Numerical Study on Flash Boiling Spray of Multi-Hole Injector.
The spray atomization process in internal combustion engines directly affects the heat release rate and the duration of combustion and subsequently impacts the thermal efficiency and emissions of engines [1, 2]. For gasoline direct injection (GDI) engines, it is desired that the homogenous fuel/air mixture can be formed rapidly, which requires the spray with a proper penetration, a wide cone angle and small droplets [3, 4]. To meet these requirements, high injection pressure is used generally to improve the atomization of the spray, but sometimes overlong spray penetration leads to fuel impingement on cylinder walls . The impingement produces thick films of fuel and rich mixture, and deteriorates the combustion. Flash boiling of spray is an effective method to improve the atomization by the explosion of vapor bubble formed in superheated liquid when the liquid temperature is higher than its boiling point or the local pressure is lower than its saturation pressure [6, 7, 8, 9] Therefore, the flash boiling of spray can decrease droplet diameter and improve liquid evaporation without increasing the injection pressure [1, 10], promote fuel/air mixture formation , flame propagation, and then improve thermal efficiency and reduce smoke emission .
For multi-hole injector the morphology of spray has an obvious change with the fuel temperature increasing or the ambient pressure decreasing [13, 14], which influences the process of mixture formation and flame propagation. According to the spray morphology of a multi-hole injector, Zeng et al.  divided the spray into non-flash boiling spray, transitional flash boiling spray and flare flash boiling spray under different superheat degrees. At the transitional flash boiling stage, the spray penetration becomes short and spray plume becomes wide; whereas spray penetration and spray plume width has inverse trends at the flare flash boiling stage [16, 17]. Further study showed that multi-hole injector spray collapsing at high superheat degree would result longer spray penetration and narrower spray angle, which subsequently leads to wall wetting and then increases fuel consumption and soot emission . This spray morphology is undesirable for the application of flash boiling in GDI engines. Donde et al.  found that the spray angle decreased and the hollow cone structure was lost when the flash boiling spray collapsed. It was considered that the collapse phenomenon was caused by the air entrainment flow. Moon et al.  investigated the effect of fuel temperature on the collapse phenomenon and considered that spray was driven toward the spray axis as a result of the augmented pressure drop inside the spray and entrained air. Yang et al.  compared the differences in spray characteristics among single-hole, two-hole, and six-hole injectors and suggested that the collapse phenomenon was caused by the combined effect of the low pressure core and the overlap region. However, in these studies, the details of the pressure and velocity fields, which determine the spray structure, are not provided due to the difficulties in the measurement.
In this study, a systematic flash boiling spray model for a multi-hole injector is built to investigate the flash boiling spray. The key physics involved in flash boiling, including bubble formation, bubble growth, as well as bubble breakup are added to the traditional spray model in KIVA-3V to describe the development process of flash boiling spray. First, the parameters of these sub-models are discussed, and then the effects of initial fuel temperature and ambient pressure on the flash boiling spray structure of multi-hole injector are investigated. In addition, experiments of flash boiling are conducted in a constant volume chamber and the macroscopic morphology of multi-hole injector spray is obtained by Mie scattering method to verify the flash boiling spray model of multi-hole injector. Subsequently, the pressure field, velocity field and vapor distribution under different conditions are analyzed.
MODEL FORMULATION OF FLASH BOILING
The flash boiling of a superheated liquid includes flash boiling inside the nozzle and outside the nozzle. Sato et al.  has investigated the effect of flash boiling inside the nozzle on the spray characteristics of superheated water, and found that the flash boiling inside the nozzle could be ignored when the ratio of the orifice length to the orifice diameter (l/d) was less than 7.0. In the present study, the ratio of the orifice length to the orifice diameter is 2.0. Thus, only the flash boiling outside the nozzle is considered. The processes of atomization and vaporization of surperheated liquid outside the nozzle mainly consist of primary breakup, bubble nucleation, bubble growth, bubble dispersion, liquid vaporization, and droplet collision and coalescence. Since the flash boiling of spray is essentially caused by the micro-explosion of vapor bubbles formed in superheated droplets, a flash boiling model of a single droplet is first built to describe the micro-explosion process of the single droplet, and then sub-models describing the process of the interaction of liquid droplets, such as droplet collision and coalescence, are added into the flash boiling model. Finally, the flash boiling model is coupled with the traditional spray model in KIVA-3V. The sub-models of flash boiling spray respectively are described in the following subsections.
