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A study of free-jet and enclosed supersonic diffusion flames
A STUDY OF FREE-JET AND ENCLOSED SUPERSONIC DIFFUSION FLAMES R. A. COOKSON, P. FLANAGAN, AND G. S. PENNY
Propulsion Department, Collegeof Aeronautics, Cranfield, England An experimental study has been made of supersonic diffusion flames produced by the subsonic and supersonic free-jet injection of hydrogen into a high-enthalpy air-stream. The air-stream was flowing at a Mach number = 1.98 and had a total temperature of approximately 1900~ and a static pressure of 14.7 psia. An axial, mid-stream mode of fuel injection was adopted. For the case of hydrogen injected subsonically, combustion was found to be complete (i.e. the concentration of unreacted hydrogen was negligible), at a distance of approximately 9 inches from the point of injection. For the supersonic injection of hydrogen this distance was increased by approximately 30%, for the range of fuel velocities used. The tests were repeated with methane as the injected fuel, but ignition did not occur even with the methane preheated to 480~ or when a bluff-body was inserted into the flow to create shock conditions. The above flames were then enclosed in various combustors of simple geometry, either of constant~area, constant-divergence or some combination of these two. For the conditions specified above, combustion in the diffusional mode was found to be impossible in a constantarea combustor. A diffusion flame was initiated in a combustor which consisted of a short parallel section followed by a section with a divergence of approximately 1% IIowever no combustion took place within a completely divergent duct even though the divergence was less than 1~ An exponential relationship between pressure, area and length has been proposed, and a one-dimensional analytical treatment for the case of heat addition in a non-constant-area duct is included in this paper. This assumption is shown to be experimentally reasonable and to result in gas dynamic equations which include the effect of process length.
Introduction The problems involved in designing propulsive systems for hypersonic air-breathing vehicles have been discussed by several authors, for example Refs. 1 and 2. Their findings indicate that the only feasible system will be one in which heat is added to a supersonic air-stream. In this way problems of structural integrity associated with high static temperatures and pressures, and the energy loss due to chemical dissociation, can be overcome. Of the possible modes of heat release in a supersonic stream, the diffusional mode has been shown to be superior to the case where combustion is shock-induced, or where shock conditions prevail. While the latter modes give relatively high combustion efficiencies and intensities, these would appear to be more than offset by the resultant loss in stagnation pressure and the problems associated with the high static conditions obtained. In the design of an efficient combustor for the
supersonic diffusional mode of heat release, there are two major problems which require investigation. First, the effect of various forms of fuel injection, for example, wall or mid-stream, sul)sonic or supersonic, on such parameters as mixing and stagnation pressure loss. Second, the effect of the combustor geometry on performance criteria. A program of research has been initiated in the Propulsion Department at Cranfield in which the effect of fuel injection and combustor geometry can be investigated. The initial phase of this research program has been the investigation of supersonic flames produced from the fl'ee-jet injection of fuel into a high-enthalpy air-stream. An attempt was then made to enclose the SUl)ersonic flames in ducts of various simple geometries, and to compare the mixing and reaction phenomena for the enclosed condition with those prevailing in the free-jet. The work described in this paper is limited to the axial midstream mode of fuel injection. I n treating the case of heat-addition in a non-
1115
1116
SUPERSONIC COMBUSTION
constant-area duct analytically, Croccoa has proposed a pressure-area relationship which has since been utilized by Refs. 4 and 5. An attempt has been made in this paper to extend this onedimensional analysis to include the effect of process length.
Experimental A pebble-bed heater utilizing alumina elements was used to provide the high-enthalpy air-stream for the experiments described in this report. The facility is capable of providing 2 pounds of air per second at a stagnation pressure of 250 psia and stagnation temperature of 2070~ A complete description of this facility is contained in Ref. 6. A Mach 1.98 convergent-divergent, axisymmetric nozzle was used for the free-jet experiments and is illustrated in Fig. 1. This nozzle has an axial, mid-stream, injector and is designed to run choked at 113 psia and to discharge to atmosphere at 14.7 psia. The problem of cooling the stainless-steel nozzle and injector created some
difficulty. In particular, boiling occurred in the mid-stream injector until the cooling water pressure was raised to 400 psia. A conventional cooled pitot probe was used to measure the stagnation pressure in the stream, and an uncooled needle probe for measuring the static pressure. This latter probe was immersed in the air-stream for short periods only, by use of a pneumatic plunger. The stream Mach number was determined both from the shock angle produced by the immersion of a wedge into the flow, and by use of a Shapiro pitot-static probe. Schlieren photographs for the former of these two techniques, are extremely difficult to obtain, presumably because of the highly turbulent shear layer surrounding the high-temperature air-stream. The static temperature of the supersonic flame was measured by the line-reversal technique. A very simple system was used, employing a cheap grating spectrometer and a tungsten strip lamp as a continuum source. Reversal was obtained visually and the source was calibrated by means of a disappearing filament pyrometer. The line reversal technique is essentially an averaging
HYDROGEN INLET COOLING WATER OUTLET WATER OUTLET
RING SEAL
I NJECTOR
COOLING WATER INLET "=--COOLING WATER INLET X-HYDROGEN
INLET
FIG. 1. Axisymmetric Mach number = 1.98 nozzle with axial fuel injection used for free-jet experiments.
SUPERSONIC DIFFUSION FLAMES
FUEL INJECTOR- /
/
1117
/--STATIC PRESSURE~ TAPPINGS
MACH;)NOZZLE/' ~
b
/'
WATERCOOLEDCOMBUSTORJ FIG. 2. Combustor geometls~ for enclosed flame experiments. process but the resulting error, in these tests, should be small as the flame is surrounded by a very hot air-stream for most of its length. For sampling the reacting flow the method suggested by Ref. 7 was used. In this technique a sharp edged probe produces a system of attached shocks, with the resulting normal shock across the orifice being swallowed by the application of a vacuum pressure to the probe outlet. Cooling the sharp leading edge presents some difficulty, but can be accomplished by forcing water through an annular passage around the probe until it is close to the tip and then ejecting it rearwards into the hot stream. Direct color photography was found to be very useful in providing a visual record of the supersonic flame and in determining the delay period before combustion begins. The ducts used for the experiments on enclosed flames were all of circular section to match the outlet of the Mach 1.98 nozzle described above. Two duct lengths were used, 12 in. and 30 in., and constant-area, combined constant area and divergent, and divergent geometries were "dl tested. A typical configuration is shown in Fig. 2. Each duct was provided with static pressure tappings throughout its length and with a watercooled jacket. A transparent vitreous silica (Vitreosil) duct was also used, having a combined constant-area and divergent geometry similar to one of the stainless steel combustors. The early tests were carried out without any attempt being made to preheat the fuel. In the later tests, and in particular the experiments with methane, some preheating has been used. This fuel heater took the form of a stainless steel coil over which hot air from the pebble-bed was passed once blow-down was begun. A temperature rise of only 200~ has been obtained so far but this will be improved by a better heater design.
