Volume 03 Issue 06-2023
217
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
A
BSTRACT
The article presents the results of the optimization (optimization) of the mode indicators of the process of
cleaning the air from solid particles by the Box-Wilson method of steep ascent. Acceptance was based on
three factors, i.e., solid content (solid particles), the hydraulic resistance of the circulation pipe that cir-
culates fine dispersed dust up to 5 μm in the device, and the spe
ed of the dust flow. Based on the computer,
studies carried out to determine the optimal opera-tion modes of the dust cleaning process, the following
conclusions were drawn: solid content is 75%; hydraulic resistance of the circulation pipe is 51.3 Pa; it was
determined that the speed of dusty air flow is 21.7 m/s.
K
EYWORDS
Optimization, cyclone, circulation pipe, vertical rise, Box-Wilson, hydraulic re-sistance, fine-dispersed
particles, structural dimensions, flow rate.
I
NTRODUCTION
Journal
Website:
http://sciencebring.co
m/index.php/ijasr
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Research Article
RESULTS OF OPTIMIZING THE PROCESS OF CLEANING AIR
FROM SOLID PARTICLES
Submission Date:
June 14, 2023,
Accepted Date:
June 19, 2023,
Published Date:
June 24, 2023
Crossref doi:
https://doi.org/10.37547/ijasr-03-06-38
Abdugaffor M. Khurmamatov
Doctor Of Technical Sciences, Professor, Institute Of General And Inorganic Chemistry, Academy Of Sciences
Of The Republic Of Uzbekistan
Navruzbek A. Mirzayev
Assistant, Fergana Polytechnic Institute, Fergana, Republic Of Uzbekistan
Farxod A. Ibragimov
Assistant, Fergana Polytechnic Institute, Fergana, Republic Of Uzbekistan
Volume 03 Issue 06-2023
218
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
The goal of the work is to find a new direction of
the gradient for the order of steep ascent. This is
the content of the second cycle of the process [1-
5].
Based on the similarities described above, we
select the variability intervals for each factor and
fill in the table of factor values during the study.
Then we make a research plan, implement it and
put the results in the research implementation
table.
Table 1. The new direction of the gradient for steep ascent order
Name of the factor
Unit of
measure
Minimum
value
Maximum
value
Process
departure
mode
Solid content
%
70
90
80
Hydraulic resistance
of the circulation pipe
Pa
28
80
54
Dust air speed
m/s
19
25
22
The value of the range of changes for each factor
is limited from below; first of all, by the errors of
the instruments and devices, and with their help
of them, the values of the factors are measured
and set during the experiment. [6-10]
As for the upper limit, it is impossible to make
clear statements.
We get as follows:
0
.05
⋅ 𝑥
0𝑗
≤ 𝛥
𝑗
≤ 0
.07
⋅ 𝑥
0𝑗
Here
𝛥
𝑗
-
𝑥
𝑗
factor change interval
𝑥
jВ
-
𝑥
𝑗
- the maximum allowable value of
𝑥
jH
-
𝑥
𝑗
n - the minimum allowable value
From this, we get:
𝛥
1
= 0,
05
⋅ (
90
−
70
) = 1
𝛥
2
= 0,
05
⋅ (
80
−
28
) = 2,6
Input parameter 1
Technological
object
Input parameter 3
Output parameter
Input parameter 2
Volume 03 Issue 06-2023
219
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
𝛥
3
= 0,
05
⋅ (
25
−
19
) = 0,3
Table 2. Table of values of factors as a result of experimentation
Name of the factor
Unit of
measure
Minimum value Maximum value
Solid content
%
69
81
Hydraulic resistance of the
circulation pipe
Pa
25.4
82.6
Dust air speed
m/s
18.7
25.3
After designing a fully factorial experiment 23, we have the following experimental results:
Table 3. Results of experiments
No
Experimental design
Result
Solid content
Hydraulic
resistance of
the
circulation
pipe, Pa
Dust air
speed
Concentration
code
Value code
value
code
value
Por.
No
value
Por.