Bubble Nucleation Model
Bubble nucleation processes can be homogeneous or heterogeneous. In homogeneous nucleation, bubbles are formed in the bulk liquid and this nucleation process becomes dominant when the tensile force can oppose to the molecular force of the liquid with the liquid pressure decreasing . In this study, this process can be ignored because the molecular force of the liquid is always much stronger than the tensile force as the pressure decreases in the numerical simulation. In contrast, heterogeneous nucleation occurs at interfaces and boundaries where gas or solid exists. In heterogeneous nucleation process, an activated cluster grows to a critical size and becomes a nucleus in the presence of crevices on the solid surface, fine solid particles, dissolved gas in the liquid. For the nucleation on solid surfaces inside nozzle, bubble nucleation on solid surface has little influence on the spray behavior when the l/d of nozzle orifice is less than 7.0 . Thus, the nucleation on solid surface is negligible for small l/d of nozzle orifice (2.0 in this study). The estimation of nucleation from dust or solid particles in liquid is difficult and the fuel used for the experiments is well filtered for flash boiling spray model calibration. Thus, the nucleation on dust or particles is also neglected in this study. Therefore, only the heterogeneous nucleation due to dissolved gas in the liquid is considered. Adachi et al.  have proved that the number of bubble nucleation only considering the heterogeneous nucleation of dissolved gas in the liquid obtained by numerical simulation agrees well with the experimental data. Thus, the same simplified bubble nucleation model is used to describe the nucleation process in this study as follows:
N = C exp([[-[DELTA]A]/[k[DELTA]T]]) (1)
[DELTA]A = [/][pi][R.sup.2][sigma] (2)
where N is the number density of bubble nucleation in liquid, C is a constant, k is the Boltzmann constant, [DELTA]T is the difference between fuel temperature (T) and its saturation temperature ([T.sub.s]), and [sigma] is the surface tension. In this study, the number density N of bubble nucleation are estimated using the following equation suggested by Senda et al. :
N = 5.575 x [10.sup.12] exp ([[-5.279]/[[DELTA]T]]) (3)
Bubble Growth Model
If the initial bubble radius is greater than a critical value [R.sub.i], a small fluctuation of the pressure on the bubble surface will result in either collapsing or bubble growth . In this study, only the bubble growth is considered. The growth of the bubble is determined by the inertial force, the surface tension, the viscosity, and the thermal diffusion [25, 26]. The growth rate is calculated by coupling the liquid momentum and energy equations through the nonlinear convection term. In addition, bubbles in a superheated droplet are assumed to be spherical during the growth, and the temperature and pressure inside bubbles are assumed to be uniform. Therefore, the Rayleigh-Plesset model is used to describe the process of bubble growth as follows :
[R.sub.i] = [[2[sigma]]/[[P.sub.v] - [P.sub.[infinity]]] (4)
[mathematical expression not reproducible] (5)
[epsilon] = 1-[[[rho].sub.v]]/[[[rho].sub.l]]] (6)
where [R.sub.b] is the bubble radius, [sigma] the surface tension of the liquid, [mu] the liquid viscosity, [[rho].sub.l] and [[rho].sub.v] the densities of the liquid and the gas phases respectively, [P.sub.v] the saturation pressure of the liquid, [P.sub.[infinity]] ambient pressure, and [T.sub.v] the vapor temperature.
Droplet Breakup Model
Being different from the breakup of droplets in traditional sprays, the breakup of droplets in flash boiling sprays is not only determined by the aerodynamic force, but also affected by the bubble growth in the superheated droplet, especially during the secondary breakup of droplets, the effect of bubble growth on droplet breakup is predominant . In this study, a modified KH-RT breakup model considering the effect of vapor bubble in liquid  was used to describe the process of breakup caused by aerodynamics force, while a bubble-droplet breakup model proposed by Zeng and Lee  was used to describe the breakup process caused by bubble growth.
