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Factors affecting combustion stability
714
T H I R D SYMPOSIUM ON COMBUSTION~ F L A M E AND E X P L O S I O N P H E N O M E N A
94
FACTORS
AFFECTING
COMBUSTION
STABILITY 1
By ~. t~. VAR~ DESCRIPTION OF OPERATING LIMITS
Continuous flow combustion chambers are usually tested for operating range by determining the fuel-air ratio limits as a function of velocity. In general there are two distinct kinds of limits. One type is often called a blow-out limit. At the blowout condition the ignition source (usually a "flame holder") can no longer propagate a flame front into the main body of the flowing mixture. Observation of the blow-out process easily shows that as the limit is approached by varying the fuel flow the flame front in the wake of the flame holder narrows and finally disappears, leaving only a weak flame immediately behind the flame holder. Blow-out limits are not accompanied by instability and hence can be called smooth. At low inlet velocities these limits are very near to the so-called static ignition limits and are characteristic of the fuel being used. As the inlet velocity is increased the blow-out limits gradually narrow as the flame velocity required for propogation into the main stream increases. Typical blow-out limits for flat plate fla~ne holders and AN-F-28 fuel are shown in figure I for inlet velocities from 10 to 100 ft./sec. The second type of limit is characterized by combustion instability and is usually designated as a rough limit. Rough limits reduce the operating range and lie inside the true blow-out limits. Blow-out limits are largely a function of the fuel (flame speed) and velocity distribution behind the flame holder while rough limits are more a function of the mixture distribution, flame speed, and combustion chamber geometry. I t is of considerable importance to clearly differentiate the two types of limits. Blow-out limits can usually be determined only in a short combustion chamber. A short chamber may be defined as one in which the reaction is not enclosed while a long chamber is taken to mean one in which the combustion is carried to completion. With short chambers there is little difficulty with rough combustion while simply adding tail pipe length to achieve a long chamber may often make the combustion so violent that operation is impossible. In order to obtain a quantitative comparison of combustion stability we have employed a hot wire anemometer to measure velocity fluctuations t This paper covers work done for the A.M.C. on contract W 33-038AC-15319.
in the burner inlet section. The velocity fluctuation for a particular burner operating at constant inlet velocity is nearly independent of F/A ratio when operating within blow-out limits but shows an increasing characteristic when a rough limit is approached. The fluctuations observed with combustion are normally several times the turbulence level for cold flow at the same inlet velocity. Data and descriptions of test results are given below. FLOW CONI)ITIONS IN THE COMBUSTION CHAMBER If one considers an idealized case of a constant cross section combustion chamber, it is possible to arrive at a qualitative description of some of the chamber flow conditions. Experimental evidence of flame fronts in short tubes indicates that after the flow interference of the flame holder has disappeared the reaction zone has little curvature. Since the unburned mixture in a~ short chamber has suffered a pressure drop, it has been accelerated and leaves the burner through a reduced area. Thus the burned gas has a lower average velocity and the unburned gas a higher velocity than would be obtained with straight flow in the chamber. The flow is thus seen to be contracting in the unburned mixture. The same type of flow must also occur in long chambers as the first gas to burn is confined by the chamber walls and the expansion of the burned gas forces a contraction of the unburned mixture. The same result is arrived at by a consideration of the momentum change across the flame front. This results in a bending or refraction of the stream lines as they cross the flame front. Considering the flame front as starting at the wall of the burner, a streamline entering the front parallel to the axis would be bent outward. At low velocities the fluid can be thought of as incompressible, and since the outward flow cannot continue it then appears that a streamline starting in the unburned mixture converges toward the axis and enters the flame front, the leaving streamline then diverges away from the axis and will finally reach the same radial distance as the initial entering streamline. Such considerations lead to the conclusion that the last part of the mixture to burn has a higher velocity than that measured at the burner inlet. In order to get complete combustion or to dose the flame
COMBUSTION
IN
ENGINES
front the flow pattern requires a higher flame velocity at the point of closure than at other points in the flame front. It is then reasonable to assume that the flame front closure would lead to unstable flow conditions when the flame speed becomes marginal. With complete combustion and a closed flame front the full theoretical chamber pressure will be built up in the inlet section. We may then consider the flame front as a pressure supporting surface. If combustion ceases momentarily at a closure point (or any part of the flame front) the excess chamber pressure will force unburned gas into the surrounding exhaust gas and after a short time lag the unburned charge will detonate with a consequent disruption of the entire flow.
