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longer injection duration is studied rarely. In order to reveal the influence of injection pressure on cavitation and atomization in high-power-marine diesel engine,.
Original Research Article

Effects of injection pressure on cavitation and spray in marine diesel engine

International Journal of Spray and Combustion Dynamics 2017, Vol. 9(3) 186–198 ! The Author(s) 2016 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1756827716672472 journals.sagepub.com/home/scd

Fei Yan1, Yuchen Du1, Lihui Wang1, Wenxian Tang1, Jian Zhang1, Bo Liu2 and Chenpeng Liu2

Abstract Numerical simulation of the cavitation and spray in a marine diesel engine is performed to investigate the effects of injection pressure on the cavitation flow and spray characteristics in the marine diesel engine, which in turn influence atomization and combustion in the cylinder. A two-phase flow model combined with single bubble dynamics and a droplet break-up model are used to simulate cavitation and spray, respectively, and the results are compared to the experimental data. With increasing injection pressure, the pressure fluctuations inside the nozzle become more intense. The spray penetration is proportional to time at the beginning of injection. Higher injection pressure increases the spray angle. In addition, massive structures on spray edge can return to the spray body, whereas the massive structures on the spray head remain unchanged throughout its lifetime. Each additional 20 MPa of injection pressure reduces the Sauter mean diameter by approximately 9%.

Keywords Numerical simulation, cavitation, spray, penetration, marine diesel engine Date received: 14 April 2016; accepted: 1 September 2016

1. Introduction Marine diesel engines are widely used in bulk carriers, oil tankers, container ships and other large ocean-going ships because of their high power. Cavitation and spray characteristics are the important factors with the greatest influence on combustion and emissions. As an important design criterion of the fuel injection system, the cavitation and spray characteristics should be fully investigated. More and more numerical approaches are being implemented for the investigation of cavitation due to the small size of the nozzle and the high-speed flow inside the nozzle. Using homogeneous flow model, He et al.1 found that the corner radius of the entrance inhibited the occurrence of cavitation. Wang and Su2 used a two-fluid model to measure inlet pressure fluctuation whose high amplitude had an obvious effect on partial cavitation and super cavitation. The inception of cavitation was sensitive to the frequency of the inlet pressure fluctuation, but they did not discuss the flow characteristics inside the nozzle. A two-dimensional, two-phase, transient model was applied to the influence of the inlet geometric parameter

on cavitation by Schmidt et al.3 They found that the inlet geometric parameter has little influence on cavitation. Using numerical analysis, Payri et al.4 focused on the influence of larger hydro-grinding radius of the orifice inlet which increased the outlet velocity and discharge coefficient, but not considering the injection pressure especially in the marine diesel engine. Wang and Su5 studied the conditions of cavitation using the homogeneous equilibrium flow model. It was found that cavitation would reduce the discharge coefficient and super cavitation enhanced the turbulent kinetic energy obviously. Zhang et al.6 found that increasing the injection pressure and reducing the discharge pressure promoted cavitation by employing a new model based on single bubble dynamics. Cavitation was 1 School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang, China 2 China Shipbuilding Power Engineering Institute Co., Ltd, Shanghai, China

Corresponding author: Fei Yan, School of Mechanical Engineering, Jiangsu University of Science and Technology, No. 2 MengXi Road, Zhengjiang, Jiangsu 212003, China. Email: [email protected]

Creative Commons CC-BY-NC: This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 3.0 License (http://www. creativecommons.org/licenses/by-nc/3.0/) which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).

