[American Institute of Aeronautics and Astronautics 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition - Orlando, Florida ()] 47th AIAA

American Institute of Aeronautics and Astronautics

1

Large Eddy Simulation of Spray Injection for Direct Injection Gasoline Engine

Kazuhiro Tsukamoto1, Yuki Hirayama1, Nobuyuki Oshima2 Hokkaido University, Sapporo, Japan

Ashwani. K Gupta3 University of Maryland, University Park, Maryland, 20742

Large Eddy Simulation (LES) of spray injection from a slit injector for direct injection gasoline engine was carried out to evaluate the effectiveness of LES to capture the droplets behavior in the combustion chamber. Lagrangian Discrete Droplet Method (DDM) combined with LES unsteady turbulent modeling is employed to solve turbulent two-phase flow field. The droplets are atomized through the primary break up induced by the liquid surface instability and secondary break up induced by relative velocity between droplet and surrounding gases. However, there is no fully established method to model for the liquid break up to form spray. Formation process of fuel spray is an unsteady and complicated phenomena. For this reason, numerical simulation is expected to solve these phenomena. In this research we use Taylor Analogy Breakup (TAB) modeling and Improved TAB modeling techniques for validating the secondary break up of droplets. We also examine the influence of initial injection condition and secondary break up modeling for spray droplet motion by considering several different initial velocities and investigate their role on the differences observed. As compared to the experimental results, LES results provides good agreement on the droplet diameter distribution and penetration, which is defined as horizontal plane where 1% volume of overall spray droplet passes through.

1. Introduction

Because of limited fossil fuel reserves, uncertainty of fuel costs and tighter control on exhaust emissions, there are ongoing increased demands to develop fuel efficient and cleaner combustor in all sectors of engineering combustion fields to keep our environment clean and conserve energy. In the case of internal combustion engines the demands for cleaner and efficient combustion are severe as this sector represents significant portion of the energy used. As an example about 20% of carbon dioxide emissions are from the transportation sector and in Japan 90% of them is from the automobiles [1]. Therefore, reductions of carbon dioxide emissions from automobile are amongst the urgent tasks that must be addressed. Gasoline engines are widely used all over the world so that any attempt made to reduce pollution from these engines offer potential solution to reduce the global and local emissions. Direct injection gasoline engines are now commonly used so that they offer good potential to solve this problem. Many researchers worldwide are now actively pursuing this research activity as this offers significant impact on the society. Direct injection engine utilize fuel-rich mixture in air near to the spark plug by direct injection of fuel into the combustion chamber. This is then followed by fuel-lean combustion. The fuel injected is rapidly vaporized that also helps to increase the engine thermal efficiency [2]. However, there are several problems associated with combustion instability due to the soot formation (black smoke) in fuel-rich regimes of the combustion chamber. To solve these phenomena, predicting penetration, which is defined as horizontal plane where 1% volume of overall spray droplet

1 Graduate Student, Department of Mechanical Engineering 2 Professor, Department of Mechanical Engineering 3 Distinguished University Professor, Fellow AIAA

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-668

Copyright © 2009 by Copyright 2009 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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passes through, amount of evaporation, spray atomization are amongst the important factors that requires our immediate attention. These phenomena are really complex so it is difficult to analyze by experiment alone. Numerical simulation provides important role as one can visualize the detailed ongoing behavior from within the engines without physically building the hardware. Most common approach for spray atomization flow utilize solving the Euler equations for gaseous phase and

Lagrange equations for droplet transport of each droplet or droplets swarm as point source between the two phases. Usually, injected spray droplets are in vast numbers from atomization of the fuel. It is difficult to trace all droplets. So, a certain amount of droplets are treated as droplets swarm based on the concept of Discrete Droplet Method (DDM) and trace [3]. In the DDM methodology, physical values in one parcel are treated as the same values. These values are weighted for number of particle in the parcel. Therefore, numerical simulation of liquid phase in spray is carried out on the basis of DDM method. The DDM enables one to reduce the cost of calculation. Some droplets are represented as a “parcel”. All droplets in a parcel have the same physical status. DDM concept is able to vary the number of droplets in a parcel, and the total summation of droplets’ volume in a parcel is constant value for each parcel. Namely, when a breakup occurs in a parcel, the number of droplets in the parcel increases and simultaneously the diameter of the droplets decreases. Under normal condition, the size of a parcel should be taken into account. In other words, the diffusion of droplets should be considered. It is known that the parcel size is an important factor in collision models. Nagaoka [4] has introduced a collision models in his study that allows one to estimate the parcel diameters. But the sizes of parcels were neglected because of low density used in this study. In contrast for the gas phase simulation, the intended flow field is turbulent. Numerical approach should be able to

solve droplet distribution, breakup, collision and dispersion as accurate as possible. In order to solve these flow field directly, grid size utilized must allow one to resolve smallest length scale in the flow field. Direct simulation is not suitable as it requires enormous computational load and cost. Reynolds Averaged Navier-Stokes equations (RANS) modeling has been used for the prediction of these flow field in the engineering field and there are many papers available in the literature that uses this method [5, 6]. In RANS modeling, whole scale of turbulence is modeled by Reynolds averaging and solution is obtained from the averaging values. Data on turbulence are defined by the turbulence energy and dissipation rate. However, in this method averaging technique is used to model the turbulence so there is concern that it reduces the accuracy of prediction in strong turbulent flow field, such as those encountered in the combustion chambers of direct injection gasoline engines. Recently the other turbulence modeling technique, called Large Eddy Simulation (LES) has emerged. LES resolves large eddies at Grid Scale (GS) which are influenced strongly by flow fields and models for small eddies at Sub Grid Scale (SGS), which have universal status. Though LES requires higher computational load and costs than RANS, it does not pose any serious disadvantage because of the continuous and rapidly growing computer performance in recent years. LES results show superior performance to RANS results to accurately predict the turbulent flow field in both simple and more realistic practical situations [7, 8]. When the fuel is injected into the chamber, fuel first forms liquid film. The liquid film then breaks up to liquid

