Auto-ignition of spontaneous hydrogen leaks

Tomas Horta e Costa Gomes da Costatomasgomesdacosta@ist.utl.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

November 2020

Abstract

This paper is devoted to the study of the self-ignition of a hydrogen leak. In order to analysethis particular case and to understand the physical phenomena behind spontaneous ignition of suddenhigh-pressure hydrogen releases, analytical calculations and a CFD simulation were carried out. Themodeling involved a shock tube where high-pressure hydrogen was separated from the atmospheric airby a rupture disk. It was concluded that due to the high-pressure difference, in the event of a suddenrelease, a shock wave could form inside the tube, mixing shock heated air with cold expanding hydrogenwhich could ignite in the presence of enough temperature and sufficient mixing. It was also found thatif the downstream geometry of the hole is too long, the mixture will fade and there will be no ignitiondue to lean mixture. This is observable by the study of a tube with downstream geometry of 0.5 meterswhere 40 bar of high-pressure hydrogen was input. The temperatures reached were as high as 1200K,well above the spontaneous ignition of hydrogen, however due to the length of the tube the mixture fadesand the necessary conditions for the mixture to ignite are not gathered. However, the same pressurewas studied for smaller tube where, although the temperature reached wasn’t as high as the previouscase, the mixture stayed stoichiometric at the necessary temperature for spontaneous ignition, meaningthat the conditions for spontaneous ignition were gathered.Keywords: Hydrogen, Spontaneous ignition, High pressure, Shock wave, CFD

1. Introduction

With the increase usage of hydrogen in several in-dustries throughout the last 100 years, several is-sues concerning safety have made it very difficultto progress and expand its usage as a clean fuel.These safety issues include its transportation, stor-age and usage. Since it is a very volatile gas andcan be very explosive as it combusts with just one-tenth of the energy required for gasoline, the safetyconcerns turn to avoid combustion at all costs. Ontop of explosive issues, hydrogen is odorless and col-orless.

When handling high-pressure hydrogen, im-proper use of valves, damage to the ducts/reservoirsor embrittlement can lead to high velocity leaksthat can ignite with minimal effort, whether it isa spark, static electricity or even just a hot surface.Many have been the reported accidents involvinghigh-pressure flammable gas with spontaneous igni-tion, for that reason many studies have been madearound the subject of hydrogen auto-ignition.

Over the last century, several combustion inci-dents have been reported due to high-pressure hy-drogen leaks without a determined cause. A plat-form called HIAD [2], Hydrogen Incident and Acci-dent Database, is a free access database that keepstrack of all the accidents related with hydrogen

worldwide. To this day there is a total of 364 acci-dents involving hydrogen that transitioned into jetfire or explosions. While most of them have an as-sociated cause (about 86%), about 14% of the acci-dents registered have no known cause.

Diffusion ignition was first studied in 1972 byWolanski and Wojcicki [12]. What they meantby ”diffusion ignition” was the ignition producedby the discharging jet, when the fuel expandingthrough a shock tube came into contact with an ox-idizing atmosphere heated by the shock wave. Thereason why it was named diffusion ignition is be-cause they identified diffusive mixing. It was pre-dicted that ignition would be achieved once an up-stream pressure of 39 bar, was obtained causing ashock-wave mach number of 2.8 or higher leading toa temperature of 575K. In 1990 Chaineaux et al. [5],coined the term ”spontaneous ignition”, which theyused after achieving it by discharging high pressur-ized hydrogen at approximately 100 bar througha 12mm hole extended by a tube with 120mm oflength and 15mm inside diameter producing a sortof CD nozzle.

Mogi et al. [10], studied the effect of the down-stream tube length from the rupture disk, by vary-ing it from 3 to 300mm, using 5 and 10mm noz-zle diameters. They were able to get jet fire ig-

1

nition at a approximately 60 bar with a 185mmtube and a 5 mm diameter nozzle. In the sameyear Golub et al.[8] made a very similar experi-mental study, accompanied with CFD work. Fromthe experimental part, ignition was achieved usinga very similar configuration as Mogi et al. withthe same pipe length and nozzle diameter but thistime ignition was achieved with just 40 bar of high-pressurized hydrogen. They concluded that the rea-son for the possible spontaneous ignition was ”theheating by the primary shock wave of the surround-ing oxidizer, resulting in gas ignition on the contactsurface”. Still in 2007, Dryer et al.[6] released apaper where more than 200 experiments were doneusing several downstream geometries (downstreamof the burst disk) and several burst pressures con-cluding that for a downstream geometry of 127mmof length and 4mm diameter ignition would be cer-tain from hydrogen pressures of 22.4 bar up, witha possible ignition at a minimum pressure of 20.6bar. With the work presented it was possible toconclude that ”within the storage and pipeline pres-sures used today and/or contemplated in the futurefor hydrogen, transient shock processes associatedwith rapid pressure boundary failure have the ca-pacity to produce spontaneous ignition of the com-pressed flammable released into air, providing suf-ficient mixing is also present”.

