model, software for calculation of ait and its validation. no.18v2.7... · safekinex –...

Programme “Energy, Environment and Sustainable Deve lopment”

Project SAFEKINEX: SAFe and Efficient hydrocarbon oxidation processes by KINetics and Explosion eXpertise

Contract No. EVG1-CT-2002-00072

Model, software for calculation of AIT and its validation

Deliverable No. 18

M.A. Silakova, V. Smetanyuk, H.J. Pasman

Delft University of Technology

April 2006

SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure) page 3 (59)

Table of Contents:

1 Introduction ....................................................................................................................................... 5

2 Approximate model of heat losses in AIT tests ............................................................................... 5

2.1 Basics......................................................................................................................................................... 5

2.2 Influences on natural convection ............................................................................................................. 7

2.3 Heat production in low temperature oxidation ...................................................................................... 10

3 Numerical modelling of cooling of heated gas............................................................................... 12

3.1 Heat loss from an inert gas to a vessel wall............................................................................................ 12

3.2 The numerical model .............................................................................................................................. 13

3.3 Calculation results with a heated inert gas ............................................................................................ 14

4 Time duration to gas self-ignition, IDT ......................................................................................... 18

4.1 Low temperature part (≤≤≤≤ 700K) with n-butane as fuel........................................................................... 18

4.2 Higher temperature part (> 700 K)......................................................................................................... 23

4.3 The effect of mixture composition .......................................................................................................... 29

4.4 The small chain hydrocarbons C1-C3 ..................................................................................................... 30

4.5 Simulations with strongly reduced mechanisms .................................................................................... 35

4.6 Alternative kinetic mechanisms and simulation software ..................................................................... 37

5 Characterisation of the conditions of natural convection enabling ignition .............................. 39

5.1 Basic gas-dynamic flow patterns ............................................................................................................ 39

5.2 Convection Effect on Induction Delay Time.......................................................................................... 41

5.3 Critical conditions for thermal explosion in a compressible gas........................................................... 42

6 Conclusions....................................................................................................................................... 44

7 References......................................................................................................................................... 45

Appendix I. Excel sheet to calculate heat transfer coefficient and adiabatic induction time ........... 47

Appendix II. Brief descriptions of the four current software packages for calculating ignition

processes and laminar flame. .................................................................................................................. 49

CHEMKIN 4.0.2 .................................................................................................................................................... 49

COSILAB 2.0.2 ...................................................................................................................................................... 49

CANTERA ............................................................................................................................................................. 50

Chemical Workbench (CWB) ................................................................................................................................ 50

References:............................................................................................................................................................. 51

Appendix III. Brief characterization of FLUENT CFD software....................................................... 53

Appendix IV. A Tentative Modeling Study of the Effect of Wall Reactions on Oxidation

Phenomena................................................................................................................................................ 55

SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation page 5 (59)

1 Introduction Safety of hydrocarbon oxidation processes for cases in which no external heat source is present, result from avoidance of run-away reactions in the process mixture leading to self-ignition. So, given ambient conditions of temperature and pressure and given a mixture in a certain section of the process equipment the first property to be established is the self-ignition or auto-ignition temperature (AIT) for that particular system. Then the question follows of how long does it take to reach the point of self ignition, that is how long is the ignition delay time (IDT), and finally whether an incipient flame can propagate and what pressure can be generated. The last of these determines the extent of product contamination and damage to equipment, which has been the subject of other deliverables in the project. Self-ignition temperatures play in general an important role in classifying the hazard of a mixture with a view on the EU ATEX Directives to control gas explosion safety. As described in Deliverable No. 5 [1] standardised test procedures exist and limited data are available, but this extends practically not to elevated conditions. For self-ignition the pressure reached has been proven to be important, as shown in Deliverables Nos. 5 and 33 [1, 2]. As described in other Deliverables of the SAFEKINEX project e.g. No. 30 [3], two acceleration mechanisms of reaction in a mixture of hydrocarbons and oxygen (or air) exist: a thermal explosion mechanism in which an increasing reaction temperature results from the exothermic reaction itself, and a radical chain branching mechanism in which the radical concentration increases exponentially. Both mechanisms play a part of varying importance in the low temperature hydrocarbon oxidation and occur, in particular, with higher alkanes and alkenes. Smaller molecules such as methane and ethylene show slow oxidation reactions but the formation and accumulation of peroxides, which at a certain stage acts as a source of reactive hydroxyl radicals (·OH), does not occur as readily as in n-butane, for example. A surge of these radicals induces cool flames. Given the right conditions the temperature (and pressure) increased by a cool flame may induce a run-away to explosion in the mixture. This phenomenon is called two-stage and, sometimes, multi-stage ignition. This deliverable will develop a model for auto-ignition as far as is possible at present. To this end (i) literature will be reviewed to obtain insight in the complexities involved, (ii) the heat transfer of a given reacting mixture to a containing wall will be analysed, (iii) the detailed kinetic models developed in the SAFEKINEX project will be briefly reviewed, (iv) the software available in the market to simulate a detailed kinetic reaction scheme will be described and (v) advice will be offered on how best to perform a simulation. The report is concluded by some calculated examples.

