Habchi_SAE97_Wave_FIPA.pdf

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Among them, two models are used for the

atomization and breakup processes in current 3D

codes. The Taylor Analogy Breakup (TAB) model

[6], and the surface wave instability (Wave) model

[2]. These models contain adjustable constants that

need to be determined from experimental data. The

TAB model which is used in the Kiva2 code [4] is

useful to simulate direct and indirect injection diesel

engines with low to moderate injection pressure

(Pinj


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estimated. This is related to the spray and gas phase

coupling which is generally very difficult to handle with

sufficient accuracy, with current mesh refinement,

even for dilute sprays.

To overcome this difficulty, Wave and TAB model

users try to correct their relative velocity (i.e. their

Weber number) by tuning the time breakup constants.

The idea presented in this paper consists of relating

the breakup time to the local spray density. Where the

spray is thick, the relative velocity of the gas phase

located between the drops is low and waves are more

damped than in dilute spray. Then the breakup time

must be increased in the dense spray region,

especially near the injector hole.

In the following, we first describe the computer code.

Then, we will present the new droplet breakup FIPA

model with some implementation details in conjunctionwith those of the Wave model. A simple method for

automatic evaluation of an appropriate value of the

Wave model B1 and FIPA model C1 constants will be

introduced thereafter, as function of the local spray

density.

Evaluation of these models will be done in two

different ways. We will use the monodisperse drop

breakup experiments of Liu and Reitz [5] to assess the

results of the FIPA secondary breakup model. The

accuracy of the overall (primary and secondary

breakup) WaveFIPA model will be evaluated by

comparison with experimental data obtained in a

diesel simulation cell which allowing the investigation

of the spray structure in temperature and pressure

conditions close to those found in Diesel engines. The

cell together with the commonrail injection system

will be described.

COMPUTER CODE AND SPRAY

The computations were performed using the

Kiva MultiBlock (KMB) code[1], a modified version of

KIVA2 [4], which solves the 3D equations of

transient, chemically reactive fluid dynamics.

Evaporating liquid sprays are represented by a

discreteparticle technique, in which each

computational particle represents a number of

droplets of identical size, velocity and temperature.

The particle and fluid interact by exchanging mass,

momentum, and energy. Furthermore, droplet

collision and coalescence are accounted for, in

conjuntion with the TAB breakup model. The

governing equations and the numerical solution

method are discussed in detail by Amsden et al. [4].

The main new capabilities of KMB are its structured

multiblock architecture [15] and local mesh

refinement and adaptation algorithms which allow

computations in very complex geometries [16,17].

Several numerical improvements and physical

submodels have been integrated into KMB as

described in [1,14,18,19,20,21].

ATOMIZATION MODEL

We will not describe in this paper the Wave

breakup model [2,5,7], but only recall here its main

hypotheses to specify its theoritical domain of validity.

The theory of Reitz and Bracco [7] considers the

stability of a column of viscous liquid issuing from a

circular orifice of radius "a" into a stationary,

incompressible invicid gas. Their linear analysis gives

the maximum growth rate and its corresponding

wavelength as function of the nondimensional

Weber We and Laplace Z numbers. It allows the

calculation of the breakup time ,

= 3.726 B1a/ ( ) (1)

where B1 is a proportionality constant related to the

initial disturbance level originating within the injector

nozzle that accounts for nonlinear aerodynamic

effects. For suddenly accelerated drops or forbreakup after wall or droplet collisions, B1=1.73 is

used as in the TAB model for relatively high Weber

number (stripping regime: 100 < We < 350). For high

injection pressure with commonrail systems, B1 is

increased from 30 for Pinj < 90 MPa [12] to 60 for

Pinj>100 MPa by Rutland et al. [13]. The wide range

of B1 values encountered is a real difficulty for

engineers and needs to be better controlled.


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the stability of the drop), the Wave model predicts a

small value of Tbu. In this case, nonphysical droplet

breakup continues indefinitely until total evaporation.

To make the spray breakup more realistic, we used

the Wave model to compute the atomization of the

liquid (primary blobs) injected and we developed a

new model, FIPA ("Fractionnement Induit Par

Acceleration") based on Pilchs experimental

correlations for droplet breakup. The main

parameters of this model are :

the breakup time ,

the maximum radius of stable drops Rs.

