|
EXAMPLE
Find the total net heat input (i.e., the enthalpy of the incoming fuel
and air above 60° F., water as vapor) to the following furnace :
| Data |
|
| Dimensions of combustion chamber |
15' x 30' x 40' |
| Tube outside diameter |
5: O.D. |
| Center to center spacing |
10" |
| Number of tubes in section |
90 arranged in a single row |
| Circumferential tube surface |
4710 sq. ft. |
| Total wall area, Ar |
4300 sq. ft. * |
| Conditions |
|
| Net heat input to oil |
70,650,000 B.t.u./hr. |
| Desired radiant rate |
15,000 B.t.u./hr./sq.ft. circumferential surface |
| Cracked gas fuel |
20,000 B.t.u./lb. (L.H.V.) |
| Excess air |
30% |
| Temperature of air leaving preheater |
460° F. |
| Estimated tube skin temperature |
1000° F. |
| Calculation of effective surface, aAcp |
|
Reference |
| Center to center distance/tube O.D. |
2 |
|
| a to one row |
0.88 |
Fig. 5 |
| Acp = (90 tubes)(10"C/12)(40' long) |
3,000 sq.ft. of Acp |
|
| aAcp = 0.88(3000) |
2,640 sq.ft. of aAcp |
|
| Calculation of exchange factor, f |
|
|
| Radiant section dimension ratio, 15/15 x 30/15 x 40/15 = 1 x
2 x 2.67 |
|
| L = 2/3(volume)1/3 = 2/3(15x30x40)1/3 |
17.5 feet |
Table I |
| P, partial pressure CO2 + H2O |
0.22 atmospheres |
Fig. 7 |
| PL = 0.22(17.5) |
3.84 (atm.) (ft.) |
|
| Assume tg (temp. flue gas leaving) |
1,800° F. |
|
| PF, flame emissivity |
0.495 |
Fig. 6 |
| AR = Ar-aAcp = 4300-2640 |
1,660 sq.ft. |
|
| AR/aAcp =
1600/2640 |
0.63 |
|
| f = |
0.56 |
Fig. 8 |
| q/aAcpf = 15,000(4710/2640)(1/0.56) |
47,900 B.t.u./hr./aAcpf |
|
| Calculation of Total Net Heat Input |
Results |
Reference |
| tg |
1,850° F. |
Fig. 2 |
| PF, as previously calculated ** is close enough |
0.495 |
|
| t'F at 30% excess air, 460-60=400° |
|
|
| air preheat, 1850° F. tg |
3,620° F. |
Fig. 3 |
| 0.98 H/aAcpf |
94,000 B.t.u./hr./aAcpf |
Fig. 2 |
| H/aAcp (94,000/0.98) x
0.56 |
53,700 B.t.u./hr./aAcp |
|
| H = Total net heat input (53,700)(2,640) |
142,000,000 B.t.u./hr. |
|
| * Area of opening to convection section equals 200 sq.ft. so
Ar = 4500-200. |
| ** When assumed temperature of flue gases leaving radiant
section is in |
| error by 100° or more, PF and f should be revised. |
RESULTS
The results of the investigation
are summarized in Tables II and III. Table II gives the
characteristics of the furnaces studied and the ratio of the actual
heat to the oil to that calculated by the proposed theoretical
equation, as well as by the empirical equation of Wilson, Lobo and
Hottel. Sketches of the general types of furnaces studied are shown
in Figures 16 through 22 in the Appendix. These should be considered
as diagrammatic only.