Exponential Pressure :Area :Length Relationships A pressure-area relationship of the form pA '/('-1) = constant
(1)
has been proposed by Crocco3 for the case of heat-addition to a gas flowing in a duct. Hence the particular processes of constant-area and constant-pressure can be described by values of e of 1 and 0, respectively. Dobrowlski4 has eraployed this relationship and further developed the concept of subcritical and supercritical heataddition. This form of pressure-area relationship has also been used by Billig,5 with the suggestion that an optimized combustor geometry might be obtained by piecing together segments of combustor of different e value. Billig also developed gasdynamic equations for inlet-to-outlet ratios of many of the flow variables, in terms of the e parameter. I t is obviously desirable to incorporate some process length dependency into the analysis if this is possible, rather than adopting the piecemeal process suggested. For this reason, and because it has been observed that the pressure-length and area-length relationships obtained from our experiments, can be approximately described by some exponential expression, the following relationships are postulated: P2 = Pl exp (Kpx)
(2)
and A o = A, exp
(KAx)
(3)
where x is the process length x2 -- xv The stations Xl and x2 are as indicated on Fig. 7, "rod the length x , , - xl is the distance over
1118
SUPEI{SONIC COMBUSTION the total teml)erature ratio call be written as
which heat is added. Therefore
(A2/AO = (p.,./pl)Ka/K" KA/Kp
or, if for simplicity, we use ~ =
A/p" =
T2/T, =
(4)
Q2/tl),
(10)
and the total pressure ratio as
constant.
P2/P1 = (Xz/xl) "~('-l) (p~/pO;
(5)
Hence it is possible to solve tim molnentmn equation and by utilizing the definition of Mach nmnber and the equations of state and contilmity, the following expressions can be obtained:
As-3,R{(312~
Xl,~
{11+ ( r / + 1)TM12/~/(~1)
(6)
+ (n + 1)uM2=J
(11)
also the change of entropy can be expressed as,
Area ratio:
A2/AI=
(X2/Xl)
r 7 ( 2 ~ + 1) + 1] [} + ("7 +
1)3":]I121/
+ (,7 + i)--~--~j].
(12)
Similarly the critical Mach number is given by
Static pressure ratio:
p2/pl=
M~2 = E3'n + 1-]-1. {}--~-(rl+ 1)%11,21u(~1) + (n + 1)%1I-~2J
(7)
Static temperature ratio:
t2/h
=
The static temperature ratio can also be expressed in the following way, ~2//tl = { ('[/~2/'t/1)exp [-(/~fA-Jr- Kp)x-]}. (14)
{1+ (,,+
1 + (,7+ 1)~.@J
\~/
(s)
and, if for simplicity, we use X = [-1 + 89 -- 1)M2J,
(9)
Thus it can be seen that the ratio of the outlet to inlet static temperatures which results from heat addition in an exponentially related pressure-area-length duct is not itself exponential, !
M2 > M1 -0-95
Su~r=onlc
-I-I
-I.3
-6"0
Subsor 15"0 I
"~'/' [~
O Qf 2-C
-0.9
I.C
I I
4-0
(13)
I
I
3-0 OUTLET
l
2.0 MACH NUMBER
t I
I
!
I*0 M2
FIG. 3. Diagram illustrating the range of flows that can be described by the parameter for an inlet Mach number = 2.
SUPERSONIC DIFFUSION FLAMES
1119
2200
Uj ~ j
= O'171
25. 8 0
2000
MP
ATURE
~. I
v'
o uJ
18OO
r162 ,,I n
160C
2(>-60
,1n
:i
uJ I.-
140C
IIn
t
15.-40
IO- 2 0 5
O
20
40
60
AXIAL DISTANCE = INJECTOR RADIUS
T
80
tt} O.
I
uJ r o~ ,,i r ft.
0.
O
FIG. 4. Variation of static temperature, static pressure, and pitot pressure along the axis of a free-jet hydrogen supersonic diffusion flame.
\
,oo
Z
~
:J, .
METHANE
Uj pj
--
=0"74
,o Z bl
HYDROGEN
:i
C
I
20
40
METHANE
_5.
AXIAL DISTANCF, = INJECTOR RADIUS
60
'
80
I00
,:C "1"
FIG. 5. Variation of fuel concentration along the axis of a free-jet hydrogen supersonic diffusion flame and an unreacted methane jet.
but is modified by the ratio of the outlet t<) inlet gas velocities. Equation (14) can obviously be written ~2/tl =
(U2//Ul)
exp
(Ktx)
(15)
where Kt = KA + Kp. From the above analysis it can be seen that the constant-area and constant-pressure cases are represented by ~ values of unity and infinity, respectively. It is interesting to note that the critical Much number for the constant-pressure case is equal to zero. This can be interpreted as
meaning that a constant-pressure heat-addition process will never thermally choke. Figure 3 illustrates the range of flows that can be described by the 71 parameter, calculated for a combustor inlet Mach number of 2 and -y = 1.32. The proposed exponential representation of pressure and area variatLon with duct length has been dealt with at greater lellgth i1~ Ref. 8, and static aud total temperature ratios and static and total pressure ratios for an inlet Much number = 2 and 7 = 1.32 (i.e., approximately the experimental conditions referred to in this paper), have been calculated.
