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Pulsating combustion of liquid fuel in partially closed vessels
PULSATING COMBUSTION OF LIQUID FUEL IN P A R T I A L L Y C L O S E D V E S S E L S J. W. PORTER Department of Aerospace Engineering. University of Texas. Austin, Texas Two modes ofcombu,,tion are possible for a liquid fl~el in a vessel that is closed except for a single orifice: constant pressure diffusion burning and pulsating combustion. An experimental and theoretical investigation has been made of the pulsating mode of combustion using methanol liquid fuel, Measurements were made of liquidfuel burning rates and of chamber pressure as a function of time in cylindrical ,.,essels for various chamber lengths and orifice diamclers. In addition, high-speed schlieren motion picture,, were laken of the pulsating combustion pr~'c~.s in order to obtain qualilativc information about flo~v ptttlcrns, mixing, and ignlllOn during each combustion cycle S¢lt:su,,~ained pulsating combustion was found to be possible only within certain limits of chuml~.'r length and orifice diameter. Within these limits, combustion frequency ranged from about 25 to 70 c/s, and was always smaller than th. Itelmhohz resonator frequency by at least a i'aetor of three. Pressure amplitudes varied from about 10 to 85 mm of mercury, Methanol burning rates were found to be as much as eight times larger than those for steady diffusio:~ burning in open-top cylinders of th~ same size. Other liquid fi~els, in addition to methanol, were found also to exhibi~ pulsating combustion. A theoretical analysis gives chamber pressure as a function of time during the prcssttrc decay part of each cycle and agrees substantially with experimental measurements,
Introduction Tu~ phenomenon of pulsating combustion is not new, and a considerable amount ofliterature exists on the subject. Much of the literature is concerned with various forms of the pulse-jet engine t- a; however, characteristics of pulsatingcombustion chambers, such as very high combustion intensity (i.e. high rate of heat release per unit volume), very high heat transfer rate to the walls of the combustion chamber, and nearstoichiometric combustion have stimulated the use of pulsating combustion for heating purposes in industrial furnaces and small space heaters4.s. One of the most interesting types of pulsating combustion occurs in the burning of liquid fuels in partially closed vessels. The process is characterized by low frequency (less than about 100 c/s), small amplitude, self-sustained pressure oscillations. The Simplest kind of combustion chamber that allows this type of pulsating combustion consists of a vertical, circular cylinder that is partially filled with a liquid fuel and completely closed except for a single, valveless, sharp-edge orifice at the top. The operation of this combustion chamber can be described by outlining the sequence of events that occurs
during a typical cycle" vaporized fuel and air burn rapidly in the chamber, increasing the pressure; combustion products flow out of the chamber through the orifice; the pressure in the chamber returns to and drops below the external ambient pressure; external air is drawn into the chamber where it mixes with vaporized fuel and hot combustion products; self-ignition occur~ and the cycle repeats itself. Hence during each cycle there is an alternat inflow of air and outflow of combustion products through the single orifice in the chamber. This phenomenon was discovered about 1933 by F. H. Reynst. In a recent collection of his works, several explanations of the mechanism of operation, ate offered; however, no theoretical or experingntal evidence is presented. Two basically different modes of combustion are possible for a liquid fuel in a vessel that is closed except for a single orifice: constant pressurediffusion bundng and pulsating combustionS:.: Diffusion burning is characterized by ~ t : pressure, relatively gentle, laminar or t ~ t diffusion flames, Pulsating coml~as~ isehar-' acterized by relatively vigorous, ~ ~:: sure and flow oscillations. The orifice ~ : i ! relation to the vessel size and the furl kvcl, i 501
502
J.w.
determines which mode will occur. Diffusion burning of liquid fuels in open-top cylindrica! vessels has been thoroughly studied by Blinov and Khudyakov 7. However, there has been no similar investigation of pulsating burning of liquid fuels in partially closed vessels. The objectives of this investigation are to determine the dependence of frequency, pressure amplitude, and fuel burning rate on chamber geometry, and to determine the mechanism of operation of pulsating combustion in partially dosed vessels. Measurements of pressure as a function of time will be compared with a theory based on an assumed mechanism of operation. The burning rate for pulsating combustion in partially closed vessels will be compared with the data obtained by Blinov and Khudyakov "t for steady diffusion burning in open-top vessels. Experimental The experimental measurements fall into tt_:ree categories: (1) measurements of chamber pressure and fuel burning rate in a 3.64 in. inside diameter, vertical, cylindrical chamber; (2) highspeed schlieren motion pictures of the pulsatingcombustion process; and (3) miscellaneous experiments. The measurements of chamber pressure as a function of time are used to obtain frequency and peak-to-peak pressure amplitude as functions of chamber length and orifice diameter; in addition, they are also used to determine approximate limits on chamber length and on orifice diameter within which selfsustained operation is possible. The high-speed schlieren motion pictures provide qualitative information about flow patterns, mixing and ignition. Technical grade methanol was used in all experiments, except in some of the miscellaneous experiments. The ambient pressure (external to the orifice) was always approximately one atmosphere. Figure 1 shows a schematic diagram of the apparatus used for measuring chamber pressure and fuel burning rate. The combustion chamber (1) is a water-cooled, 3.64 in. i.d. cylindrical, iron pipe that is do .s,~_at the top by a plate with a sharp-edge circular orifice (2)and dosed at the bottom by a piston (3). The piston allows the length of the chamber to be varied from about 5 to 12 in. The system was prepared for an
Vol. 1 I
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experiment by adding liquid fuel (4) to a depth of one inch and covering the orifice loosely to allow equilibrium to be established at ambient pressure. The flowrate and inlet temperature of the cooling water were kept at 60 g/see and 3¢'C, respectively. Ignition was accomplished by a spark-plug ignition system (5)---the spark discharge being terminated immediately after the initial explosion. After about 30 ,seconds of self-sustained operation, chamber pressure as a function of time was measured with a straingauge pressure transducer (6) and was recorded using an oscilloscope (7) equipped with a Polaroid camera. The duration of the pressure trace was never more than about one second {corresponding to about 50 combustion cycles).
