AN EXPERIMENT AL INVESTIGATION OF SPHERICAL COMBUSTION FOR THE UTIAS IMPLOSION DRIVEN LA UNCHER
by Andr~ Benoit
t
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AN EXPERlMENTAL lNVESTlGATlON OF SPHERlCAL COMBUSTlON FOR THE UTlA IMPLOSION DRlVEN LAUNCHER
by Andr~ Benoit
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ACKNOWLEDGEMENT
I wish to express my thanks to Dr. G. N. Patterson for the opportunity to conduct this work at the Institute of Aerophysics.
I shouid like to express my gratitude to Dr. 1. 1. Glass who sug-gested this research His enthusiastic guidance, continuous interest aner numerous discussions are greatly appreciated.
Thanks are due to Dr. G. F. Wright, Department of Chemistry, for his assistance on the use of explosives andtoDr. A".R. Makomaski for
his critical reading of the manuscript.
It is with pleasure that I acknowledge the friendly help re-ceived from Mr. J. J. L. Brennan and Mr. W. Seidel in conducting the ex-periments .
I am indebted to the "Comité BeIge de Sélection des Bourses de Recherche Scientifique O. T .A. N.11 for a research fellowship.
The technical and financial support received from the
Canadian Armament Research and Development Establishment through DDP Contract No. 69-912180, and the financial assistance received from the Aeronautical Research Laboratories under Contract No. AF-33(657)-7874 are acknowledged with thanks .
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SUMMARY
An experimental investigation of the combustion processes oc.currin-,in the UTIA implosion chriven hypervelocity launcher combustion
chamber has been conducted in stoichiometric mixtures of hydrogen-oxygen diluted with an excess of hydrogen or helium.
The mixtures were ignited using a spark gap or an exploding wire at the geometric center of the hemispherical vessel and piezo-pressure gauge histories were recorded for various dilutions and initial pressures ranging from 75 to 1000 psi. Heat transfer and ionization gauges were used to measure average combustion wave speeds and to investigate the wave symmetry.
Calculatipns of the final conditions after complete combus-tion (constant volume combuscombus-tion assuming no dissipative effects) have been done taking dissociations into a'ccount. The derived pressures have been compared with those obtained experimentally .
1. . 2. 3. 4. 5.
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TABLE OF CONTENTS NOTATION INTRODUCTIONTHERMODYNAMIC PROPERTJES OF INITIAL MIXTURES THERMODYNAMIC PROPERTJES AFTER COMPLETE COMBUSTION
COMBUSTION WAVES
3. 1 Spherical Deflagrations 3.2 Spherical Detonations
DESCRIPTION OF THE EXPERIMENTAL EQUIPMENT. APPARATUS AND PROCEDURE
4. 1 Combustion Chamber and Loading System 4. 2 Loading Procedure
4. 3 Ignition System 4.4 Instrumentation
RESULTS AND DISCUSSION
5. 1 Initial Conditions Leading to Deflagrating or to Detonating" Combustions
5.2 Records of Deflagrating Combustion 5.3 Records of Detonating Combustion 5.4 Symmetry of Combustion Waves CONCLUSIONS REFERENCES TABLES FIGURES APPENDIX A by J . J.L. Brennan v 1 3 6 13 16
17
19 19 20 21 22 25 25 26 28 29 32a c C E
,
F H i I K m M n N 0 P Q r R~
S t T U v NOTATION speed of sound specific heat center internal energy mass fraction enthalpy electrical current observation stationequilibrium constant based on partial pressures molecular weight total mass dilution index number of moles observation station pressure
chemical energy of combustion radius
electrical resistance. gas constant universal gas constant
name velocity time
absolute temperature particle velocity specific volume
V volume
W wal!
7f
specific heat ratiof
density/ Subscripts
C-I mean value between C and I
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C-O mean value between C and 0
'of
1-0 mean value between I and 0
i initial conditions f final conditions b burned gas u unburned gas p constant pressure v constant volume
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INTRODUCTION
This report deals with an initial study of a broader project undertaken at the UTIA, the main purposes of which are:
a.
b.
the development of a hypervelocity launcher capable of launching small projectiles (6 mm diameter, 150 mgr. ) at ideal velocities up to 20 km / sec.
the subsequent investigation of aerophysical problems associated with reentry at hypervelocities and meteoroid impact.
In order to achieve hypervelocities of this order of magni-tude, it is necessary to have driver gases at extreme pressure and tem-perature. A method of achieving such gaseous states, based on the use of implosion waves, was suggested by Dr.!. 1. Glass (Ref. 1 to 3). The launcher is to operate as follows:
A liner of solid explosive is applied on the hemispherical surface of the combustion chamber. Then this vessel is filled with a com-bustible mixture compesed Ol stoichiometrie hydrogen-oxygen diluted with helium or hydrogen. This mixture is ignited at the geometrical center of the hemisphere. A spherical combustion wave moves radially toward a properly sensitized solid explosive liner, which detonates and sends an implosion wave toward the center, producing the desired high enthalpy driver gas.
This facility consists essentially of four main parts: the hemispherical combustion chamber, the gun barrel, the blast chamber or dump tank, the range and associated instrumentation. The two last parts are shown in Fig. la, and a~cherriaiic view of the driving section is shown in Fig. lb.
To ga in maximum information concerning the factors affect-ing the performance of the launcher it was decided to conduct independently the following investigatiohs:
a. b.
c.
d.
a study of the gaseous combustion
a study of the surface detonation ignition of the secondary explosive by means of combustion waves.
an investigation of the properties of the implosion wave and its stability.
This report describes an experimental investigation of the combustion process (stage a. ) produced by using initial mixtures of
where
o
~ n ~ 14and X represents helium or hydrogen. Initial pressures range from 75 to 1000 psi, or about 5.28 to 70. 31 ~g/cm2, the initial mixture being at room temperature.
Among the properties investigated, are the maximum pressure and temperature in the chamber, the histories of pressure and heat transfer from the gas to the wall, the speed of the combustion wave, the initial conditions leading to a deflagrating or detonating combustion and
the wave symmetry. .
Moreover some specific problems associated with the mea-surements of several of these properties are given a special attention, for example, the relation between the burning velocity and the pressure history in a slowly burning combustion wave, the development of a spherical de-tonation wave and the oscillatory character of the flow associated with a detonating combustion.
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1. THERMODYNAMIC PROPER TIES OF INITIAL MIXTURES
The initial mixture is composed of hydrogen and oxygen in stoichiometric proportions diluted with helium or hydrogen:
with:
o
~n ~14x
= He or H2 and the initial conditions:Ti = 298. 160K 75
:s; Pi
~ 1000 psi.The properties of this initial mixture are described by the thermally per-fect equation of state. The partial pressures are obtained through Dalton's law.
The dilution of the mixture can be defined in several wa;ys: a. by the value of n. i. e .• the number of moles of diluting gas per
mole of oxygen in the hydrogen-oxygen stoichiometric mixture. b. by the molar fraction (or the partial pressure or the partial
volume) of the diluting gas in the initial mixture. c. by the mass fraction of X in the initial mixture.