In 2010, Bragin et al.[4] validated a LES modelby comparing the results with the results printedfrom Mogi [10]. The paper had the objective ofstudying the ”physical phenomena underlying thespontaneous ignition of hydrogen following a sud-den release from high-pressure storage and transi-tion to sustained jet fire” creating a LES model forengineering design of pressure relief devices.

The objective of this paper is to study what ex-actly happens inside the hole that leads to a possibleignition. Since the behaviour inside a hole is similarto a shock tube, the problem is portrayed as a shocktube like geometry where the driver is designed asthe high-pressured reservoir and the driven sectionas the atmosphere.

2. Background

In order to better understand the physical andchemical phenomena behind spontaneous ignitionthrough diffusive ignition, an analytical approachis required to complement the numerical study. Inorder to do so an overview of the theoretical com-ponent that involves shock tube theory and whathappens inside it, is studied.

2.1. Overview of the shock tube theory

2.1.1 The Shock tube

The shock tube is composed of two parts which aredenoted as the driver section and the driven sec-

tion presented in figure 1. The driver section con-tains high-pressure gas at pressure P4, while thedriven section contains low-pressure gas at pressureP1, which are separated by a diaphragm designedto burst at a certain pressure.

Figure 1: Diagram illustrating the driver and drivensections of a shock tube(at t=0), similar to themodel used numerically.

Once the designed pressure is achieved the di-aphragm bursts releasing the high-pressure gas,very rapidly, through the driven section creatinga shock wave moving in the same direction. Inthe driver section, rarefaction waves (taken fromShapiro [11]) move in the opposite direction ofthe shock wave due to the expansion of the high-pressured gas. Once the diaphragm is ruptured,two additional regions appear as regions 2 and 3.Region 2 is located behind the shock wave and re-gion 3 is right behind it separated by the contactsurface as shown in figure 2.

Figure 2: Position of contact surface in a shock en-vironment as a function of time. (From Shapiro,1954.[11])

Since hydrogen and methane are going to betested in the driver section, a lot of properties thatlead to the calculations, are different. Although theinitial temperatures, both in the driver and drivensections, are the same (300K), the species in bothregions are different with different gas constantswhich leads to different speed of sound values inboth sections of the shock tube. For that, the speedof sound for each species can be calculated as,

a =√γRT (1)

where γ is the adiabatic exponent of the gas at 300Kand R is the universal gas constant.

PressureA shock tube works by implementing a big pres-sure difference. With the burst of the diaphragm,

2

the high-pressured gas is released into the low pres-sured zone. This being said pressure is the key fora shock tube to work. Since pressure in the driversection and in the driven section is known (regions4 and 1 respectively), it is possible to design a pres-sure profile along the tube length using the follow-ing equations from Liepmann et al. [9].

P4

P1= P2

P1

[1− (γ4−1)(a1/a4)(P2/P1−1)

(√2γ1)(√

2γ1+(γ1+1)(P2/P1−1)

]−2γ4γ4−1

(2)P3

P4=P2/P1

P4/P1(3)

These equations allow the construction of the pres-sure profile in figure 3.

Figure 3: Pressure profile along the length of thetube

TemperatureDue to rapid release of high-pressure flow withgreat velocity, a shock wave is formed, heating thelow pressured gas as it travels through the drivensection. On the other way around, flow of high-pressure driver gas expands through the driver sec-tion on the opposite direction of the shock wave,cooling it. Since the pressure profile was alreadydesigned and the results of the previous equationscalculated, it is possible to construct a temperatureprofile with the following equations from Liepmannet al. [9].

T3T4

=

(P3

P4

) (γ4−1)γ4

=

(P2/P1

P4/P1

) (γ4−1)γ4

(4)

T2T1

=1 + γ1−1

γ1+1P2

P1

1 + γ1−1γ1+1

P1

P2

(5)

This leads to a temperature profile inside the tubewhere, although temperature in region 4 and in re-gion 1 is constant, in regions 2 and 3 the gas heatsup and cools respectively. Therefore, the temper-ature profile is supposed to look like the followingfigure 4.

