Fuel 90 (2011) Contents lists available at ScienceDirect. Fuel. journal homepage:

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1 Fuel 90 (2011) Contents lists available at ScienceDirect Fuel journal homepage: Numerical simulation of cavitation in the conical-spray nozzle for diesel premixed charge compression ignition engines Ming Jia a, Maozhao Xie a, Hong Liu a, Wei-Haur Lam a, Tianyou Wang b, a School of Energy and Power Engineering, Dalian University of Technology, PR China b State Key Laboratory of Engines, Tianjin University, PR China article info abstract Article history: Received 29 June 2010 Received in revised form 12 April 2011 Accepted 15 April 2011 Available online 1 May 2011 Keywords: Conical-spray nozzle Diesel premixed charge compression ignition (PCCI) engine Numerical simulation The conical-spray injector is capable of achieving lean mixture with high homogeneity in the cylinder for diesel Premixed charge compression ignition (PCCI) engine with advanced injection timing. To better understand the cavitating flow inside the conical-spray injector, numerical simulations have been conducted by using a mixture multiphase model and a full cavitation model in this study. The results indicate that the cavitation evolution significantly affects the liquid sheet thickness and velocity at nozzle exit, which further change the spray angle and droplet Sauter mean diameter (SMD) dramatically. Based on the cavitation distribution inside the nozzle, the cavitating flow inside the conical-spray nozzle can be classified into four regimes with no cavitation, cavitation inception at inlet, developing cavitation at nozzle exit and super cavitation respectively. The extension of cavitation to nozzle exit in the super cavitation regime significantly improves the fuel atomization by increasing the injection velocity and decreasing the thickness of the liquid sheet. A cavitation map for the conical-spray injector has been developed by sweeping the ambient pressure and injection pressure simultaneously. It is found that the phenomenon of super cavitation only occurs in a narrow region where ambient pressure is very low. Therefore, the start of injection timing should be kept well before top dead center (TDC) to ensure the occurrence of super cavitation inside the nozzle in order to provide more homogeneous fuel/air mixture for diesel PCCI engines. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Premixed charge compression ignition (PCCI) combustion attracts increasing attentions in recent years, since it can provide extremely low nitrogen oxides (NO x ) and particulate matter (PM) emissions, while maintaining high diesel-like efficiency. In PCCI combustion, the fuel is injected early in the compression stroke to provide substantial time for fuel/air mixing, and the combustion occurs nearly spontaneously throughout the cylinder without diffusion flame. As a result, the combustion temperature and local equivalence ratio are very low, which dramatically reduce engine-out NO x and PM emissions. However, for PCCI engines with early fuel injection, it is easy to produce wall wetting that can cause combustion inefficiency and oil dilution due to the over-penetration of the fuel. Thus, the fuel injector must be carefully designed to improve the homogeneity of the fuel/air mixture and reduce the adhesion of fuel to the wall. In order to meet such severe requirement, significant efforts have been taken on the fuel injector development recently. Corresponding author. Tel.: ; fax: address: wangtianyou@tju.edu.cn (T. Wang). The injector with narrow spray cone angle was proposed by Walter and Gatellier [1] to limit fuel liner impingement. In order to form more uniform fuel/air mixture and avoid the wall impingement, the micro-hole nozzle of 0.08 mm and ultra-high injection pressure of 300 MPa have been carried out by Nishida et al. [2]. The group-hole nozzle [3,4] with two close micro-orifices was further suggested to help the momentum transfer of the two sprays and increase the penetration of the spray. Another type of nozzle known as impinging-spray nozzle [5] was used by Yamamoto and Niimura to impinge the fuel from two injector holes at their orifice exit, so that the spray penetration could be reduced. All above injectors are based on the solid-cone spray with holetype nozzle, and excessive spray penetration and/or large droplet size are still problems associated with them for PCCI engines with early injection timing. Hu et al. [6] proposed a pintle-type nozzle to form the conical-shaped spray and create the homogeneous mixture in order to achieve low exhaust emissions in the premixed diesel combustion. Harada et al. [7] indicated that the conicalspray injector is suitable for the PCCI diesel engine, because it produces a comparatively uniform mixture and avoids collision of the fuel spray with the cylinder linear. Lee et al. [8] also found that the conical-spray injector could achieve lean mixture with high homogeneity in the cylinder for advanced diesel injection. Leng et al. [9] /$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.fuel

