**3. Results**

To assess the computational method two sources of experimental data were used for the case of a polydisperse spray with a co-axial flow at atmospheric pressure (Heitor & Moreira, 1994) or elevated pressures (Barros, 1997). The method yielded reasonable results and revealed capabilities to improve the knowledge of the particle dispersion phenomena in more complex configurations. An example of the results obtained is shown in Figure 2, and a more complete analysis can be found in previous publications (Barata et al., 1999; Barata & Silva, 2000). The method was then extended to the case of an evaporating spray in a crossflow, and the evaporation models used by Chen and Pereira (1992) and Sommerfeld (1998) were tested and compared with the present model (see Barata, 2005 for details).

Figure 3 presents a parallel projection of the droplet trajectories in the vertical plane of symmetry (X=0) for two volatile fuels: n-Heptane and Ethanol. The former is used to define the zero limit of the anti-knock (resistance to pre-ignition) quality of fuels, while the other can be used to increase the octane number of gasoline. The higher volatility level of Ethanol can be inferred from Fig.3b) by the more uniform distribution at the right side of the domain and the trajectories in the direction of the top wall (at Y=0.05m). Due to the high volatility level of both fuels the droplets are injected and start almost immediately to evaporate, which gives rise to smaller droplets that follow quite closely the gaseous flow. Further downstream of the injection point, the trajectories of the droplets of Ethanol are more directed downwards than those of n-Heptane due to the higher fuel density and higher latent heat of vaporization. As a consequence, although a colder region near the injector is observed with Ethanol, the domain shows in general a much more uniform temperature distribution.

Numerical Simulation of Biofuels Injection 115

Figure 4 shows the droplet temperature and diameter variation time for the different fuels and test conditions used in the present work that are summarized in Table 5. The horizontal part of the line of the temperature variation with time (Fig.4a) reveals the equilibrium of the evaporation process that corresponds to the horizontal part of the droplet diameter variation with time. It should be pointed out that since the droplet is moving in the direction of the Z coordinate (with the crossflow), the ambient temperature may not be constant, and the

> **D2 (m2**

Fig. 4. Droplet temperature (a) and diameter (b) variation with time (Wcross=10m/s and Vp=-

The Rapeseed Methyl Ester (RME) and the Diesel Fuel (DF-2) have a higher boiling temperature and do not attain the equilibrium temperature in the first 50miliseconds (Fig.5a). As a consequence of the "pre-heating period" (about 20miliseconds in Fig.4b) the droplets diameters remain approximately constant and the evaporation starts later (Fig.4b). Figure 5 shows parallel projections of the droplet trajectories in the vertical plane of symmetry, and confirms the main evaporation characteristics of the DF-2 and RME described in the previous paragraph. The pattern is similar for DF-2 and RME, although in the latter case there is a higher concentration of droplets in the core of the deflected monosize spray. This result is consistent with the slightly poorer evaporation characteristics of the RME deducted from Fig.5, and taking into account the average time that a droplet takes to reach the right hand side of the domain (at Z=0.3m) it is expected that its diameter would be (in average) at the exit of the channel about 92.2% of the initial diameter. So, in general the diameters of the droplets will be larger with DF-2 and RME, and the dispersion will be more difficult, because the slip between the gaseous phase and the dispersed phase will be more pronounced. Some collisions with the bottom wall are observed, but were not taken into account in the present study, although this phenomena has been investigated and

Increasing the injection temperature of RME improves the evaporation of the droplets, and a more uniform distribution is obtained (Fig.5c). As shown in Fig.4, to obtain the equilibrium stage of evaporation near the injection point a pre-heating of 150K is required, which will be

particularly difficult to implement in most of the practical situations.

2.5E-08

3E-08

3.5E-08

4E-08

**RME Tp+150K**

4.5E-08

5E-08

5.5E-08

**)**

**b)**

evolution of the droplet diameter with time is also influenced by its velocity.

**n-Heptane**

**Ethanol**

**Time (s)**

0 0.01 0.02 0.03 0.04 0.05

**RME**

**n-Heptane**

**DF-2**

**Ethanol**

**RME**

**Time (s)**

reported elsewhere (see Barata & Silva, 2005).

**RME Tp+150K**

**DF-2**

0 0.01 0.02 0.03 0.04 0.05

**T (k)**

**a)**

250

1m/s and Tp=293K).

300

350

400

450

500

Fig. 2. Radial profiles of the mean axial velocity, *U*, at X/D=0.2 (a), and 6.5 (b). Experiments (Heitor & Moreira, 1994): ● , 30-35m; ■ , 40-45m; , 60-65m; , gaseous phase. Predictions: , particles; \_\_\_\_\_\_ , gaseous phase.

Fig. 3. Parallel projection of droplet trajectories in the vertical plane of symmetry (X=0) for Wcross=10m/s, Vp=-1m/s and Tp=293K: (a) n-Heptane; (b) Ethanol.

