Concentration Distribution Characteristics of Two-component Fuel Spray under High-pressure Injection Conditions

In present study, a novel fuel design concept for low emission and combustion control in engine systems have been proposed [1][2]. Two-component fuels mixed with different volatility components form a two-phase region where the liquid and vapor of both components co-exist due to the intramolecular interaction. This two-phase region gradually shifts to the lower pressure side due to the early vaporization of the higher volatility component from the droplet. This phenomenon, so-called batch distillation, results in the heterogeneous concentration distribution of the two components in the fuel spray. In this paper, the concentration distribution of two-component fuel was measured by laser induced fluorescence and calculated numerically using a multicomponent fuel model in higher injection pressure than conventional injection conditions. It was found that increasing the injection pressure and ambient density accelerated the mixing, resulting in a similar concentration distribution of each component.


Introduction
In compression-ignition engines, the physical and chemical properties of the fuel are important factors that control the mixture formation process and the combustion process thereafter. The authors have proposed a fuel design concept of mixing high boiling point fuel with low boiling point fuel as a spray design method for low emission and combustion control in engine systems [1] [2]. Figure1 shows the characteristics of the spray formation of a two-component fuel. A multi-component fuel spray model has been proposed to estimate vapor-liquid equilibrium and physical properties of the fuel mixture, and two-component fuel spray has been analyzed using the KIVA code. It is well known that fuel spray is mixed and diluted with small hole diameter nozzle and high-pressure fuel injection. However, no numerical analysis of two-component fuel spray has been performed under the high fuel injection pressures. It is necessary to select a model to represent the breakup phenomenon of diesel spray under highpressure fuel injection conditions and analyze the heterogeneous concentration distribution unique to two-component fuel spray. In this paper, the spray characteristics were measured using the laser-induced fluorescence method (LIF) for single-component and two-component fuel sprays, and a breakup model suitable for high-pressure injection conditions was selected. The effects of fuel injection pressure and ambient density on heterogeneous component concentrations were also investigated.

Numerical Analysis of Two-Component Fuel Spray
Various models have been proposed by various research institutes to numerical analyze the spray properties of multicomponent fuels. In order to analyze the physical effects of multicomponent fuels in detail, the multicomponent spray model constructed by Kawano et al [2]. The model gives transport properties of multicomponent fuels shown in Figure 2. The source program of the NIST Mixture Property Database was used to estimate the property values of mixed fuels [3]. The surface tension and diffusion coefficients were calculated separately.
In a high-pressure fuel spray, a liquid column (potential core) is generated in which injection velocity is maintained. On the other hand, in the middle of the spray where the velocity difference with the surrounding gas decreases due to momentum exchange, the breakup due to the deformation of the fuel droplet is considered to be dominant. Therefore, the WAVE-MTAB model, which is a combination of the WAVE model, which models the breakup due to the velocity difference with the surrounding gas, and the MTAB model, which models the breakup due to droplet deformation, is considered to be effective [4][5][6] [7]. The outline of the model is shown below. The WAVE model simulates the instability due to the speed difference acting on the droplet surface, the breakup phenomenon due to the instability of so-called Kelvin Helmholtz (KH) [4]. The droplet diameter rc after breakup due to the instability of KH is calculated by equation (1) using the wavelength ΛKH which grows at the liquid column or the surface of the droplet at the fastest speed. The division time τKH is defined by equation (2).
Here, B0 is the experimental constant, given as 0.61. B1 is an experimental constant. The smaller B1, the shorter the time required for breakup, hence the breakup is completed early.

Figure 2.
Flowchart of multicomponent fuel model [2] Conversely, as B1 gets bigger, the time required for breakup becomes longer and the time to complete breakup becomes longer. In this non-evaporative spray analysis, B1=30 is given, and numerical calculation is performed. The droplet breakup process is modelled by Taylor analogy breakup (TAB) model, which is standard stochastic breakup model [5]. In TAB model, oscillations of the droplet are modelled in the framework of a spring mass system and breakup occurs when the oscillations exceed a critical value. The rate of oscillations is given by equation (3). The drop sizes after breakup are determined by an equation based on energy conservation. In this analysis, we assume that the energy of the parent drop before breakup is equal to the combined energies of the product drops after breakup. Thus, Sauter mean diameter r32 after breakup is given by equation (4). Here K is the ratio of the total energy in distortion and oscillation to the energy in the fundamental mode. The value of K must be determined by comparisons with experimentally measured drop sizes. For the distribution of the product drop sizes, χ-squared distribution with two-degree of freedom is used in TAB model. Senda et al. modified the degrees of freedom to 6 and K to 8/9 under the condition that collision and coalescence were not considered [6].

