Thermo-kinetic explosions: safety first or safety last?
TThermo-kinetic explosions: safety first or safety last ? Julyan H. E. Cartwright a,b, ∗ a Instituto Andaluz de Ciencias de la Tierra,CSIC–Universidad de Granada, 18100 Armilla, Granada, Spain b Instituto Carlos I de F´ısica Te´orica y Computacional,Universidad de Granada, 18071 Granada, SpainVersion of September 24, 2020
Abstract
Gas and vapour explosions have been involved in industrial accidents since thebeginnings of industry. A century ago, at 11:55 am on Friday 24th September1920, the petroleum barge
Warwick exploded in London’s docklands and sevenmen were killed. Understanding what happened when it blew up as it was beingrefurbished, and how to prevent similar explosions, involves chemistry plus fluidmechanics. I recount the 1920 accident as an example, together with the history ofthermo-kinetic explosions prior to 1920 and up to the present day, and I review thehistory and the actual state of the science of ignition. The science of explosionshas been aware of its societal implications from the beginning. Despite advancesin health and safety over the past century, is there still work to do?
One risk of using a public toilet in ancient Rome was of getting one’s bottom singed (orworse); methane explosions in sewers were known from classical times [1, 2, 3]. Minestoo have always accumulated inflammable gases, in particular firedamp (methane),which has caused explosions for as long as mining itself. So it is not surprising that itis in mining that we see the first research on preventing gas explosions.The 1812 disaster at Felling pit near Gateshead, where 92 men were killed through amethane explosion, was one of the stimuli for the invention of safety lamps to preventexplosions [4]. Humphry Davy and George Stephenson were two of the key figuresinvolved in developing safe miners’ lamps— the Davy lamp [5] and the Geordie lamp[6] respectively — designed to supersede the use of naked candle flames to illuminatemines. Davy’s lamp used a wire gauze to supply air; Stephenson’s Geordie lamp usednarrow tubes for the same purpose. (There was a somewhat squalid dispute betweenthe two men and their supporters over priority in the invention [4, 6].)1 a r X i v : . [ phy s i c s . pop - ph ] S e p umphry Davy had an assistant when working on the safety lamp. That wasMichael Faraday. Faraday later took over Davy’s position at the Royal Institution andwrote a beautiful book, The Chemical History of a Candle [7]. About mine explosions,he wrote that“In olden times the miner had to find his own candles, and it was supposedthat a small candle would not so soon set fire to the fire-damp in the coalmines as a large one ... They have been replaced since then by the steel-mill, and then by the Davy-lamp, and other safety-lamps of various kinds.”Early safety lamps were dimmer than candles and the gauze or tube did not completelyeliminate the risk of explosion, and improvements to the designs of miners’ safetylamps continued to be worked on throughout the 19th century [4, 8].As well as gases, inflammable vapours were likewise the cause of explosions.Thomas Graham, of Graham’s law fame, was one of those who investigated the loss ofthe paddle steamer Amazon in 1852. While the cause of the fire that led to 105 to 115deaths when she sank off the Isles of Scilly on her maiden voyage was never absolutelyestablished, Graham thought that the presence of volatile inflammable liquids in thestore room near to the engines was a key factor [9]:“The sudden and powerful burst of flame from the store-room, which oc-curred at the very outset of the conflagration, suggests strongly the inter-vention of a volatile combustible, such as turpentine, although the pres-ence of a tin can of that substance in the store-room appears to be leftuncertain. I find, upon trial, that the vapour given off by oil of turpentineis sufficiently dense, at a temperature somewhat below 100 ◦ , to make airexplosive upon the approach of a light. Any escape of turpentine fromthe heated store-room would therefore endanger a spread of flame by thevapour communicating with the lamps burning in the boiler room or evenwith the fires of the furnaces.”On 2nd October 1874, the Tilbury , a barge on the Regent’s Canal in London, ex-ploded killing its crew of four; it was carrying both barrels of petroleum and gunpow-der. The spot, at the edge of Regent’s Park under a bridge over the canal, is now called
Blow Up Bridge . It was lucky, as it were, that this happened at 5am, otherwise manymore people would have died [10, 11]. Frederick Abel, developer of guncotton andinventor of cordite, mentioned this example in a lecture “On Accidental Explosions”he gave at the Royal Institution in 1875 that was subsequently printed in Nature [12]:“Among other “accidents” referred to as arising from a similar cause, wasthe recent explosion of the powder-laden barge in the Regent’s Canal. Itwas established by a sound chain of circumstantial evidence that this ex-plosion must have been caused by the ignition, in the cabin of the barge, ofan explosive mixture of air and of the vapour of petroleum, derived from There is no difference between a gas and a vapour in terms of their fluid physics or chemistry; only interms of their thermodynamics. The different terms simply indicate that a gas is a substance found at thattemperature and pressure only in the single thermodynamic gaseous state, whereas a vapour is also found inits condensed phase at the same temperature and pressure.
