Результаты расчетов Сравнение численных решений с аналитическим
Корни характеристического уравнения:
μ1 |
μ2 |
μ3 |
μ4 |
μ5 |
μ6 |
1,7717 |
4,4458 |
7,3971 |
10,4466 |
13,5356 |
16,2516 |
Время |
Аналитический метод |
МКР (явная схема) |
МКР (неявная схема) |
||
Град. |
Град. |
% |
Град. |
% |
|
=1600c, на оси |
52,534 |
51,822 |
1,355 |
51,872 |
1,26 |
=1600c, на пов. |
28,411 |
28,174 |
0,834 |
28,195 |
0,76 |
=3200c, на оси |
27,505 |
27,220 |
1,036 |
27,301 |
0,742 |
=3200c, на пов. |
19,457 |
19,364 |
0,478 |
19,393 |
0,329 |
Зависимости температуры по сечению
T(r),C (аналитический метод) |
||||
r, мм |
=0 |
=32c |
=1600c |
=3200c |
0 |
96,705 |
95,407 |
52,534 |
27,505 |
1 |
96,539 |
95,356 |
52,468 |
27,483 |
2 |
96,074 |
95,220 |
52,269 |
27,417 |
3 |
95,411 |
95,046 |
51,939 |
27,306 |
4 |
94,719 |
94,894 |
51,480 |
27,152 |
5 |
94,212 |
94,817 |
50,893 |
26,955 |
6 |
94,077 |
94,839 |
50,182 |
26,717 |
7 |
94,387 |
94,944 |
49,351 |
26,439 |
8 |
95,031 |
95,077 |
48,403 |
26,121 |
9 |
95,720 |
95,169 |
47,344 |
25,767 |
10 |
96,092 |
95,166 |
46,179 |
25,377 |
11 |
95,888 |
95,063 |
44,914 |
24,954 |
12 |
95,119 |
94,911 |
43,555 |
24,501 |
13 |
94,123 |
94,796 |
42,110 |
24,018 |
14 |
93,459 |
94,772 |
40,586 |
23,510 |
15 |
93,644 |
94,797 |
38,991 |
22,978 |
16 |
94,832 |
94,663 |
37,333 |
22,426 |
17 |
96,587 |
93,985 |
35,621 |
21,855 |
18 |
97,871 |
92,253 |
33,864 |
21,270 |
19 |
97,312 |
88,945 |
32,070 |
20,674 |
20 |
93,721 |
83,684 |
30,249 |
20,068 |
21 |
87,063 |
76,448 |
28,411 |
19,457 |
Рис. 1. Зависимость температуры от сечения (аналитический метод):
1 – =0; 2-=32c; 3 - =1600c; 4 – =3200c.
T(r),C (МКР явная схема) |
||||
r, мм |
=0 |
=32c |
=1600c |
=3200c |
0 |
95 |
95 |
51,822 |
27,220 |
1 |
95 |
95 |
51,822 |
27,220 |
2 |
95 |
95 |
51,646 |
27,162 |
3 |
95 |
95 |
51,336 |
27,058 |
4 |
95 |
95 |
50,889 |
26,910 |
5 |
95 |
95 |
50,320 |
26,719 |
6 |
95 |
95 |
49,621 |
26,487 |
7 |
95 |
95 |
48,807 |
26,215 |
8 |
95 |
95 |
47,873 |
25,905 |
9 |
95 |
95 |
46,833 |
25,558 |
10 |
95 |
95 |
45,683 |
25,176 |
11 |
95 |
95 |
44,439 |
24,761 |
12 |
95 |
95 |
43,098 |
24,316 |
13 |
95 |
95 |
41,676 |
23,843 |
14 |
95 |
95 |
40,172 |
23,344 |
15 |
95 |
95 |
38,601 |
22,822 |
16 |
95 |
94,653 |
36,966 |
22,279 |
17 |
95 |
94,024 |
35,279 |
21,719 |
18 |
95 |
91,858 |
33,546 |
21,145 |
19 |
95 |
88,430 |
31,779 |
20,559 |
20 |
95 |
82,415 |
29,985 |
19,965 |
21 |
95 |
74,266 |
28,174 |
19,364 |
Рис. 2. Зависимость температуры от сечения (явная схема):
1 – =0; 2-=32c; 3 - =1600c; 4 – =3200c.
T(r),C (МКР неявная схема) |
||||
r, мм |
=0 |
=32c |
=1600c |
=3200c |
0 |
95 |
95 |
51,872 |
27,301 |
1 |
95 |
95 |
51,872 |
27,301 |
2 |
95 |
95 |
51,698 |
27,243 |
3 |
95 |
95 |
51,385 |
27,138 |
4 |
95 |
95 |
50,940 |
26,988 |
5 |
95 |
95 |
50,368 |
26,796 |
6 |
95 |
95 |
49,671 |
26,563 |
7 |
95 |
95 |
48,854 |
26,289 |
8 |
95 |
94,999 |
47,921 |
25,977 |
9 |
95 |
94,998 |
46,878 |
25,627 |
10 |
95 |
94,995 |
45,730 |
25,243 |
11 |
95 |
94,988 |
44,482 |
24,826 |
12 |
95 |
94,971 |
43,142 |
24,377 |
13 |
95 |
94,928 |
41,716 |
23,901 |
14 |
95 |
94,827 |
40,212 |
23,399 |
15 |
95 |
94,599 |
38,638 |
22,873 |
16 |
95 |
94,103 |
37,002 |
22,327 |
17 |
95 |
93,082 |
35,312 |
21,764 |
18 |
95 |
91,111 |
33,577 |
21,186 |
19 |
95 |
87,600 |
31,807 |
20,596 |
20 |
95 |
81,937 |
30,010 |
19,997 |
21 |
95 |
73,846 |
28,195 |
19,393 |
Рис. 3. Зависимость температуры от сечения (неявная схема):
1 - =0; 2-=32c; 3 - =1600c; 4 –=3200c.