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Model investigations into the factors affecting the mixing of gas and air in coke oven flues
Model Investigations into the Factors affect&g the Mixing of Gas and Air in Coke Oven Flues V.
JAYARAMAN*, C .
HULSE and
M.
W.
TH R IN G
The length o[ the heating flame in a coke oven flue is governed only by the mixing o[ the gas antt the air, but the [actors that govern such mixing are not clear. This model work is an attempt to establish these for the case o[ rich (coke oven) gas firing. It has been found that a wide range o[ flame lengths can be obtained for the same flow rates by employing burners and airports of different cross sectional area. A scale theory is put [orward to render the model results applicable to actual systems. The theory has been roughly confirmed [or a particular case, by carrying out fnll scale trials in an operating coke oven flue. Work on further confirmation is in hand at Sheffield.
THERE are two major problems in obtaining uniform heating of the walls of a vertical-flue coke oven. The temperature uniformity along the length of the oven wall depends on the distribution of the gas and the air to the various flues, while that along the height is dependent on the length of the heating flames in the flues. The distribution problem has engaged the attention of coke oven designers for a long time, and a large measure of success can be said to have been achieved in perfecting the distribution. The problem of the flame length has, however, not been satisfactorily solved to this date. This work is an attempt to analyse this latter problem from an aerodynamic point of view. The only other work, done along similar lines, is described in two papers 1. ~, but there are no useful conclusions. The approach is based on the facts that the flame in the coke oven flue is a diffusion flame and that the combustion is subject to a dynamic r6gime: that is, the combustion rate at the prevailing high temperatures is decided essentially by the rate at which the fuel and the air are brought together. Investigations have been carried out on a cold model, under conditions of a fair degree of dynamic similarity, and partial confirmation of the model results has been obtained on an actual flue. Only the case of rich gas firing is dealt with. MODEL WORK
Similarity criteria A l/10 scale model of a twinflue of a typical Underjet compound coke oven was built in Perspex (Figure 1). Calculations show that the dimensions of modern flues and the rates of carbonization in modern practice (i.e. the flow rates of the heating gases in the flues) are such that the Reynolds *V. Jayaraman, Ph.D.. A.M.Inst.F.. is now with the Thermal Engineering Del~anment, Tata Locomotive and Engineering Co. Ltd. Jamshedpur, India.
97
V. JAYARAMAN, C. HULSE AND M. W. THRING
number in the flues, DV/v, is of the order of 700 where D is the hydraulic mean diameter of the flue, V the actual gas velocity and v the hot gas kinematic viscosity in the same set of units. The volume of air normally employed for combustion is about 6n.ft 3 per n.ft 3 of coke oven gas, representing 30 per cent excess air. For a coke oven gas specific gravity
Figure 1. Perspex model of a twin-
Oue
of 0"4, the mass ratio of air and gas in a coke oven flue therefore becomes 15. Working with water or air as the model fluid at a Reynolds number of 700 in the flue, the total flow being divided in the ratio 1 : 15 between the burner and the two airports, the effect of various factors on the mixing was studied. In particular, the areas of the burner and the airports were varied over a wide range (Figure 2). Buoyancy effects, known to exist in the hot system, could not be simulated on the cold model, since this would require the use of miscible fluids of greatly different densities, which are not easily available.
Photographs of [tow patterns A number of flow patterns, corresponding to various burner diameterairport size combinations, were first photographed with water as the model fluid (Figure 3). For the dimensions of the model, the Reynolds number of 700 fixed the total flow at 28.4gall/h of water at 10°C. This was appropriately divided among the 'gas' and the 'air' streams. Flow visualization was achieved by employing a very dilute (but deeply coloured) solution of malachite green in water, for the stream representing the gas. 98
FACTORS AFFECTING THE MIXING OF GAS AND AIR IN COKE OVEN FLUES
Mixing
measurements
Using air as the model fluid, the 'gas' stream being mixed with a small quantity of nitrous oxide as a tracer, many of the arrangements of the water model were then examined quantitatively to obtain the rate of mixing in each case, by analysing the nitrous oxide concentration at various points with the help of an infra-red gas analyser. For the same Reynolds number, with the air model, the velocity has to be greater, since the kinematic viscosity of air is greater. The flow is calculated to be 48"8 ft3/h of air at 10°C.