AND
effect of the walls is present to reduce the reaction rate. The effect of increasing length on roughness is not abrupt because of ignition lag and the amount of unburned gas which can be injected into the exhaust region inside the burner. At low inlet velocities the momentum change pressure drop due to burning is small and increases with increasing mixture velocity. Any interruptions in the flame front produce only small pressure changes at low speeds and the same amount of instability of the flame front at high speeds will give rise to large fluctuations. 10C RICH ROUGH LIMIT
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FIo. 1. Gasoline blowout limits. Flat plate flame holders. I n support of these conclusions we find that short chambers, which do not have a closed flame front, burn smoothly indicating no fundamental instability in the beginning stages of the combustion process. Experiments with 3[ inch cylindrical chambers 48 inches long showed that when burning propane with an orifice type flame holder, reasonably wide operating limits were obtained while a central disk holder produced such roughness that operation was impossible. In this case the orifice holder produces a conical flame front which ideally closes at a point. The amount of gas which can leak through the point is small and the surrounding hot gases are conducive to a faster reaction rate by preheating of the unburned core flow. The central holder closes the front at the base of a conical surface on the wall. Here the area involved is much greater and the quenching
,
20 O33
50 40 50 60 7'0 BURNER INLET VELOGITY-FTISEC O36 036 041 044 O46 9-~V'S VELOCITY, NO BURNING
80 ,O.49
FIG. 2. Burning roughness and limits for flame holder 0345-42 in a 388 I.D. x 48 inch length burner with unobstructed inlet. Pressure: ambient sea level. Fuel : propane Inlet mixture temperature: 135~ # ' / U measured by hot wire anemometer at axis of burner inlet 16 in. upstream of flame holder. ( # ' / U = Longitudinal velocity fluctuation/mean velocity at hot wire.) Runs: 942-989. EXPERIMENTAL DATA
Experimental results on burner stability tests are presented in figures 2, 3 and 5 using propane and a 21 inch I.D. orifice flame holder in a 3~ inch I.D. tube section. The burners for the figures 2 and 3 are both of constant cross-section and of 48 inch length (orifice to open exhaust end). I n figure 2 the inlet to t h e burner is unobstructed, except for heating and metering sections located about 6 ft. upstream of the flame holder. The lean operating limit is a typical blow-out limit curve. At the bottom of the figure are given the cold flow velocity fluctuation values and in the operating region are found similar measurements made in the inlet section with burning. The average fluctuation level while burning is around five times that obtained without combustion. A
716
THIRD SYMPOSIUM ON COMBUSTION~ FLAME AND EXPLOSION PHENOMENA
general increase in velocity fluctuation level with increasing velocity is noted for b o t h the cold and hot flows. T h e rich limit is rough over the entire range. The low velocity roughness in this case is due to flash-back instability a t the flame holder.
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d a m p i n g action of the screen. Disturbances which were regenerative w i t h o u t the screen h a v e now been reduced to a point where relatively stable operation is possible. Figure 4 shows the dimensions of an expansion-contraction chamber where the flame front ends in a low velocity region of the flow. T h e operating and stability curves shown in figure 5 for this c h a m b e r have the same general 120]
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FIG. 3. Burning roughness and limits for flame holder 0345-42 in a 388 I.D. x 48 in. length burner with 20-mesh wire screen in inlet to burner 12 in. upstream of flame holder. Pressure: ambient sea level Fuel: propane. Inlet mixture temperature: 135~ ;z'/U measured by hot wire anemometer at axis of burner inlet 16 in. upstream of flame holder. ( p ' / U = Longitudinal velocity fluctuation/mean velocity at hot wire.) Runs: 99-1034.
X ~;~ tOx 125 ~ / FIG. 4. Diagram of expansion-contraction chamber No. 2-12-12-12 (49{).