Although these three characteristics are equivalent. the first one is more convenient and is used in this report as the index of dilution. The second is generally used but when the mixture is hydrogen diluted. it is often characterised by its partial pressure of hydrogen (totàl) in-stead of the partial pressure of diluting hydrogen. The third definition is less useful in this application because it involves the molecular weights.
For convenience •. the following functions of n have been computed and represented graphically:
1. The partial pressures (Tables 1 and 2 and Fig. 2). n
2 PH 2
=
n+3 p. 1 1 Po=
n+3 p. 1 2when X
=
H2' the combined partial pressure of hydrogen in the mixture is: n+2Pl·
n
+ 3
2. The specific heat ratio (Tables 1 and 2 and Fig. 3). Cpi = C Vi = n CpX+2CPH2 + C P02 n C vX + 2 CVH2 + CV02 3. The speed of sound (Tables 1 and 2 and Fig. 4).
with 1 a·
=
(Y. 'R· T·)2 1 UI 1 1~
~
and mi=
m· 1 nmx+ 2 mH2 + m02 n+ 3
4. The total chemical energy (Q) stored in the initial mixture (Tabie 3, Fig. 5).
If
A
Q, in kcal per mole of hydrogen, is written for the heat released by the reaction at constant volume of a stoichio-metrie gaseous hydrogen-oxygen mixture, transforIT)ed into water vapor, then Q is given by:where NH2 is the total number of moles of hydrogen in the initial mixture which contains a total number of moles Nt . NH2 and Nt are given by
2
(Dalton's law) n+3
(perfect gas)
where V is the volume of the combustion chamber. This gives for Q:
2 Q
=
A
Q. n+3This is given for any value of Pi in Fig. 5, for: À Q
=
57. 5 kcal/moleTi = 298. 20K V
= 2197
. cm 3o
~n ~ 12.(Note: in Fig. 5, r can take on values of 0, 1 etc. ) Then: 5. where: Q = A Pi n+3 A = Gonst. = .7037 if Pi in psi = 9. 9931 if Pi in kJg / cm 2 .
To permit a ready comparison with other results, the following relations can be used:
=
Px
Pi MX nmX=
n=
n+3 M n mX + 2 mH2 + m0 2These results are given in Tables 1 and 2, and are plotted in Fig. 6.
2. THERMODYNAMIC PROPERTIES AFTER COMPLETE COMBUSTION The initial combustible mixture:
(2 + m) H 2 + 02 + n He
is burned and the final composition, pressure and temperature are obtain-ed assuming:
a. the only species in appreciable concentration are H20, OR H2' 02' H, 0, He.
b. the final products are in thermodynamic equilibrium, c. the different species obey. the thermally perfect gas law, d. the g~seous system is free of any external influence.
With these assumptions, the presence of other radicals (H02, H202, .. ) and electrically charged species are disregarded. Dissipative effects such as viscosity, radiations, heat loss through the wall are neglected. Enthalpy variation with pressure is neglected. The most restrictive assumption is probably to neglect the heat lost through the wall by conduction,~nd.radiation.
The equations to be taken into account are: a. The combustion relation (chemical reaction):
3 7
:::E:
n" A .. - -~
nfJ' AfJ' j = 1 lJ lJ J = 1where i and f refer to the initial and final conditions respectively. Initial products: Ail = He Ai2
=
H2 Ai3=
02 Final products: Afl=
H 20 Af2=
OH Af3=
H2 nil=
n ni2'=
2+
m ni3= 1.
Af4
=
O 2 Af5 = H Af6 = 0)I': Af7 = He
b. The dissociation equations:
OH ~ 0 +H
(4. a) (4. b)
(4. c) (4. d) The different spec.ies are in their gaseous state and the relevant equilibrium Qonstants corresponding to each 'reaction are given by:
PtI20
=
n H20 KH20 (T)==
Kl (T)=
2 2 PHPo n ano
(5. a) ._ POH = nOH(~)
KOH (T)==-
K 2 (T)Po
PH nH nO Pf (5. b) P n H2 K H2 (T)=-
K3 (T) = M2 ( nf ) = p 2 n 2. Pf H' H (5. c) K 02 (T)=-
K 4 (T) P0 2 n02 nf ::;: =( - )
PÖ n 2 0 Pf (5. d)Where the last equality in each of the relations (5) has been obtained by . using Dalton's law valid for a perfect gas:
(6 ) where 7 Pf =
: L
. Pfj" j = 1 (7 ) 7 nf =z:
nfj . j = 1 (8 )c. Conservation of mass. i) of each species: 1. for hydrogen: 2(2+m)
=
2nr1 +nf2+2nf3+nf5 (9) or 2. for oxygen: 2 = nU +nf2+ 2nf4+ n f6 3. for helium: n=
nf7ii) The total volume being constant, the density remains unchanged: 3
2-j :: 1 n·· m·· IJ IJ=
J
i =ff
7::E
j=
1 nfJ· m fJ· (10) (11) (12a) (12b) with the assumption that the hot and cold mixtures are thermally perfect,(12) gives:
Pf T f
- = - .
(13)Pi Ti d. Conservation of energy.
As far as the final conditions are concerned, the process is assumed to be equivalent to the following: The reaction leading to the final composition takes place at the initial temperature and all the chemical energy released, contributes only to increase the internal energy by heat-ing the final mixture to its final temperature:
AU
Tf=
AQ
A
UTf is the total internal energy change:7 . 3
~UTf
=~
n. Uï T -2:
J :: 1 Jf J, f j=
1 7 n .J I J . U·· T 1, iA
UTf=
~Uro
+?t
1 njf (Ujf, T f - Ujf, T o ) 3 -~
n.. (U.. T - UJï T ' ) j=
1 Jl Jl, i ' 0 (14) (15) (16)'w where
Ll
UT o 7=
~
n'f U'f T j = l J J, 0 3~
n.·U·· T j=
1 JI JI. 0r;
I:'" j tt 't. (17)an'd,': Q represents the total amount of chemical energy available, which for perfect gases can be written as: " 1
7 3 7 3
Q ,= ~ .n·f.6Hor ~f' - .~- n·. AHof .. - l~ T· (~ n'
f - . .Eo n .. ) (18) , 'J ::: 1 J ' iJ ' J = 1 "Jl • J I '" I J =, 1 ~ 'J = 1 J I
where the
A
HOf are tnehe~ts
of forrpation of the' diffe:ç-ent components at the initial temperaturec. From Ref. 4. we hàve reproduced iniTable 4 the values of4!1
HOf' at the :temperatures of 0 oK and 298. 16o K.The initial mixture is at room temperature
=
298. 16oK, it is assumed: , . '1 ... 1 T.=
T .' _ '::- " I O· ~ :.l ( \ i -) ft (Ti)' SinceMaking Use lof thè fact that all the species obey the perfect "
gas law. and writing H(T') for the sum of the sensible enthalpy and chemical energy at OOK for a standard state (cal/mole), the relation (18) becomes
, j'l •
simp,ly: \ .. , ~
'I 7 V:,:.3
'2::
j
=
1 nfj Hfj ((
.'