Tilbury accident accelerated the passing of the Explosives Act in 1875, which inthe UK regulated the manufacture and carriage of dangerous substances.The industrializing world was demanding more and more chemical products. Thepetrochemical industry was, figuratively speaking, exploding. Abel returned to thetheme of accidental explosions a decade later for another lecture at the Royal Insti-tution in 1885, this time entitled “Accidental Explosions Produced by Non-ExplosiveLiquids”, in which he specifically discussed “accidents connected with the transport,storage, and use of volatile inflammable liquids which are receiving extensive applica-tion, chiefly as solvents and as illuminating agents” [13].Redwood wrote a very thorough report in 1894 on ‘the transport of petroleum inbulk’ [14] motivated by the explosion of the petroleum tank-steamship
Tancarville while being worked on in Newport, Wales in 1891, in which 5 men were killed. Red-wood comments“In a lecture delivered at the Royal Institution, on the 12th March, 1875,Sir Frederick Abel called attention to the special danger arising from theaccumulation of the vapour of petroleum spirit, or or the similar liquid,in unventilated places and referred to several cases of fire and explosionin illustration of his remarks, including one which occurred with coal-tarnaphtha in 1847. In a more recent lecture (on the 13th March, 1885) heenlarged upon this theme, and gave particulars of explosions due to theuse on board Her Majesty’s ships of paint-driers containing dangerouslyinflammable liquid hydrocarbons. For many years past Colonel Majendiehas briefly described in the Annual Reports of H.M. Inspectors of Explo-sives, the more noteworthy of the petroleum accidents which have takenplace during the preceding twelvemonths (although petroleum, not beingan explosive substance, does not come within the scope of the ExplosivesAct); and his reports constitute most valuable contributions to the literatureof the subject.”In his report Redwood lists many other similar incidents that give a depressinglitany even at this early date of the petrochemical industry.“These accidents arose from the incautious handling of a material whichwas not generally known to contain a liquid readily converted into vapour,and in that condition capable of forming a powerfully explosive mixturewith air”,he writes. Of the
Tancarville in particular he relates“The evidence given at the Board of Trade inquiry conclusively demon-strated that the accident was due to the ignition of an explosive mixtureof petroleum vapour and air in the ballast tank, but did not clear up thequestion of how the ignition took place. Samples of the petroleum wereexamined by Dr. Dupr´e and by the Author, with the result that it was ascer-tained that one gallon of such oil would render 200 cubic feet of air feebly,3nd, about 58 feet of air strongly, explosive; therefore 20 cubic feet of oilwould have sufficed to render the atmosphere of the water-ballast tank, thecapacity of which was about 6,000 cubic feet, explosive.”As we shall see, the 1920 accident was to be very similar in its origin. Just the yearbefore the accident that is our principal example, on 15th July 1919 there occurred theCardiff dockland disaster when the oil tanker
Roseleaf exploded, killing the 12 menworking on her. This was determined to be owing to a man carrying a naked flamedown into the ship.
Warwick , on24th September 1920
The Isle of Dogs, a tongue of land formed by a large curve of the River Thames ineast London, was once marshes but by the turn of the 20th century had become a greathub of industrial activity related to the river. Samuel Hodge & Sons, engineers andship repairers, had premises at Union Iron Works, 104 Westferry Road in Millwall,the Isle of Dogs, from the 1850s to the mid-1920s. The site of these works where theaccident that killed 7 men occurred is now part of a public park on the riverbank, theSir John McDougall Gardens. My grandfather, Charles James Cartwright (1882–1920)travelled across the river from Bermondsey to the Isle of Dogs every day. He workedas a welder at Samuel Hodge’s until his death in this accident alongside his brother,who was also killed, and his father-in-law, my great-grandfather, Thomas Tilling, whosurvived the explosion. The following account of the accident is taken from the reportwritten by G. Stevenson Taylor, Inspector of Factories [15].The
Warwick was a petroleum barge, designed to carry 42 000 gallons of petrol inits tank (Fig. 1a). It had last been used for that purpose from 17th to 20th September1920, before being sent for cleaning prior to work being carried out on it. On 22ndSeptember it was cleaned out by pumping out the remaining 19 gallons of petrol andmopping up the remainder with cotton rags. Then on 23rd September it underwentsteam cleaning by putting a steam hose into the tank. On the morning of 24th Septem-ber the barge was towed up the river from Purfleet where the cleaning had been carriedout to the Isle of Dogs. As it approached the wharf it could be seen from the bargethat a work party was ready to come aboard with acetylene torches; clearly they wereintending to get to work straight away, and this alarmed the lighterman (bargeman)on board. My great-grandfather “Tilling heard Lazell, the lighterman, tell James [theforeman] that, if they were going to use lights [i.e, flames] on the barge, he was off.”The barge was moored at 11:45.The idea was to remove the petrol tank from the barge to alter its bulkheads accord-ing to the latest regulations. For this, the first job was to fit lifting lugs onto the tank,which entailed removing rivets from the tank top with welding apparatus. As Taylor’sreport states“Charles Cartwright (deceased) was using an oxy-acetylene burner, andwith this he was seen to burn the heads from a number of rivets along thecentral joint in the tank top.” 4igure 1: Above: the design of the petroleum barge,