DensityAssuming ideal gas across the shock tube, P = ρRTis used for the calculation of density across the con-tact surface. Remembering that P3 = P2 it is pos-sible to conclude that the density ratio is inverselyproportional to the temperature ratio,

ρ2ρ3

=

(R2T2R3T3

)−1(6)

Figure 4: Temperature profile along the length ofthe tube

Mach numberGaydon and Hurle [7] in 1963, developed equationsfor the relations between the initial pressure ra-tio with the shock Mach number and the ratio oftemperatures across the shock wave with the shockMach number, as seen in the following equations.

P4

P1= 2γ1Ms2−(γ1−1)

γ1+1

[1− γ4−1

γ1+1a1a4

(Ms− 1

Ms

)]−2γ4γ4−1

(7)

T2T1

=

[2γ1Ms2 − (γ1 − 1)

][(γ1 − 1)Ms2 + 2

](γ1 + 1)2Ms2

(8)

These simplified equations lead to the possibil-ity of studying the critical pressure to which theflammable driver gas would auto-ignite. By know-ing T2, it is possible to calculate at what Machnumber the gas would reach those temperaturesand then calculate the minimum critical pressureto produce such shock wave. Using these equationsand the information from the engineering toolbox[1] it was possible to calculate the critical ignitionpressures for several common gaseous fuels and theMach number produced by releases at these pres-sures, as it is possible to see from table 1.

TimeA shock wave is transient phenomena so it is timedependent as it is possible to understand throughfigure 2. As the shock Mach number increases, sodoes its speed and the lesser time the shock waveneeds to travel through the length of the tube. Thefollowing equations explain just that.

Ms =cs

a1(9)

∆t =l

cs(10)

Boundary layer influenceAlthough a lot of the properties behaviour in theshock tube are explained in the above sections, noneof the governing equations take into account the vis-cosity present in the gas. With the appearance of aboundary layer near the wall, as the flow developsthrough the tube, the shock wave will reflect offof it leading to the appearance of oblique shocks,resulting in a bigger increase of temperature of thefuel/air mixtures formed in the contact region alongwith better mixing influenced by turbulent mixing.

3

Table 1: Theoretical critical pressure of ignition of common gaseous fuels

In figure 5, we see just that, where as the flow de-velops, the boundary layer near the tube, in lightgrey, grows influencing more as the shock travelsthe length of the tube.

Figure 5: Development of a normal shock in a ductafter the burst of a disk that was once separating ahigh-pressure flammable gas from the ambient air,by Dryer et. al[6]

3. Numerical model

In the present chapter the numerical implementa-tion of the experiment will be approached. Thischapter serves the purpose of showing and explain-ing the process behind the CFD work. Ansys Fluentwas the program used to run the numerical model.

3.1. Implementation of the numerical model

Since this study consists of a real case, the use ofFluent must be as close to reality as possible. Justlike mentioned before, in order to study what hap-pens when a high-pressure gas spouts into the at-mosphere, the best approach is to model a shocktube. This being said, a 2D rectangle separated intwo equal sections (driver and driven) was designedin Fluent. Since there were two different cases be-ing studied, several dimensions were studied. Forthe first case where the results were compared tothose of the analytical approach, the dimensionsused were 1 meter by 0.02 meters in order to varyonly the initial pressure. On the second case, theinitial pressure was fixed and the length varied as0.36m, 0.42m and 0.48m with the driver and driven

section each owning half of this length.

After designing the geometry, the next step wasto mesh. Since the program used was the studentversion, it only permitted up to 512k nodes. Eachone of the sections was face meshed with the quadri-lateral symmetry and with a particular element sizewhere after the refinement study the number of ele-ments went from 120k to 501k in order to maximizethe allowed number of nodes and to print out thebest solution possible.