column by the growing unstable wave that breakup the liquid column to large number of droplets [9]. This breakup process is defined as primary liquid breakup. Moriyoshi et al. [10] proposed the way to calculate the liquid film width by using VOF method and analyzed the two- phase flow from the injector. They injected the same diameter of liquid film width for the primary breakup. Droplets generated after primary breakup were further disintegrated into smaller droplets due to their relative velocity with ambient gas. This breakup process is called secondary breakup of droplets. For the secondary breakup, Taylor Analogy Breakup (TAB) Model [11] and wave model [12] are well known. In the TAB modeling, droplet oscillations are modeled as a spring mass system so that the droplet breakup occurs when oscillation exceeds the critical value. However, this modeling has room for improvements. This modeling does not consider the droplet deformations by the wind drag and underestimate the breakup time and drag. To address this problem, Improved TAB model has been proposed by Park and Yoon [13]. This model considers droplet deformation by aerodynamics drag in the TAB model so that one can achieve better results theoretically. Many researches have been actively pursuing research efforts on spray flows in engine cylinders. Nagaoka reported

on the spray flow in a port injection type engine [14]. Analysis of the swirl spray flow in direct injection engine has been reported by Apt or Ito [15, 16]. Studies have also been carried out on slit injector [17, 18]. Presently numerical simulation can provide good information on qualitative behavior so that these tools can be used to provide a guideline for engine design and development. However, it is not at a stage of alternative to experiments. In this research, LES model together with TAB model and Improved TAB model for secondary breakup has been

employed for the simulation of spray evolution in direct injection gasoline engines. LES formulation for two-phase flow and breakup modeling are presented first (section 2), followed by numerical conditions (section 3), results and discussion (section 4) and conclusions (section 5).


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2 Governing Equations

2.1 Eulerian Equation Governing equations of the eulerian phase are spatial filtered continuity and momentum equations given as

follows:

0=∂∂

i

i

xu

(1)

i

iji

ij

ij

i

xu

xp

xu

ut

u∂

∂−∇+

∂∂

−=∂∂

+∂∂ τ

ρμ

ρ21

(2) where, τij is given as:

jijiij uuuu −=τ. (3)

τij denotes the effects of SGS components fluctuation, called residual stress. In LES, some model methods are essential to close the equations. According to SGS eddy viscosity model, known as the most elementary method, it is modeled by means of νe, ,coefficient eddy viscosity, as follows:

( ) ijsijeij SShCS 222 Δ−=−= ντ (4)

where, GS strain rate, S , is given by

ijij SSS 2=

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂∂

=i

j

j

iij x

uxu

s21

(5) In this research we employed standard Smagorinsky modeling technique [19]. Cs is Smagorinsky constant which

is only model parameter in this model. Recently, dynamic model that defines Smagorinsky constant as fluctuation component have been suggested. Though dynamic model is an ideal one, practically a fixed value agrees as well as, and possesses an advantage over steady numerical calculation. However, dynamic model have instability for numerical scheme. For this reason, standard Smagorinsky model which uses constant value for model parameter is used in this research.

2.2 Lagrangian Equations

The droplets are treated as point-source and trace them. As parcel approximation can control the number of particles in the parcel, droplet volume in the each parcels are constant in this study. Actually inside the parcel there exists lot of droplets, so that parcel has a certain amount of size. And parcels diffuse due to the turbulence. For this reason, size of the parcel is an important factor for the collision model. However, particle density, such as in this research, does not consider the collision effect. Therefore, droplets are distributed evenly and we did not consider the parcel extent. Governing equations of the Lagrangian phase are the equations of motion which can be expressed as follows:

idid u

dtdx

,, =

(6)

iiid mgf

dtdu

m +−=,

(7) where, fi is the force due to the interaction between a liquid and gas phase. In this research, only the drag force is considered for fi and drag coefficient CD is expressed by Schiller-Nauman equation [20] as:


4

)(42

1,

2

iidsDi uuuCDf −=rπ

(8)

)Re1(Re24 687.0

DD

DC += (9)

where, ReD is particle Reynolds number using a relative velocity and a droplets diameter as characteristic quantity defined as:

μρ Dus

D

r

=Re (10)

When net drag force on particle is calculated, the velocity related to the gas phase is needed. However, gas phase velocity calculated by LES is a spatially filtered value. This issue has been treated by random walk model [21]. SGS turbulent energy, ks and the turbulent velocity component follows Gaussian distribution which has a peak value in u’ in this random walk model.

si ku32ζ=′

(11) 22

ijT

s ShCC

k Δ=ε

ν

(12)

ijijij SSS 2= (13)

where, CνT and Cε stand for dimensional analysis constants; their values are equal to 0.05 and 1.0, respectively. ζ denotes a normal distribution random number. These equations are used in RANS calculation. However, random walk model in RANS represents the total effect of turbulent. In contrast, in LES, fluctuations less than a grid scale are not resolved. 2.3 Primary Breakup model

