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The effect of vessel size and degree of turbulence on gas phase explosion pressures in closed vessels
T H E E F F E C T OF V E S S E L S I Z E A N D D E G R E E O F TURBULENCE ON GAS PHASE EXPLOSION PRESSURES IN C L O S E D V E S S E L S G, F, P, HARRIS Imperial Chemical Industries Ltd, Mancher,zer ') The effect of vessel ,;ize tm the masimum pressure and rates of pressure rise in explosions of air-pentane mixtures has been investigaqed in closed spherical ,,essel i with eapa¢ilie~, of 05 htre, 4 lilrcs and 60 fl ~. It was found that on scaling.up from the 4 I. Io the 60 fl s vessel, t~e maximum pressure of the mosl ¢xplosi',~cair pcntanr' mixtures remainrd ~.'on~t;,nt. whilsl tire pressurt: gcnerzted in tean and in very rich pentane air mixtures decreased wilh increase in vessel s~ze, Possible e~.planations for these eff~.'clsare put Ibrward. The effect of turbulence on maximum pressure in the 60 It j ves~l was also investigated. It was found that m:,ximum explosion pressure increased slightly with increase in turbuJenee, but the average and maximum rates of pressure rise increased linearly with turbulence,
Introductiuu Fog some time it has been standard practice to attempt to limit the pressure in gas phase explosions in chemical plants by the use of vents, The provision of such vents requires a knowledge of the ¢xplosibility of the inflammable mixture under consideration and the strength of the vessel to be vented.Though it is relatively easy to carry out the necessary measurements or maximum explosion pressure and rate of pressure rise in small closed vessels, there is little information on the scaling-up of these measurements to large vessels and no reliable method of designing explosion vents for plant vessels from these data. Cousins and Cotton t carried out experiments on the ventingof mixturesof known explosibility (air-hydrogen and air--propane)in Four vessels with a range of shapes and sizes, but did not investigate the effect of turbulence on the measured explosion pressure. Cubbage and Siremends ~ made a thorough investigation of the venting of towns' gas-air explosions in drying ovens, Their data apply only to the venting of the relativelyweak structures of the ovens, where the explosion pressure must be limited to a low value and a large vent is. therefore, required, Burgoyne and Wilson3 investigated air-pentane explosions in pressure vessels argo and 200 ft~
capacity and showed that turbulence produced by operating a fan during the explosion caused a considerable increasein the maximum pressure produced in a vented explosion. The present investigation was carried out to provide data for the design of vents for relatively strong vessels, The initial stage of the work was carried out in closed vesselsand the effectsof scaling.up on maximum explosion pressure and rates of pressure rise were investigated, The second part of the work concerned the venting of explosions in a large vessel and wi;i be pub. lished shortly. Experimental Throe closed vessels with capacities of 0.5 1., 4 I. and 60 ft~were used in this stage ofthe work. The 60 ft3 vessel is illustrated in Figure 1. It was a cylinder with dished ends so that it had a nearly spherical shape and was ,4 ft 6 in. in diameter and 4 Ft 9 in. in overall length. On one end of the vessel was a 24 in. diameter neck, which was blanked off For the dosed vessel measurements. To produce turbulence in this vessel a four bladed 18 in. diameter fan was mounted with the centre of the blades 10 in, above the centre of the vessel.The blades were surrounded by a 10 in, deep cylindrical casing and the fan was driven by a 1 h.p. motor 17
Vol. II
(L I'. t'. flhRttlS
through a variable speed gearbox so Ihal speeds up to 2000 rev/min could be obtained. The 0.5 Land 4 I, bombs were botlt spherical in shape and were not fitted with vents or with any means of producing turbulence. The combustible substance used in all this work was pentane. In the small ves~l experiments air penlane mixtures were produced by a conlinuous flow melhod. 11 OtanO
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All lhe explosive mixtures in the closed vessel experiments were ignited at the centre of the vessel since this is the ignition position giving the highest value of the explosion pressure. Ignition was produced by melting a short length or fine wire by passing a high energy pulse through it. The pressures developed in the explosion were measured by capacitance transducers and recorded on a two-channel oscillograph. The average and maximum rates of pressure rise were also delermincd for each explosion,
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ur,,t
coaxObs~r~r compressor
Gas ¢lfeu~d~
i I I Experiments with .~tationary #as mixtures The maximum explosion pressure and rules of pressure rise were measured for the complete range of inflammable air-pentane mixtures in all three yes,Is and Figure 2 shows a plot of explosion pressure against concentration of pentane in air for the 0.5 I, and 4 I. bombs. As is usual there is a maximum in the explosion pressure curves for both vessels al a pentanc 1201
Fa(aJRl~ I. 60 fl+vessd
Air was saturated with pentane vapour at 0~C and then diluted with excess air in a mixing vessel to give the desired proportions of air and pentane, The explosive mixture was passed through the bomb until about ten changes of volume had taken place. This mixing technique was not practicable for the 60 fx3 vessel work and the air-pentane mixtures were produced by spraying a measured volume of pentane into the vessel with the fan operating at full speed. In both large and small scale experiments ~mples were taken from the bomb and analysed to determine the actual concentration of pentane in air. In the 60 ft3 vessel the analytical measure. merits showed that the vessel was filled with a homogeneous inflammable mixture, The pentane concentration determined by analysis was always less than that calculated on the basis of vessel volume and amount of pentane injected. This was presumably due to loss of pentane vapo,r through the vesseljoints.
/ ~100 .~ 85 ~ 90
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75
15
2.5
3!5
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.Concentration of pentanein air, mole per cent FJ~um~ 2. Maximum explosion pressure/explosive mJxlurc composition for 05 I, and 4 I, bombs:. 0,5 I. bomb results, x 4 I. bomb r¢.',ulls,
February 19fi7
I~I:FE('TOF TI.]RI~.IILI~N('IiON GAS PIIASEEXPt.OSION PRIiSSUI,IEStN CLOSED VI~SELS
concentration slightly to the fuel-rich side of the stoichiometric mixture t2.56 mole per eenl). The measured pressures in the two bombs agree reasonably well except for the most explosive mixture where the 4 I. bomb pressures were higher. Figure 3 shows a comparison of the maximum explosion pressure in the 41. and 60 fl 3 vessels for all the inflammable air peillane mixtures. The exglosion pressures for 1he most explosive
19
mixtures agree well for the two vessels, but the measured pressures were considerably lower in the larger vessel for mixtures which were lean or rich in pentane. The effect of vessel size on rate of pressure rise is shown in Table I for a range ofair-pentane mixtures. Both average and maximum rates of pressure rise decreased with increase in vessel size for all the air- pentane mixtures.
TAIIIrI! ]. Effect of VeSSelSiR Off rates
0'5 I, re~sd
of
pressure rise
4 L I:essd
60 Sf~ t'essel
Cmu'entratiolt Arera;le Max, A~'era~le Max. Aeeragle Max. t ( pentatie rate of raw o]' rate o/ rate o] rate of rule of m air, prc,,~+~ure pre.~,~ure pressure pre,~sure pr¢.ssure pressure mole rise, rise, rise, rise. ri,~e, rise. per cent ib in" 1 sec" i Ih in - l .~ec- i tb in- ~ sec- i Ib in - ~ sec- i Ib in- z s e c ~ lh in- ~ sec- i .............................................................................................................