Yan et al. compared between two types of nozzle, but the study of pressure fluctuation was overlooked. The experiment conducted by Ohrn et al.7 indicated that the length– diameter ratio and inlet shape of the orifice had a great effect on the discharge coefficient. Sou et al.8 proposed a new combination of large eddy simulation, the Eulerian–Lagrangian method and the Rayleigh–Plesset (RP) equation to simulate an incipient cavitation. They focused on the quantitative analysis of the length and thickness of cavitation area. Schmidt et al.,9 Dumont et al.10 and Margot et al.11 developed a homogeneous two-phase mixture model that could accurately predict the process of cavitation inside the nozzle. In recent works, numerical simulation and experiments have been combined to study the characteristics of spray. Some researchers have improved the quality of spray by increasing the injection pressure.12,13 Minato et al.14 found, through a combination of simulation and experiment, that decreasing the orifice diameter had a great influence on mixing time, and a higher injection pressure was able to improve atomization quality. Planer laser-induced fluorescence was used by Huang et al.15 to observe the spray process. Their studies concluded that the spray penetration and cone angle were enlarged by increasing the injection pressure and decreasing the nozzle diameter. However, the injection pressure in the experiment reached 200 MPa, while the injection pressure in a marine diesel engine remains less than 100 MPa. Cao et al.16 found, using photographic technology, that reducing the injection pressure can reduce the spray angle and increases the Sauter mean diameter. However, the spray shape and penetration, which are significant factors for spray, were not analyzed in that paper. Song et al.17 used a constant volume chamber to simulate the engine cylinder. It was observed by high-speed camera that the spray penetration was proportional to time at the beginning of the injection and to the square root of time in the middle and later portions of the injection. However, the velocity distribution, Sauter mean diameter and spray shape were not mentioned in their paper. Park et al.18 studied the influence of temperature in the cylinder on spray and combustion by high-speed camera and found that the penetration and spray angle became increased and decreased, respectively, when reducing the temperature. Agarwal et al.19 observed by high-speed camera that a higher injection pressure improved the penetration and spray volume, whereas the velocity distribution and Sauter diameter were not discussed due to experimental limitations. Vujanovic´ et al.20 applied Eulerian multiphase flow model to simulate the spray and found that the chamber pressure and injection pressure can suppress and promote, respectively, the development of the spray. Hohmann and Renz21 investigated the influence of the chamber pressure and the

187 temperature in the cylinder on the rate of spray droplet evaporation using Eulerian–Lagrange model and found that higher pressure and temperature improved the rate of droplet evaporation. The Eulerian–Lagrange model was modified by Pogorevc et al.22 to examine spray characteristics using different biodiesel. Most researches are limited to the injection system of the general diesel engine. However, the injection system of the high-power marine diesel engine with the larger nozzle size, the higher chamber air density23 and the longer injection duration is studied rarely. In order to reveal the influence of injection pressure on cavitation and atomization in high-power-marine diesel engine, research using a larger nozzle diameter, higher chamber density23 and longer injection duration is necessary. This is of fundamental significance and thus becoming an objective of this study. First, a two-phase flow model combined with single bubble dynamics was used to simulate cavitation, and then a droplet break-up model was used to simulate spray based on the cavitation flow parameters and address the influence of injection pressure on pressure fluctuations, diesel flow, spray penetration, spray angle, space shape and Sauter mean diameter.

2. Numerical models In this study, the WAVE model is used to calculate the break-up of the oil droplets, and the detailed description is in the literature.24–26 In addition, a droplet collision and coalescence model based on a statistical model established by O’Rourke27 was used in this paper. This model is especially for calculating the rebound and coalescence of discrete droplets. The cavitation model will be introduced in the next step work.

2.1. Cavitation model The two-phase flow model, based on the two-fluid formulation, is used to solve the mass transfer between the gas phase and liquid phase. This model includes two sets of conservation equations. The outline of this model is as follows. Mass conservation equation 2 X @ðk k Þ þ r  ðk k Vk Þ ¼ kl @t l¼1,l6¼k

ð1Þ

Momentum conservation equation @ðk k Þ þ r  ðk k Vk Vk Þ @t   ¼ k rp þ r  k k þ Ttk þ k k gþ

2 X l¼1,l6¼k

Mkl þVk

ð2Þ 2 X

l¼1,l6¼k

kl

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where the subscripts k and l represent gas phase (vapor) and liquid phase, respectively. k and k denote the vapor volume fraction and vapor density, respectively. Vk is the vapor velocity vector. k represents vapor shear stress. Ttk and g are Reynolds stress and gravity, respectively. Mkl denotes the momentum transfer. In equation (1), kl is the interphase mass transfer and is modeled by the following formula kl ¼ k

N000 4R2 R_ ¼ lk cCR



n0

c  0:5

2ðn0  1Þð1  c Þ þ 1

c 4 0:5

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 2 l  4 R_  psat  ppart  3l R R ð8Þ

where Ce and Cv are the evaporation and condensation parameters, respectively, designed to account for the fact that may occur at different rates (condensation is usually much slower than evaporation).

ð3Þ

3. Computational details

where cCR is an empirical coefficient that is set to 1 in the paper; R is the fuel bubble radius and R_ is the first derivative of the bubble radius versus time. In equation (3), N000 , the bubble number density, is generally influenced by the injection pressure, chamber pressure, nozzle geometry, fuel density and surface tension,28 and the formula is N000 ¼

3c l m ¼ Cv R þ

The Fluent14.5 software is applied to perform the simulation in this paper. In order to improve the increasing accuracy of simulation, the simulation of spray is separated from the simulation of cavitation. The simulation of cavitation is first carried out. Second, the numerical results of cavitation, including the mass flow rate, the actual diameter of liquid jet and velocity of fuel, are applied to the simulation of spray.