| Table II. - Characteristics of
Furnaces and Tests |
|
|
|
|
|
|
Total |
Total |
|
Mean |
|
|
|
|
Ratio: |
|
|
Tube |
|
Circum |
Effective |
Furnace |
Effective |
|
Length |
|
|
|
|
|
|
|
|
Outside |
Tube |
ferential |
Tube |
Wall |
Refractory |
Ratio |
Radiant |
Air |
Flue Gas |
No.of |
Actual/Calculated |
| Furnace |
|
Diameter |
Spacing |
TubeArea |
Area |
Surface |
Surface |
AR/Acp |
Beam |
Preheat |
Recirculation |
Fuel |
Tests |
Heat to Oil |
|
(h) |
|
|
|
|
|
|
|
|
|
|
|
|
(g) |
|
| Symbol |
General |
O.D. |
C-C |
Ac |
aAcp |
AT |
AR |
|
L |
|
|
|
|
Empirical |
Theoretical |
| Unit |
Type |
Inches |
Inches |
Sq.Ft. |
Sq.Ft. |
Sq.Ft. |
Sq.Ft. |
|
Feet |
|
|
|
|
Equation |
Equation |
| *1 |
A |
5 |
10 |
2,389 |
1,340 |
3,080 |
1,740 |
1.30 |
14.3 |
Yes & No |
Yes & No |
Gas |
16 |
1.03 |
1.02 |
| *2 |
B |
4 |
6.75 |
1,496 |
756 |
3,271 |
1,515 |
2.00 |
19.6 |
Yes |
No |
Oil |
17 |
0.93 |
0.94 |
| *3 |
C |
5 |
10 |
2,945 |
2,255 |
3,855 |
1,600 |
0.71 |
17.0 |
|
No |
Gas |
10 |
0.95 |
0.99 |
| 4 |
B |
5 |
10 |
2,394 |
1,343 |
4,277 |
2,934 |
2.18 |
17.8 |
Yes |
No |
Gas |
7 |
0.94 |
0.97 |
| *5 |
D |
5 |
17.3(a) |
4,443 |
2,303 |
3,362 |
1,059 |
0.46 |
24.0(c) |
Yes |
No |
Gas |
3 |
0.92 |
1.00 |
| 6(d) |
E |
5 |
9 |
3,060 |
1,608 |
3,174 |
1,566 |
0.97 |
12.8 |
No |
No |
Gas |
2 |
1.02 |
0.99 |
| 7(d)#1 |
E |
5.5 |
9.75 |
12,467(b) |
3,610 |
6,560 |
2,950 |
0.82 |
22.2 |
No |
No |
Gas |
1 |
1.18 |
1.11 |
| 7 #2 |
E |
5 |
9.25 |
7,153 |
3,698 |
6,560 |
2,862 |
0.77 |
22.2 |
No |
No |
Gas |
1 |
1.11 |
1.14 |
| *8 |
F |
4 |
8.75 |
284 |
216 |
1,628 |
1,412 |
6.55 |
11.2 |
No |
No |
Gas |
7 |
1.04 |
0.98 |
| 9 |
B |
5 |
8.75 |
4,775 |
1,844 |
2,976 |
1,132 |
0.61 |
14.7 |
Yes |
No |
Gas |
4 |
1.04 |
1.03 |
| 10 |
G |
4 |
8.75 |
1,347 |
465 |
1,875 |
1,410 |
3.04 |
11.2 |
No |
No |
Oil |
3 |
0.94 |
0.99 |
| 11 |
G |
4 |
8.75 |
1,466 |
498 |
1,608 |
1,110 |
2.23 |
8.28(e) |
No |
No |
(f) |
3 |
0.77 |
1.07 |
| 12 |
B |
5 |
8.75 |
2,314 |
1,197 |
3,423 |
2,226 |
1.86 |
15.9 |
No |
No |
Oil |
2 |
0.98 |
1.08 |
| 13 |
D |
5 |
10.25 |
5,780 |
2,108 |
3,333 |
1,225 |
0.58 |
22.5(c) |
Yes |
No |
Gas |
1 |
1.02 |
0.99 |
| 14 |
D |
5 |
10.25 |
5,780 |
2,108 |
3,049 |
941 |
0.45 |
22.5(c) |
Yes |
No |
Gas |
1 |
0.94 |
0.91 |
| 15 |
D |
5 |
10.25 |
2,890 |
1,928 |
3,067 |
1,139 |
0.59 |
22.5(c) |
Yes |
No |
Gas |
1 |
0.99 |
0.93 |
| 16 |
D |
5 |
10.25 |
5,780 |
2,108 |
3,049 |
941 |
0.45 |
22.5(c) |
Yes |
No |
Gas |
1 |
0.99 |
0.98 |
| 17 |
B |
5 |
8.75 |
1,718 |
887 |
2,369 |
1,482 |
1.67 |
13.2 |
No |
No |
Gas |
1 |
0.92 |
0.94 |
| 18 |
B |
5 |
8.75 |
1,867 |
965 |
2,143 |
1,178 |
1.22 |
12.6 |
No |
No |
Gas |
3 |
0.96 |
1.02 |
| 19 |
E |
5.5 |
9.25 |
3,616 |
1,820 |
3,885 |
2,065 |
1.14 |
17.1 |
No |
No |
Oil |
1 |
0.90 |
1.08 |
| FOOTNOTES : |
|
(a) |
Two rows with center lines 2.62 inches
apart. |
|
(b) |
Double row of tubes. |
|
(c) |
Circular furnace, L = diameter. |
|
(d) |
Double radiant type furnace. |
|
(e) |
L = 1.8 (minimum distance). |
|
(f) |
Products of combustion from furnace No.
10. |
|
(g) |
Wilson, Lobo, and Hottel Empirical
Equation. |
|
(h) |
For sketches of general type of furnace see
Figs. 16 through 22 in the Appendix. |
|
* |
Furnaces used by Wilson, Lobo and Hottel
(2). |
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