Experimental and Numerical Analysis Conditions
The laser sheet light was incident to visualize the spray, and the fluorescence was captured. The images were taken at 0.5 ms after the start of fuel injection. The concentration distribution images of each component were taken in separate shots. In addition, the fuel remaining in the nozzle tip was removed by creating a negative pressure in the vessel before the experiment. The conditions for the experiments and numerical analyzes are shown in Table 1. The fuel injection nozzle was a single hole nozzle (hole diameter dn = φ0 125 differential pressure ΔPinj was changed from 100 MPa to 60 MPa and 140 MPa. The ambient temperature Ta was set at 450 K, and the ambient density ρa was changed from 15.0 kg/m 3 to 16.9 and 18.7 kg/m 3 . The experimental conditions were set at an ambient pressure above the saturation pressure of the fuel, where the single-component fuel spray and the multicomponent fuel spray was not under flash boiling conditions. The injection period tinj was set so that the fuel injection amount mf was 3.2 mg, and the fuel injection rate measured by the Bosch injection rate measurement method was input to the numerical analysis as the initial condition. Since the fuel injection pressure was changed, the amount of fuel in the images measured 0.5 ms after the start of fuel injection was different from each condition. The test fuel was a two-component fuel consisting of a mixture of normal pentane (nC5H12: Pentane) which is a low boiling point component and normal tridecane (nC13H28: Tridecane) which is a high boiling point component at a volume fraction of 8:2. It is necessary to select a fluorescence tracer with evaporation characteristics similar to those of the fuel. When measuring the normal tridecane component, 7 vol % tetralin was added as a fluorescence tracer. When measuring the normal pentane component, 5 vol% acetone was added as a fluorescence tracer. The saturation vapor pressure curves of the test fuels and fluorescence tracers are shown in Figure 4. The conditions for the numerical models are shown in Table 2.
The RNG k-ε model was used as the mass diffusion model to simulate the mass diffusion phenomenon under high atmospheric pressure conditions. One of the input values, the spray angle, was calculated from the experimental equation by Inagaki and Mizuta [8], and the parcel was formed uniformly within the spray angle. The computational area was 40 mm in diameter and 100 mm in height, assumed to be a cylindrical container, and divided into 20, 12, and 80 meshes in the radial, circumferential, and axial directions. The obtained experimental spray image is the cross-sectional information where the test volume is the thickness of the laser sheet light (about 0.4 mm), and the calculated results are the central cross-section. Since the fluorescence intensity in the laser-induced fluorescence method is approximately proportional to the fuel concentration, the analysis results can be compared by adding the liquid phase information given in the parcel to the vapor phase information of the fuel given in the mesh [9]. In order to take into account the spatial dispersion of the parcels, which contain thousands of fuel droplets, the number density of the parcels relative to the spray volume was used to   2 calculate the mass of the parcels in the mesh and the surrounding mesh. In the numerical analysis results, the average concentration within the mesh (about 1 mm apart) is shown, so the concentration near the nozzle where is no dispersion is under-represented.

Select the Breakup Model
Conventionally, the MTAB model has been used to model the breakup of multi-component fuel sprays under low injection pressure conditions. In this study, a comparison was made between the WAVE-MTAB model and the MTAB model for the breakup model to analyze a two-component fuel spray. The spatial distribution of each fuel concentration obtained by the laser-induced fluorescence method and the spatial distribution of each fuel concentration in the parcel and fuel obtained by each breakup model at 0.5 ms after the start of fuel injection are shown in Figure 5. The fluorescence intensity in the laser-induced fluorescence method is corrected by assuming Gaussian distribution of the laser beam [10]. It is approximately proportional to the fuel concentration. The difference in the spray shape of each fuel obtained by the laser-induced fluorescence method was due to shot-to-shot variation and the dilution of the normal pentane component at the outer edge of the spray, which reached the lower limit of the fluorescence intensity measurement. Figure 6 shows the experimental results and the numerical analysis results of the concentration distribution. The experimental results are calculated by using the assumption that the spray is concentric circles and integrating the intensity in three dimensions at each spray axial distance. Therefore, the concentration distribution of the normal pentane component, which has a region below the measurement limit at the spray tip, is evaluated to be small. Compared with the experimental results of the axial concentration distribution of each fuel, the MTAB model overestimates the spray dispersion, resulting in a large difference in the axial concentration distribution, but the accuracy is greatly improved by using the WAVE-MTAB model. For this reason, the WAVE-MTAB model was used in the following analyzes.

Analysis of Heterogeneity in Concentration
The spatial distribution of the concentration of each component at 0.5 ms after the start of fuel injection was obtained by the laser-induced fluorescence method and numerical analysis.  The exponential values of the distance of mass center of gravity of the low-boiling point fuel are close in the experiment and calculation, but their values are greatly different. This is probably because the low boiling point fuel component at the outer edge of the spray was dilute in the experiment and the fluorescence intensity reached the measurement limit. Figure  9 shows the distance of mass center of gravity for different ambient densities at 0.5 ms after the start of fuel injection. The experimental results show that the distance of mass center of gravity of the high-boiling point fuel component of the two-component fuel changed more significantly with the increase of the ambient density than that of the single-component fuel.
On the other hand, the low boiling point fuel component did not change significantly, and the difference in the mass center of gravity distance of each component became smaller as the ambient density increased. The numerical results also show that the difference in the distance of mass center of gravity becomes smaller with the increase in the ambient density. It is probably due to the enhancement of mixing inside the evaporated spray.

Conclusions
In this report, the concentration distribution of two-component fuel was measured by laserinduced fluorescence and calculated numerically using a multicomponent fuel model. It was found that the WABE-MTAB model was more suitable than the MTAB model under highpressure injection conditions, and that increasing the injection pressure and ambient density enhanced mixing and resulted in a similar concentration distribution for each component.