a
b
c
d
Figure 2. Flame lengths obtainable with various airport sizes [or a burner 4"00 m m in diameter. (a) Each airport 7 7 0 m m sq. (b) Each airport 10"25 m m sq. (c) Each airport 1340 m m sq. (d) Each airport 15"80 m m sq.
From the nitrous oxide concentration at various points in the model, contours were drawn showing lines of equal mixing in the model. The line along which the gas-air mixture is stoichiometric may be taken to represent the flame front, and the highest point on this line therefore gives the height of the flame. Conclusions [rom the model
work
(1) The sizes of the gas and air inlets to the flue have the greatest effect on mixing. A wide range of mixture rates, i.e. flame lengths, can be obtained for the same flow rates by employing burners and airports of different cross sectional area. 99
V. JAYARAMAN, C. HULSE AND M. W. THRING
(2) As a rule, for any given burner diameter, increasing the size of the airports leads to longer flames. Figures 2(a) (4'00, 7-70)*, 2(b) (4"00, 10"25), 2(c) (4"00, 13"40) and 2(d) (4-00, 15-80) illustrate this effect on a particular burner, 4"00 mm in diameter. Figure 4(a) gives the flame lengths (derived from mixing measurements) against the airport size for various burners, while Figure 4(b) gives flame length versus burner diameter for the different airport sizes. Contours similar to those of Figure 3 represent the general nature of the flow pattern usually obtained.
I i#
Figure 3. Concentration (mixing) contours obtained with various airport sizes ]or different burners using water: (a) 1"75 m m diameter burner, airport size 15"80 mm sq. each; (b) 3.14 m m diameter burner, airport size 13.40 m m sq. each; (c) 3"14 m m diameter burner, airport size 15"80 m m sq.
II//
r,ll/
IlJ/
(a)
each
(b)
(c)
(3) The effect of factors like excess air percentage, spacing of the airports with respect to the burner, entry conditions, etc., is, within limits, secondary. INTERPRETATION OF THE MODEL RESULTS
The observations on the model, summarized by Figure 4, can be explained at least partly as follows. *Values
in parentheses are the burner diameter and the airport side, respectively, in rnillirnetres.
100
FACTORS AFFECTING THE MIXING OF GAS AND AIR 1N COKE OVEN FLUES As the air streams enter the flue, a certain amount of recirculation takes place due to the sudden increase in cross sectional area, and if the gas stream has enough momentum to break through this return flow, without itself getting broken up to any appreciable degree, the mixing is thereafter slow. Such recirculation of the air stream would normally be less the bigger the proportion of the flue area occupied by the airports, and the chances of the gas stream breaking up while passing through are less. This explains why the mixing is delayed with bigger airports for any given burner diameter (Figure 4).
oBurner ,~ Burner oBurner ×Burner
175 254 314 400
mm mm mm mm
o Airports 7.70 mm sq. Airports 1340 mm sq. o Airports 1580 mm sq.
diam diam. diam. diam.