2 M. Jia et al. / Fuel 90 (2011) Nomenclature Symbols A effective A th C a C d C v CN L exit _m NO x p i p b p vapor Re area occupied by the liquid fuel at nozzle exit area of the geometrical cross section at nozzle exit area contraction coefficient discharge coefficient velocity coefficient cavitation number needle lift mass flow rate calculated from the simulation nitrogen oxides injection pressure ambient pressure fuel vapor pressure of diesel fuel Reynolds number V exit q fuel l fuel averaged flow velocity at nozzle exit density of diesel fuel viscosity of diesel fuel. Acronyms AIS adaptive injection strategies CFD computational fluid dynamics PCCI premixed charge compression ignition PM particulate matter SMD Sauter mean diameter SOI start of injection TDC top dead center VCO valve covered orifice improved the conical-spray nozzle by impinging the fuel jets on the guide wall shortly before the nozzle tip forming a conicalshape spray. It has been demonstrated that the lean mixture can be formed at 20 CA after the start of injection (SOI) without wall wetting. However, understanding of the high-pressure conical diesel spray is far less than those of the solid spray or hollow-cone gasoline spray [10], and many of the aspects are just beginning to be revealed. Obokata et al. [11] studied the characteristics of the flow velocity and particle diameters in the conical spray using laser Doppler anemometry and phase Doppler anemometry. Long et al. [12] analyzed and improved the conical sprays using the laser sheet and high speed camera imaging. Yang et al. [10] modeled the high-pressure conical spray under different ambient pressures with a new relative velocity correction model. has been recognized as one of the most important parameters affecting fuel spray atomization [13]. For diesel fuel injectors, cavitation has beneficial effects to the development of the fuel sprays, since the primary break-up and subsequent atomization of the liquid jet can be enhanced. Many researchers have concentrated in using both the experimental and numerical methods to gain a better understanding of this phenomenon and its effects on the performance and durability of diesel fuel injection [14 16]. Andriotis and Gavaises [15] experimental observed that two distinct forms, referred to as geometric-induced cavitation and string cavitation, appear in the in the nozzle, and found that the spray angle increases significantly with the presence of string cavitation. By reviewing the influence of cavitation on internal nozzle flow, engine performance and exhaust emissions and surface erosion in valve covered orifice (VCO) nozzle under diesel engine operating conditions, Gavaises [16] concluded that the cavitation damage correlates well with areas of bubble collapse and the string cavitation structure inside nozzle may be associated with increased engine exhaust emissions. However, few research studies were found in reporting the cavitation within the conical diesel sprays. Because of the difficulties associated with the determination of the flow characteristics inside the nozzle, computational fluid dynamics (CFD) represents a useful tool to provide an insight to the flow within the nozzle. Schmidt et al. [17] develops a model for high-speed cavitating nozzle flow with consideration of the compressibility of both liquid and gas phases, and the predictions show that the model can accurately predict discharge coefficient and exit velocity for flow in sharp nozzles. Payri et al. [18] carried out a CFD analysis of the flow through various nozzle geometries with the commercial software Fluent. Roth et al. [19] studied the effect of transient injection conditions on cavitation inception and development with a cavitation model recently developed. Som et al. [20] investigated the effects of injection pressure, needle lift position, and fuel type on the internal nozzle flow and cavitation behavior in a diesel injector with a mixture model. By comparing with a large number of experimental data, Giannadakis et al. [21] assessed the cavitation model based on the Eulerian Lagrangian approach, which accounts for many primary physical processes pertinent to cavitation. The results revealed that the model can accurately identify many cavitation structures in internal nozzle flows. Recently, Wang and Su [22] used a two-fluid model to reveal the relationship between the injection pressure fluctuations and the unsteady cavitation processes inside the high-pressure diesel nozzle holes. In this paper, the numerical simulation of the cavitation in a conical-spray injector is presented. Firstly, the full cavitation model is validated by using the flow and cavitation measurements acquired from a transparent, quasi two-dimensional throttle. Secondly, the evolution of cavitation in the conical-spray injector is analyzed. Thirdly, the influences of injection pressure and ambient pressure on the cavitation inside the nozzle are investigated. Finally, a cavitation map for the conical-spray injector is developed. 2. Computational model The commercial code Ansys Fluent 12.0 was used to perform the CFD calculations presented in this study. The mixture model was chosen to describe the multiphase flow. The realizable k-epsilon turbulent model was applied to all the simulations because of its numerical stability under a condition of large pressure gradient. Non-equilibrium wall function was used due to the size of nozzle channel is extremely small. The cavitation model used in this study is Singhal s full cavitation model [23], which could take all the effects of phase change, bubble dynamics, turbulent pressure fluctuations, and non-condensable gases on cavitation into account. The liquid phase is assumed to be an artificial single-component diesel surrogate with a H/C ratio of 29/16, and their corresponding properties can be found in [24]. In the Singhal s full cavitation model [23], the working fluid is assumed to be a mixture of liquid, vapor and non-condensable gases. The turbulence-induced pressure fluctuations are taken into account by raising the phase-change threshold pressure value from the liquid saturation vapor pressure. The phase change rates are derived from the Rayleigh Plesset equations. A more complete description of the numerical model can be found in Ref. [23].

