Gaseous Explosions’ I-Initial Temperature and Rate of Rise of Pressure By G. G. Brown, E. H. Leslie, and J. V. Hunn DEPARTMENT OF CHEMICAL E ~ C I N E E R IU NNCI V, E R S I T Y
I
O F ?VzICHIGAN,
ANN
.kRBOR, h f I C H .
ameter and 12 inches high ignited from the bottom, and on made concerning the nature of gaseous explosions, the the same time scale recorded the pressure-time curve as subject offers many fundamental problems for solution. indicated by a Nidgley pressure element in the upper end of .4 study of the literature reveals no conclusive evidence of the bomb. They report data showing that initial temperathe effect of varying conditions of initial temperature upon ture has a very interesting effect. They found that high the characteristics of gaseous explosions; much of it is con- initial temperature tends to inhibit the initiation of the deflicting and apparently irreco :ilable. tonation wive. Dixon’s2 work brought OL the fact that an increase in In a written discussion of the paper by Woodbury, Lewis, and C a n b ~ Dixon6 ,~ says: initial temperature from 20” “If the initial temperature to 100” C. a t constant The existent literature concerning the effect of initial of the gas is raised 100” C. initial pressure decreases the temperature on gaseous explosions is inconclusive and this rise is not added to the velocity of the detonation apparently irreconcilable. Because rate of rise of pressure flame temperature.” In wave when “ t h e o r e t i c a l and rate of combustion are frequently confused with rate discussing some pressuremixtures” are used. of chemical reaction, it is generally assumed that an intime curves of the exploiYage13 studied the effect crease in initial temperature must increase the rate of sions of petrol-air mixtures of initial temperature upon combustion. Experimental work with a constant-volume obtained by Fenning a t the the rate of inflammation in bomb demonstrates that an increase in initial temperaSational Physical Laborathe same bomb previously ture above a definite critical value decreases the rate of tory, Ricardo’ says: “An used by L a ~ i g e 40 , ~ cm. in rise of pressure of a homogeneous gaseous explosion. increase of 101” C. in the diameter and of 33.61 liters Theoretical considerations indicate that the existence of initial temperature means a capacity. The bomb was such a critical initial temperature is to be expected from similar increase in the flame immersed in a water bath temperature.” our knowledge of gases and gaseous reactions. In mixfor temperature control, and tures containing an excess of fuel the critical initial temMidgley,8 RicardoJg and equipped with a spark gap othersl0 found that the perature is about 75” C. In mixtures containing an exlocated at the center of the engine knock becomes more sphere. Nagel worked with cess of air or oxygen the critical temperature has not been noticed in work at room temperature or above. pronounced as the temperahydrogen, Dresden city gas ture of the mixture is in(10 Der cent CO. 49 uer cent creased. H 2 , >i per cent‘CH4, 3 per Tizard” suggests that the knock in an internal combustion cent C2H4,0.3 per cent C6H6,3 per cent COZ,1 per cent 0 2 , 6.7 per cent Sz), and producer gas (18.1 per cent H2, 2 . 2 engine “occurs when the rate of rise of pressure exceeds a per cent CH4, 0.2 per cent C2H4, 18.9 per cent CO, 0.5 per certain unknown amount,” but regards this suggestion as 6.9 per cent C02, 0.2 per cent 0 2 , 53 per cent Nz). “a comparatively secondary consideration.” He “accepts cent An increase in initial temperature from 15” to ‘75” C. de- the view that the rate of combustion increases rapidly with the creased the rate of rise of pressure upon explosion of a city temperature” and “is led to the conclusion that ‘knocking’ gas-air mixture containing 8 per cent of gas. At an initial will occur if, some time before combustion is complete, the pressure of 0.5 atmosphere a slight increase was noted in one whole or part of the gas exceeds a certain temperature,” or “if the maximum flame temperature exceeds a certain case. With 11 per cent and 16 per cent of gas in city gas-air mixtures an increase in initial temperature to 75” C. increased temperature, which is characteristic of the fuel.” This the rate of rise of pressure in all cases. Nagel’s producer conclusion is based on the assumptions “that the rate of gas-air mixtures showed an increase in rate of rise of pressure Combustion increases rapidly with the temperature”and that as the initial temperature was raised to 75” C. rate of combustion is equivalent to rate of pressure rise. This brief review of the literature shows almost complete T a b l e I-Effect of T e m p e r a t u r e at C o n s t a n t Pressure on Velocity of disagreement as to the effect of initial temperature upon F l a m e Propagation in 1 2 - I n c h B o m b s gaseous combustion. It seems absolutely necessary that Initial temperature Average velocity C?Hz in air mixture c. Ivf/sec. Per cent the question of the effect of initial temperature upon combus15 10 25 tion be settled before gaseous combustion can be understood. 60 12.2 S SPITE of the many investigations that have been
e,&,
10.8 10.38
i0 80
Apparent increase from 25’ C. t o 75’ C. and then a decrease on further rise t o 125’ C.