Warwick , showing its petrol tank;below: the remains of the
Warwick after the explosion. Taken from the accident report[15]. 5t 11:55, the barge exploded (Fig. 1b); “all the witnesses describe the explosion as ofgreat violence.” One of these witnesses was Thomas Tilling, who “was on the wharf atthe time of the explosion and was blown against a wall and slightly injured.”Let us continue with Taylor, who pieces together the facts of the matter in the bestdetective tradition.“The nature and extent of the damage to the tank and barge, as well asthe evidence of the witnesses, definitely indicate that a violent explosionoccurred within the tank itself and not in the surrounding spaces of thebarge. The fire, which lasted several minutes after the explosion, and theblackening of parts of the interior of the tank by a slight sooty deposit, aswell as the general nature of the damage indicate that the explosion wasdue to the ignition of some carbonaceous material (gas or vapour)”wrote Taylor.“The only hole which was burnt through the plate by the oxy-acetyleneburner was a small one, which was not finished at the time of the explo-sion.” “Acetylene gas may ... be dismissed as a possible source of theexplosion”; “it must .. be concluded that the combustible matter in thetank was present when the barge arrived at the wharf”and “the whole of the circumstances of the explosion are consistent with thetheory that it was caused by the ignition and subsequent explosion of amixture of petrol vapour and air in the tank.”Taylor pointed out that “no test of the atmosphere of the tank for petrol was madeafter the steaming”. He then performed the following calculation:“The quantity of petrol required to render the atmosphere of the tank ex-plosive can be readily ascertained. The tank has a capacity of 7,040 cubicfeet and the vapour of petrol of the quality carried in the tank is explosivewhen mixed with air in proportions from 1 1/2 to 6 per cent., and about 3per cent. of vapour or 210 cubic feet would produce a violently explosivemixture in the tank. One cubic foot of petrol produces about 147 cubicfeet of vapour at normal temperature and pressure, so that 1 1/2 cubic feetof petrol would produce over 210 cubic feet of vapour. The total area ofthe interior surface of the tank and bulkheads is over 3,200 square feet,so that an extremely thin film of petrol remaining on the whole interiorsurface would produce explosive conditions when vapourised. Even a filmless than 1/450th of an inch in thickness on the bottom alone would be suf-ficient to produce such conditions, whilst 1 1/2 cubic feet of liquid couldeasily be disposed in and around the various angle and plate joints”.Taylor’s findings were clear and unequivocal:6Having reached the conclusion that the tank contained a mixture of petrolvapour and air on its arrival at Messrs. Hodge’s wharf, the source of theignition is not difficult to trace in the light of subsequent events. It is clearfrom the evidence of several witnesses that an oxy-acetylene burner wasused to remove rivet heads on the outside of the tank, and that just whenthe burner was being used to burn a hole in the plate of the tank top, theexplosion occurred. An examination of the damaged tank confirms thisevidence in every respect and shows that the explosion took place as soonas the flame of the burner penetrated the plate.”Taylor laid the responsibility with the barge owners:“I consider that adequate precautions were not taken by the owners of thebarge to ensure that the tank was free from petrol vapour before handingher over for repairs”.It turned out, Taylor found, that other barges of the same type had previously beentaken to Hodge’s for the same modifications to be carried out, after the same cleaningprocedure, and had not exploded. The difference in those previous cases was that thebarges had lain a day at the wharf before being worked on. That must inadvertentlyhave saved the men who had worked on them, as the remaining liquid would have havean extra day to evaporate, and the vapours would have had an extra day to dispersebefore work began.G. Stevenson Taylor was the first Senior Engineering Inspector in the newly formedEngineering Branch of the inspectorate of factories for the Home Office. Taylor hadbeen appointed in April 1920 and the Warwick explosion was his first report in thiscapacity [16]. Around this time there was a new drive for health and safety at work,both in Britain and beyond, with the slogan “safety first”. In 1917 the Industrial “SafetyFirst” Committee was established in Britain, and in 1918 the British Industrial SafetyFirst Association was formed [17]. Harold Lloyd’s 1923 film “Safety Last!”, famousfor the image of Lloyd dangling from the hands of a clock high on a skyscraper, playedwith the slogan. Ironically, Lloyd himself had lost a finger and thumb in an explosion:a 1919 filming accident with a fake bomb that wasn’t.
