PRESUPUESTO DEL PROYECTO

So far in this w ork, the subject of the form ation of d rops and sprays has only been touched upon. This section will attem pt to give an overview of the general processes involved. For a m ore complex review , references [44] an d [83] are recom m ended. Lefebvre's book [44] is the source of a large p a rt of the following tiieory.

1.8.1 Basic Principles

Sprays m ay be produced in various ways, but m any of the fundam ental processes are common to all of them . Lefebvre [44] described the process of atom ization as "a d isru p tio n of the consolidating influence of surface tension by the action of internal and external forces". The following will attem pt to describe these processes applied to fuel sprays in the fuel systems of si engines.

Fuel em erging from a carburettor or injector nozzle/orifice, will initially be in the form of a colum n or sheet. Liquid viscosity will exert a stabilising influence by opposing any change in the system geom etry. However, instabilities will grow in die sheet or colum n, disrupting the liquid. A erodynam ic forces acting on the liquid surface, caused by the relative velocity betw een the air and fuel, may prom ote this disruption process by applying an external force to the bulk liquid. Break-up of the liquid will occur w hen the m agnitude of the disruptive force just exceeds the consolidating surface tension force.

Surface tension w ill act on the ligam ents and dro p s produced and try to pull them into spheres, these h av in g the m inim um surface energy. H ow ever, m any of th e larger drops pro d u ced by the initial disintegration process w ill be unstable. These w ill d isintegrate further, until there is insufficient disruptive energy rem aining to continue the process.

Thus a range of drop sizes is produced from any given fuel preparation device. In devices such as the carburettor, prim ary atom ization occurs as the fuel leaves the jet or orifice, w hilst very h igh aerodynam ic forces at the throttle-plate (at p a rt throttle) pro m o te secondary atom ization as the droplets become unstable once m ore. Thus the d ro p sizes are further refined, w ith the final distribution being largely dependent on this secondary process.

The basic processes described above seem fairly straightforw ard, b u t as investigations are m ade in greater d e p th it is found that w ithin these processes there are m any sub-processes which m ay take various forms.

1.8.2 Break-up of liquid jets

Rayleigh [69] m ade some of the m ost fam ous investigations into the break-up of liquid jets. In an ideal case, he found that a lam inar liquid jet, em erging from a circular orifice, w ith axial (relative) velocity, developed small disturbances on its surface, w hich led to break-up into d rops alm ost twice the diam eter of the jet.

Studies have been m ade by various researchers into the grow th of waves on the surface of jets/lig am en ts and sheets, and how this causes break-up. It seem s th at for m ost conditions there is a m inim um wavelength of disturbance, w hich will overcom e the surface tension forces a n d increase in m agnitude, eventually leading to break-up. There is also one optim um w avelength for drop formation, for a given condition. The effect of relative air velocity is to reduce this optim um wavelength.

There have been four distinct regimes of break-up observed in the disintegration of a liquid jet.

1. Drop form ation w ithout the influence of air. This is the m echanism studied by Rayleigh. Radially sym m etric (dilational) waves are form ed by the interaction of prim ary disturbances in the liquid and surface tension forces. This regim e is characterized by a linear relationship betw een length of jet prior to break-up and jet velocity. This is illustrated in figure 1.7a.

2. D rop form ation w ith air influence (figure 1.7b). As the relative velocity betw een the jet and the surrounding air increases, the aerodynam ic forces are no longer negligible and tend to accentuate the waves formed under regim e 1. The point at w hich break-up occurs m oves closer to the nozzle.

3. Drop form ation d u e to waviness of the jet (figure 1.7c). This is som etim es called the flapping' or sinuous' m ode. This regim e is associated w ith increasing effectiveness of aerodynam ic forces and lessened relative influence of surface tension.

4. C om plete disintegration of the jet, ie, atom ization. The liquid is broken u p a t the nozzle in a chaotic and irregular m anner (figure 1.7d).

It should be noted that there is no sharp dem arcation betw een these regimes.