Woodbury:, Lewis, and Canby5 took photographic records of the flame travel in explosive mixtures of acetylene and oxygen with nitrogen in a cylindrical bomb 4 inches in di1 2
*
4
6
Received January 15, 1925. Trans. R o y . SOC.(London), 1848, S i (1893). Mitteilungen iiber Forschungsarbeiten, 1908, Heft 54 I b i d . , 1908, Heft 8. J. SOL.Automotine Eng., 8, 209 (1921).
Apparatus
The apparatus as finally developed consists of an explosion bomb, 23/r inches inside diameter and 7 inches long, machined from steel bar stock and assembled with valves and 6
7
8 9
J. SOC.Automotive Eng., 9, 237 (1921). J. Roy. Aeronaut. Soc., 17, 60 (1924). J . SOC. Automotive Eng., 10, 357 (1922); 12, 367 (1923). Automobile Eng., 11, 51, 92, 130, 169, 201, 242 (1921); 11, 265, 299,
329 (1922). 10 Holloway, Huebotter, and Young, J . SOC. Automotive Eng., 12 111 (1923); 14, 315 (1924); 15, 255 (1924); Horning, Automobile Eng., 14, 142 (1924). 1 1 X, E . Coast Znst. Exg. Shipbuilders, T r a n s . , 37, 381 (1921).
398
INDUSTRIAL A N D ENGINEERING CHEMISTRY
fittings, and pressure indicator with optical system to record the pressure-time curves. The spark plug at the lower right end of the bomb is a porcelain core Champion plug as used on Ford engines. The terminals of the plug are kept a t l/32 (0.03125) of an inch. The igniting spark is obtained
Vol. 17, No. 4
pressures of wide range, without exceeding the limit of the indicator spring. A 6-volt, 32-c. p. automobile head lamp is used as the light source. In order to record the extremely rapid pressure rise of detonating explosions, i t is necessary to pass 12 volts through the 6-volt lamp during the pressure rise, but the very intense light must be reduced or shut off on the cooling curves to prevent blurring of the curves and destruction of the lamp filament. The lamp control is obtained by a special switch. As the switch handle is manually moved in a clockwise direction 12 volts are passed through the lamp, then the primary circuit of the spark coil is closed, and a spark, properly timed by the timer on top of the camera box and driven by the shaft of the rotating mirror, ignites the mixture in the bomb. The switch is released and springs back to its original position passing 8 volts through the lamp filament, or it may be moved still further in a clockwise direction, thus breaking the lamp circuit. Procedure
The fuel used in these experiments was the fraction boiling between 66.9' and 67.4' C. obtained by careful fractionation of a paraffin base gasoline prepared by the Elk Refining Company from crude oil from the Cabin Creek Field, Kanawha Co., W. Va., and was largely isohexane. Before each experiment the bomb was repeatedly swept out with one of the constituents (nitrogen or oxygen) of the mixture to be exploded. Both valves were closed, the spark plug removed, and the desired amount of hexane immediately introduced into the bomb and spread over the metal surface by means of a small special pipet. The spark plug was replaced and tightened immediately. The desired amount of oxygen and nitrogen, in addition to that already in the bomb, was introduced through the needle valve. The bomb was set in position in the dark room and firmly fastened to the camera box of the Midgley indicator. The gas heater was adjusted to raise the temperature of the mixture in the bomb slowly to the desired temperature as indicated on the galvanometer connected to the thermocouple in the bomb. Figure 1-Assembly of Bomb a n d I n d i c a t o r When the desired temperature and pressure were obtained from a Ford spark coil using 7.5 volts on the