With the mesh done, all that is left to do is thesetup and calculate the solution. In the setup tab,the solution was calculated using 4 solver processeswith double precision for more accurate results. Us-ing the density based-solver with transient time, en-ergy equation on, and species transport the solutionwas run for both hydrogen/air and methane/airmixtures. Ideal gas, Sutherland viscosity and tur-bulent k-w standard flow with adiabatic conditionswere used. Using implicit formulation with Roe-FDS and second order upwind discretization, thesolution was initialized. For the first case the pres-sures studied were 5, 10, 20, 30 and 40 bar. For thesecond case, the solution was always initialized with20 bar in order to only vary the length of the tube.Besides pressure, temperature was initialized bothin driver and driven sections as 300K. The drivensection was initialized with 1 atm of pressure. Massfractions of both methane and hydrogen were set as1 in the driver with 0.23 of O2 and 0.77 of N2 in thedriven for the first case. For the second case onlyhydrogen was studied in the driver section. Finally,the solution was run with 2000 iterations consistingof 100 time steps of 20 iterations each, with a time-step calculated for each case. However, in order toachieve the best solution, the time-step used wascalculated by trial and error.

4. Results

In this section, the results from both analytical andCFD approaches are going to be addressed whileconsidering both cases studied in Fluent.

4

4.1. Analytical ResultsConsidering the equations 1 through 10, the prop-erties studied inside the shock tube were pressure,temperature, density and the Mach number. Al-though the pressure profile is not the most impor-tant of the four properties to be studied, the initialpressure of the system prior to the burst disk rup-ture, is the most important and influential propertyas all the other properties depend on it. With equa-tion 7, we have a direct relationship between theinitial pressure ratio and the shock Mach number.This leads to the understanding that the bigger theratio of pressures, the stronger the shock wave pro-duced. Figure 6 shows the progression of the Machnumber as a function of the initial pressure ratio forhydrogen, methane, ethane, propane and butane.

Figure 6: Shock wave Mach number(Ms) as a func-tion of the driver pressure(P4), using equation 7

As it is possible to observe for hydrogen, theMach number produced increases a lot faster thanthe other gases presented in the figure 6. Using theresults from equation 7, it is possible to print theratio of temperatures across the shock wave as afunction of the initial pressure ratio with equation8. The results in figure 7 represent the tempera-ture behind the shock wave, T2 (as T1 is constantat 300K), as a function of the initial pressure ratioof the system.

With the values from the engineering toolbox [1],only hydrogen will achieve high enough tempera-tures at ”low pressure” leaks. While methane andhydrogen appear to be capable of reaching compres-sion values of P4 to cause ignition, ethane, propaneand butane being liquefied gaseous fuels, are unableto reach the necessary driver pressures to do so, andso from now on the calculations presented will beon hydrogen and methane. From table 1, althoughthe auto-ignition temperatures for the various gasesdoes not vary much, the critical pressure of ignitionis enlightening on how hydrogen can be very dan-gerous in the event of a leak.

Although the figures above show the calculationfor ratios of pressure up to 100 bar, for compar-

Figure 7: Temperature behind the shock wave(T2)as a function of the driver pressure(P4), using equa-tions 7 and 8

ing purposes with the results from Fluent, only thepressure ratios of 5, 10, 20, 30 and 40 bar were usedfor both mixtures of hydrogen and methane/air asthey are more realistic.

4.2. Fluent Results for case 1As previously said, Fluent was used to study 2 dif-ferent cases. The first one had the objective ofstudying and comparing the results from the an-alytical approach. For this, using the assumptionsdescribed in the implementation section, Fluent wasrun for both hydrogen/air and methane/air mix-tures for 5, 10, 20, 30 and 40 bar in order to comparethe results. The values from pressure, temperature,density and velocity were compared.

4.2.1 Pressure

As said before, both mixtures were run in orderto compare results from the governing equations.These presented similar graphs to figure 3. For this,since P4 and P1 are known, the only sections neededto be studied were P2 and P3, which as previouslysaid, are assumed equal. In order to calculate P2

equation 2 was used.For the hydrogen/air mixtures, the values for P2

extracted from Fluent are very similar to the re-sults from the analytical approach. Calculating thepercentile error between the two approaches, by as-suming the results from Fluent as true, with theresults from the last time step, we get a maximumerror of 2%, allowing the conclusion that the as-sumptions made are correct. The same happensfor the methane/air mixture although this time themaximum error calculated is of 6.5%

4.2.2 Temperature

Looking at figure 4 it is possible to see the howthe temperature profiles inside the shock tube areprinted.

5

With the results taken from Fluent it was possi-ble to see that there was a considerable differencebetween the temperatures in region 2 from both ap-proaches. This is due to the fact that turbulent flowis assumed and from figure 5, we know that as theflow develops, the boundary layer gets thicker andreflects the shock creating oblique shocks which leadto more heating applied to the mixture. Becauseof this, the maximum error for T2, calculated forthe last time step, from both approaches is 20.11%which is quite considerable. However, when lookingat T3, calculated for the last time step, a differ-ence between values practically doesn’t exist as theboundary layer ends up not affecting region 3 as theflow moves in the other direction. This leads to amaximum error of just 1.33%.