**U (m/s)**

Fig. 2. Radial profiles of the mean axial velocity, *U*, at X/D=0.2 (a), and 6.5 (b). Experiments

(Heitor & Moreira, 1994): ● , 30-35m; ■ , 40-45m; , 60-65m; , gaseous phase.

**Injection point**

0

0 0.05 0.1 0.15 0.2 0.25

0 0.05 0.1 0.15 0.2 0.25

Fig. 3. Parallel projection of droplet trajectories in the vertical plane of symmetry (X=0) for

2

4

6

8

10

12 **b)**

**r (mm)**

0 10 20 30 40

**r (mm)**

0

0

**Z (m)**

Wcross=10m/s, Vp=-1m/s and Tp=293K: (a) n-Heptane; (b) Ethanol.

0.02

**Y (m)**

0.04

**Z (m)**

**Injection point**

0.02

**Y (m)**

0.04

**Crossflow**

**Crossflow**

**b)**

**a)**

Predictions: , particles; \_\_\_\_\_\_ , gaseous phase.

0 5 10 15

**U (m/s)**

0

2

4

6

8

10

12 **a)**

Figure 4 shows the droplet temperature and diameter variation time for the different fuels and test conditions used in the present work that are summarized in Table 5. The horizontal part of the line of the temperature variation with time (Fig.4a) reveals the equilibrium of the evaporation process that corresponds to the horizontal part of the droplet diameter variation with time. It should be pointed out that since the droplet is moving in the direction of the Z coordinate (with the crossflow), the ambient temperature may not be constant, and the evolution of the droplet diameter with time is also influenced by its velocity.

Fig. 4. Droplet temperature (a) and diameter (b) variation with time (Wcross=10m/s and Vp=- 1m/s and Tp=293K).

The Rapeseed Methyl Ester (RME) and the Diesel Fuel (DF-2) have a higher boiling temperature and do not attain the equilibrium temperature in the first 50miliseconds (Fig.5a). As a consequence of the "pre-heating period" (about 20miliseconds in Fig.4b) the droplets diameters remain approximately constant and the evaporation starts later (Fig.4b).

Figure 5 shows parallel projections of the droplet trajectories in the vertical plane of symmetry, and confirms the main evaporation characteristics of the DF-2 and RME described in the previous paragraph. The pattern is similar for DF-2 and RME, although in the latter case there is a higher concentration of droplets in the core of the deflected monosize spray. This result is consistent with the slightly poorer evaporation characteristics of the RME deducted from Fig.5, and taking into account the average time that a droplet takes to reach the right hand side of the domain (at Z=0.3m) it is expected that its diameter would be (in average) at the exit of the channel about 92.2% of the initial diameter. So, in general the diameters of the droplets will be larger with DF-2 and RME, and the dispersion will be more difficult, because the slip between the gaseous phase and the dispersed phase will be more pronounced. Some collisions with the bottom wall are observed, but were not taken into account in the present study, although this phenomena has been investigated and reported elsewhere (see Barata & Silva, 2005).

Increasing the injection temperature of RME improves the evaporation of the droplets, and a more uniform distribution is obtained (Fig.5c). As shown in Fig.4, to obtain the equilibrium stage of evaporation near the injection point a pre-heating of 150K is required, which will be particularly difficult to implement in most of the practical situations.

Numerical Simulation of Biofuels Injection 117

0

X Y

0

0

0.05 **X**

0

Tp=293oK; (b) RME, Tp=293oK, (c) RME, Tp=443oK.

0

0.05

X Y

**Y**

0.05 **X**

0.180 0.150 0.120 0.090 0.060 0.030 0.005

**YF**

**c)**

0.05

**Y**

0.05 **X**

0.180 0.150 0.120 0.090 0.060 0.030 0.005

**YF**

**b)**

0

0

0

Z

0

Z

Z

0.05

0.05

0.05

Fig. 6. Mass fraction distribution for Wcross=10m/s and Vp=-1m/s: (a) Diesel fuel (DF-2),

0.1

0.1

0.1

0.15

0.15

0.15

**Z**

**Z**

**Z**

0.2

0.2

0.2

**RME Tp=443<sup>o</sup>**

0.25

**DF-2**

0.25

**RME**

0.25

**K**

0.05

0.180 0.150 0.120 0.090 0.060 0.030 0.005

**YF**

**a)**

X Y

**Y**

Fig. 5. Parallel projection of droplet trajectories in the vertical plane of symmetry (X=0) for Wcross=10m/s and Vp=-1m/s and Tp=293K.: (a) Diesel fuel (DF-2), Tp=293K; (b) RME, Tp=293K, (c) RME, Tp=443K.