3 2654 M. Jia et al. / Fuel 90 (2011) Experimental validation Before applying the model for simulation of the cavitation in the conical-spray injector, it is necessary to validate the computational model. A large number of experiments on cavitation in multi-hole diesel Injector [25 27], high-pressure swirl atomizer [28], and pintle-type outwards-opening gasoline injector [29,30] have been extensively investigated by Arcoumanis et al. and Gavaises et al. at City University London. Due to the simple geometry configuration and similar tested conditions, including pressure difference, channel size and operating fluid, to those investigated in this study, the fundamental experimental data from Winklhofer et al. [31] was used to validate the computational model in this study. In the experiment, the flow and cavitation characteristics in a transparent, quasi two-dimensional throttle with diesel were studied by using the optical measurements in detail. The tested nozzle consists of a rectangular-sharp channel with a sheet of 0.3 mm in thickness, an inlet of mm in width, an outlet of mm in width, an inlet of 0.02 mm in radius, and a throttle of 1 mm in hole length. A two-dimensional grid with 60,000 cells in the nozzle block was employed to discretize the geometry in this study. The experiment was conducted at a fixed inlet pressure of 10 MPa and an inlet temperature of 300 K. The outlet pressure was varied to generate different flow rates. Fig. 1 shows the comparisons between the predicted vapor distributions and the experimental images under two different outlet pressures. Both the experiment and the simulation show that the small cavitation only incepts at the throttle entrance when the outlet pressure is 4 MPa. As the outlet pressure decreases to 2 MPa, the cavitation gas covers the whole throttle, and extends to the exit. Model predictions and experimental data for the mass flow rates under various pressure differences between the inlet and the outlet are shown in Fig. 2. The experiment indicates that the mass flow rate increases rapidly with the growth of the pressure difference, and reaches a constant value after the pressure difference excesses approximately 7 MPa. This trend is well reproduced by the computational model. It should be noted that there are still some discrepancies between the measurements and the predictions. In Fig. 1, the predicted cavitation area with black color is much smaller than the Mass Flow Rate (g/s) Experiment Model Pressure Difference (MPa) Fig. 2. Comparison of experimental and modeling results for the influence of pressure difference on mass flow rate. experimental image. This is mainly due to the fact that the experimental results are taken from the photographs of a model nozzle. The nozzle is backlit, and the intensity of the transmitted light was used to indicate the cavitating area. A high transmitted intensity means that only one phase exists, whereas a weak light means that a vapor/liquid mixture exists. Thus, it is impossible to determine the exact volume fraction of the cavitated gas in the experiment, and only whether the cavitation occurs or not can be revealed. Thus, the measured cavitation area with a high volume fraction of vapor is much larger than the predictions in Fig. 1. The predicted regions with vapor volume fraction between 0.1 and 0.35 in Fig. 1b would probably appear black if they were actually measured in the experiment due to the inherent inability to experimentally capture a high resolution of the vapor volume fraction. In addition, the flow rates predicted by the model are higher than the experimental data as shown in Fig. 2, especially when the pressure difference is beyond 7 MPa. This is mainly caused by the simplification of the Experiment Model (a) inlet pressure: 10 MPa, outlet pressure: 4 MPa (b) inlet pressure: 10 MPa, outlet pressure: 2 MPa Fig. 1. Comparisons between the predicted vapor volume fraction with experimental data.