40
=E~ 3C C
E
20
U-
10
(a) 0
(b) I
5
I
I0 15 Side of airporls
20 mm
I I 2 3 Burner diameter
4 mm
Figure 4(a). Flame length versus airport size for various burners Figure 4(b). Flame length versus burner diameter for various airport sizes
As regards the gas stream, there are two opposing considerations. For a given mass flow, burners of smaller diameter pass streams of greater momenta, which must have a greater capacity to break through the return air flow. Smaller burners, however, also lead to more turbulent gas streams, which of themselves have a tendency to break up and recirculate. The mean is struck by a burner which produces enough momentum while, at the same time, keeping turbulence down to the necessary extent. The crossing of the lines in Figure 4 can be attributed to this. SCALE THEORY The question of formulating a scale theory becomes difficult in this case. In view of the low Reynolds numbers involved, the recirculation of the air stream would probably be controlled mainly by the Reynolds numbers in 101
V. JAYARAMAN, C. HULSE AND M. W. THRING
the system, while the breaking through of the gas stream would depend on its momentum, the extent of dispersal depending again on the turbulence level, as determined by the Reynolds number. Mixing is the net result of these various factors. In the absence of a suitable theory, which can adequately take into account all these factors, and in view of the predominant effect of Reynolds numbers on the process of mixing, it is suggested that any model flow pattern can be reproduced substantially in full scale if: (1) the Reynolds numbers in the burner and the airports in full scale are made equal to those on the model (in addition to the Reynolds number in the main chamber being the same in both cases), and (2) the mass ratio of air and gas flows is also the same on the model as on full scale. These two requirements can be shown to lead to the relations: Dr = K
d,,~ole,
D~=Kd,~/I~
.
.... .
.
.
.
[1] [2]
where D is the full scale linear dimension, d the linear dimension on the model, K the scale factor and ~ the absolute viscosity. Subscripts ~, o and refer to air, combustion products and gas respectively. Since ~ is greater than ~g and 1~ (the difference depends largely on the difference between T~, Tg and T~, where T is the temperature), the burner and the airports in full scale would be larger than those obtained by direct scaling up. For example, in a flue ten times as big as the model, the flow pattern of F i g u r e 3(b) should be expected to be reproduced not by employing a burner diameter of (3-14 x 10) or 31.4mm, but by employing one about 65 mm. This is based on /~ corresponding to 925°C, which has been found independently from actual measurements to be the order of gas temperatures at the burner mouth to be expected in the Underjet design. The airports can be similarly scaled up. FULL SCALE TRIALS
The purpose of these trials was to establish the flame length in an operating coke oven flue for any known conditions of flow and compare this with the flame length given by the model when run under conditions of dynamic similarity, as expressed by equations 1 and 2. The flame length was established from analysis of quenched gas samples drawn from the flue, by using the formula r = a "/(2 CO2 + 2 O2 + CO) - (rnC,nH~m+ 2 CH, + H:) where CO2, 02, etc., refer to the percentages of these gases in the sample. m has been taken as 3 here, and the values of a and b, for a typical coke oven gas, are 1"09 and 2.465 respectively. Similar relations can be derived 102
FACTORS AFFECTING THE MIXING OF GAS AND AIR IN COKE OVEN FLUES
for any gas from material balances on any three of carbon, oxygen, hydrogen and nitrogen, r is the volume air/gas ratio. After a series of five trials on a twinflue, it was established that for normal flow rates, the flame length was about 3 ft 6 in. above the burner block. Parallel experiments on the model, using suitable burners and airports to give the same Reynolds numbers as in the flue, showed that the scaled flame lengths given by the model, though not exactly equal (the model flame lengths were 25 per cent shorter), were of the same order. The discrepancy can be explained as being due, among other things, to the fact that buoyancy effects have not been allowed for in the model work. It was also found from the gas analyses that the stoichiometric mixture was formed about 9 in. below the point where combustion was complete, indicating the presence of an 'unmixedness' factor in the flow pattern. In other words, the flow (despite the low Reynolds numbers) was such that, at any point, the concentration alternated between two values: and at points where it alternated between gas-rich and air-rich mixtures, the final quenched samples contained both combustibles and oxygen. These alternate pockets mix as they move along and burn completely eventually. The point at which all combustion ceases is, really, of interest for the problem of even heating. For comparison with model results, however, the position at which the stoichiometric mixture is formed is the one of interest (a noncooled probe is adequate for this purpose alone), because the model technique employed here gives only the time-average value of the concentration and cannot throw any light on unmixedness. CONCLUSIONS