The same happens for methane, however sincethe shock is much weaker, the temperature reachedin region 2 is smaller than for hydrogen. Comparingboth approaches we extract a maximum error of18.9% for T2 and 0.93% for T3.

4.2.3 Density

With equation 6 it is possible to calculate the entiredensity profile of the mixtures, as the density atregions 1 and 4 are known from the ideal gas law.

If the gas was the same in both regions, the den-sity would rely only on the temperature leading toa density profile very similar to the pressure pro-file, however since the gases are different the den-sity profile for hydrogen/air mixture is very similar,visually, to the temperature profile due to the factthat the universal gas constant for hydrogen is 14times greater than the one from air. This lead to amaximum error of just 5.06% between the two ap-proaches, calculated for the last time step, whichproves the validity of the assumptions made. Formethane/air mixtures the results came out very dif-ferent printing a ρ2

ρ3much smaller than the one for

hydrogen/air. However, the calculated error for thelast time step, was bigger at 8.57%

4.2.4 Velocity

Through Bernoulli’s principle we know that for twofluids at constant height with different pressures,the flow will move in the direction of the low pres-sured fluid in order to try to find a balance. Thebigger the pressure difference, the faster the velocityof the flow which means that, when we increase thepressure of the driver section, the velocity will alsoincrease when comparing to lower pressured driversections. With this, as the initial pressure is in-creased, so does the flow velocity increase.

Considering turbulent flow, we know that in theboundary layer the flow is sped up, which means

that the maximum velocity reached is at the bound-ary layer. Using equation 9, values for velocitiesusing both approaches are calculated. Consideringthat hydrogen/air creates a much stronger shockwave, the flow velocities reached will be much faster.For example at 40 bar of driver pressure the flowreaches a velocity of 1102.2m/s. Comparing thevalues from both approaches, for the last time stepcalculated, we get a maximum error of 21.52% forhydrogen and 37.96% for methane. Since methaneproduces weaker shocks, the flow velocities will bemuch lower leading to a max velocity at 40 bar of699.5 m/s. The main reason that leads to the dif-ference in results is the assumption of viscous flow.Since viscosity is not applied to the equations inthe analytical approach, the flow velocities calcu-lated are much faster than the ones printed in thenumerical work.

Considering that all of these results were takenfor the last time step calculated and only for com-parison purposes, the originated error from bothapproaches is flexible. This means that it mightbe different if other tube dimensions or other timesteps are chosen to be compared with the analyti-cal results. However, the main difference relies onthe way that both approaches are calculated. Inthe analytical approach a steady state is studiedwith simple 1D equations, while for the numericalwork a transient state is assumed with complicatedNavier-Stokes equations used. This obviously leadsto different results.

4.3. Fluent Results for case 2In case 2 the effects of the length of the tube weretested. For this a geometry, just like the one used incase 1, was designed with the dimensions of 360mm,420mm and 480mm all with the same diameter of20mm. As previously, driver and driven sectionswere designed with the same length meaning thathalf of the total length of the tube belonged to thedriver section and the other half to the driven sec-tion. With all the assumptions mentioned before,the driver section was initialized for all 3 lengthswith 20 bar, as it was proven that it was enoughto reach the spontaneous ignition of hydrogen, andthe driven section with atmospheric conditions. Forthis reason only hydrogen is going to be tested andthe results are shown for the last time step calcu-lated.

4.3.1 Pressure

As mentioned above the pressure was the same foreach case so that there would be just one variable,the length of the tube. From the results gatheredfrom Fluent it was possible to conclude that thepressure profile wont change with the current set-tings. The only possible thing to be observed is the

6

fact that for smaller lengths of tube, region 2 and3 are more unstable creating some fluctuations ofpressure across the diameter of the tube. However,it was possible to clearly identify all for regions ofthe shock tube as it is possible to see in the follow-ing figure 8 for the length of 360mm, at the lasttime step calculated.