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(3) • FIGUaE 1, Schematic diagram of the apparatus us~ for measuring pressure and burning rate:O) 3.64 in, i.d. cylindrical combustion chamber, (2) orifice plate, (3) piston, (4) liquid fuel, (5) spark plug, (6) strain-gauge pressure transducer, and (7) oscilloscope
The procedure was repeated with fresh fuel, for various chamber lengths and orifice diameters. In a similar series of experiments, average burning rates of methanol were measured for various chamber lengths and orifice diameters. Each experiment consisted of measuring the fuel level before and after a timed period of operation. Fuel level was measured with a micrometer depth gauge, and time intervals were measured with an electric stopciock. Typically, the time
December 1967
PULSATING ('OMilUSTIONOF LIQUIDFUEL IN PARTIALLYCLOSED VESSELS
interval was about one and one-half minutes, and the change in fuel level was about 0.5 in. Figure 2(a) shows a schematic diagram of the special combustion chamber that was used to obtain high-speed schlieren motion pictures of the pulsating combustion process 8. The chamber consists of a metal frame with Pyrex glass walls. The top of the chamber is composed of four, overlapping, metal plates that can be individually adjusted by screw mechanisms (not shown) to
503 condensed water on the glass walls evaporated (about 15 see), at which time, high-speed photographs were made using a 16 mm Wollensak Fastax camera (5) with Kodax TXR 430 fi~. The maximum framing rate in each run was about 5000 frames per second. The miscellaneous experiments included experiments to determine if eperation with fuels other than methano! (such as kerosene and gasoline) is possible. Also included was an
lop view
~
Exhaust duct Manifold
-%
'"'~"Adjustable orifice plates Orifice Pyrex glass walls
~ir/O~yge~ m~xture
Metat frame I iquid fuel Liquid fuel. "--""-"-
Side view
(a}
U (b}
FI(iURI~ 2. Schematic diagram of special pulsating-combustion chambers for {a) obtaining high-speed schlieren photographs of the pulsating combustion process, and (b) varying the oxygen concentration of the ambient air
form a rectangular orifice of any size up to 3 in. x 3 in. The inside cross section of the chamber is 3~- in. x 3~ in. and the height of the empty chamber is 12~ in. The inside length of the chamber during operation is determined by the fuel level. In each run, the length of the chamber was set at 5.5 in. so that the field of view included most of the chamber and half an inch above the orifice. The orifice plates were adjusted to form a 0.43 in. x 1.0 in. rectangular orifice (with the long side parallel to the schlieren light) in an attempt to make the process as nearly two-dimensional as possible. Combustion was initiated by an open flame at the orifice. The system was allowed to run until
experiment to determine the effect on pulsating combustion of varying the oxygen concentration of the ambient air. Figure 2 (b) shows the apparatus that was used to increase the oxygen concentration gradually in the air stream during pulsating combustion. Finally, experiments were conducted to determine the effects of orifice shape and location, multiple orifices, and chamber diameter and shape. Theoretical Considerations A typical combustion cycle consists of the following sequence of events. Explosion in the chamber is accompanied by a rise in pressure above atmospheric pressure. Next follows a
Vol. I I J.w. I'OR'n!R is some constant average density in the relatively long period of pressure decay in which the pressure drops from a maximum value chamber, At = A(2p/p,,)~ and Az ~ A(2)~ are above atmospheric pressure to a minimum value modified orifice areas for discharge and suction, respectively, and A is the actual orifice area. below atmospheric pressure. During the time that the pressure is below atmospheric pressure, The assumptions involved in neglecting the non-steady acceleration term may be determined ambient air is sucked into the chamber where it by considering the complete non-steady momenmixes with hot vaporized fuel and combustion products. The suction period is terminated by tum equation. Assuming small departures of chamber pressure and density from the unignition and explosion, and the cycle repeats disturbed values Pa and p~, respectively, the itself. The analysis in this section is concerned momentum equation may be integrated across with determining the chamber pressure as a a sharp-edge orifice of diameter ($to yield function of time during the pressure-decay part of the cycle in order to determine the mechanism ) 2 = (p - Pa) + (t/ton)2dZp/dt2 [4] t,,u,. whereby the chamber ~ressure drops below where u,. is the gas velocity at the orifice, atmospheric pressure. Heat transfer to chamber walls and heat of vaporization of the liquid fuel on = aa[{3nz/32)(5/V)] ~ is the classical Helmhoitz resonator frequency, and ao = (TpJp,) t is are included in the analysis. Chemical reaction rates are assumed to be negligible in this part of the speed of sound. In deriving equation 4 the effective mass that experiences acceleration in the cycle. Assuming that conditions are uniform the vicinity of the orifice has been replaced° by throughout the chamber and that the gases are (32/3nzl(poA2/& Use has also been made of perfect, the equations of conservation of mass the equation u,, = - (V/~,'p~A)(dp/dt) obtained and energy for the gases in the chamber, during by combining equations 1 and 2 with )he = the: pressure-decay period, become (~ = 0. Finally, for simplicity the average chamdo/dr := (~)/- fit,)/V [1] ber density has been replaced by p~. The last term in equation 4 represents the acceleration and of gas through the orifice. Writing (p - p~) .7: dr/dr - ('ip/p)(dp/dt) = exp(icot), the ratio of the acceleration term to the -(~ - l)(~d. + (2)iv [2] pressure difference term in equation 4 may be written as (~o/ou)2, where (o is the oscillation respectively, where p and p are the pressure and frequency. The ratio of the kinetic energy term density, respectively, of the chamber gases; t p~u~ to the pressure difference term { p - p~) denotes time i ~ is the fuel vaporization rate; may be written as (3/28) (V/63)l(pm..,~ - pA~p,.] ~,, is the mass flow rate of gases through the (cO/On)z. From these results it can be seen that orifice; V is chamber volume; L represents equation 4 can be reduced to the Helmholtz the heat ofvaporization of the liquid fuel: Q is the oscillation equation 9 if(to/(on)z is of order unity total rate of heat loss through the chamber or less and if 10'm.~.,.- P~)/P,I/('9/V) ~ 1. On walls; and 7 -- cjc~ is the ratio of specific heats the other hand if (t'J/cOn)z ,~ 1 and if (63/V)/ of chamber gases. Assuming I{P - P3/Pot < 1, I(Pm,. - P,)/P~I ~ 1, equation 4 can be reduced I(P - P)/Pl '~ 1, and neglecting the non-steady to the familiar steady-state Bernoulli equation. acceleration term in the momentum equation, Consequently, equation 3, which is based on it can be shown that the mass flowrate through the steady-state Bernoulli equation, involves the orifice is the assumptions that {~o/(~n)a < 1 and (63/V)/ IlPm,.~.- P,,)/P*I '~ 1. Experimental justification f,l, [p.0' p,)1~, for these assumptions and the assumptions that for disehargc (p > po) [{p - p~)/p~[ ~ i and ](p - P)/I~[ <~ 1 are prem' "- i.'ta [p,,0'. p)]~, [31 sented in the next section. Letting p - p,,.,~, at time t - 0 (correspond[. for suction {p < p.) ing to the beginning of pressure decay), and assuming that the fuel vaporization rate ~hyand where the subscript a refers to the ambient air, 504
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-
December 1967
Pt:LSAT~<~CO~mVSUONOVUOtStD~:UEL~ P~a'n~tL'~ CLOSEDVESSELS
the wall heat transfer rate Q are constant,
equations 1, 2 and 3 may be combined and integrated to yield (Y, ..... - y , ) - iog[(i + y, . . . . . )/(| q- Yl)] = ~, for 0 ~< t ~< to [5]
505
combustion processes. Finally, two additional equations would be needed to relate the fuel vaporization rate m/and the rate of heat loss (~ to conditions in the chamber. However, in view of the limited objective stated at the beginning of this section, no attempt is made here to develop a more complete theory.
and Iog[t/(I - y,.i] - y., : i_,. for to ~< t ~ r
[-6]
whele "
I;' ~ l lip,, ;'l,,)lliifL + 0.1 - ~h
- p,,I/po] l,.~ - 17i.-I~._,i" l',, 'l It=- lllpJ)'p<,)
x i,i, sL
+
[-6a]
Oi- , s]it
and Yi....... is the value of Yi when p is equal to i~,,,,~. The time to tat which transition from discharge to suction occurs) may be obtained by setting .l't = 0 in equation 5 to yield {[!)o = .'Fl..... --Iog(l
+ Yl,max)
[7]
The time z represents the time at which rapid combustion begins and the suction period ends, i.e. it represents the end of the pressure-decay part of the cycle. In this analysis suction is obtained solely by the continued cooling of the gases after the chamber pressure has dropped to atmospheric pressure. Acceleration of the gases through the orifice and the associated effect on chamber pressure has been neglected for the reasons discussed in the text following equation 3, Neither ~ nor Pmax. is predicted by this analysis, because chemical reactions have not been included. The time z - to is the time during which the chamber pressure is less than ambient pressure; it may be regarded as a mixing/ignition time that depends on mixing and chemical reaction rates between vaporized fuel and the incoming air jet. A more complete analysis would have to include the species conservation equations and a chemical heat release term in. the energy equation. In addition, some account would have to be taken of non-uniformities in temperature, composition and gas vdocity in the chamber, in order realistically to describe the mixing and
Results and Discmsioa Pressure as a jhnction of time Several traces of chamber pressure as a function of time are shown in Figure 3. A representative experimental curve of one cycle is shown in Figure 4, together with a theoretical curve according to equations 5 and 6. Values. of maximum pressure, fuel burning rate and wall heat transfer rate appearing in these equations were obtained from experimental measurements. Heat transfer rates to the walls oftbe combustion chamber were calculated approximately using thermocouple measurements of the inlet and outlet temperature of the cooling water. The
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Fmvm~ 3. Typical oscillo.,~'ope traces showing chamber pressure as a function of time for tbe 3-64 in. i.d. cylindricat chamber with ~ in. orifg'¢ diam=;~r and 8-5 in. chamber length. Vertical scale: 3.9 cm of mercury [ha:ssur¢ per major grid division. Horizontal scales: [a) O-tO see/major grid division. (b) lifO ms/major grid division, and t¢) 5~) ms/major grid division. Atmospheric pressure p. ~ Iatm
506
5 and 6 of the previous section. It appears therefore that pulsating-combustion frequency and pressure are governed by fluid mechanical and heat transfer processes and not by the momenIum effect involved in the Heimholtz.oscillalions.