Figure 3 shows the same configuration with the addition of a 20 mesh wire screen placed one foot upstream of the flame holder. B o t h the rich a n d lean limits are of the smooth blow-out type. T h e low speed flash-back region is clearly discernible and is the only rough limit shown. T h e entire fluctuation level has dropped due to the pulse
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FIG. 5. Burning roughness and limits for flameholder 0345-42 in expansion-contraction burner 2-1212-12 (4988 with 20-mesh wire screen in inlet to burner 12 in. upstream of flame holder. Pressure: ambient sea level. Fuel: propane. Inle~ mixture temperature: 135~ p ' / U * measured by hot wire anemometer at axis of burner inlet 16 in. upstream of flame holder. ( p ' / U = Longitudinal velocity fluctuation/mean velocity at hot wire.) Runs: 1160characteristics as the straight chamber except t h a t the velocity fluctuation level has been decreased. Comparison of the three burners a t a single velocity shows t h a t the screen produces a 40 percent reduction of the fluctuation level of the first b u r n e r while the expansion c h a m b e r gives a 60 percent reduction, or a 20 percent i m p r o v e m e n t over t h a t of the screen alone. These results clearly indicate the i m p r o v e m e n t s in performance which can be obtained by control of impulses generated in the combustion process. A similar situation exists in starting large volume combustion chambers where special measures m u s t be used or the initial disturbances will be so violent as to prevent operation. Results obtained with liquid fuel injection are
COMBUSTION
IN
ENGINES
often quite different than those found with vaporized fuel in the same combustion chamber. Velocity fluctuation measurements made in a cylindrical chamber similar to the one whose performance was presented in figure 3 are given for a liquid fuel in figure 6. The injector was a pneumatic nozzle giving various degrees of atomization over the operating range. The drop sizes become larger as the fuel rate is increased. Slight variations in fluctuation level are noted at the 24 inch length and become extreme at 72 inches9 The peak in
AND
717
ROCKETS
about 20 percent less than that obtained with the high nozzle air pressure. It appears that when e " ~'4 zo FUEt.--~,N-F'M F/A,O.OG3 NOMINAL BY WEI(;HT
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PSI ~R PR(SSUR( I 40
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Fzo. 7. Chamber pressure vs. chamber length.
PHFUMATIG NOZZ .E ItC
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COOLING WATER I_B/MIN FIG. 8. Effect of cooling of 6-inch length 5 inches from end of tailpipe.
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Fzo. 6. Inlet velocity fluctuations. the long tube curve is believed to be due to the changing nozzle spray characteristics. With liquid fuel it was found that centrally located flame .holders could be operated in chambers of such a length as to render vaporized fuel unusable. Further information on the performance of liquid fuels injected with a pneumatic nozzle is presented in figure 7. The static pressure measured upstream of the flame holder is plotted against chamber length. The top curve shows operation at a relatively high nozzle air pressure and indicates that combustion was completed in a 20 inch length with high efficiency. The lower curve, taken under poor atomizing conditions shows a slower reaction rate up to a length of 23 inches with some burning taking place throughout the remaining length on the longer chambers. Efficiency with the poorly atomized mixture is
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INt,ET Ft,OW VEt,OCITY--FT/$EC
FzG. 9. Apparent flame velocity as a function of inlet velocity. Fuel--propane. F/A = .064. [] = .034542 flame holder. O = 4-mesh screen 589 in. upstream of flame holder. X = 20-mesh screen 5~ in. upstream of flame holder. the drop size distribution in a fuel spray contains a sufficient amount of large drops the pressure rise curve flattens out and no discrete flame front
718
T H I R D SYMPOSIU~I ON COMBUSTION~ I~LAME AND E X P L O S I O N P I I E N O M E N A
is to be found. This effect may be used to secure stability when a rapid reaction rate or high efficiency with limited chamber length is not required. Another factor affecting the stability of a burner is illustrated in figure 8 which shows the result of water cooling near the exhaust of a 48 inch long burner. As the water rate is increased a positive pressure gradient is built up in the tube and this tends to produce unstable flow conditions. A single run made with the cooling water applied to the center of the tube near the end of the flame front resulted in a 400 percent increase in velocity fluctuation. Average flame velocity measurements based on total reaction length and inlet mixture velocity are shown in figure 9. The top line gives the results with unobstructed inlet, the next line results with a four mesh screen and the bottom line with a twenty mesh screen. In all cases the apparent flame velocity increases with inlet velocity as does the turbulence level in the tube. The screens show increasing degrees of turbulence reduction and also flame speed reduction. Tests made with a rotating cage to produce large scale high intensity turbulence showed only small effects on apparent flame velocity and a slight decrease in stability. The results indicated
that large scale turbulence was not effective in increasing reaction rates. CONCLUSIONS
The results of work done to date indicate that for vaporized and well mixed fuels operating limits are primarily dependent upon flame speed which appears to determine the blow-out characteristics of flame holders and the rough limits due to closure failure in the flame front. Turbulence is found to increase flame speeds and permits operation over an extended inlet velocity range. Once a disturbance has been created such factors as pressure pulse attenuation and reflection in the burner exert a strong influence on the degree and continuance of the unstable burning. The rate of heat loss in various sections of the combustion chamber can cause adverse pressure gradients and lead to flow instability. Flow variations which affect the fuel flow rate will usually make the instability worse. A mixture which contains only partially vaporized fuel will show a practical degree of stability in chambers where a gas mixture will not allow operation. This effect appears to be due to the removal of any definite high velocity closure point and the substitution of a rather indefinite pressure drop and reaction rate down the chamber with combustion proceeding throughout the chamber volume.