(1) It appears to be quite possible to lengthen flames in a coke oven flue sufficiently for higher ovens by a suitable choice of burners and airports. As a rule, in any existing flue design where the flame is short, making the airports bigger should increase the flame length. To what extent the flame would be lengthened for any given increase in airport size, and whether or not the necessary increase in flame length can be achieved by this means alone would depend on the burner diameter. The present work can give this information (Figure 4). The results are applicable to all flues of ratio of sides 1.4 (and probably to those flues in the range of side ratio 1.2 to 1.6), where the Reynolds number is 700 + 150. (2) The scale theory, which is the basis of the above recommendation, has been roughly confirmed for one case. Work on further confirmation is in hand at the University of Sheffield. (3) Rich gas in a coke oven heating system has been found to get quite hot on its way to the flue. In a typical Underjet design, the temperature of the gas rises to between 850 and 1 000°C. The same effects must be expected in the gas gun system, but here the temperatures in the various flues of any heating wall should be expected to be different. The present work indicates that if, for example, the gas temperature in the end flues is 100°C and that at the central flues is 1 000°C, the burners at the end may have to be more than twice as big as those at the centre, to give the same flame lengths. 103
V. JAYARAMAN, C. HULSE AND M. W. THRING
The work was carried out in the Department o[ Fuel Technology and Chemical Engineering at the University of Sheffield, under a bursary from Simon-Carves Limited, and grate[ul thanks are due to this firm for their help. Department of Fuel Technology and Chemical Engineering, University of Sheffield (Received September 1958) REFERENCES
A6ROSKIN, A. A. and GUBERGRITS, M. Y. Izvest. Akad. Nauk S.S.S.R., OtdeL tekh. Nauk (No. 11) (1949) 1626 2Gt~ERCRITS, M. Y. Ivest. Akad. Nauk S.S.S.R., Otdel. tekh. Nauk (No. 5) (1950) 695
104
JAYARAMAN*, C .
HULSE and
M.
W.
TH R IN G
The length o[ the heating flame in a coke oven flue is governed only by the mixing o[ the gas antt the air, but the [actors that govern such mixing are not clear. This model work is an attempt to establish these for the case o[ rich (coke oven) gas firing. It has been found that a wide range o[ flame lengths can be obtained for the same flow rates by employing burners and airports of different cross sectional area. A scale theory is put [orward to render the model results applicable to actual systems. The theory has been roughly confirmed [or a particular case, by carrying out fnll scale trials in an operating coke oven flue. Work on further confirmation is in hand at Sheffield.
THERE are two major problems in obtaining uniform heating of the walls of a vertical-flue coke oven. The temperature uniformity along the length of the oven wall depends on the distribution of the gas and the air to the various flues, while that along the height is dependent on the length of the heating flames in the flues. The distribution problem has engaged the attention of coke oven designers for a long time, and a large measure of success can be said to have been achieved in perfecting the distribution. The problem of the flame length has, however, not been satisfactorily solved to this date. This work is an attempt to analyse this latter problem from an aerodynamic point of view. The only other work, done along similar lines, is described in two papers 1. ~, but there are no useful conclusions. The approach is based on the facts that the flame in the coke oven flue is a diffusion flame and that the combustion is subject to a dynamic r6gime: that is, the combustion rate at the prevailing high temperatures is decided essentially by the rate at which the fuel and the air are brought together. Investigations have been carried out on a cold model, under conditions of a fair degree of dynamic similarity, and partial confirmation of the model results has been obtained on an actual flue. Only the case of rich gas firing is dealt with. MODEL WORK
Similarity criteria A l/10 scale model of a twinflue of a typical Underjet compound coke oven was built in Perspex (Figure 1). Calculations show that the dimensions of modern flues and the rates of carbonization in modern practice (i.e. the flow rates of the heating gases in the flues) are such that the Reynolds *V. Jayaraman, Ph.D.. A.M.Inst.F.. is now with the Thermal Engineering Del~anment, Tata Locomotive and Engineering Co. Ltd. Jamshedpur, India.