Droplet Breakup Due to Aerodynamic Force
For the primary breakup of spray, the breakup process is mainly controlled by the Kelvin-Helmholtz (KH) unstable wave at the gas-liquid interface. For the flash boiling spray, the bubble growth in the superheated liquid increases volume of droplets, decreases equivalent density, and then changes the Reynolds number and Weber number. Thus, considering the effect of vapor bubble in droplets, the maximum growth rate of KH unstable waves [[OMEGA].sub.KH] and its [[LAMBDA].sub.KH] wavelength are given respectively as below:
[mathematical expression not reproducible] (7)
[mathematical expression not reproducible] (8)
where [We.sub.g] is the gas Weber number, [We.sub.g] = [[[[rho].sub.g][U.sup.2.sub.r][R.sub.e]]/[[sigma]]], [We.sub.l] is the liquid Weber number, [We.sub.l] = [[[[rho].sub.l][U.sup.2.sub.r][R.sub.e]]/[[sigma]]], Oh is the Ohnesorge number, [??], [T.sub.a] is the Taylor number, [??], [Re.sub.l] is the Reynolds number of liquid, [Re.sub.l] = [[[[rho].sub.i][U.sub.r][R.sub.e]]/[[sigma].sub.l]]], [U.sub.r] is the relative velocity between the liquid and gas, [R.sub.e] is the equivalent radius of droplets, [??], [[rho].sub.e] is the equivalent density of droplet, [[rho].sub.e] = (1 - [phi]) [[rho].sub.l] + [phi][[rho].sub.g], and [phi] is the void ratio of droplets, [??].
When the equivalent radius of droplet ([R.sub.e]) is greater than the critical radius of the KH unstable wave ([R.sub.KH]), small droplets are assumed to be peeled off from parent droplets, . The critical radius of KH unstable wave ([R.sub.KH]), the change rate of droplet radius ([[[dR.sub.r]]/[dt]]), and the breakup time of KH unstable wave ([[tau].sub.KH] are given respectively as follows:
[R.sub.KH] = [B.sub.0][[LAMBDA].sub.KH] (9)
[[[dR.sub.e]]/[dt]] = [[[R.sub.e] - [R.sub.KH]]/[[[tau].sub.KH]]] (10)
[[tau].sub.KH]] = [[[3.726[B.sub.1][R.sub.e]]/[[[OMEGA].sub.KH][[LAMBDA].sub.KH]]] (11)
where [B.sub.0] = 0.61 is the constant of critical radius of the KH unstable wave, and [B.sub.1] = 20 is the a constant for the breakup time of KH unstable wave.
For the secondary breakup process, the droplet breakup mainly depends on the critical wave length of Rayleigh-Taylor (RT) unstable wave. Considering the effect of vapor bubble in droplets, its frequency [[OMEGA].sub.RT] and wavelength [[LAMBDA].sub.RT] are given respectively as follows :
[mathematical expression not reproducible] (12)
[mathematical expression not reproducible] (13)
where [alpha] = [/] [C.sub.D] [[[[rho].sub.g][U.sup.2.sub.r]]/[[[rho].sub.e][R.sub.e]]] is the acceleration.
When the life time of a droplet is greater than the breakup time of RT unstable wave ([[tau].sub.RT]) and the critical wave length of RT unstable wave ([[LAMBDA].sub.RT]) is less than the droplet diameter (2[R.sub.d]), the droplet is assumed to break up . The breakup time of Rayleigh-Taylor unstable wave ([[tau].sub.RT]) and the equivalent radius of droplet ([R.sub.e(n+1)]) after breakup are given respectively as follows:
[[tau].sub.RT] = [[[C.sub.[tau]]]/[[[OMEGA].sub.RT]]] (14)
[R.sub.e(n+1)] = [[[C.sub.RT][[LAMBDA].sub.RT]]/] (15)
where [C.sub.[tau]] = 1.0 is the breakup constant of RT unstable wave, [C.sub.RT] = 0.1 is the constant of critical radius of RT unstable wave.
Droplet Breakup Due to Bubble Growth
Based on the elastic force theory and the linear stability analysis, Zeng and Lee  developed a bubble-droplet breakup model to describe the breakup process caused by bubble growth. It is assumed that the bubble growth will result in shock disturbance at radial direction and if the disturbance growth rate exceeds the critical value, the bubble-droplet system will break up. For the bubble-droplet system, the breakup variable K is defined as
[mathematical expression not reproducible] (16)
where [R.sub.e] is the equivalent droplet radius, [R.sub.b] the bubble radius, [R.sub.e0] the initial equivalent droplet radius, and [omega] the disturbance growth rate.