2 Approximate model of heat losses in AIT tests 2.1 Basics Following Ten Holder [9] and Pekalski [4], the Appendix of Deliverables No. 29 and the Addendum A of Deliverable No. 33 [5, 6] give a preliminary basis to provide simple models for the heat losses obtained in the self-ignition tests, where the main content was focussed on experiments to measure the heat losses under a variety of conditions. Heat loss from a gas at relatively small temperature difference with a confining wall will at some motion of the gas mainly be by convection. When modelling, in the first place a distinction has to be made between steady flowing mixture as is mostly the case in process equipment and an initially quiescent gas as usually prevails in laboratory equipment. In the case of steady flow in a pipe one can distinguish a heat exchanging surface area per unit of length of pipe, A, a temperature of the bulk of the flow as a function of location, T(x), the wall temperature at a certain location, Tw(x), and hence a driving force temperature difference


T(x)-Tw(x). Depending on flow conditions such as turbulence, boundary layer properties etc, one can then estimate a heat transfer coefficient, h. Heat loss follows then from the Newtonian relationship, h·A·(T-Tw), assuming the conditions in x-direction do not change. For a gas in a closed vessel the situation is more difficult to describe. Heat losses from exothermic gas-phase reactions in unstirred vessels occur by conduction and convection. At very low gas densities and heat release rates, the gas is stagnant, heat losses are almost exclusively conductive, so the temperature distribution in the reacting gas has a near parabolic shape with the maximum temperature rise occurring at the centre of the reaction vessel. In the case of an ideal conductive heat loss from a sphere filled with gas initially at uniform temperature ∆Ti above ambient, an analytical solution of the partial differential equation describing the temperature drop in time as a function of the temperature gradient can be derived [7] in terms of the Fourier number, Fo = κ t/ r2, where κ is thermal diffusivity, t time and r inner radius of sphere. At Fourier number 0.139 in the centre of the sphere the temperature decreased to ½∆Ti and hence the cooling half-time, ∆t½ is found, or:

κ ∆t½/ r2= 0.139 (1)

For air at 1 bara and 400 K (κ = 3.5.10-5 m2/s) and a 0.5 litre flask a value for ∆t½ is thus found of 10 seconds. For a 20 l sphere this time is roughly a factor 10 longer. However, temperature gradients in a gas result in density differences. Lighter parts are subjected to buoyancy force and so-called “natural convection” sets in. The onset of convection in a gaseous reaction system can be estimated by calculation of the dimensionless Rayleigh number (Ra). The Rayleigh number is as many other dimensionless numbers, a ratio of forces and is defined as:

3 2 /pRa g r C Tβ ρ λη= ∆ (2)

where g = acceleration due to gravity [ms-2], β = coefficient of cubical expansion of the gas [K-1], (here, reciprocal of the absolute temperature) r = radius of the (spherical) vessel [m], Cp = specific heat of the gas at constant pressure [J kg-1 K-1], ρ = density of the gas [kg m-3], ∆T = temperature difference between the centre and the wall of the reaction vessel [K], λ = thermal conductivity of the gas [W m-1 K-1], η = viscosity of the gas [kg m-1 s-1]. Experiments and calculations have shown that the following critical values for Ra can be distinguished:

Ra < 600: conduction 600 < Ra < 104 : conduction and convection Ra > 104 : convection

These critical values of the Rayleigh number should be independent of the temperature of the vessel and should apply to all gaseous systems and also to non-spherical vessels.