Figure 8: Pressure profile inside the 360mm shocktube

4.3.2 Temperature

Although there was no visible change in the pressureprofile with the increase of length, temperature pro-files had the opposite reaction. It is known that theturbulent boundary layer thickness grows with thelength of the tube and with this increase, the shockwave is more affected by shock reflections of offthe boundary layer. With these reflections, obliqueshocks are created which lead to a higher temper-ature of the flow. This being said, it was expectedthat the temperature would increase with the in-crease of tube length. This assumption was veri-fied. It was found that at a tube length of 360mm,the shock produced by a downstream pressure of20 bar was enough to cause a spike of tempera-ture up to 836.6K, at the last time step registered,which means that for this length of tube smallerpressures could lead to spontaneous ignition of thehydrogen/air mixture in the presence of good mix-ing. On the opposite thought for this downstreampressure, a smaller tube might be able to cause thesame effect. Although it was verified that with theincrease of length the maximum temperature wouldrise, the minimum temperature on the other hand,remains constant which is expected since region 3is not affected by the shock wave. In the followingfigure 9 we can see how the temperature profile be-haves inside the tube with the use of contours, forthe 360mm long tube, at the last time step.

As it is possible to see, the four regions are eas-ily identifiable with the highest temperature beingrecorded at the tube walls due to the boundarylayer.

Figure 9: Temperature profile inside the 360mmshock tube

4.3.3 Density

As previously discussed the density profile insidethe shock tube is very similar to the temperatureprofiles. It was possible to observe that due to theincrease of temperature in region 2 and the tem-perature in region 3 maintaining similar values, thedensity ratio across the shock wave, ρ2

ρ3, becomes

smaller as ρ2 decreases with the increase of temper-ature. In the following figure 10 we can see thatthe density profile at the last time step, once againfor the 360mm long tube, is very similar to the oneshown in figure 9 as the density varies with the tem-perature of the region.

Figure 10: Density profile inside the 360mm shocktube

4.3.4 Velocity

Through Bernoulli, it is known that with the in-crease of pressure on the driver side, the flow ve-locity will be faster. However, with the increase oflength and the pressure remaining constant, the ve-locity profile is much harder to predict. With theincrease of tube length it is known that the tur-bulent boundary layer will have more influence onthe flow. Also it is also known that the turbulentboundary layer increases the speed of the fluid nearthe walls. So with these two arguments it could beexpected that the velocity would increase with theincrease of length. However, with more surface forthe fluid to run through, viscous forces will have

7

more influence and therefore the flow velocity willactually decrease through adhesion and friction.

Figure 11: Velocity profile inside the 360mm shocktube[10]

In the previous figure 11 we see just that. Forthe 360mm long tube we have the fastest flow nearthe walls of the tube, with the boundary layer beingquite visible.

Although the results shown are only for the360mm long tube the following table presents allthe results for the four lengths tested which allowfor better conclusions.

Table 2: Temperature profile inside the 360mmshock tube

By looking at table 2, as the length of the tubeincreases, only two properties are affected directly,the temperature behind the shock wave and the ve-locity of the flow. With the increase of tube lengthnot only does the maximum temperature increasebut the velocity of the flow decreases. Therefore, alonger tube might have a higher probability of caus-ing spontaneous ignition of the mixture fuel/air.Since the numerical work was presented for the lasttime step, different results for different time stepscan be expected. This being said, the next sectionis dedicated to the study of the shock through timeinside the tube.

4.4. Shock Through timeIn this section an evaluation of what happens insidethe shock-tube throughout the flow time, in termsof temperature is going to be made.

Several studies were made in terms of ignitiontimes and the delay it takes for the spontaneous ig-nition to happen. One of those studies was doneby Mogi et al.[10] in 2007 where jet fire ignitionwas achieved with an experimental set consisting of

a tube with 185mm with 5mm in diameter with adriver pressure of 145 bar with hydrogen/air mix-ture. With this setting, spontaneous ignition of hy-drogen was achieved. With the careful observationof this paper, it was possible to conclude that ig-nition might start inside the tube and not outside,meaning that at the burst of the contact surface,mixing might start right away leading to the igni-tion. With this information, this section is dedi-cated to studying what happens inside the shock-tube through time.

In previous sections the properties of the mix-tures are addressed and what happens to them incase of shock inside of a tube. However, one of themost important things to study when consideringcombustion is the quality of the mixture. Whenquality of a mixture is addressed the main aspectto be addressed is the equivalence ratio (Φ). Theequivalence ratio studies if a mixture is rich (> 1),lean (< 1) or stoichiometric (=1) by dividing theFuel-air ratio of the mixture by the stoichiometricFuel-air ratio.