95
SOME CONSIDERATIONS IN DETERMINING THE OPTIMUM PROPELLANT COMBINATION FOR A ROCKETPOWERED MISSILE By T. F. REINHARDT AND J. R. PISELLI
The purpose of this paper is to present some of the fundamental problems confronting the rocket engineer in the selection of rocket propellants to achieve optimum performance consistent with reasonable cost, availability, safety, and handling problems. The performance of a rocket propellant is judged principally from its Specific Impulse, which is the pounds of thrust produced per pound of propellants consumed per second. The specific impulse is related to the jet velocity, and hence the kinetic energy of the propellants in a very simple manner.
The thrust of a rocket is easily derived from momentum considerations as: F = ( w / g ) V , lb.
where w is the rate of propellant flow, lb./see., V is the jet velocity, ft./see., g is the acceleration of gravity, 32.2 ft./sec. 2 Whence the specific impulse becomes, by definition: I~p = F / w = V / g sec.
Thus the specific impulse is directly proportional to the jet velocity. The jet velocity may, in turn.
T H I R D SYMPOSIUM ON COMBUSTION~ F L A M E AND E X P L O S I O N P H E N O M E N A
94
FACTORS
AFFECTING
COMBUSTION
STABILITY 1
By ~. t~. VAR~ DESCRIPTION OF OPERATING LIMITS
Continuous flow combustion chambers are usually tested for operating range by determining the fuel-air ratio limits as a function of velocity. In general there are two distinct kinds of limits. One type is often called a blow-out limit. At the blowout condition the ignition source (usually a "flame holder") can no longer propagate a flame front into the main body of the flowing mixture. Observation of the blow-out process easily shows that as the limit is approached by varying the fuel flow the flame front in the wake of the flame holder narrows and finally disappears, leaving only a weak flame immediately behind the flame holder. Blow-out limits are not accompanied by instability and hence can be called smooth. At low inlet velocities these limits are very near to the so-called static ignition limits and are characteristic of the fuel being used. As the inlet velocity is increased the blow-out limits gradually narrow as the flame velocity required for propogation into the main stream increases. Typical blow-out limits for flat plate fla~ne holders and AN-F-28 fuel are shown in figure I for inlet velocities from 10 to 100 ft./sec. The second type of limit is characterized by combustion instability and is usually designated as a rough limit. Rough limits reduce the operating range and lie inside the true blow-out limits. Blow-out limits are largely a function of the fuel (flame speed) and velocity distribution behind the flame holder while rough limits are more a function of the mixture distribution, flame speed, and combustion chamber geometry. I t is of considerable importance to clearly differentiate the two types of limits. Blow-out limits can usually be determined only in a short combustion chamber. A short chamber may be defined as one in which the reaction is not enclosed while a long chamber is taken to mean one in which the combustion is carried to completion. With short chambers there is little difficulty with rough combustion while simply adding tail pipe length to achieve a long chamber may often make the combustion so violent that operation is impossible. In order to obtain a quantitative comparison of combustion stability we have employed a hot wire anemometer to measure velocity fluctuations t This paper covers work done for the A.M.C. on contract W 33-038AC-15319.