It is assumed that the bubble-droplet system breaks up when the breakup variable K is greater than a threshold [K.sub.crit]. In this study, [K.sub.crit] is equal to 5 as suggested by Zeng and Lee . A linear stable analysis was used to determine the disturbance growth rate ([omega]) through combining the linearized momentum and continuity equations. A normalized formula for disturbance growth rate ([omega]) is given as follows:
[mathematical expression not reproducible] (17)
The distribution of droplet diameter is assumed to obey [chi square] distribution after breakup and its velocity consists of the velocity of parent and the additional velocity. The Sauter mean radius ([R.sub.32]) and the additional velocity ([U.sub.a]) of droplet after breakup can be determined as:
[mathematical expression not reproducible] (18)
[mathematical expression not reproducible] (19)
Evaporation Model of Superheated Droplets
For the evaporation of flash boiling spray, the evaporation rate mainly depends on local vapor concentration, superheat degree and heat transfer at droplet surface. An evaporation model of superheated droplet has been proposed by Zuo et al.  based on three assumptions: the surface temperature of the superheated droplet is equal to the saturation temperature; all the heat transferred from ambient gas to droplet is used for evaporation and does not change droplet temperature; the evaporation due to superheat at droplet surface restrains the heat transfer from ambient to droplet and decreases evaporation rate. For a spherical superheated droplet, the evaporation formula is given as follows:
[mathematical expression not reproducible] (20)
where [m.sub.f] is the evaporation rate due to flash boiling, [m.sub.t] is the evaporation rate due to heat transfer. [m.sub.f] is given as follows:
[m.sub.f] = 4[pi][R.sup.2.sub.d][[alpha].sub.s] [[[DELTA][theta]]/[L]] (21)
where [[alpha].sub.s] is heat transfer coefficient given as follows:
[mathematical expression not reproducible] (22)
[m.sub.t] is given as follows:
[mathematical expression not reproducible] (23)
where [k.sub.L] is the thermal conductivity of liquid, [c.sub.pl] is specific heat capacity at constant pressure for liquid, Nu is the Nusselt number; [B.sub.t] is the Spalding mass transfer number.
With the evaporation of superheated droplet, the temperature of the droplet will decrease. If the droplet has not been completely evaporated when the droplet temperature goes below the saturation temperature, the evaporation is calculated using the Spalding evaporation model built-in original KIVA-3V.
The simulation conditions are listed in Table 1. The calculation time was 1.0 ms. The maximum time step was 0.05 ms and the minimum time step was 1 [micro]s. Fuel injection quantity and injection velocity were calculated through a virtual injection rate generator proposed by Payri  and Pickett . The initial droplet parcels was set as 2000 and the initial Sauter mean radius (SMR) was 95 [micro]m. The fuel properties provided by fuellib in original KIVA-3 V were invoked by sub-models and updated at each time step. The calculation region (Figure 1) set as a circular cylinder with a height of 100 mm and a diameter of 100 mm. The computational grid size was 2 mm x 2 mm x 1.25 mm, and the number of cells was about 2,000,000.
Experiments were carried out in a constant volume chamber to validate the simulation results. The experimental setup, as shown in Figure 2, consists of a constant volume chamber, a fuel supply system, a control unit, and an optical diagnostic system. Four cylinder quartz windows were installed in the four sides of the constant volume chamber for optical access. A six-hole gasoline direct injector (Bosch HDEV5) was installed on the top of the chamber. The schematic diagram of the spray plumes of the six-hole injector was shown in Figure 3. The nozzle diameter is 0.19 mm and the nozzle length is 0.2 mm. The six holes evenly distributed in the nozzle with an angle of 60[degrees]. The spray plumes of 1, 3, 5 were symmetric with the spray plumes of 2, 4, 6. A heating coil was installed around the injector to heat the fuels. A thermocouple was embedded within the nozzle tip to measure the fuel temperature. The injection pressure was provided by a fuel pressure accumulator with a maximum pressure of 15 MPa. The pressure in the chamber was adjusted by a vacuum pump from atmospheric pressure to sub-atmospheric pressure. A 100W xenon lamp was used to illuminate the spray and a high-speed camera was used to capture the development of the spray at a frame rates of 20,000 frames per second. Spray image was obtained through the Mie scattering method .