r:t)
-
ff='1 nij Hij (Ti)I
(19)
The above ,equations for,rH a complete system of 9 algebraic. non linear equations:
• 1, t" I • ~ •
, - ~ass conservation for each species (9). (10). (11)
'31[1 t')-:l~é!ëid:l.Ü&:riUrh: bf'éaell' drssociafiÓn1readión (5at (5b), (5c)
t"19'}v" 'I
'. ;,;'t 1 .1".:. " . ..;.. t.J ..' ' , . b j ! ~ ... -~. • ::., t ~,(
5
à)
\
f~. ,conservation of energy (14)
or
(19) - constant volume reaction .,(l.ah
(I j \ , 1..'
which makes itpossible to solve for the 9 unknowns:
") 8 - composition: njf (j
=
1 •... ; -7·): \.l:! , final pressure: Pf ( , r 1')1 -f(" final temper:ature Tf" ,,' Sn., cr! ... ,~ ( ' ,-1 -fl ' I " I .1' f t "The the,rrnodynamic' uatatüs!e'd tor s6lving'thi~ system are' thQs'e given in
Ref. 4. ..,
,.. (, /' . ~ -' _ 14.. t • ( )
, , ' The s6l~tion is ol?~ai!led by trial and. erro~. For known initiàI éondihons, a temperatur'e'T
f
is. assuhled. j'From (13) the followingratios nf/ni is obtained:
=
(20)and the remaining equations provide a system of six equations for the six unknowns (nfj = 1, 2, ... , 6): nU = Al (Tf ) n2 f5 nf6 with (5a') K 2(Tf) with A 2
=
( nf) (5b' ) Pf-
K3 (Tf) with A3 --(nf) (5c' ) Pf K4(T f) with A4-
=
(nf ) (5d') Pf and (9) and (10).The elimination of all tp.e njf with the exception of nf5 between (-Ba to d), (9) and (10) leads to a polynomlal of the sixth order in n f5 , given by: 6 ~. k = 0 C k (Tf) nf5 = 0 (21) Co
=
8 (2+
m)2 A4 Cl= 2 (2
+
m) (A2 - 4 A4 ) C 2=
2 (2 + m) (A ~ - 8 A3 A4 + 2 Al) + 2 A4 - A2 (1 + 2 A 2) C3=
6 A 1A 2 (2 +m) - A~ +8 A3A4 - 2A1 - 2 A2A 3 - 8A 1A 2 C4=
4A1 (2+m)-3A1A2-2A~A3+8A~A4-4A1A3-8A21
..
2 A21 - 6 Al A2 A3 2
4 A 1 A3 •
When a real positive root has been obtained, nf6 is found from
eliminat~on of nf1' nf2 and nf3 through (5a to c):
2
2(2
+
m) - 2 A3 nf5 - nf5 nf5 (2 Al nf5 + A 2)The solution will only be acceptable if nf6 is also positive.
(9) after
nfl to 4 are then obtained from (5.a') to(5.d'). As a final check, the energy equation (19) has to be satisfied. lf not a new T f is chosen and the procedure is repeated until it is. The convergence is good and the Tf are determined within one degr:.ee Kelvin.·
The following quantities have -been computed* for the range of initial pressures (inátrn):
1 ~ Pi ~10, 000
and the two types of mixtures:
a) (2 +m) H 2 +02 (n
=
0) whereo
~ m ~ 15 b) (m=
0) whereo
~ n ~ 151. The final temperature (Tf) and the final-to-initial temperatureJTatio (T fiT i)'
2. The final pressure (Pf) and the final-to-initial pressure ratio (Pf/pi)'
3 . The concentrations of each species (nfj Inf) in the final mixture.
* The calculations were made by Mr. J. Galipeau, c.on-qultant,.
(National Computing Services) on the IBM 7090 computer at the Computation
4. The final specific heat at constant pressure (Cpf)' *)
5. The final specific heat ratio (Cpf/Cvf) *)
7
~
nfJ' CpfJ' j=
17
7
L"
nï CPf"-~':E
nf" ' 1 J J ' 1 J J=
J ::;6. The final average molecular weight: 7
'2::
nfJ' m fJ' j=
1 7~
nfJ' j=
17. The speed of sound in the final mixture
-1 .!.
af = (T f
"t
f~'f
m f ) 2and the final-to-initial speed of sound ratio (af/ai)'
*) (23)
(24)
*) (25)
(Tabulated and graphical results wil! be given in Ref. 36). *} Frozeri flow Notes: 1. A first approximation is readily obtained if dissociation is dis-regarded. The system to be solved then, reduces to:
where,
Tf nf Pf=Pi . - '
Ti ni
2 HH20 (Tf) +m HH2 (Tf) +nHHe (Tf )-H02 (Ti)-(2 +m) HH2 (Ti) - nHHe (Ti) - ~(Tfnf-Tini) = 0
nf = m + n + 2 ni
=
m + n + 3(26)
(27)
(Tabulated and graphical results wil! be given in Ref. 36). They confirm and extend the values given in Ref. 5.
2. The final conditions have been obtained for the two basic cases m = 0 (helium dilution) and n = 0 (hydrogen dilution). lf desired, the program can be run readily for anyset of values mand n, both different from zero (stoichiometric hydrogen-oxygen diluted in a mixture of hydrogen and helium).
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3. COMBUSTION WAVES
In Section 2, the conditions af ter complete combustion were obtained as if the total mass of gas had burned simultaneously. Actually the mixture is ignited at the center and a combustion wave moves radially to-ward the hemispherical wall of the combustion chamber.
This wave is considered as a surface of discontinuity propa-gating into the unburned mixture with a speed S relative to a frame of re-ference fixed to the combustion chamber. If the combustion wave propagates into the unburned gas with a velocity smaller than its s.pei'!d of sound the wave is refered to as a deflagration wave, otherwise it is called a detonation wave.
An historical introduction to combustion waves can be found in Manson's publication (Ref. 6) and the numerous references given therein.
The general properties of these two types of waves and the basic relations from which they can be derived will only be given here in brief form. It may be noted that if a discontinuity is moving with variabIe
speed in a gas which is itself accelerating (or decelerating), and where the flow quantities vary in space and time, the steady flow conservation laws (with respect to the discontinuity) may be applied between the gas properties immediately before and behind the discontinuity, provided th at the discon-tinuity zone itself may be regarded as a (mathematical)surface (se~ Refs. 7 and 8). For the components of the velocities normal to the discontinuity, the following symbols are used (see sketch, SK. 1, where the arrows indi-cate positive directions).
S is the absolute velocity of the flame frQnt, i. e. measured in a frame of reference attached to the combustion chamber.
Uu and Ub are the absolute velocities of the unburned and burned gases respectively, measured in the same frame of reference. Su and Sb the relative velocities of the flame front with respect to the
unburned and burned gases respectively. Su is generally called the burning velocity of the combustible mixture ..