2.2 Influences on natural convection When the Rayleigh number is again considered it can be seen that it is a complicated function. Its dependencies can be presented as in [9]:

{ } , ( ), , ( , ), ( , , ), ( , , ), ( , , ),pRa f g T r C T p T T p T p Tβ ρ λ η= Φ Φ Φ Φ ∆ (3)

In the following an assessment will be given of the extent of its variation in the present studies. For a 9.5% n-butane in air mixture (equivalence ratio Φ = 3) an analysis is made of the Rayleigh number as function of temperature difference. The volume of the vessel is 500 ml. Initial pressure is 1 bara. It is assumed that mixture composition is constant. The mixture properties were calculated as shown in Appendix I. Figure 1 shows the separate regimes of heat transport. On the abscissa the ambient temperature is plotted, on the ordinate the temperature difference between the centre of the vessel and the temperature of the surface (Ta) is plotted.

0

10

20

30

40

50

60

70

80

500 550 600 650 700 750 800 850 900

Ambient Temperature [K]

∆∆ ∆∆T [K

]

Ra = 10^4Ra = 600

Convection

conduction

Convection + Conduction

Figure 1. Different regimes of heat transport as function of ambient temperature with constant composition (9.5% n-butane in air). Vessel size= 500 ml, p = 1 bar.

Above the upper line (Ra = 104) convection is the dominating process of heat transfer. Under the lowest line (Ra =600) heat transfer is purely conductive. In the region between the two lines both convection and conduction play a role. The lines have a parabolic shape due to the change in density (Ra ~ ρ2). The influence of the mixture properties on the Rayleigh number is evident. Since the specific heat (Cp) is in the numerator, and the product λ·�η forms the denominator of the fraction in Equation 2, the Rayleigh number will decrease during consumption of n-butane, when temperature in the vessel and of the surface will remain constant. The Rayleigh number is proportional to the cube of the radius, r3, and thus is proportional to volume. This means that the Rayleigh number for a 20 l vessel will be 100 times that of a 200 ml vessel. Therefore, at constant ambient temperature, the temperature difference needed to reach the critical condition of Ra = 104 value is 100 times lower. The different regimes of heat transfer, are shown in Figure 2 as a function of vessel size. Ambient temperature (Ta) and composition (Φ) are kept constant. The Rayleigh number is plotted as a function of vessel radius. The curves represent various temperature differences (∆T) between the gas and the


vessel wall. It is apparent that in the range of test vessels used in the project the Rayleigh number can vary over some orders of magnitude. In a volume of the 20-l vessel, small temperature differences are sufficient to generate convective heat transfer. In this vessel tests can be performed also at higher pressure. Since Ra = f(ρ2) = f(p2): the Rayleigh number will increase strongly with pressure. This trend is confirmed by the measurements described in Deliverable No. 33, Addendum A [4], although the relation found is linear (approximately h = p with h in W/m2K and p in bara) rather than parabolic. Mixture composition after 3 and last cool flame, p = 1 bar. T a=610 K.

0.0E+00

2.0E+03

4.0E+03

6.0E+03

8.0E+03

1.0E+04

1.2E+04

0 1 2 3 4 5 6 7 8 9 10

Vessel radius [cm]

Ray

leig

h N

umbe

r [ -

]

∆Τ = 1

∆Τ = 5

∆Τ = 16

∆Τ = 41

∆Τ = 70

∆Τ = 100

Convection &Conduction

Convection

Conduction

Ra = 104

Ra = 600

100 ml 200 ml200 ml

500 ml

∆Τ= 1

∆Τ = 16

∆Τ= 5

∆Τ= 41

∆Τ= 100

∆Τ= 82

Figure 2. Rayleigh number vs vessel radius. The influence of radius and temperature differences on the mode of heat transfer. Typical post-cool flame mixture (initial 9.5% n-butane in air). p = 1 bar, Ta=610 K. The radius of a 20-l vessel is 16.8 cm.