1120
SUPERSONIC COMBUSTION Results
Free-Jet Studies
Figure 4 shows the variation of several flow properties, measured along the axis of the jet, with distance from the point at which hydrogen was injected into the high-enthalpy air-stream. Similarly Fig. 5 illustrates the variation of the unreacted hydrogen concentration with axial distance, and Fig. 6 the radial variation at three positions along the jet. For the particular experiment illustrated by Figs. 4, 5, and 6, the hydrogen injection was subsonic at a velocity of 2300 ft/sec, the air-stream was at a l%{ach number of 1.98, and a stagnation temperature of 1870~ Results have also been obtained for other flow conditions, and for both subsonic and supersonic fuel injection. These results are to be found in Ref. 9. From the hydrogen free-jet results obtained it can be seen that stable, shock-free, supersonic diffusion flames can be produced from both subsonic and supersonic fuel injection. For the range of flow conditions investigated, the distance
required for complete reaction, or more exactly, for the concentration of molecular hydrogen to become negligible, was up to 30% greater for supersonic fuel injection than for the subsonic case. Mixing was found to be dependent upon the ratio pjui/p,ue , and this served to confirm the findings of other researchers. The distance from the fuel injector to the commencement of visible flame radiation, was found to be approximately 8 injector diameters for subsonic fuel injection, and 10 diameters for the case where injection was supersonic. These distances did not appear to vary with temperature, and in the cases where experiments were carried out at stagnation temperatures below the normal operating range, the result was not a marked increase in the ignition delay, but instead a ragged flame in which small detonations could be heard to occur. The injected methane could not be ignited even when it was preheated to 470~ or when a bluff body was inserted into the flow to create a normM shock. The mixing results for methane injection without reaction are included in Fig. 5, from which it can be seen that mixing is much
30
25 Z Q Zi,i U
Z
Uj = Ur = tj = 1:r
2280 FT/SEC 3840 FT/SEC 295~ 1140~
| ~
Uj pj Uepr --0.171
/~i
/I 3C= 1"
12
20
15
O U
---~- = 18
i./) !0
35 0
3
2
I
0
I
2
3
SAMPLE RADIUS INJECTOR RADIUS Fie.. 6. Radial variation of hydrogen concentration-at-three stations along a supersonic hydrogen diffusion flame.
SUPERSONIC I)IFFUSION 1;'LAMIiXS
1121
I
I
XI= S-O INS.
Ln uJ -r z_ I u~ 09
30,
.
.
.
.
0 t3=2150~162
20
2100~ EXIT (~
_u
J
.
X2= 28.5 INS.
IO
M I
M2
T~
~
O
0-45
1,776
1-500
-- 2 - 0 2 0
A
O'33
I "816
1.788
--1-302
~j
0.23
1.872
2.310
-0-753
I
I IO COMBLISTOR
I
SHOCKS 1990OK
w
KclI2 = 0 , 0 2 8 8
I 2o L E N G T H - - INCHES
I
I 30
Fro. 7. Wall static pressure variation with combustor length, for supersonic diffusion flames enclosed in a 5 in. parallel, 25 in. divergent combustor. slower than for hydrogen. I t can also be seen that stoichiometric proportions are reached at a distance of 35 jet diameters downstream.
Enclosed Flames I t was found that a hydrogen diffusion flame could not be maintained within any of the parallel combustors, of various lengths, which were tested, or within a simple conical combustor of 0.75 ~ divergence and 30 in. long. In the case of the parallel ducts the heat-addition process broke down in each instance to one of shock-initiated combustion. For the divergent duct, combustion was observed to occur after the Mach disc which was formed at the combustor exit. Three combustors of combined constant-area and divergent geometries were tested, and for convenience these will be specified as a/b, where a and b are the dimensions shown in Fig. 2. The first of these combined geometries was a 10 in./20 in. combustor with a 1.5 ~ divergent section. As with the parallel combustors described above, this duct also resulted in shock-initiated combustion taking place in the 10 in. section. The second of these combustors was a 5 in./12 in. duct with a 3 ~ divergent section. This combustor resulted in combustion taking place after the Mach disc which was formed at exit. The third and successful combustor had a 5 in./25 in.
geometry with a 1~ divergence and resulted in a supersonic diffusion flame existing within the divergent section. Figure 7 shows the static pressure variation along the 5 in./25 in. combustor for three equivalence ratios, together with the measured Mach numbers and static temperatures at exit. It should be emphasized however that the static temperatures given were measured after the exit shock formation, and as such are included simply to indicate the order of temperature to be expected. For the experiment illustrated by Fig. 7, the air stagnation and fuel temperatures were 1870 ~ and 350~ respectively. Sampling carried out at the combustor exit plane for each of the equivalence ratios failed to detect any appreciable concentration of unreacted hydrogen. A further successful combustor was created by adding a 5 in. parallel section to the conical combustor described above, and producing a 5 in./30 in. geometry with 0.75 ~ divergence. This combination, when tested was found to support a supersonic diffusion flame within the divergent section. Another 5 in./12 in. combustor with a 3 ~ divergent section was tested. However, in this instance the test section was manufactured of vitreous silica (Vitreosil). This combustor withstood the high temperature conditions extremely well, but also produced combustion after the exit Mach disc.
1122
SUPERSONIC COMBUSTION
Calculated Results An exponential relationship of the form suggested earlier is found to fit the coinbustor geometry and the experimental static pressure results with reasonable accuracy. For example, an exponential relationship with a value for the constant Ka = 0.029, results in a maximum deviation of less than 0.030 in. from the actual combustor profile. The values of the exponent ,7 = Ka/Kp for the three equivalence ratios have been calculated and are shown in Fig. 7. The Maeh numbers M1 are also calculated for station (1) since this is where the heat-addition is considered to begin, these values are also given by Fig. 7. If the values of ,7 and M1 are substituted, together with the measured exit Mach numbers M2, into Eq. (7), theoretical values for the exit static pressures can be obtained. These calculated values are 21.71, 18.27, and 11.03 in. Hg abs for equivalence ratios of 0.45, 0.33, and 0.23, respectively. Comparing the above values with the measured static pressures of 22.2, 19.6, and 11.6 in. Hg abs indicates a maximum error of approximately 5%.