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o
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14
16
18 +
Ftt+t;Rl~4. One cycleof dimensionlesspressure{p - P3/P~ as a functionof timet for the 3.64in. i,d.cylindricalchamber with orificediameter ~ = -~ in. and chamberlength h 8-5in,; fullline:experimentalcurve;brokenline:theoretical curve obtained from equations 5 and 6 using the experimental values~ = 575 cal/sec, the = 0.692 g/see, L = 263 cal/g, (p,,~,- p,) = 6.58 cm Hg, p, = 75"1 cm Hg, T, = 30ffK, ~/p, ", TiT "- ~, and }' = 1.4 assumptions of uniform conditions in the chamber and of zero chemical reactions, that were used in the theoretical derivation, probably account for the deviation of the theoretical curve from the experimental curve. The substantial agreement of theory with experiment indicates that heat transfer to the chamber walls and to the vaporizing fuel is the mechanism whereby the pressure in the chamber drops below the ambient pressure. The Heimholtz frequency for a chamber of volume V and a sharp edge orifice of diameter 6 is given9 by
f = (a/4)(3,~/SV)~ c/s
Freqm'n(')" of pres.~,re oscillations The mcasurentents of chamber pressure as a functio,~ of timc ~vcre used to obtain frequency as a function of chamber length and orifice diameter. Figure 5 shows frequency as a function of inverse chamber length for various orifice diameters. Figure 6 shows the same data replotted in the form of frequency as a function of orifice diameter for various chamber lengths. 80
70
5O
so
g 40
[8]
where a = (?RT) ½ is the speed of sound and T is the temperature of the gas in the neighbourhood of the throat. For a cylindrical chamber with a diameter equal to 3.64 in., a length equal to lif0 in,, and an orifice diameter ~ equal to 0,5 in. and for an estimated temperature T equal to 350°K, equation 9 yields f~- 153 c/s. it can easily be shown that experimental values of frequency are less than the corresponding
Helmholtz resonator frequency by a factor ranging from about three to six. This provides experimental justification for the assumption (o~/(o.) 2 ,( I that was used in deriving equations
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0.10 0.~2 0.i4 ¢""0.~6 ::"~: Inverse chamber ten§th, 1/h (in.) "1
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FmURE 5. Experimental values of pulsating-combustion frequencyJ'as a functionof the inversechamberlength I/ll for variousorificediameters6, in the 3.64in. i.d.cylindrical chamberwith methanolfuel:p~ ~- I atm Figure~3 shows an approximately linear increase in frequency with the inverse of the chamber length, for all values of orifice diameter. The dependence of frequency on orifice diameter, for fixed chamber length, is not so simple, as
December 1967
PULSATING('OMFIUSIION OF LIQUID FUEL tN PARTIALI.YCLOSEt) VESSELS
approximately proportional to 1/62. Consequently t'j¢ t ~ 1/62 and t= oc h62. It follows then that the period of a cycle may be written as hlc~i32 + c2~2~, and the frequencyj~ as f ~- [h(ct/~ z + c262)]-t [9]
70
60 u
5O
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40
Symbol •
30
507
,, o =
h,in. 6.5 70 80 9.0
2"o Orifice chameter b, (in.) x 32
FmunE 6. Experimental values of pulsating-combustion frequencyf as a function of orificediameter6 Ibr various chamber lengthsh; in the 3.64in. i.d, cylindricalchamber with methanolfuel;po -~ i arm can be seen from Figure 6. These results may be explained qualitatively by noting that the period of a cycle is approximately the sum of the blowdown time to (see equation 7 in which to is the time required for the pressure lo drop from its maximum value Pm,x. to ambient pressure po) and a mixing/ignition time t, (defined as the time after suction begins at which ignition and rapid combustion begin). According to equations 7 and 6a, to is approximately proportional to hi62, where h is the chamber length and 6 is the orifice diameter. Ba~d on the high-speed photographs (see section on high-speed schlieren photographs), t,, is approximately equal to the time required for the incoming air jet to reach the surface of the liquid fuel; hence t., is approximately proportional to h/vj,t, where vj=¢ is the maximum velocity of the incoming air jet. But the maximum jet velocity is proportional to the ~uare root of the maximum suction pressure, IPo - Pmi,.fL Front Figure 4 and equation 6. it can be seen that (Y2)~=, ~- (Y2h== = 1; therefore [Pa - Pmi,.t~ is
where cl and c2 are constants. Equation 9 shows that foc l/h, for constant 6 ; f ~ 62, for constant h if 6 is sufficiently small; andfu: I/62 for constant h if 6 is sufficiently large. These results are in qualitative agreement with the experimental results shown in Figures 5 and 6. Consequently the experimental result that frequency decreases with increasing chamber length h, for constant orifice diameter & can be explained qualitatively as an increase in mixing/ ignition time and blowdown time--ea~ of which is directly proportional to the chamber length. Likewise, the experimental result that, for constant chamber length, the frequency at first increases and then decreases with orifice diameter can be qualitatively explained as transition from a situation in which the blowdown time controls the frequency to one in which the mixing/ignition time controls the frequency.
Pressure amplitude The measurements of chamber pressure as a function of time were also used to obtain average, peak-to-peak, pressure amplitude as a function of chamber length and orifice diameter. These results ate shown in Figure 7. Each point represents an average taken over approximately fifty cycles. The results show that, for a given chamber length, the pressure amplitude increases monotonically with decreasing orifice diameter for those values of chamber length and orifice diameter for which pulsating combustion is possible, it should be noted that for all values of orifice diameter and chamber length, the pressure amplitude is less than or apwoximat~ equal to one-tenth of the ambient pressure. This provides experimental justification of the assumption that ](p - P.)]P.I ~ 1, which was in the analysis in the preceding section. I n ~ same analysis it was also assumed t h a t ( ~ 3 / ~ Figure 7, the ratio (6+/V)/l(p~m. - P.~/IP.[~ be shown to be less than 0-1 for orifice diameters
Vol. 11 the chamber, and m= is the mass of a column of air of diameter equal to one-third the chamber diameter and of length equal to the chamber length (based on high-speed photograpb~, that show ignition and combustion begm,'~ing very shortly after the air jet reaches the bottom of the chamber). Substituting T~ ~ 300°K, T,,~.,.-. 2100°K, and (mjm<)! - 1/3 into equation 10 yields
50~
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9 S#milol " & ,n.
8
n
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,
,,132
o z,,~2
"I-
~r~ d
I
"~ o\
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/Z'
~4 2
I(ro..,.- Tm,,.llr,.,,,. I-"
~2 I; 6
? 8 9 10 Chamber length h, in.
1t
12
FICUR~ 7. Average peak-to-peak pressure amplitude as a function of chamber length h for various orifice diameters & in the 3-64 in. i,d. cylindrical chamber with methanol fuel; p~ ~- I arm
less than or equal to 20/32 in. and to be approximately I/3 for ~ = 22/32 in. and approximately I/6 for ~ = 21/32 in. Consequently, the assumption that (6~/V)/i(pmx. - p)/p,[ ~ 1 hegins to break down for # ,~ 21/32 in. In view of the equation of state p ffi pRT and the !nequality i(P - P3/Poi '~ 1, the ass .umption_that I(P - P)/Pl ~ 1 is equivalent to I ( T - T)/TI 1. An upper limit for the quantity I(T - T)/T] may b¢ estimated easily by calculating I(Tm~. Tm~.)/T,i,. ], where Turn. is the maximum temperature of the combustion products and Trash. is the minimum temperature of the gases in the chamber (i.e. the temperature after the air jet and combustion products have mixed and immediately before combustion begins). We may write an approximate energy equation to descrihe the overall mixing of cold ambient air with hot combustion products, as
mJ',,,. +
m.~ =
[11]
Approximate geometrical limits for se!f-sustained pulsating combustioa
~3
5
0.1
(m, + m,,I l',,~..