1.7 2"0 2'5 3'0
2 I00 3600 5001) 5400
4200 7000 I0500 12500
3,5
3300
8200
4,0
1000
25~
81)11 1400 2900 3300
2~ 3200 6600 7 :~,00
40 15(I 440 600
150 400 I I00 2000
2200
5 700
560
3400
2 200
200
800
¢.
Pressure calil~ation hnes
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700
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Pcessure cahbrafion tines
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___._L . . . . • ........ 15 2.0 25 30 35 40 45 ConcentralJ~'~ of pentane ;n a~r, mole p ~ ctm!
I:lcaJ~l 3. Maximum explosion pre,~pr¢/¢xpl(~,~iw: mixlur¢
composilion Ibr 4 1 banlb and 60 FP vcss¢!: ', 60 rP wssd, stationary g a s . , • 60 fl~ vt:ss¢l, lurbulem gas. -4 I. bomb. stationary gas; ~ data of Burgoyne atzd Wilson
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...........
S~. hlT~ m&fks FI(iI~Kli 4, [aJ Normal ~.'xp~osiorl trace; (b) vibratory ex. plosion trace
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20
All the experimentsin the small bombs and most of lhos: in the 60 ft"~ves,,d gave explosion pressure traces of the form shown in Figure 4tat, However, for a fairly well defined concenlration region (2.7 to 4.0 mole per cent pentanel in the 60 ft"~ vessel a peculiar type of explosion was observed. All ignitions in this region gave vibratory traces of the type illustrated in Figure 4lbh which made it difficult to measure the maximum pressure precisely, and the mixture burned with a prolonged screech instead of the normally silent combustion. The maximum rate of pressure ri~ for explosion in the 2.7 to 4.0 mole per cent region was parlicularly high and a plot of Ibis variable against concentration is shown in Figure 5. Instead of the normal curve with a maximum at about 3,0 mole per cent the maximum rate continues to increase rapidly until a concentration of 4.0 mole per cent is reached when vibratory explosions cease and the maximum rate falls sharply, 7" U ql
~4000
':" 3000
VOl, I I
complete range of explosive mixtures and the fan operating at 1560 roy/rain llhe maximum speed attainable in the early stages of the work) showed that the rates of pressure rise and maximum explosion pressure curves were of the same form as Ihose for the stationary gas mixtures with maxima in the curves at an explosive mixlurc containing 30 mole per cent pentane, An interesting feature of this work was that there were no vibratory explosions for any air pentane mixtures, and subsequent experiments showed that this was so even with very little turbulence (.ranspeeds of 500 rev/min), To reduce the experimental work to reasonable proportions the rest of the measurements were carried out with three standard explosive mixtures a lean mixture (I.70 mole per cent), a moderately explosive one 12"50mole per cent) and the most explosive mixture (3"0 mole per cenl). The effect c,f turbulence on the explosion pre~j,,.re charaeterislics of these mixtures was investng0,ted by running the fan at a range of speeds during the explosions. The results of the experiments with the 1'7 and 3.0 mole per cenl pentane in air mixtures are shown in Figures 6, 7 and 8. which are plots of turbulence as measured by fan speed against maximum explosion pressure, average and maximum rates of pressure rise. The results obtained with the
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,11
t'5 2'0 2 5 30 35 Conee~ratmn of pent,me it'l~lir, mole Ix'r ce'd FIGUnE 5. 60 fl :~ vessel, maximum rate of pre~,urc ris¢/ mixture ¢omposilion ._E eo:
(2) F,xperiraents with turbulent gas mixtures All this work was carried out in the 60 ft-~vessel and the 18 in, diameter fan was used to produce turbulence in the explosive mixture. An initial series of measurements carried out with the
:E 7O 0
tOO0 1500 2000 Fan spied, roy/rain
I:I(JORJ!6, 611fl ,~vc~l. t~.n speedmaximum pressure; ~ 3'0 molt I~r ¢~:ntpentane in air, 0 1"70 ino)~ I'~r cent pentun¢ in air
I!FFI!('T OF II:RIH,TIIN('Ii ON (I~.S PIIASE EXPLOSIONPRIESSURESIN (!I,OSED VESSELS
Fcbn'uary 1967
3o0o
o/
~- 20~0
0
5O0 IOO0 1 5 0 0 2000 Fan speed, tev/min
J:tc.itit~l: 7. 61) I't'~ VC'~',r,'l.fan sp~:cd/a~.eragt: rate t)f pressure ri:~¢; A ]'ll inolc per ~:cnl perilune in air, O 1'70 unohr per ¢~:nt pent;me in air 8000 &
7000
~6~0 C.
pooo ~.4000
____L
soo
lo'oo
.... 1_ 2OOO
Lran speed, rev/mln FIt;Uxti 8. 60 ft J ves~el. I'an specdlm;~Jtimum role of pn,'~,ur¢ rise; A 3,0 mole per e,:nt peman¢ in air, O 1.70 mole per cent t'rcntar~e in air
2"5 mole per cent pentane in air mixture are not shown in these figures, but were inlet'mediate in magnitude between those of the lean and most explosive mixtures.
21
Examination of Figures 6, 7 and 8 shows that increase in turbulence ouses a rapid increase in the rate of combustion, The average and maximum rates of pressure rise increase linearly with increase in fan speed, but Ihe effect of increase in turbulence on maximum explosion pressure is not quite so well defined. The measured values of the explosion pressure show a considerable scatter (see Figure 6) especially at the highest I~an speeds making it difficult Io decide on the precise value [or the maximum pressure at any given fan speed. However, the indications are that for the two more explosive mixtures 12.50 and 3.0 mole per cent pentane in air} maximum pressure increases slightly with fan speed to reach a maximum value. The maximum explosion pressure for the 1'70 mole per cent mixture which is near the lower inflammability limit, increases to a greater extent with fan speed increase, but this also reaches a maximum value. To complete the investigation of the effect of vessel size on maximum explosion pressure a few measurements were carried out for air--pentane mixlures richer than 3.0 mole per cent with the fan operating at the maximum speed (2000 rev/ rain) during the explosion. Maximum explosion pressure for these highly turbulent conditions is plotted against composition of air-.pentane mixture in Figure 3.
Discussion
Co.rparL~on of the results with literature dattl Burgoyne and Witson 3 carried out measuremerits of the explosion pressure characteristics of air pentan¢ mixturos in a 60 fta vessel with the same geometry as the vessel used in the present work, The two sets of resuhs are compared in Table 2 and Burgoyne and Wilson*s maximum explosion pressure results are also plotted on Figure 3, The agreement between the two sets of maximum explosion pressures is good for most air-pcntane mixtures and there is reasonable agreement between th= rates of pressure rise measurements. Where discrepancies exist they are probably due to mixture concentration effects. Burgoyne and Wilson used the same technique of explosive mixture preparation as used in the present work--vaporizing a known
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Vol. l I
IIARRIS
'[.*,1111 ..2.Comparison ¢)~rcsull.~ o1"prcsrnl work If)t1fl " ,¢essell with liurgo).ne and Wils,m's d~,ta
th, rgoy~,, .trd IVll~l,f.~ d,,ta Pe/Ilan¢ c , m ..
m,h" p,.r ~em
Ma.=;inlum pressure,
ib in ~ yaU~le
A rrrtgtc rak" O[ prc,~;~l,r'l,
R.u~llIl:i of I 'r~'~('tll ~tt'l,
3ftt'( fdh' ~J pr,..,s.qtre
rise.
rise. IbJrl 2~.ec.a Ihill "~',¢c i
20 2'3 2"7 3"0 3'25 YSO 4-0
93 108 113 I 17 122 110 106
154 257 3,13 404
4,3
I Io
227
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prl'ssllrg
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ri~e.
ri~e.