97
V. JAYARAMAN, C. HULSE AND M. W. THRING
number in the flues, DV/v, is of the order of 700 where D is the hydraulic mean diameter of the flue, V the actual gas velocity and v the hot gas kinematic viscosity in the same set of units. The volume of air normally employed for combustion is about 6n.ft 3 per n.ft 3 of coke oven gas, representing 30 per cent excess air. For a coke oven gas specific gravity
Figure 1. Perspex model of a twin-
Oue
of 0"4, the mass ratio of air and gas in a coke oven flue therefore becomes 15. Working with water or air as the model fluid at a Reynolds number of 700 in the flue, the total flow being divided in the ratio 1 : 15 between the burner and the two airports, the effect of various factors on the mixing was studied. In particular, the areas of the burner and the airports were varied over a wide range (Figure 2). Buoyancy effects, known to exist in the hot system, could not be simulated on the cold model, since this would require the use of miscible fluids of greatly different densities, which are not easily available.
Photographs of [tow patterns A number of flow patterns, corresponding to various burner diameterairport size combinations, were first photographed with water as the model fluid (Figure 3). For the dimensions of the model, the Reynolds number of 700 fixed the total flow at 28.4gall/h of water at 10°C. This was appropriately divided among the 'gas' and the 'air' streams. Flow visualization was achieved by employing a very dilute (but deeply coloured) solution of malachite green in water, for the stream representing the gas. 98
FACTORS AFFECTING THE MIXING OF GAS AND AIR IN COKE OVEN FLUES
Mixing
measurements
Using air as the model fluid, the 'gas' stream being mixed with a small quantity of nitrous oxide as a tracer, many of the arrangements of the water model were then examined quantitatively to obtain the rate of mixing in each case, by analysing the nitrous oxide concentration at various points with the help of an infra-red gas analyser. For the same Reynolds number, with the air model, the velocity has to be greater, since the kinematic viscosity of air is greater. The flow is calculated to be 48"8 ft3/h of air at 10°C.
a
b
c
d
Figure 2. Flame lengths obtainable with various airport sizes [or a burner 4"00 m m in diameter. (a) Each airport 7 7 0 m m sq. (b) Each airport 10"25 m m sq. (c) Each airport 1340 m m sq. (d) Each airport 15"80 m m sq.
From the nitrous oxide concentration at various points in the model, contours were drawn showing lines of equal mixing in the model. The line along which the gas-air mixture is stoichiometric may be taken to represent the flame front, and the highest point on this line therefore gives the height of the flame. Conclusions [rom the model
work
(1) The sizes of the gas and air inlets to the flue have the greatest effect on mixing. A wide range of mixture rates, i.e. flame lengths, can be obtained for the same flow rates by employing burners and airports of different cross sectional area. 99
V. JAYARAMAN, C. HULSE AND M. W. THRING
(2) As a rule, for any given burner diameter, increasing the size of the airports leads to longer flames. Figures 2(a) (4'00, 7-70)*, 2(b) (4"00, 10"25), 2(c) (4"00, 13"40) and 2(d) (4-00, 15-80) illustrate this effect on a particular burner, 4"00 mm in diameter. Figure 4(a) gives the flame lengths (derived from mixing measurements) against the airport size for various burners, while Figure 4(b) gives flame length versus burner diameter for the different airport sizes. Contours similar to those of Figure 3 represent the general nature of the flow pattern usually obtained.
I i#
Figure 3. Concentration (mixing) contours obtained with various airport sizes ]or different burners using water: (a) 1"75 m m diameter burner, airport size 15"80 mm sq. each; (b) 3.14 m m diameter burner, airport size 13.40 m m sq. each; (c) 3"14 m m diameter burner, airport size 15"80 m m sq.