Despite
Safety First , despite the advance of both science and technology, an inflammablevapour– or gas–air mixture plus a source of ignition continued to cause accidents. After1920, such explosions have continued, even into recent decades. Just a few of these,that illustrate the variety of detailed causes of such accidents, are the following. On7th September 1951, a storage tank exploded at the Royal Edward Dock, Avonmouth,Bristol, while being filled with gas oil, and killed two men [18]. The Apollo 13 missionof April 1970, meant to be the third space mission to land on the moon, was abortedhalf way to the moon, and its crew was narrowly saved after an explosion aboard thespacecraft that occurred when stirring an oxygen tank for its fuel cells, which had beenincorrectly assembled leaving damaged electrical insulation on the wiring, which ig-nited [19]. The Clarkston explosion of October 1971 killed 22 people at a shopping7entre in Scotland when a gas leak ignited. The Flixborough disaster of 1974 was anexplosion at a chemical works that killed 28 people and “rattled the confidence of everychemical engineer in the country” [20] when a pipe joint in a poorly modified cyclo-hexane plant failed and the resulting gas cloud was ignited [21, 22, 23]. A fuel tankerexplosion of July 1978 in Los Alfaques, near Tarragona, Spain, killed 217 people whena tanker lorry carrying propene leaked gas which exploded on encountering an ignitionsource in a neighbouring seaside campsite.
Piper Alpha was an oil rig in the NorthSea that exploded in July 1988 killing 167 people working on it when methane hy-drate blocked a pump and another pump, partially dismantled for maintenance, leakedinflammable gas when mistakenly switched on to take its place [24]. Flight TWA800was a Boeing 747 aircraft that exploded in July 1996 minutes after taking off fromNew York killing its 230 passengers and crew. Its loss was determined to be owing toan explosion in its empty central fuel tank in which inflammable vapour was ignited bya short circuit in the electrical connections [25]. The Buncefield accident of December2005 at an oil storage facility in Hertfordshire killed no-one but caused an immenseexplosion and fire when a petrol tank was overfilled and a cloud of vapour from it wasignited [26]. The
Deepwater Horizon was an oil rig in the Gulf of Mexico that suffereda blowout of inflammable gas that was ignited probably by coming into contact withthe diesel generators on board [27]; 11 people died in that April 2010 explosion, and itproduced a huge oil spill that caused environmental devastation in the Gulf of Mexico.
An explosion is a rapid increase in volume. Whether or not a chemical reaction ina fluid leads to an explosion depends on the interaction between fluid mechanics andchemical reaction. We may call these explosions thermo-kinetic because, as we shallsee, the explosion — i.e., fast reaction — can result from self-heating (thermal) or fromthe chemical kinetics (chemical chain reaction) or from both factors.Combustion science [28] is now a field with some beautiful and elegant theory[29, 30], and experiments [31]. However, not everything is known. There are still areasin which more knowledge of the processes taking place is needed [32], as we shalldiscuss. It must also be noted that, as we have seen, the impact of thermal radiationfrom these explosions is a major factor in terms of human health, and this aspect is alsothe object of study [33, 34]. Combustion theory began to be developed in 1880s Francewhere Mallard and Le Chatelier worked on inflammability of gases; combustion andits application to mine safety [35]. They developed a laminar flame speed theory forthe rate of expansion of the flame front in a combustion reaction [36, 37]. At almostthe same time, van’t Hoff worked on autoignition of gases and suggested a criterion forwhen ignition would occur [38].Semenov and his student Frank-Kamenetskii took up these ideas in 1930s Russia.Semenov’s theory [39, 40] pertains to the case where convection is so vigorous thatthe temperature in the vessel is uniform; Frank-Kamenetskii’s [41, 42] covers the otherlimit where the transport of heat occurs by conduction only. For well-mixed systems,8he reacting gas explodes when the Semenov number exceeds a critical value, when ψ = k c n qE/ ( χS v RT ) is greater than /e . (Here k is the initial kinetic constant for first-order reaction A → B, c o is the initial concentration of species A, n is the order of the reaction, q is thereaction exothermicity, E is the activation energy, χ is the heat transfer coefficient, S v is the surface area per unit volume, R is the universal gas constant, T is the constantwall temperature.) When heat is transferred by thermal conduction alone, explosionoccurs when the Frank-Kamenetskii number is greater than a critical value, when δ = l k c n qE/ ( κρ C p RT ) is greater than δ c . (Here l is the reactor size, k is the initial kinetic constant for first-order reaction A → B, c is the initial concentration of species A, n is the reaction order, q is the reaction exothermicity, E is the activation energy, κ is the thermal diffusivity, ρ is the initial density, C p is the specific heat at constant pressure, R is the universalgas constant, T is the constant wall temperature. The critical value depends on thegeometry of the system; it is 3.32 for a sphere, 2.00 for a cylinder and 0.88 for parallelplates [42].) But in most reacting systems heat loss occurs due to the combined effectsof