No
value
1
-1
69
-1
25.4
-1
18.7
7
41.53
1
40,61
2
+1
81
-1
25.4
-1
18.7
5
42,43
3
42,14
3
-1
69
+1
82.6
-1
18.7
9
45.00
13
42.40
4
+1
81
+1
82.6
-1
18.7
6
46.81
16
46,41
5
-1
69
-1
25.4
+1
25.3
4
45,27
11
43.50
6
+1
81
-1
25.4
+1
25.3
2
46.00
12
45.30
7
-1
69
+1
82.6
+1
25.3
14
48,41
15
48.02
8
+1
81
+1
82.6
+1
25.3
8
49.10
10
50.03
The result of the estimation values of the regression coefficients:
Table 4. Table of estimation of coefficients of the model
Rate
estimation
Appraisal
value
Statistical
value
t
kr
Hypothesis test
result
𝒃¯
𝟎
45,1850
204.5625345
2.31
1
𝒃¯
𝟏
-0.8425
3.814184692
2.31
1
Volume 03 Issue 06-2023
220
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
𝒃¯
𝟐
-1.8375
8.318770768
2.31
1
𝒃¯
𝟑
1.7688
8.007524243
2.31
1
𝒃¯
12
0.2225
1.007306937
2.31
0
𝒃¯
13
-0.1888
0.854513188
2.31
0
𝒃¯
23
0.0987
0.447063191
2.31
0
Mean squared deviation of regression coefficients
0.220886
The number of remaining coefficients
4
Thus, the model will look like this in the normalized variables:
𝑦 =
45
− 0,
84
⋅ 𝑥
1
− 1,
83
⋅ 𝑥
2
+ 1,
77
⋅ 𝑥
3
Table 5. Checking the adequacy of the model
Average
According to the
model
Dispersion
41.07
40.74
0.222778125
42.29
42,42
0.037128125
43.70
44,41
1.011753125
46.61
46.10
0.527878125
44.39
44.27
0.024753125
45.65
45.96
0.190653125
48,22
47.95
0.141778125
49.57
49.63
0.009453125
Adequacy variance
0.541544
Repetition Dispersion
0.78065
F statistics
1.441527
Fisher's criterion
F=Sad2/Se
2
(1)
F=2.79,
ν
1
=4,
ν
2
=8,
From the Fisher distribution table, we determine
F
kr
=3.84.
It can be seen that the obtained model is
adequate. The model will look like this in natural
variables:
𝑦 =
45
+ 0,
84
⋅ (𝑥
1
−
80
) 1
⁄ + 1,
83
⋅ (𝑥
2
−
54
) 2,8
⁄
− 1,
77
⋅ (𝑥
3
−
22
) 0,3
⁄
from this:
Volume 03 Issue 06-2023
221
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
𝑦 =
72
,
31
+ 0,
84
⋅ 𝑥
1
+ 0,
65
⋅ 𝑥
2
− 5,9 ⋅ 𝑥
3
Here x1
—
Solid content, %;
x
2
—
Hydraulic resistance of the circulation pipe,
Pa;
x
3
—
Speed of dusty air, m/s;
y
—
output parameter concentration, %.
To obtain the coordinates of the first point using
the
Box-Wilson
method,
the
following
multiplication should be obtained: [10,11]
𝛿
𝑗
= 𝑏
𝑗
⋅ 𝛥
𝑗
(2)
here,
−
j
j
-
factor coefficient estimation value;
−
j
b
jм
- factor evaluation coefficient;
−
j
j -
change interval for the factor;
For this option
𝛿
1
= 0,
84
⋅ 1 = 0,
84
(3)
𝛿
2
= 1,
83
⋅ 2,6 = 4,
76
(4)
𝛿
3
= 1,
77
⋅ 0,3 = 0,
53
(5)
Then, according to the procedure, the maximum
of all
j
was selected and
0
was taken as the
base value.
In this case, for a variable (factor)
𝛿
𝑗
is called the
maximum baseline
and the baseline step λ is
chosen for this variable. The sign and size of the
steps for each factor are determined by a general
formula.
𝜆
𝑗
= 𝜆
б
⋅ 𝛿
𝑗
|𝛿
0
|
⁄
(6)
here,
λ
j
-
j
-
step movement by the j-factor;
δ
j
-
j
-
calculation value;
δ
0
–
basic value;
λ
b
is the base step.
In our case, we consider when choosing a basic
step equal to half of the change interval for the
second factor
𝜆
б
= 3,5 ⋅ 𝛥
1
= 3,5 ⋅ 1 = 3,5
:
05
,
0
72
,
8
/
84
,
0
5
,
0
/
0
1
1
=
=
=
б
Volume 03 Issue 06-2023
222
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
27
,
0
72
,
8
/
76
,
4
5
,
0
/
0
2
2
=
=
=
б
03
,
0
72
,
8
/
53
,
0
5
,
0
/
0
3
3
=
=
=
б
Table 6. The main parameters of the model
Model:
𝒚 =
72
,
31
+ 𝟎,
84
⋅ 𝒙
𝟏
+ 𝟎,
65
⋅ 𝒙
𝟐
− 𝟓, 𝟗 ⋅ 𝒙
𝟑
Factors
Results
Naming
Solid
conten
t
Tsir-ya
pipe
hydra
tion
resist.
