0 2 4 6
0 20 40 60 80
SMD ( μ m)
Air/liquid ratio (ALR)
Rizk and Lefebvre Lorenzetto and Lefebvre PDA-centerline
PDA-maximum flux PDA-Average y=50 mm
Figure 5.7: Comparison of the PDA-derived SMD measurements against the empirically-correlated values for diesel fuel.
The PDA-derived data for the profile of 50 mm downstream of spray outlet are compared to the empirical values derived from correlations developed by Lorenzetto and Lefebvre [2] and Rizk and Lefebvre [3]. The PDA data are presented in three forms;
(i) the centreline droplet SMD value, (ii) the droplet SMD value at the location of
Non-reacting spray results maximum flux and (iii) the averaged droplet SMD of the radial profile. The equation developed by Lorenzetto and Lefebvre is
( )
0.33 1.70 2 0.5 1.732 0.37 0.3
1 1
0.95 L L 1 0.13 L o 1
L A R L L
W d
D U ALR ALR
σ μ
ρ ρ σ ρ
⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞
= ⎢⎢⎣ ⎥⎥⎦⎜⎝ + ⎟⎠ + ⎜⎝ ⎟⎠ ⎜⎝ + ⎟⎠ (4.1)
where D32 is Sauter mean diameter, σ is surface tension, μ is dynamic viscosity, W is the mass flow rate, ρ is the density, UR is the relative velocity, do is the liquid orifice diameter whilst the subscript A and L represent air and liquid respectively. The SMD correlation was derived from low viscosity liquids and the SMD is independent of the initial jet diameter, do. Rizk and Lefebvre [3] developed an equation for SMD using a light scattering technique. The SMD correlation is expressed as
σ μ
ρ σρ
⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞
= ⎜ ⎟ ⎜ + ⎟ + ⎜ ⎟ ⎜ + ⎟
⎝ ⎠ ⎝ ⎠
⎝ ⎠ ⎝ ⎠
0.4 0.4 2 0.5
32
2
1 1
0.48 1 0.15 L 1
o A R o L o
D
d U d ALR d ALR (4.2)
where ALR represents the atomizing air-to-liquid ratio. Comparison of the PDA-measured droplet SMD values with the empirical values is shown in Fig. 5.7. In general, the global trend shows that droplet size decreases with increasing ALR. The PDA-derived droplet SMD values at the centreline of the profile demonstrate the power dependence of -0.55 on ALR, (D32 α ALR-0.55), while the droplet SMD at the location of
the maximum volume flux shows the power dependence of -0.78 on ALR (D32 α ALR-0.78). The SMD values at the location of maximum volume flux shows good
agreement when compared to the droplet SMD values derived from the equation by Lorenzetto and Lefebvre [2], except for ALR = 1 which shows the lower PDA-derived droplet SMD by a factor of 2.4. The droplet SMD values obtained by averaging the radial profile of droplet SMD at location y = 50 mm shows a negative power dependence of -0.85 to ALR (D32 α ALR-0.85). The SMD values are in good agreement with the empirical values predicted from the correlation by Lorenzetto and Lefebvre for ALR = 2 and above, but the droplet SMD is overpredicted at ALR = 1 by a factor of 2.
Comparison to the correlated values of Rizk and Lefebvre [3] shows a systematic lower droplet SMD values across the whole ALR range.
It is noted that the empirical correlations developed using atomizers that are not completely geometrically similar to the present atomizer. Differences in atomizer
Non-reacting spray results configuration such as the angle at which the atomizing air impinges on the liquid jet could have significant influence on the spray atomization. Besides, the empirical correlations were derived from light scattering technique that does not elucidate the information of droplet distribution spatially. Instead, the ensemble droplets in the spray structure including the larger droplets at far downstream were averaged. The current PDA method measures the droplets velocity and size distribution at each spatial location within the spray. Despite the difference in measurement method, the empirical correlation and PDA-derived data are able to show the droplet SMD trend in relation to ALR. The advantage of PDA measurement method is that detailed information such as the spatial and pdf distribution of the spray droplets can be obtained.
0 2 4 6
0 15 30 45 60
Axial velocity (m/s)
Air-to-liquid mass ratio (ALR) (a)
y=30 mm y=50 mm
0 2 4 6
0 5 10 15 20
SMD (μm)
Air-to-liquid mass ratio (ALR)
(b) y=30 mm
y=50 mm
Figure 5.8: The diesel fuel droplets (a) axial velocity and (b) SMD values as a function of ALR at the centreline of 30 and 50 mm downstream of the atomizer outlet.
The measured droplet mean axial velocity at the spray centreline (x = 0 mm) and downstream axial locations (y = 30 and 50 mm) from the nozzle tip as a function of ALR is shown in Fig. 5.8a. The droplet velocity at the spray centreline shows a linear relation to ALR for both axial positions. The increase of ALR results in higher relative velocity, which translates into higher droplet momentum from the nozzle outlet.
The droplet velocity decreases from position y = 30 mm to downstream y = 50 mm due to the loss of momentum, and deceleration of droplets is highest for ALR = 6. The corresponding droplet SMD values are shown in Fig. 5.8b. Droplet SMD values exhibit negative power dependence to ALR. At ALR = 1 and 2, the droplet SMD values at axial location y = 30 mm is lower than those at y = 50 mm downstream, For ALR = 6,
Non-reacting spray results the droplets at y=50 mm is smaller than those at y = 30 mm downstream, which suggests secondary droplet breakup due to the sufficiently high shear force imposed on the gas and liquid. Similar droplet SMD values at the centreline of y=30 and 50 mm is observed for ALR = 4.
The droplet SMD values as a function of Weber number at the radial position where the maximum volume flux and droplets concentration locations are shown in Fig.
5.9a and 5.9b respectively. In general, the trend shown in both cases is rather similar.
At We1/2 < 50 which corresponds to ALR < 3, the droplet SMD values show an increase of ~ 2-3 µm as the droplets travel downstream from the axial location of y = 30 mm to 50 mm. For We1/2 > 50, the reverse is observed where the droplet SMD values at downstream location 50 mm is lower than those at 30mm. According to the airblast atomizer breakup regimes proposed by Lasheras and Hopfinger [7] as shown in Fig. 4.3, Chapter 4, the current atomizer exhibits fiber-type breakup due to the high Weber number of We1/2 > 25. At ALR=1, atomization occurs at the membrane-type regime which explains the formation of large droplets as shown in Fig. 5.1.
0 25 50 75 100
0 10 20 30 40
SMD (μm)
We1/2 (a)
Location-volume flux peak
y=30 mm y=50 mm
0 25 50 75 100
0 10 20 30 40 50
SMD (μm)
We1/2 (b)
Location-droplet concentration peak
y=30 mm y=50 mm
Figure 5.9: The SMD values of diesel fuel droplets at the position of (a) maximum volume flux (b) maximum droplet concentration as a function of Weber number.
Non-reacting spray results