In this research, any primary breakup is not employed. Initial conditions for droplets have substituted a primary breakup. Initial conditions, velocities and distributions of diameters of droplets are defined by Equation of Nukiyama-Tanazawa[22, 23], which has been widely employed in spray investigations. The equation based on the number of droplets is given as follows:

323232 DdD

DDB

DDA

ndn

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

βα

(14)

( ){ }( ){ } ( ){ }βα

ββαβα

α

/1/3/4

1

+Γ⎥⎦

⎤⎢⎣

⎡+Γ+Γ

=+

A (15)

( )( ){ }

β

βαβα⎥⎦

⎤⎢⎣

⎡+Γ+Γ

=/3/4B

(16) where, n is the total number of droplets, dn denotes the number of droplets in the range from D to D+dD. α and β

are constant values that are determined from experimental conditions. This study utilized α=2.0 and β=1.0 for the

constant. These are recommended values in spray analysis. Function Γ is Gamma function, it is expanded into an infinite product shown in the equation below:

( ) C∞

=

−−

⎟⎠⎞

⎜⎝⎛ +=Γ

1

1

1n

nzz

enz

zez

γ

(17)


5

Here, γ is Euler constant and a limit value of the equation is given as:

( ) ...65120901532860605772156649.0ln1lim1

=⎟⎠

⎞⎜⎝

⎛−= ∑

=∞→

n

knn

kγ

(18) 2.4 Secondary Breakup Models

Liquid fuel injected from a nozzle forms a liquid film and liquid columns prior to their final atomization to droplets [9]. This breakup process is defined as primary breakup. The distribution of droplets was treated as one of the initial condition by Eq. (14). Droplets generated after primary breakup becomes smaller droplets due to their relative velocity with the ambient gas. This breakup process is called secondary breakup. Since the correlation between gas phase and liquid phase was one of the interests in this study, secondary breakup models were introduced into the spray calculation. TAB model [11] and Improved TAB model [13] are applied into this study as the secondary breakup models. The concepts of these three secondary breakup models are now described in this section. 2.4.1 Taylor Analogy Breakup (TAB) model

TAB model [11], one of the secondary breakup models, is described in this section. This model has been widely employed in numerical simulations for engines. This breakup model is based on the analogy between the oscillation and distortion of droplet and the spring-mass system. The external force on the mass, the restitution force of the spring, and the damping force have analogies with the gas aerodynamics force, the surface tension, and the liquid viscosity, respectively. The dimensional deformation x is transformed into non-dimensional value y by Eq. (19) and the amount of deformation is calculated from as Eq. (20) as follows:

rCxyb

= (19)

yr

Cy

rC

ruu

CCy

d

dd

d

kd

db

F ′−−−

=′′ 232 ρμ

ρσ

ρρ

rr

(20) where, CF, Cb, Ck, Cd are dimensionless constants. The constant Ck is obtained by matching to the fundamental oscillation frequency, Ck = 8. For oscillations of the fundamental mode, Cd = 5. When it is postulated that breakup occurs if and only if the amplitude of oscillation of the north and south poles equals the drop radius, the criterion gives, Cb = 1/2, and in conjunction with Ck and the critical Weber number assumed as 12, CF = 1/3. These values are substituted into Eq. (20) and the equation is resolved analogically, to give the following non-dimensional deformation with time, t. Breakup occurs when y >1.

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ −++⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−+= t

t

WeCC

CyytcasWe

CCCy

ttWe

CCCty

d

rbk

F

rbk

F

dr

bk

F ωω

ω sin1exp)(0

00 &

(21) where,

WeruWer 212

==σ

ρ

(22)

221

rC

t d

dd

d ρμ

= (23)

( )00 yy = (24)

( )00 dtdyy =&

(25)


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To predict the drop size after breakup, we use an equation motivated by an analysis based on energy conservation. In this analysis, we equate the energy of the parent droplet before breakup to the combined energies of the product droplets after breakup. The Sauter mean diameter of a disintegrated droplet [24] is estimated from the following equation:

⎟⎠⎞

⎜⎝⎛ −

++=120

562081

)1(

,

KyKr

r d

childSMD σρ

(26) The value of K must be determined from comparison with the experimentally measured droplet size. In this calculation, a default value of K = 10/3 has been used. When breakup occurs, the number of particles in a parcel is changed based on the mass conservation. The diameter distribution after breakup is determined by the Nukiyama-Tanazawa distribution function as well as the diameter distribution after the primary breakup. 2.4.2 Improved TAB model Improved TAB model has been proposed by Park and Yoon [13]. This is an improved model than TAB model and DDB model [25]. These two models have been most widely used. However, TAB model neglects the effects of aerodynamic force on droplet deformation and subsequent change in the droplet drag. Furthermore, the DDB model can not be applied to vibrating and bag-type breakup regime of spray droplet deformation (typically We < 20). TAB model assumes that droplet oscillation involves a damped, forced harmonic oscillator. The equation describing this behavior is as follows:

xdkxFxm &&& −−= (27) In accordance with the Taylor analogy, the physical coefficients in Eq. (27) are given as follows:

0

2

ruC

mF

dF ρρ

= (28)

30r

Cmk

dk ρ

σ=

(29)