1611 340 561~ 580 59(t 550 21~t
4(10 ~(KJ 12511 2~X)0 261X) 36(X~. 700 2(10
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3~X) 750 I Ii)~l ~71XI 33110 371X) 3(~1 2g00
5t11
347 209
volume of pcntanc ,and mixing it with air in the vessel. They calculated thdr mixture concentration on the basis of volume of pentane injected and ~,esset volume without a regular analytical cheek. Pentane concentration cal. culated in this way in the present work was always greater than that determined by analysis. and the difference was most marked for the richer mixtures where more pentane was lost during the longer injection period. It is likely. therefore, thai Burgoyne and Wilson's mixtures were leaner than staled. This ,vould explain the most marked discrepancies in the maxim,m| pressure (Figure 31 and the dtfferences between
Ibitl :~ul I 1,='in ~,ec I
~5 1117 115 117 116 I t(t g5 69
40
Ihc maximum rates of pressure rise for the 4.0 and 4,3 mole per cenl mixtures (Table 2~. Various workers '~ '~ have noted thai turbulence causes an increase in the ra:es of pressure rise in an explosion but. due to the difl?=ully in specifying degree of turbulence in yes.Is of different shape and size. only Ihe results of B u r g o y n e ~lnd Wilson are comparable with the present investigation~ These workers operated a fall at a cot'lstant speed of 1420 rev:min in their fg) ft "~ vessel and varied Ihe lurbulenee by changing 1he filn diameter. Table 3 shows their resulls for a 2.7 mole per cenl pcntane in air mixture compared with the resalls of the present
T,ia~Ll!3, Comparisonof resullsof present work with Burgoyneand Wilson'sdala [or I~lrhulenlexplosivernixtur¢~ Results o/ presem work
Conditions
2"7mole
30 molep'er
per cenr
,,.tit tmx~ure
mixlure stationary
18 in, diam.
Oas
fan at 1420 rer/rain.
Data ~ I~urg,yne trod Wikof for 2.7 #z,le per cent nit ~ture 12 in, diam,
Slationgey /an
fan ~1 1420 rer;min.
18 in, diam.
/i,i.~
24 in. diam, JfltT nf
1420 I'(q'r)'BIIL 1420 rer/rain,
M a x , pres~re,
lb/in ~ 0a~¢ Time to max, presswe. see
Av. rate of pressuJ e rise. Ib In" 2 sec" t
I 15
0'23 500
122
13.060 2 ] 50
113 0-275
410
108 0"1 tO
tJ83
119 0'(k55
1583
0,053
225O
February 1967
EI-FECTof: "ftm,ULli~(~linN GASPlIhSEEXPLOSIONPRESSURESINCLOSEDVESSELS
investigalion with a 3.0 mole per cent mixture. Burgoyne and Wiison's results for the 18 in. diameter fan are lower than those obtained with the same diameter fan in this work. This is probably due to the slight difference in *h.~ explosive mixtures 13'0 mole per cent compared with 2.7 mole per cent) or to differences in the pitch of the fan blades producing a different degree of turbulence.
23
explosive mixtures in all three vessels are relatively short 10,021 to 0.25 sect. For the lean and very rich mixtures the times to maximum pressure in the small vessels are still relatively short, but much longer times (0,56 to 7,1 ,~ec) are required to attain maximum pressure in the 60 ft 3 vessel, II is likely that considerable heat loss through the vessel walls occurs during the long reaction
"F~IJI.J~4. Times 1o maximum pressure and flame velocities in ~he 0.5 i., 4 1 ;rod 60 it ~ vessels Ctmc perilune in air. nlole
0,5 I. i,essel 4 I. ces~el 60 fi J t'e.ssel ........................................................................................................................... T,m, to Areralte "l m e to Acera#¢ Time to Avera~le ,lax. pre~s., flat,e spt'ed, max, press., flame speed, ,lax, press~, flame speed,
per cefll
?/1'["
t:m/sec
.we
cmYsec
set:
cnl/se£'
1'5 1.7 20 2.3 2,5
0"081 0'O41 0027 0.023 0'022
617 123"4 '83.1 213.7 228'3
1) 1.15 0.099 (1.070 04)47 0.1~40
74'1 I01' I 142.g 214,5 250.0
7/2 1'63 0.567 0,315 0,254
988 43.2 124.1 223,3 277'0
2,8 3'0 3'3 3'5 4.0 4'3
0021 0'021 0,0241 0,033 0090 0400
238,1 241,5 2.07.5 151.5 5.5.5 12'5
0-0364 0036 0,043 0.051 O.126 094
274.7 279 3 234.7 196,1 79.4 10'6
0,219 0,205 0,20L 0,204 0,85 160
321'2 343'2 350,0 344,8 82.8 44,0
&~lin~#up ejji,ets As shown in Figure 2 the maximum explosion pressures in the 0'5 I. and 4 1, bombs agree well for 10an mixtures, but the explosion pressures arc higher in the larger vessel for mixtures richer than about 2'30 mole per cent. This is in geueral agmtnem with Statham and Wbeeler 6. who found that the maximum explosion pressure re: the most explosive airu-mcthane mixtures increased with increase in vessel size until a volume of 4 I. was reached, when there was no further increase in maximum pressure. Figure 3 shows that for stationary gas mixtures in 1h¢ 4 I. and 60 ft~ vessels agreement between the maximum explosion pressure for the most explosive mixtures is good, but the pressures in the larger vessels are considerably lower than those in the 4 1. vessel for lean and very rich mixtures. "fable 4 shows that the times to reach maximum explosion pressure for the most
time. and so the maximum pressure will be lower for these mixtures in the lat~ge vessel. An attempt was made to calculate the magnitude of the effects of heat loss through the vessel walls, but this was not successful due to the lack of data on heat transfer coeflicients at high |¢mperatures (above 600°C) and the fact that there is no steady state between beat production in the reaction and heat loss through the vessel walls. In addition to its effect on maximum pressure the influence of vessel size on time to reach maximum pressure is of interest. For all the small bomb experiments and most of those in the 60 ft3 vessel pressure/time curves of the form shown in Figure 41a) were obtained, and for the region BC [see Figure 41a)] the equation P = at ~
fits this curve, where P denotes pressure
Yol, I 1 G , I j,. H,~auJs 24 inlcrfering with any pressure waves tr:|velling lib;in 2 ,gauge)at time t and a is constant. This indicates that the flame propagates spherically ahead of the flame front, from the central ignition point. Table 4 lisls the average flame speed fratlius li{]i'~'tof mrhuh,nce o~ exphJshm pres,ture Figure 3 shows thai .;1high degree of turbulence of vessel divided by time from ignition to maximum pressure) for a range of air pent,'tne cause.,, a slight increase in maximum explosion mixtures in all three vessels. As expected the pressure for the most explosi,,c mixtures and a most explosive mixtures give the highest flame more m=trked increase for the lean and very rich mixl ures, The times from apparent ignition speeds. However. for mixtures with concentralions leaner than about 2'25 mole per cent fl,'|me Io maximum pressure for stationary and turspeeds decrease with increase in vessel size. bulent ~ts mixtures in the ¢~0 fr~ vessel and for while the opposite effect occurs for the richer stationary gas mixlur¢; in lhe 4 I. bomb are shown in "l'ublc 5. mixtures. Some explanation for these observed effects is provided by the work of Agnew and GraitF. fAat~ 5 firn¢., fret] ,ipp:trenl ignilion to who measured the flame speeds of a number o~ illil~,illlt.llll prc',',ur¢, set" air-Lhydrocarbonmixtures ignited at the cent re of a spherical bomb. They found that for le~n mixtures the flame accelerated initially and t",m' ~!j' 4 / hoolb, t~lJff3 re.