# Modeling the effect of piston crown temperature on the fuel spray mechanism.

IntroductionOne of the primary challenges introduced with the design of direct injection engines is to understand the behavior of the fuel spray distribution and vaporization. The spray structure and targeting must be optimized to evaporate in a short time and be distributed in a desired manner, under a variety of ambient conditions and with a number of injection strategies [1-2]. Nevertheless, in modern high- direct injection diesel engines for passenger vehicles, there is extensive impingement of the fuel speed sprays on to the piston bowl walls. Recent trends towards smaller engine sizes, equipped with high- pressure common-rail fuel injection systems, have tended to increase the spray/piston wall interaction. Currently most DISI engines use a wall--guide direct injection system. In the wall guide combustion system the spray which is injected late during compression impinges on the piston crown that guides the spray towards the spark plug just prior to ignition [3].

Several investigators have shown that raising the wall temperature can affect, considerably, both the fluid mechanics close to the piston surface as well as the spray evaporation and droplet size distribution

Christoph, E and John, E [2] conducted that for diesel engine during cold operation or cold start, up to 25% of injection mass forms a liquid film on the piston bowel bottom and cylinder wall. This largely affects the combustion efficiency and exhaust emission. Experimental results by [4] show that in a high-speed direct injection diesel engine, equipped with high-pressure unit injectors, 75 per cent of the injected fuel reached the piston bowl walls at high engine loads. This resulted in fuel-rich local mixtures and higher unburned hydrocarbon emissions in the exhaust. For stratified charge operation, injection is realized near the end of compression stroke. Fuel is transported to the spark plug by air entrainment and by impingement and sliding on the piston top. Therefore, the flow field, the injector features, and the piston shape and temperature are of prime importance. For stratified cold operation, the spray impingement on piston may yield to film formation and large HC and soot exhaust emissions [4, 5]. To study the influence of piston temperature on the mixture preparation under stratified charge operating conditions numerical calculations are performed.

Theoretical Analysis

The problem of modeling fuel spray heating and evaporation has been widely discussed with CFD (computation fluid dynamic) code. Any effect that the piston surface temperature might have on the combustion and pollutant emission generation has not been a prime consideration in both gasoline and diesel engines design.

Currently the most common spray description is based on the Lagrangian discrete droplet method (DDM) (dispersed phase). While the continuous phase is described by the standard Eulerian conservation equations. The transport of the dispersed phase is calculated by tracking the trajectories of a certain number of representative parcels (particles). A parcel consists of a number of droplets and it is assumed that all the droplets within one parcel have the same physical properties and behave equally when they move, breakup, or evaporate. The coupling between the liquid and the gaseous phases is achieved by source term exchange for mass, momentum, energy, and turbulence (conservation equations).

In the present work wall spray interaction and liquid film transport with two dimensional codes on cold and hot internal engine surface are developed. So the effect of wall temperature on the film thickness is studied with different liquid fuel and start of injection angle degree.

O, Rouke et al included a liquid film model in the code Kiva-3V, using the particle Lagranian approach of the Kiva spray description [3].

Ahmadi-Befrui et al [4] has developed liquid film models using Eulerian continuous approaches.

The major physical mechanisms affecting the liquid film are :

* The film formation by impinging droplet and vapor condensation.

* The film spreading due to air and wall shear.

* The heat exchanger with wall a shear surrounding gas.

The evaporation, boiling and splashing are shown in figure (1). In this work, the basic assumptions for the liquid film modeling are presented. Then the governing equations are derived and numerical schemes incorporated:

* quasi-steady gas film around the droplet.

* uniform physical properties of the surrounding fluid.

* the equation of state is based on the ideal gas law.

* the air is insoluble in the liquid phase

* uniform pressure around the droplet.

* liquid/vapor thermal equilibrium on the droplet surface.

* radiation and gravity effects are not considered.

* liquid phase viscosity is generally taken as variable but density and other properties are typically taken as constant.

[FIGURE 1 OMITTED]

Liquid Film Model

To build liquid film equations the following assumptions have been made:

* The liquid film is assumed to be thin enough so that the incompressible boundary layer approximations can be applied. This thin film assumption is justified by estimations done in which reveals that the maximum film thickness is less than 500 um for typical SI engine and DI engine conditions.