primary. -4 the gas heater was extinguished, a piece of bromide paper standard pressure Bourdon gage is connected to the bomb was fastened against the curved glass on the camera box, through a needle valve for the purpose of taking the pressure and the revolving mirror was started. The temperature of the gases in the bomb before and after the explosion. A and pressure of the mixture in the bomb were taken and second needle valve is used to control the admission of gases recorded as the temperature and pressure of the mixture to the bomb and to remove samples of the gases for analysis. when ignited. The needle valve between the bomb and the In the top of the bomb a thermocouple is mounted in a pressure gage was closed and the mixture fired a t once by gas-tight joint in such a way that its hot junction is in the means of the switch. The maximum temperature indicated approximate center of the combustion chamber. The ther- by the thermocouple was recorded, the lamp turned off, mocouple is insulated by winding with asbestos string. The and the pressure-time curve developed. The temperature winding of asbestos is overlapped repeatedly to form a nodule, and pressure of the gases within the bomb were then reat the desired distance from the hot junction, of sufficient corded, and the products of combustion analyzed by means size to fill the gland. This construction is perfectly satis- of the regular laboratory e q ~ i p m e n t . 1 ~ Before the experiments were started the pressure element factory and far superior to any known method of cementing was calibrated by direct dead load, and its calibration was the wires in a gas-tight joint. The university was in possession of a Midgley indicator'* checked against the standard gage a t regular intervals. It may be noticed that some of the pressure-time curves which was known to give satisfactory results; and although better adapted for engine work than for individual explosions show what appears to be negative time. These peculiar in a bomb, and by no means gas-tight, this indicator was loops can be duplicated exactly in repeated runs and are due used for these tests.13 Mounted as shown in Figure 1 over to a weakness in the support of the indicator mirror that a gas-tight copper foil diaphragm, the Midgley indicator allows a slight rotation of the mirror in the horizontal plane, gave satisfactory results. This construction makes a gas- when subjected to rapid rotation in the vertical plane. The pressure is plotted as pressure rise, the zero abscissa tight indicator that remains so for twenty-five to fifty explosions unless violent detonation takes place. The pressure representing initial pressure in the bomb. The time is plotted adapter allows the use of pistons of varying diameter, and with the zero ordinate representing the instant the primary circuit of the spark coil is closed through the switch and timer. 12 Midgley, J . SOC.Automotive Eng., 7, 491 (1920). There is a limited variable lag between this time and the
18 The authors acknowledge the generous loan of the Midgley indicator by Prof. W. E. Lay, of the Department of Mechanical Engineering.
14
White, "Gas and Fuel Analysis," 1921.
McGraw-Hill Book e o .
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1925 Mixture
CsHt4
Plate
Figure Test C. Initial temperature Initial pressure, Ibs:/sq. in. gage Average rate of rise of pressure, Ibs./sq. in./sec. Combustion Final pressure a t initial temp. lbs /sq. in. gage
Table 11-Test
+ 6I----0-2----4- 3 Nz
-1-
Data
+ 6.9
CSHN
CSHl4
0 2 I
1 54 60
S!
(J
3 52 80
1 1064 20
2 1091 187
1 1032 20
34
34
37
Atmos.