~d. ~)Jt ~ ve.~sel, ])L'HIdAIP' ht ,lit. "~hlflvp?hir~ 'daHollOry IlirhlllFff( ~]/15. then reached a constant velocity which deBIrJ[t" I~'~' t i'/1! ,ttJ, Otl~ ]~Itt al 200) creased again as the flame approached the vessel rev/min walls. The more rapidly burning mixtures behaved in the same way except that after the 1.7 009') I fi3 0072 period of constant velocity the flame accelerated 21) 0117(I 0'567 2"5 0i}40 t1254 (11145 again. Thus it appears that in large vessels near 2.8 0036 0219 inflammability limit (less than about 2.25 mole 3.0 (9I)36 0 205 0045 per cent pentane in air) flames tend to die away. 33 01143 o201 while those for more rapidty burning mixtures 36 01156 0.2t2 0.052 40 O126 q185 accelerate. The concentration range of mixtures which give accelerating flames corresponds reasonably closely with that giving vibratory or screeching in the stationary gas experiments in the 60 fi3 explosions [see Figure 4tb)] and there is litlle vessel the times to maximum pressure were doubt that the two effects are related. These considerably longer than those in the 4 I. bomb, vibratory explosions have been observed by a and hence there was considerable heat loss number of workers, but only in large vessels. through the vessel walls and a consequent Markstein s found that vibratory explosions decrease in the maximum explosion pressure in were associated with a cellular flame structure the large vessel, As shown in Table 5 the times which would give a flame front of increased to maximum pressure are much shorter under surface area and a consequent increase in turbulent conditions, heat loss through the burning velocity. The explanation for this effect walls is less and maximum explosion pressure is not known, but it is possible that pressure is therefore higher. waves travelling ahead of the flame are reflected The times to m,'tximum explosion pressure from the vessel walls and cause distortion of the under turbulent conditions in the 60 fl~ vessel flame front and consequent acceleration in ~'. are comparable with those for stationary mixsimilar manner to the build up to a detonatior, tures in the 4 I. bomb and any heat losses due to in a long pipe, The fact that no vibratory exlength of reaction time will be of the same order plosions were observed when the fan was for these two systems. Thus surface area/volume operating during the explosion could be ex- ratio will now become the controlling factor for plained by the turbulence produ,:ed by the fan the relative heat losses from the two vessels.
Febrttary 1%7
I~FFECTo f II!RBUI.I!N['I! IIIN GAS PHASE liXPLI[ISlONPRI;,SSURI~.SIN CLOSI!D VESSIJLS
Since the smaller vessel has the higher surface area/volume ratio the heat losses through its walls are grealer, and the maximum pressure will be lower in this vessel as shown by the experimental results in Figure 3. There is only a certain amount of energy in any given explosive mixture and increase in the turbulence apparently causes it to be released more quickly with a consequent increase in maximum pressure (because of decreased heat iossesl, l-|owever, there should be a limit to this process, where reaction lime is so short that heat losses are negligible, As shown in Figure 6 this limit seems to have been reached at least for the 1.70 mole per cent mixlure, A logical development of this increase in the rate of eneff:y release with increase in ~urbulence is the back mixing of the unburnt mixture with burnt gas, Thi~ would result in a quenching of the flame and a consequent decrease in the explosion pressure. This situation did not occur with the maximmn turbulence which could be produced in the 60 ft3 vessel, while the small bombs were not fitted with any device to produce turbulence.
Nature ~'the turbulelree in tl~e60 ji ~ ~t,,~,~el There is no completely satisfactory method of defining the degree of turbulence in a particular vessel so that it can be related to that existing in other vessels of different size and geometry. One simple turbulence parameter is Reynolds number, and it was possible to calculate that this varied between 3000000 and 12000000 for fan speeds of S00 to 2000 roy/rain in the 60 ft ~ vessel. Thus in terms of this parameter highly turbulent conditions exist inside the large vessel, A few measurements were carried out with a very sensitive pressure transducer suspended at various points inside the vessel, These experiments showed that degree of turbulence as measured by the root mean square of the amplitude of the pressure fluctuations recorded
3"5
by the transducer increased linearly with increase in fan speed. The nature of the gas circulation in the large vessel was shown to be as indicated in Figure ! with a large turbule in each half of the vessel and little turbulence at the centre and near the vessel walls. Biggs and Swift~ showed that the maximum explosion pressure of airr gasoline mixtures in cylindrical pipes increased with increase in linear velocity of the gas. It is possible, therefore, that actual gas flow rate in a turbulent explosive mi;~ture is the factor which controls ils explo:~ion pressure characteristics. According to the manufacturers of the tim used in the present work the rate of gas circulation produced by it was directly proportional to shaft speed and equal to 1250 to 5 000 ft~/min for speeds of 500 to 2000 roy/rain, Though it is difficult to relate this rate to conditions in vessels of different size and geometry to lhe 60 ft~ vessel, it does give some indication of the conditions under which lhe experimental da;a were obtained,
(Retvired May 1066; amen&d June !966) References C~;usl.,,,:s,I!. W. ~md CoI Iox, P. E. ('&,m~ EngrJg,~ , 133 11951) 2 (,i;llJt,,tAii:, I', A ~ll]~JSJkl,~ltlSO~, W, A. 'All im¢,',ligiltion
O1 exphs',ion relict',, in indu~,lrial drying t;'~,ren% ' I~'~lrt,, I and tl, ~ia~ Council Be~. ('ommtm. Nm, G(' 2J (1~)55~and GC4.¢ 11957) ltt!Rclo't~l:. J. |:1. und WIi,.'9"IN, M. J. (~, htstitufitm Of Chemic'a! l".n.~ha,ers S~'mp~J.~tlmt Op! Ctlettlh'al Pro~'e,~ Ila-a~'¢ls. Mam'hesler, 19611 and Wll.~it~,N,M, J, (i, Jail.I). llte~Js. University of London (1954) "'I'II,',I~.N. H, and I|,~1(;, J..v,~#].i,.Min. Res. Rcp. No. II il9501 "nl(J(i~. R. It, ;rod SWll:l. R. l). Nttt. Gas Turh. F..~t.Rep. No, :25 (1958) " SIAIIIA,'~, J, ~lnd WHI:I;I.I'R, R. V, .~;aL.L-Mhs, Re,s, Pap. No. 5 t 19241 ~' h(i";I;W. J. T. uild (]ttAIFE. L, B, Cr.plhu~;liorl d .l"hlttle, ~, 209(1961) s M~,I~KS'O!J.~,CJ. It. Fourth S,vmpositt, I (InfernutJonul) ~m (',mh,stmn, p 49. Williams ~nd Wilkin~: Ilaltimore ( 1953~