The experimental conditions are summarized in Table 2. N-hexane was selected to calibrate the flash boiling model of multi-hole injector. N-hexane was injected into the constant volume chamber at 10 MPa. The ambient pressure changed from 0.4 bar to 1.0 bar and the fuel temperature was set at 20, 50, 80, 110[degrees]C. Injection duration was held constant at 1.0 ms pulse-width for all conditions.
RESULTS AND DISCUSSION
Figures 4 and 5 show the experimental and numerical results of spray morphology at 1.0 ms after start of injection (ASOI). The fuel injection pressure is held constant at 10 MPa, the ambient pressure is changed from 0.4 to 1.0 bar, and the fuel temperature is heated from 20[degrees]C to 110[degrees]C. Table 3 lists the superheat degree of n-hexane under different fuel temperatures (T) and ambient pressures ([P.sub.b]). The superheat degree (1) is defined as [lambda] = [[[T - [T.sub.s]]/[[T.sub.s]]]. The spray was divided into non-flash boiling spray ([lambda] < 0.3), transitional flash boiling spray (0.3 [less than or equal to] [lambda] < 0.6), and flare flash boiling spray ([lambda] [greater than or equal to] 0.6) under different superheat degrees according to the spray structure. In the all cases of T=20[degrees]C and T=50[degrees]C., the spray is at non-flash boiling stage. All spray plumes develop along with the predetermined direction of orifices and the spray plumes are independent from each other, which indicates poor plumes atomization and weak interferences between plumes. When the fuel is heated to 80[degrees]C at [P.sub.b] = 1.0 and [P.sub.b] = 0.7 bar, the spray is at transitional flash boiling stage. The spray plumes get close to the axis of the injector, swirl structures form at spray tip, and the spray penetration decreases, which indicates that the interferences between plumes change the spray predetermined trajectory. With the fuel temperature further increasing (110[degrees]C) or the ambient pressure decreasing, the spray goes to the flare flash boiling stage. The spray collapses to form a 'corn' structure, the spray penetration increases inversely, and the swirl structures vanish at the spray tip. Comparing the experimental and numerical results, the numerical results well reproduce the morphology transformation observed in experiments under different stages.
Figure 6 gives the spray penetration of simulations and experiments. The ambient pressure is 0.7 bar, the injection pressure is 10 MPa, and the fuel temperature changes from 20[degrees]C to 110[degrees]C. It can be found that the simulation results can describe well the spray development trends observed in experiments at different stages. In the case of T=20[degrees]C and T=50[degrees]C, the spray penetration process is similar suggesting that the fuel temperature has little influence on spray penetration at non-flash boiling stage. The spray penetrates rapidly before 0.40 ms, then the penetration speed decreases due to increasing aerodynamic resistance. When the fuel is heated to 80[degrees]C, the spray penetration speed decreases after 0.15 ms ahead of that at T=50[degrees]C and T=20[degrees]C. This can be attributed to the micro-explosion of superheated droplets that leads to the secondary breakup of spray in advance than that at non-flash boiling stage. With the spray development, swirl structures are formed in spray tip which further decreases spray penetration, which results the spray penetration is much shorter than that of T=50[degrees]C and T=20[degrees]C. If the fuel temperature is increased to 110[degrees]C, the spray penetrates slowly as the fuel is discharged from the injector, but with the spray development, the spray penetration will overtake the penetration of T=80[degrees]C. It can be understood that the micro-explosion occurs after fuel discharged from the injector at T=110[degrees]C, which decreases the inertia force at axial direction. But with the spray development, spray collapses, which results the droplets collisions and coalescences and then increases the axial velocity of droplets, eventually results the spray penetrating over that of T=80[degrees]C. Figure 7 shows the spray penetration at different ambient pressures. It can be found that the numerical results agree well with the experimental results. With the ambient pressures increasing, the spray penetration decreases. The spray penetrates rapidly before 0.35 ms, then the penetration speed decreases due to increasing aerodynamic resistance. In short, the numerical results well reproduce penetration transformation of multi-hole injector spray observed in experiments under different stages. Therefore, the above results demonstrate that the improved flash boiling model built in this study is suitable for the simulation study of flash boiling spray.