0 0.05 0.1 0.15 0.2 0.25

0 0.05 0.1 0.15 0.2 0.25

0 0.05 0.1 0.15 0.2 0.25

Fig. 5. Parallel projection of droplet trajectories in the vertical plane of symmetry (X=0) for Wcross=10m/s and Vp=-1m/s and Tp=293K.: (a) Diesel fuel (DF-2), Tp=293K; (b) RME,

0

0

0

**Z (m)**

0.02

**Y (m)**

0.04

**Z (m)**

**Injection point**

0.02

**Y (m)**

0.04

**Z (m)**

**Injection point**

**Injection point**

0.02

**Y (m)**

0.04

**Crossflow**

**Crossflow**

**Crossflow**

Tp=293K, (c) RME, Tp=443K.

**c)**

**b)**

**a)**

Fig. 6. Mass fraction distribution for Wcross=10m/s and Vp=-1m/s: (a) Diesel fuel (DF-2), Tp=293oK; (b) RME, Tp=293oK, (c) RME, Tp=443oK.

Numerical Simulation of Biofuels Injection 119

in many applications that utilize diffusion flames. The use of RME in homogeneous combustion systems may require a prohibitive level of pre-heating, and the use of Ethanol

The present work has been performed in the scope of the activities of the AFTUR project. The financial support of the European Commission under Contract nº ENK5-CT-2002-00662

Abramzon, B. and Sirignano, W.A., Droplet Vaporization Model for Spray Combustion Calculations, *Int. J. Heat Mass Transfer*, vol.12, no.9, 1989, pp.1605-1648. Arcoumanis, C., Whitelaw, D.S. and Whitelaw, J.S., "Gasoline Injection against Surfaces and

Bai, C.X., Rusche, H. and Gosman, "Modeling of Gasoline Spray Impingement", *Atomization* 

Barata, J.M.M., Lopes, P.N.S.D. and Perestrelo, N.F.F., "Numerical Simulation of

Barata, J.M.M. and Silva, A.R.R., "Numerical Study of Spray Dispersion in a Premixing

Barata, J.M.M. and Silva, A.R.R., "The Impingement of a Deflected Spray". Eighth

Barros, A., "Projecto e Construção de um Labotatório de Atomização a Alta Pressão", MSc

Berlemont, A., Grancher, M.S. and Gouebet, G., Heat and Mass Transfer Coupling Between

Chen, X.Q., and Pereira, J.C.F., "Numerical Prediction of Nonevaporating and Evaporating

Faeth, G. M., "Current Status of Droplet and Liquid Combustion", *Prog. Energy Combust. Sci.*,

Faeth, G. M., "Evaporation and Combustion of Sprays", *Prog. Energy Combust. Sci.*, vol. 9,

Faeth, G. M., "Mixing, Transport and Combustion in Sprays", *Prog. Energy Combust. Sci.*, vol.

Faeth, G. M., "Spray Combustion Phenomena", Twenty-Sixth Symposium (International) on

Godsave, G. A. E., "Studies of the Combustion of Drops in a Fuel Spray-the Burning of

Single Drops of Fuel, Fourth Symposium (international) on Combustion". Williams

Combustion/The Combustion Institute, 1996/pp. 1593-1612.

Polydisperse Two-Phase Turbulent Jets". AIAA Paper 99-3760, 30th AIAA Fluid

Chamber for Low-NOx Engines". Millennium International Symposium on

International Conference on Energy for a Clean Environment, Lisbon, Portugal, 27-

Vaporizing Droplets and Turbulence Using a Lagrangian Approach, *Int. J. Heat and* 

Fuels Sprays Under Nonreactive Conditions", *Atomization and Sprays*, Vol.2, 1992,

(obtained from sugar or starch crops) may be a better alternative.

Films, Atomization and Sprays, vol.7, pp.437-456, 1997.

Dynamics Conference, Norfolk, VA, 28 June-1 July, 1999.

Thesis, *Instituto Superior Técnico*, Lisbon, December, 1997.

*Mass Transfer*, vol.38, no.17, 1995, pp.3023-3034.

& Wilkins, Baltimore, 1953, pp. 818-830.

Thermal and Fluid Sciences, Xi'an, China, 18-22 September, 2000.

*and Sprays*, vol.12, pp.1-27, 2002.

**5. Aknowledgements** 

is gratefully acknowledged.

30 June, 2005.

pp.427-443.

1983, pp. 1-76.

Vol. 3, 1977, pp. 191-224.

13, 1987, pp. 293-345.

**6. References** 


Table 5. Summary of test conditions.

The evaporative characteristics of RME can be further analysed with the help of Fig.6 that shows a three-dimensional perspective of the mass fraction distribution with and without additional pre-heating. The results obtained with DF-2 and RME without additional preheating (Figs.6a and b) show that the mass fraction of fuel is always less than 0.04. For the DF-2 there is a larger evaporation near the injector, but further downstream the RME gives the higher values. When the additional pre-heating of 150K is used with RME, the domain shows a large region with a concentration of fuel vapour greater than 0.06, and the resulting pattern is quite similar to those obtained with more volatile fuels such as n-Heptane or Ethanol.