Conclusions
Experiments with supersonic diffusion flames, produced by the free-jet injection of hydrogen into a high-enthalpy air-stream, have confirmed that mixing is controlled by the parameter ujpj/uepe. Other properties of free-jet flames provide a good indication of the probable geometry of a combnstor, to be used with the same mode of fuel injection and for the same operating conditions. For example, the distances from the fuel injector to the point at which combustion begins, and that at which all of the fuel is reacted, are a useful guide in determining the dimensions of a combustor. The methane free-jet tests described in this paper have been disappointing to the extent that diffusion flames were not produced. However, the mixing of the methane jet with the high-enthalpy air-stream was found to be quite good. Hence it is expected that an increase in the air stagnation temperature, to the facility maximum of 2070~ combined with an increased performance from the fuel preheater, will result in combustion taking place. The experiments with enclosed flames have shown that for the mode of fuel injection and operating conditions described, it is not possible for a supersonic diffusion flame to exist within a parallel duct or a simple divergent duct. The expansion process which is associated with the
heat release from the diffusion flame, must be accompanied by an increase in duct area. In the case of the parallel duct the resulting constraint leads in some way to the formation of a shock. wave, which in turn produces shock-initiated combustion. However, in the case of the conical combustor, the increase in area and hence reduc. tion in static pressure, begins before heat release can take place, with the result that combustion is inhibited. This is borne out by the fact that the addition of a parallel section to the conical combustor resulted in a diffusion flame forming within the duct. Combustion was also seen to be inhibited in the combined constant-area and divergent combustors which had a divergence of 3 ~ The fact that this inhibition occurred both in the Vitreosil and water-cooled sections, indicates that this phenomena was due more to the duct divergence than to heat loss to the duet wail. From the tests described in this paper it is seen that the required geometry for a combustor capable of enclosing a supersonic diffusion flame, is a combination of a parallel (or possibly convergent) section and a divergent section. The parallel section must have a length approximately equal to that required for ignition to occur, and the divergent section must have a divergence of approximately 1~ This divergence will be influenced to some unknown extent by the viscous boundary layer growth. However, this effect cannot be very large since there is a considerable static pressure fall in the duet for no heat addition. The proposed exponential relationships between area, static pressure and combustor length are seen to be experimentally reasonable. The exit static pressures, calculated from the derived gasdynamie equations, agree quite well, with the measured static pressures zonsidering the onedimensional, perfect gas, frictionless conditions assumed. The proposed analytical treatment, represented by Fig. 3, also shows the correct qualitative Mach number variation when compared with the experimental values. For r/~---- 1.3, the Maeh number in the duct remains nearly constant, while it increases and decreases for r/~--_ -- 0.7 and --2.0, respectively. Nomenclature
A
KA Kp Kt M
;lie p P
flow area exponential flow constant for area exponential flow constant for pressure exponential flow constant for temperature Mach number critical Mach number static pressure total pressure
SUPEP, SONIC DIFFUSION FLAMES R s t 7' u x
p r
characteristic gas constant specific entropy static temperature total temperature gas velocity process length isentropic flow index Crocco type flow index exponential type flow index density equivalence ratio
3.
4.
Subscripts e j
5.
free stream conditions jet conditions 6.
ACKNOWLEDGMENTS This research was supported in part by the National Gas Turbine Establishment of the Ministry of Technology. Acknowledgment must be made to the many members of the technical staff of the Propulsion Department for their considerable assistance, but in particular to Mr. Eric Barnes for his help in carrying out the experimental program.
7.
8.
REFERENCES 1. F~Rm, A. : Supersonic Combustion Technology, AGARD Lecture Series on Turbo-Machinery, Varena, 1967. 2. SWITHE.','BAXK, J.: Experimental Investigation
9.
1123
of Hypersonic Ramjets, Third International Congress of the Aeronautical Sciences, Stockhohn, Aug1~st, 1962. CROCCO, L.: One-Dimensional Treatment of Steady Gas Dynamics, Fundamentals of Gas Dynamics, Vol. I I I of High Speed Aerodynamics and Jet Propulsion, Princeton University Press, 1958. DOBROWLSKI, A.: Analysis of Non-ConstantArea Combustion and Mixing in Ramjet and Rocket-Ramjet Hybrid Engines, Lewis Research Center, NASA TN-3626, 1966. BILLIG, F. S.: Eleventh Symposium (International) on Combustion, p. 755, The Combustion Institute, 1967. COOKSON, R. A.: Supersonic Combustion Studies; I. Design, Construction and Performanee of a High-Enthalpy Facility, College of Aeronautics Report Aero No. 200, November, 1967. LEWIS, J. B. AND HARRISON, D.: Eighth Symposium (Iiderr~ational) on Combustion, p. 366, Williams and Wilkins, 1962. FLANGAN,P. AND COOKSON, R. A.: Supersonic Combustion Studies; II. Exponential Relationships between Pressure, Area and Process Length, for Heat Addition in a Non-ConstantArea Duet, College of Aeronautics Report Aero No. 204, March, 1968. PENNY, G. S.: Diffusion Controlled Supersonic Combustion Utilizing a High Enthalpy Blowdown System, College of Aeronautics Thesis, 1967.
COMMENTS R. G. Dunn, Aerospace Research Laboratories, U.S. Air Force, Wright-Patterson Air Force Base, Dayton, Ohio. The authors describe an unsatisfactory condition relating to the midstream fuel injector, that is water cooled and has a very high heat-transfer rate. I want to point out the obvious fact that any cooling at this point extracts heat from the ah' stream, which should be avoided if at all possible. We have found a means for avoiding this heat loss from the air stream--under very similar operating conditions, that is, air temperatures around 2000~ Our hydrogen nozzle and injector unit is fabricated from molybdenum, and its external surface is coated with nlolybdenum disilicide (a G.E. process). This coating permits exposure to the oxidizing atmosphere of a 2000~ airstream for long periods, with no cooling. Also, a modest attempt at preheating the fuel was mentioned in the same paper. I feel that heating the fuel is desirable in this type of
experiment, and would like to mention a hydrogen heater we have developed and that has operated very successfully. I t is constructed mostly of molybdenum internally and the power used is 440-V A.C. The heater is capable of heating hydrogen to as high as 1700~ at massflow rates up to 0.04 Ib/sec (at pressures of 1 atm and below). The power consumption for this maximum case is 350 kW. Concerning the experimental results and the combustion-chamber design found to be best by the Cookson group, I refer to the experiments reported in which a diffusion flame was initiated within a reasonably short length in a combustor comprised of a 5-in. co~tant-area section followed by a 1~ divergent section 25 in. long. The air stagnation temperature was 1870~ and the pressure slightly under 1 atm. These conditions show a striking similarity to some results we have obtained. We are operating in a slightly lower temperature range (about 1500~ and
1124
SUPERSONIC COMBUSTION
at much lower densities (1/7 atm.). The Math number of the air flow is slightly different also, being 1.5 in our case. We have performed a number of experiments, but, as yet, none with a satisfactory combustion chamber with respect to constant-area length and wall-divergence angle. However, the experiments thus far, together with the results of a parametric study we made by computer, have led us to a design in which we have considerable confidence. (The computer program is one developed by the General Applied Sciences Laboratory and adapted for our use.) The design to which we were led by our results involves a constant-area section 3 in. in length, followed by a l~ divergent
section 36 in. in length. Indications are that combustion will start within the first 15 hydrogen injector diameters. The eombustor is now being installed and experiments with it will begin in about two weeks.
R. Cookson. I t was very interesting for us to hear that Dunn has carried out work similar to our own, and to see that he appears to be reaching the same sort of experimental results as those that we obtained. Concerning the fuel preheater suggested by Dunn, we are at present constructing a preheater and hope to have it working soon. Dunn's suggestion of a coated fuel injector is one that we will surely try.