Transformation Mechanism of Spray Structure
The numerical results of gas phase pressure distribution and velocity distribution are shown in Figure 8 and Figure 9 respectively. The first row shows the distributions at the vertical section and the second row shows the distributions at the cross section of the spray tip (the distance from the injector is 60 mm at 50[degrees]C, 40 mm at 80[degrees]C, and 50 mm at 110[degrees]C). The fuel injection pressure is 10 MPa, the ambient pressure is held constant at 0.7 bar, the ambient temperature is 20[degrees]C, and the fuel temperature is changed from 50[degrees]C to 110[degrees]C.
In the case of T=50[degrees]C, the pressure distribution is uniform at both the vertical section and the cross section. The maximum pressure drop is about 0.1 kPa which is too small to change the development direction of the plumes. All spray plumes develop along the predetermined direction of the orifices. When the fuel is heated to 80[degrees]C, low pressure regions are formed at the position where entrainment effect takes place (see Figure 4 and Figure 5). From the cross section, the low pressure region is an low pressure loop with higher pressure in loop center, which results the gas moving outward as shown in Figure 9. The moving gas pushes the droplets outward and then increases the spray width. The eddies formed around the low pressure loop swirl the droplets upward restraining the spray development.
When the fuel is heated to 110[degrees]C, three obvious low pressure regions are observed at vertical section: one is near the injector where the micro-explosion occurs and the two others are at spray tip. Comparing with the velocity distribution, it can be found that the low pressure regions make the gas move inward. Micro-explosion occurs as the fuel discharged from the injector at the fuel temperature of 110[degrees]C and a large number of small droplets are produced . The droplets near injector are pushed into spray center by the inward moving gas as the fuel discharged, which makes spray collapse. At the spray tip, the inward moving gas also drags the droplets move toward spray center which prevents the spray from dispersing and strengthen the spray penetration.
From the above results, the low pressure region has a significant effect on the formation of eddies in velocity fields. The greater the pressure drop is, the more intense the eddy is. The interactions of low pressure regions and eddies change the trajectories of droplets and then change the spray structure under different conditions.
Figure 10 shows the numerical results of the total vaporized n-hexane at various temperatures. Figure 11 shows the vaporized n-hexane due to heat transfer and flash boiling. Figure 12 shows the vapor distributions at the vertical section and the cross section at [t.sub.inj]=1.0 ms. The mass fraction in Figure 12 represents the ratio of the total vaporized n-hexane to the total gas in each mesh. In the case of T=50[degrees]C, the evaporation rate is slow and the vapor mass of flash boiling is equal to zero. Flash boiling does not occur and the evaporation process is determined by heat transfer (Eq. (23)). The vapor is mainly distributed in the spray region without extension to adjacent region and the vapor concentration is highest at spray tip. It can be understood that the vaporized fuel flows to spray tip with the moving gas as shown in Figure 9. From the cross section, it is observed that the vapor concentration decreases gradually from plumes centers to plumes periphery. It is because the droplets aggregate at plumes centers and the temperature of droplets in plumes is higher than that of plumes peripheries.
When the fuel is heated to 80[degrees]C, the vaporized fuel increases greatly. It is because on the one hand, the heat transfer is improved leading to the increase of [m.sub.t] in Eq. (23); on the other hand, the flash boiling occurs at T=80[degrees]C which further improves the evaporation of fuel. But the vapor mass due to flash boiling is much less than vapor mass due to heat transfer, which indicates the vaporization of spray is mainly controlled by heat transfer. From the vertical section, it is observed that the vapor plumes get close to the axis of the injector and the vapor structure is similar to the spray structure in Figure 5. At the cross section, the vapor distribution is more uniform than that of T=50[degrees]C. The vapor expands to adjacent region of spray which promotes the fuel/gas mixture.