in the burner inlet section. The velocity fluctuation for a particular burner operating at constant inlet velocity is nearly independent of F/A ratio when operating within blow-out limits but shows an increasing characteristic when a rough limit is approached. The fluctuations observed with combustion are normally several times the turbulence level for cold flow at the same inlet velocity. Data and descriptions of test results are given below. FLOW CONI)ITIONS IN THE COMBUSTION CHAMBER If one considers an idealized case of a constant cross section combustion chamber, it is possible to arrive at a qualitative description of some of the chamber flow conditions. Experimental evidence of flame fronts in short tubes indicates that after the flow interference of the flame holder has disappeared the reaction zone has little curvature. Since the unburned mixture in a~ short chamber has suffered a pressure drop, it has been accelerated and leaves the burner through a reduced area. Thus the burned gas has a lower average velocity and the unburned gas a higher velocity than would be obtained with straight flow in the chamber. The flow is thus seen to be contracting in the unburned mixture. The same type of flow must also occur in long chambers as the first gas to burn is confined by the chamber walls and the expansion of the burned gas forces a contraction of the unburned mixture. The same result is arrived at by a consideration of the momentum change across the flame front. This results in a bending or refraction of the stream lines as they cross the flame front. Considering the flame front as starting at the wall of the burner, a streamline entering the front parallel to the axis would be bent outward. At low velocities the fluid can be thought of as incompressible, and since the outward flow cannot continue it then appears that a streamline starting in the unburned mixture converges toward the axis and enters the flame front, the leaving streamline then diverges away from the axis and will finally reach the same radial distance as the initial entering streamline. Such considerations lead to the conclusion that the last part of the mixture to burn has a higher velocity than that measured at the burner inlet. In order to get complete combustion or to dose the flame
COMBUSTION
IN
ENGINES
front the flow pattern requires a higher flame velocity at the point of closure than at other points in the flame front. It is then reasonable to assume that the flame front closure would lead to unstable flow conditions when the flame speed becomes marginal. With complete combustion and a closed flame front the full theoretical chamber pressure will be built up in the inlet section. We may then consider the flame front as a pressure supporting surface. If combustion ceases momentarily at a closure point (or any part of the flame front) the excess chamber pressure will force unburned gas into the surrounding exhaust gas and after a short time lag the unburned charge will detonate with a consequent disruption of the entire flow.
AND
effect of the walls is present to reduce the reaction rate. The effect of increasing length on roughness is not abrupt because of ignition lag and the amount of unburned gas which can be injected into the exhaust region inside the burner. At low inlet velocities the momentum change pressure drop due to burning is small and increases with increasing mixture velocity. Any interruptions in the flame front produce only small pressure changes at low speeds and the same amount of instability of the flame front at high speeds will give rise to large fluctuations. 10C RICH ROUGH LIMIT
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2b 2'5 3b INLET
MIXTURE
4b 5b ~7bob~Jo,oo VELOGITY--FT/SEG.
FIo. 1. Gasoline blowout limits. Flat plate flame holders. I n support of these conclusions we find that short chambers, which do not have a closed flame front, burn smoothly indicating no fundamental instability in the beginning stages of the combustion process. Experiments with 3[ inch cylindrical chambers 48 inches long showed that when burning propane with an orifice type flame holder, reasonably wide operating limits were obtained while a central disk holder produced such roughness that operation was impossible. In this case the orifice holder produces a conical flame front which ideally closes at a point. The amount of gas which can leak through the point is small and the surrounding hot gases are conducive to a faster reaction rate by preheating of the unburned core flow. The central holder closes the front at the base of a conical surface on the wall. Here the area involved is much greater and the quenching
,
20 O33
50 40 50 60 7'0 BURNER INLET VELOGITY-FTISEC O36 036 041 044 O46 9-~V'S VELOCITY, NO BURNING
80 ,O.49
FIG. 2. Burning roughness and limits for flame holder 0345-42 in a 388 I.D. x 48 inch length burner with unobstructed inlet. Pressure: ambient sea level. Fuel : propane Inlet mixture temperature: 135~ # ' / U measured by hot wire anemometer at axis of burner inlet 16 in. upstream of flame holder. ( # ' / U = Longitudinal velocity fluctuation/mean velocity at hot wire.) Runs: 942-989. EXPERIMENTAL DATA
Experimental results on burner stability tests are presented in figures 2, 3 and 5 using propane and a 21 inch I.D. orifice flame holder in a 3~ inch I.D. tube section. The burners for the figures 2 and 3 are both of constant cross-section and of 48 inch length (orifice to open exhaust end). I n figure 2 the inlet to t h e burner is unobstructed, except for heating and metering sections located about 6 ft. upstream of the flame holder. The lean operating limit is a typical blow-out limit curve. At the bottom of the figure are given the cold flow velocity fluctuation values and in the operating region are found similar measurements made in the inlet section with burning. The average fluctuation level while burning is around five times that obtained without combustion. A
716
THIRD SYMPOSIUM ON COMBUSTION~ FLAME AND EXPLOSION PHENOMENA
general increase in velocity fluctuation level with increasing velocity is noted for b o t h the cold and hot flows. T h e rich limit is rough over the entire range. The low velocity roughness in this case is due to flash-back instability a t the flame holder.