For a gas mixture reacting exothermically in a closed vessel the above discussion, by definition, implies the existence of a non-uniform distribution of temperature. As soon as reaction sets in, a temperature difference between wall and gas is generated and heat transfer to the (fixed temperature) wall will start. If the conditions are such that natural convection occurs, warm gas in the centre will rise, flow towards the walls at the top of the vessel and downwards along the walls, during which process cooling will occur. This way the temperature gradients will be mitigated, but the heat transport is greatly enhanced. Due to buoyancy the highest temperature will not remain in the centre of the vessel but be displaced towards the top. If the rate of heat production becomes higher enough, convection flow will become turbulent and large eddies will occur. As a result of this motion, gas pockets of different temperature will exist which may drift through the vessel and which will exchange heat by mixing with and by conduction to gas of different temperature. Models of batch reactor vessels in which the full detailed kinetics of hydrocarbon oxidation can be taken into account as in CHEMKIN’s module Aurora [10], allow at this moment at best calculations based on zero-dimensional conditions, signifying a spatially uniform temperature, that is with heat loss introduced on the basis of a constant heat transfer coefficient, an surface area to volume ratio of the vessel and a temperature difference between vessel content and wall. However, from the above it is clear that a uniform temperature of a reacting gas can exist only in a special case where vigorous mixing is induced mechanically. In a closed vessel it is also not possible to determine a volume or mass averaged temperature, which would approximate to some uniform value. Since the location of a maximum


temperature is also not fixed, the alternative that remains in an attempt to keep the approach simple, is to choose as reference temperature the temperature of the vessel centre. Therefore in experiments to determine h, this centre temperature was measured. In the smaller glass vessels in these experiments a small resistor in the centre was fed with a constant electric current to heat the gas to a steady state after which current was interrupted, while in the 20 l pressure vessel the gas (air) was heated by adiabatic compression when opening a fast acting valve to a canister containing pressurized air.

Assuming the spatial temperature distribution to remain similar for various conditions, Newton’s cooling law: / ( )aV C dT dt hA T Tρ− ⋅ = ⋅ − can be integrated to yield a ‘heat transfer

coefficient’ h as: 2 1

2 1

ln{( ) /( )}· a aT T T TV C

hA t t

ρ − −= −

− (4)

with V volume vessel, A interior surface area sphere, ρ density, C specific heat gas (here, at constant volume), and T – Ta temperature difference with ambient at two different times t1 and t2. Plotting the logarithmic temperature difference (T – Ta) versus time should produce a straight line if the heat transfer coefficient is constant. From the gradient an (average) heat transfer coefficient based on the temperature difference between centre and wall, can be derived and determined as a function of pressure by repeating over a range of pressures. Since as a result of natural convection, as we have discussed above, the conditions change with temperature difference and in time, so a constant heat transfer coefficient does not exist and the tangent produces a mean value over a certain range. As cooling just starts its value will quickly increase to a maximum and eventually it asymptotically reduces to zero. In the limiting case of pure conduction for a spherical vessel, applying Equation (4) above, the heat transfer coefficient based on ∆t½ can be derived from:

- ln (½∆Ti /∆Ti ) = 0.69 = h A ∆t½ / (ρ C V) (5)

Over a time interval, ∆t½, to half the initial temperature difference between centre of the vessel and wall at any initial value of temperature, the logarithmic term yields 0.69. Substitution of Equation (1), using κ = λ/ρ C and rearranging, in case of pure conduction an ‘equivalent value’ of h for the unsteady case can be derived via:

λ∆t½ / (0.139 ρ C r2) = h(4π r2)∆t½ /{0.69ρ C (4/3 π r3)}

yielding: h = 1.65 λ/r (6)

in which λ is the thermal conductivity of the gas and r is the radius of the vessel. For a vessel filled with air at 400 K, λ is 0.032 W/(m·K); at a volume of 500 ml r is 0.0492 m, hence h = 1.1 W/(m2K), while at 20 l r is 0.168 m and h = 0.31 W/(m2K). The experimental value found in the 500 ml vessel was lower, probably due to a systematic error in the set-up with the resistor. In the case of the 20 l vessel with an initial temperature difference of about 10 K, experimental results with compressed air can be fitted, see [6], with the relation: h = p. Because thermal conductivity does not vary much with pressure heat transfer by conduction would not be pressure dependent, so clearly natural convection plays an increasingly important role in heat transfer at increasing density, and hence pressure. Natural convection is very readily generated in a self-heating reacting gas. Kee et al. [11] performed a detailed study with tritium as a heat producing fluid both experimentally and numerically by solving the conservation equations for cylindrical and spherical geometry in the steady state. Their results for a sphere can be correlated to a line in a diagram of the surface averaged Nusselt number, Nu (= h’·2r/λ) and modified Grashof number, expressed as Gr {= q·g·β·ρ2(2r)5/(λ η2)}, see Figure 3.