20r

Cmd

d

dd ρ

μ=

(30) In this model, it is considered that the deformed droplet shape is an oblate spheroid having an ellipsoidal cross section with a major and minor semi-axis. Hence, the droplet normal aerodynamic external drag force is proportional to the droplet normal cross-sectional area. It is also assumed that the aerodynamic external force, F, in Eq. (27) is proportional to this external force. This assumption yields the following relationships:

20

2

0

2

ra

ruC

mF

dF ρρ

= (31)

)5.01()1( 000 yryCrxra b +=+=+= (32) The fourth-order Runge-Kutta ordinary differential solver can obtain a numerical solution of the present model equation. The surface tension restoring force and the viscous damping force given by Eq. (28) and Eq. (29), respectively, are assumed to be the same as in the TAB model by ignoring the additional effects of droplet deformation. The dimensionless constants are the same as those of the TAB model, expect that for CF. The aerodynamic external force coefficient, CF, is determined to be 4/19 by assuming the critical Weber number to be 6. Droplet radius (not diameter) is used as characteristic length. In the TAB model, the droplet criterion corresponds to a value of y equal to unity for all Weber numbers, which corresponds to a/r0 of 1.5. This is shown to be unrealistic because the droplet breakup occurs at different levels of the droplet deformation for various Weber numbers. Therefore, an improved breakup criterion is proposed for physically more rigorous predictions of breakup by considering the equilibrium of the external gas-phase pressure, interfacial surface tension pressure, and internal liquid-phase pressure. Breakup occurs when the Eq. (33) shown below is satisfied. This inequality implies that the liquid pressure at the pole is greater than that at the equator because the pole is stagnation point of the internal


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circulation flow caused by shear flow in the droplet. It is assumed that this constraint cannot be satisfied until the droplet break-up occurs.

Weyyy 5107.2)5.01(4)5.01()5.01(2 415 >+−+++ −− (33)

The right- and left-hand sides of Eq. (33) must be compared to decide the breakup condition for given values of y and We at a given condition. Breakup can be determined if and only if the condition given by Eq. (33) is satisfied. The conventional TAB model does not take into account change in droplet drag caused by droplet deformation. The droplet drag coefficient is assumed to be related to the magnitude of droplet deformation, given as:

( )yCC sphereDD 632.21, += (34)

( )687.0, Re15.01

Re24

dd

sphereDC += 000,1Re ≤d

43.0, =sphereDC 000,1Re >d (35)

Per Liu et al.[26], the droplet drag model of the TAB model significantly underestimates droplet drag effects for high-speed droplet. The reason is that it does not consider the change of normal cross-sectional area of droplet during droplet deformation. Improved TAB model assumes that the drag coefficient is proportional to the deformed droplet normal cross sectional area, as follows:

( )2,2

0

2

, 5.01 yCraCC sphereDsphereDD +==

(36) As a comparative test calculation between the conventional TAB model and previous improved TAB model, one droplet breakup calculation was conducted here. The initial diameter was 100 micron and relative velocity was 150m/s at all times. Figure 1 shows the droplet diameters and the non-dimensional deformations calculated by employing TAB model and improved TAB model.

Fig. 1. Breakup Time and Nondimensionalized Deformation in TAB model and Improved TAB model; Initial diameter is 100 μm and Relative velocity is held constant at 150 m/s at all times.

3. Numerical Setup

3.1 Object and Condition for Calculation

Fundamental investigation of a direct injection engine is calculated in this paper. The LES for the spray behavior is calculated using a rectangular duct into which spray particles are injected, see Fig. 2. Two flow conditions of without and with cross wind are mainly investigated. For the with-cross wind case, inlet velocity of cross wind velocity is held uniform. The detail conditions and the parameters are shown in Table.1. Injected fuel is dry solvent


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which is difficult to evaporate. A direction of injected droplet was determined in random order within the ranges, θ,

φ and α, see Fig. 6. The velocities of droplets were basically constant in calculations. The values of θ, φ and α were determined by means of visualized images in experimental spray, which had injection pressure condition of 12 MPa, θ=60degree, φ=9 degree, and α=22 degree. The slit width was set at 1.5 mm, which was also determined from the experimental setup.

z

y

z

y

(a) Without Flow (b) With Flow

Fig. 2. Side view of the Spray Images

Liquid density 770 kg/m3 ;dry solvent

Surface tension coefficient 0.024 N/m ;dry solvent

Ambient fluid Air , Under atmospheric pressure

Initial velocity of particles 150 m/s

Number of parcels 40,000

Inject duration 1.0 ms

Inject volume 13.0 ml

Turbulence model LES

Model constant Cs, Smagorinsky coefficient 0.1 Time increment 1.0 μs Number of nodes 96x96x96

Table 1. Calculated conditions and characteristics of spray in LES

Calculation grid is shown below in Fig. 3. The calculation region is a square having 75mm side and possess hexahedral cell. The grid size was of uniform size. The boundary condition was set to free-slip condition, and the number of vertexes had 96 points in each direction.

Slit Width

θx

y

φ

αz

y

Fig. 3. The grid size used calculation (96x96x96) Fig. 4. A schematic diagram for the initial condition


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Nukiyama-Tanazawa equation was used to define the initial conditions for velocity and distribution of droplet diameters. We employed parcel approximation so that distribution of parcel is needed for the inlet condition. In order to fix a distribution of parcels, it is necessary to consider the number of droplets included in the parcels. The summation of droplets volume in a parcel was maintained constant in this study. Therefore, it is necessary to transform Eq. 14 into an equation which weighted as the cube of a diameter. The basic equation and the transformed equation distributions are indicated in Fig.5. As compared to the basic equation, the transformed equation has more large parcels because the number of droplets in small parcel becomes large while that in large parcel becomes small.