[.lo]
where me is the mass of combustion products in
For the 3.64 in. diameter cylindrical combustion chamber, the chamber lengths h and orifice diameters ~ for which self-sustained pulsating combustion was the most regular were found to be 7-5 in. < h < 11-0 in. and ~ in. < / / < ~ in. The system was most stable for h " 9'0 in. and -21/32 in. The larger the deviation from these values, the more irregular was the combustion process. The irregularities take the form of noticeable pauses which, if persistent and frequent enough, extinguish combustion.
Fuel burning rate Experimental curves of methanol fuel burning rate as a function of chamber length for various orifice diameters are shown in Figure 8, for the 3.64 in. diameter cylindrical combustion chamber shown in Figure I. It can be sccn that the burning rates vary from about 12 g/min to 42 g/min for the values of orifice diameter and chamber length that allow self-sustained operation. These mass burning rates correspond to fuel surface regression rates of 2.3 mm/min and 8.1 mm/min, respectively. The maximum regression rate of 8-1 mm/min occurs for an orifice diameter ~ ~ 9/16 in. For the highest burning rate of 42 g/min, the combustion intensity can be shown to be approximately 1 x 106 Btu/ft3h. The dependence of burning rate on chamber length is not very strong within the limits of self-sustained operation. Blinov and Khudyakov ~ have reported surface regression rates of 0.9 nm.'.-~ia ~nd 1.2 mm/min for steady diffusion burning of methanol in open-top vertical, quartz tubes with diameters of 4.2 in. and 2-4 in., respectively.
December 1967
equal to one-fifth of the period of a cycle, the jet .virtually disappears. In the remaining part of the cycle, until suction begins, the chamber density is relatively uniform.
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40
509
PULSATING('OMBUSTION[)F LIQUIDFUEL IN PARTIALI.YCLOSEDVESSELS
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air jet
20/32
• 1
"lurbutent
16/3; 18/32
*
22/32 I
lO
'T1
in.
I
FmuR~ 8. Average methanol burning rate as a function of
chamb¢; length h for various orifice diameters 6, in the 3"64 in. i.d. cylindrical chamber. 1 g/rain ~ (>02 cm/min
. _ Vortex
reg=on
[b! •. -TurbuIer~t
These measurements were made with the fuel level kept flush with the top of the tube. When the fuel level was kept below the top of the tube, the burning rates were even smaller. Similar regression rate data have been given by Akita and Yumoto =°. Hence, for the same size burner, pulsating combustion yields burning rates that are from two to eight times larger than those for steady diffusion burning.
aFr jet
..... Uquid fuet
FIGURt:9. Schematic diagram showing (a) incoming air jet and shed vortex and (b) turbulent jet and vortex region below orifice as obtained from high-speed schlicren motion pictures
High-speed schlieren photographs The high-speed schlieren photographs show that as the pressure in the chamber drops below atmospheric pressure, a jet of air is drawn into the chamber. As the jet enters the chamber, a symmetrical vortex is shed below the orifice. The shed vortex seems to merge with and to re-enforce a more or less permanent vortex region located directly below the top of the chamber (see Figure 9). Immediately below the .orifice the jet is laminar; however, the main body of the jet is turbulent. Rapid combustion and discharge generally begin shortly after the jet reaches the liquid surface. Ignition occurs at isolated locations in the mixing region of the air jet. The combustion process reduces very rapidly the diameter of the jet; in a time approximately
Miscellaneous experiments In the miscellaneous qualitative experiments, it was found that the 3.64 in. diameter cylindrical combustion chamber would operate just as well with commercial grade kerosene or gasoline as with methanol. In another experiment, using the apparatus shown in Figure 2(b), it was found that the introduction of oxygen into the air stream caused a sharp decrease in frequency and amplitude of the pressure oscillations, and that only a very small percentage of pine oxygen caused cessation of pulsating combustion. Additional miscellaneous experiments have shown that pulsating combustion occurs for the following chamber and orifice configmtions: (0 a 3.64 in. diameter, vertical, cylindrical chamber
511,)
J . w . POR'II!R
with a ~ in. diameter hole in the side wall about one inch above the fuel level, in addition to the usual single orifice in the centre of the top end; however, the additional hole in the side reduced both frequency and amplitude of the pulsations; (ii) a vertical 3~ in. x 3~ in. x 10 in. chamber with a single rectangular orifice in the top end whose dimensions ranged from 0.75 in. x 0.75 in. to 0-25 in. x 1.25 in. and whose off-centre position could be varied by as much as one inch; (iii) the 3.64 in. diameter cylindrical chamber in a horizontal position with the usual single orifice centred in one end; and (iv) a 2.5 in. diameter, vertical cylindrical chamber with a range of orifice diameters and chamber lengths similar to those used for the 3.64 in. diameter chamber. The preceding results support the assumption made implicitly in the analysis that the pulsating-combustion process depends on chamber volume and orifice area and not on chamber Or orifice shape. Finally pulsating combustion could not be established in the 3,64 in. diameter, vertical, cylindrical chamber with seven 0.24 in. diameter holes in the top end arranged in a hexagonal duster whose total area was equal to that ofa singlel in. diameter orifice. Conclmiom it has been found that pulsating-combustion of methanol in partially dosed vessels yields burning rates that are as much as eight times larger than those for steady diffusion burning of methanol in open-top vessels of the same size. Combustion intensities as large as about 1 x 106 Btu/ft3h were measured. For fixed.diameter cylindrical v6~sels,self-sustained pulsating combustion was found to be possible only within
VOI. I I
certain limits of chamber length and orifice diameter. Within these limits, frequency and pressure amplitude could be varied from 25 to 70 c/s and 10 to 85 him of mercury, respectively. Outside these limits steady diffusion-flame combustion generally occurs. The measured values of oscillation frequency were always smaller than the Helmholtz resonator frequency by at least a factor of three. These studies were supported by the National Science Foundation under (;rant GK-22L (Received Jmze 1967; revised August 1967) References I SCllULIZ-GRUNOW, F. N.A.CA, Te('h. Memo. No. 1131 (1947) ' BERLIN.,J. AGJRD Sel,'cted (~nnhlistion Probh'm.~. p 490, Eds. W, R. HAWltlORn~: and J. FAnRI. Buuerworths: London (1954) 3 Dt'('ARME, J. Combu.srion Rv.wurche.sand Reriews. p ! 12. AGARDograph No. 13, Eds. b. P. Mt!LIa.'qSand J, FARRt. Buttcrworths: London (195"7) GELLI'R. L. B., L,!F, G. K, and MII('HI!I£, E. R, ASHRAE Journal, 6, 41 {1964b s Fga,,,;cls, W. E., H(gi(iAglu, M. L, ahd R~AY, D. "A stud.',' c,f gas-fired pulsating combusldvs for. industrial applications'. Gas Council Res. ('ommm~. 3'd. GC 91 (Midlands Research Station): London (1%2} t, REYN~;T' F. H. Pul.~aling ('ombustion. The Colh'cted Work:; ¢!/'F, H. R,.ynst. Ed. M, W, TIIRISG. Pergamon: New York (t951) ~ BLINOY,V. I..'|nd KllUI}YAKOY,G. N. Dif]it.~ion Burning of Liquid~'. p 96, Izdatel'stro Akad, Nauk S.S,S,R.: Moscow (1961) s BICKI.I!, L. W. M. S. l'he.~i.s. Univer~,ity of Texas at Au,,lin ! 1%7~ '~R~AIIIGIt. I ~
~ IfJ, II.'ml ,'t % . . , i , Vt,1. II. pp 174 182. l)otcr Pubhcat,on?,: N~'~ ~~ork (t~)45) to AKIIA, K. anti '¥trMl]|(}, "[, l'4'll]lh ,~VlllposhlOI (lnl~'r. nalional) on Combu,~zion, p 943, 1"he Cornbusllon Insli. lute: Pittsburgh (1965)
Introduction Tu~ phenomenon of pulsating combustion is not new, and a considerable amount ofliterature exists on the subject. Much of the literature is concerned with various forms of the pulse-jet engine t- a; however, characteristics of pulsatingcombustion chambers, such as very high combustion intensity (i.e. high rate of heat release per unit volume), very high heat transfer rate to the walls of the combustion chamber, and nearstoichiometric combustion have stimulated the use of pulsating combustion for heating purposes in industrial furnaces and small space heaters4.s. One of the most interesting types of pulsating combustion occurs in the burning of liquid fuels in partially closed vessels. The process is characterized by low frequency (less than about 100 c/s), small amplitude, self-sustained pressure oscillations. The Simplest kind of combustion chamber that allows this type of pulsating combustion consists of a vertical, circular cylinder that is partially filled with a liquid fuel and completely closed except for a single, valveless, sharp-edge orifice at the top. The operation of this combustion chamber can be described by outlining the sequence of events that occurs
during a typical cycle" vaporized fuel and air burn rapidly in the chamber, increasing the pressure; combustion products flow out of the chamber through the orifice; the pressure in the chamber returns to and drops below the external ambient pressure; external air is drawn into the chamber where it mixes with vaporized fuel and hot combustion products; self-ignition occur~ and the cycle repeats itself. Hence during each cycle there is an alternat inflow of air and outflow of combustion products through the single orifice in the chamber. This phenomenon was discovered about 1933 by F. H. Reynst. In a recent collection of his works, several explanations of the mechanism of operation, ate offered; however, no theoretical or experingntal evidence is presented. Two basically different modes of combustion are possible for a liquid fuel in a vessel that is closed except for a single orifice: constant pressurediffusion bundng and pulsating combustionS:.: Diffusion burning is characterized by ~ t : pressure, relatively gentle, laminar or t ~ t diffusion flames, Pulsating coml~as~ isehar-' acterized by relatively vigorous, ~ ~:: sure and flow oscillations. The orifice ~ : i ! relation to the vessel size and the furl kvcl, i 501
502
J.w.