Propulsion Department, Collegeof Aeronautics, Cranfield, England An experimental study has been made of supersonic diffusion flames produced by the subsonic and supersonic free-jet injection of hydrogen into a high-enthalpy air-stream. The air-stream was flowing at a Mach number = 1.98 and had a total temperature of approximately 1900~ and a static pressure of 14.7 psia. An axial, mid-stream mode of fuel injection was adopted. For the case of hydrogen injected subsonically, combustion was found to be complete (i.e. the concentration of unreacted hydrogen was negligible), at a distance of approximately 9 inches from the point of injection. For the supersonic injection of hydrogen this distance was increased by approximately 30%, for the range of fuel velocities used. The tests were repeated with methane as the injected fuel, but ignition did not occur even with the methane preheated to 480~ or when a bluff-body was inserted into the flow to create shock conditions. The above flames were then enclosed in various combustors of simple geometry, either of constant~area, constant-divergence or some combination of these two. For the conditions specified above, combustion in the diffusional mode was found to be impossible in a constantarea combustor. A diffusion flame was initiated in a combustor which consisted of a short parallel section followed by a section with a divergence of approximately 1% IIowever no combustion took place within a completely divergent duct even though the divergence was less than 1~ An exponential relationship between pressure, area and length has been proposed, and a one-dimensional analytical treatment for the case of heat addition in a non-constant-area duct is included in this paper. This assumption is shown to be experimentally reasonable and to result in gas dynamic equations which include the effect of process length.
Introduction The problems involved in designing propulsive systems for hypersonic air-breathing vehicles have been discussed by several authors, for example Refs. 1 and 2. Their findings indicate that the only feasible system will be one in which heat is added to a supersonic air-stream. In this way problems of structural integrity associated with high static temperatures and pressures, and the energy loss due to chemical dissociation, can be overcome. Of the possible modes of heat release in a supersonic stream, the diffusional mode has been shown to be superior to the case where combustion is shock-induced, or where shock conditions prevail. While the latter modes give relatively high combustion efficiencies and intensities, these would appear to be more than offset by the resultant loss in stagnation pressure and the problems associated with the high static conditions obtained. In the design of an efficient combustor for the
supersonic diffusional mode of heat release, there are two major problems which require investigation. First, the effect of various forms of fuel injection, for example, wall or mid-stream, sul)sonic or supersonic, on such parameters as mixing and stagnation pressure loss. Second, the effect of the combustor geometry on performance criteria. A program of research has been initiated in the Propulsion Department at Cranfield in which the effect of fuel injection and combustor geometry can be investigated. The initial phase of this research program has been the investigation of supersonic flames produced from the fl'ee-jet injection of fuel into a high-enthalpy air-stream. An attempt was then made to enclose the SUl)ersonic flames in ducts of various simple geometries, and to compare the mixing and reaction phenomena for the enclosed condition with those prevailing in the free-jet. The work described in this paper is limited to the axial midstream mode of fuel injection. I n treating the case of heat-addition in a non-
1115
1116
SUPERSONIC COMBUSTION
constant-area duct analytically, Croccoa has proposed a pressure-area relationship which has since been utilized by Refs. 4 and 5. An attempt has been made in this paper to extend this onedimensional analysis to include the effect of process length.
Experimental A pebble-bed heater utilizing alumina elements was used to provide the high-enthalpy air-stream for the experiments described in this report. The facility is capable of providing 2 pounds of air per second at a stagnation pressure of 250 psia and stagnation temperature of 2070~ A complete description of this facility is contained in Ref. 6. A Mach 1.98 convergent-divergent, axisymmetric nozzle was used for the free-jet experiments and is illustrated in Fig. 1. This nozzle has an axial, mid-stream, injector and is designed to run choked at 113 psia and to discharge to atmosphere at 14.7 psia. The problem of cooling the stainless-steel nozzle and injector created some
difficulty. In particular, boiling occurred in the mid-stream injector until the cooling water pressure was raised to 400 psia. A conventional cooled pitot probe was used to measure the stagnation pressure in the stream, and an uncooled needle probe for measuring the static pressure. This latter probe was immersed in the air-stream for short periods only, by use of a pneumatic plunger. The stream Mach number was determined both from the shock angle produced by the immersion of a wedge into the flow, and by use of a Shapiro pitot-static probe. Schlieren photographs for the former of these two techniques, are extremely difficult to obtain, presumably because of the highly turbulent shear layer surrounding the high-temperature air-stream. The static temperature of the supersonic flame was measured by the line-reversal technique. A very simple system was used, employing a cheap grating spectrometer and a tungsten strip lamp as a continuum source. Reversal was obtained visually and the source was calibrated by means of a disappearing filament pyrometer. The line reversal technique is essentially an averaging
HYDROGEN INLET COOLING WATER OUTLET WATER OUTLET
RING SEAL
I NJECTOR
COOLING WATER INLET "=--COOLING WATER INLET X-HYDROGEN
INLET
FIG. 1. Axisymmetric Mach number = 1.98 nozzle with axial fuel injection used for free-jet experiments.
SUPERSONIC DIFFUSION FLAMES
FUEL INJECTOR- /
/
1117
/--STATIC PRESSURE~ TAPPINGS
MACH;)NOZZLE/' ~
b
/'
WATERCOOLEDCOMBUSTORJ FIG. 2. Combustor geometls~ for enclosed flame experiments. process but the resulting error, in these tests, should be small as the flame is surrounded by a very hot air-stream for most of its length. For sampling the reacting flow the method suggested by Ref. 7 was used. In this technique a sharp edged probe produces a system of attached shocks, with the resulting normal shock across the orifice being swallowed by the application of a vacuum pressure to the probe outlet. Cooling the sharp leading edge presents some difficulty, but can be accomplished by forcing water through an annular passage around the probe until it is close to the tip and then ejecting it rearwards into the hot stream. Direct color photography was found to be very useful in providing a visual record of the supersonic flame and in determining the delay period before combustion begins. The ducts used for the experiments on enclosed flames were all of circular section to match the outlet of the Mach 1.98 nozzle described above. Two duct lengths were used, 12 in. and 30 in., and constant-area, combined constant area and divergent, and divergent geometries were "dl tested. A typical configuration is shown in Fig. 2. Each duct was provided with static pressure tappings throughout its length and with a watercooled jacket. A transparent vitreous silica (Vitreosil) duct was also used, having a combined constant-area and divergent geometry similar to one of the stainless steel combustors. The early tests were carried out without any attempt being made to preheat the fuel. In the later tests, and in particular the experiments with methane, some preheating has been used. This fuel heater took the form of a stainless steel coil over which hot air from the pebble-bed was passed once blow-down was begun. A temperature rise of only 200~ has been obtained so far but this will be improved by a better heater design.