4 M. Jia et al. / Fuel 90 (2011) two-dimensional computational model in order to reduce the computational time and be consistent with the experimental image. However, the thickness of the experimental channel is only 0.3 mm, which is close to the inlet width. The two-dimensional model therefore ignores the near-wall friction and accelerates the flow velocity compared to the three-dimensional flow. It is extremely serious for the conditions with pressure difference higher than 7 MPa, where the mass flow rate is overpredicted than the measurement as shown in Fig. 2. Overall, the major characteristics including both the vapor distribution and mass flow rate obtained from the simulation are in close agreement with the experimental results. Therefore, the computational model is applied to investigate the cavitation phenomenon inside the conical-spray nozzle in the following study. 4. The cavitation in the conical-spray nozzle The calculations were conducted to investigate the cavitating flow characteristics in the conical-spray nozzle in this section. The conical-spray nozzle used in this study is a typical pintle-type injector with a wide-range conical tip at the bottom of the pintle to produce a hollow cone spray as shown in Fig. 3a. In order to reduce the computational resource requirements, the computational domain is represented by an axisymmetrical grid by taking the advantage of the circumferential symmetry of the injector. The computational domain is extended up to the in-cylinder region in order to take account of the physical effects which concern the interaction between the cavitating flow and the external jet from the nozzle. The two-fluid calculations including diesel and diesel vapor was employed in this study. The corresponding computational mesh is shown in Fig. 3b. The computations were performed under the assumption that the needle is at a fully opened position. As shown in Fig. 3a, the maximum needle lift was taken from an actual conical-spray nozzle. This can be justified as the flow is expected to be quasisteady during this period since the needle is fully opened for approximately 90% of the injection duration [20]. The initial conditions of all the calculations presented in this section are the injector internal flow domain filled with still diesel. The boundary conditions for the inlet and outlet are prescribed as a static pressure and the injector wall is simply a no-slip wall boundary condition. In order to investigate the propensity of cavitation and turbulent flow inside the nozzle, the non-dimensional number, cavitation number and Reynolds number, are used in this study. The cavitation number (CN) definition used by Arcoumanis and Gavaises [32] is employed CN ¼ p i p b p b p vapor where p i is the injection pressure, p b is the ambient pressure, and p vapor represents the fuel vapor pressure of diesel fuel. The Reynolds number (Re) is calculated as Re ¼ q fuel V exitl exit l fuel where V exit is the averaged flow velocity at nozzle exit, L exit is the needle lift as shown in Fig. 3, q fuel is the density of diesel fuel and l fuel is the viscosity of diesel fuel. To evaluate the pressure losses due to both the area contractions and viscous work at nozzle exit, several classical coefficients are examined in this study. The discharge coefficient (C d ) is calculated from _m C d ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3þ 2q fuel ðp i p b Þ A th where _m is the mass flow rate calculated from the simulation, A th is the area of the geometrical cross section at nozzle exit. The reduction of fuel flow area at nozzle exit due to the occupancy of the cavitation is represented by the area contraction coefficient C a as C a ¼ A effective A th where A effective is the area occupied by the liquid fuel at nozzle exit. The velocity coefficient C v, which accounts the velocity losses due to friction and cavitation, can be obtained from the following relationship C d ¼ C a C v 4.1. evolution The calculations are first carried out for the case with 100 MPa injection pressure and 0.1 MPa ambient pressure. Fig. 4 shows the sequence of the cavitating flow inside the conical-spray nozzle after SOI. It is clear that the cavitation inception occurs at the corner areas in the nozzle where both the pressures and flow velocities are relatively low at the time of 5 ls. After 10 ls, the cavitation extends up to the nozzle exit, and covers most of areas at nozzle exit. It reaches a steady state at 20 ls for a fully developed cavitation, and a large amount of liquid diesel has been vaporized to be gas phase. It should be noted that air entertainment into the cavitation bubbles could possible occurs when the ð1þ ð2þ ð4þ ð5þ (a) Schematic Representation (b) Computational Mesh Fig. 3. The schematic representation and computational mesh for the conical-spray nozzle.