* The liquid film flow is laminar through it may have waves on its surface. The liquid Reynolds number is assumed to be less 600 [5].

* Each control volume for contain both liquid wall and gas wall, then the boundary layer of the conservations equations have been integrated across fuel jet cone and the film thickness in each wall cell through the finite volume method [6].

Since the liquid is incompressible, integral continuity, momentum and enthalpy equations are written using the liquid volume ([V.sub.D]). The film thickness (h) per each cell is calculated using.

h = [V.sub.D] / [A.sub.W] ... (1)

Where: [A.sub.W] is the wall cell face area which may change due to the piston wall motion.

Continuity equation into two dimensional form

[dV.sub.D] / dt + [??] h([bar.u] - [bar.v]) x [bar.n] x dt = S (2-a)

S = 4[pi] / 3[DELTA]t [n.summation over (p)] [[delta].sub.p] x [r.sup.3.sub.p] (2-b)

where: S is source term represents the rate of fuel at the liquid -gas interface due to the droplet impingement, splashing, evaporation or condensation.

Momentum equation can be define as:[6, 7]

[??] = [rho] x [V.sub.D] x [bar.u]

Its transport equation across the boundary lines can be written as follows.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The total pressure (Ph) includes two contributions:

[P.sub.h] = [P.sub.d] + [P.sub.g] (4)

The pressure ([P.sub.d])is due to the spray impact on the liquid film interface. If we note the number of droplet (n) which have impinged ([[delta].sub.p]=1) and splashed( [[delta].sub.g] = -1) on the wall area ([A.sub.w]) during the time interval [[DELTA].sub.t], the pressure is given by:

[P.sub.d] = 4[pi] / 3[DELTA]t [n.summation over (p)] [[delta].sub.p] [r.sup.3.sub.p] ([bar.v] x [??])

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Where:

[r.sub.p] is the radius of the incident or splashed droplet,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is relative velocity

The liquid gas shear stress is given by:[6] respestivly.

[[tau].sub.w] = 3 [mu][A.sub.w] / h ([bar.u.] - [[bar.v].sub.w]) - [[bar.[tau]].sub.g] / 2 (7)

[[tau].sub.g] = [A.sub.w][mu] [[[partial derivative]u.sub.g] / [partial derivative]Z |.sub.Z=H] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the speed Of impinging or splashing droplet (p)

Energy equation can be defined as [6]:

H = [C.sub.p] x [rho] x [V.sub.D] x T

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Where: [J.sub.g] is the gas heat flux and obtained by:

[J.sub.g] = [A.sub.w]k [partial derivative]T / [partial derivative]Z = [A.sub.w] ([j.sub.g] x [m.sub.v] x L) .(11)

The wall heat flux [J.sub.w] is obtained from:

[J.sub.w] = 3 x k [A.sub.w] / h (T - [T.sub.w]) - [J.sub.g] / 2 .(12)

[S.sub.H] = 4[pi]p / 3DELTA]t [n.summation over (p)] [delta]p x [r.sup.3.sub.p][C.sub.p] x [T.sub.d] (13)

Where: [T.sub.d] is the temperature of the impinging or splashing droplet.

Spray wall impingement

Two splashing regimes are introduced to take into account the atomization induced by high impact droplet velocity on dry or wet surface form. Splashing criteria may be expressed using the Weber and Reynolds numbers as shown in fig.(2), [7].:

We = [rho] [([[bar.V].sub.p] x [[bar.n].sub.w]).sup.2] [d.sub.d] / [sigma](14)

Re = p [([[bar.V].sub.p] x [[bar.n].sub.w]).sup.2] [d.sub.d] / [mu] (15)

where [d.sub.d] is droplet diameter and [[bar.n].sub.w] is the unit outward normal vector to the wall..