Exponential Pressure :Area :Length Relationships A pressure-area relationship of the form pA '/('-1) = constant
(1)
has been proposed by Crocco3 for the case of heat-addition to a gas flowing in a duct. Hence the particular processes of constant-area and constant-pressure can be described by values of e of 1 and 0, respectively. Dobrowlski4 has eraployed this relationship and further developed the concept of subcritical and supercritical heataddition. This form of pressure-area relationship has also been used by Billig,5 with the suggestion that an optimized combustor geometry might be obtained by piecing together segments of combustor of different e value. Billig also developed gasdynamic equations for inlet-to-outlet ratios of many of the flow variables, in terms of the e parameter. I t is obviously desirable to incorporate some process length dependency into the analysis if this is possible, rather than adopting the piecemeal process suggested. For this reason, and because it has been observed that the pressure-length and area-length relationships obtained from our experiments, can be approximately described by some exponential expression, the following relationships are postulated: P2 = Pl exp (Kpx)
(2)
and A o = A, exp
(KAx)
(3)
where x is the process length x2 -- xv The stations Xl and x2 are as indicated on Fig. 7, "rod the length x , , - xl is the distance over
1118
SUPEI{SONIC COMBUSTION the total teml)erature ratio call be written as
which heat is added. Therefore
(A2/AO = (p.,./pl)Ka/K" KA/Kp
or, if for simplicity, we use ~ =
A/p" =
T2/T, =
(4)
Q2/tl),
(10)
and the total pressure ratio as
constant.
P2/P1 = (Xz/xl) "~('-l) (p~/pO;
(5)
Hence it is possible to solve tim molnentmn equation and by utilizing the definition of Mach nmnber and the equations of state and contilmity, the following expressions can be obtained:
As-3,R{(312~
Xl,~
{11+ ( r / + 1)TM12/~/(~1)
(6)
+ (n + 1)uM2=J
(11)
also the change of entropy can be expressed as,
Area ratio:
A2/AI=
(X2/Xl)
r 7 ( 2 ~ + 1) + 1] [} + ("7 +
1)3":]I121/
+ (,7 + i)--~--~j].
(12)
Similarly the critical Mach number is given by
Static pressure ratio:
p2/pl=
M~2 = E3'n + 1-]-1. {}--~-(rl+ 1)%11,21u(~1) + (n + 1)%1I-~2J
(7)
Static temperature ratio:
t2/h
=
The static temperature ratio can also be expressed in the following way, ~2//tl = { ('[/~2/'t/1)exp [-(/~fA-Jr- Kp)x-]}. (14)
{1+ (,,+
1 + (,7+ 1)~.@J
\~/
(s)
and, if for simplicity, we use X = [-1 + 89 -- 1)M2J,
(9)
Thus it can be seen that the ratio of the outlet to inlet static temperatures which results from heat addition in an exponentially related pressure-area-length duct is not itself exponential, !
M2 > M1 -0-95
Su~r=onlc
-I-I
-I.3
-6"0
Subsor 15"0 I
"~'/' [~
O Qf 2-C
-0.9
I.C
I I
4-0
(13)
I
I
3-0 OUTLET
l
2.0 MACH NUMBER
t I
I
!
I*0 M2
FIG. 3. Diagram illustrating the range of flows that can be described by the parameter for an inlet Mach number = 2.
SUPERSONIC DIFFUSION FLAMES
1119
2200
Uj ~ j
= O'171
25. 8 0
2000
MP
ATURE
~. I
v'
o uJ
18OO
r162 ,,I n
160C
2(>-60
,1n
:i
uJ I.-
140C
IIn
t
15.-40
IO- 2 0 5
O
20
40
60
AXIAL DISTANCE = INJECTOR RADIUS
T
80
tt} O.
I
uJ r o~ ,,i r ft.
0.
O
FIG. 4. Variation of static temperature, static pressure, and pitot pressure along the axis of a free-jet hydrogen supersonic diffusion flame.
\
,oo
Z
~
:J, .
METHANE
Uj pj
--
=0"74
,o Z bl
HYDROGEN
:i
C
I
20
40
METHANE
_5.
AXIAL DISTANCF, = INJECTOR RADIUS
60
'
80
I00
,:C "1"
FIG. 5. Variation of fuel concentration along the axis of a free-jet hydrogen supersonic diffusion flame and an unreacted methane jet.
but is modified by the ratio of the outlet t<) inlet gas velocities. Equation (14) can obviously be written ~2/tl =
(U2//Ul)
exp
(Ktx)
(15)
where Kt = KA + Kp. From the above analysis it can be seen that the constant-area and constant-pressure cases are represented by ~ values of unity and infinity, respectively. It is interesting to note that the critical Much number for the constant-pressure case is equal to zero. This can be interpreted as
meaning that a constant-pressure heat-addition process will never thermally choke. Figure 3 illustrates the range of flows that can be described by the 71 parameter, calculated for a combustor inlet Mach number of 2 and -y = 1.32. The proposed exponential representation of pressure and area variatLon with duct length has been dealt with at greater lellgth i1~ Ref. 8, and static aud total temperature ratios and static and total pressure ratios for an inlet Much number = 2 and 7 = 1.32 (i.e., approximately the experimental conditions referred to in this paper), have been calculated.