natural convection and heat conduction.In parallel to these works, fluid mechanics was developing. The equations for themovement of a fluid were written down in the early 19th century by Navier, Cauchy,Poisson, Saint Venant, and Stokes [43]. In the second half of the 20th century, withthe advent of the electronic computer it became possible to solve the Navier–Stokesequations numerically. Computational fluid dynamics, CFD, methods are now ubiq-uitous. One can couple these computational methods with the equations of chemicalkinetics to solve numerically how a reaction behaves in a fluid medium. Three physicalprocesses combine in a reacting flow: fluid dynamics, thermodynamics, and chemicalreaction. Each process has its own space- and timescales, which may be very differentfrom those of the other processes. Such differences of scales, on one hand, can allowsimplification of a theoretical model (but on the other hand, they can also be a sourceof numerical difficulties). The fluid dynamics is a balance between the temporal evo-lution and the spatial convection of the flow properties governed by the conservationof mass, momentum and energy. Reactive fluid thermodynamics includes microscopicheat transfer between gas molecules, work performed with pressure and associatedvolume change. And chemical reactions determine the generation and destruction ofchemical species while observing mass conservation.One application of the theory of chemically reactive flows is to mining, as its pio-neers had studied. We may note that both original types of miners’ safety lamps workbecause the mesh or tubes function as a flame arrestor. The metal absorbs heat from aflame front, so that the front decays and the flame dies. This mechanism depends criti-cally on the size of the tubes or the mesh. As well as mining, a further application, thistime one where explosions are wanted, but need to be controlled, is the internal com-bustion engine. An amount of work has been carried out under the heading of knock,or preignition, in the internal combustion engine [44, 28]. (It should be noted that thisis generally a two phase system, as droplets of fuel, not vapour are the reactant. It has9 Fig. 2. The regime diagram summarising simulations [3] without consumption of reactant ( RH (cid:87)(cid:87) / = 0), (cid:90)(cid:76)(cid:87)h (cid:404) (cid:81)(cid:82) e(cid:91)(cid:83)(cid:79)(cid:82)(cid:86)(cid:76)(cid:82)(cid:81) a(cid:81)d (cid:380) e(cid:91)(cid:83)(cid:79)(cid:82)(cid:86)(cid:76)(cid:82)(cid:81), f(cid:82)(cid:85) (cid:536) = 0.027, Pr = Le = 1, n = 1.4 and (cid:534) = 1.018. The horizontal axis denotes the well-mixed limit; the vertical axis represents the purely conductive limit. The solid and dotted lines, respectively, represent the explosion limit in the laminar and turbulent regimes. Figure 2: The regime diagram summarizing simulations without consumption of re-actant, with closed circles representing no explosion and open circles, explosion. τ H is the timescale for heating by reaction; τ C is the timescale for convection, τ D is thetimescale for diffusion. The horizontal axis then denotes the well-mixed limit; the ver-tical axis represents the purely conductive limit. The relative importance of thermalconduction and natural convection in the system is shown by the Rayleigh number Ra ;when Ra < , heat transfer is controlled by conduction; laminar convection dom-inates heat transfer for < Ra < ; for Ra > , the flow is turbulent. Theother solid and dotted lines, respectively, represent the explosion limit in the laminarand turbulent regimes. From [47].been argued that fuel involved in the Buncefield explosion, described above, may havebeen in the form of such a mist of droplets [45].) Knock in internal combustion engineshas been associated with cool flame formation, and cool flames resulting from complexthermo-kinetic interactions [46] in turn have been implicated in the TWA800 explosionmentioned above.Recent theoretical work in the last two decades, which takes the Semenov andFrank-Kamenetskii approaches and moves them forward, is by the group of Cardoso inCambridge. Following an approach first put forward by Cardoso et al. [49, 50], Liu etal. [47] proposed that in these systems the occurrence or not of an explosion dependson the relative magnitudes of three timescales: that for chemical reaction to heat upthe fluid to ignition, the timescale for thermal conduction and that for natural convec-tion. They summarized their results in a two-dimensional regime diagram, Fig. 2, inwhich Frank-Kamenetskii’s purely conductive system and Semenov’s well-mixed sys-tem appear as two limiting cases, represented by the two axes. The plane in betweenthe two axes contains all the systems with different relative magnitudes of heat loss byconduction and by natural convection. This approach has the advantage of quantifying10 Fig. 1. Schematic regime diagram with the three axes, (cid:11) (cid:12) CH (cid:87)(cid:87) / , (cid:11) (cid:12) DH (cid:87)(cid:87) / and (cid:11) (cid:12) RH (cid:87)(cid:87) / , for an exothermic reaction occurring inside a closed spherical vessel. The grey surface separates the inner region, where explosions occur, from the outer one, where they do not. Figure 3: Schematic regime diagram with the three axes, τ H /τ C , τ H /τ D and τ H /τ R ,for an exothermic reaction occurring inside a closed spherical vessel. τ H is thetimescale for heating by reaction; τ C is the timescale for convection, τ D is the timescalefor diffusion and τ R is the