Introductiuu Fog some time it has been standard practice to attempt to limit the pressure in gas phase explosions in chemical plants by the use of vents, The provision of such vents requires a knowledge of the ¢xplosibility of the inflammable mixture under consideration and the strength of the vessel to be vented.Though it is relatively easy to carry out the necessary measurements or maximum explosion pressure and rate of pressure rise in small closed vessels, there is little information on the scaling-up of these measurements to large vessels and no reliable method of designing explosion vents for plant vessels from these data. Cousins and Cotton t carried out experiments on the ventingof mixturesof known explosibility (air-hydrogen and air--propane)in Four vessels with a range of shapes and sizes, but did not investigate the effect of turbulence on the measured explosion pressure. Cubbage and Siremends ~ made a thorough investigation of the venting of towns' gas-air explosions in drying ovens, Their data apply only to the venting of the relativelyweak structures of the ovens, where the explosion pressure must be limited to a low value and a large vent is. therefore, required, Burgoyne and Wilson3 investigated air-pentane explosions in pressure vessels argo and 200 ft~
capacity and showed that turbulence produced by operating a fan during the explosion caused a considerable increasein the maximum pressure produced in a vented explosion. The present investigation was carried out to provide data for the design of vents for relatively strong vessels, The initial stage of the work was carried out in closed vesselsand the effectsof scaling.up on maximum explosion pressure and rates of pressure rise were investigated, The second part of the work concerned the venting of explosions in a large vessel and wi;i be pub. lished shortly. Experimental Throe closed vessels with capacities of 0.5 1., 4 I. and 60 ft~were used in this stage ofthe work. The 60 ft3 vessel is illustrated in Figure 1. It was a cylinder with dished ends so that it had a nearly spherical shape and was ,4 ft 6 in. in diameter and 4 Ft 9 in. in overall length. On one end of the vessel was a 24 in. diameter neck, which was blanked off For the dosed vessel measurements. To produce turbulence in this vessel a four bladed 18 in. diameter fan was mounted with the centre of the blades 10 in, above the centre of the vessel.The blades were surrounded by a 10 in, deep cylindrical casing and the fan was driven by a 1 h.p. motor 17
Vol. II
(L I'. t'. flhRttlS
through a variable speed gearbox so Ihal speeds up to 2000 rev/min could be obtained. The 0.5 Land 4 I, bombs were botlt spherical in shape and were not fitted with vents or with any means of producing turbulence. The combustible substance used in all this work was pentane. In the small ves~l experiments air penlane mixtures were produced by a conlinuous flow melhod. 11 OtanO
ii
i
//'" '"*L,
,~r -~
,'
~
' :
,.f ~
; :
'
// "''+*+
II ~"~. II IL,~ "+~J,I ,
k
't
Rex.Its
,t Pyrolt~aJt 4 :['
~,
i
!Wa. '00~
/
",
\ -
o,a ¢~
Ir-~qF.,4 L,
| 31;, ~'
le,~
All lhe explosive mixtures in the closed vessel experiments were ignited at the centre of the vessel since this is the ignition position giving the highest value of the explosion pressure. Ignition was produced by melting a short length or fine wire by passing a high energy pulse through it. The pressures developed in the explosion were measured by capacitance transducers and recorded on a two-channel oscillograph. The average and maximum rates of pressure rise were also delermincd for each explosion,
-4~t-9~
,:I "]
.....
ur,,t
coaxObs~r~r compressor
Gas ¢lfeu~d~
i I I Experiments with .~tationary #as mixtures The maximum explosion pressure and rules of pressure rise were measured for the complete range of inflammable air-pentane mixtures in all three yes,Is and Figure 2 shows a plot of explosion pressure against concentration of pentane in air for the 0.5 I, and 4 I. bombs. As is usual there is a maximum in the explosion pressure curves for both vessels al a pentanc 1201
Fa(aJRl~ I. 60 fl+vessd
Air was saturated with pentane vapour at 0~C and then diluted with excess air in a mixing vessel to give the desired proportions of air and pentane, The explosive mixture was passed through the bomb until about ten changes of volume had taken place. This mixing technique was not practicable for the 60 fx3 vessel work and the air-pentane mixtures were produced by spraying a measured volume of pentane into the vessel with the fan operating at full speed. In both large and small scale experiments ~mples were taken from the bomb and analysed to determine the actual concentration of pentane in air. In the 60 ft3 vessel the analytical measure. merits showed that the vessel was filled with a homogeneous inflammable mixture, The pentane concentration determined by analysis was always less than that calculated on the basis of vessel volume and amount of pentane injected. This was presumably due to loss of pentane vapo,r through the vesseljoints.
/ ~100 .~ 85 ~ 90
~ 8O
S+
"..i
i!i/.;
75
15
2.5
3!5
Lo
.Concentration of pentanein air, mole per cent FJ~um~ 2. Maximum explosion pressure/explosive mJxlurc composition for 05 I, and 4 I, bombs:. 0,5 I. bomb results, x 4 I. bomb r¢.',ulls,
February 19fi7
I~I:FE('TOF TI.]RI~.IILI~N('IiON GAS PIIASEEXPt.OSION PRIiSSUI,IEStN CLOSED VI~SELS
concentration slightly to the fuel-rich side of the stoichiometric mixture t2.56 mole per eenl). The measured pressures in the two bombs agree reasonably well except for the most explosive mixture where the 4 I. bomb pressures were higher. Figure 3 shows a comparison of the maximum explosion pressure in the 41. and 60 fl 3 vessels for all the inflammable air peillane mixtures. The exglosion pressures for 1he most explosive
19
mixtures agree well for the two vessels, but the measured pressures were considerably lower in the larger vessel for mixtures which were lean or rich in pentane. The effect of vessel size on rate of pressure rise is shown in Table I for a range ofair-pentane mixtures. Both average and maximum rates of pressure rise decreased with increase in vessel size for all the air- pentane mixtures.
TAIIIrI! ]. Effect of VeSSelSiR Off rates
0'5 I, re~sd
of
pressure rise
4 L I:essd
60 Sf~ t'essel
Cmu'entratiolt Arera;le Max, A~'era~le Max. Aeeragle Max. t ( pentatie rate of raw o]' rate o/ rate o] rate of rule of m air, prc,,~+~ure pre.~,~ure pressure pre,~sure pr¢.ssure pressure mole rise, rise, rise, rise. ri,~e, rise. per cent ib in" 1 sec" i Ih in - l .~ec- i tb in- ~ sec- i Ib in - ~ sec- i Ib in- z s e c ~ lh in- ~ sec- i .............................................................................................................
1.7 2"0 2'5 3'0
2 I00 3600 5001) 5400
4200 7000 I0500 12500
3,5
3300
8200
4,0
1000
25~
81)11 1400 2900 3300
2~ 3200 6600 7 :~,00
40 15(I 440 600
150 400 I I00 2000
2200
5 700
560
3400
2 200
200
800
¢.
Pressure calil~ation hnes
--(,sJ
~1~
~
700
lIC
. ......
'
"
//. ,/'
~.
"% •
"x
~.- .--Lifo...]
.................
,
125 ..4
\
V~Osec
hme
marks
Pcessure cahbrafion tines
8C 4,
.
