Question

(a) Describe the primary break-up mechanism for spray formation and explain the different regimes for this mechanism.

(b) Consider a 110 μm diameter liquid n-Octane (C8H18) droplet evaporating in a quiescent ambient environment of air at 500 K and 1 atm. Assume that the liquid droplet temperature is reached at its boiling point. Determine the lifetime of the n-Octane droplet with the aid of the given information and Tables Q3(a)-(c).

Answer 1

a)Mixture preparation in diesel combustion starts with spray formation after the fuel leaves the injection nozzle. The fuel spray atomizes into droplets, vaporizes, and mixes with air. The process of fuel spray penetration and droplet formation can be described by jet penetration models. In the mixing controlled phase, diesel combustion occurs with a lifted flame that consists of diffusion flame at the periphery of the fuel jet and a rich premixed reaction zone that exists downstream of the lift-off length in the core. In-cylinder mixing of fuel and air can be further enhanced by measures downstream or upstream of the lift-off length.The first step in the mixture formation process in the conventional, mixing controlled diesel engine combustion is spray formation. Figure 1 shows a spray formed by injecting fuel from a single hole in stagnant air [Henein 1972]. Upon leaving the nozzle hole, the jet becomes completely turbulent a very short distance from the point of discharge and mixes with the surrounding air. This entrained air is carried away by the jet and increases the mass-flow in the x-direction and causes the jet to spread out in the y-direction. Two factors lead to a decrease in the jet velocity: the conservation of momentum when air is entrained into the jet and frictional drag of the liquid droplets. Figure 1 gives the velocity distribution at two cross sections. The fuel velocity is highest at the centerline and decreases to zero at the interface between the zone of disintegration (or the conical envelope of the spray) and ambient air.Primary Atomization. Near the injector nozzle, the continuous liquid jet disintegrates into filaments and drops through interaction with the gas in the cylinder. This initial break-up of the continuous liquid jet is referred to as primary atomization.

In general, the atomization of a jet can be divided into different regimes depending on the jet velocity [Heywood 1988]:

• Rayleigh Regime. In this low jet velocity regime, breakup is due to the unstable growth of surface waves caused by surface tension and results in drops larger than the jet diameter.
• First Wind Induced Breakup Regime. In this medium jet velocity regime, forces due to the relative motion of the jet and the surrounding air augment the surface tension force, and lead to drop sizes of the order of the jet diameter.
• Second Wind-Induced Breakup Regime. In this high jet velocity regime breakup is characterized by divergence of the jet spray after an intact or undisturbed length downstream of the nozzle. The unstable growth of short-wavelength waves induced by the relative motion between the liquid and surrounding air produces droplets whose average size is much less than the jet diameter.
• Atomization Regime. At very high jet velocity, breakup of the outer surface of the jet occurs at, or before, the nozzle exit plane. The average droplet diameter is much smaller than the nozzle diameter. Aerodynamic interactions at the liquid/gas interface appear to be one major component of the atomization mechanism in this regime.

  Initial break-up in diesel fuel jets generally occurs in the atomization regime. The dominant mechanisms driving this process are not entirely clear. Interdependent phenomena such as turbulence and collapse of cavitating bubbles may initiate velocity fluctuations in the flow within the nozzle of the injector that destabilize the exiting liquid jet. The unsteadiness of the injection velocity and drop shedding also play an important role [Gorokhovski 2008].

  For most diesel fuel injection systems, jet atomization at the nozzle exit plane occurs when:

  √(ρa/ρf) < 18.3/√A(1)

  where ρa and ρf are the densities of ambient gas and fuel, respectively, and A is a function of the length/diameter (Lo/Do) ratio of the nozzle:

  A = 3.0 + 0.28 (Lo/Do)(2)

  Secondary Break-Up. After the initial disintegration of the liquid jet and the initial formation of droplets, aerodynamically induced droplet breakup further reduces the size of the droplets as they penetrate into the surrounding air. This secondary breakup combined with evaporation ensures that droplets continue to decrease in size as they move along the x-axis (see Figure 1).

  Secondary break-up is assumed to be controlled by the droplet Weber Number (We) which is defined as the ratio of the inertia forces to the surface tension forces:

  We = ρa Dd urel2 / σf(3)

  where
  ρa - ambient density
  Dd - droplet diameter
  urel - relative velocity between droplet and the ambient gases
  σf - surface tension of fuel.

  This secondary break-up can be classified into a number of different modes depending on Weber number.

  In modern diesel engines, the droplet Weber number are typically in excess of 100 indicating that stripping and catastrophic regimes are the most important modes of secondary breakup. Secondary break-up starts at a finite distance from the injector, on the order of several mm, and then stops about 15-20 mm from the injector. Further reductions in droplet size downstream of this distance can be attributed almost entirely to evaporation.

• Droplets experience considerable deformation during break-up and are not in fact spherical. Droplet distortion, as measured by the ratio of the long axis diameter of an elongated drop to a spherical drop, can be about 5 under typical modern diesel injection conditions. This increases the surface area of the drop by a factor of 7-10 and has a profound effect on fuel vaporization. This deformation ensures that the fuel vaporization rate equals the injection rate shortly after the start of injection.