timescale for reaction. The grey surface separates the innerregion, where explosions occur, from the outer one, where they do not. From [48].separately the stabilizing effects of conduction and natural convection on an explosion.In a subsequent paper, they then extended the these ideas to explore how the con-sumption of reactant alters the onset of a thermal explosion [48]. They showed thatwhether or not a chemical reaction in a fluid leads to an explosion is shown to dependon four timescales: (1) that for the chemical reaction to heat up the fluid containing thereactants and products, τ H = ρ C p ∆ T s k c n q ,ρ being the initial density, C p the specific heat at constant pressure, k is the initialkinetic constant for first-order reaction A → B, c o is the initial concentration of speciesA, n is the order of the reaction, q is the reaction exothermicity, and ∆ T s = RT /E ( E being an activation energy) is a temperature increase scale; (2) for cooling by heatconduction or diffusion out of the system, τ D = l κ ,l being the reactor size and κ the thermal diffusivity; (3) for natural convection in thefluid, τ C = lU ,U being a characteristic velocity; and finally (4) for chemical reaction that uses up thereactant. τ R = 1 /k , his journal is © the Owner Societies 2014 Phys. Chem. Chem. Phys., , 23365--23378 | the temperature starts rising at the bottom of the vessel,accompanied by reactant depletion, and buoyancy is triggeredwithin the fluid. However, since the natural convection inten-sity is weaker (lower t H / t NC ), it takes longer for the hot regionto shift upwards than any of the cases examined so far. Theinversion of the flow at the centre occurs only at t = 4.93 s, alsolater than in cases I and II. Owing to the interaction betweenbuoyancy and forced convection the hot region expands furtherto both sides of the reactor where the cooling by di ff usion ofcolder species from the inlet stream is not so e ffi cient. Thisallows the fluid to heat up by reaction quite rapidly, leading toexplosion at t = 11.5 s.The behaviour of case V is shown in Fig. 8. In this case, sinceconvection is stronger than in previous cases, the hot regiontravels swiftly to the centre of the vessel and starts spreadingaway from the vertical axis. As heat is readily lost through thewalls, the temperature does not rise as high as for cases withweaker natural convection and, for the same reason, the reactant does not deplete as extensively as in cases II or IV. Thus, forcedconvection counterbalances the upward buoyant flow and reversesthe flow at the centre once again, at t = 5.90 s. The hot region ispushed downwards and closer to the walls, enhancing heat loss,and the temperature drops to a minimum at t = 10.0 s. Heating byreaction continues to occur at the bottom of the vessel, with thefeed of pure species A from the injected stream, and reheats thesystem ( t = 17.5 s). However, owing to strong buoyancy present inthe system, the heat is quickly lost to the surroundings and thefuel is replenished, completing the second oscillation of tempera-ture, concentration and flow at t = 23.5 s. The temperature andconcentration in the vessel continue to oscillate after thismoment, with decreasing amplitude, to become almost uni-dentifiable (Fig. 8). Yet, if one observes time points t = 23.5 sand t = 30.0 s, the di ff erence in the size of the hot region isindeed recognisable, being slightly larger in the latter.The evolution of temperature, concentration of A and flow fieldsfor case VI, with t H / t NC = 13.0, is shown in Fig. 9. This case showsan extremely quick development of buoyant flow, deforming thehot region into the v-shape in less than 5 seconds, and promotingimmediate heat loss through the walls. In fact, the reaction is sofast that a steady state is attained before t = 10.0 s.Fig. 10 compares the temporal evolution of the heat flowthrough the walls for cases II and IV to VI. This figure clearly Fig. 7
Evolution of the fields of (a) temperature, (b) reactant concentrationand (c) streamlines for case IV, with t D / t FC = 5.0, t H / t R = 0.05, t H / t D = 0.16and t H / t NC = 7.0. Fig. 8
Evolution of the fields of (a) temperature, (b) reactant concentrationand (c) streamlines for case V, with t D / t FC = 5.0, t H / t R = 0.05, t H / t D = 0.16and t H / t NC = 11.0. Fig. 9
Evolution of the fields of (a) temperature, (b) reactant concentrationand (c) streamlines for case VI, with t D / t FC = 5.0, t H / t R = 0.05, t H / t D = 0.16and t H / t NC = 13.0. Fig. 10
Evolution of heat fluxes through the wall of the vessel for case IV(dotted line), case II (solid line), case V (densely dashed line) and case VI(loosely dashed line). All cases are for reactions with t D / t FC = 5.0, t H / t R = 0.05and t H / t D = 0.16. PCCP Paper P ub li s h e d on S e p t e m b e r . D o w n l o a d e d by I n s tit u t o A nd a l u z d e C i e n c i a s d e l a T i e rr a (I A C T ) on / / : : P M . View Article Online