E 7(
5(
___._L . . . . • ........ 15 2.0 25 30 35 40 45 ConcentralJ~'~ of pentane ;n a~r, mole p ~ ctm!
I:lcaJ~l 3. Maximum explosion pre,~pr¢/¢xpl(~,~iw: mixlur¢
composilion Ibr 4 1 banlb and 60 FP vcss¢!: ', 60 rP wssd, stationary g a s . , • 60 fl~ vt:ss¢l, lurbulem gas. -4 I. bomb. stationary gas; ~ data of Burgoyne atzd Wilson
.............
~;~,O.
125 -
...........
S~. hlT~ m&fks FI(iI~Kli 4, [aJ Normal ~.'xp~osiorl trace; (b) vibratory ex. plosion trace
,r;, I, I'. ilAIIIIIS
20
All the experimentsin the small bombs and most of lhos: in the 60 ft"~ves,,d gave explosion pressure traces of the form shown in Figure 4tat, However, for a fairly well defined concenlration region (2.7 to 4.0 mole per cent pentanel in the 60 ft"~ vessel a peculiar type of explosion was observed. All ignitions in this region gave vibratory traces of the type illustrated in Figure 4lbh which made it difficult to measure the maximum pressure precisely, and the mixture burned with a prolonged screech instead of the normally silent combustion. The maximum rate of pressure ri~ for explosion in the 2.7 to 4.0 mole per cent region was parlicularly high and a plot of Ibis variable against concentration is shown in Figure 5. Instead of the normal curve with a maximum at about 3,0 mole per cent the maximum rate continues to increase rapidly until a concentration of 4.0 mole per cent is reached when vibratory explosions cease and the maximum rate falls sharply, 7" U ql
~4000
':" 3000
VOl, I I
complete range of explosive mixtures and the fan operating at 1560 roy/rain llhe maximum speed attainable in the early stages of the work) showed that the rates of pressure rise and maximum explosion pressure curves were of the same form as Ihose for the stationary gas mixtures with maxima in the curves at an explosive mixlurc containing 30 mole per cent pentane, An interesting feature of this work was that there were no vibratory explosions for any air pentane mixtures, and subsequent experiments showed that this was so even with very little turbulence (.ranspeeds of 500 rev/min), To reduce the experimental work to reasonable proportions the rest of the measurements were carried out with three standard explosive mixtures a lean mixture (I.70 mole per cent), a moderately explosive one 12"50mole per cent) and the most explosive mixture (3"0 mole per cenl). The effect c,f turbulence on the explosion pre~j,,.re charaeterislics of these mixtures was investng0,ted by running the fan at a range of speeds during the explosions. The results of the experiments with the 1'7 and 3.0 mole per cenl pentane in air mixtures are shown in Figures 6, 7 and 8. which are plots of turbulence as measured by fan speed against maximum explosion pressure, average and maximum rates of pressure rise. The results obtained with the
I/I
l
"5 ¢.
,11
t'5 2'0 2 5 30 35 Conee~ratmn of pent,me it'l~lir, mole Ix'r ce'd FIGUnE 5. 60 fl :~ vessel, maximum rate of pre~,urc ris¢/ mixture ¢omposilion ._E eo:
(2) F,xperiraents with turbulent gas mixtures All this work was carried out in the 60 ft-~vessel and the 18 in, diameter fan was used to produce turbulence in the explosive mixture. An initial series of measurements carried out with the
:E 7O 0
tOO0 1500 2000 Fan spied, roy/rain
I:I(JORJ!6, 611fl ,~vc~l. t~.n speedmaximum pressure; ~ 3'0 molt I~r ¢~:ntpentane in air, 0 1"70 ino)~ I'~r cent pentun¢ in air
I!FFI!('T OF II:RIH,TIIN('Ii ON (I~.S PIIASE EXPLOSIONPRIESSURESIN (!I,OSED VESSELS
Fcbn'uary 1967
3o0o
o/
~- 20~0
0
5O0 IOO0 1 5 0 0 2000 Fan speed, tev/min
J:tc.itit~l: 7. 61) I't'~ VC'~',r,'l.fan sp~:cd/a~.eragt: rate t)f pressure ri:~¢; A ]'ll inolc per ~:cnl perilune in air, O 1'70 unohr per ¢~:nt pent;me in air 8000 &
7000
~6~0 C.
pooo ~.4000
____L
soo
lo'oo
.... 1_ 2OOO
Lran speed, rev/mln FIt;Uxti 8. 60 ft J ves~el. I'an specdlm;~Jtimum role of pn,'~,ur¢ rise; A 3,0 mole per e,:nt peman¢ in air, O 1.70 mole per cent t'rcntar~e in air
2"5 mole per cent pentane in air mixture are not shown in these figures, but were inlet'mediate in magnitude between those of the lean and most explosive mixtures.
21
Examination of Figures 6, 7 and 8 shows that increase in turbulence ouses a rapid increase in the rate of combustion, The average and maximum rates of pressure rise increase linearly with increase in fan speed, but Ihe effect of increase in turbulence on maximum explosion pressure is not quite so well defined. The measured values of the explosion pressure show a considerable scatter (see Figure 6) especially at the highest I~an speeds making it difficult Io decide on the precise value [or the maximum pressure at any given fan speed. However, the indications are that for the two more explosive mixtures 12.50 and 3.0 mole per cent pentane in air} maximum pressure increases slightly with fan speed to reach a maximum value. The maximum explosion pressure for the 1'70 mole per cent mixture which is near the lower inflammability limit, increases to a greater extent with fan speed increase, but this also reaches a maximum value. To complete the investigation of the effect of vessel size on maximum explosion pressure a few measurements were carried out for air--pentane mixlures richer than 3.0 mole per cent with the fan operating at the maximum speed (2000 rev/ rain) during the explosion. Maximum explosion pressure for these highly turbulent conditions is plotted against composition of air-.pentane mixture in Figure 3.
Discussion
Co.rparL~on of the results with literature dattl Burgoyne and Witson 3 carried out measuremerits of the explosion pressure characteristics of air pentan¢ mixturos in a 60 fta vessel with the same geometry as the vessel used in the present work, The two sets of resuhs are compared in Table 2 and Burgoyne and Wilson*s maximum explosion pressure results are also plotted on Figure 3, The agreement between the two sets of maximum explosion pressures is good for most air-pcntane mixtures and there is reasonable agreement between th= rates of pressure rise measurements. Where discrepancies exist they are probably due to mixture concentration effects. Burgoyne and Wilson used the same technique of explosive mixture preparation as used in the present work--vaporizing a known
(;.
I . I',
Vol. l I
IIARRIS
'[.*,1111 ..2.Comparison ¢)~rcsull.~ o1"prcsrnl work If)t1fl " ,¢essell with liurgo).ne and Wils,m's d~,ta
th, rgoy~,, .trd IVll~l,f.~ d,,ta Pe/Ilan¢ c , m ..
m,h" p,.r ~em
Ma.=;inlum pressure,
ib in ~ yaU~le
A rrrtgtc rak" O[ prc,~;~l,r'l,
R.u~llIl:i of I 'r~'~('tll ~tt'l,
3ftt'( fdh' ~J pr,..,s.qtre
rise.
rise. IbJrl 2~.ec.a Ihill "~',¢c i
20 2'3 2"7 3"0 3'25 YSO 4-0
93 108 113 I 17 122 110 106
154 257 3,13 404
4,3
I Io
227
A1'¢r~I~¢c,
,q,~a~:.
