray momentum) is kept the same, the liquid penetration is highly dependent on the evaporation rate only.

So a lower liquid penetration is obtained with the growth of ambient temperature due to the enhanced evaporation rate. Similar vapor penetrations can be explained by the same spray momentum and ambient density for various cases.

(a)

(b)

Figure 23. Comparison of the predicted spray penetrations under various (a) injection pressures and (b) ambient temperatures.

Conclusions

This work investigated both the non-vaporizing and vaporizing Spray A characteristics using the Eulerian and Lagrangian models. The X- ray measured nozzle geometries were employed for the Eulerian VOF modeling. An extensive parametric study was conducted to analyze the effects of minimum mesh size, C1, nozzle geometry, and initial gas volume within the injector sac on the spray predictions.

The effects of injection pressure and ambient temperature on the spray features were also evaluated. The results will provide more

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guidance for the injector design and spray model development. The key findings are summarized as follows:

(1) No cavitation was observed for the Spray A injector at various simulated injection pressures (1000-2000 bar) and ambient temperatures (300-900 K).

(2) Different C1 values had a marginal effect on the internal nozzle prediction by the Eulerian spray model.

(3) For the single-nozzle Spray A injector, the manufacturing defects had limited effects on the Eulerian spray predictions. Compared to the conventional Lagrangian model, the one-way Lagrangian model was able to better reproduce the experimental result.

(4) The initial gas volume within the injector sac had a significant effect on the precise predictions of ROI profile and spray

penetrations. A 30% volume fraction of gas as recommended by the ECN committee was able to reproduce the experimental results reasonably well.

(5) The higher injection pressure promoted the vapor penetration but it had a limited effect on the liquid penetration, which is owing to the competitive relationship between the higher spray momentum and evaporation rate. The higher ambient temperature reduced the liquid penetration because of the higher evaporation rate but it had a limited effect on the vapor penetration length due to the same spray

momentum and ambient density.

Contact Information

Xinlei Liu, Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.

Email: [email protected].

Acknowledgments

This work was sponsored by King Abdullah University of Science and Technology. The computational simulations utilized the clusters at KAUST Supercomputing Laboratory. The authors thank

Convergent Science Inc. for providing the CONVERGE license.

Abbreviations

3D Three-dimensional AMR Adaptive mesh refinement ASOI After the start of injection CFD Computational fluid dynamics CI Compression ignition DI Direct injection

 Dissipation of turbulent kinetic energy

ECN Engine combustion network HRIC High-resolution interface

capturing

ICE Internal combustion engine Pinj Injection pressure

ROI Rate of injection

Spray A n-Dodecane spray TKE or k Turbulent kinetic energy VOF Volume of fluid Vx Axial velocity

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