In this device, the size of the spray particle is mainly determined by the pressure of the air source and the structure of the nozzle. The nebulization principle is as follows: two liquid reagents collide at a certain angle at the intersection of channels, and meanwhile, the high-speed airflow impinges on the liquid reagent to form nebulized particles and eject out from the nozzle.
The high-speed airflow has a crucial influence on the size of the spray particles. In order to generate high-speed airflow, the nozzle outlet is designed to be a Laval structure. Laval structure consists of three parts: contraction section, throat section and expansion section16, 17. Driven by pressure, the low-speed airflow from the contraction section reaches the throat section. The gas flow velocity will be greatly increased due to the significant reduction of the throat diameter18–20. The structure of the Laval nozzle is shown in Fig. 1c. Different structural parameters and air source pressures result in different air velocities, which affect particle size and injection velocity. Thus, the various parameters that affect the nebulization results will be studied in detail in the following section.
3.1 Influence of Laval nozzle structure on spray particle size
The diameter of the central tube d0 is a constant value, which is determined by the size of the air connector. Here, d0 is set to 3 mm. Structure parameters that affect the nebulization result of the Laval nozzle mainly includes: semi-cone angle of contraction section (α), throat diameter (d1), throat length (Lh), reagent outlet diameter (d2), reagent outlet angle (γ), semi-cone angle of expansion section (β). In order to analyze the influence of the six parameters on the nebulization result, the orthogonal experimental method is adopted. Five levels for each parameter and \({\text{L}}_{25}({5}^{6})\)orthogonal table are used for the experimental test.
According to experience, the semi-cone angle of contraction section α is generally assumed to be 30°21. The semi-cone angle of expansion section β is in the range of 8° ~ 15°22. Theoretically, the larger the ratio of central pipe diameter d0 to throat diameter d1 is, the better to nebulization23. As long as the cross sections of the contraction section and expansion section are smooth, the throat length Lh can be 021. Combined with the actual situation of nasal spray vaccination, the 5 levels selected for each parameter are shown in Table 1.
Table 1
Structural factors and levels of Laval nozzle
level
|
factors
|
α/°
|
d1/mm
|
Lh/mm
|
d2/mm
|
γ/°
|
β/°
|
1
|
20
|
0.4
|
0.1
|
0.1
|
55
|
8
|
2
|
25
|
0.5
|
0.2
|
0.15
|
60
|
10
|
3
|
30
|
0.6
|
0.3
|
0.2
|
65
|
12
|
4
|
35
|
0.7
|
0.4
|
0.25
|
70
|
14
|
5
|
40
|
0.8
|
0.5
|
0.3
|
75
|
16
|
The orthogonal experiment is carried out with the diameter of spray particles as the test index. The nebulization diameter of the particles is measured by laser particle size analyzer (Winner311-XP, Jinan Micro and Nano Particle Instrument Co., Ltd.). The analyzer can measure particles with a diameter of 0.1~100um, and the measurement error is less than 1%. During the test, the nozzle outlet is kept close to the test tube of the laser particle size analyzer. Experimental diagram is shown in Figure 2. Water is used as the nebulization reagent and the outlet pressure of the nitrogen cylinder is set to 2 bar. The spray particle diameter when the volume fraction of the nebulized particles reaches 50% (Xv50) was taken as the recorded value. The orthogonal experiment results are shown in Table 2.
Table 2
The orthogonal test results
No.