5 2656 M. Jia et al. / Fuel 90 (2011) Vapor Distributions Vapor and Velocity Distributions at Nozzle Exit (a) 5 µs (b) 8 µs (c) 10 µs (d) 20 µs Fig. 4. Transient cavitating flow evolution in the conical-spray nozzle (p i = 100 MPa, p b = 0.1 MPa). cavitation extend to the nozzle exit, which is referred to as hydraulic flip. Marchin et al. [29] observed that the coexistence of air entrainment and cavitation bubbles in an enlarged model of a pintle-type outwards-opening gasoline injector. Since extremely high injection pressure is used to gain better vaporization of diesel fuel in this study, it is found that the backflow is insignificant from the vapor velocity distribution at the nozzle exit as shown in Fig. 4d. Therefore, the fully developed cavitation is only considered when the cavitation bubbles reach the nozzle outlet. From the evolutions of fuel vapor and velocity at nozzle exit in Fig. 4, it can be seen that the spray angle, spray penetration and droplet diameter are significantly affected by the cavitation inside the nozzle. Although it is well known that the evolution of the spray angle and droplet diameter are directly associated with the cavitation inside the multi-hole nozzle [33], the effect of cavitation on conicalspray development has not been well understood yet. Qiao et al. [34] have reported that the average sound velocity of the fuel in the conical-spray nozzle is dramatically lower than the theoretical value of the pure diesel fuel, thus they concluded that the cavitation exists in the injector. It was also found that the spray angle in the conical-spray nozzle decreases significantly as the time going on, and approximately constant spray angle is achieved after 1 ms. It was suspected that this phenomenon is associated with the motion of the needle tip. In fact, the evolution of the spray angle is also affected by the cavitation inside the nozzle. From the fuel vapor and velocity distributions at nozzle exit in Fig. 4, the liquid fuel flows out the nozzle exit from the wall (point B in Fig. 3) at the start of injection. The continuous developed cavitation occupies the area at nozzle exit, so fuel spray angle is reduced remarkably. As the cavitating flow reaches a steady state, the spray angle does not change any more. Similar findings have also been revealed by the study of Marchin et al. [29], in which the effect of internal nozzle flow on spray angle in a pintle-type outwards-opening gasoline injector was well understood. Yang et al. [10] studied the high-pressure conical-spray nozzle for diesel injection experimentally. It was found that the SMD is large at the beginning of injection, and decreases significantly after 0.5 ms. It may be due to the fact that the liquid spray width from the nozzle to the cylinder reduce rapidly as the cavitation develops with time. Yang et al. [10] therefore can not reproduce the tendency of the SMD using spray model without the considerations of cavitation effect in the nozzle. The velocity and droplet diameters of a conical-spray nozzle were measured by Obokata et al. [11] using a Laser Doppler anemometry and a phase Doppler anemometry. It was found that the spray was well atomized immediately after the nozzle exit, but there were large velocity losses at nozzle exit. Their experiment also shows that the smallest diameter of the droplet increases with distance along the spray direction. This can be attributed to the strong cavitation tendency inside the nozzle. The choked cavitating flow at nozzle exit leads to the velocity losses and a very thin liquid sheet as shown in Fig. 4, so it is expected that the liquid diesel can be atomized easily. However, part of the fuel vapor turns back to the liquid status when flowing into the cylinder due to the cylinder pressure is much higher than the liquid saturation vapor pressure. From above analysis, it can be concluded that the cavitation in the conical-spray nozzle plays an important role in the fuel atomization processes Influence of ambient pressure In diesel PCCI engines, the injection timing is well before TDC to provide more time for fuel air mixing prior to the ignition and combustion. The ambient environment for the liquid spray varies dramatically with a large ambient pressure range depending on the start of injection timing. It is widely accepted that the ambient pressure has a major impact on the spray formation. The simulations were therefore performed by varying the ambient pressure from 0.1 MPa to 35 MPa with a fixed injection pressure of 100 MPa in order to investigate the influence of ambient pressure on cavitation inside the conical-spray nozzle. All the simulation cases reach a steady state at 50 ls after the start of injection and therefore the steady results are only presented in the following sections. Fig. 5 shows the vapor volume fraction contours at five different ambient pressures. For the case with 35 MPa ambient pressure, nearly no cavitation is observed inside the nozzle, and the flow