~~\
\ \ u \
\b~ 'I--_S~ ~
))1/
. ~ Nonsta.tiona1-y Flame SK.1~b~~~
. . Uu -s
/I/y~)
J
J
/
/
//
IIJ
. Stationary Flam eFrom these definitions it comes
Su
=
S - U u = - (U u - S) (28. a)Sb = S - Ub
= -
(Ub - S), (28. b)where the last parantheses contain the relative velocities of the unburned and burned gases respectively with respect to the f~ame front.
Disregarding dissipative effects, the conservation laws are written:
1. maSs:
r
u (Uu-S)
=
~b
(Ub - S) (29) 2. momenturn: Pu + <Uu - S)2?
u = Pb+
(Ub - S)2~
b (30) 3. energy:Ju
~u (ts~
+Eu)+puSu=
fbSb(tSt+~b)+PbSb
(31) where E is the sum of the internal energy and heat of formation.The existence of two different types of combustion waves can be predicted by rearranging Eqs. (24) to (31). Combining (29) and (30):
S2
=
fb Pb - Pu uyu
~b
- fu (32. a)fu
Pb - Pu S2=
-~b
-~u
b fb (32. b)Introducing these expressions of Su and Sb in the energy equation (31), the two equivalentexpressions are obtained:
1 1
(pu
+
Pb) <)u -fb)
=
2(Eb - Eu) (33. a)1 1
(Pb - pu)
(ru
+
fb) = 2 (Hb - Hu) (33. b) where E and H ar~ respectively the total energy and enthalpy per unit mass including the heats of formation.Equation ( 33) defines the locus of the states (Pb, ~ b) related to a given state (Pu' fu) through the combustion wave. From ( 3~ ) it is seen that only the states for which .the relations . . . ..
Ph) Pu and
f
b)f
u (34. a)..
or
(34. b)
are simultaneously satisfied, have a physical meaning.
These described by (34. a) are called detonation waves.
They give rise to a compression through the wave front and as can be shown they travel into the unburned gas with supersonic velocity. The others
(34. b) are referred to as deflagration waves. The gas expands through such a wave and they propagate subsonically into the unburned gas.
When a combustible mixture is ignited, it generally starts burning in a deflagrating way, and it takes a certain time before a detona-tion develops - if at all. This time depends on the mixture, its initial con-ditions, the boundary conditions and the method of ignition. It can be as short as one microsecond or infinitely large. The distance required for this transition to take place is called the "induction distance". This in-duction distance considered as a global parameter has been investigated ex-perimentally and theoretically in Refs. 9 to 15. In the case of constant area duct, formulas have been suggested to re late it to the flow parameters and the tube diameter (Ref. 14).
The above equations which treat combustion processes as waves (association of compression and combustion waves) do not provide a means of determining the transition from deflagration to detonation. In general, the problem of predicting the flow field from the instant of ignition to the moment when a detonation has fully developed, given
a) a combustible mixture,
b) initial conditions of temperature and pressure, c) a m ethod of ignition,
d) the geometry of the combustion chamber,
appears to be still unsolved. Among the important parameters which are not yet theoretically predictable, although they are functions of the thermo-dynamic state for a given mixture, are probably the burning velocity and the heat released per unit mass through a travelling wave.
Theories of the flame acceleration mechanism during the transition period have been proposed. In 1956, Chu, (Ref. 16) indicates that the generation of pressure waves at the flame front is mainly due to a
.change in the rate of heat released by the chemical reaction in the com-bustion zone, whatever the ·cause(s) of this· change (variations of the burn-ing velocity, of the flame area ... ). Under certain conditions he proves the equivalence between the pressure and velocity fields induced by a flame and a moving heater with a variable rate 'bf heat release. Chu's theory
assumed a constant pressure deflagration and negle~ed kinetic contribution in the energy equation. These assumptions were removed by Laderman and Oppenheim in 1961 (Ref. 17). So modified, the moving heater model
appears useful to give quantitative information in the initial phase of the flame acceleration.
A few points concerning spherical combustion waves are now recalled briefly.
3. 1 Spherical Deflagrations
Recently, deflagration investigations hav..e be.enconducted in
closed spherical vessels in order to measure the burning velocity of a given mixture, mainly as a function of pressure. A review and discussion of the work done and the various assumptions generally made appear in a recent paper by Rallis and Tremeer (Ref. 18).
A typical slow deflagration process is illustrated in Figs. 23 and 24. Af ter ignition at the center, C, the flam e front moves radially towards the wall, W, at a low speed compressing the unburned gas which will later be transformed. The combustion is accompanied by an expansion across the flame front and an appreciable temperature rise due to the heat released by the exotherm ic reaction process. The traces obtained from a thin-film resistance thermometer clearly show that the increase in tem-perature in the unburned gas (C' to I') due to the precompression, is
negligible compared to the temperature jump (I'F) across the wave. When crossing the flame, the particles of unburned gas are accelerated away from it as it is seen from (29) and (30) rearranged in the form:
Pu - Pb
U u - U b
=
Sbf
b=
Su~
u (35)(Since with the configuration suggested in Sketch SK. 1, Su and Sb are both positive.) The pressure jump across the flame can be obtained from (35):
Pb
=
1 -S~ ~u
( Sb - 1)Pu Pu Su
(3·5' ) or for a perfect gas:
Pb
1 -
'I
u (:u )2 Sb=
( - - 1)Pu u· Su
(36)
The validity of the assumption of equality of pressure on
both side~ of the flame which is generally made in analyses dealing with
sueh deflagrations is illustrated by the .ptessure traces in Fig. 24. At
low initial pressure, in the early stage of the combustion, this expansion
is clearly observable. But when the pressure increases and the w~ve slows
down, the pressure difference vanishes (see trace 0, Fig. 24. a).
-- - - -
-3. 2 Spherical Detonations.
Among the family of possible planar detonations, a special and very important case is the so-called Chapman-Jouguet detonation, for which the entropy change across the front reaches an extrem urn. This detonation wave propagates with velocity Sb equal to the speed of sOUl).d (ab) in the burned gas. Theoretically several arguments have been offered to prove that this detonation is the only stable one (see for instance ReL
19 and the original papers referred to therein), and practically in a one dimensional space (for instance in a cylindrical pipe open at one end and filled with a combustible gaseous mixture ignited at the closed end) it has been observed that detonation waves, after a short distance of
formation (induction distance) were propagating at the uniform Chapman-Jougllet velocity. This speed of propagation computed from the conserva-tiort'laws, together with the equations of state and the dissociation equili-brium constants would depend only on the type of combustible mixture for a given set of initial thermodynamic conditions.
Whether or not a spherical detonation wave would propagate af ter the induction period, with "this uniform speed is a question which was considered at the very beginning of this century when, independently,
Chapman in England and Jouguet in France, had proposed their macroscopic theory of flame propagation. This question cannot as yet be regarded as completely solved.