8
20
430,000 Click
600.000 Click
300,000 Click
530.000 Click
27
35
35
...
I6 9 0 2
21.25 0 55 0 6 20.9
20 4 0.2 2.1 19 6
1 0
22 6
. . ...
2
... ... ...
... , . .
...
69,000 Quiet 12
48.8 0.5 2.2 24.8 3,l5
32.5
...
3.9 24
...
... ...
l?.? 3.0
soot deposited. Same charge ignited spontaneously at 2000 c.
time the spark ignites the mixture, so that zero time does not represent the instant of ignition with absolute precision. The rate of pressure rise is the most important consideration, and this factor is shon-n with as much precision as present methods allow. The numbers in the lower right-hand corners of the graphs represent the test number and are placed there for ease in identification. Discussion of Results
The results of this investigation of the effect of initial temperature on homogeneous gaseous combustion are in complete agreement with the available record of similar work. Woodbury, Lewis, and Canby5found a slight increase in the rate of flame propagation when rich mixtures-i. e., mixtures containing an excess of fuel-were heated to 75" C. a t constant pressure before ignition, and a decrease in the rate of flame propagation as the mixtures were heated above 75' to 125" C. With mixtures containing an excess of oxygen, these investigators found a steady decrease in the rate of flame propagation as the initial temperature was raised a t constant pressure from 25" to 80" C. (Table I). Nage13 found that an increase in initial temperature from 15' to 75" C. decreased the rate of rise of pressure when a mixture of city gas and air containing an excess of air was exploded a t constant initial pressure. I n mixtures containing an excess of gas an increase in initial temperature up to 75" C. increased the rate of rise of pressure. Most of the work of the present investigation on the effect of initial temperature was done under conditions of constant volume or density, because i t was considered that the effect of a decrease in density of the charge might obscure the effect of increasing temperature. In fact, the decrease in density was the reason advanced by Dixon2 to explain the lower velocity of detonation a t 100' C. than a t 20" C., and by Woodbury, Lewis, and CanbyJ to explain the lower rate of flame propagation a t higher temperatures. I n the case of mixtures containing an excess of fuel there is a critical temperature, about 75" C., which must be exceeded before the retarding influence of increasing initial temperature is noticed. Below this critical initial temperature an increase in temperature increases to a limited extent the rate of rise of pressure and combustion. In mixtures containing an excess of oxygen this critical temperature has not been noticed in work conducted a t room temperature or above. I n every case an increase in the initial temperature of the explosive mixture, above 75" C., decreased the rate of pressure rise. These definite results, taken with the limited data given by Woodbury, are direct evidence that a critical initial temperature giving a maximum rate of pressure rise exists in
399
-t 7.1 Oz I11
+ 5.15 Nz
CsHtr
1-v-
f 8 014-
1
72.5
3 1025 I52
1033 25
23.3
32
40
2
1030
47,500 Quiet
14 Ni
2 1023
150 67.5
32,800 Quiet
230,000 Click
455,000 Click
138,000 Slight
11
20
31
36
61
44.0 0.1 1.8 6.2
39.9 0 0 1.4 7.9
23 4 0.2 2 6 0 2
23.7
46.0 +0.0 2.6 2.2
...
...
...
... ...
...
... ... ...
...
...
0.0 2.0 0.0
... t . .