Here h’ is based on a volumetric averaged gas temperatureT and a fixed wall temperature. Gr is modified by taking into account the volumetric heat generation q in W/(m3s) instead of the relative density difference; all other symbols have been defined earlier (see Eqn. 2). The correlation holds for a fluid for which Prandtl number (υ/κ) is about 0.7 where υ = η /ρ.

Figure 3. Heat transfer by natural convection in the steady state to the wall of a spherical vessel filled with a heat producing gas. Correlation between the Nusselt number averaged over the surface of the sphere versus a modified Grashof number, Kee et al., 1976. Nu is minimal in the case of pure conduction and is calculated by Kee et al. for a sphere to have the value 10 (steady state). With h based on an unsteady cooling (or heating) situation and centre temperature Tc as a reference, according to equation (6) at time ∆t½ the equivalent Nu would be 2×1.65 = 3.3, hence three times lower. The volume averaged temperature in unsteady state (e.g. cooling) at that point of time can be derived from the solution in [7] of the differential heat balance equation mentioned in relation with Equation (1). Here it yields a ratio: (Tc-Ta)/(T -Ta) = 3.23 or Nu = 3.3×3.23 = 10.7. However in the unsteady state the ratio of temperature differences is time-dependent and has at the start and end of a cooling or heating process the value 1. If, by way of a mean, a parabolic temperature profile is assumed (T = Tc-Cr2 with C = constant) the temperature ratio is 2.5 and Nu = 2.5 × 3.3 = 8.25. It is clear that as soon as convection becomes significant, the difference Tc -T becomes unimportant.

2.3 Heat production in low temperature oxidation In the oxidation of hydrocarbons heat generation is not constant but increases strongly during the process. It can increase by many orders of magnitude as shown for example by simulations with the CHEMKIN code of a perfectly stirred batch reactor applying the detailed kinetics model for C4-C10 hydrocarbons developed in the SAFEKINEX project (Deliverable No. 35 [12]). For a typical case described in Deliverable No. 29 [5], of fuel rich n-butane in pure oxygen at higher pressure the rate of heat production versus time is shown in Figure 4A. Roughly the time weighted mean value over the first 700 seconds is 1 W/m3 and over the remainder up to 1200 seconds 300 W/m3. These values were used to calculate h on the basis of the graph of Figure 3, despite the graph being, strictly speaking, only applicable to a steady state. Reading the graph can be done conveniently using the spread sheet of Appendix I. In Table 1 also an experimental value of h is given although the reference temperature is not exactly equal.


1,00E-07

1,00E-05

1,00E-03

1,00E-01

1,00E+01

1,00E+03

1,00E+05

0 500 1000 1500

Time [s]

Hea

t pro

duct

ion

[W /

m3 ]

Figure 4A. Example of calculated rate of heat production, q in W/m3 in a simulation run with CHEMKIN, Aurora for a mixture of 78% n-butane in oxygen initially at 4 bara and 500 K in a 20 l vessel with an assumed heat transfer coefficient of 4 W/(m2K) as described in Deliverable No. 29 [5]. For the 500 ml vessel at 575 K q has to be taken over the first 3 seconds (average 1.5 W/m3), but increases further rapidly to a mean of 7 kW/m3 up till 5 seconds when cool flame occurs. The value of h measured in air was similar to that by conduction alone: about 1 W/(m2K), as described in Deliverable No. 29 [5], but when derived from the first part of cooling curves after an AIT test in which explosion occurred, a value of about 7 W/(m2K) was obtained, see [4] and [9]. At 685 K initial temperature two-stage ignition and explosion takes place in the simulation. The ignition process takes 0.3 seconds and over that time the mean rate of heat production is high: 350 kW/m3. In Table 1 the calculated values of h’ are shown in comparison with the measured ones. Table 1: Heat transfer coefficient values in a self-heating gas in a spherical vessel calculated according to the method proposed by Kee et al. [11] and measured in a heated gas for two typical volumes: 20 l steel vessel and 500 ml glass one.