ð4Þ

3.1. Numerical simulation of cavitation

where n0 is the initial bubble density, which depends both on liquid quality and flow conditions, and is set to 1.01 in this paper. c is the volume fraction of the gas phase. This is a rather heuristic formula used to model coalescence effects at higher volume fraction levels. A cavitation model based on a single bubble dynamics equation29 was used in this paper. Growth and collapse of cavitation bubbles and nuclei are computed by solving the following Rayleigh–Plesset equation (5)   3 _2 1 2 l _ € 4 R ð5Þ RR þ R ¼ psat  ppart  2 l R R where psat is the pressure (assumed to be the vapor pressure in the local temperature), and ppart is the local pressure in the liquid surrounding the bubble. l is the liquid viscosity coefficient, and R€ is the second derivative of the bubble radius versus time. l is the liquid density, and  is the surface tension between the liquid and vapor. Neglecting the R and the second-order terms, this equation reduces to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 2 l _ _ ð6Þ 4 R R¼ psat  ppart  3l R R

A certain diesel engine fuel injector was analyzed in the paper. The injector has four nozzles. One of the nozzles was studied, based on symmetry. The needle movement is listed in Table 1. Figure 1 shows the geometric model. The nozzle diameter D and nozzle length L were 0.85 and 3.18 mm, respectively. The grids were generated by Nastran, and a partial mesh encryption was utilized near the nozzle entrance as shown in Figure 2. The total number of grid was 545,078, and the minimum cell size is 0.0095 mm. Due to the tiny effects of environmental pressure on the diesel density, the liquid is treated as being incompressible. At the same time, the influences of temperature are ignored because of the instantaneous occurrence (lasting only 3.5 ms). According to the working condition of diesel engine, the outlets of four nozzle exits are all set to 8 MPa. In order to reveal the effects of injection pressure on cavitation, three injection pressures of 60, 80 and 100 MPa are set in the inlet of nozzle entrance. The outlets and inlet are all based on pressure. The specific settings are listed in Table 4.

Table 1. The needle movement of fuel injector.

The representative liquid–vapor evaporation and condensation rates for this category are shown as the following sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   3 ð 1   Þ 2 2 l _ c c  m ¼ Ce 4 R psat  ppart  3l R R R ð7Þ

Classification

Value

Maximum open time of needle Minimum close time of needle Oil pressure fluctuation Piston supercharging pressure fluctuation Fuel supply advance angle

3 ms 4 ms 4% 4% 17 CA

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3.2. Numerical simulation of spray

Figure 1. Geometric model of injector.

Figure 2. Grid of the injector.

A cuboid of 150  150  200 mm was designed for the numerical domain of the spray. Because grid density and size have a great influence on the accuracy of numerical simulation, the model is calculated with several different densities of the grid. As shown in Figure 3, the spray penetration is plotted with different grid numbers under the injection pressure of 80 MPa. It can be seen that when the grid number increased from 1.29 million to 4.5 million, the difference among computing results becomes small. The spray penetration of 3.06 million, 4.07 million and 4.5 million is almost same at the same time. Therefore, the grids number of 4.5 million was selected in this study, and the minimum cell size is 0.4 mm. Figure 4 shows the fluid domain of 4.5 million grids. The nozzle with a downward jet was set at the point A, as shown in Figure 4. The fuel parameters are given in Table 2. The environmental temperature was 300 K, and the specific settings are listed in Table 3. In the Fluent14.5 software, a virtual injector, including the settings of the liquid column diameter Dl, the injector position, the injection direction, the mass

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flow rate Qm, the velocity of the fuel vl, is selected to play the role of the actual injector. The mass flow rate Qm is obtained by calculating the averages of mass flow rate, as shown in Figure 5. The velocity of the fuel vl is the time averaged outlet velocity, and the injector position and the injection direction are set according to the cuboid position. When initial cavitation and partial cavitation occur, the Dl is equal to nozzle diameter D. However, when super cavitation occurs, the Dl is less than nozzle diameter D. So, in order to improve the accuracy of simulation, the cavitation parameters, including the mass flow rate Qm and the velocity of the fuel vl, are first applied to calculating the liquid column diameter Dl, as shown in equation (9) rffiffiffiffiffiffiffi Qm ð9Þ Dl ¼ 2  vl 

where Qm is the mass flow rate of the fuel and vl is the velocity of the fuel. In addition, the air density a is calculated by the following equation a ¼

Pch M Ra T

ð10Þ

Table 2. Diesel technical data. Technical parameters

Parameter values

Type of diesel fuel Density (kg/m3) Kinematic viscosity (mm2/s) Dynamic viscosity (kg/ms) Saturated vapor pressure (Pa) Surface tension coefficient (N/m)

0# diesel fuel 840 3.5 0.00294 1329 0.00225

Table 3. Detailed settings of the virtual injector under three injection pressure.