Fig. 5. Volume-Based and Number-Based Nukiyama-Tanazawa Distirbutions

3.2 Comparison with the Experiments

Simulation results are compared with the experimental results of Muto and Salim [27, 28] in order to evaluate the adequacy of simulations. Experimental data were mainly on two parameters, namely, global visualization of the central cross-sections of the spray using a laser sheet, and measurement of the individual droplet velocities and droplet diameters in the spray by interferometric laser imaging diagnostic system for droplet sizing (ILIDS). In the experiment, the duration of injection was 1.1 ms. However, this duration was set to 1.0 ms in the numerical simulations to account for the mass flow delay from the opening and shutting of nozzle valve in the experiment. A high-speed pulsed laser sheet, obtained using a LeeLaser, model LDP-100MqG, was used to visualize the spray. VisionResearch PHANTOM V5.1 CMOS camera was used to capture the spray images in the PIV measurements. ILIDS is a measurement technique used by Maeda [29] and provides both velocity and diameter of transparent spherical particles. In the PIV measurement, laser sheet irradiates the spray and the diameters of droplets are obtained from the interferograms generated by transparent spherical droplets. The velocities associated with individual droplets are determined from the distance between droplets from the known time interval of the double pulse laser. It is impossible to capture images of droplets with diameters less than 10 μm because of the measurement resolution. It is also not capable at elevated droplet concentration regions due to overlapped interference patterns. Therefore, it is essential to remove droplets of small diameters and high density droplet regions in comparison between simulation and ILIDS measurement results. Actual measurement areas and the actual results captured are shown in Figs. 6 and 7.

-40

-20

0

20

100 80 60 40 20 0

Ver

tical

vel

ocity

[m

/s]

Diameter [μm]

EXP.

-40

-20

0

20

100 80 60 40 20 0

Ver

tical

vel

ocity

[m

/s]

Diameter [μm]

EXP.

Upper area (y=40 mm) lower area (y=25mm)

Fig. 6. Measurement region Fig. 7. Droplet velocity versus diameter at the local areas in ILIDS experiment

0

250

500

750

1000

1250

1500

1750

2000

2250

� � � � � �

NUMBERVOLUME


10

4. Results and Discussion

4.1 Effect of Secondary Breakup Model The effects of secondary breakup models on the penetration length and structure of sprays is now described. Figures 8 and 9 show the spray flow images from experimental results and numerical results, respectively. Figure 10 shows the penetration of spray tip both with and without secondary break up model. Figures 8 and 10 (a) are injection without the cross wind flow case. Figure 9 and 10 (b) are for the cross wind case. The experimental images were captured at the cross-section, whose method has been shown in the former section. The numerical results obtained also indicate particles in the center cross-section.

In a spray simulation without the secondary breakup, it is found that the numerical results are different for both the spray structure and spray tip penetration as compared with the experimentally captured images. Numerical results could not capture internal fluctuation and most of particles transport straight and are hardly influenced with the ambient flow.

Results obtained from the secondary breakup model are now presented. In Fig. 8, most of the particles go straight and there are only few particles accumulated after injection. The results obtained from TAB model and ITAB model show that although the images for 0.5 ms and 1.0 ms are slightly different, the images for 1.5ms and 2.0 ms seem to have similar spray structure and can also capture the vortex at inner regions of the spray. Breakup seems to occur frequently to generate smaller diameter droplets. These small droplets reshape the spray structure. In the crosswind case, the spray behavior is influenced with crosswind and particles flow in a horizontal direction in both TAB model and Improved TAB model, wherein a number of small droplets are generated by breakup. Spray tip penetrations obtained with introducing secondary breakup models are shown Fig. 10 along with the experimental data. The figure indicates that tip penetration is improved with the introduction of secondary breakup model and that the TAB model reveals the best reproducibility and comparison with the experimental data. Improved TAB model does not show any advantage for tip penetration, although the overall spray structure is well predicted.

The droplet diameters and velocities are investigated with both the TAB model and Improved TAB model which respectively provide good results of the spray structure as shown in Figs. 8 and 9. Figure 10 shows the correlation between droplet diameter and vertical velocity for all particles at the end of the injection for both the aforementioned models. Black dots represent numerical results. All particles existing in the calculation domain are plotted. Red dots represent experimental data obtained from ILIDS at area A with the numerical results. Red line in the figure indicates the approximate upper boundary of the experimental data. Relatively low velocity droplets are widely distributed in experiments. The results show wide existence of particles at high velocity, over 100 m/s, at all diameters. However, at low velocity the distribution of particles is limited to less than 30 μm. On the other hand, the results show that particles with low velocity are widely distributed against diameter with the Improved TAB model. Note that upper boundary of the numerical results show better agreement with the approximate line. These differences in results are caused by the breakup criterions and the rules of drag force in the two models. The breakup time is short and evolved droplet size is smaller in TAB model but the time is longer. In contrast the droplet size is bigger in Improved TAB model.


11

0.5ms 1.0ms 1.5ms 2.0ms

Fig. 8. Spray images from numerical results with the introduction of secondary breakup models, TAB model, Pilch and Erdman model, and Improved TAB model, at every 0.5 ms after the start of injection. Injection is into static flow field.