6 M. Jia et al. / Fuel 90 (2011) Vapor Distributions Vapor and Velocity Distributions at Nozzle Exit Ambient Pressure (a) 35 MPa (b ) 30 MPa (c) 10 MPa (d) 1 MPa (e) 0.1 MPa Fig. 5. The influence of ambient pressure on cavitation distribution in the conical-spray nozzle (p i = 100 MPa). Vapor Volume Fraction at Nozzle Exit Developing at Nozzle Exit Inception at Inlet Ambient Pressure (MPa) No Fig. 6. Mass flow rate and vapor volume fraction at nozzle exit for various ambient pressures (p i = 100 MPa). Mass Flow Rate (kg/s) at nozzle exit has a core liquid flow with a relatively flat velocity profile. As the ambient pressure decreases to 30 MPa, the cavitation occurs at the upstream of the nozzle exit, and later extends along the nozzle wall with a decrease of ambient pressure. The cavitation reaches the nozzle exit with further decrease of the ambient pressure down to 1 MPa. Eventually, the fully developed cavitation is observed at the ambient pressure of 0.1 MPa. Based on the cavitation distribution inside the nozzle, the cavitating flow can be classified into four regimes including no cavitation, cavitation inception at inlet, developing cavitation at nozzle exit and super cavitation as shown in Fig. 5a, b, d and e, respectively. The quantitative definitions of these four regimes can be found in Fig. 6, in which the vapor volume fraction at nozzle exit and mass flow rate versus the ambient pressure are presented. The vertical lines in Fig. 6 indicate the transition points of the different flow regimes. In the no cavitation region, the mass flow rate decreases dramatically with the increase of ambient pressure. As the flow is beyond the no cavitation region, the mass flow rate is independent of the ambient pressure and remains nearly constant due to the chocking effect induced by the cavitation inside the nozzle. In the region of cavitation inception at inlet, the exit stream is purely liquid, even though the cavitation was generated at the orifice entrance. The amount of vapor in the exit stream increases significantly as the ambient pressure decreases in the region of developing cavitation at nozzle exit. A further decrease in ambient pressure leads to the cavitating flow reaching a super cavitation region, where the steady vapor volume fraction remains at nozzle exit. From the variations of C d, C a and C v with an designated injection pressure in Fig. 7, it is clear that the transition from no cavitation regime to the regime of cavitation inception at inlet leads to a rapid decrease in C d. This means that the flow efficiency decreases as the cavitation begins to incept at nozzle entrance. Further reduction of the ambient pressure gives small effects in C d no matter in super cavitation region. Both the rapid decrease of C a and increase of C v can be observed when the cavitating flow comes into the super cavitation region due to the nozzle exit is occupied by the increasing levels of cavitation. From above results, it can be found that the primary break-up of the conical spray is affected by the cavitation inside the nozzle significantly. Both the thickness and velocity of the initial liquid sheet at nozzle exit vary in a large range depending on the cavitating flow patterns. Long et al. [12] studied the macroscopic characteristics of the conical spray using a laser sheet and high speed camera imaging at 24.5 MPa injection pressure and at three different ambient pressures. It was found that the conical-spray pattern changes considerably with the variation of ambient pressure. A thin vacant region is observed in the spray center at the MPa ambient pressure. When the ambient pressure is increased to 0.98 MPa, the spray penetration decreases suddenly and the inner spray cone is filled with the liquid fuel. As the ambient pressure is further increased to 1.96 MPa, the spray penetration becomes much weaker. The transition of the spray from vacant region to a solid liquid cone can be possibly related with the transformation of the flow inside the nozzle from the super cavitation regime to the cavitation inception at inlet or no cavitation regime. For the cases with a

7 2658 M. Jia et al. / Fuel 90 (2011) Coefficient Developing at Nozzle Exit Ambient Pressure (MPa) low ambient pressure, the extension of cavitation to the nozzle exit improves the fuel atomization by increasing the injection velocity and decreasing the thickness of the liquid sheet, which can be found in Fig. 5. The spray angle is also affected by the ambient pressure due to the presence of cavitation at nozzle exit. The definition of the spray angle is shown in Fig. 3. According to the experiment of Long et al. [12], the spray angle is 114 at the ambient pressure of MPa, and it increases up to a 121 angle at the ambient pressure of 1.96 MPa. Consistent with the experimental results, the spray angle slightly increases by increasing the ambient pressure from 0.1 MPa to 35 MPa in the simulations of Fig Influence of injection pressure Inception at Inlet C d C a C v No Fig. 7. Discharge coefficient (C d ), area contraction coefficient (C a ) and velocity coefficient (C v ) for various ambient pressures (p i = 100 MPa). For diesel engines, the injection pressure can be varied from few hundred bars to even more than 300 MPa. The examination of the internal flow characteristics is therefore necessary over a wide range of the injection pressure. Simulations were performed by varying the injection pressure from 20 MPa up to 350 MPa at a fixed ambient pressure of 1 MPa in order to better understand the influence of injection pressure on the cavitating flow in the conical-spray nozzle. It should be noted that fuel density and viscosity will change simultaneously with the variation of injection pressure, which is not taken account of in this study. Recently, Giannadakis et al. [35] numerically investigated the effect of compressibility and viscosity due to pressurization on flow characteristics in diesel nozzles. The results indicated that the predicted discharge coefficient with variable density and viscosity has only 2% difference compared to the one with constant fuel properties for highly cavitating flow with 165 MPa injection pressure. Thus, it is believed that the model used in this study could capture the fundamental cavitation behavior in the conical-spray nozzle under diesel PCCI operating conditions with satisfactory accuracy. Fig. 8 shows the vapor fraction