Figure 3. Effect of grid resolution on spray penetration.

Figure 4. Grid of physical model.

Classification

60 MPa

80 MPa

100 MPa

Injection type Position Dl (mm) Start and stop time (ms) Azimuthal angle ( ) Injection direction Velocity vl (m/s) Cone angle ( ) Mass flow rate (kg/s)

Solid-cone (0, 0, 0) 0.85 0–3.5 0–360 (0, 0, 1) 286.1 13.4 0.119

Solid-cone (0, 0, 0) 0.85 0–3.5 0–360 (0, 0, 1) 357 13.4 0.14

Solid-cone (0, 0, 0) 0.749 0–3.5 0–360 (0, 0, 1) 410.1 13.4 0.146

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Table 4. Detailed settings of the simulation. Classification

Settings of cavitation simulation

Settings of spray simulation

Solver

Pressure-Based Type Absolute Velocity Formulation Transient Time Standard k-epsilon (2 equations) Standard Wall Functions Mixture Phase

Pressure-Based Type Absolute Velocity Formulation Transient Time Large Eddy Simulation (LES) Simagorinsky-Lily Discrete Phase, Wave (B0 0.61, B1 5) Collision and Coalescence Stationary wall No slip PISO Skewness-Neighbor Coupling Least Squares Cell Based Second Order Bounded Central Differencing \ \ \ 1 e-06

Turbulence Model Phase Model Wall Scheme Gradient Pressure Momentum Volume Fraction Turbulent kinetic energy Turbulent dissipation Time Step Size (s)

Stationary wall No slip SIMPLE Least Squares Cell Based Standard Second-Order Upwind QUICK Second-Order Upwind Second-Order Upwind 1 e-06

Figure 6. Locations of pressure fluctuation. Figure 5. Mass flow rate under the different injection pressures.

where Pch is chamber pressure, and M is air mole quality. Ra denotes ideal air coefficient, which is set to 8.314 in this study. T is absolute temperature which is 300 K. The detailed settings of the virtual injector are listed in Table 3.

4. Results and discussion 4.1. Influence of injection pressure on pressure fluctuation A coordinate system is built by setting the center of nozzle inlet as the origin, the nozzle axis as the X axis and the radial coordinate as the Y axis, as shown in

Figure 6. Figure 7 shows the pressure fluctuation at three locations, x ¼ 0 mm (the entrance of injection, x1/L ¼ 0, location C1), 1.59 mm (the middle of injection, x2/L ¼ 1/2, location C2) and 3.18 mm (the exit of injection, x3/L ¼ 1, location C3) under different injection pressures. It is clear that there are no pressure fluctuations at C1. In contrast, pressure fluctuation is very intense at C2 and C3, and the pressure fluctuation increases gradually along the X axis because of the increasing amplitude of the pressure fluctuation, because C1 is at the entrance of the nozzle, while C2 and C3 are inside the nozzle. The flowing area decreases rapidly, leading to the intense pressure fluctuation. Figures 5(c) and 7(b) show that the pressure fluctuation inside the nozzle becomes more intense with increasing

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Figure 7. Influence of injection pressure on pressure fluctuations inside the nozzle.

injection pressure. In conclusion, the analysis of cavitation cannot ignore the pressure fluctuation inside the nozzle because of the high influence of the pressure fluctuations. In order to identify the frequency unsteady effects on cavitation, the pressure fluctuations at the location of C3 are processed by fast Fourier transform, as shown in Figure 8. It is found that three pronounced peaks appear in the range of 300–500 Hz under the different injection pressures. In addition, the peak under the injection pressure of 100 MPa exhibits the largest value, which caused by cavitation. It also indicates that cavitation has a great influence on the pressure fluctuations. Moreover, the higher injection pressure improves the cavitation. Figure 8. Influence of frequency on pressure fluctuation.