explosive gases. It must be admitted that an increase in initial temperature above a definite critical point decreases the rate of rise of pressure even when the initial pressure is increased so as to maintain the density of the charge. It is common experience that an increase in temperature invariably increases the rate of chemical action. Because combustion is a chemical reaction it is apparently reasonable to expect that the rate of gaseous combustion must be increased by an increase in temperature. This is no doubt true where the gases are passed through a hot zone which serves to ignite the succeeding layers of gas, as is the case of furnaces, surface combustion, ammonia oxidation , and similar
d J
5
1400
0
processes. But in combustion in a closed vessel where the gases are ignited a t one point only, it becomes necessary for each succeeding layer of gas t o be ignited by the adjacent burning layer. Under these conditions the rate of inflammation (spread of flame) is limited by the rate a t which a burning
IXDUSTRIAL A N D ENGINEERING CHEMISTRY
400
layer of gas will ignite the adjacent unburnt layer, and this rate may be quite different from the rate of chemical action. Also, the rate of rise of pressure is not the same as the rate of combustion or even of inflarnmati~n.'~The precise distinction between rate of pressure rise, rate of flame travel, rate of chemical reaction, and rate of combustion may be difficult,
Vol. 17, No. 4
Equation 2 indicates that the increase in pressure varies directly with the initial pressure and temperature rise, but inversely as the initial temperature. These facts have been well known to engineers for some time.lB When an explosive mixture is ignited under these conditions the temperature rise ( A T )is determined by dividing the amount of heat supplied to the gases in the bomb during the explosion (Q) by the specific heat of the combustion products (C,) * AT
=
Q C.
(3)
(4)
Fe C,H
Z
.-
8*G*oc AT 187'C INC-SW~ b 9 0,
7t-e In b ~ c w o s T t n 4 R A r u r t A ~C O I S T ~ D W B N pv.7-E
II
but is absolutely necessary if accurate assumptions are to be made. The subject is admittedly complicated and can best be attacked by making no unnecessary assumptions as to the mechanism of combustion, but by applying only those fundamental laws of thermodynamics that are applicable to any isolated system.
This equation may be used to explain in a precise manner many facts that are frequently misstated. It is generally stated that a greater pressure rise is obtained with a cooler charge because a greater weight of mixture has been taken into the cylinder. This is not an accurate statement; the greater weight of charge does not increase the initial pressure, or the rise in temperature, because the increase in heat liberated (Q) is absorbed by the equivalent increase in specific heat (C"). A cooler mixture gives a greater pressure rise because it is a t a lower temperature. Concerning the rate of rise of pressure (dP/dt), by a similar process, dP - P dQ dt T C , dt where t 16
Theoretical Considerations
When stagnant gaseous explosive mixtures are ignited in a constant-volume bomb a t the same temperature as the gaseous mixture, by an electric spark, the resulting explosion takes place in the gas phase and is a homogeneous reaction. The following theoretical considerations of a qualitative nature show that a critical initial temperature giving a maximum rate of rise of pressure is to be expected from our knowledge of gases and chemical reactions. EFFECTOF INITIAL TEMPERATURE, PER SE, UPON PRESSURE RIsE-If a volume of gas a t 300" K. (absolute) is heated sufficiently to raise its temperature 300' C. to 600' K. (absolute), its absolute initial pressure is doubled. If the gas is initially a t 900" K. and its temperature is raised 300' C. to 1200" K., the absolute initial pressure is increased only one-third. If the gases in each case are a t the same initial pressure the ratio of pressure rise is 3:l. Expressed in terms of the gas laws, PV = NRT
where P = absolute pressure of gas within the bomb V = volume of contents of the bomb T = absolute temperature of gas in the bomb R = a constant
(1)
Concerning the magnitude of the pressure rise when the charge is heated a t constant volume with no change in the number of molecules, SVdP = JNRdT
AP
=
AP =
N R AT V
$ AT
where d = differential or infinitesimal increment A = finite increment or change 15
Hopkinson, Proc. Roy. SOC.(London), 1 7 8 , 3 8 7
(1906).
6W
400
zoo
=
time
Clerk, "Gas, Petrol, and Oil Engines," 1909. John Wiley & Sons., Inc.
