ULTRASONIC NOZZLE FOR USE IN METALLURGICAL INSTALLATIONS AND METHOD FOR DIMENSIONING A ULTRASONIC NOZZLE
An ultrasonic nozzle for use in metallurgical installations, in particular for the top blowing of oxygen in a Basic Oxygen Furnace (BOF) or an electric arc furnace (EAF), has a convergent portion and a divergent portion, which are adjacent to each other at a nozzle throat, wherein the ultrasonic nozzle is defined by the following group of nozzle forms in a respective design case: Radius in Volumetric flow narrowest cross- Outlet max. nozzle Pressure rate V 0 in Nm/ section r* in mm radius r e length 1 p 0 in bar min (throat) in mm in mm 4 20 12.0 14.0 50 ± 20 4 200 39 44.0 160 ± 20 14 20 6 10.0 50 ± 20 14 200 21 33.0 160 ± 20.
1 . A supersonic bell-shaped nozzle for use in metallurgical installations, such as a basic oxygen furnace (BOF), argon oxygen decarburization (AOD) converter, and electric arc furnace (EAF), with a convergent portion and a divergent portion which are adjacent to each other at a nozzle throat (DK), characterized in that an inside contour of the supersonic nozzle corresponds to a contour determined numerically with a modified Method of Characteristics, and the supersonic nozzle is defined by the following group of nozzle shapes in their respective design case:
Radius in
Volumetric flow
narrowest cross-
Outlet
max. nozzle
Pressure
rate V 0 in Nm/
section r* in mm
radius r e
length 1
p 0 in bar
min
(throat)
in mm
in mm
4
20
12.0
14.0
50 ± 20
4
200
39
44.0
160 ± 20
14
20
6
10.0
50 ± 20
14
200
21
33.0
160 ± 20
wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r*, i.e. l/r* is between 2.1 and 11.6.
2 . The supersonic nozzle pursuant to claim 1 , wherein the convergent portion comprises a bell-shaped contour and the divergent portion comprises a bell-shaped contour, wherein the bell-shaped contours of the convergent portion and of the divergent portion are uniformly merging into one another at the nozzle throat.
3 . The supersonic nozzle pursuant to claim 1 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 8.3.
4 . The supersonic nozzle pursuant to claim 3 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 5.4.
5 . The supersonic nozzle pursuant to claim 4 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 5.
6 . The supersonic nozzle pursuant to claim 1 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is 11.6, 8.3, 5.4, 5.0, 4.8, 4.2, 3.6, 3.3, 3.1, or 2.1.
7 . A supersonic bell-shaped nozzle for use in metallurgical installations, such as basic oxygen furnace (BOF), argon oxygen decarburization (AOD) converter, and electrical arc furnace (EAF), characterized in that a inside contour of the supersonic nozzle corresponds to the contour determined numerically with a modified Method of Characteristics, and by a following dimensioned interior contour in following design cases:
wherein x is an axial coordinate and a radial coordinate
Inlet pressure p 0 = 10 bar
Volumetric Inlet flow rate
V 0 = 50 Nm 3 /min
Ambient pressure p u =
1.013 bar
With
Without
boundary
boundary
layer
layer
correction
correction
x in mm
r in mm
r in mm
−17.32
16.68
16.66
−16.77
16.66
16.63
−16.22
16.62
16.59
−15.67
16.57
16.53
−15.12
16.51
16.46
−14.57
16.43
16.38
−14.03
16.34
16.29
−13.48
16.24
16.18
−12.93
16.13
16.06
−12.38
16.00
15.93
−11.83
15.86
15.79
−11.28
15.70
15.63
−10.73
15.54
15.46
−10.18
15.35
15.27
−9.63
15.16
15.07
−9.08
14.96
14.87
−8.53
14.76
14.67
−7.98
14.57
14.47
−7.43
14.37
14.27
−6.88
14.17
14.07
−6.33
13.98
13.87
−5.78
13.78
13.67
−5.23
13.58
13.47
−4.69
13.38
13.27
−4.14
13.19
13.07
−3.59