1120
SUPERSONIC COMBUSTION Results
Free-Jet Studies
Figure 4 shows the variation of several flow properties, measured along the axis of the jet, with distance from the point at which hydrogen was injected into the high-enthalpy air-stream. Similarly Fig. 5 illustrates the variation of the unreacted hydrogen concentration with axial distance, and Fig. 6 the radial variation at three positions along the jet. For the particular experiment illustrated by Figs. 4, 5, and 6, the hydrogen injection was subsonic at a velocity of 2300 ft/sec, the air-stream was at a l%{ach number of 1.98, and a stagnation temperature of 1870~ Results have also been obtained for other flow conditions, and for both subsonic and supersonic fuel injection. These results are to be found in Ref. 9. From the hydrogen free-jet results obtained it can be seen that stable, shock-free, supersonic diffusion flames can be produced from both subsonic and supersonic fuel injection. For the range of flow conditions investigated, the distance
required for complete reaction, or more exactly, for the concentration of molecular hydrogen to become negligible, was up to 30% greater for supersonic fuel injection than for the subsonic case. Mixing was found to be dependent upon the ratio pjui/p,ue , and this served to confirm the findings of other researchers. The distance from the fuel injector to the commencement of visible flame radiation, was found to be approximately 8 injector diameters for subsonic fuel injection, and 10 diameters for the case where injection was supersonic. These distances did not appear to vary with temperature, and in the cases where experiments were carried out at stagnation temperatures below the normal operating range, the result was not a marked increase in the ignition delay, but instead a ragged flame in which small detonations could be heard to occur. The injected methane could not be ignited even when it was preheated to 470~ or when a bluff body was inserted into the flow to create a normM shock. The mixing results for methane injection without reaction are included in Fig. 5, from which it can be seen that mixing is much
30
25 Z Q Zi,i U
Z
Uj = Ur = tj = 1:r
2280 FT/SEC 3840 FT/SEC 295~ 1140~
| ~
Uj pj Uepr --0.171
/~i
/I 3C= 1"
12
20
15
O U
---~- = 18
i./) !0
35 0
3
2
I
0
I
2
3
SAMPLE RADIUS INJECTOR RADIUS Fie.. 6. Radial variation of hydrogen concentration-at-three stations along a supersonic hydrogen diffusion flame.
SUPERSONIC I)IFFUSION 1;'LAMIiXS
1121
I
I
XI= S-O INS.
Ln uJ -r z_ I u~ 09
30,
.
.
.
.
0 t3=2150~162
20
2100~ EXIT (~
_u
J
.
X2= 28.5 INS.
IO
M I
M2
T~
~
O
0-45
1,776
1-500
-- 2 - 0 2 0
A
O'33
I "816
1.788
--1-302
~j
0.23
1.872
2.310
-0-753
I
I IO COMBLISTOR
I
SHOCKS 1990OK
w
KclI2 = 0 , 0 2 8 8
I 2o L E N G T H - - INCHES
I
I 30
Fro. 7. Wall static pressure variation with combustor length, for supersonic diffusion flames enclosed in a 5 in. parallel, 25 in. divergent combustor. slower than for hydrogen. I t can also be seen that stoichiometric proportions are reached at a distance of 35 jet diameters downstream.
Enclosed Flames I t was found that a hydrogen diffusion flame could not be maintained within any of the parallel combustors, of various lengths, which were tested, or within a simple conical combustor of 0.75 ~ divergence and 30 in. long. In the case of the parallel ducts the heat-addition process broke down in each instance to one of shock-initiated combustion. For the divergent duct, combustion was observed to occur after the Mach disc which was formed at the combustor exit. Three combustors of combined constant-area and divergent geometries were tested, and for convenience these will be specified as a/b, where a and b are the dimensions shown in Fig. 2. The first of these combined geometries was a 10 in./20 in. combustor with a 1.5 ~ divergent section. As with the parallel combustors described above, this duct also resulted in shock-initiated combustion taking place in the 10 in. section. The second of these combustors was a 5 in./12 in. duct with a 3 ~ divergent section. This combustor resulted in combustion taking place after the Mach disc which was formed at exit. The third and successful combustor had a 5 in./25 in.
geometry with a 1~ divergence and resulted in a supersonic diffusion flame existing within the divergent section. Figure 7 shows the static pressure variation along the 5 in./25 in. combustor for three equivalence ratios, together with the measured Mach numbers and static temperatures at exit. It should be emphasized however that the static temperatures given were measured after the exit shock formation, and as such are included simply to indicate the order of temperature to be expected. For the experiment illustrated by Fig. 7, the air stagnation and fuel temperatures were 1870 ~ and 350~ respectively. Sampling carried out at the combustor exit plane for each of the equivalence ratios failed to detect any appreciable concentration of unreacted hydrogen. A further successful combustor was created by adding a 5 in. parallel section to the conical combustor described above, and producing a 5 in./30 in. geometry with 0.75 ~ divergence. This combination, when tested was found to support a supersonic diffusion flame within the divergent section. Another 5 in./12 in. combustor with a 3 ~ divergent section was tested. However, in this instance the test section was manufactured of vitreous silica (Vitreosil). This combustor withstood the high temperature conditions extremely well, but also produced combustion after the exit Mach disc.
1122
SUPERSONIC COMBUSTION
Calculated Results An exponential relationship of the form suggested earlier is found to fit the coinbustor geometry and the experimental static pressure results with reasonable accuracy. For example, an exponential relationship with a value for the constant Ka = 0.029, results in a maximum deviation of less than 0.030 in. from the actual combustor profile. The values of the exponent ,7 = Ka/Kp for the three equivalence ratios have been calculated and are shown in Fig. 7. The Maeh numbers M1 are also calculated for station (1) since this is where the heat-addition is considered to begin, these values are also given by Fig. 7. If the values of ,7 and M1 are substituted, together with the measured exit Mach numbers M2, into Eq. (7), theoretical values for the exit static pressures can be obtained. These calculated values are 21.71, 18.27, and 11.03 in. Hg abs for equivalence ratios of 0.45, 0.33, and 0.23, respectively. Comparing the above values with the measured static pressures of 22.2, 19.6, and 11.6 in. Hg abs indicates a maximum error of approximately 5%.