Non

e-br

eaku

p TA

B m

odel

Im

prov

ed

TAB

mod

el

Expe

rimen

tal

dat

a


12

0.5ms 1.0ms 1.5ms 2.0ms

Fig. 9. Spray images from numerical results with the introduction of secondary breakup models, TAB model, Pilch and Erdman model, and Improved TAB model, at every 0.5 ms after injection. Injection is into uniform cross flow field.

Expe

rimen

tal

dat

a N

one-

brea

kup

TAB

mod

el

Impr

oved

TA

B m

odel


13

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.5 1 1.5 2

Pene

tratio

n [m

]

Time [ms]

EXPNONE

TABITAB

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.5 1 1.5 2

Pene

tratio

n [m

]

Time [ms]

EXPNONE

TABITAB

(a) Without crosswind (b) With crosswind

Fig. 10. Spray tip penetration obtained with the numerical simulations using secondary breakup models, TAB model and Improved TAB model.

Experimental data and numerical results are also included without secondary breakup model.

(a) TAB model (b) ITAB model

Fig. 11. Diameter versus vertical velocity for all particles. Black dots represent numerical results and red dots represent experimental data on

droplets data at the local area A. The following points can be made from the results obtained here. Introduction of secondary breakup model in the numerical simulation provides improved penetration. In particular, TAB model provides good reproducibility on precision in both penetration and spray structure. However, TAB model underestimates the droplet diameter after breakup, while experimental data shows the presence of both large and slow moving droplet in out of the core. Despite our overestimates in the penetration, Improved TAB model showed better results on the local correlation between droplet velocity and diameter. 4.2 The effect of inlet velocity distribution on TAB and ITAB modeling

The above section provided an investigation of the effect of secondary break up modeling. However, fine agreement was not obtained on the diameter-velocity correlation between calculations and the experimental results obtained from ILIDS. Larger particle sizes, with diameters more than 20 μm, are not captured in any numerical simulation cases, although experiments showed the existence of particles larger than 80 μm.

The initial velocity of all particles was set to be same value though the injection location. The direction was determined in random order using uniform random numbers. However, it is expected that actual fuel flow associated with the internal nozzle forms velocity distribution and that low velocity droplets exist in the vicinity of the nozzle wall. Therefore, calculations were carried out with particles possessing velocity profile. Quadratic and quartic function profiles are given to particles against the direction of spray-angle, φ, as shown in Fig. 12. Also the injection frequency profiles are shown in Fig. 13. The four cases simulated in this section is summarize in Table.2. These cases are calculated using both the TAB and Improved TAB model.


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Fig.12. Injection Velocity Profile – Quadratic and Quartic Function

Uniform Quartic Function Quadratic Function

Fig. 13. The frequency of injected particles versus the spray-spread angle (0-18 deg).

Case Distribution of velocity Distribution of injection frequency

Default Uniform uniform

A Quartic distribution Quartic distribution

B Quadratic distribution Quadratic distribution

a’ Quartic distribution uniform

b' Quadratic distribution uniform

Table 2. Inlet conditions for the distribution of velocity and inject frequency

Results for case a and b using TAB model are shown in Fig. 14. The results indicate that the dispersion of particles in case a is smallest and that the apical part of spray is sharpest amongst the three cases. Figure 15 shows results obtained from cases a and b using the Improved TAB model. These results captured the sharpest apical part for case a. A comparison of the injection velocity distributions shown in Fig. 12 reveals that the Quadratic function is sharper than Quartic function at the center line of slit. The reason why these results are obtained with the respective droplets distributions is that a large number of high velocity particles are injected at central line of the spray.


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default: uniform case b: quartic function case a: quadratic function

Fig. 14. Comparison of inlet profiles for TAB modeling case. Left diagram: uniform random numbers; Center diagram: quartic weighted

random number; Right diagram: quadratic weighted random number

default: uniform case b: quartic function case a: quadratic function

Fig. 15. Comparison of inlet profiles for Improved TAB modeling case. Left diagram: uniform random numbers; Center diagram: quartic

weighted random number; Right diagram: quadratic weighted random number

The simulation results obtained on setting only velocity profile, [vel. profile], setting velocity profile and inlet frequency profile, [vel. & freq. profile] are presented here. The results obtained for case a and a’ using TAB model and Improved TAB model are shown in Figs. 16 and 17, respectively. Note that the red dots, representing larger droplets in the spray core, are distributed uniformly in case a, while they are distributed around the surface of the spray core in case a’.

case a: vel. & freq. profile case a’ : vel. profile

Fig. 16. Comparison of inlet velocity profile with injection frequency distribution using TAB model


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case a: vel. & freq. profile case a’ : vel. profile

Fig. 17 Comparison of inlet velocity profile with injection frequency distribution using Improved TAB model

Spray tip penetration introduced in each inlet profile is shown in Table 2. The corresponding experimental data are shown in Figs. 18 and 19. Figure 18 shows results obtained from the TAB model case. The penetration velocity [vel. profile] is improved slightly. On the other hand in cases [vel. & freq. profile], no significant differences can be observed. The minor differences emanate from the difference in summation of momentum of the particles. In cases [vel. profile], the entire momentum of spray is reduced remarkably because particles are injected from a low velocity location at same frequency than at the high velocity location. Although the momentum in cases [vel. & freq. profile] is also reduced, the decrease is not too large. Figure 19 shows results obtained from Improved TAB model case. Same trends can be observed in this case. However, because the effect of break up, improved vel. & freq. profile are smaller than TAB model case. Larger droplets diffuse to locations outside the core in the vel. profile case as compared to the vel. & freq. profile case. This assists in improved penetration in vel. & freq. profile (smaller) than that for the TAB case. However, both vel. profile and vel. & freq. profile reveal good improvement than that obtained for the constant profile case.