,~l/te Of
pr¢.',sur¢,
i",.l[lJ ,!~ p~'e~Url'
prl'ssllrg
Ih hizqau~/e
ri~e.
ri~e.
1611 340 561~ 580 59(t 550 21~t
4(10 ~(KJ 12511 2~X)0 261X) 36(X~. 700 2(10
,I,/(/Ji/',IIIB/
3~X) 750 I Ii)~l ~71XI 33110 371X) 3(~1 2g00
5t11
347 209
volume of pcntanc ,and mixing it with air in the vessel. They calculated thdr mixture concentration on the basis of volume of pentane injected and ~,esset volume without a regular analytical cheek. Pentane concentration cal. culated in this way in the present work was always greater than that determined by analysis. and the difference was most marked for the richer mixtures where more pentane was lost during the longer injection period. It is likely. therefore, thai Burgoyne and Wilson's mixtures were leaner than staled. This ,vould explain the most marked discrepancies in the maxim,m| pressure (Figure 31 and the dtfferences between
Ibitl :~ul I 1,='in ~,ec I
~5 1117 115 117 116 I t(t g5 69
40
Ihc maximum rates of pressure rise for the 4.0 and 4,3 mole per cenl mixtures (Table 2~. Various workers '~ '~ have noted thai turbulence causes an increase in the ra:es of pressure rise in an explosion but. due to the difl?=ully in specifying degree of turbulence in yes.Is of different shape and size. only Ihe results of B u r g o y n e ~lnd Wilson are comparable with the present investigation~ These workers operated a fall at a cot'lstant speed of 1420 rev:min in their fg) ft "~ vessel and varied Ihe lurbulenee by changing 1he filn diameter. Table 3 shows their resulls for a 2.7 mole per cenl pcntane in air mixture compared with the resalls of the present
T,ia~Ll!3, Comparisonof resullsof present work with Burgoyneand Wilson'sdala [or I~lrhulenlexplosivernixtur¢~ Results o/ presem work
Conditions
2"7mole
30 molep'er
per cenr
,,.tit tmx~ure
mixlure stationary
18 in, diam.
Oas
fan at 1420 rer/rain.
Data ~ I~urg,yne trod Wikof for 2.7 #z,le per cent nit ~ture 12 in, diam,
Slationgey /an
fan ~1 1420 rer;min.
18 in, diam.
/i,i.~
24 in. diam, JfltT nf
1420 I'(q'r)'BIIL 1420 rer/rain,
M a x , pres~re,
lb/in ~ 0a~¢ Time to max, presswe. see
Av. rate of pressuJ e rise. Ib In" 2 sec" t
I 15
0'23 500
122
13.060 2 ] 50
113 0-275
410
108 0"1 tO
tJ83
119 0'(k55
1583
0,053
225O
February 1967
EI-FECTof: "ftm,ULli~(~linN GASPlIhSEEXPLOSIONPRESSURESINCLOSEDVESSELS
investigalion with a 3.0 mole per cent mixture. Burgoyne and Wiison's results for the 18 in. diameter fan are lower than those obtained with the same diameter fan in this work. This is probably due to the slight difference in *h.~ explosive mixtures 13'0 mole per cent compared with 2.7 mole per cent) or to differences in the pitch of the fan blades producing a different degree of turbulence.
23
explosive mixtures in all three vessels are relatively short 10,021 to 0.25 sect. For the lean and very rich mixtures the times to maximum pressure in the small vessels are still relatively short, but much longer times (0,56 to 7,1 ,~ec) are required to attain maximum pressure in the 60 ft 3 vessel, II is likely that considerable heat loss through the vessel walls occurs during the long reaction
"F~IJI.J~4. Times 1o maximum pressure and flame velocities in ~he 0.5 i., 4 1 ;rod 60 it ~ vessels Ctmc perilune in air. nlole
0,5 I. i,essel 4 I. ces~el 60 fi J t'e.ssel ........................................................................................................................... T,m, to Areralte "l m e to Acera#¢ Time to Avera~le ,lax. pre~s., flat,e spt'ed, max, press., flame speed, ,lax, press~, flame speed,
per cefll
?/1'["
t:m/sec
.we
cmYsec
set:
cnl/se£'
1'5 1.7 20 2.3 2,5
0"081 0'O41 0027 0.023 0'022
617 123"4 '83.1 213.7 228'3
1) 1.15 0.099 (1.070 04)47 0.1~40
74'1 I01' I 142.g 214,5 250.0
7/2 1'63 0.567 0,315 0,254
988 43.2 124.1 223,3 277'0
2,8 3'0 3'3 3'5 4.0 4'3
0021 0'021 0,0241 0,033 0090 0400
238,1 241,5 2.07.5 151.5 5.5.5 12'5
0-0364 0036 0,043 0.051 O.126 094
274.7 279 3 234.7 196,1 79.4 10'6
0,219 0,205 0,20L 0,204 0,85 160
321'2 343'2 350,0 344,8 82.8 44,0
&~lin~#up ejji,ets As shown in Figure 2 the maximum explosion pressures in the 0'5 I. and 4 1, bombs agree well for 10an mixtures, but the explosion pressures arc higher in the larger vessel for mixtures richer than about 2'30 mole per cent. This is in geueral agmtnem with Statham and Wbeeler 6. who found that the maximum explosion pressure re: the most explosive airu-mcthane mixtures increased with increase in vessel size until a volume of 4 I. was reached, when there was no further increase in maximum pressure. Figure 3 shows that for stationary gas mixtures in 1h¢ 4 I. and 60 ft~ vessels agreement between the maximum explosion pressure for the most explosive mixtures is good, but the pressures in the larger vessels are considerably lower than those in the 4 1. vessel for lean and very rich mixtures. "fable 4 shows that the times to reach maximum explosion pressure for the most
time. and so the maximum pressure will be lower for these mixtures in the lat~ge vessel. An attempt was made to calculate the magnitude of the effects of heat loss through the vessel walls, but this was not successful due to the lack of data on heat transfer coeflicients at high |¢mperatures (above 600°C) and the fact that there is no steady state between beat production in the reaction and heat loss through the vessel walls. In addition to its effect on maximum pressure the influence of vessel size on time to reach maximum pressure is of interest. For all the small bomb experiments and most of those in the 60 ft3 vessel pressure/time curves of the form shown in Figure 41a) were obtained, and for the region BC [see Figure 41a)] the equation P = at ~
fits this curve, where P denotes pressure
Yol, I 1 G , I j,. H,~auJs 24 inlcrfering with any pressure waves tr:|velling lib;in 2 ,gauge)at time t and a is constant. This indicates that the flame propagates spherically ahead of the flame front, from the central ignition point. Table 4 lisls the average flame speed fratlius li{]i'~'tof mrhuh,nce o~ exphJshm pres,ture Figure 3 shows thai .;1high degree of turbulence of vessel divided by time from ignition to maximum pressure) for a range of air pent,'tne cause.,, a slight increase in maximum explosion mixtures in all three vessels. As expected the pressure for the most explosi,,c mixtures and a most explosive mixtures give the highest flame more m=trked increase for the lean and very rich mixl ures, The times from apparent ignition speeds. However. for mixtures with concentralions leaner than about 2'25 mole per cent fl,'|me Io maximum pressure for stationary and turspeeds decrease with increase in vessel size. bulent ~ts mixtures in the ¢~0 fr~ vessel and for while the opposite effect occurs for the richer stationary gas mixlur¢; in lhe 4 I. bomb are shown in "l'ublc 5. mixtures. Some explanation for these observed effects is provided by the work of Agnew and GraitF. fAat~ 5 firn¢., fret] ,ipp:trenl ignilion to who measured the flame speeds of a number o~ illil~,illlt.llll prc',',ur¢, set" air-Lhydrocarbonmixtures ignited at the cent re of a spherical bomb. They found that for le~n mixtures the flame accelerated initially and t",m' ~!j' 4 / hoolb, t~lJff3 re.