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d a m p i n g action of the screen. Disturbances which were regenerative w i t h o u t the screen h a v e now been reduced to a point where relatively stable operation is possible. Figure 4 shows the dimensions of an expansion-contraction chamber where the flame front ends in a low velocity region of the flow. T h e operating and stability curves shown in figure 5 for this c h a m b e r have the same general 120]
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FIG. 3. Burning roughness and limits for flame holder 0345-42 in a 388 I.D. x 48 in. length burner with 20-mesh wire screen in inlet to burner 12 in. upstream of flame holder. Pressure: ambient sea level Fuel: propane. Inlet mixture temperature: 135~ ;z'/U measured by hot wire anemometer at axis of burner inlet 16 in. upstream of flame holder. ( p ' / U = Longitudinal velocity fluctuation/mean velocity at hot wire.) Runs: 99-1034.
X ~;~ tOx 125 ~ / FIG. 4. Diagram of expansion-contraction chamber No. 2-12-12-12 (49{).
Figure 3 shows the same configuration with the addition of a 20 mesh wire screen placed one foot upstream of the flame holder. B o t h the rich a n d lean limits are of the smooth blow-out type. T h e low speed flash-back region is clearly discernible and is the only rough limit shown. T h e entire fluctuation level has dropped due to the pulse
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FIG. 5. Burning roughness and limits for flameholder 0345-42 in expansion-contraction burner 2-1212-12 (4988 with 20-mesh wire screen in inlet to burner 12 in. upstream of flame holder. Pressure: ambient sea level. Fuel: propane. Inle~ mixture temperature: 135~ p ' / U * measured by hot wire anemometer at axis of burner inlet 16 in. upstream of flame holder. ( p ' / U = Longitudinal velocity fluctuation/mean velocity at hot wire.) Runs: 1160characteristics as the straight chamber except t h a t the velocity fluctuation level has been decreased. Comparison of the three burners a t a single velocity shows t h a t the screen produces a 40 percent reduction of the fluctuation level of the first b u r n e r while the expansion c h a m b e r gives a 60 percent reduction, or a 20 percent i m p r o v e m e n t over t h a t of the screen alone. These results clearly indicate the i m p r o v e m e n t s in performance which can be obtained by control of impulses generated in the combustion process. A similar situation exists in starting large volume combustion chambers where special measures m u s t be used or the initial disturbances will be so violent as to prevent operation. Results obtained with liquid fuel injection are
COMBUSTION
IN
ENGINES
often quite different than those found with vaporized fuel in the same combustion chamber. Velocity fluctuation measurements made in a cylindrical chamber similar to the one whose performance was presented in figure 3 are given for a liquid fuel in figure 6. The injector was a pneumatic nozzle giving various degrees of atomization over the operating range. The drop sizes become larger as the fuel rate is increased. Slight variations in fluctuation level are noted at the 24 inch length and become extreme at 72 inches9 The peak in
AND
717
ROCKETS
about 20 percent less than that obtained with the high nozzle air pressure. It appears that when e " ~'4 zo FUEt.--~,N-F'M F/A,O.OG3 NOMINAL BY WEI(;HT
14C 9
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I 20
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PSI ~R PR(SSUR( I 40
/ 60
I 50
/ 70
80
Fzo. 7. Chamber pressure vs. chamber length.
PHFUMATIG NOZZ .E ItC
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0
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I
4
6
8
COOLING WATER I_B/MIN FIG. 8. Effect of cooling of 6-inch length 5 inches from end of tailpipe.