determines which mode will occur. Diffusion burning of liquid fuels in open-top cylindrica! vessels has been thoroughly studied by Blinov and Khudyakov 7. However, there has been no similar investigation of pulsating burning of liquid fuels in partially closed vessels. The objectives of this investigation are to determine the dependence of frequency, pressure amplitude, and fuel burning rate on chamber geometry, and to determine the mechanism of operation of pulsating combustion in partially dosed vessels. Measurements of pressure as a function of time will be compared with a theory based on an assumed mechanism of operation. The burning rate for pulsating combustion in partially closed vessels will be compared with the data obtained by Blinov and Khudyakov "t for steady diffusion burning in open-top vessels. Experimental The experimental measurements fall into tt_:ree categories: (1) measurements of chamber pressure and fuel burning rate in a 3.64 in. inside diameter, vertical, cylindrical chamber; (2) highspeed schlieren motion pictures of the pulsatingcombustion process; and (3) miscellaneous experiments. The measurements of chamber pressure as a function of time are used to obtain frequency and peak-to-peak pressure amplitude as functions of chamber length and orifice diameter; in addition, they are also used to determine approximate limits on chamber length and on orifice diameter within which selfsustained operation is possible. The high-speed schlieren motion pictures provide qualitative information about flow patterns, mixing and ignition. Technical grade methanol was used in all experiments, except in some of the miscellaneous experiments. The ambient pressure (external to the orifice) was always approximately one atmosphere. Figure 1 shows a schematic diagram of the apparatus used for measuring chamber pressure and fuel burning rate. The combustion chamber (1) is a water-cooled, 3.64 in. i.d. cylindrical, iron pipe that is do .s,~_at the top by a plate with a sharp-edge circular orifice (2)and dosed at the bottom by a piston (3). The piston allows the length of the chamber to be varied from about 5 to 12 in. The system was prepared for an
Vol. 1 I
poR lt!k
experiment by adding liquid fuel (4) to a depth of one inch and covering the orifice loosely to allow equilibrium to be established at ambient pressure. The flowrate and inlet temperature of the cooling water were kept at 60 g/see and 3¢'C, respectively. Ignition was accomplished by a spark-plug ignition system (5)---the spark discharge being terminated immediately after the initial explosion. After about 30 ,seconds of self-sustained operation, chamber pressure as a function of time was measured with a straingauge pressure transducer (6) and was recorded using an oscilloscope (7) equipped with a Polaroid camera. The duration of the pressure trace was never more than about one second {corresponding to about 50 combustion cycles).
./ :
(2) /,
/
:(I) /,(6)
......"'~ //
:,.-
./'/
(S)/
. 7 i.(1
:/
:i U\
'"~'~-(4)
\\
\
(3) • FIGUaE 1, Schematic diagram of the apparatus us~ for measuring pressure and burning rate:O) 3.64 in, i.d. cylindrical combustion chamber, (2) orifice plate, (3) piston, (4) liquid fuel, (5) spark plug, (6) strain-gauge pressure transducer, and (7) oscilloscope
The procedure was repeated with fresh fuel, for various chamber lengths and orifice diameters. In a similar series of experiments, average burning rates of methanol were measured for various chamber lengths and orifice diameters. Each experiment consisted of measuring the fuel level before and after a timed period of operation. Fuel level was measured with a micrometer depth gauge, and time intervals were measured with an electric stopciock. Typically, the time
December 1967
PULSATING ('OMilUSTIONOF LIQUIDFUEL IN PARTIALLYCLOSED VESSELS
interval was about one and one-half minutes, and the change in fuel level was about 0.5 in. Figure 2(a) shows a schematic diagram of the special combustion chamber that was used to obtain high-speed schlieren motion pictures of the pulsating combustion process 8. The chamber consists of a metal frame with Pyrex glass walls. The top of the chamber is composed of four, overlapping, metal plates that can be individually adjusted by screw mechanisms (not shown) to
503 condensed water on the glass walls evaporated (about 15 see), at which time, high-speed photographs were made using a 16 mm Wollensak Fastax camera (5) with Kodax TXR 430 fi~. The maximum framing rate in each run was about 5000 frames per second. The miscellaneous experiments included experiments to determine if eperation with fuels other than methano! (such as kerosene and gasoline) is possible. Also included was an
lop view
~
Exhaust duct Manifold
-%
'"'~"Adjustable orifice plates Orifice Pyrex glass walls
~ir/O~yge~ m~xture
Metat frame I iquid fuel Liquid fuel. "--""-"-
Side view
(a}
U (b}
FI(iURI~ 2. Schematic diagram of special pulsating-combustion chambers for {a) obtaining high-speed schlieren photographs of the pulsating combustion process, and (b) varying the oxygen concentration of the ambient air
form a rectangular orifice of any size up to 3 in. x 3 in. The inside cross section of the chamber is 3~- in. x 3~ in. and the height of the empty chamber is 12~ in. The inside length of the chamber during operation is determined by the fuel level. In each run, the length of the chamber was set at 5.5 in. so that the field of view included most of the chamber and half an inch above the orifice. The orifice plates were adjusted to form a 0.43 in. x 1.0 in. rectangular orifice (with the long side parallel to the schlieren light) in an attempt to make the process as nearly two-dimensional as possible. Combustion was initiated by an open flame at the orifice. The system was allowed to run until
experiment to determine the effect on pulsating combustion of varying the oxygen concentration of the ambient air. Figure 2 (b) shows the apparatus that was used to increase the oxygen concentration gradually in the air stream during pulsating combustion. Finally, experiments were conducted to determine the effects of orifice shape and location, multiple orifices, and chamber diameter and shape. Theoretical Considerations A typical combustion cycle consists of the following sequence of events. Explosion in the chamber is accompanied by a rise in pressure above atmospheric pressure. Next follows a