Figure 4: Numerical simulations with computational fluid dynamics of explosion in aspherical reactor with mixed convection; evolution of the fields of (a) temperature, (b)reactant concentration and (c) streamlines. The temperature starts rising at the bottomof the vessel, accompanied by reactant depletion, and buoyancy is triggered within thefluid. Owing to the interaction between buoyancy and forced convection the hot regionexpands further to both sides of the reactor where the cooling by diffusion of colderspecies from the inlet stream is not so efficient. This allows the fluid to heat up byreaction, leading to explosion at t = 11 . s. From [51]. k being the initial kinetic constant for first-order reaction A → B.The behaviour of the system can be depicted on a three-dimensional regime dia-gram, as shown in Fig. 3, where the three ratios of the four timescales are the coordi-nates. There is a surface separating the region near the origin where explosions occurfrom the region further from the origin where the stabilizing effects of heat conduction,natural convection and consumption of reactant prevent explosions. The vertical axis τ H /τ D represents the purely conductive limit ignoring depletion of reactant, i.e., thesystems considered by Frank-Kamenetskii. The right-hand axis, τ H /τ C gives the well-mixed limit of Semenov with no consumption of reactant. And the third, left-hand axis τ H /τ R measures the effect of the disappearance of reactant on the heating up of thefluid; for example, if the chemical reaction in effect depletes the reactant much fasterthan fluid is heating up (e.g., because the heat of reaction is very small), then τ H (cid:29) τ R and we expect the temperature rise in the fluid to be small and explosion not to occur.The synthesis of these two limits into one — thermal and kinetic effects into a thermo-kinetic theory — is a beautiful piece of theory, bridging and bringing together pointsoften seen as separate, but which really are not separate at all, as the figures show.The Cardoso group also performed numerical CFD simulations of the effects ofcombined natural and forced convection on thermal explosion in a spherical reactorwith upward natural convection from internal heating caused by a chemical reaction towhich they added downward forced convection driven by injecting fluid at the top andremoving it at the bottom of the reactor [52, 51]. They found oscillatory behaviour formoderate forced convection. They also found that that explosive behaviour is favoured12y a balance between the natural and forced flows, owing to a nearly stagnant zoneclose to the centre of the reactor that quickly heats up to explosion; Fig. 4. It is counter-intuitive that explosion may occur in an otherwise stable reactor by injecting cold fluidor enhancing natural convection.The foregoing theory is for a homogeneous mixture of reactants in a vessel with itswalls at constant temperature. One important aspect where theory has been inadequateand computational fluid dynamics needed is the deflagration to detonation transition[54]. In deflagration there is a subsonic flame propagation velocity and in the reactionzone, chemical combustion progresses through the medium by the diffusion of heatand mass. In contrast, in a detonation there is a supersonic flame propagation velocity,and the reaction zone is a shock wave where the reaction is initiated by compressiveheating caused by the shock wave. This regime has generally needed numerical simu-lations of computational fluid dynamics for its understanding. A general theory of thedeflagration-to-detonation transition (Fig. 5) has recently been presented together withan interesting astrophysical application to the explosion of stars. Poludnenko et al showthat thermonuclear combustion waves in type Ia supernovae are qualitatively similar tochemical combustion waves on Earth because they are controlled by the same physicalmechanisms and are not sensitive to the details of the equation-of-state, microphysi-cal transport, or reaction kinetics [53]. They discuss how a deflagration-to-detonationtransition may have been involved in some industrial accidents, such as at Buncefield.At the same time, the astrophysical application demonstrates how interdisciplinary thisfield at the interface between fluid mechanics and chemistry is, and how far from ter-restrial concerns it can get. During the past century, combustion theory has grown from its incipient state to fullyfledged. The understanding of chemical reaction kinetics has evolved immensely. Fluidmechanics has developed both theory and also numerical solutions with CFD methodsas computers first appeared and subsequently have doubled in speed every eighteenmonths or so. Engineering — chemical, but also mechanical, civil, and other branches— has likewise advanced at an ever increasing pace. And health and safety planninghas progressed enormously in foreseeing and eliminating risks since the early daysof factory and engineering inspectors and safety first . Nonetheless, gas and vapourexplosions have killed many people, and in many of these cases a container or tankwas involved, as in the accident of my grandfather.In the last 100 years, there have been developed and implemented systems for mak-ing safer such (especially) fuel tanks with a nitrogen or similar inert atmosphere, or anon-combustible atmosphere such as carbon dioxide. Some second world war aircraftused inerting systems, and tanker ships trialled them in the 1920s. On-board inertgas generation systems have been developed for aircraft [55]. Tanker ships use ei-ther gases produced in combustion by the ship engines, or they generate inert gases[56]. Likewise, so-called hypoxic or oxygen-reduced air systems with low-oxygen-concentration air have been developed for buildings: for archives, warehouses, electri-cal substations and other buildings where reducing is preferred to eliminating oxygen13 igure 4:
Simulated (A-E) and experimental (F-J) schlieren images of the turbulent flameduring the pressure runaway and subsequent detonation formation.