4.2. Influence of injection pressure on cavitation flow The cavitation coefficient C was defined by Wang in equation (11) C¼

pin  psat pin  pch

ð11Þ

where pin is the injection pressure, pch is the chamber pressure and psat is the saturated vapor pressure of fuel. C becomes smaller with increasing injection pressure. The results of Wang and Su5 show that when C is more than 1.2, initial cavitation occurs. When C is between

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Figure 9. Cavitation under different injection pressures at the time of 0.05 ms.

1.10 and 1.2, partial cavitation occurs. When C is less than 1.10, super cavitation occurs. Figure 9 shows the cavitation inside the nozzle under the different injection pressures at the time of 0.05 ms. As shown in the images, partial cavitation occurred at injection pressures of 60 and 80 MPa, and super cavitation occurred at an injection pressure of 100 MPa. According to equation (11), the values of the cavitation coefficient C at 60, 80 and 100 MPa are 1.15, 1.111 and 1.087, respectively. Cavitation at injection pressures of 60 and 80 MPa was partial, and super cavitation occurred at the injection pressure of 100 MPa, according to the research by Wang and Su.5 The similarity between Wang and Su’s5 theory and the numerical simulation supports the accuracy of the simulation. As shown in Figure 9, under the injection pressure of 100 MPa conditions, the gas volume fraction that can be observed is relatively large compared with 60 MPa and 80 MPa, indicating that higher injection pressure strengthens the cavitation. In addition, the gas bubbles generated from the nozzle entrance becomes closer to the nozzle exit. When the injection pressure reaches 100 MPa, super cavitation extends from the entrance to the exit, and the flow area is smaller than the

nozzle diameter. Super cavitation will improve first atomization30 because of the smaller flow area.

4.3. Influence of injection pressure on spray penetration Figure 10 shows the influence of injection pressure on the penetration. It is consistent with the results Sun et al.31 that increasing injection pressure will increase spray penetration. Higher injection pressure can increase the kinetic energy of diesel liquid. Diesel droplets have larger kinetic energy to penetrate. The penetration in marine diesel engine exhibits higher value compared with that proposed by Hwang et al.32 It is necessary to consider the impingement on a wall when designing the cylinder. At the same time, the growth of penetration slows because of the energy loss caused by friction between the fuel and air. Each additional 20 MPa injection pressure improves penetration by 11%. Figure 11 shows the influence of injection pressure on the penetration within 0.4 ms. As shown in Figure 11, penetration is proportional to time. These results are consistent with that of Song et al.17 Cavaliere et al.33 proposed that there was a continuous liquid column near the nozzle and that the liquid

194

Figure 10. Influence of injection pressure on penetration.

International Journal of Spray and Combustion Dynamics 9(3)

Figure 11. Influence of injection pressure on penetration (0.1– 0.4 ms).

column exchanged no momentum with air at the beginning of the spray due to the short injection time, huge injection energy and weak interaction between liquid and air. In conclusion, penetration is determined only by injection speed at the beginning of the spray.

4.4. Influence of injection pressure on spray angle The spray angle before 0.5 ms was not considered because spray exists in liquid column before 0.5 ms. Figure 12 shows the spray angle at different injection pressures. With increasing injection pressure, the spray angle becomes larger, but the growth is small. Each additional 20 MPa increases the spray angle by 0.8 . Increasing injection pressure can increase the kinetic energy of the fuel which promotes friction between liquid and air resulting in breaking up. Compared with the results by Hwang et al.,32 it is obvious that the spray angle in marine diesel engine exhibits fewer changes according to the time and ranges from 16 to 19 , while the spray angle in general diesel engine ranges from 15 to 65 . This is because the larger nozzle in marine diesel engine changes the outlet flow pattern, which leads the fuel squirting along the axis of nozzle relatively, whereas the fuel is squirted divergently in general diesel engine.

4.5. Influence of injection pressure on spray shape Figure 13 shows the evolution of the spray at different injection pressures. As shown in Figure 13(a), the fuel is initially squirted in the shape of a liquid column. Then, the turbulence generated by the K-H instability wave causes the liquid column to split up. Finally, the fuel droplets under air friction spread into space in the shape of a ‘‘mushroom’’ which is consistent with Deng et al.’s34 research on spray shape. At the beginning of the spray, the massive structures are generated

Figure 12. Influence of injection pressure on spray angle.

on the spray edge and then return to the spray body, due to the larger turbulence stress and velocity gradient on the spray edge. Figure 13(b) and (c) exhibits the same phenomenon. As seen in Figure 13, when the injection pressure is raised from 60 to 80 MPa, the volume of the spray head becomes larger. Increasing injection pressure promotes large-scale vortex, which leads to larger massive structures on the spray head. However, when the injection pressure is raised from 80 to 100 MPa, the volume of the spray head shows little increments. This is because the super cavitation occurs under the pressure of 100 MPa, which caused the decrease of flow area. The mass flow rate of 100 MPa in small increments causes the little change of volume of spray head. The massive structures on the spray head are not like that on the spray edge which can return to the spray body, because the massive structures on the spray head have relatively

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Figure 13. Influence of injection pressure on spray shape.