Ohnesorge proposed w hat are probably the m ost com m only quoted criteria for classifying jet disintegration. He classified the jet disintegration data according to the relative im portance of gravitational, inertial, surface tension and viscous forces, by studying photographic records of sprays. He then used dim ensional analysis to show th at the break-up m echanism of a jet could be expressed in three stages, each stage characterized by the m agnitudes of the liquid Reynolds num ber ReL, and a dimensionless num ber Z.

Z = 5/ .-1 PL"LD (1.5) ( W ) w h ere UL = liquid velocity (m /s) D = orifice diam eter (m)

PL = liquid density (kg/m^) OL = surface tension (kg/sec^)

[IL = liquid dynamic viscosity (k g /m s)

This is variously know n as the viscosity group, O hnesorge n um ber (Oh), o r the stability num ber (the latter because it provides an indication of the resistance of the globule to further disin teg ratio n ).

The three stages are;

1. Low Reynolds num ber - jet disintegrates into large drops of fairly uniform size (Rayleigh) 2. Interm ediate Reynolds num ber - break-up by jet oscillations w ith respect to jet axis. M agnitude of oscillations increases witih air resistance until com plete disintegration of the jet occurs. A w ide range of drop sizes is produced.

3. H ig h R eynolds num bers - com plete atom ization w ith in a sh o rt distance from the discharge orifice.

The chart produced by Ohnesorge is shown in figure 1.8. For a given liquid and orifice size the O h num ber is constant, and thus a variation in Reynolds num ber describes a horizontal line. T hus low Reynolds num bers give prim arily varicose break-up, w ith high Reynolds num bers giving atom ization as the jet emerges (referred to as secondary atom ization on the chart). M odifications have been m ade to this type of chart since O hnesorge, in particular Lefebvre [44] illustrated the w ork of Reitz, w ho d ivided the chart up into four zones to correspond m ore closely w ith the four break-up regimes quoted earlier. The four regim es are defined as follows.

1. Rayleigh jet break-up - caused by the grow th of axisym m etric oscillations of the jet surface, induced by surface tension. Drop diam eters exceed jet diam eter.

2. First w ind-induced break-up - surface tension augm ented by relative velocity betw een jet and am bient gas, producing a static pressure distribution across the jet. This accelerates the break-up process. As w ith regime 1, break-up occurs m any jet diam eters dow nstream of the nozzle. Drop diam eters are about the same as the jet diam eter.

3. Second w in d -in d u ced break-up - drops p roduced by the un stab le grow th of short w avelength surface waves, caused by the relative m otion betw een jet and am bient gas. This w ave grow th is opposed by surface tension. Break-up occurs several diam eters dow nstream of the nozzle exit, w ith average drop diam eters m uch less than the jet diam eter.

4. A tom ization - jet disrupts com pletely at the nozzle exit. A verage d ro p diam eters are m uch less than the jet diameter.

This chart can be seen in figure 1.9. The atom ization region is often considered to be the m ost desirable, b u t the m echanism involved is the least understood.

D espite probable know ledge of the Reynolds num ber of the liquid passing through the nozzle, it is n o t usually straightforw ard to tell if this flow is lam inar, tu rb u len t or some com bination of both. Generally, a smooth shaped tubular orifice w ith high viscosity liquid is conducive to lam inar flow, whereas turbulent flow is prom oted by large tube size, w ith surface

roughness and rapid changes in cross-sectional area, w ith a low er viscosity liquid. How ever, turbulence takes a finite distance to develop, so that if the orifice is short, the flow on exit m ay still be lam inar, or partially lam inar, even if the Reynolds num ber is above the upper critical point.

A turbulent jet will be far m ore conducive to early break-up than a lam inar one, and it will m ake full use of the friction forces betw een itself an d the air. C avitation in the nozzle will also enhance jet break-up. A typical jet stability curve is show n in figure 1.10.

The am b ien t pressu re into w hich the liquid is sp ray ed can have a significant effect. Lefebvre [44] reported a strong effect on break-up length in the range 0.1-3 MPa. There w as a decrease in break-up length as the am bient pressure w as increased (which m ight be expected as the m edium into which the jet is penetrating becomes m ore dense).