In 1907, J ougllet, considering as im possible all detonations " which would travel with supersonic speed with respect to the gas immediate-ly behind the flame front, deduced that a spherical detonation wave cannot propagate with a uniform speed which would dep end only on the initial conditions (ReL 20). In his work in 1941, Taylor (ReL 21)disregarded this restriction and presented a theoretical solution for the propagation of a spherical detonation compatible with the constant detonation velocity (for given initial conditions) as defined by the Chapman-Jouigllet conditions.
Similar conclusions were also reached by Zeldovitch (ReL 22).
Experiments made by Lafitte (1923) showed that spherical
detonation waves propagating with the same velocity as planar detonations could be produced. Similar experiments conducted with more care and improved techniques were"made by Manson and Ferrie (Ref. 23). They confirmed Lafitte's conclusion. Moreover, they showed that if the mix
-ture is rich enough to support a detonation wave, the ignition source pro
-vided that it induces a detonation did not affect the wave velocity.
Cassut in 1961 (Ref. 24) conducted experiments to determine the detonability of unconfined hydrogen-oxygen mixtures for various ni-trogen dilutions. He showed that spherical detonations could be produced for the mixtures which would nor.mally detonate in confined tubes, provided that the ignition method was adequate. No measurements of the wave velocity were reported.
More recently, Litchfield induced detonations in different
systems, including hydrogen-oxygen mixtures, by electrical discharges only, and obtained results which would indicate that above a minimum
ignition energy level, these waves were propagating with the Chapman-Jouguet velocity (Ref. 25).
Experiments have also been conducted (Ref. 26) to study the effect of additives on the formation of spherical detonation waves in
hydro-gen-oxygen mixtures. It was found there that some components, as
ethylene, reduces the minimum initial energy required to induce a
detona-tion, while others like propylene and isobutene inhibit detonátion. It may be wor th noting that water and nitrogen have only a slight effect - these are gases which could have been present as "additives" in the experiments des-cribed in this report.
Most of the works mentioned above give experimental support to the condition of a minimum energy required to produce a spherical detonation wave in a gaseous combustible mixture (Ref. 27).
Several of them indicate that the wave would travel with the C. -J, velocity
provided that the ignition energy is larger than a minimum level
depend-ing on the initial conditions .
4. DEOCRIPTION OF THE EXPERIMENTAL EQUIPMENT, APPARATUS AND PROCEDURE
4. 1 Combustion Chamber and Loading System
A schematic view of the hemispherical chamber, which was designed by Mr. G.F. Bremner (Ref. 1 and 2) is shown ~n Fig. 25. It com-prises . four main parts:
a. The 8 in. dia. hemispherical vessel itself.
b. The top plate closing the combustion chamber which also serves to house the various gauges, the ignition plug, the entrance for the charging gases and the exhaust for the com-bustion gases.
c. The ignition plug supporting the electrodes . d. The cylindrical clamp to fasten b) to a).
A view of the combustion chamber when open is shown in Fig. 26 and when in a firing position in Fig. 27.
A general diagram of the plumbing system is shown in Fig. 28. The vacuum gauge (VG) is a Wallace and Tierman gauge, type FA 160,
o
to 50 mm of mercury. Two high pressure gauges were used; both were Heise gauges, 12 in. diameter, 2700 scales. The first (0 to 4,000 mm Hg)was used for the experiments made at low initial pressure (75 psi), while the second (0 to 1000 psi) was connected when runs were conducted at higher initial pressures. Both were provided with blow-out protection.
The combustion chamber entrance and exhaust valves as well as the part of the plumbing system connecting them to the chamber were designed to operate safely up to 100, 000 psi. The remainder of the lines were designed to operate safely up to 10,000 psi.
The whole system was enclosed in a barricade (6 in. of sand held by a wood structure) reinforced by a 1/4 in. thick steel plate on the operating console side. Part of this barricade appears in Fig. 29 showing a view of the operating console and in Fig. 30 showing part of the electronic apparatus.
The three valves connecting the gas cylinders of helium, hydrogen and oxygen to the common line were operated fr om the console by extension rods going through the barricade wall. The other valves having to be operated during a loading phase were air operated, remotely controlled.
An electrical interlock prevented any accidental firing if any of the remotely air operated valve would not be in its correct firing position. Needless to say, all the above precautions were taken to insure safety.
4. 2 Loading Proc edure
When the combustion vessel was placed in a firing position with all accessories connected, the barricade door was closed. The vacuum pump put in operation until a pressure of the order of one mm of mercury was obtained. When the first gas to be introduced was helium or oxygen, a smal! quantity was first let in to a pressure of about 30 to 40 mm Hg and then evacuated to less than one mm Hg. This was done to reduce the amount of impurities left in the vessel and plumbing. The pump valve was closed and the initial mixture introduced. If the dilution were due to helium, the gases were introduced in the following sequence: hydrogen, helium, oxygen. If the diluting gas were hydrogen, the load-ing was made in two steps only: hydrogen first, then oxygen. A few tests were made in order to see
if
the loading sequence had any effect on the resulting mixture (He - H2 - He - 02 - He; 02 - He - H2). Judging by the maximum pressure measured af ter combustion, the answer appeared to be negative. Af ter complete loading, the combustion chamber entrance valve was closed and about five minutes were allowed before firing. This time interval was used to check the adjustment of the electronic apparatus.Af ter a run, if the vessel did not have to beopen~d,the igni-tion plug was removed and dry air was blown through the chamber to re-move the water which had been formed. Depending on the amount of water, this took between ten and thirty minutes.
. When a new crimped copper wire (or a pair of new spark electrodes) had been fixed on the ignition plug, this was replaced in its original position and the system was ready for a new cycle.
After five or six runs the chamher was opened and cleaned thoroughly. However, if gauges were damaged, this was done more fre-quently. When detonating combustion took place it'was at times very difficult to unlock the clamp which became seized. Sharp blows from a ram had to be used to uncouple it. For th is reason, another way of fasten-ing the top plate to the cham ber might be more convenient.
With the gauges used for the loading, the error
E
in the pressure readings was estimated as:E.~ 0.1 psi in the range 0 - 75 psi.
6S
0.3 psi in the range 100 - 1000 psi.The gases were obtained from commercial cylinders and did not receive any special treatment before use.
4. 3 Ignition System
. It was desired to have a point ignition at the geometrical center of the hemispherical combustion chamber. In order to approach this ideal requirement, three methods of ignition were tried:
1. a crimped copper wire 2. a spark ignition
3. a small detonating cap.
In the three cases, the ignition energy was provided by the discharge of a capacite:t: _ through a low impedance circuit. This firing unit was supplied by the Canadian Armament Research and Development Establishment. A block diagram of it is shown in Fig. 31. A total energy of 400 joules could be stored in the 8 " F-capacitance but it appeared that a very small fraction of it was released through the electrodes . The main 1 part was lost in the remainder of the circuit probably in the mechanical switch SW3.