Alcock et al. [3], demonstrated that hydrogen/airstoichiometric mixture requires a minimum ignitionenergy of just 0.02 mJ, however the flammabilitylimits present a very wide range of % of hydrogenin air. With this, it is possible to conclude thatthe easiest way for hydrogen to ignite when mixedwith air, is to have a concentration mixture at stoi-chiometric conditions which is 29.5% of hydrogen inair. Since this is a numerical study, it is impossibleto say for sure that combustion happens, however,through temperature and quality of the mixture itis possible to say if the conditions necessary for themixture to ignite are gathered. In order to studythis, two tube lengths, 1m and 0.36m, were usedto test two initial pressures, 5 and 40 bar, to a to-tal of four different analysis. Since Fluent does notproduce the equivalence ratio as a result property,a user defined function was developed where themass fraction of H2 was divided by stoichiometrichydrogen% in air

4.4.1 360mm Long tube

As mentioned before, two different pressure ratiosare going to be tested, 5 and 40 bar. As seen fromcase 1, it is known that for 5 bar of initial pressure,the temperature achieved by the mixture is not go-ing to be enough to cause spontaneous ignition asthe maximum temperature recorded was 471.6K.However, analysing the equivalence ratio hydro-gen/air mixtures, it was possible to conclude thatthe location of the highest temperature achievedwas also where the mixture was stoichiometric.This being said it is possible to say that if thereis a bigger input of pressure that leads to a bigger

8

spike of temperature, it might lead to spontaneousignition.

From the figure 12 we prove the assumption madein the previous paragraph where, for 40 bar of pres-sure, the temperature achieved by the stoichiomet-ric mixture is higher than the recorded spontaneousignition for hydrogen at 737k. As it is possibleto see from the figure, in the temperature profiles,right from 5e−5s, the temperatures recorded behindthe shock wave are already enough to cause spon-taneous ignition of the mixture. Moreover, fromthe equivalence ratio profiles, it is possible to saythat the mixture stays stoichiometric throughoutthe length of the tube, meaning that at the interfaceseparation of the mixture with air, the conditionsare stoichiometric. Combining these two factors itis possible to say that for a driven section of 180mmand an initial pressure input of 40 bar, the condi-tions necessary to ignite and produce flame from ahydrogen/air mixture are gathered.

Figure 12: Hydrogen/air equivalence ratio profile(top), and temperature profile (bottom) for the360mm long tube at 40 bar of initial pressure.

4.4.2 1m Long tube

As said before, from case 1, with an input pressureof 5 bar for a 1m long tube, the temperatures pro-duced are not high enough to lead the mixture tospontaneous ignition as the maximum temperatureachieved is of 533.5K with a lean mixture. However,when analyzing the 40 bar profiles for 1 meter longtube with figure 13, the profiles observed are verydifferent than for 5 bar. In the temperature pro-file observed it is possible to see that the maximumtemperature achieved by the shock wave is 1233Kwhich is well above the spontaneous ignition tem-perature but is located at the boundary layer. How-ever, most of the temperature profile exhibits tem-peratures in the range of 1000K (in yellow) whichis still well above the temperature required. Whenlooking at the equivalence ratio profile, a very in-teresting conclusion can be taken from its obser-

vation. Although in the beginning of the tube, at7.9e−5s, the mixture creates a shape that resemblesa horse shoe where near the edges, the mixture inlight blue, is stoichiometric. However with the flowdevelopment, at the time stamp of 4e−4s the mix-ture starts to face and becomes lean with Φ < 1.So, although the conditions at 7.9e−5s are gatheredfor a possible spontaneous ignition of the mixture,with the flow development, the mixture becomeslean which leads to bad conditions for ignition. Soalthough a longer tube might produce higher tem-peratures, with the flow development mixture fadesover time, where Φ decreases below the stoichiomet-ric value and ignition is no longer possible. So inthe early stages there might be combustion but atthe end of the tube the combustion will be extinctproducing no flame to the outside.

Figure 13: Hydrogen/air equivalence ratio profile(top), and temperature profile (bottom) for the360mm long tube at 40 bar of initial pressure.

With all the analysis made with fluent, it is pos-sible to conclude at what lengths and pressure theremight be an ignition considering that the conditionsare gathered for such phenomena to take place.With the studied analysis, it is concluded that for5 bar of initial pressure, much like for 10 bar, theshock wave produced is not strong enough to causeenough increase of temperature to lead the mixtureto spontaneous ignition. However, for 20 bar andup, it is possible to see that for some tube lengthsthe conditions are gathered for spontaneous ignitionto take place. With the results from case 1 and 2 itis possible to conclude that the higher the pressureinput, the longer the mixture quality is sustained.With the results from the analysis made it is pos-sible to plot the following graph where ignition isexpected to occur under such conditions of initialpressure and tube length.

