Jorge Barata and André Silva

*Aerospace Sciences Department, University Beira Interior, Covilhã, Portugal* 

## **1. Introduction**

102 Fuel Injection in Automotive Engineering

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The use of alternative biofuels in the co-generation of electricity and heat, as well as in the transportation sector, presents major benefits, such as the conservation of the environment due to their renewable origin, the reduction of fossil fuels use or the conservation of agricultural activity in regions where the food production is being reduced.

The more important biofuels currently under investigation are the bio-alchohols and their derived ethers, and the vegetable oils and their derived esters. Methyl esters of rapeseed oils or soybean oils have been tested in Diesel engines, and in spite of the strong dispersion of the published results, there are indications that their use is a promising solution to the problems originated with the raw vegetable oil due to their higher viscosity, boiling temperature, final temperature of distillation and point of obstruction of cold filter (Tinaut, 2005).

The present work presents a numerical study on evaporating biofuel droplets injected through a turbulent cross-stream. This study uses an Eulerian/Lagragian approach to account for turbulent transport, dispersion, evaporation and coupling between both processes in practical spray injection systems, which usually include air flows in the combustion chamber like swirl, tumble and squish in I.C. engines or crossflow in boilers and gas turbines. An array of evaporating biofuel droplets through a crossflow is studied, and a comparison of the droplet fuel dispersion and evaporation with conventional fuels is performed. A summary of the main general characteristics properties of the conventional fuels and biofuels tested in the present investigation is presented in Table 1.

The evaporation of droplets in a spray involves simultaneous heat and mass transfer processes in which the heat for evaporation is transferred to the drop surface by conduction and convection from the surrounding hot gas, and vapour is transferred by convection and diffusion back into the gas stream. The overall rate of evaporation depends on the pressure, temperature, and transport properties of the gas; the temperature, volatility and diameter of the drops in the spray; and the velocity of the drops relative to that of the surrounding gas (Faeth, 1983, 1989, 1986).

Godsave (1953) and Spalding (1953) gave the basic droplet vaporization/combustion model for an isolated single-component droplet in a stagnant environment. Since then this model has been studied extensively both experimentally and theoretically. These studies have been reviewed extensively by several authors during the past decades (e.g. Williams, 1973; Faeth, 1977; Lefebvre 1989; Law, 1982; and Sirignano, 1978), and are mostly dedicated to study the

Numerical Simulation of Biofuels Injection 105

The method to solve the continuous phase is based on the solution of the conservation

model of Launder and Spalding (1974), which is widely and thoroughly tested, and was found to predict reasonably well the mean flow (Barata, 1998). In order to reduce the numerical errors to an acceptable level, the higher-order QUICK scheme of Leonard (1979) is used to evaluate the convection terms. A similar method has been used for threedimensional (Barata, 1998) or axisymmetric flows (Shuen et al., 1985; Lilley, 1976; Lockwood

The governing equations (continuity, momentum, turbulent kinetic energy, dissipation, enthalpy, and vapour mass fraction) constitute a set of coupled partial differential equations that can be reduced to a single convective-diffusive conservation equation of the form

*i ii*

is the convection term, whilst the first and the second terms on the right-hand side are the

*SS S* 

*<sup>g</sup> S*

*j t i*

*<sup>T</sup>* <sup>0</sup>*ST* ,*<sup>p</sup>* Pr Pr

*Sk*,*<sup>p</sup>*

*S*

*U*

, *Ui <sup>S</sup> <sup>p</sup>*

 

as divided into two parts, which yields the following expression:

 

*X XX*

*S*

(1)

. The term on the left-hand side

*<sup>p</sup>* , specifies the source term of the

*<sup>p</sup>*

,*<sup>p</sup>* -

*T T*

*T Sc ScT* 

> *T k*

> > *T*

 

 *T*

*g p* (2)

,*p* " turbulence

equations for momentum and mass. Turbulence is modelled with the "*k-*

& Naguib, 1975) and only the main features are summarized here.

 

is the effective diffusion coefficient for quantity

*<sup>g</sup>* , specifies the source term of the gas and *S*

2 2 ( ) 3 3

 

*i ji*

*P k <sup>g</sup> X XX* 

*Yp* 0 , *Yk S <sup>p</sup>*

  1 - *S*

diffusion term and the source term, respectively.

*S*

*k G*

*C GC* 1 2 *<sup>k</sup>*

Table 2. Terms in the general form of the differential equation.

where

where *S*

particle.

*Ui*

The source term *S*

*<sup>i</sup>*

*U*

dynamics of a single droplet. Abramzon and Sirignano (1989) and Berlemont et al. (1995) presented droplet vaporization models for the case of a spray in stagnant surroundings, and showed that the convective effects were most relevant. The same type of configuration was studied by Chen and Pereira (1992), and the predictions were found to follow satisfactorily the measurements presented. More recently, Sommerfeld (1998) presented a study on stationary turbulent sprays, using a droplet evaporation model based on the model proposed by Abramzon and Sirignano (1989), and revealed a general good agreement with experiments.


Table 1. Characteristic properties of biofuels compared with n-Heptane and Diesel Fuel.

If special attention is dedicated to the biofuels injection and evaporation, then practically no numerical or experimental studies can be found. Recently Bai et al. (2002) presented a most relevant numerical study of a spray in wind tunnel using the Arcoumanis et al. (1997) experiments, but concentrated on the development of the spray impingement model and the fuel used was gasoline.