contours at five different injection pressures. It is clear that the cavitating flow lies in the regime of developing cavitation at nozzle exit as the injection pressure increases from 20 MPa to 300 MPa. In this range, the injection pressure has small effect on the cavitation distribution inside the nozzle and the slight increasing levels of cavitation at nozzle exit are observed, as shown in Fig. 8a d. The super cavitation does not occur until a high injection pressure of 350 MPa. The trends of averaged velocity and vapor volume fraction at nozzle exit with variation of injection pressure are shown in Fig. 9. It found that the vapor volume fraction at the exit stream is less than 0.2 for the cases with injection pressure less than 300 MPa, which corresponds to the regime of developing cavitation at nozzle exit. The vapor volume fraction only slightly increases when the injection pressure increases from a pressure of 20 MPa up to 300 MPa. Further increase of the injection pressure up to 350 MPa may cause a sudden increase of both vapor volume fraction and injection velocity at nozzle exit due to the effect of super cavitation. Previous study [20] indicates the increase of injection pressure results in a significant drop of the flow efficiency as the flow is in the cavitation regime due to the growing cavitation inside the nozzle. Thus, it leads to the decrease in C d. However, it can be seen from Fig. 10 that C d increases slightly when the cavitating flow is transformed from the regime of developing cavitation at nozzle exit to the regime of super cavitation. This is mainly due to the fact that the cavitation is well incepted and fully developed at the nozzle entrance as the flow is within these two regimes. The further increase in injection pressure could both improve the flow efficiency and increases C d. It also shows that C v increases steadily with the increase of injection pressure in the regime of developing cavitation at nozzle exit and the rapid increase of C v happens as soon as the super cavitation occurs according to Fig. 10. The reversed trend for C a is observed. This is mainly due to the occupancy of the cavitated fuel vapor at nozzle exit. In conclusion, it can be inferred that the super cavitation inside the nozzle enhances the fuel atomization characteristics and Vapor Distributions Injection Pressure (a) 20 MPa (b) 50 MPa (c) 100 MPa (d) 300 MPa (e) 350 MPa Fig. 8. The influence of injection pressure on cavitation distribution in the conical-spray nozzle (p b = 1 MPa).

8 M. Jia et al. / Fuel 90 (2011) Vapor Volume Fraction at Nozzle Exit Developing at Nozzle Exit Injection Pressure (MPa) Fig. 9. Averaged velocity and vapor volume fraction at nozzle exit for various injection pressures (p b = 1 MPa) Averaged Velocity at Nozzle Exit (m/s) 20 MPa to 350 MPa simultaneously, a cavitation map for the conical-spray nozzle is developed as shown in Fig. 11. It is clear that the cavitation map could be separated into four regions including no cavitation, cavitation inception at inlet, developing cavitation at nozzle exit and super cavitation, as labeled in Fig. 11a. For the conditions with ambient pressure higher than 9 MPa, there is no cavitation inside the nozzle as the injection pressure is kept relatively low. The cavitation inception begins at the entrance corner with the increasing injection pressure. As the ambient pressure increases and reaches 6 MPa, the line above the boundary of the cavitation inception at inlet becomes a horizontal line, suggesting that the regime of cavitation inception at inlet is almost entirely a function of injection pressure and independent from the influences of the ambient pressure. The cases with high ambient pressure and high injection pressure indicate that most of the region is covered by the regime of developing cavitation at nozzle exit. It can be observed from Fig. 11a that the phenomenon of super cavitation only occurs in a narrow region where the ambient pressure is extremely low. As the injection pressure increases to 350 MPa, the upper boundary of the ambient pressure for super cavitation slightly extends to a pressure of 1 MPa. Previous sections have indicated that the super cavitation dramatically changes the spray characteristics, and enhances the spray primary break-up Coefficient Developing at Nozzle Exit C d C a C v Injection Pressure (MPa) Developing at Nozzle Exit Inception at Inlet No 0.2 improves the flow efficiency. The conical spray with super cavitation could provide a good solution in term of a better fuel/air mixture and improve fuel efficiency for diesel PCCI engines map Injection Pressure (MPa) Fig. 10. Discharge coefficient (C d ), area contraction coefficient (C a ) and velocity coefficient (C v ) for various injection pressures (p b = 1 MPa). Several studies have been performed to produce a predictive theory of the cavitating flow inside the nozzle by amassing a large body of data [36]. However, the complex trends of cavitation regime are observed at high injection velocities due to the influence of the nozzle geometry. It indicated that each nozzle has its own distinct cavitation characteristics with the variation of ambient and injection pressure [37]. Therefore, it is necessary to examine the cavitation behavior of the conical-spray nozzle under various ambient and injection pressures. By sweeping the ambient pressure from 0.1 MPa to 50 MPa and the injection pressure from Reynolds Number Ambient Pressure (MPa) (a) dimensional coordinates Developing at Nozzle Exit Inception at Inlet No Number (b) non-dimensional coordinates Fig. 11. map for the various ambient and injection pressure (dashed line: experiments from Schmidt et al. [39]).