An image of the discharge current is shown in Fig. 32a. The two upper traces (1) were obtained with the electrodes short circuited by a heavy copper wire. The lower traces (2) were obtained with the same conditions of voltage and low impedance, but a crimped copper wire or a pair of spark electrodes replaced the previous short circuit. Since neither the self-inductance nor the capacitance of the circuit had been affected by this substitution., the ratio of the logarithmic decrements corresponding to (2) and (1) is also the ratio of the corresponding resistances. A value of about 1. 12 was found, which tends to confirm the above statement that most of the stored energy was dissipated outside the electrodes . If it is now assumed, which is reasonably well justified by the traces obtained
(Fig. 32a) that the current magnitude has not been appreciably changed by this substitution, it is concluded that not more than twelve percent of the total stored energy would have been effectively dissipated in the ignition wire or spark gap.
When energy values .are quoted in some of the results (see for instance Fig. 96) they correspond to the energy stored in the capacitance and not to the energy dissipated in the wire or gap which appears to be at least an order of magnitude smaller.
Most of the experiments were conducted using a copper wire, 0.32 mm dia .. (#28), 25 mm long, crimped at the center to about O. 10 to 0.15 mmo When the mixture was. ignited by means of a spark, copper wire (1. 5 mm dia. ) electrodes replaced the exploding wire and the size of the gap ranged between 1 and 2 mm. This distance was considered small enough to approximate the point source ignition, and it was suitable for the discharge to take place in the useful pressure range . The ignition plug is shown in Fig. 32b. Traces obtained with these two methods of ignition are showD; in Fig. 3 2c.
Although the ignition system in the present arrangement is quite suitable for producing deflagration wa.ves, it should be modified when it comes to induce detonations which have to be studied quantitatively. That is the discharge circuit should be redesigned so that the energy dissipated in the gap is well known and the duration of the discharge much smaller.
Indeed the duration of the discharge is now of the order of sixty microseconds,
i. e., of the same order.as the time interval required for a detonation wave fully developed in a matter of microseconds, to reach the hemispherical wall. The noise associated with this discharge and picked up by the gauges completely blanks out the useful signals. These parasite signals are illus-trated in Fig. 33. In order to obtain such traces, the various gauges were placed in their respective positions and the combustion chamber filled with a non-combustible gas at a pressure within the range of interest. In the particular case of Fig. 33, hydrogen was used at a pressure of 300 psi. In deflagration study, these signals were hardly disturbing since then the ob-servation intervals generally were of several milliseconds.
When the above discharge circuit will have been modified in such a way that the ignition energy is known, it will probably be possible, if desired, to determine the energies which were used in these experiments. For this purpose it would be necessary to adjust the known stored energy in order to reproduce a few of the experiments reported here.
4. 4 Instrumentation
All the sensors which were used were placed in the top plate of the combustion chamber. The general configuration of the gauge positions is shown ih Fig. 34. The stations I and 0 were situated at distances of
1. 875 in. and 3.750 in., respectively, from the center C. All the signals were recorded on Tektronix oscilloscopes, types 535, 551 and 555.
Kistler SLM piezogauges, type 605-B in connection with Kistler piezo calibrators, type 652-B were used to measure the transient pressures. The manufacturer indicates very good agreement between static and dynamic calibrations. This fact was confirmed, at least in the low pressure range (0 - 60 psi), using the UTIA 4 in. x 7 in. shock tube
(Ref. 28). '
A typical static calibration curve for a piezo-gauge 605-B combined with a 652-B piezo calibrator is shown in Fig. 35. The pressure reference was provided by a dead-weight tester, Mansfiel~ and Green T-130. The linearity was within a few percent in the range indicated by the
manu-facturer. Frequent checks of the calibration factor (gauge-piezocalibrato.r) .... 8.'. ._~,.!.L have been: found necessary since variations as large as 16 percent were
noticed between calibrations made less than a week apart. The fact that the piezo calibrator, sensitive to atmospheric humidity had to be used in a room without air-conditioning, could undoubtedly have contributed to cali-bration variations . But since the gauges were occasionally used in
tem-perature conditions beyond the manufacturer's recommendations, it was believed that they could be affected by the experiments themselves. Effect-iyely, in a run conducted in a 2 H2
+
02+
3 He mixture at an initialpressure of 400 psi, two gauges, although protected by a layer of silicone grease, were irremedütlitydamaged while the third one showed a calibration factor variation of 18 percent. For this reason the recording of detonat-ing combustion pressure histories were restricted to those runs made at low initia I loading pressures
«
300 psi). Such a restriction could be re-moved if ballistic adapters (or~n other type of gauge) are used. Provision for such adapters was made but their installation required J;llodifications which were not completed in time to use them in this present work.In order to obtain a proper idea of the response time of the system consisting of the 605-B gauge and the 652-B piezocalibrator, two tests we re made in the UTIA 4" x 7" shock tube. The runs were conducted in air at a shock Mach number of the order Ms = 14. The pressure his-tories are shown in Fig. 36. The time interval required for the pressure to increase from PI to P2 as a result of the passing of the shock wave should be less than two microseconds, which is the response time of the gauge given by the manufacturer. A value as large as six microseconds was measured on the trace. The piezocalibrator is probably responsible for this appreciabIe difference.
*
Thin platinum film thermometers were used to detect the wave front, "lo measure the wave speed and to obtain an indication of the wall surface temperature variation. At first, following the experience with shock tubes, glass was tried as a backing material. The results were satisfactory in slow burning combustion. However, in detonating combus-tion the surface layers of glass shattered in every experiment, destroying the platinum film.
Quartz was substituted for glass and although this could not be considered successful, a few valuable records were obtained. However in most of the experiments, the thin-film was again destroyed.
During these experiments, a paper by Laderman, R€cht.
and Oppenheim (Ref. 29)was published. This paper seems to be the first one dealing with the use of thin film thermometry in combustion. The backing material used was a magnesium silicate ceramic, Lava 1136. This technique was tried and the results in deflagration were satisfactory. However, when detonating èombustion took place (even at initia I pressures as low as 100 psi) the film seldom withstood more than one run. It was suggested (Ref. 30) that the trouble may arise from a lack of a smooth
*
Charge amplifier with a better response time would now be available from the same manufacturer.finish of the ceramic surface, which appears to be important to insure a good bond between the film and the backing. But ha ving se en the damage
caused to pressure and ionization gauges (0. 6 rn m dia. cornrnerical stai
n-less steel sewing needles, 6 rn. rn. long were cornpletely rnelted in deto
nat-ing combustion) in such experirnents it is doubtful if the thin platinum film
is really suitable for detonation experiments at high pressure.
Several heat transfer records appear in this report, see for
instance Fig. 23 and Fig. 101, for deflagration and detonation runs, re
-spectively. The circuitry used in connection with the heat transfer gauges is shown in Fig. 37. The gauge is part of a voltage divider. A DC-current (25 m A) is kept practically constant by a backing resistance R which is
larger than the gauge (HTG) resistance variations. A picture of a gauge is
shown in Fig. 38.