II//
r,ll/
IlJ/
(a)
each
(b)
(c)
(3) The effect of factors like excess air percentage, spacing of the airports with respect to the burner, entry conditions, etc., is, within limits, secondary. INTERPRETATION OF THE MODEL RESULTS
The observations on the model, summarized by Figure 4, can be explained at least partly as follows. *Values
in parentheses are the burner diameter and the airport side, respectively, in rnillirnetres.
100
FACTORS AFFECTING THE MIXING OF GAS AND AIR 1N COKE OVEN FLUES As the air streams enter the flue, a certain amount of recirculation takes place due to the sudden increase in cross sectional area, and if the gas stream has enough momentum to break through this return flow, without itself getting broken up to any appreciable degree, the mixing is thereafter slow. Such recirculation of the air stream would normally be less the bigger the proportion of the flue area occupied by the airports, and the chances of the gas stream breaking up while passing through are less. This explains why the mixing is delayed with bigger airports for any given burner diameter (Figure 4).
oBurner ,~ Burner oBurner ×Burner
175 254 314 400
mm mm mm mm
o Airports 7.70 mm sq. Airports 1340 mm sq. o Airports 1580 mm sq.
diam diam. diam. diam.
40
=E~ 3C C
E
20
U-
10
(a) 0
(b) I
5
I
I0 15 Side of airporls
20 mm
I I 2 3 Burner diameter
4 mm
Figure 4(a). Flame length versus airport size for various burners Figure 4(b). Flame length versus burner diameter for various airport sizes
As regards the gas stream, there are two opposing considerations. For a given mass flow, burners of smaller diameter pass streams of greater momenta, which must have a greater capacity to break through the return air flow. Smaller burners, however, also lead to more turbulent gas streams, which of themselves have a tendency to break up and recirculate. The mean is struck by a burner which produces enough momentum while, at the same time, keeping turbulence down to the necessary extent. The crossing of the lines in Figure 4 can be attributed to this. SCALE THEORY The question of formulating a scale theory becomes difficult in this case. In view of the low Reynolds numbers involved, the recirculation of the air stream would probably be controlled mainly by the Reynolds numbers in 101
V. JAYARAMAN, C. HULSE AND M. W. THRING
the system, while the breaking through of the gas stream would depend on its momentum, the extent of dispersal depending again on the turbulence level, as determined by the Reynolds number. Mixing is the net result of these various factors. In the absence of a suitable theory, which can adequately take into account all these factors, and in view of the predominant effect of Reynolds numbers on the process of mixing, it is suggested that any model flow pattern can be reproduced substantially in full scale if: (1) the Reynolds numbers in the burner and the airports in full scale are made equal to those on the model (in addition to the Reynolds number in the main chamber being the same in both cases), and (2) the mass ratio of air and gas flows is also the same on the model as on full scale. These two requirements can be shown to lead to the relations: Dr = K
d,,~ole,
D~=Kd,~/I~
.
.... .
.
.
.