9 2660 M. Jia et al. / Fuel 90 (2011) in the conical-spray nozzle. Thus, the injection timing should be kept well before TDC to ensure the occurrence of super cavitation inside the nozzle in order to provide more homogeneous fuel/air mixture for diesel PCCI engines. However, the premixed compression combustion is only suitable for the low and medium engine loads in diesel PCCI engine due to the limitation of engine knock. When an engine is operated under the high load, it must transit to the conventional diesel diffusion-flame combustion with the injection timing around TDC. Since the conical-spray nozzle exhibits poor atomization characteristics under such a high ambient pressure, it makes the nozzle difficult to be applied under a condition of high engine load. Sun and Reitz [38] proposed an adaptive injection strategies (AIS) to solve the problem, in which both a swirl injector and a multi-hole injector were equipped in a cylinder. The entire engine operating range can be covered by using the swirl injector for PCCI combustion and the multi-hole injector for the conventional diesel combustion. Fig. 11b shows the cavitation map as a function of two most widely used non-dimensional parameters, i.e., cavitation number and Reynolds number, to deeply understand the cavitating behavior inside the conical-spray nozzle. The solid line is plotted based on the computational results from this study and the dashed line is a references from Schmidt et al. s work [39]. It can be seen that the inception of cavitation at inlet and the transition to developing cavitation at nozzle exit are predominately in the function of cavitation number, and it is nearly independent of Reynolds number as the Reynolds number is higher than The findings are consistent with the experimental works by Tullis [40], who indicate that cavitation inception is indeed independent of the Reynolds number at a high Reynolds number. It can be seen from Fig. 11b that the occurrence of super cavitation is nearly a function of cavitation number, especially for those cases with a high Reynolds number. For the conditions with a high ambient pressure, the injection pressure must be kept high enough to reach the value of critical cavitation number for super cavitation. However, the increase in injection pressure also significantly increases the Reynolds number due to the velocity increase of the injection, which further improves the criterion for super cavitation regime. It is therefore extremely difficult to realize the super cavitation under a high ambient pressure condition. As shown in Fig. 11b, all the three boundaries used to divide the cavitation regimes become a vertical line for the high Reynolds number. Thus, it can be concluded that the cavitation number is the dominant parameter for the cavitating flow in a diesel conical-spray injector. 5. Conclusions The cavitating flow inside the conical-spray injector has been investigated numerically by using a mixture multiphase model and a full cavitation model. The conclusions can be summarized as follows: 1. The cavitation evolution dramatically affects the liquid sheet thickness and velocity at nozzle exit, which could further change the spray angle and droplet SMD significantly. 2. The cavitating flow inside the conical-spray nozzle can be divided into four regimes including no cavitation, cavitation inception at inlet, developing cavitation at nozzle exit and super cavitation based on the cavitation distribution inside the nozzle. 3. Rapid decrease in the area contraction coefficient and the increase in velocity coefficient are observed when the cavitating flow enters into the super cavitation regime. 4. For the cases with a low ambient pressure, the extension of cavitation to nozzle exit significantly improves the fuel atomization by increasing the injection velocity and decreasing the thickness of the liquid sheet. 5. The phenomenon of super cavitation only occurs in a narrow region where ambient pressure is very low. The cavitation within the nozzle is predominately the function of cavitation number, and nearly independent of the Reynolds number for those cases with a high Reynolds number. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No ), National Basic Research Project of China (Grant No. 2007CB210002) and State Key Laboratory of Engines, Tianjin University (Grant No. K ). References [1] Walter B, Gatellier B. Development of the high-power NADIST concept using dual-mode diesel combustion to achieve zero NOx and particulate emissions. SAE Paper ; [2] Nishida K, Zhang W, Manabe T. 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