Solid
content
Output parameter
The starting point
80
54
22
Working step
0.05
0.27
0.03
Step
number
Type of
experim
ent
Accordi
ng to the
model
Experiments
Average
y
y
2
y
1
Y
1
M
79.50
53.73
21.97
41.67
2
M
79.00
53.46
21.94
44.87
3
M
78.50
53.19
21.91
48.08
4
P
78.00
52.92
21.88
51.28
50.37
50.39
50.38
5
M
77.50
52.65
21.85
6
P
77.00
52.38
21.82
52.06
52,51
52.78
7
M
76.50
52.11
21.79
8
P
76.00
51.84
21.76
55.37
55.21
55.79
9
R
75.50
51,57
21.73
10
R
75.00
51.30
21.70
60.20
60.74
60.97
11
R
74.50
51.03
21.67
54.75
55,46
54.60
12
R
74.00
50.76
21.64
55.49
56,66
55,58
13
R
73.50
50.49
21.61
56,38
56.00
57.69
14
R
73.00
50.22
21.58
57.82
55.35
56.08
15
R
72.50
49.95
21.55
58.03
59.82
57.92
16
R
72.00
49.68
21.52
57.89
57.35
58.01
17
R
71.50
49,41
21.49
59.75
60.15
58.50
18
R
71.00
49.14
21.46
59.85
59.15
60.50
19
R
70.50
48.87
21.43
56.49
58,66
56,58
20
R
70.00
48.60
21.40
57,38
57.00
58,69
21
R
69.50
48.33
21.37
58.82
56.35
59.08
22
R
69.00
48.06
21.34
56.03
58.82
58.92
23
R
68.50
47.79
21,31
58,49
55,66
58,58
24
M
68.00
47.52
21,28
56,38
57.00
55.69
25
M
67.50
47.25
21.25
55.82
54,35
56.08
Volume 03 Issue 06-2023
223
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
The purpose of the experiment is to determine the new direction of the gradient for the Box-Wilson
procedure, which constitutes the second cyclic content of this procedure [3,5].
Similar to the above, we select ranges of variation for each of the factors and record the values of the factors
in a table during the experiment. Then, we plan the experiment, execute it, and put the results in the
experiment execution table.
Table 7. Process execution mode
Name of the factor
Unit of
measure
Minimum
allowed
value
Maximum
allowed
value
Process
execution
mode
Solid content
%
70
90
72
Hydraulic resistance
of the circulation pipe
Pa
28
80
49.68
Dust air speed
m/s
19
25
21.52
Table 8. Table of factor values as a result of experimentation
Name of the factor
Unit of
measure
Minimum
value
Maximum
value
Solid content
%
68
76
Hydraulic resistance of the
circulation pipe
Pa
48.2
51.16
Dust air speed
m/s
18.7
24,34
After designing a fully factorial experiment 23, we have the following experimental results:
Table 9. Schedule of the experiment
No
Experimental design
Result
Solid
content
Hydraulic
resistance of
the circulation
pipe
Dust air speed
code
value
cod
e
value
code
value
Por.
No
value.
Por.
No
value
1
-1
68
-1
48.2
-1
18.7
2
56,38
14
59.15
2
+1
76
-1
48.2
-1
18.7
8
57.82
9
58,66
3
-1
68
+1
51.16
—
1
18.7
3
58.03
1
57.00
4
+1
76
+1
51.16
-1
18.7
6
60.20
11
56.35
Volume 03 Issue 06-2023
224
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
5
-1
68
-1
48.2
+1
24,34
4
59.85
12
58.82
6
+1
76
-1
48.2
+1
24,34
10
59.85
16
55,66
7
-1
68
+1
51.16
+1
24,34
5
56.49
15
57.00
8
+1
76
+1
51.16
+1
24,34
7
57,38
13
54,35
The results of calculating the estimation of regression coefficients and testing their significance are
summarized in the table:
Table 10. Table of estimation of coefficients of the model
Coeff.
evaluation
Appraisal
value
Statistic value t
кр
Hypothesis test
result
0
b
57,6869
127,60378
2.31
1
1
b
-0,1531
0,3387136
2.31
0
2
b
-0,5869
1,2981717
2.31
0
3
b
-0,2619
0,5792694
2.31
0
12
b
0,1231
0,2723534
2.31
0
13
b
-0,4619
1,0216708
2.31
0
23
b
-0,5331
1,1792763
2.31
0
Thus, the model will look like this in normalized
variables: y=57.69
Fisher criterion F=1,765 ν1=7, ν2=8, Fкр
=3,50
The results of the experiment showed that the
corresponding coordinates of the special extreme
in the central area showed that only the
coefficient b0 is significant.
Its evaluation value is 57.69. As a result, the
optimal mode of process implementation was
achieved.
Thus, based on the results of the research on the
purification of atmospheric air from catalyst dust,
the following results were obtained: a
technological line consisting of two-stage cyclone
devices of a new design was developed for the
purification of atmospheric air from catalyst dust.
To determine the optimal (optimal) operating
modes of the dust cleaning process on the
computer: solid content - 75%; hydraulic
resistance of the circulation pipe - 51.3 Pa; the
speed of dusty airflow - 21.7 m/s.
Volume 03 Issue 06-2023
225
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
03
ISSUE
06
Pages:
217-225
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
(2023:
6.741
)
OCLC
–
1368736135
R
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