13.01
12.89
−3.04
12.88
12.74
−2.49
12.73
12.61
−1.94
12.64
12.51
−1.39
12.56
12.44
−0.84
12.52
12.39
−0.29
12.49
12.36
0.26
12.49
12.36
0.81
12.50
12.36
1.36
12.52
12.38
1.91
12.54
12.39
2.46
12.57
12.42
3.01
12.60
12.45
3.56
12.64
12.49
4.11
12.69
12.53
4.65
12.74
12.58
5.20
12.80
12.63
5.75
12.87
12.69
6.30
12.94
12.76
6.85
13.02
12.83
7.40
13.10
12.91
7.95
13.18
12.98
8.50
13.27
13.07
9.05
13.36
13.16
9.60
13.44
13.24
10.15
13.53
13.32
10.70
13.62
13.41
11.25
13.71
13.49
11.80
13.80
13.58
12.35
13.89
13.87
12.90
13.98
13.75
13.46
14.07
13.64
13.99
14.16
13.92
14.54
14.24
14.00
15.09
14.33
14.09
15.64
14.42
14.17
16.19
14.50
14.25
16.74
14.59
14.33
17.29
14.67
14.41
17.84
14.76
14.49
18.39
14.84
14.57
18.94
14.92
14.65
19.49
15.00
14.73
20.04
15.08
14.80
20.59
15.16
14.68
21.14
15.23
14.95
21.69
15.31
15.02
22.24
15.39
15.10
22.78
15.48
15.17
23.33
15.53
15.24
23.88
15.60
15.30
24.43
15.67
15.37
24.98
15.74
15.44
25.53
15.81
15.50
26.08
15.88
15.56
26.63
15.94
15.62
27.18
16.01
15.89
27.73
16.07
15.74
28.26
16.13
15.80
28.83
16.19
15.86
29.38
16.26
15.92
29.93
16.31
15.97
30.48
16.37
16.02
31.03
16.42
16.08
31.58
16.48
16.13
32.12
16.53
16.18
32.67
16.58
16.22
33.22
16.63
16.27
33.77
16.68
16.32
34.32
16.73
16.36
34.87
16.78
16.41
35.42
16.82
16.45
35.97
16.87
16.49
36.52
16.91
16.53
37.07
16.96
16.57
37.62
17.00
16.60
38.17
17.04
16.64
38.72
17.08
16.68
39.27
17.11
16.71
39.82
17.15
16.74
40.37
17.18
16.78
40.92
17.22
16.81
41.46
17.25
16.84
42.01
17.28
16.86
42.56
17.32
16.89
43.11
17.34
16.92
43.56
17.37
16.94
44.21
17.40
16.97
44.76
17.43
16.99
46.31
17.45
17.01
45.86
17.46
17.03
46.41
17.50
17.05
46.96
17.53
17.07
47.51
17.55
17.09
48.06
17.57
17.11
48.61
17.59
17.13
49.16
17.61
17.14
49.71
17.62
17.16
50.26
17.64
17.17
50.80
17.66
17.18
51.35
17.67
17.19
51.90
17.69
17.21
52.45
17.70
17.22
53.00
17.71
17.23
53.55
17.73
17.23
54.10
17.74
17.24
54.65
17.75
17.25
55.20
17.76
17.26
55.76
17.77
17.26
56.30
17.78
17.27
56.85
17.78
17.27
57.40
17.79
17.28
57.95
17.80
17.28
58.50
17.80
17.28
59.05
17.81
17.29
59.60
17.81
17.29
60.14
17.82
17.29
60.69
17.82
17.29
61.24
17.83
17.29
61.79
17.83
17.29
8 . A supersonic bell-shaped nozzle for use in metallurgical installations, such as basic oxygen furnace (BOF), argon oxygen decarburization (AOD) converter, electrical arc furnace (EAF), characterized in that an inside contour of the supersonic nozzle corresponds to a contour determined numerically with a modified Method of Characteristics, and by a following dimensioned interior contour in following design cases:
Inlet pressure p 0 = 12 bar
Volumetric Inlet flow rate
V 0 = 140 Nm 3 /min
Ambient pressure p u = 1.013 bar
With
Without
boundary
boundary
layer
layer
correction
correction
x in mm
r in mm
r in mm
−27.00
25.49
25.47
−26.44
25.48
25.45
−26.87
25.46
25.42
−25.30
25.42
25.38
−24.74
25.38
25.33
−24.17
25.33
25.27
−23.60
25.27
25.21
−23.03
25.20
25.14
−22.47
25.12
25.06
−21.90
25.04
24.96
−21.33
24.94
24.87
−20.76
24.83
24.76
−20.20
24.72
24.64
−19.63
24.60
24.51
−19.06
24.47
24.38
−18.50
24.32
24.23
−17.99
24.17
24.08
−17.36
24.01
23.91
−16.79
23.84
23.74
−16.23
23.68
23.56
−15.66
23.47
23.36
−15.09
23.27
23.16
−14.53
23.07
22.95
−13.96
22.86
22.75
−13.39
22.66
22.54
−12.82
22.46
22.33
−12.26
22.25
22.13
−11.69
22.05
21.92
−11.12
21.85
21.71
−10.56
21.64
21.51
−9.99
21.44
21.30
−9.42
21.23
21.09
−8.85
21.03
20.69
−8.29
20.83
20.68
−7.72
20.62
20.46
−7.15
20.42
20.27
−6.59
20.21
20.06
−6.02
20.02
19.86
−5.45
19.84
19.68
−4.88
19.68
19.52
−4.32
19.54
19.38
−3.75
19.41
19.25
−3.18
19.31
19.15
−2.62
19.22
19.06
−2.05