Heat transfer coefficient [W/(m2K)]

Mixture composition

[mol%]

Vessel volume

[m3]

Initial Pressure [bara]

Initial Tempera-

ture [K]

Calculatedmean rate

of heat generation [W/m3] over ([s])

Via Nu calculated

Experi-ment

n-C4H10-O2: 78-22 0.020 4 500 1 (0-700) 3.2 4 n-C4H10-O2: 78-22 0.020 4 500 300 (700-

1200) 9.7 4

n-C4H10-O2-N2: 9.5-19-71.5

5.10-4 1 575 1.5 (0-3) 4.7 6.9

n-C4H10-O2-N2: 9.5-19-71.5

5.10-4 1 575 7000 (3-5) 7.4 6.9

n-C4H10-O2-N2: 9.5-19-71.5

5.10-4 1 685 3.5.105 (0-0.3)

14.5 6.9

Heat production also varies with temperature. Griffiths et al. [13] calculated maximum rate of heat production of n-butane oxidation in a simulated perfectly stirred batch reactor. A result is given in Figure 4B. Thus the value of the heat transfer coefficient varies considerably.


Figure 4B. Simulation of the dependence of maximum heat release rate on vessel temperature from the isothermal reaction in a closed vessel for different mixtures of n-C4H10 + air at 1 bar according to Griffiths at al. [13]. With temperature and higher n-butane content heat release rate increases, but at 700 K clearly a transition can be seen. Currently the CHEMKIN suite of models is not the only one capable of simulating oxidation processes under various conditions. There are, at least, three other software packages: COSILAB, CANTERA and Chemical Workbench, which on the basis of detailed kinetics calculate both ignition in a perfectly stirred batch reactor and laminar burning velocity. For further details brief summaries are given in Appendix II of the capabilities of the packages and some background on their producers. In Chapter 4 in comparison some further results will be shown.

3 Numerical modelling of cooling of heated gas 3.1 Heat loss from an inert gas to a vessel wall To obtain an improved picture of the heat loss of an exothermically reacting gas in which natural convection develops and temperature gradients occur, the conservation equations of mass, momentum and energy have to be solved numerically in combination with a source term and boundary conditions. As a model vessel the 20 l one was chosen. The equation used for determination of heat transfer coefficient is:

d ln( )1

3 dwall

V

T Th rC

tρ

−= (7)

Where kgKJCV /750= , r = 0.168 m and density ρ follows from pressure and temperature through the ideal gas law. The heat transfer coefficient will depend on a reference temperature T. In the case of non-uniform temperature distributions inside the vessel under consideration there are three ways for determination of the reference temperature. First of all there is the maximum temperature but this way is not applicable in experiments. The second approach is from the average temperature, which also is not easily estimated in experiments. And third there is the temperature at a local point of the internal sphere, e.g. the centre. Thermocouple positions are drawn in Figure 6. The same local points were used in simulations. The model calculations will be compared with experimental measurements; to start with this will be measured cooling curves from air as reported in Deliverable No. 33 Addendum A [2].

600 650 700 750 800 8500.00

0.25

0.50

0.75

(0.15 : 1.00 : 3.76)

R /

W c

m-3

T / K

φφφφ = 10.7

φφφφ = 6.5

φφφφ = 1

(1.00 : 1.00 : 3.76)

(n-C4H10 + O2 + N2 = 1.65 : 1.00 : 3.76)


In that respect the limitation of the accuracy in the experimental measurements should be considered. There are errors of determination of wall temperature Twall and reference temperature T. Let us estimate the error in heat transfer coefficient related with the natural logarithm temperature errors. Equation (7) after integration is used for this purpose:

−−

=

−−

⇒

−−

1

1lnlnln~

2

1

2

1

2

1

l

l

nl

nl

TT

TTh

wall

wall (8)

where l1 = T1/Twall and l2 = T2/Twall at two points on the cooling curve over which the tangent is measured and n is the quotient of real wall temperature, Ťwall and an assumed value for Twall. Consider the example of Figure 5 taken from Deliverable No. 33 Addendum A [2] and select for a straight line part l1 is 1.04 (312 K or 4% more then assumed wall temperature – 300 K), and l2 is 1.003 (301 K or 0.3% more than the assumed wall temperature – 300 K). Then in this example the value of h is:

3.131003.1

104.1ln~ =

−−

h W/m2·K

Let us suppose that wall temperature is determined with relative error n of 1%. For example: one assumes Twall = 300 K but in reality Ťwall = 297 K. This error may occur due to non-uniform wall heating. (Temperature difference for T4 position becomes in the given example, even if it is negative, which confirms the inaccuracy of Twall).

Figure 5. Example (Ex. 45d pini =2.1 bara, Twall = 300 K, ∆T0 = 12 K) of temperature profiles of cooling compressed air in 20 l sphere at a wall temperature of 300 K.