Conclusions
Experiments with supersonic diffusion flames, produced by the free-jet injection of hydrogen into a high-enthalpy air-stream, have confirmed that mixing is controlled by the parameter ujpj/uepe. Other properties of free-jet flames provide a good indication of the probable geometry of a combnstor, to be used with the same mode of fuel injection and for the same operating conditions. For example, the distances from the fuel injector to the point at which combustion begins, and that at which all of the fuel is reacted, are a useful guide in determining the dimensions of a combustor. The methane free-jet tests described in this paper have been disappointing to the extent that diffusion flames were not produced. However, the mixing of the methane jet with the high-enthalpy air-stream was found to be quite good. Hence it is expected that an increase in the air stagnation temperature, to the facility maximum of 2070~ combined with an increased performance from the fuel preheater, will result in combustion taking place. The experiments with enclosed flames have shown that for the mode of fuel injection and operating conditions described, it is not possible for a supersonic diffusion flame to exist within a parallel duct or a simple divergent duct. The expansion process which is associated with the
heat release from the diffusion flame, must be accompanied by an increase in duct area. In the case of the parallel duct the resulting constraint leads in some way to the formation of a shock. wave, which in turn produces shock-initiated combustion. However, in the case of the conical combustor, the increase in area and hence reduc. tion in static pressure, begins before heat release can take place, with the result that combustion is inhibited. This is borne out by the fact that the addition of a parallel section to the conical combustor resulted in a diffusion flame forming within the duct. Combustion was also seen to be inhibited in the combined constant-area and divergent combustors which had a divergence of 3 ~ The fact that this inhibition occurred both in the Vitreosil and water-cooled sections, indicates that this phenomena was due more to the duct divergence than to heat loss to the duet wail. From the tests described in this paper it is seen that the required geometry for a combustor capable of enclosing a supersonic diffusion flame, is a combination of a parallel (or possibly convergent) section and a divergent section. The parallel section must have a length approximately equal to that required for ignition to occur, and the divergent section must have a divergence of approximately 1~ This divergence will be influenced to some unknown extent by the viscous boundary layer growth. However, this effect cannot be very large since there is a considerable static pressure fall in the duet for no heat addition. The proposed exponential relationships between area, static pressure and combustor length are seen to be experimentally reasonable. The exit static pressures, calculated from the derived gasdynamie equations, agree quite well, with the measured static pressures zonsidering the onedimensional, perfect gas, frictionless conditions assumed. The proposed analytical treatment, represented by Fig. 3, also shows the correct qualitative Mach number variation when compared with the experimental values. For r/~---- 1.3, the Maeh number in the duct remains nearly constant, while it increases and decreases for r/~--_ -- 0.7 and --2.0, respectively. Nomenclature
A
KA Kp Kt M
;lie p P
flow area exponential flow constant for area exponential flow constant for pressure exponential flow constant for temperature Mach number critical Mach number static pressure total pressure
SUPEP, SONIC DIFFUSION FLAMES R s t 7' u x
p r
characteristic gas constant specific entropy static temperature total temperature gas velocity process length isentropic flow index Crocco type flow index exponential type flow index density equivalence ratio
3.
4.
Subscripts e j
5.
free stream conditions jet conditions 6.
ACKNOWLEDGMENTS This research was supported in part by the National Gas Turbine Establishment of the Ministry of Technology. Acknowledgment must be made to the many members of the technical staff of the Propulsion Department for their considerable assistance, but in particular to Mr. Eric Barnes for his help in carrying out the experimental program.
7.
8.
REFERENCES 1. F~Rm, A. : Supersonic Combustion Technology, AGARD Lecture Series on Turbo-Machinery, Varena, 1967. 2. SWITHE.','BAXK, J.: Experimental Investigation
9.
1123
of Hypersonic Ramjets, Third International Congress of the Aeronautical Sciences, Stockhohn, Aug1~st, 1962. CROCCO, L.: One-Dimensional Treatment of Steady Gas Dynamics, Fundamentals of Gas Dynamics, Vol. I I I of High Speed Aerodynamics and Jet Propulsion, Princeton University Press, 1958. DOBROWLSKI, A.: Analysis of Non-ConstantArea Combustion and Mixing in Ramjet and Rocket-Ramjet Hybrid Engines, Lewis Research Center, NASA TN-3626, 1966. BILLIG, F. S.: Eleventh Symposium (International) on Combustion, p. 755, The Combustion Institute, 1967. COOKSON, R. A.: Supersonic Combustion Studies; I. Design, Construction and Performanee of a High-Enthalpy Facility, College of Aeronautics Report Aero No. 200, November, 1967. LEWIS, J. B. AND HARRISON, D.: Eighth Symposium (Iiderr~ational) on Combustion, p. 366, Williams and Wilkins, 1962. FLANGAN,P. AND COOKSON, R. A.: Supersonic Combustion Studies; II. Exponential Relationships between Pressure, Area and Process Length, for Heat Addition in a Non-ConstantArea Duet, College of Aeronautics Report Aero No. 204, March, 1968. PENNY, G. S.: Diffusion Controlled Supersonic Combustion Utilizing a High Enthalpy Blowdown System, College of Aeronautics Thesis, 1967.
COMMENTS R. G. Dunn, Aerospace Research Laboratories, U.S. Air Force, Wright-Patterson Air Force Base, Dayton, Ohio. The authors describe an unsatisfactory condition relating to the midstream fuel injector, that is water cooled and has a very high heat-transfer rate. I want to point out the obvious fact that any cooling at this point extracts heat from the ah' stream, which should be avoided if at all possible. We have found a means for avoiding this heat loss from the air stream--under very similar operating conditions, that is, air temperatures around 2000~ Our hydrogen nozzle and injector unit is fabricated from molybdenum, and its external surface is coated with nlolybdenum disilicide (a G.E. process). This coating permits exposure to the oxidizing atmosphere of a 2000~ airstream for long periods, with no cooling. Also, a modest attempt at preheating the fuel was mentioned in the same paper. I feel that heating the fuel is desirable in this type of
experiment, and would like to mention a hydrogen heater we have developed and that has operated very successfully. I t is constructed mostly of molybdenum internally and the power used is 440-V A.C. The heater is capable of heating hydrogen to as high as 1700~ at massflow rates up to 0.04 Ib/sec (at pressures of 1 atm and below). The power consumption for this maximum case is 350 kW. Concerning the experimental results and the combustion-chamber design found to be best by the Cookson group, I refer to the experiments reported in which a diffusion flame was initiated within a reasonably short length in a combustor comprised of a 5-in. co~tant-area section followed by a 1~ divergent section 25 in. long. The air stagnation temperature was 1870~ and the pressure slightly under 1 atm. These conditions show a striking similarity to some results we have obtained. We are operating in a slightly lower temperature range (about 1500~ and
1124
SUPERSONIC COMBUSTION
at much lower densities (1/7 atm.). The Math number of the air flow is slightly different also, being 1.5 in our case. We have performed a number of experiments, but, as yet, none with a satisfactory combustion chamber with respect to constant-area length and wall-divergence angle. However, the experiments thus far, together with the results of a parametric study we made by computer, have led us to a design in which we have considerable confidence. (The computer program is one developed by the General Applied Sciences Laboratory and adapted for our use.) The design to which we were led by our results involves a constant-area section 3 in. in length, followed by a l~ divergent
section 36 in. in length. Indications are that combustion will start within the first 15 hydrogen injector diameters. The eombustor is now being installed and experiments with it will begin in about two weeks.
R. Cookson. I t was very interesting for us to hear that Dunn has carried out work similar to our own, and to see that he appears to be reaching the same sort of experimental results as those that we obtained. Concerning the fuel preheater suggested by Dunn, we are at present constructing a preheater and hope to have it working soon. Dunn's suggestion of a coated fuel injector is one that we will surely try.