Glow discharge gauges were also used to detect the arrival
of the ionization in the wave front but not to record the gas conductivity history. A single pin protruding into the charnber coristituted one of the
electrodes, the other being the chamber itself. The gauge and the circuity
used are shown in Figs. 39 and 40 respectively. Exarnples of traces can be
seen in Figs. 109 and 110.
In the continuing development of the UTIA irnplosion driven
hypervelocity launcher (ignition of secondary explosives by cornbustion
wave in a one-dimensional cornbustion chamber; investigation of hemisphe
ri-cal irnplosion waves) it is intended (Ref. 3) to use light sensors to detect
the passage of the combustion wave. These gauges would essentially con
-sist of a photodiode similar to the type OAP12 (Philips). Preliminary tests
5. RESULTS AND DISCUSSION
From the appearance of the pressure records, it is seen that two different combustion processes did take place. A deflagration process is illustrated in Fig. 24 and is characterized by a pressure rise continuously smooth from the origin (instant of ignition) to the end of the cycle. When cooling by heat conduction through the wall becornes predomin-ant (practically af ter complete combustion, i. e. when the flame front
has reached the wall) the sign of the pressure slope changes and the pressure decreases monotonically. In the second type of records, the pressure increases first uniformly but after a certain period (of the order of one millisecond in the examples of Figs. 99 and 100) a sudden increase takes place and as observed in some cases (see Fig. 99a (trace I) and Fig. 100b (trace 0) ) but not in.all·pressure ratios ( Pf/Pi) as high as 35 were recorded. Another characteristic of this type of traces is their oscillatory nature (see Fig. 101): In the present experiments an accurate measurement of the propagation velocity of this steep pressure front
could not be made (see Section 5.3). Such a measurement would have
shown conclusively whether or not the wave was travelling with the detonation velocity. Despite the lack of a direct and continuous measurement of the wave speed the data provided by the pressure gauges, heat transfer gauges, ionization gauges, and similarities with other one-dimensional combustion experiments, it is safe to assume that detonation waves were in fact obtained.
5. 1 Initial Conditions Leading to Deflagrating or to Detonating Combustions With the present firing unit and a
o
.
32 mm dia. copper wire crimped to O. 13 mm or a l t o 2 mm gap spark as igniters, it was found that for the initial mixtures (2 H2+
02)+
nX where X represents helium or hydrogen, a smooth deflagration always took place when the dilution index n was larger than a certain "critical" value (until, of course, the mixture did not ignite at all). Below this value a detonating combustion developed. It should be emphasized again that a change in the actual firing energy probably would have modified these limits.For helium diluted mixtures, detonating combustion took place for
and deflagra tion for
The upper limit (n = 15) was defined as the dilution for which three consecutive attempts failed to ignite the mixture. At the nominal value of n = 3, both types of combustion were obtained as weU as "transition type of combustion" as shown in Fig. 41.
At 100 psi for hydrogen diluted mixtures, n
=
7 was found to be the critical value and n=
10 the maximum dilution at which the mix~ ture could be ignited.Runs were conducted in helium diluted mixtures with n
=
4 and an initial pressure, ranging from 100 tÇ> 1000 psi. No detonatingcom-bustion did take place,which indicates that n ~ 3 remains the critical
value for this pressure range, since an increase in initial pressure would promote detonation. The same set of runs were conducted for hydrogen dilution at n
=
8., e·xcept in two experiments (at 400 and 500 psi), onlyde-flagrations were ptoduced.
5.2 Records of Deflagrating Combustion
Sets of deflagration pressure histories recorded in helium
and hydrogen diluted mixtures, at initial pressures ranging from 100 to 1000 psi, are shown in Figs. 42 to 84.
The final to initia I pressure ratio measured from these
experiments are reported in Figs. 85 to 87. In these figures the cirles represent arithmetic mean values. The number of records used and
the range of the values obtained are indicated for each pressure. The time (tw) required for the pressure to reach its maximum value is shown in Figs. 88 and 89 for several dilutions. It is seen in this last figure that
the' dispersion of the results increases when the dilution becomes larger. This is not too surprising since then the relative accuracy of the partial
pressures in the initial mixture decreases for a given initia I pressure. Since the magnitude of the pressure slope is appreciably smaller during the cooling period than during the later stages of combustion, the time
(tw ) can be considered as a good approximation of the time for the flame
to reach the wall.
Using heat transfer records such as those shown in Fig. 90 and 107, the average speed of the wave between stations C and I, C and
o
and land 0 was measured for various dilutions at an initial pressure of75 psi. The results appear in Fig. 91 and 92. The number of runs and
the dispersion of the measurements is indicated for each dilution. Figure 91 also shows how the dispersion of the results increases with dilution. The ave rage wave speed is found to be larger in the region C - I than in
C - O. This meins that for these deflagrations th~ wave accelerates mainly before reaching station I, i~ e., before the pressure increases appreciaoly in the vessel as shown in Fig. 90. These mean values are
plotted in Fig. 92 to obtain a first approximation of the ave rage flame
speed variation in the vessel. In Fig. 93 the average velocities between stations C and I, C and 0, land 0, 0 and Ware plotted at the points A, B, C, and D respectively.
The repeatability of the combustion runs is illustrated in
within three to seven percent. The variation in te -0 (time for the wave to reach station 0) were within ten percent but variations in te-I could be as large as twenty percent as Fig. 97 indicates. Therefore, although relatively important variations are noted in the initial acceleration of the wave, the variations found in the time for complete combustion are rela-tively small. The variations in the final-to-initial pressure ratio for six
traces (two gauges a~d three runs see Fig. 95) were found to be the same
within six percent. It is seen that the agreement is better from run to run
than from station to station.
In Figs. 71 'to 73 and 84, the pressure appears to decrease
to a value lower than the pressure which would be expected in the chamber after complete condensation of the water. This is of course not possible. In the case of Fig. 84, the pressure in the chamber was applied to a static gauge at least two seconds af ter the run was over, and it was still far
above its initial value. It has been found that such gauges are thermally
sensitive. Therefore in order to reduce this effect, a layer of silicone grease provided by the gauge manufacturer was applied to the gauge dia-phragm. This improved the gauge behavior but the grease was removed too fast to be the real solution.
An important parameter which arises in the c.ombustion
wave propagation is the burning velocity of the mixture, which is constant for a given mixture provided that the unburned state (pressure and tem-perature) remains unchanged. As far as it is known theoretical rnethods
for predicting this velocity are not yet available. In order to rneasure this
parameter from experiments conducted in a closed vessel, besides the
pressure history, at least one of the following records is necessary.
a) the radius of the flame front as a function of time.
b) the temperature of the flame as a function of the flame radius.
When such measurernents are made in spherical vessels it is also i
m-portant to see that the wave is really symmetrical. It can be shown (Ref.
31) that if the wave is a prolate spheroid with a minor-to-major axis ratio
of O. 95, an error as large as 25 percent can be expected in the value of the
burning velocity cornputed on the assumption of spherical symrnetry.