195

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International Journal of Spray and Combustion Dynamics 9(3) little energy due to the energy consumption of largescale vortex. However, the massive structures are not evident in Zhao et al.35 This is because that the K-H surface wave, which cause the massive structures on the spray edge, is fully influenced by liquid–air density ratio. The lower chamber air density in general diesel engine suppresses the growth of K-H surface wave. In addition, because of the shorter injection duration, the droplets have not enough time to further break-up, which lead to the quite small spay head and penetration. The air entrainment in the surface of spray body becomes weaker which prevents the growth of largescale vortex. Therefore, the massive structures are not evident in general diesel engine. It is the significant information for the design of cylinder.

Figure 14. Influence of injection pressure on Sauter mean diameter.

Table 5. Experimental conditions. Technical parameters

Parameter values

Type of diesel fuel 20 C fuel density (kg/m3) Mass fraction of oxygen (%) 20 C fuel kinematic viscosity (mm2/s) Single injection quantity (mL) Nozzle diameter (mm) Injection pressure (MPa) Chamber pressure (MPa)

0# diesel fuel 873 10.56 4.4 8 0.12 100 1.4

Figure 15. Simulated and experimental spray shape.

4.6. Influence of injection pressure on Sauter mean diameter Figure 14 shows the Sauter mean diameter from the numerical simulation and the empirical formula by Hiroyasu and Arai.36 The mean error between the simulation and empirical formula is 0.5%, which demonstrates the validity of the simulation. As the injection pressure increases, the Sauter mean diameter becomes smaller, as shown in Figure 14, because the higher injection pressure increases the kinetic energy of the fuel oil that strengthens the flow disturbances and friction between the air and droplets, and the droplets have more energy for breaking up. At the same time, fuel burns more intensely at the higher injection pressure. The higher pressure and temperature promote

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Figure 16. Simulated and experimental spray penetration.

droplet break-up and atomization37 in the cylinder. Each additional 20 MPa decreases the Sauter mean diameter by 9%.

5. Experimental verification To validate the simulation, the simulated spray was compared with high-speed photography taken by Zhao et al.35 The experimental conditions are given in Table 5. As shown in Figure 15, the simulated spray shows good agreement with the experimental data. Figure 16 shows the simulated and experimental penetration. The mean error between the experiment and simulation is within 1%.

197 3. The spray angle increases with increasing injection pressure. Each additional 20 MPa increases the cone angle by 0.8 . The spray angle in marine diesel engine exhibits fewer changes according to the time and ranges from 16 to 19 . 4. Fuel is issued in the shape of a liquid column and then spreads into space. Massive structures on the spray edge can return to the spray body, while massive structure on spray head remains unchanged throughout its lifetime. 5. With increasing injection pressure, the areas of the spray head and massive structures become larger. However, the massive structures are not evident in general diesel engine caused by short injection duration and low chamber air density. The Sauter mean diameter decreases, indicating that the atomization quality improves. Each additional 20 MPa decreases the Sauter mean diameter by 9%. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The author wishes to acknowledge support given to him by Natural Science Foundation of Jiangsu Province of China (No. BK20140512) and Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry.

6. Conclusions Numerical models were built to study the cavitation in an injector nozzle and the spray under different injection pressures, and the important results are summarized below. 1. With increasing injection pressure, the pressure fluctuation inside the nozzle becomes more intense, and the pressure fluctuation increases gradually along the nozzle axis. As the injection pressure increases, the volume fraction of diesel vapor increases, and cavitation becomes more obvious. 2. At the beginning of the spray, spray penetration is proportional to time because there is no momentum exchange between the liquid column and the air. The increase of penetration slows gradually during the middle and later periods of the spray. The spray penetration and angle increase with increasing injection pressure. Each additional 20 MPa increases the cone angle by 0.8 . In addition, the penetration in marine diesel engine exhibits higher value compared with that in general diesel engine.

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