19.15
18.99
−1.48
19.10
18.94
−0.91
19.07
18.90
−0.35
19.06
18.88
0.22
19.06
18.88
0.79
19.06
18.88
1.35
19.07
18.89
1.92
19.09
18.90
2.49
19.11
18.92
3.06
19.13
18.94
3.62
19.16
18.96
4.19
19.19
18.99
4.76
19.23
19.03
5.32
19.27
19.06
5.89
19.32
19.11
6.46
19.37
19.15
7.03
19.42
19.20
7.59
19.48
19.26
8.16
19.54
19.32
8.73
19.61
19.38
9.29
19.68
19.45
9.86
19.76
19.52
10.43
19.84
19.60
11.00
19.92
19.68
11.56
20.01
19.76
12.13
20.10
19.85
12.70
20.20
19.94
13.26
20.29
20.03
13.83
20.39
20.12
14.40
20.48
20.22
14.97
20.58
20.31
15.53
20.68
20.41
16.10
20.78
20.50
16.67
20.88
20.60
17.23
20.98
20.69
17.80
21.08
20.79
18.37
21.18
20.89
18.94
21.28
20.98
19.50
21.38
21.08
20.07
21.48
21.18
20.64
21.58
21.27
21.21
21.68
21.37
21.77
21.78
21.47
22.34
21.88
21.56
22.91
21.97
21.66
23.47
22.07
21.75
24.04
22.17
21.85
24.61
22.27
21.94
26.18
22.37
22.03
25.74
22.46
22.13
26.31
22.56
22.22
26.88
22.65
22.31
27.44
22.75
22.40
28.01
22.84
22.50
28.58
22.94
22.59
29.16
23.03
22.68
29.71
23.12
22.77
30.28
23.21
22.85
30.85
23.31
22.94
31.41
23.40
23.03
31.98
23.49
23.12
32.56
23.58
23.20
33.12
23.65
23.29
33.68
23.75
23.37
34.25
23.84
23.45
34.82
23.92
23.54
35.36
24.01
23.62
35.95
24.09
23.70
36.52
24.18
23.76
37.09
24.26
23.86
37.65
24.34
23.94
38.22
24.42
24.02
38.79
24.51
24.09
39.35
24.58
24.17
39.92
24.66
24.25
40.49
24.74
24.32
41.06
24.82
24.40
41.62
24.90
24.47
42.19
24.97
24.54
42.76
25.05
24.61
43.32
25.12
24.68
43.89
25.19
24.75
44.46
25.26
24.82
45.03
25.34
24.89
45.59
25.41
24.96
46.16
25.48
25.02
46.79
25.55
25.09
47.29
25.61
25.15
47.86
25.68
25.22
48.43
25.75
25.28
49.00
25.81
25.34
49.56
25.88
25.40
50.13
25.94
25.46
50.70
26.00
25.52
51.26
26.07
25.58
51.89
26.13
25.64
52.40
26.19
25.70
52.97
26.25
25.75
53.53
26.30
25.81
54.10
26.36
25.86
54.67
26.42
25.92
55.23
26.48
25.97
55.60
26.53
26.02
56.37
26.59
26.07
56.94
26.64
26.12
57.50
26.69
26.17
58.07
26.74
26.22
58.64
26.60
26.27
59.20
26.85
26.32
59.77
26.90
26.36
60.34
26.94
26.41
60.91
26.99
26.45
61.47
27.04
26.50
62.04
27.09
26.54
62.61
27.13
26.58
63.18
27.18
26.63
63.74
27.22
26.67
64.31
27.26
26.71
64.88
27.31
26.75
65.44
27.35
26.78
66.01
27.39
26.82
66.56
27.43
26.86
67.15
27.47
26.90
67.71
27.51
26.93
68.28
27.55
26.97
68.85
27.58
27.00
69.41
27.62
27.03
69.98
27.66
27.07
70.55
27.69
27.10
71.12
27.73
27.13
71.68
27.76
27.16
72.25
27.79
27.19
72.82
27.82
27.22
73.38
27.86
27.25
73.95
27.89
27.27
74.52
27.92
27.30
75.09
27.95
27.33
75.65
27.97
27.35
76.22
28.00
27.38
76.79
28.03
27.40
77.35
28.06
27.43
77.92
28.08
27.45
78.49
28.11
27.47
79.06
28.13
27.49
79.62
28.16
27.51
80.19
28.18
27.53
80.76
28.20
27.55
81.32
28.23
27.57
81.89
28.25
27.59
82.46
28.27
27.61
83.03
28.29
27.63
83.59
28.31
27.64
84.16
28.33
27.66
84.79
28.35
27.69
85.29
28.37
27.69
85.86
28.38
27.70
86.43
28.40
27.72
87.00
28.42
27.73
87.56
28.43
27.74
88.13
28.45
27.76
88.70
28.46
27.77
89.26
28.48
27.78
89.83
28.49
27.79
90.40
28.50
27.80
90.97
28.52
27.81
91.53
28.53
27.82
92.10
28.54
27.83
92.67
28.55
27.84
93.23
28.56
27.84
93.80
28.57
27.85
94.37
28.58
27.86
94.94
28.59
27.86
95.50
28.60
27.87
96.07
28.61
27.88
96.64
28.62
27.88
97.20
28.62
27.89
97.77
28.63
27.89
98.34
28.64
27.89
98.91
28.64
27.90
99.47
28.65
27.90
100.04
28.66
27.90
100.61
28.66
27.91
101.17
28.67
27.91
101.74
28.67
27.91
102.31
28.67
27.91
102.88
28.68
27.91
103.44
28.68
27.91
104.01
28.69
27.91
104.58
28.69
27.92
105.14
28.69
27.92
105.71
28.69
27.92