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[vel. & freq. profile] [vel. profile]

Fig. 18. The penetration obtained with various inlet profiles versus time in TAB modeling case


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Fig. 19. The penetration with various inlet profiles versus time for Improved TAB modeling case

Diameter and vertical velocity correlations at a local square area are shown in Figs. 20 and 21 along with the experimental data obtained with ILIDS. In this figure the red dots represent experimental data. Simulation dots can be distinguished into two groups of high density with high velocity, and low density with low velocity. Particles in the core of spray belong to the former group. The other groups contain particles that are striped out from the core by drag force. The results shown in Fig. 20 for the TAB model case reveals that inlet conditions affect the distribution of particles present in the core only and that the effect on the latter group is not large. In contrast, the results shown in Fig. 21 for Improved TAB model case shows that the inlet condition affects not only the core area but also the latter group. Larger diameter of droplets can be seen without any droplet break up. However, the magnitude of velocity is still larger than those obtained experimentally.

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Fig. 20. Comparison of results from TAB modeling with experimental results with ILIDS showing correlation between particle diameter and vertical velocity at a local square area with central point location at (y=40mm. z=-9mm)


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Fig.21 Comparison of Improved TAB modeling results with experimental results from ILIDS showing correlation between particle diameter and vertical velocity at a local square area with central point location at (y=40mm. z=-9mm)

5. Conclusions

Fundamental studies aimed at the analysis of direct injection gasoline engine have been performed. The numerical simulation of spray behavior injected from a slit nozzle has been carried out using Large Eddy Simulation and Discrete Droplet Model. The following conclusions can be drawn from this investigation.

. 1. Introduction of secondary breakup models: Tip penetration was improved. In particular, TAB model revealed a high reproducibility for the prediction of penetration and spray structure. In contrast, ITAB model has the advantage of providing good correlation between diameter and velocity in a local area. 2. Effect of inlet condition in TAB model and Improved TAB model:

The effects of inlet condition are large in spray core with both TAB model and Improved TAB model. Inlet condition in Improved TAB model also affects the particles stripped from core because of the strong

drag force. Slight improvements in the distribution of diameter in local area are recognized.

Further direction of this study will be to address the following issues.

1. Introduce an advanced model, such as primary break up model or wall collision model. Improved TAB model are affected by initial velocity and diameter distribution. If these efforts are found to be fruitful, more detailed modeling as well as numerical simulation will be carried out in our quest for grasping more detail phenomena.

2. Perform spray simulation using a grid size appropriate for the combustion chamber by closely considering the shape of inlet manifolds and piston head.

Nomenclature ui i component of gas phase velocity [m/s] ui' SGS component gas phase velocity [m/s] ur velocity of gas phase [m/s] ud,i i component of droplet velocity [m/s]

dur velocity of droplet [m/s]

x x component in orthogonal coordinate system, displacement of the equator from the spherical radius in TAB or ITAB model

y y component in orthogonal coordinate system, dimensionless displacement z z component in orthogonal coordinate system xi i component in coordinates [m] xd,i position coordinate of droplet [m] t time [s] P pressure [Pa] Fi source term in Navier-Stokes [m/s2] Μ viscosity coefficient of gas phase [Pa s] ρ density of gas phase [kg/m3]


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ρ0 density of gas phase under atmospheric pressure [kg/m3]

μd viscosity coefficient of droplet [Pa s]

ρd density of droplet [kg/m3]

D droplet diameter [m] CD drag coefficient Red particle Reynolds number We Weber number using diameter Wer Weber number using radius md mass of droplet [kg] Cs Smagorinsky coefficient νe SGS eddy viscosity [m2/s]

Sij mean rate of strain tensor [1/s] Δh grid width [m]

gi i component of gravity force [m/s2] ks SGS turbulent energy [m2/s2] k turbulent energy [m2/s2] kr spring constant [N/m] d damping constant [kg s] Fo external force [N] D32 Sauter Mean Diameter（SMD）[m] Cd : model constant in TAB model Cf model constant in TAB model K model constant in TAB model r radius of droplet [m] r32 Sauter mean radius [m] θ spray angle [deg.]

α parameter in Nukiyama-Tanazawa distribution，injecting direction [deg.]

β : parameter in Nukiyana-Tanazawa distribution

φ spray spread angle [deg.]

c flow rate coefficient Ae area of nozzle exit [m2] ζ normal random number

Var variance of parcel [m2] xp,i,n location of parcel [m] xg,i mass center of all parcels [m] (¯) filtered physical value (˙) first order time derivative (¨) second order time derivative