Cnder actual conditions, as the specific heat (C',) increases with temperature, more heat is required to raise the temperature from 900" to 1200" K. than from 300' to 600" K., and heat would have to be supplied more than three times as fast t o a gas \*-glumeat 900" K. than at 300" K. to give the same rate of rise of pressure. hk
-dQ =
at
h k
= heat of molecular reaction = reaction velocity expressed in number of mols per mol
of fuel per unit of time dP- _ _ Phk -
dt
(7)
- TCv
Equation 7 makes clear the distinction between rate of rise of pressure ( d P / d t ) and rate of reaction ( k ) . The rate of rise of pressure varies inversely as the initial temperature and directly as the rate of chemical reaction ( k ) . which in turn varies directly as the temperature. It is therefore evident that the reaction velocity ( k ) cannot be substituted for rate of rise of pressure, as some writers have done. EFFECTOF INITIAL TEMPERATURE UPON RATE OF REACTIos-An increase in temperature increases the velocity of a chemical reaction, but an increase in temperature at constant pressure decreases the density or concentration. Therefore, the effect of increasing the initial temperature a t constant pressure upon reaction velocity is twofold, one directly increasing the rate of reaction and the other tending to decrease the rate of reaction if above the first order. From the following equation due to van't Hoff,l7 d- = log, k B
given initial pressure at some finite positive temperature when the order of the reaction is greater than 1. If the reaction is of the first order, or the initial density of the gaseous mixture is the same, the rate of reaction increases without limit as the initial temperature is increased. Under these same conditions the rate of rise of pressure has been shown to decrease as the initial temperature was increased beyond a limit (about 75" C.). EFFECTO F INITIAL TEMPERATURE O N RATE O F R I 5 E OF PRESSURE-BY combining Equations 7 and 13 an expression for the rate of rise of pressure of a gaseous explosion at constant volume as a function of initial temperature and pressure is obtained.
h
If it is assumedlthat - is constant, the rate of rise of CV pressure (dP/dt) is a maximum for a given mixture at a - E B given initial pressure when e T is a maximum or T = a T.
As B and a are always positive and finite it is evident that the initial temperature ( T ) has a positive finite value for maximum rate of rise of pressure under these conditions.
F2
dT where k = reaction velocity B = a constant
an expression for k as a function of T may be obtained
- BT + C'
log. k =
B
k = C" e- T For a gaseous mixture of given composition at constant temperature, where k = reaction velocity C"' a constant D = density a = order of reaction-i. e., the number of molecules entering into reaction
PLATE
IV
Combining Equations 9 and 10,
With all actual gases C, is not constant but increases with the temperature. For the present qualitative discussion the specific heat of the products of combustion may be represented by the following expression:
For a gaseous reaction
Substituting this expression for C, in Equation 14,
+
C, = b CT where b and c are positive constants
(g)
D = C"
+
Combining Equations 11 and 12
T('
0
B - a- -
T
-
ae-r
For maximum dP/dt a t constant initial pressure ( P )
=It constant pressure and composition k varies as - _B e
R
d_P = - C X h P dt (b cT)
T2
T
b +cT
=o
B
This expression has a maximum T-alue when T = a--As - I B is always positive arid a is always a positive integer not less than 1, the velocity of reaction X: is a maximum for a 17 Nernst, "Theoretical Chemistry," 1911, Macmillan Co.; Washburn, "Principles of Physical Chemistry," McGraw-Hi11 Book Co.
As all these constants, a, b, c, and B , are positive and finite, the initial temperature ( T ) has a real positive value for the maximum rate of rise of pressure of an explosive mixture a t a given initial pressure. In considering the case of constant initial density of the
INDUSTRIAL AND ENGINEERISG CHEJIISTRY
402
explosive mixture, P / T is constant and the expression is simpler. For maximum dP/dt from Equation 15, .-"=I3
d(
T+b
T = fB f1/B2
+ 4bB/c
2
As b, C, and B are positive and finite, the initial temperature (T)has a real positive value for the maximum rate of rise of pressure for a given density of an explosive mixture.