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50
40
I 2
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f I l t 05 .06 .07 .06 NOMINAL F/A BY WEIGHT
09
Fzo. 6. Inlet velocity fluctuations. the long tube curve is believed to be due to the changing nozzle spray characteristics. With liquid fuel it was found that centrally located flame .holders could be operated in chambers of such a length as to render vaporized fuel unusable. Further information on the performance of liquid fuels injected with a pneumatic nozzle is presented in figure 7. The static pressure measured upstream of the flame holder is plotted against chamber length. The top curve shows operation at a relatively high nozzle air pressure and indicates that combustion was completed in a 20 inch length with high efficiency. The lower curve, taken under poor atomizing conditions shows a slower reaction rate up to a length of 23 inches with some burning taking place throughout the remaining length on the longer chambers. Efficiency with the poorly atomized mixture is
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INt,ET Ft,OW VEt,OCITY--FT/$EC
FzG. 9. Apparent flame velocity as a function of inlet velocity. Fuel--propane. F/A = .064. [] = .034542 flame holder. O = 4-mesh screen 589 in. upstream of flame holder. X = 20-mesh screen 5~ in. upstream of flame holder. the drop size distribution in a fuel spray contains a sufficient amount of large drops the pressure rise curve flattens out and no discrete flame front
718
T H I R D SYMPOSIU~I ON COMBUSTION~ I~LAME AND E X P L O S I O N P I I E N O M E N A
is to be found. This effect may be used to secure stability when a rapid reaction rate or high efficiency with limited chamber length is not required. Another factor affecting the stability of a burner is illustrated in figure 8 which shows the result of water cooling near the exhaust of a 48 inch long burner. As the water rate is increased a positive pressure gradient is built up in the tube and this tends to produce unstable flow conditions. A single run made with the cooling water applied to the center of the tube near the end of the flame front resulted in a 400 percent increase in velocity fluctuation. Average flame velocity measurements based on total reaction length and inlet mixture velocity are shown in figure 9. The top line gives the results with unobstructed inlet, the next line results with a four mesh screen and the bottom line with a twenty mesh screen. In all cases the apparent flame velocity increases with inlet velocity as does the turbulence level in the tube. The screens show increasing degrees of turbulence reduction and also flame speed reduction. Tests made with a rotating cage to produce large scale high intensity turbulence showed only small effects on apparent flame velocity and a slight decrease in stability. The results indicated
that large scale turbulence was not effective in increasing reaction rates. CONCLUSIONS
The results of work done to date indicate that for vaporized and well mixed fuels operating limits are primarily dependent upon flame speed which appears to determine the blow-out characteristics of flame holders and the rough limits due to closure failure in the flame front. Turbulence is found to increase flame speeds and permits operation over an extended inlet velocity range. Once a disturbance has been created such factors as pressure pulse attenuation and reflection in the burner exert a strong influence on the degree and continuance of the unstable burning. The rate of heat loss in various sections of the combustion chamber can cause adverse pressure gradients and lead to flow instability. Flow variations which affect the fuel flow rate will usually make the instability worse. A mixture which contains only partially vaporized fuel will show a practical degree of stability in chambers where a gas mixture will not allow operation. This effect appears to be due to the removal of any definite high velocity closure point and the substitution of a rather indefinite pressure drop and reaction rate down the chamber with combustion proceeding throughout the chamber volume.
95
SOME CONSIDERATIONS IN DETERMINING THE OPTIMUM PROPELLANT COMBINATION FOR A ROCKETPOWERED MISSILE By T. F. REINHARDT AND J. R. PISELLI
The purpose of this paper is to present some of the fundamental problems confronting the rocket engineer in the selection of rocket propellants to achieve optimum performance consistent with reasonable cost, availability, safety, and handling problems. The performance of a rocket propellant is judged principally from its Specific Impulse, which is the pounds of thrust produced per pound of propellants consumed per second. The specific impulse is related to the jet velocity, and hence the kinetic energy of the propellants in a very simple manner.
The thrust of a rocket is easily derived from momentum considerations as: F = ( w / g ) V , lb.
where w is the rate of propellant flow, lb./see., V is the jet velocity, ft./see., g is the acceleration of gravity, 32.2 ft./sec. 2 Whence the specific impulse becomes, by definition: I~p = F / w = V / g sec.
Thus the specific impulse is directly proportional to the jet velocity. The jet velocity may, in turn.