ω frequency in TAB model Wec Critical Weber number

References

[1] Makoto Koike “Present and Future Direct Injection Gasoline Engines”, Engine Technology, Vol. 04, 2002. [2]Yasuo Moriyoshi, “Fundamental studies of gasoline direct injection spray”, Engine Technology, Vol.04, pp. 34-39, 2002. [3] John K. Dukwic, “ A Paritcle-Fluid Numerical Model for Liquid Sprays”, Journal of Computational Physics, Vol.35, pp. 229-253, 1980. [4] Makoto Nagaoka et. al., “A Deformation Droplet Model for Fuel Spray in Direct-Injection Gasoline Engines”, SAE 2001-01-1225. [5] Edward S. Suh, Christopher J. Rutland, “Numerical Study of Fuel/Air Mixture Preparation in GDI Engine” SAE Paper no. 1999-01-3657, 1999. [6] Yong-Jim Kim, Sang H. Lee and Nam-Hyo Cho, “Effect of Air Motion on Fuel Spray Characteristics in a Gasoline Direct Injection Engine”, SAE Technical Papers, 1999-01-0177. [7] V.K. Chakravarthy and S. Menon, “Large-Eddy Simulation of Turbulent Premixed Flames in the Flamelet Regime”, Combustion Science and Technology, 2001, Vol. 162, pp. 175-222. [8] Takuii Tominaga et., al., “Large-Eddy Simulation of a Turbulent Flowfield in a Gas Turbine Combustor Using an Unstructured Grid System”, B7-3, 18th JSFM Symposium, 2004. [9] Atomization Technology, Morikita Publishing co. Ltd., Edited by the Institute for Liquid Atomization and Spray Systems-Japan, 2001. [10] Masahid Takagi and Yasuo Moriyoshi, “Numerical Analysis of a Hollow-Cone Spray Using a Swirl-Type Injector”, Transactions of the Japan Society of Mechanical Engineers. B, Vol. 67, No. 657(20010525), 2001, pp. 1289-129. [11] Peter J. O’Rourke, Anthony A. Amsden, “The TAB Method for Numerical Calculation of Spray Droplet Breakup”, SAE872089, 1987. [12] R.D. Reitz, “Modeling atomization processes in high- pressure vaporization spray”, Atomization Spray Technology, 3, 307, 1987.


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[13] Jong-Hoon Park and Youngbin Yoon, “Improved Tab Model for Prediction of Spray Droplet Deformation And Breakup”, Atomization and Spray, Vol. 12, pp. 387-401, 2002. [14] Makoto Nagaoka, “3D Simulation of Fuel Behavior in Port-Injection Gasoline Engines”, TOYOTA CENTRAL R&D LABS., INC., R&D Review, Vol.33, No.2, 1998 [15]S.V. Apt, M. Gorokhovski, P. Moin, “LES of atomizing spray with stochastic modeling of secondary breakup”, International Journal of Multiphase Flow, 29, 2003, pp. 1503-1522. [16] Yuichi Itoh, Nobuyuki Taniguchi, Toshio Kobayashi, "Numerical Prediction of Vaporizing Spray by using Large Eddy Simulation in Swirling Flows", Procs. of 5th Asian Computational Fluid Dynamics Conference (ACFD5), pp. 636-643, 2003. [17] Jun Arai, Nobuyuki Oshima, Marie Oshima, Hisashi Ito and Masato Kubota, “Large Eddy Simulation of Spray Injection to Turbulent Flows from a Slit Nozzle”, Journal of Fluid Science and Technology, Vol. 2, No. 3 (2007), pp. 601-610. [18] Daniel Lee, Eric Pomraning, Chistopher J. Rutland, “LES Modeling of Diesel Engines”, SAE paper no. 2002-01-2779, 2002. [19] Smagorinsky, J., Monthly Weather Rex. 91-3, 1963, pp.99-164. [20] CD-Adapco, “Methology”, STAR-CD Version 3.2. [21] Kangbin LEI, Nobuyuki Taniguchi, Toshio Kobayashi, “A Proposal of Dynamic Random Walk SGS Model(Effect of Fluid SGS Component on Particle Motion in Large Eddy Simulation of Particle-Laden Turbulent Flows)”, JSME journal B 69 681 , No.02-0496, pp. 1073-1080, 2003. [22] Shiro Nukiyama, Tasusi Tanazawa, “An Experiment on the Atomization of Liquid by means of an Air Stream (first report)”, JSME journal, 4, 86, pp. 86-93, 1938. [23]Shiro Nukiyama, Tasusi Tanazawa, “An Experiment on the Atomization of Liquid by means of an Air Stream (second report)”, JSME journal, 4, 86, pp. 138-143, 1938. [24] M. Pilch, C.A. Erdman, ”Use Of Breakup Time And Velocity History Data to Predict the Maximum Size of Stable Fragments for Acceleration-Induced Breakup of A Liquid Drop”, International Journal of Multiphase Flow, Vol.13, No.6, pp. 741-757, 1987. [25] E.A. Ibrahim, H.Q. Yang and A.J. Przekwas, “Modeling of Spray Droplets Deformation and Breakup”, Journal of Propulsion and Power, vol. 9, pp. 651-654, 1993. [26] Liu, A.B., et al., “Modeling the Effects of Drop Drag and Breakup on Fuel Sprays”, SAE 930072, 1993. [27] Muto Masaya, Nobuyuki Oshima, Marie Oshima, Masato Kubota, “The behavior of spray particles generated by slit nozzle in the turbulent flow”, JSAE symposium 2005, No.132-05, pp. 11-12, 2005.09.28-30. [28] SM.M. Salim, T. Saga, N. Taniguchi and F. Okumura, “Experimental analysis of the control of turbulent intensity in a square channel by the turbulent promoter”, Vol. 2004, No.10, pp. 563-564. [29] Kawaguchi, Akasaka, Kobayashi, Maeda, “Applications of Interferometric Laser Imaging Technique to the Spatial Analysis on a Transient Spray Flow”, JSME Journal, B 68, 666,No.01-0888, pp. 576-583.

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[American Institute of Aeronautics and Astronautics 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition - Orlando, Florida ()] 47th AIAA