With all the analysis made it is possible to con-clude whether it is possible or not to have ignition.In figure 14 we see just that, where above the blackline it is concluded that the conditions to have spon-taneous ignition are gathered and such phenomenais possible to occur.

9

Figure 14: Initial pressure as a function of thelength of the tube where the conditions are or notgathered for spontaneous ignition to occur.

5. Conclusions

This dissertation had two objectives. For the firstobjective analytical calculations were compared tothe CFD work. For this the governing equationswere used for the analytical part and fluent was usedfor the CFD part. The same setting was impliedto both approaches where certain assumptions weremade in fluent. Comparing the results it was pos-sible to conclude that the assumptions made werecorrect where the error printed between the two ap-proaches, even though sometimes considerable, wasminimal in most cases. The biggest difference inresults was seen for the temperature and velocityprofiles as both are affected by viscous flow. How-ever, considering that only the last time step wasused to compare values, it is possible to say that fora different time step, the error might be different.

For the second objective, various lengths of tubewere tested. This allowed the study of the prop-erties with the increase of length and the study ofexactly what happens inside the shock tube. It ispossible to say that a longer tube allows for a biggerbuild of temperature behind the shock wave. How-ever, in order to have combustion, good mixtureis also necessary and for a longer tube, the mixturemight fade with time, whereas for a smaller tube themixture maintains better quality for longer time.This leads to the conclusion that for a smaller tube,if the input pressure leads to a temperature abovethe spontaneous ignition line, ignition is more likelyto happen than for a longer tube. This being said,for certain tube lengths, there is a minimum criticalpressure that might lead the mixture to ignite, asseen in figure 14.

6. Future Work

In order to complement the work done in thisdissertation, further work on what happens whenthe mixture spouts into the atmosphere is needed.Work such as what conditions lead to stabilized jet

fire of hydrogen spontaneous ignited leaks could bevery useful.

References[1] Engineering toolbox, 2001. Last accessed on

2020/08/30.

[2] Hiad, 2020. Last accessed on 2020/08/22.

[3] J. Alcock, L. Shirvill, and R. Cracknell. Com-pilation of existing safety data on hydrogenand comparative fuels. Deliverable Report,EIHP2, May, 2001.

[4] M. V. Bragin and V. V. Molkov. Physics ofspontaneous ignition of high-pressure hydrogenrelease and transition to jet fire. InternationalJournal of Hydrogen Energy, 36(3):2589–2596,2011.

[5] J. Chaineaux, G. Mavrothalassitis, andJ. Pineau. Modelization and validation testsof the discharge in air of a vessel pressurizedby a flammable gas. Progress in Astronauticsand Aeronautics, 134:104–137, 1991.

[6] F. L. Dryer, M. Chaos, Z. Zhao, J. N. Stein,J. Y. Alpert, and C. J. Homer. Spontaneousignition of pressurized releases of hydrogen andnatural gas into air. Combustion science andtechnology, 179(4):663–694, 2007.

[7] A. G. Gaydon and I. R. Hurle. The shock tubein high-temperature chemical physics. Chap-man and Hall, 1963.

[8] V. Golub, D. Baklanov, T. Bazhenova, M. Bra-gin, S. Golovastov, M. Ivanov, and V. Volodin.Shock-induced ignition of hydrogen gas dur-ing accidental or technical opening of high-pressure tanks. Journal of Loss Prevention inthe process industries, 20(4-6):439–446, 2007.

[9] H. W. Liepmann and A. Roshko. Elements ofgasdynamics. Courier Corporation, 2001.

[10] T. Mogi, D. Kim, H. Shiina, and S. Horiguchi.Self-ignition and explosion during discharge ofhigh-pressure hydrogen. Journal of Loss Pre-vention in the process industries, 21(2):199–204, 2008.

[11] A. H. Shapiro. The dynamics and thermo-dynamics of compressible fluid flow. NumberBOOK. John Wiley & Sons, 1953.

[12] P. Wolanski. Investigation into the mechanismof the diffusion ignition of a combustible gasflowing into an oxidizing atmosphere. In Four-teenth Symposium (International) on Combus-tion, 1973, 1973.

10