Vol. I I J.w. I'OR'n!R is some constant average density in the relatively long period of pressure decay in which the pressure drops from a maximum value chamber, At = A(2p/p,,)~ and Az ~ A(2)~ are above atmospheric pressure to a minimum value modified orifice areas for discharge and suction, respectively, and A is the actual orifice area. below atmospheric pressure. During the time that the pressure is below atmospheric pressure, The assumptions involved in neglecting the non-steady acceleration term may be determined ambient air is sucked into the chamber where it by considering the complete non-steady momenmixes with hot vaporized fuel and combustion products. The suction period is terminated by tum equation. Assuming small departures of chamber pressure and density from the unignition and explosion, and the cycle repeats disturbed values Pa and p~, respectively, the itself. The analysis in this section is concerned momentum equation may be integrated across with determining the chamber pressure as a a sharp-edge orifice of diameter ($to yield function of time during the pressure-decay part of the cycle in order to determine the mechanism ) 2 = (p - Pa) + (t/ton)2dZp/dt2 [4] t,,u,. whereby the chamber ~ressure drops below where u,. is the gas velocity at the orifice, atmospheric pressure. Heat transfer to chamber walls and heat of vaporization of the liquid fuel on = aa[{3nz/32)(5/V)] ~ is the classical Helmhoitz resonator frequency, and ao = (TpJp,) t is are included in the analysis. Chemical reaction rates are assumed to be negligible in this part of the speed of sound. In deriving equation 4 the effective mass that experiences acceleration in the cycle. Assuming that conditions are uniform the vicinity of the orifice has been replaced° by throughout the chamber and that the gases are (32/3nzl(poA2/& Use has also been made of perfect, the equations of conservation of mass the equation u,, = - (V/~,'p~A)(dp/dt) obtained and energy for the gases in the chamber, during by combining equations 1 and 2 with )he = the: pressure-decay period, become (~ = 0. Finally, for simplicity the average chamdo/dr := (~)/- fit,)/V [1] ber density has been replaced by p~. The last term in equation 4 represents the acceleration and of gas through the orifice. Writing (p - p~) .7: dr/dr - ('ip/p)(dp/dt) = exp(icot), the ratio of the acceleration term to the -(~ - l)(~d. + (2)iv [2] pressure difference term in equation 4 may be written as (~o/ou)2, where (o is the oscillation respectively, where p and p are the pressure and frequency. The ratio of the kinetic energy term density, respectively, of the chamber gases; t p~u~ to the pressure difference term { p - p~) denotes time i ~ is the fuel vaporization rate; may be written as (3/28) (V/63)l(pm..,~ - pA~p,.] ~,, is the mass flow rate of gases through the (cO/On)z. From these results it can be seen that orifice; V is chamber volume; L represents equation 4 can be reduced to the Helmholtz the heat ofvaporization of the liquid fuel: Q is the oscillation equation 9 if(to/(on)z is of order unity total rate of heat loss through the chamber or less and if 10'm.~.,.- P~)/P,I/('9/V) ~ 1. On walls; and 7 -- cjc~ is the ratio of specific heats the other hand if (t'J/cOn)z ,~ 1 and if (63/V)/ of chamber gases. Assuming I{P - P3/Pot < 1, I(Pm,. - P,)/P~I ~ 1, equation 4 can be reduced I(P - P)/Pl '~ 1, and neglecting the non-steady to the familiar steady-state Bernoulli equation. acceleration term in the momentum equation, Consequently, equation 3, which is based on it can be shown that the mass flowrate through the steady-state Bernoulli equation, involves the orifice is the assumptions that {~o/(~n)a < 1 and (63/V)/ IlPm,.~.- P,,)/P*I '~ 1. Experimental justification f,l, [p.0' p,)1~, for these assumptions and the assumptions that for disehargc (p > po) [{p - p~)/p~[ ~ i and ](p - P)/I~[ <~ 1 are prem' "- i.'ta [p,,0'. p)]~, [31 sented in the next section. Letting p - p,,.,~, at time t - 0 (correspond[. for suction {p < p.) ing to the beginning of pressure decay), and assuming that the fuel vaporization rate ~hyand where the subscript a refers to the ambient air, 504
-
-
December 1967
Pt:LSAT~<~CO~mVSUONOVUOtStD~:UEL~ P~a'n~tL'~ CLOSEDVESSELS
the wall heat transfer rate Q are constant,
equations 1, 2 and 3 may be combined and integrated to yield (Y, ..... - y , ) - iog[(i + y, . . . . . )/(| q- Yl)] = ~, for 0 ~< t ~< to [5]
505
combustion processes. Finally, two additional equations would be needed to relate the fuel vaporization rate m/and the rate of heat loss (~ to conditions in the chamber. However, in view of the limited objective stated at the beginning of this section, no attempt is made here to develop a more complete theory.
and Iog[t/(I - y,.i] - y., : i_,. for to ~< t ~ r
[-6]
whele "
I;' ~ l lip,, ;'l,,)lliifL + 0.1 - ~h
- p,,I/po] l,.~ - 17i.-I~._,i" l',, 'l It=- lllpJ)'p<,)
x i,i, sL
+
[-6a]
Oi- , s]it
and Yi....... is the value of Yi when p is equal to i~,,,,~. The time to tat which transition from discharge to suction occurs) may be obtained by setting .l't = 0 in equation 5 to yield {[!)o = .'Fl..... --Iog(l
+ Yl,max)
[7]
The time z represents the time at which rapid combustion begins and the suction period ends, i.e. it represents the end of the pressure-decay part of the cycle. In this analysis suction is obtained solely by the continued cooling of the gases after the chamber pressure has dropped to atmospheric pressure. Acceleration of the gases through the orifice and the associated effect on chamber pressure has been neglected for the reasons discussed in the text following equation 3, Neither ~ nor Pmax. is predicted by this analysis, because chemical reactions have not been included. The time z - to is the time during which the chamber pressure is less than ambient pressure; it may be regarded as a mixing/ignition time that depends on mixing and chemical reaction rates between vaporized fuel and the incoming air jet. A more complete analysis would have to include the species conservation equations and a chemical heat release term in. the energy equation. In addition, some account would have to be taken of non-uniformities in temperature, composition and gas vdocity in the chamber, in order realistically to describe the mixing and
Results and Discmsioa Pressure as a jhnction of time Several traces of chamber pressure as a function of time are shown in Figure 3. A representative experimental curve of one cycle is shown in Figure 4, together with a theoretical curve according to equations 5 and 6. Values. of maximum pressure, fuel burning rate and wall heat transfer rate appearing in these equations were obtained from experimental measurements. Heat transfer rates to the walls oftbe combustion chamber were calculated approximately using thermocouple measurements of the inlet and outlet temperature of the cooling water. The
7.- .... :-7-~7 - - r - i
~'!
tai ; ..........
f--t
~+-.--z--
:&l
..
,
-.+ - - + .
-- ~.---,---4
~g:
!
~. i
,
! ! (ci
i
!