Assuming low viscosity liquid, the averaged radius Rs

is obtained at time from the definition of the Weber

number using the diameter d of the drop and

assuming a critical Weber number Wec=12 :

Rs= 6/ ( g Vr2) (3)

and the breakup time is defined by :

= C1 Tbu0.5(d / Vr) (4)

where C1 is a constant analogous to the constant B1

in the Wave model, Vris the relative velocity between

the flow field and the drop, is the surface tension of

the drop, is ratio of the gas to the liquid density

=(g/) and Tbu is the dimensionless breakup time

given by the following correlations of Pilch (Figure 1):

Tbu = 6.00 ( We 12 )0.25 12 < We < 18

Tbu = 2.45 ( We 12 )+0.25 18 < We < 45(5)

Tbu = 14.1 ( We 12 )0.25 45 < We < 351

Tbu = .766 ( We 12 )+0.25 351 < We < 2670

Tbu = 5.5 We > 2670

DROPLET BREAKUP MODEL

Figure 1 shows the nondimensional breakup

time (Tbu) given by the Pilch et al. [3] correlations and

those predicted by the Wave model with B1=10 and

two Laplace numbers representative of the range

encountered in Diesel engine applications (Z=0 and

Z=0.01). The Wave dimensionless breakup time Tbu

is of Eq.(1) nondimensionalized (following Pilch et al.

[3]) as follows:

Tbu = 0.5 (Vr/d) (2)

where is the ratio of the gas to liquid density

=(g/). We note that the Wave Tbu curves

approach the horizontal line proposed by Pilch at high

Weber numbers, but do not reproduce the behaviorobserved experimentally as the Weber number

decreases towards and past its critical value (around

Wec=12). While Pilchs experimental correlations

show a W shape at low to moderate Weber numbers,

typically less than 1000, the Wave model predicts a

nearly linear behavior. For example, whereas the

experiments show clearly that Tbu goes to infinity in

the vicinity of the critical Weber number (expressing

Figure 1: Comparison of dimensionless breakup time

predicted by Wave model and the correlations

proposed by Pilch et al.[3].

101

102

103

104

105

Gas Weber Number : We

2

4

6

8

10

12

Dimension

lessBreakupTime:Tbu Tbu ( Pilch correlations)

Tbu Wave model ( Z=0 , B1=10. )

Tbu Wave model ( Z=0.01 , B1=10. )


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model) with the current parent drop radius being the

maximum value allowed. The child parcel keeps the

same thermodynamic characteristics as the parent

parcel. The number of product droplets Ns in the

current parcel is evaluated using mass conservation

taking into account possible vaporization.

Ns= (N N0) (r / rs)3

(6)

A similar relationship is used for Wave model to

insure mass conservation when the evaporation

model is activated.

EVALUATION OF THE FIPA MODEL We used the

experimental data of Liu and Reitz [5] to evaluate the

FIPA droplet breakup model and to fit its constant.

Their experimental apparatus consisted of a liquid

drop generator and a converging air nozzle whichwere arranged in a cross flow pattern as shown in

Figure 2. The velocity and size distribution of drops

were measured by phase doppler anemometry at 29

mm and 47 mm from the exit nozzle. The trajectory of

the parent drops was measured from photographs of

the entire spray.

Figure 2 : Schematic diagram of experimental

apparatus and measurement locations.

(Dcol=9.52mm, Dcyl=52mm, Vinj= 16m/s, rinj=85m).

The FIPA breakup process is modeled by postulating

that new droplets of Sauter Mean Radius SMR=Rsare

formed from the original drop (parent drop) during the

breakup time period . The characteristic size r of

unstable parent drop (which has a Weber number

greater than 12) changes continuously with time

following the rate equation:

dr/dt = ( r Rs) / ( s)

(5)

(


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DETERMINATION OF B1 AND C1 We assume that

in dense spray zones, the liquid occupies a significant

volume fraction but is still structured as discrete

entities ( blobs or drops) in a continuous gas phase.

There are a number of factors which could be taken

into account in the estimation of B1 and C1. The idea

suggested here is based on the assumption that

unstable waves are more damped in dense spray

than in dilute one. The determination of B1and C1 is

based on the local spray density. Via B1 and C1, we

try to provide to the breakup time computation local

spray density information. In Figure 6, we define two

critical droplet spacings (x/d)1=3 and (x/d)2=50 (x

and d are defined in Figure 7). The critical spacing is

related to the wake length behind a sphere. The value

of the critical droplet spacing should have a similar

dependence on local Reynolds number as the dropletwake length. However, following Mulholland et al. [10]

who show that the droplet drag coefficient reaches a

nearly constant value when the critical droplet

spacing is greater than 50, we assume droplets are

not influenced by other droplets when x/d > 50 (i.e.