Experiment in panelsF-H was carried out at = 0 . (cf. Fig. 2B), experiment in panels I and J was carried out at = 0 . . Simulated schlieren images shown in panels A-E are from the same simulation asFig. 1. 28 Figure 5: Simulated (A–E) and experimental (F–J) schlieren images of turbulent flameevolution. Once the flame front has developed, it begins to propagate toward the openend of the channel (A and F). Pressure waves generated within the turbulent flamepropagate into the unburned material and form a compressed region ahead of the flame(B and G). As the runaway process develops, multiple pressure waves coalesce into aflame-generated shock, the strength of which grows with time (C and H). Eventually,the shock triggers a deflagration-to-detonation transition, DDT (D and I) and gives riseto detonation (E and J). From [53]. 1457]. And racing-car fuel tank or fuel cell technology involves filling the tank with anopen-cell foam, again to reduce the explosion risk. We can see all these safety systemsas playing with the parameters of the theory that we have described above, to movefrom an explosive to a non-explosive part of the parameter space. So why have suchsafety systems not, like miners’ safety lamps, become the norm? It is arguable thatin some instances, that of cars, for instance, car fuel tank explosions are (despite themythopoeia of Hollywood) rather rare. This does not appear to be the case, however,for tanker ships. Devanney [58] compiled a long list of tanker ship accidents caused byexplosions in fuel tanks. He asks regarding inerting,“why was the industry so slow to adopt such an obvious, effective, safetymeasure which probably pays for itself in reduction of tank corrosion?”and answers his own question“the cost[s] of implementing inerting to these ships were more than thedollar benefits of the lives and ships saved”,because“a tanker owner rarely suffers any loss when one of his ships blows up. HisP&I [Protection and Indemnity] insurance pays off the dead crew’s family,in most past cases a few thousand dollars per head. His hull insurancecovers the loss of the ship. In many cases, the insured value is more thanthe market value and the owner comes out ahead.”This review has demonstrated how, from the very beginning, the science of explo-sions has been inextricably intertwined with its societal implications. As I write, withthe centenary of my grandfather’s death approaching, I do wonder whether more couldnot be done, with more innovative solutions from scientific and technological ideas, toreduce further the risk of explosion, in the same way that miners’ safety lamps weredeveloped and used. Despite great advances in both science and engineering, gas andvapour explosions continue. I began this review with sewer explosions of two millenniaago; these still occur on occasion. A fuel tanker blew up a century ago owing to incor-rect working methods with fuel vapour. That was then, but how can it be that a centuryon fuel tankers are still blowing up for the same reason? Has it really been safety first ,or safety last ? Whether or not further regulatory action is needed is a question thatscientists involved with the societal responsibilities of science should consider. Fromthe point of view of the science itself, in this field, science has always engaged withthe practical questions arising from explosions, from the Felling pit explosion of 1812leading to the miners’ safety lamp, to the Deepwater Horizon explosion of 2010 andthe resulting oil spill in the waters below the rig that has led to a great quantity of re-search into the dynamics of two-phase plumes [59], and from the Buncefield explosionof 2005 to the latest results on supernovae explosions [53], I am sure that new scientificadvances will continue to emerge from the fluid mechanics of explosion.15 cknowledgements
I thank Silvana Cardoso and John Davidson (1926–2019) for many interesting discus-sions in the tea room of the Department of Chemical Engineering and Biotechnologyin Cambridge over the years that have contributed to this review, ranging from the fluidmechanics of explosions, to the lessons of Flixborough for the education of engineers,to how Tom Bacon developed, first at C. A. Parsons in Newcastle and then in thatdepartment, the hydrogen–oxygen fuel cell used by NASA in the Apollo programme.
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