When the liquid film is formed on the surface the splashing Weber number is depended on the friction factor (f) and given by [7]:

We > [We.sub.s] = [18.sup.2] [d.sub.d] [([rho]/[sigma]).sup.1/2] [([mu]/p]).sup.1/4] [f.sup.3/4] (16)

The Weber number criteria is illustrated bellow and as shown in fig.(2):

film formation We < [We.sub.s]

film splashing We > [We.sub.s]

[We.sub.out] = 0.67 [We.sub.in] exp (-4.4* [10.sup.-2] x [We.sub.in]) (17)

So the splashing setter mean diameter (SMD) is [7]:

SMD = [d.sub.32] = r / 1 + 2[C.sub.k][C.sup.2.sub.b] / 3 + [p.sub.d] x [r.sup.3] / 6 x [sigma]d (18)

where: the constants [C.sub.b] = 0.5, [C.sub.k] = 1.0 [7]

Thus, in the analysis, the case that wall temperature ([T.sub.w]) was less than liquid temperature ([T.sub.L]) ([T.sub.W] < [T.sub.L]) when of the impingement fuel droplet on the cold piston wall such as starting into cold weather or light load engine operation. Submodels on fuel film formation, film breakup process and dispersion on fuel the spray breakup droplets are considered. We can estimate the spray dispersion process of non - vaporizing spray from equation (18) [7].

In the case that the droplet impinges on dry hot surface [T.sub.W] > [T.sub.L], the impinged droplet spreads as a fuel film in radical direction on the wall for a cretin period, and thereafter the film shrinks and it rebounded or it breaks up.

[FIGURE 2 OMITTED]

Droplet-Droplet Collision

It was shown by Fig.(3) that collision processes are important in fuel sprays behavior, especially in regions with high droplet number density. Collision is responsible for the growth of the droplets, due to the coalescence and the exchange of momentum between droplets. In this sense, the collision and breakup processes can be seen as two competing mechanisms whose outcomes determine the local droplet size distribution (DSD) as below:

[FIGURE 3 OMITTED]

Collision Rate

The droplet-droplet collision model is semi-empirical and has two stages. The first stage is to determine collision rate between droplets and then the rate of liquid film creating from equation (1). Collision rates are expressed by a collision coefficient [[beta].sub.12] defined such that [[beta].sub.12] [nd.sub.1][nd.sub.2] is the number of collisions per unit volume and time of droplets having number densities [nd.sub.1] and [nd.sub.2]. According to the kinetic theory [7] the collision coefficient is given by:

[[beta].sub.12] = [pi][d.sup.2.sub.12] [u.sub.rel] (19)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the average relative velocity between the two droplet classes. The following form for the relative velocity between colliding droplets is assumed:[8]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] .(20)

Velocity vectors into any direction are calculated from momentum equations (3) where [u.sub.rel] is the relative velocity of the interacting droplets [d.sub.1] and [d.sub.2] is the diameter of the smaller droplet.

Outcome of Collision

The binary droplet collision phenomenon is discussed in this section. The outcome of collisions can be described by three non-dimensional parameters: the collisional Weber number, the impact parameter, and the droplet size ratio [8]. The collisional Weber number is defined as

[We.sub.coll] = [p.sub.L][u.sup.2.sub.rel][d.sub.2] / [sigma] (21)

The non-dimensional impact parameter is calculated as

B = 2b / [d.sub.1] + [d.sub.2] = sin[theta] (22)

The dimensional impact parameter(B) is defined as the distance from the center of one droplet to the relative velocity, placed on the center of the other droplet. This definition is illustrated in Figure (3) where: [d.sub.1] is the diameter of the larger droplet and [theta] is the angle between the line of centers of the droplets at the moment of impact and the relative velocity[9]

Finally the drop size ratio can be obtained from equation (18)

Fluent Setup With Boundary Conditions

When the fuel start to injection from the nozzle, two phase flow will be presented in the cylinder, therefore adding the following procedure through the Fluent Setup :

* Define [??] model [??] Discrete phase.

* Define [??] materials, includes air and droplet- particle properties.

* From the discrete phase model set the injection properties.

* Define [??] injector. Define [??] costume field function to calculate X slip velocity and Y slip velocity form the multiphase flow model.

* Define [??] Boundary Conditions as follow.