[1] [2]
where D is the full scale linear dimension, d the linear dimension on the model, K the scale factor and ~ the absolute viscosity. Subscripts ~, o and refer to air, combustion products and gas respectively. Since ~ is greater than ~g and 1~ (the difference depends largely on the difference between T~, Tg and T~, where T is the temperature), the burner and the airports in full scale would be larger than those obtained by direct scaling up. For example, in a flue ten times as big as the model, the flow pattern of F i g u r e 3(b) should be expected to be reproduced not by employing a burner diameter of (3-14 x 10) or 31.4mm, but by employing one about 65 mm. This is based on /~ corresponding to 925°C, which has been found independently from actual measurements to be the order of gas temperatures at the burner mouth to be expected in the Underjet design. The airports can be similarly scaled up. FULL SCALE TRIALS
The purpose of these trials was to establish the flame length in an operating coke oven flue for any known conditions of flow and compare this with the flame length given by the model when run under conditions of dynamic similarity, as expressed by equations 1 and 2. The flame length was established from analysis of quenched gas samples drawn from the flue, by using the formula r = a "/(2 CO2 + 2 O2 + CO) - (rnC,nH~m+ 2 CH, + H:) where CO2, 02, etc., refer to the percentages of these gases in the sample. m has been taken as 3 here, and the values of a and b, for a typical coke oven gas, are 1"09 and 2.465 respectively. Similar relations can be derived 102
FACTORS AFFECTING THE MIXING OF GAS AND AIR IN COKE OVEN FLUES
for any gas from material balances on any three of carbon, oxygen, hydrogen and nitrogen, r is the volume air/gas ratio. After a series of five trials on a twinflue, it was established that for normal flow rates, the flame length was about 3 ft 6 in. above the burner block. Parallel experiments on the model, using suitable burners and airports to give the same Reynolds numbers as in the flue, showed that the scaled flame lengths given by the model, though not exactly equal (the model flame lengths were 25 per cent shorter), were of the same order. The discrepancy can be explained as being due, among other things, to the fact that buoyancy effects have not been allowed for in the model work. It was also found from the gas analyses that the stoichiometric mixture was formed about 9 in. below the point where combustion was complete, indicating the presence of an 'unmixedness' factor in the flow pattern. In other words, the flow (despite the low Reynolds numbers) was such that, at any point, the concentration alternated between two values: and at points where it alternated between gas-rich and air-rich mixtures, the final quenched samples contained both combustibles and oxygen. These alternate pockets mix as they move along and burn completely eventually. The point at which all combustion ceases is, really, of interest for the problem of even heating. For comparison with model results, however, the position at which the stoichiometric mixture is formed is the one of interest (a noncooled probe is adequate for this purpose alone), because the model technique employed here gives only the time-average value of the concentration and cannot throw any light on unmixedness. CONCLUSIONS
(1) It appears to be quite possible to lengthen flames in a coke oven flue sufficiently for higher ovens by a suitable choice of burners and airports. As a rule, in any existing flue design where the flame is short, making the airports bigger should increase the flame length. To what extent the flame would be lengthened for any given increase in airport size, and whether or not the necessary increase in flame length can be achieved by this means alone would depend on the burner diameter. The present work can give this information (Figure 4). The results are applicable to all flues of ratio of sides 1.4 (and probably to those flues in the range of side ratio 1.2 to 1.6), where the Reynolds number is 700 + 150. (2) The scale theory, which is the basis of the above recommendation, has been roughly confirmed for one case. Work on further confirmation is in hand at the University of Sheffield. (3) Rich gas in a coke oven heating system has been found to get quite hot on its way to the flue. In a typical Underjet design, the temperature of the gas rises to between 850 and 1 000°C. The same effects must be expected in the gas gun system, but here the temperatures in the various flues of any heating wall should be expected to be different. The present work indicates that if, for example, the gas temperature in the end flues is 100°C and that at the central flues is 1 000°C, the burners at the end may have to be more than twice as big as those at the centre, to give the same flame lengths. 103
V. JAYARAMAN, C. HULSE AND M. W. THRING
The work was carried out in the Department o[ Fuel Technology and Chemical Engineering at the University of Sheffield, under a bursary from Simon-Carves Limited, and grate[ul thanks are due to this firm for their help. Department of Fuel Technology and Chemical Engineering, University of Sheffield (Received September 1958) REFERENCES
A6ROSKIN, A. A. and GUBERGRITS, M. Y. Izvest. Akad. Nauk S.S.S.R., OtdeL tekh. Nauk (No. 11) (1949) 1626 2Gt~ERCRITS, M. Y. Ivest. Akad. Nauk S.S.S.R., Otdel. tekh. Nauk (No. 5) (1950) 695
104