9 . A supersonic bell-shaped nozzle for use in metallurgical installations, such as basic oxygen furnace (BOF), argon oxygen decarburization (AOD) converter electric arc furnace (EAF), with a convergent portion and a divergent portion which are adjacent to each other at a nozzle throat (DK), characterized in that an inside contour of the supersonic nozzle corresponds to a contour determined numerically with a modified Method of Characteristics, wherein the ratio of a nozzle length l to a radius in the narrowest cross-section r*, i.e. l/r* is between 2.1 and 11.6.
10 . The supersonic nozzle pursuant to claim 9 , wherein the inner contour of the supersonic nozzle corresponds to the contour, which is determined by numeric solution of partial gas dynamic differential equations, in which a stationary, isentropic, axisymmetrical gas flow is represented by means of spatially discretized characteristics equations, taking into account corresponding conditions of compatibility.
11 . The supersonic nozzle pursuant to claim 10 , wherein with the solution of the partial, numerical differential equations, the influence of a friction-affected, boundary layer close to the wall is taken into account.
12 . The supersonic nozzle pursuant to claim 9 , wherein the convergent portion comprises a bell-shaped contour and the divergent portion comprises a bell-shaped contour, wherein the bell-shaped contours of the convergent portion and of the divergent portion are uniformly merging into one another on the nozzle throat.
13 . The supersonic nozzle pursuant to claim 9 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 8.3.
14 . The supersonic nozzle pursuant to claim 13 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 5.4.
15 . The supersonic nozzle pursuant to claim 14 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 5.
16 . The supersonic nozzle pursuant to claim 9 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is 11.6, 8.3, 5.4, 5.0, 4.8, 4.2, 3.6, 3.3, 3.1, or 2.1.
17 . A method for determination of the dimensions of a supersonic bell-shaped nozzle, which is used in metallurgical installations, such as basic oxygen furnace (BOF), argon oxygen decarburization (AOD) converter, electric arc furnace (EAF), with a convergent portion and a divergent portion which are adjacent to each other at a nozzle throat (DK), wherein the method comprises the step of:
determining a contour numerically with a modified Method of Characteristics, and designing the interior contour of the supersonic nozzle by means of the contour determined, and wherein the ratio of a nozzle length l to the radius in the narrowest cross-section r*, i.e. l/r* is between 2.1 and 11.6.
18 . The method pursuant to claim 17 , wherein the contour is determined by the numeric solution of the partial gas dynamic differential equations, in which a stationary, isentropic, axisymmetrical gas flow is represented by means of spatially discretized characteristic equations, taking into account corresponding conditions of compatibility.
19 . The method pursuant to claim 18 , wherein the solution of the partial, numerical differential equations is corrected by the influence of a friction-affected, boundary layer close to the wall.
20 . The method pursuant to claim 17 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 8.3.
21 . The method pursuant to claim 20 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 5.4.
22 . The supersonic nozzle pursuant to claim 21 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is between 2.1 and 5.
23 . The supersonic nozzle pursuant to claim 17 , wherein the ratio of the nozzle length l to the radius in the narrowest cross-section r* is 11.6, 8.3, 5.4, 5.0, 4.8, 4.2, 3.6, 3.3, 3.1, or 2.1.