If the fuel is heated to 110[degrees]C, the evaporation mass further increases. From Figure 11, it can be found that the vapor mass due to flash boiling increases greatly and the vapor mass due to heat transfer increases slightly compared with T=80[degrees]C, which indicates flash boiling plays a dominant role in fuel evaporation at high superheat degree. But the fuel vapor is relatively concentrated in spray center due to spray collapse, which is undesired for fuel/air mixing in cylinder
In this study, a systematic flash boiling spray model for multi-hole injector is built to investigate the flash boiling spray of multi-hole injector. The key physics involved in flash boiling, including bubble formation, bubble growth, as well as bubble breakup are added to the traditional spray model in KIVA-3V to describe the development process of flash boiling spray. First, the flash boiling spray model for multi-hole injector are validated by experimental results of spray structure and spray penetration. Then, the numerical results of the gas phase pressure field, velocity field and vapor distribution are analyzed under different superheat degree. The main conclusions of this study are summarized as follows:
1. By comparing the macroscopic characteristics of the experimental and numerical results, it is found that the simulation results well reproduce the spray morphology transformation and describe the spray development trends observed in experiments at different stage, which indicates that the flash boiling model for multi-hole injector built in this study is suitable for the simulation study of the flash boiling spray for multi-hole injector.
2. The low pressure region has a significant effect on the formation of eddies in velocity fields. The greater the pressure drop is, the more intense the eddy is. The interactions of low pressure regions and eddies change the trajectories of droplets and then change the spray structure under different conditions. At the fuel temperature of 80[degrees]C, the eddy formed around the low pressure loop swirls the droplets upward restraining the spray development and change the spray structure. At the fuel temperature of 110[degrees]C, the low pressure regions near nozzle injector and spray tip make the gas move inward, and then push the droplets into spray center leading spray collapsing.
3. At the fuel temperature of 50[degrees]C, the vapor is mainly distributed in the spray area and the vaporized fuel is low. When the fuel is heated to 80[degrees]C, the vaporized fuel increases greatly and the vapor distribution is more uniform than that of T=50[degrees]C. But the vapor mass due to flash boiling is much less than that due to heat transfer, and this indicates the vaporization of spray is mainly controlled by heat transfer. If the fuel is heated to 110[degrees]C, the vapor mass due to flash boiling increases greatly and the vapor mass due to heat transfer increases slightly compared with T=80[degrees]C, and this indicates flash boiling plays a dominant role in fuel evaporation at high superheat degree. The vapor is relatively concentrated in spray center due to collapse phenomenon, which is undesired for fuel/air mixing in cylinder.
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State Key Laboratory of Engines, Tianjin University, Tianjin, China
Address: No. 92, Weijin Road, Nankai District, Tianjin, China
Phone number: +86 (0)22 27403434; fax: +86 (0)22 2740 6890
This work is supported by the the National Science Fund for Distinguished Young Scholars (No. 51525603) and the National Science and technology support program (No. 2015BAG16B00).
Shiquan Shen, Zhizhao Che, and Tianyou Wang Tianjin University
Dalian University of Technology
Table 1. Numerical simulation conditions. Fuel N-hexane Fuel injection pressure 10 MPa Fuel temperature 20-110[degrees]C Ambient temperature 20[degrees]C Ambient pressure 40-100 kPa Injection duration 1.0 ms Computation time 1.0 ms Initial SMR 95 [micro]m Turbulence model RNGk-[epsilon] Bubble nucleation model Senda's Model  Bubble growth model Sato's Model  Droplet breakup model M-KH-RT+LSA Evaporation model Zuo's Model  Initial droplet parcels 2000 Table 2. Experimental conditions. Fuel N-hexane Injection pressure 10 MPa Fuel temperature 20,50,80, 110[degrees]C Ambient pressure 0.4,0.7, 1.0 bar Ambient temperature 20[degrees]C Injection duration 1.0 ms Nozzle diameter 0.19 mm Nozzle length 0.2 mm Table 3. Superheat degree for n-hexane under different conditions. [P.sub.b] T 20[degrees]C 50[degrees]C 80[degrees]C 110[degrees]C 1.0 bar -0.71 -0.28 0.31 0.61 0.7 bar -0.65 -0.12 0.52 0.93 0.4 bar -0.52 0.19 0.90 1.62
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|Author:||Shen, Shiquan; Che, Zhizhao; Wang, Tianyou; Jia, Ming; Sun, Kai|
|Publication:||SAE International Journal of Fuels and Lubricants|
|Date:||Jun 1, 2017|
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