>0.99999). In this case, the value of B1 is taken to

be equal to B12=10. This choice is related to the fact

that this value allows the Wave model curves in

Figure 1 to approach the horizontal part of Pilchs

correlations which are based on low viscosity (Z 3). This method did not take

into account packets of droplets separated from the

spray and is coherent with the postprocessing of

experimental data depicted previously. Figure 13 and

14 show the computational results obtained in

nonevaporating and evaporating conditions (Table

2). Experimental data were limited to penetrations of

less than about 7 cm because of the size of the

windows in the highpressure cell (Figure 9). This is

sufficient to show the predictive behavior of the

WaveFIPA breakup model, especially in evaporating

conditions. In this case and for (Pinj=80MPa,

Tg=800K), the evolution of the spray is depicted in the

series of images of Figure 15. The shape of the

numerical spray agrees well with that observed

experimentally. Further investigations are needed to

explain why the nonevaporating cases give results

not as good as the evaporating cases.

CONCLUSION AND FUTURE PROSPECTS

A new numerical model called FIPA

(Fractionnement Induit Par Acceleration) has been

developed for calculating aerodynamic droplet

breakup in spray computations. This model was

evaluated separately and in conjunction with the

Wave atomization model.

A simple method for automatic evaluation of

appropriate breakup time constants was introducedas function of the local spray density.

A new experimental installation with a high

pressure and high temperature cell equipped with a

commonrail injection system has been developed to

simulate Diesel engine conditions and provide

reference data.

Comparison of calculated and experimental

liquid and vapor penetrations shows a good

performance of this spray model combination. Further

validations using drop size data in vessel or in real

engine configurations with different operating

conditions are needed to assess the capabilities of

this new model. Morever, in order to improve the

liquidair coupling, it could be interesting to relate

drag coefficient Cd to the drop spacing (x/d).

Future experimental and numerical studies

should also deal with the initial injection conditions.


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Figure 14: Evaporating cases.Calculated and experimental liquid penetrationand vapor penetration.Experiments (liquid: circle and vapor: plus),Computations (liquid: solid line and vapor: dashed line)

Figure 13: Nonevaporating cases.Calculated and experimental liquid penetrationand vapor penetration.Experiments (liquid: circle),Computations (liquid: solid line and vapor: dashed line)

0.0 0.5 1.0 1.5 2.0

time (ms)

0

2

4

6

8

Penetration(cm)

Tg= 400 K, P

inj= 150 MPa

0.0 0.5 1.0 1.5 2.0

time (ms)

0

2

4

6

8

Penetration(cm)

Tg= 400 K, P

inj= 80 MPa

0.0 0.5 1.0 1.5 2.0

time (ms)

0

2

4

6

8

Penetr

ation(cm)

Tg= 400 K, P

inj= 40 MPa

0.0 0.5 1.0 1.5 2.0

time (ms)

0

2

4

6

8

Penetration(cm)

Tg= 800 K, P

inj= 150 MPa

0.0 0.5 1.0 1.5 2.0

time (ms)

0

2

4

6

8

Penetration(cm)

Tg= 800 K, P

inj= 80 MPa

0.0 0.5 1.0 1.5 2.0

time (ms)

0

2

4

6

8

Penetr

ation(cm)

Tg= 800 K, P

inj= 40 MPa


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0.11 0..32 0.62 1.12 Time (ms)

AKNOWLEDGMENTS

This work was supported by the GSM

(Groupement Scientifique Moteurs). We are grateful

to Marc Zolver (IFP) for generating meshes for the

present study. We thank Bruno Algourdin for his

technical assistance. The authors are also indebted to

Dr. Philippe Beard (ALTRAN), Dr. Bruno Dillies

(Peugeot SA) and Dr. Bruno Argueyrolles (Renault

SA) for stimulating discussions.

REFERENCES

[1] Torres A., and Henriot S., "Modeling the Effects of

EGR Inhomogeneities Induced by Intake Systems in

Four Valve Engine", SAE Paper 961959 (1996).

[2] Reitz R. D.,"Modeling Atomization Processes in

Highpressure Vaporizing Sprays", Atomization and

Spray Technology 3 pp. 309337 (1987).

[3] Pilch M., and Erdman C.A.,"Use of breakup time

data and velocity history data to predict the Maximum

Figure 15 : Comparison of calculated and measured spray shape during injection; evaporating case (P inj=80MPa,

Tg=800K). Computed drop locations are projected on the midaxis plane of the spray.


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[15] Habchi C., and Torres A., "A 3D MultiBlock

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