|
A
|
B
|
C
|
D
|
E
|
F
|
Xv50/um
|
α/°
|
d1/mm
|
Lh/mm
|
d2/mm
|
γ/°
|
β/°
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
25.36
|
2
|
1
|
2
|
2
|
2
|
2
|
2
|
23.15
|
3
|
1
|
3
|
3
|
3
|
3
|
3
|
25.89
|
4
|
1
|
4
|
4
|
4
|
4
|
4
|
24.55
|
5
|
1
|
5
|
5
|
5
|
5
|
5
|
26.76
|
6
|
2
|
1
|
2
|
3
|
4
|
5
|
17.75
|
7
|
2
|
2
|
3
|
4
|
5
|
1
|
21.05
|
8
|
2
|
3
|
4
|
5
|
1
|
2
|
23.49
|
9
|
2
|
4
|
5
|
1
|
2
|
3
|
22.60
|
10
|
2
|
5
|
1
|
2
|
3
|
4
|
29.56
|
11
|
3
|
1
|
3
|
5
|
2
|
4
|
24.24
|
12
|
3
|
2
|
4
|
1
|
3
|
5
|
14.27
|
13
|
3
|
3
|
5
|
2
|
4
|
1
|
17.73
|
14
|
3
|
4
|
1
|
3
|
5
|
2
|
31.61
|
15
|
3
|
5
|
2
|
4
|
1
|
3
|
30.91
|
16
|
4
|
1
|
4
|
2
|
5
|
3
|
13.81
|
17
|
4
|
2
|
5
|
3
|
1
|
4
|
16.75
|
18
|
4
|
3
|
1
|
4
|
2
|
5
|
18.83
|
19
|
4
|
4
|
2
|
5
|
3
|
1
|
31.41
|
20
|
4
|
5
|
3
|
1
|
4
|
2
|
29.93
|
21
|
5
|
1
|
5
|
4
|
3
|
2
|
26.50
|
22
|
5
|
2
|
1
|
5
|
4
|
3
|
24.67
|
23
|
5
|
3
|
2
|
1
|
5
|
4
|
16.61
|
24
|
5
|
4
|
3
|
2
|
1
|
5
|
24.72
|
25
|
5
|
5
|
4
|
3
|
2
|
1
|
35.53
|
K1
|
125.70
|
107.65
|
130.03
|
108.78
|
121.23
|
131.08
|
∑K = 597.68
|
K2
|
114.45
|
99.90
|
119.83
|
108.96
|
124.35
|
134.67
|
K3
|
118.76
|
102.55
|
125.83
|
127.52
|
127.63
|
117.89
|
K4
|
110.73
|
134.88
|
111.65
|
121.84
|
114.62
|
111.71
|
K5
|
128.03
|
152.70
|
110.34
|
130.57
|
109.85
|
102.33
|
R
|
17.30
|
52.79
|
19.68
|
21.79
|
17.78
|
32.34
|
—
|
As can be seen from Table 2, the max factors difference R of each factor from largest to smallest is B, F, D, C, E, and A, d1 (throat diameter) has the greatest effect on the spray particle diameter Xv50, β (semi-cone angle of expansion section) is second, while d2 (reagent outlet diameter), γ (reagent outlet angle) and Lh (throat length), α (semi-cone angle of contraction section) has less influence. The results of the orthogonal experiment indicate that the optimal solution is A4B2C5D1E5F5, that is: α = 35°, d1 = 0.5mm, Lh =0.5mm, d2 = 0.1mm, γ = 75°, β = 16°.
3.2 Influence of Laval nozzle structure on spray velocity
For nasal spray vaccination, the high spray velocity is easy to cause nasal discomfort of the vaccinate people. Therefore, it is better to reduce the rate of spraying while ensuring the efficiency of vaccination. According to the principle of Laval nozzle, throat diameter d1 plays a crucial role in the spray velocity. According to the results of the orthogonal experiments in Table 2, it is clear that the throat diameter d1 has a significant effect on the nebulized particle diameter Xv50. However, the results of K2 and K3 of throat diameter d1 (factor B) are 99.90 and 102.55, respectively. These two values are very close. Therefore, for the two cases of d1 = 0.5mm and d1 = 0.6mm, finite element simulation was used to analyze their spray velocity.
The κ-ε model of COMSOL software is used to simulate the supersonic airflow in the Laval nozzle. Since the gas flow rate determines the spray velocity, only the gas flow field distribution is simulated and the air velocity is used to represent the spray velocity. In the model, the liquid channel is removed and the pressure of the airflow inlet is set to 2bar. The simulation results are shown in Fig. 3. As can be seen from the figure, the maximum airflow velocity of these two Laval nozzles is 495m/s and 480m/s, respectively. The maximum velocities all appear at the position of the expansion section, and then the airflow velocity drops rapidly. Since too high a spray rate would reduce the comfort of the vaccinator, d1 = 0.6 mm was selected as the preferred option based on the simulation results.
3.3 Influence of Laval nozzle structure on spray angle
To facilitate the nasal spray vaccine into nostril, the angle of the spray nozzle should be as small as possible. Among the related parameters of the Laval nozzle structure, the semi-cone angle of expansion section β is the main parameter that causes the change of spray angle. For investigating the spraying angle for different β, the spray angles for Laval nozzles with β of 8°, 10°, 12°, 14° and 16° are measured by photographing. According to the univariate principle, the other parameters of the nozzle are unified as follows: d0 = 3 mm, α = 35°, d1 = 0.6mm, Lh=0.5mm, d2 = 0.1mm, γ = 75°. The air source pressure is 2bar. The test results are shown in Fig. 4.
As can be seen from the pictures, there is no significant change in the spray angle when the β is changed from 8° to 16°. The spray angle is all about 15°. It is small enough for the nasal spray vaccine to get into nostril as the nozzle is close to the nostril when vaccinating.
Based on the results above, the optimal Laval nozzle parameters are selected as follows: d0 = 3 mm, α = 35°, d1 = 0.6mm, Lh=0.5mm, d2 = 0.1mm, γ = 75°, β = 16°. The following tests use the Laval nozzle with these structural parameters.