~d. ~)Jt ~ ve.~sel, ])L'HIdAIP' ht ,lit. "~hlflvp?hir~ 'daHollOry IlirhlllFff( ~]/15. then reached a constant velocity which deBIrJ[t" I~'~' t i'/1! ,ttJ, Otl~ ]~Itt al 200) creased again as the flame approached the vessel rev/min walls. The more rapidly burning mixtures behaved in the same way except that after the 1.7 009') I fi3 0072 period of constant velocity the flame accelerated 21) 0117(I 0'567 2"5 0i}40 t1254 (11145 again. Thus it appears that in large vessels near 2.8 0036 0219 inflammability limit (less than about 2.25 mole 3.0 (9I)36 0 205 0045 per cent pentane in air) flames tend to die away. 33 01143 o201 while those for more rapidty burning mixtures 36 01156 0.2t2 0.052 40 O126 q185 accelerate. The concentration range of mixtures which give accelerating flames corresponds reasonably closely with that giving vibratory or screeching in the stationary gas experiments in the 60 fi3 explosions [see Figure 4tb)] and there is litlle vessel the times to maximum pressure were doubt that the two effects are related. These considerably longer than those in the 4 I. bomb, vibratory explosions have been observed by a and hence there was considerable heat loss number of workers, but only in large vessels. through the vessel walls and a consequent Markstein s found that vibratory explosions decrease in the maximum explosion pressure in were associated with a cellular flame structure the large vessel, As shown in Table 5 the times which would give a flame front of increased to maximum pressure are much shorter under surface area and a consequent increase in turbulent conditions, heat loss through the burning velocity. The explanation for this effect walls is less and maximum explosion pressure is not known, but it is possible that pressure is therefore higher. waves travelling ahead of the flame are reflected The times to m,'tximum explosion pressure from the vessel walls and cause distortion of the under turbulent conditions in the 60 fl~ vessel flame front and consequent acceleration in ~'. are comparable with those for stationary mixsimilar manner to the build up to a detonatior, tures in the 4 I. bomb and any heat losses due to in a long pipe, The fact that no vibratory exlength of reaction time will be of the same order plosions were observed when the fan was for these two systems. Thus surface area/volume operating during the explosion could be ex- ratio will now become the controlling factor for plained by the turbulence produ,:ed by the fan the relative heat losses from the two vessels.
Febrttary 1%7
I~FFECTo f II!RBUI.I!N['I! IIIN GAS PHASE liXPLI[ISlONPRI;,SSURI~.SIN CLOSI!D VESSIJLS
Since the smaller vessel has the higher surface area/volume ratio the heat losses through its walls are grealer, and the maximum pressure will be lower in this vessel as shown by the experimental results in Figure 3. There is only a certain amount of energy in any given explosive mixture and increase in the turbulence apparently causes it to be released more quickly with a consequent increase in maximum pressure (because of decreased heat iossesl, l-|owever, there should be a limit to this process, where reaction lime is so short that heat losses are negligible, As shown in Figure 6 this limit seems to have been reached at least for the 1.70 mole per cent mixlure, A logical development of this increase in the rate of eneff:y release with increase in ~urbulence is the back mixing of the unburnt mixture with burnt gas, Thi~ would result in a quenching of the flame and a consequent decrease in the explosion pressure. This situation did not occur with the maximmn turbulence which could be produced in the 60 ft3 vessel, while the small bombs were not fitted with any device to produce turbulence.
Nature ~'the turbulelree in tl~e60 ji ~ ~t,,~,~el There is no completely satisfactory method of defining the degree of turbulence in a particular vessel so that it can be related to that existing in other vessels of different size and geometry. One simple turbulence parameter is Reynolds number, and it was possible to calculate that this varied between 3000000 and 12000000 for fan speeds of S00 to 2000 roy/rain in the 60 ft ~ vessel. Thus in terms of this parameter highly turbulent conditions exist inside the large vessel, A few measurements were carried out with a very sensitive pressure transducer suspended at various points inside the vessel, These experiments showed that degree of turbulence as measured by the root mean square of the amplitude of the pressure fluctuations recorded
3"5
by the transducer increased linearly with increase in fan speed. The nature of the gas circulation in the large vessel was shown to be as indicated in Figure ! with a large turbule in each half of the vessel and little turbulence at the centre and near the vessel walls. Biggs and Swift~ showed that the maximum explosion pressure of airr gasoline mixtures in cylindrical pipes increased with increase in linear velocity of the gas. It is possible, therefore, that actual gas flow rate in a turbulent explosive mi;~ture is the factor which controls ils explo:~ion pressure characteristics. According to the manufacturers of the tim used in the present work the rate of gas circulation produced by it was directly proportional to shaft speed and equal to 1250 to 5 000 ft~/min for speeds of 500 to 2000 roy/rain, Though it is difficult to relate this rate to conditions in vessels of different size and geometry to lhe 60 ft~ vessel, it does give some indication of the conditions under which lhe experimental da;a were obtained,
(Retvired May 1066; amen&d June !966) References C~;usl.,,,:s,I!. W. ~md CoI Iox, P. E. ('&,m~ EngrJg,~ , 133 11951) 2 (,i;llJt,,tAii:, I', A ~ll]~JSJkl,~ltlSO~, W, A. 'All im¢,',ligiltion
O1 exphs',ion relict',, in indu~,lrial drying t;'~,ren% ' I~'~lrt,, I and tl, ~ia~ Council Be~. ('ommtm. Nm, G(' 2J (1~)55~and GC4.¢ 11957) ltt!Rclo't~l:. J. |:1. und WIi,.'9"IN, M. J. (~, htstitufitm Of Chemic'a! l".n.~ha,ers S~'mp~J.~tlmt Op! Ctlettlh'al Pro~'e,~ Ila-a~'¢ls. Mam'hesler, 19611 and Wll.~it~,N,M, J, (i, Jail.I). llte~Js. University of London (1954) "'I'II,',I~.N. H, and I|,~1(;, J..v,~#].i,.Min. Res. Rcp. No. II il9501 "nl(J(i~. R. It, ;rod SWll:l. R. l). Nttt. Gas Turh. F..~t.Rep. No, :25 (1958) " SIAIIIA,'~, J, ~lnd WHI:I;I.I'R, R. V, .~;aL.L-Mhs, Re,s, Pap. No. 5 t 19241 ~' h(i";I;W. J. T. uild (]ttAIFE. L, B, Cr.plhu~;liorl d .l"hlttle, ~, 209(1961) s M~,I~KS'O!J.~,CJ. It. Fourth S,vmpositt, I (InfernutJonul) ~m (',mh,stmn, p 49. Williams ~nd Wilkin~: Ilaltimore ( 1953~