Despite these remarks the burning velocity has been computed in two cases
using a simple approach based on the pressure history only, which assumes a linear relation between the mass fraction (mass ratio of the gas already burned to total mass of gas) and the pressure (Refs. 18 and 19):
1 3 dF . -l/V _ ( p )
'u
Tt .
r . Pi (1 - (1-F) (-2...)-l/'tu )
2/3 Pi .wherF 'fu- l (-p-) ~u :- (~) Pi Pi F = lu- l
(----E- )
~ Pf Pi Pir= radius of the combustion chamber.
The resultant burning velocity versus pressure is shown in
Fig. 98. Due to the assumptions involved in the relations used, the
inaccuracy resulting from taking the derivative of F and the sensitivity of Su to small variations of P/Pi' the values obtained tl=nd only to give a first o.rder of magnitude of the burning velocity in these mixtures, even in the
early stage of combustion. In the later stage, when the flame front
approaches the wall the flame speed may be a good first approximation of the
burning velocity since then the particular velocity tends to zero and Su tends
to S (see 93, SO-W at points D). Eventuallya special combustion chamber tOf:t-plate could be designed to allow recording of the flame radius as a
function of time and to complete the information required to obtain a
realistic value of the burning velocity.
In some of the traces a peculiarphenomenom appears (see Figs.49 and 50 for instance) as if simultaneously the three gauges would sense a very sharp negative pressure pulse. It is impossible to attribute
this to flow phenomena. Since no ignition source is present at this time to
affect simultaneously the various circuits, it is believed tpat an external electronic disturbance which has not been located may be responsible for it.
Other irregularities sometim es were present in a set of pressure traces, as for instance in the run at 900 psi initial pressure in Figs. 61 and 62. These do not have the sharp character of the previous ones and may be thought of as a result of non-homogeneities in the mixture. However, both explanations are not completely satisfactory.
5.3 Records of Detonating Combustion
Some typical detonating eombustion pressure traces are
shown in Figs. 99 and 100. To make sure th at t~e oscillatory character of
the records was not due to a mechanical excitation of the gauge or its housing, a heat transfer history was recorded simultaneously. T·he
re-sults are shown in Fig. 101a. From here it appears that the wave first develop s as a smooth deflagration. The pressure rises in the whole vessel as a result of the pressure pulses which are continuously sent from the flame front. This wave is still in its deflagrating stage when it reaches statiop I as Fi.g. 101 (trace b) indicates. Then somewhere between station l a n d the wall it develops into a detonating process characterized by
a sudden pressure increase apd the oscillatory shape of the pressure and heat transfer histories. 1
To explain, at ,least qualitatively, the oscillatory nature, of the traces, the fo11owing model is proposed (*). When formed(at point A in Fig. 101b) the detonation wave moves toward the hemispherical wall where it reflects as a shock wave. At the same instant a shock wave (re-tonation) moves inward (implodes) from A and reflects at the centre. Sub-sequently, a complex process of wave interactions takes place, as shown on the (r, t)-plane and the :i.nstantaneous sketches 1 to 4 in Fig. 101b. An observer located at a station I or 0 would see a successiori of compression and expansion waves separated by contact surfaces, giving rise to positive and negative variations of the thermodynamic quantities. Since the energy of the gas isbeing dissipated continuously, it can be expected that the strength of the waves wi11 decrease and their corresponding wave speeds will in general decrease with time. This is in agreement with the records obtained. In Fig. 101a, for instance, if the beginning of the detonating process is taken as the origin of time, the average frequency is found to be (in kc/sec): 6.3 during the first two mi11iseconds, 6.0 from 2 to 4 ~J)il:se.c., 5.5 from 4 to 6 msec, and 5.2 from 7 to 9 msec. It would be very wortp,-while to develop an analysis based on this model in order to determ ine if it really describes the flow conditions and the wave processes. The main difficulty ~rises in expressing the boundary conditibns. Such requirements have some similarities with the Manson-Fay theory of spinning detonation
(Refs. 6 and 32) as developed analytically by Chu (Ref. 33).
Figures 99 and 100 show traces obtained from the same initial conditions . They give an indication of the repeatability of detonating combustion. Since this type of combustion did damage 'piezogauges, as already mentioned, the recording of pressure histories was restricted to low initial pressures. Traces obtained in ,hydrogen diluted mixtures at initial pressures of 200 and 300 psi are shown iI} Figs. 102 and 103.
When the diluting gas was hydrogen it wasfoundthat the in-duction time was appreciably longer 'than in the ca,se of helium dilution
(compare Figs. 104 and 103). This induction delay can be artificially in-creased by the addition of some dust around the electrodes as shown in Fig. 105, where s'ome Lava powder (from heat transfer gauge material) was used for this purpose. It is also noted that the predetonàtion pressure history is much flatter with hydrogen dilution than with helium ..
5.4 Symnie.!r.y..of Coinbustion w.,aves~ ~-'v
To investigate the symmetry of the wave, observations were made on three different radii 1200 apart as indic.áted in Fig. 34, and on each radius, two test stations were available (I and 0).
a) Pressure gauges would indicate the passq.ge of a detonation wave since a sharp pressure jurnp occurs across the shock wave-flame front transition. However, for the deflagrations, the expansion through the flame is very weak (see for example Fig. 106) and is hardly visible at all when the initial pressure is larger than 200 psi. Even at lower initial pressures this expansion has not been properly detected at the stations 0 because of its small amplitude. For these reasons sensors responding to other flow parameters have been used.
b) Across a combustion wave (detonation or deflagration) the temperature jump is appreciable and it was intended to use thin-film heat transfer gauges to detect the passage of such waves. In detonating combustion
(see Section 4.4) it was very seldom that a gauge survived more than one run, and when a set of six was placed in the chamber, generally one or several were damaged during the first experiment. In deflagration, the failures were less numerous and it was possible to obtain six records sim-ultaneously. Two such sets of traces are shown in Figs. 107 and 108. The thin film of platinum was placed normal to the radius.
" .
'c) Since ionization is always present in a combustion wave, a simple glow-discharge gauge can be used te detect its arrival. If the wave is a deflagration wave the ionization is due to the flame only and the gauge
really detects the passage of the flame zone. However, if the wave is a detonation w~ve, ionization can arise from the shock wave and the flame front. Two sets of results obtained thisway are presented in Figs. 109 and 110.
The information gathered from heat-transfer and glow dis-charge records are summarized in Figs. 111 and 112. Instead of the time intervals for the wave to reach land 0, the average velocities between C-I and C-O are plotted for the three radii'. The measurements marked by a triangle (radius 2) were made on the radius which was parallel to the exploding wire. In some cases, station I situated on this radius (2) was reached first by the combustion wave, while appreciably later the two other stations I were reached practically to'gether. Figures 109 and the follow-ing table illustFate this point (the time inte.rvals are in msec. ).
x
n PiHe 5 400 3.74 .2.94 3.56
8 100 3.62 3.26 3. 59
.1
This suggests that the wave has