1-01. 17, S o . 4
Conclusion
Because rate of rise of pressure and rate of combustion have been confused with rate of reaction, it has generally been assumed that an increase in initial temperature must increase the rate of combustion or of rise of. pressure of a gaseous explosion. The experimental work reported in this paper shows that an increase in initial temperature above a definite critical value decreases the rate of rise of pressure of a gaseous explosion. The theoretical considerations presented show that the existence of a critical initial temperature is to be expected from our knowledge of gases and gaseous reactions.
The Measurement of the Temperature of a Flowing Gas' By R. T. Haslam and E. L. Chappell MASSACLW6ETTS INSTITWTa O F TECENOLOOY, CAMBRIDGP,MASS
The various methods in use for eliminating errors in temperature measurements of flowing gases are discussed. These methods are (1) protecting thermometer or pyrometer couple with a polished metal shield of low radiating power, (2) the use of a thermocouple of very small diameter, (3) the use of a series of thermocouples of varying diameters and extrapolating the apparent temperature-diameter of couple curve to zero diameter of couple, and (4) reducing radiation from the thermocouple by the use of a heat insulating shield or sleeve. A new method of gas temperature measurement is discussed which employs a high gas velocity past the thermocouple to bring it to as near the true gas temperature as possible.
T
H E accurate measurement of the temperature of a flowing gas is more complicated than the measurement of the temperature of a solid or a liquid. A thermocouple or thermometer is ordinarily inserted in the gas and the temperature of this device taken as the true gas temperature. However, such a thermometer or thermocouple reading may be seriously in error since the flow of heat by radiation between the surrounding solids and the thermocouple affects the apparent gas temperature. The tremendous effect of radiation may be illustrated by the following data (Table I) taken from work describc 1 later. Air a t a known velocity was blown through a short length of red hot pipe in the center of which mas placed a thermocouple. Table I Gas velocity Temperature of pipe surface T r u e temperature of air a t couple Apparent temperature (couple reading)
6.0 feet per second 1350' F. 270' F. 890' F.
I n this case the thermocouple indicated a temperature 620" F. higher than the true gas temperature and only 460" F. lower than the temperature of the surrounding pipe walls. A flowing gas, as in recuperators, blast furnace stoves, stacks, boiler settings, or furnaces, may be a t a tbnperature hundreds of degrees from that of its surroundings, and when such a temperature difference exists a large error is Presented before t h e Section of Gas and Fuel Chemistry a t t h e 68th Meeting of t h e American Chemical Society, Ithaca, N. Y., September 8 t o 13, 1924. 1
A method of calculation is developed whereby the equation
is made more valuable by the use of the following equation for the value of V0.67
h , = 0.51 T,,,0.4
+ 0.09logD D
0.0
A summary of the advantages and disadvantages of all these methods is given in Table VIII, while the error involved in the use of these methods is illustrated by examples in Table IX.
possible. For example? a handbook2 mentions an engineer's report on a boiler plant in which a flue gas temperature of 386" F. and steam pressure of 162 pounds were given. As 371" F. corresponds to the pressure of 162 pounds, it was indicated that the flue gases were only 15 degrees hotter than the water in the tubes. Investigation showed that this gas temperature had been measured by a thermometer placed among the boiler tubes, which really measured the tube temperature, the gases probably being 200 to 300 degrees hotter. It may be noted that boiler plant heat balances generally account for only 92 to 97 per cent of the heat. In many cases this "unaccounted for" heat is carried out the stack by the gases whose temperature was read too low by an improperly exposed thermometer. It is necessary to recognize that a thermometer or thermocouple measurement of a gas temperatureis asmuch influenced by the temperature of the surroundings as by that of the gas itself, and special precautions and methods must be considered for the measurement of the temperature of gas streams. It is the object of this paper to summarize some of these methods and to suggest means for the true measurement of high gas temperatures. Factors Determining Reading of Thermometers or Thermocouples
The temperature of a thermocouple in a gas will always lie between the temperatures of the surroundings and of the gas
* H. S.B. W.- Cochrane Co., "Finding a n d Stopping Waste in Modern Boiler Rooms," Vol. 11, 1921.