I
Fmvm~ 3. Typical oscillo.,~'ope traces showing chamber pressure as a function of time for tbe 3-64 in. i.d. cylindricat chamber with ~ in. orifg'¢ diam=;~r and 8-5 in. chamber length. Vertical scale: 3.9 cm of mercury [ha:ssur¢ per major grid division. Horizontal scales: [a) O-tO see/major grid division. (b) lifO ms/major grid division, and t¢) 5~) ms/major grid division. Atmospheric pressure p. ~ Iatm
506
5 and 6 of the previous section. It appears therefore that pulsating-combustion frequency and pressure are governed by fluid mechanical and heat transfer processes and not by the momenIum effect involved in the Heimholtz.oscillalions.
o,lo 6. Q; o.oB o.o~
0,02 ,_o
Vol. i l
). W. PORIIiR
0
E -0-02 Q
o
4
6
B 10 12 Time, t, ms
14
16
18 +
Ftt+t;Rl~4. One cycleof dimensionlesspressure{p - P3/P~ as a functionof timet for the 3.64in. i,d.cylindricalchamber with orificediameter ~ = -~ in. and chamberlength h 8-5in,; fullline:experimentalcurve;brokenline:theoretical curve obtained from equations 5 and 6 using the experimental values~ = 575 cal/sec, the = 0.692 g/see, L = 263 cal/g, (p,,~,- p,) = 6.58 cm Hg, p, = 75"1 cm Hg, T, = 30ffK, ~/p, ", TiT "- ~, and }' = 1.4 assumptions of uniform conditions in the chamber and of zero chemical reactions, that were used in the theoretical derivation, probably account for the deviation of the theoretical curve from the experimental curve. The substantial agreement of theory with experiment indicates that heat transfer to the chamber walls and to the vaporizing fuel is the mechanism whereby the pressure in the chamber drops below the ambient pressure. The Heimholtz frequency for a chamber of volume V and a sharp edge orifice of diameter 6 is given9 by
f = (a/4)(3,~/SV)~ c/s
Freqm'n(')" of pres.~,re oscillations The mcasurentents of chamber pressure as a functio,~ of timc ~vcre used to obtain frequency as a function of chamber length and orifice diameter. Figure 5 shows frequency as a function of inverse chamber length for various orifice diameters. Figure 6 shows the same data replotted in the form of frequency as a function of orifice diameter for various chamber lengths. 80
70
5O
so
g 40
[8]
where a = (?RT) ½ is the speed of sound and T is the temperature of the gas in the neighbourhood of the throat. For a cylindrical chamber with a diameter equal to 3.64 in., a length equal to lif0 in,, and an orifice diameter ~ equal to 0,5 in. and for an estimated temperature T equal to 350°K, equation 9 yields f~- 153 c/s. it can easily be shown that experimental values of frequency are less than the corresponding
Helmholtz resonator frequency by a factor ranging from about three to six. This provides experimental justification for the assumption (o~/(o.) 2 ,( I that was used in deriving equations
L~
c
2~L
O-08
~?:32
0.10 0.~2 0.i4 ¢""0.~6 ::"~: Inverse chamber ten§th, 1/h (in.) "1
O.1O
FmURE 5. Experimental values of pulsating-combustion frequencyJ'as a functionof the inversechamberlength I/ll for variousorificediameters6, in the 3.64in. i.d.cylindrical chamberwith methanolfuel:p~ ~- I atm Figure~3 shows an approximately linear increase in frequency with the inverse of the chamber length, for all values of orifice diameter. The dependence of frequency on orifice diameter, for fixed chamber length, is not so simple, as
December 1967
PULSATING('OMFIUSIION OF LIQUID FUEL tN PARTIALI.YCLOSEt) VESSELS
approximately proportional to 1/62. Consequently t'j¢ t ~ 1/62 and t= oc h62. It follows then that the period of a cycle may be written as hlc~i32 + c2~2~, and the frequencyj~ as f ~- [h(ct/~ z + c262)]-t [9]
70
60 u
5O
U-
40
Symbol •
30
507
,, o =
h,in. 6.5 70 80 9.0
2"o Orifice chameter b, (in.) x 32
FmunE 6. Experimental values of pulsating-combustion frequencyf as a function of orificediameter6 Ibr various chamber lengthsh; in the 3.64in. i.d, cylindricalchamber with methanolfuel;po -~ i arm can be seen from Figure 6. These results may be explained qualitatively by noting that the period of a cycle is approximately the sum of the blowdown time to (see equation 7 in which to is the time required for the pressure lo drop from its maximum value Pm,x. to ambient pressure po) and a mixing/ignition time t, (defined as the time after suction begins at which ignition and rapid combustion begin). According to equations 7 and 6a, to is approximately proportional to hi62, where h is the chamber length and 6 is the orifice diameter. Ba~d on the high-speed photographs (see section on high-speed schlieren photographs), t,, is approximately equal to the time required for the incoming air jet to reach the surface of the liquid fuel; hence t., is approximately proportional to h/vj,t, where vj=¢ is the maximum velocity of the incoming air jet. But the maximum jet velocity is proportional to the ~uare root of the maximum suction pressure, IPo - Pmi,.fL Front Figure 4 and equation 6. it can be seen that (Y2)~=, ~- (Y2h== = 1; therefore [Pa - Pmi,.t~ is
where cl and c2 are constants. Equation 9 shows that foc l/h, for constant 6 ; f ~ 62, for constant h if 6 is sufficiently small; andfu: I/62 for constant h if 6 is sufficiently large. These results are in qualitative agreement with the experimental results shown in Figures 5 and 6. Consequently the experimental result that frequency decreases with increasing chamber length h, for constant orifice diameter & can be explained qualitatively as an increase in mixing/ ignition time and blowdown time--ea~ of which is directly proportional to the chamber length. Likewise, the experimental result that, for constant chamber length, the frequency at first increases and then decreases with orifice diameter can be qualitatively explained as transition from a situation in which the blowdown time controls the frequency to one in which the mixing/ignition time controls the frequency.
Pressure amplitude The measurements of chamber pressure as a function of time were also used to obtain average, peak-to-peak, pressure amplitude as a function of chamber length and orifice diameter. These results ate shown in Figure 7. Each point represents an average taken over approximately fifty cycles. The results show that, for a given chamber length, the pressure amplitude increases monotonically with decreasing orifice diameter for those values of chamber length and orifice diameter for which pulsating combustion is possible, it should be noted that for all values of orifice diameter and chamber length, the pressure amplitude is less than or apwoximat~ equal to one-tenth of the ambient pressure. This provides experimental justification of the assumption that ](p - P.)]P.I ~ 1, which was in the analysis in the preceding section. I n ~ same analysis it was also assumed t h a t ( ~ 3 / ~ Figure 7, the ratio (6+/V)/l(p~m. - P.~/IP.[~ be shown to be less than 0-1 for orifice diameters
Vol. 11 the chamber, and m= is the mass of a column of air of diameter equal to one-third the chamber diameter and of length equal to the chamber length (based on high-speed photograpb~, that show ignition and combustion begm,'~ing very shortly after the air jet reaches the bottom of the chamber). Substituting T~ ~ 300°K, T,,~.,.-. 2100°K, and (mjm<)! - 1/3 into equation 10 yields
50~
J . W. P I I R I I ! R
9 S#milol " & ,n.
8
n
"~E132
,
,,132
o z,,~2
"I-
~r~ d
I
"~ o\
E7 ~6
/Z'
~4 2
I(ro..,.- Tm,,.llr,.,,,. I-"
~2 I; 6
? 8 9 10 Chamber length h, in.
1t
12
FICUR~ 7. Average peak-to-peak pressure amplitude as a function of chamber length h for various orifice diameters & in the 3-64 in. i,d. cylindrical chamber with methanol fuel; p~ ~- I arm
less than or equal to 20/32 in. and to be approximately I/3 for ~ = 22/32 in. and approximately I/6 for ~ = 21/32 in. Consequently, the assumption that (6~/V)/i(pmx. - p)/p,[ ~ 1 hegins to break down for # ,~ 21/32 in. In view of the equation of state p ffi pRT and the !nequality i(P - P3/Poi '~ 1, the ass .umption_that I(P - P)/Pl ~ 1 is equivalent to I ( T - T)/TI 1. An upper limit for the quantity I(T - T)/T] may b¢ estimated easily by calculating I(Tm~. Tm~.)/T,i,. ], where Turn. is the maximum temperature of the combustion products and Trash. is the minimum temperature of the gases in the chamber (i.e. the temperature after the air jet and combustion products have mixed and immediately before combustion begins). We may write an approximate energy equation to descrihe the overall mixing of cold ambient air with hot combustion products, as
mJ',,,. +
m.~ =
[11]
Approximate geometrical limits for se!f-sustained pulsating combustioa
~3
5
0.1
(m, + m,,I l',,~..