Note: In the injection period there are two different fluid movements, Liquid speed from nozzle define by the (velocity - inlet). Air speed from the position movements, define by the (moving wall).

For unsteady state condition select the droplet initial values as:

Time step 0.001s--Number of time step 1000- Max iteration per time step

Results and Discussion

In this part the computational results are presented and discussed. The effect of the several parameters such as injection duration time for both gasoline and diesel fuel, start of injection degree, piston surface temperature are investigated.

Fig.(4) presents the film thickness contour for Diesel fuel spray on the cold operation condition at SOI 310 degree ATDC(50 degree BTDC) with different injection time durations. The film thickness reached about 230 um at the little region on the piston as shown at Fig(a) (4 ms after SOI) while the wet area increases at the end of injection as in Fig (b) and decreases thickness to 180um. The results show that high film thickness at the cold piston surface near the jet impinging reached 290 um, and decreased near the cylinder wall due to evaporation.

[FIGURE 4 OMITTED]

At the same operation conditions for gasoline fuel spray shown in Fig.(5). Film thickness about 45um at the cold part (4 ms) from the start of injection (a) and reached the maximum value at the end of injection (b) 32 um covered all the piston surface. High different values between diesel and gasoline are observed due to the variation of each liquid properties.

[FIGURE 5 OMITTED]

Figs.(6&7) illustrate fuel spray behavior when the start of injection at 330 degree ATDC and cold operation.

Fig.(6) shows diesel fuel film on the piston surface about 47 um after 4 ms from SOI and reduces to 37 um after 6 ms as a result of high pressure and increases surface temperature. Also the wetting area are increased at the end of injection like in Fig.(4).

[FIGURE 6 OMITTED]

Fig.(7) shows gasoline fuel film at the same operation conditions. The results indicate same conclusion for Fig.(6) but these results are less value than diesel fuel due to low temperature evaporation. Maximum thickness was reached to 36 [micro]m and decreases to 30 um at the end of injection.

[FIGURE 7 OMITTED]

Fig.(8) Illustrates the relation between the splashing spray Weber number to the impinging Weber number on the cold wall for both diesel and gasoline fuel. For high fuel velocity the injected fuel spray impinges on the piston surface due to the short distance between the nozzle and surface. The behavior of both diesel and gasoline fuel the impinging spray have a great influence on the dispersion of the fuel, evaporation and mixture formation process, and further on the combustion process. When the impinging Weber number([We.sub.in]) increases the out Weber number [We.sub.out] also increases, until [We.sub.in] reached more than 50 [We.sub.out] began to decreased due to decreased of splash droplet diameter.

[FIGURE 8 OMITTED]

Figure 9 presents the fuel behavior when contact on the piston surface with different temperatures above the start operating condition.

The results show the normal boiling point of diesel is determined by the location where the curves reached 1 atm at 400 K. Its high boiling point is an indication of its low volatility. The critical properties (pressure, volume, and temperature) are also used to estimate the fuel vapor pressure. Hence it is particularly important to accurately predict the fuel critical properties, as they will influence the prediction of the other fuel properties. Both fuels evaporate with high surface temperature while illustrate the same pressure at temperature 350K (present work operation).

[FIGURE 9 OMITTED]

Fig.(10) shows the effect of wall temperature on the droplet Sater mean diameter(SMD)at low temperature high surface tension and increased droplet diameter for both diesel and gasoline fuel.

[FIGURE 10 OMITTED]

Figs.(11 & 12) represent the important results from the present work.

The film thickness vs crank angle degree foe both diesel and gasoline fuel at surface temperature 350K and 400 K are obtained respectively. The film thickness decreases at high temperature when the piston position BTDC degree and reached to minimum value 40 degree BTDC, then distinguish near bottom dead center. At the beginning of injection maximum value of film reached 13% from total amount of injection fuel. This result gives acceptable agreement with [10].

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

Conclusions

The studying of the wall-spray interaction and liquid film behavior may contribute a better understanding of the mixture preparation, combustion and exhaust gases emission during cold starts. This study shows that at cold piston temperature near 400 K, up to 13% of the injected gasoline remains liquid (e.g.unburned) on the piston bowl surface. No significant liquid film remains on the piston when its temperature exceeds the mean of the boiling temperatures.

High pressure swirl injector prevents the liquid film occurrence. Some further evidence that piston temperature can affect exhaust emissions so high technology sensors is provided.

Nomenclature

[A.sub.w] wall face area

n number of droplet

h mean film thickness (um)

d drop

D diameter

P impinging or splashing droplet method spark ignition

[T.sub.g] gas temperature center

[T.sub.d] droplet temperature

u velocity

[??]relative gas velocity

V volume

[??]relative liquid velocity

B collection coefficient

Sp splash droplet

2D two dimensional

SOI start of injection

CFD computation fluid dynamics

DSD droplet size distribution

g body force

l wall length

[[tau].sub.g] gas shear stress

[[tau].sub.w] wall shear stress

DDM discrete

DISI direct injection

ATDC after top dead

References

[1] Naber, J., Enright, B.and Farrell, P., " Fuel Impingeent in a Direct Injection Diesel Engine" SAE paper, NO.1316, PP.1-14, 1988.

[2] Christoph, E., and John, E., " The effect of TDC Temperature and density on the liquid - phase fuel penetration in a D.I. Diesel engine" SAE paper, No 952456, pp.1-17, 1995.

[3] Le Coz, J.F., Catalano, C. and Baritaud, T. "Application of Laser Induced fluorescence for Measuring the Thickness of Liquid Films on Transparent Wall". 7th Int. Symp. On Application of Laser Techniques to Fluid Mechanics, Lisbon. 1994.

[4] Ahmadi-Befrui, B., Uchil, N., Gosman, A.D. and Issa, R.I "Modeling and Simulation of Thin Liquid Films Formed by Spray Wall Interaction". SAE, No. 960627..(1996)

[5] Stanton, D.W., Lippert, A.M., Reitz, R.D. and Rutland, C.J. "Influence of Spray-Wall Interaction and Fuel Films on Cold Starting in Direct Injection Diesel Engines". SAE, No. 982584. (1998).

[6] David Rochaya "Numerical Simulation of Spray Combustion using Bio-mass Derived Liquid Fuels" PhD Thesis Cranfield University.2007.

[7] Jesper Madsen "Computational and Experimental Study of Sprays from the Breakup of Water Sheets"Ph.D. thesis, Aalborg University, Denmark, 2006.

[8] Ruger, M., S. Hohmann, M. Sommerfeld and G. Kohnen " The effect of droplet collisions and coalescence". Journal of Atomization and Sprays 10, pp. 47-81. 2000.

[9] Fatma, A., Nobuyuki, k., and Eiji, T."Characterization of spray of the DISI multi hole injector by means of phase Doppler anemometer "Journal of thermal science and technology. vol 5, No1, Japan, 2010

[10] Schmehl, R., G. Maier and S. Wittig (2000)." CFD analysis of fuel atomization, secondary droplet breakup and spray dispersion in the premix duct of a LPP combustor". Proc. ICLASS 2000, pp. 918-925.

Sadoun Fahad Albahadily

Technical College of Basrah

E-mail: drsadoun1@yahoo.com

Table 1: The boundary conditions zone. Name Zone Type Fluid 1 Fluid Nozzle 2 Velocity-Inlet Piston 5 Moving Wall Top 3 Wall Side 4 Wall Default-Interior 7 Interior Calculation conditions for both Gasoline and Diesel fuel Gasoline Diesel Air temperature(compression) [T.sub.a] (K) 350 400 Wall Temperature [T.sub.w] (K) 450 500 Injection duration [t.sub.in] (ms) 4 5 Injection fuel amount [m.sub.inj] (mg) 6.2 7.2 Injection velocity [U.sub.inj] (m/s) 50 60 Spray cone angle 2[theta] (deg) 30 30 Number of parcel [N.sub.p] 3000 3000 Number of mesh - 60 * 1 * 60 60*1*60 Initial SMD [D.sub.32] (mm) 0.004 0.008 Initial droplet temperature [T.sub.d] (K) 300 300 Splashing number - 4 4