[.lo]
where me is the mass of combustion products in
For the 3.64 in. diameter cylindrical combustion chamber, the chamber lengths h and orifice diameters ~ for which self-sustained pulsating combustion was the most regular were found to be 7-5 in. < h < 11-0 in. and ~ in. < / / < ~ in. The system was most stable for h " 9'0 in. and -21/32 in. The larger the deviation from these values, the more irregular was the combustion process. The irregularities take the form of noticeable pauses which, if persistent and frequent enough, extinguish combustion.
Fuel burning rate Experimental curves of methanol fuel burning rate as a function of chamber length for various orifice diameters are shown in Figure 8, for the 3.64 in. diameter cylindrical combustion chamber shown in Figure I. It can be sccn that the burning rates vary from about 12 g/min to 42 g/min for the values of orifice diameter and chamber length that allow self-sustained operation. These mass burning rates correspond to fuel surface regression rates of 2.3 mm/min and 8.1 mm/min, respectively. The maximum regression rate of 8-1 mm/min occurs for an orifice diameter ~ ~ 9/16 in. For the highest burning rate of 42 g/min, the combustion intensity can be shown to be approximately 1 x 106 Btu/ft3h. The dependence of burning rate on chamber length is not very strong within the limits of self-sustained operation. Blinov and Khudyakov ~ have reported surface regression rates of 0.9 nm.'.-~ia ~nd 1.2 mm/min for steady diffusion burning of methanol in open-top vertical, quartz tubes with diameters of 4.2 in. and 2-4 in., respectively.
December 1967
equal to one-fifth of the period of a cycle, the jet .virtually disappears. In the remaining part of the cycle, until suction begins, the chamber density is relatively uniform.
:--.,
t"
Y:
40
509
PULSATING('OMBUSTION[)F LIQUIDFUEL IN PARTIALI.YCLOSEDVESSELS
50
~
~ 3o O~ C
cL 20 D n
..Onhce
~ ....
i ""-Shed vortex .,
Symbol, -
u~ "tO
d', ir =.
o 7
I
8 Chamber
~, 9 l e n g t h , h,
air jet
20/32
• 1
"lurbutent
16/3; 18/32
*
22/32 I
lO
'T1
in.
I
FmuR~ 8. Average methanol burning rate as a function of
chamb¢; length h for various orifice diameters 6, in the 3"64 in. i.d. cylindrical chamber. 1 g/rain ~ (>02 cm/min
. _ Vortex
reg=on
[b! •. -TurbuIer~t
These measurements were made with the fuel level kept flush with the top of the tube. When the fuel level was kept below the top of the tube, the burning rates were even smaller. Similar regression rate data have been given by Akita and Yumoto =°. Hence, for the same size burner, pulsating combustion yields burning rates that are from two to eight times larger than those for steady diffusion burning.
aFr jet
..... Uquid fuet
FIGURt:9. Schematic diagram showing (a) incoming air jet and shed vortex and (b) turbulent jet and vortex region below orifice as obtained from high-speed schlicren motion pictures
High-speed schlieren photographs The high-speed schlieren photographs show that as the pressure in the chamber drops below atmospheric pressure, a jet of air is drawn into the chamber. As the jet enters the chamber, a symmetrical vortex is shed below the orifice. The shed vortex seems to merge with and to re-enforce a more or less permanent vortex region located directly below the top of the chamber (see Figure 9). Immediately below the .orifice the jet is laminar; however, the main body of the jet is turbulent. Rapid combustion and discharge generally begin shortly after the jet reaches the liquid surface. Ignition occurs at isolated locations in the mixing region of the air jet. The combustion process reduces very rapidly the diameter of the jet; in a time approximately
Miscellaneous experiments In the miscellaneous qualitative experiments, it was found that the 3.64 in. diameter cylindrical combustion chamber would operate just as well with commercial grade kerosene or gasoline as with methanol. In another experiment, using the apparatus shown in Figure 2(b), it was found that the introduction of oxygen into the air stream caused a sharp decrease in frequency and amplitude of the pressure oscillations, and that only a very small percentage of pine oxygen caused cessation of pulsating combustion. Additional miscellaneous experiments have shown that pulsating combustion occurs for the following chamber and orifice configmtions: (0 a 3.64 in. diameter, vertical, cylindrical chamber
511,)
J . w . POR'II!R
with a ~ in. diameter hole in the side wall about one inch above the fuel level, in addition to the usual single orifice in the centre of the top end; however, the additional hole in the side reduced both frequency and amplitude of the pulsations; (ii) a vertical 3~ in. x 3~ in. x 10 in. chamber with a single rectangular orifice in the top end whose dimensions ranged from 0.75 in. x 0.75 in. to 0-25 in. x 1.25 in. and whose off-centre position could be varied by as much as one inch; (iii) the 3.64 in. diameter cylindrical chamber in a horizontal position with the usual single orifice centred in one end; and (iv) a 2.5 in. diameter, vertical cylindrical chamber with a range of orifice diameters and chamber lengths similar to those used for the 3.64 in. diameter chamber. The preceding results support the assumption made implicitly in the analysis that the pulsating-combustion process depends on chamber volume and orifice area and not on chamber Or orifice shape. Finally pulsating combustion could not be established in the 3,64 in. diameter, vertical, cylindrical chamber with seven 0.24 in. diameter holes in the top end arranged in a hexagonal duster whose total area was equal to that ofa singlel in. diameter orifice. Conclmiom it has been found that pulsating-combustion of methanol in partially dosed vessels yields burning rates that are as much as eight times larger than those for steady diffusion burning of methanol in open-top vessels of the same size. Combustion intensities as large as about 1 x 106 Btu/ft3h were measured. For fixed.diameter cylindrical v6~sels,self-sustained pulsating combustion was found to be possible only within
VOI. I I
certain limits of chamber length and orifice diameter. Within these limits, frequency and pressure amplitude could be varied from 25 to 70 c/s and 10 to 85 him of mercury, respectively. Outside these limits steady diffusion-flame combustion generally occurs. The measured values of oscillation frequency were always smaller than the Helmholtz resonator frequency by at least a factor of three. These studies were supported by the National Science Foundation under (;rant GK-22L (Received Jmze 1967; revised August 1967) References I SCllULIZ-GRUNOW, F. N.A.CA, Te('h. Memo. No. 1131 (1947) ' BERLIN.,J. AGJRD Sel,'cted (~nnhlistion Probh'm.~. p 490, Eds. W, R. HAWltlORn~: and J. FAnRI. Buuerworths: London (1954) 3 Dt'('ARME, J. Combu.srion Rv.wurche.sand Reriews. p ! 12. AGARDograph No. 13, Eds. b. P. Mt!LIa.'qSand J, FARRt. Buttcrworths: London (195"7) GELLI'R. L. B., L,!F, G. K, and MII('HI!I£, E. R, ASHRAE Journal, 6, 41 {1964b s Fga,,,;cls, W. E., H(gi(iAglu, M. L, ahd R~AY, D. "A stud.',' c,f gas-fired pulsating combusldvs for. industrial applications'. Gas Council Res. ('ommm~. 3'd. GC 91 (Midlands Research Station): London (1%2} t, REYN~;T' F. H. Pul.~aling ('ombustion. The Colh'cted Work:; ¢!/'F, H. R,.ynst. Ed. M, W, TIIRISG. Pergamon: New York (t951) ~ BLINOY,V. I..'|nd KllUI}YAKOY,G. N. Dif]it.~ion Burning of Liquid~'. p 96, Izdatel'stro Akad, Nauk S.S,S,R.: Moscow (1961) s BICKI.I!, L. W. M. S. l'he.~i.s. Univer~,ity of Texas at Au,,lin ! 1%7~ '~R~AIIIGIt. I ~
~ IfJ, II.'ml ,'t % . . , i , Vt,1. II. pp 174 182. l)otcr Pubhcat,on?,: N~'~ ~~ork (t~)45) to AKIIA, K. anti '¥trMl]|(}, "[, l'4'll]lh ,~VlllposhlOI (lnl~'r. nalional) on Combu,~zion, p 943, 1"he Cornbusllon Insli. lute: Pittsburgh (1965)