Hence from the value 1 in both numerator and denominator 0.01 shall be subtracted:

8.399.0003.1

99.004.1ln~ =

−−

h W/m2·K

This means that the error in the heat transfer coefficient determination is a factor 3 and this also explains the dispersion in the experimental results shown in [2].

3.2 The numerical model The numerical model of a sphere1 is represented as two-dimensional circular cavity. The initial conditions for inert gas and reactive flow are almost the same. The fluid was assumed to remain quiescent at start. The spherical wall is constrained by no-slip and iso-thermal condition. The internal domain is filled with air and all the fluid properties are calculated at a reference temperature given by T. Initially the temperature of air inside the domain is assumed constant at fixed temperature T0. In case of reactive flow a constant volumetric source is injected.

1 The contribution of Nitesh Goyal in calculating the heat transfer coefficient is gratefully acknowledged.


T1T3 T2 Tcen

T6

T4

Figure 6. Position of thermocouples inside the 20 l sphere and used mesh.

The numerical model of the spherical shell is modelled in Gambit 2.1. The grid is meshed with quadrilateral elements to make it structured over the entire domain. During the simulation run the temperature in local points, average and maximum, maximum velocity and pressure was written. The temperature-time derivative for determining the value of h was determined as a ratio between the nearest differences and not between distant points:

∂ x∂ y

=xn− xn− 1

yn− yn− 1 (9)

The analysis is based on small temperature difference in the experimental work, so the assumptions of constant transport and material properties are well justified. Viscous dissipation is neglected because the velocities are small. The density variation, as it is very small, is accounted for by using the ideal gas law. The flow field is described by the continuity equation, and conservation of momentum and thermal energy. The equations were solved by means of the FLUENT package, see Appendix III for some additional information.

3.3 Calculation results with a heated inert gas Below in Figures 7A and B results of calculation are shown. Initial parameters coincide with the experimental values. Conditions are chosen as in Experiment 45d of Deliverable No. 33, Addendum A [6]: Spherical volume 20 l, pini = 2.1 bara, Twall = 300 K, ∆T0 = 12 K. The heat transfer coefficient determined by the volumetric average temperature as a reference in the first moments is high when gas at the wall is cooled and the motion of the gas is initiated. In this stage the change in maximum temperature is moderate and therefore the heat transfer coefficient based on the maximum temperature as a reference is relatively low. A similar time history is observed for heat transfer coefficients determined by a local temperature as appears from Figure 7B.


1 10 1000

2

4

6

8

10

h, W

/(m

2 K)

t, s

1 2

Fig. 7A. Computed heat transfer coefficient time histories for reference temperature

determined: 1 – by average temperature, or 2 – by maximum temperature. pini = 2.1 bara, Twall = 300 K, ∆T0 = 12 K

As a result of the evolution of gas motion after the first stage of low heat transfer coefficient up to 10 seconds with local temperature as a reference, a second stage arrives of fast increasing and a subsequent gradual decrease after 10 seconds. This is clearly shown in Figure 7B.

1 10 1000

2

4

6

8

10

12

h, W

/(m

2 K)

t, s

1 2 3 4 5

Fig. 7B. Heat transfer coefficient time histories in case reference temperature is determined in different positions : 1- in P1; 2 – in P2; 3 – in P3; 4 – in P4; 5 – in P6. Points P refer to the positions of the thermocouples in Figure 6. pini = 2.1 bara, Twall = 300 K, ∆T0 = 12 K Therefore one cannot correlate the whole time history by a single simple dependence. However one could pick out two different parts e.g. from 1-2 s and 10-100 s and describe each part separately. A similar pattern was found at higher pressure, see Figures 8 and 9. To describe the influence of initial pressure on heat exchange of a 20 l vessel over a range of pressures calculations were made and the results shown in Figure 10. So, the pressure was increased to 12.8 bars and other conditions kept as before: Twall = 300 K, ∆T0 = 12 K.


1 10 1000

2

4

6

8

10

12

14

16

h, W

/(m

2 K)

t, s

1 2

Fig. 8. Heat transfer coefficient time histories for reference temperature determined via

different ways: 1 – by average temperature; 2 – by maximum temperature. pini=4.25 bara; Twall =300 K, ∆T0 = 12 K

1 10 1000

2

4

6

8

10

12

14

16

h, W

/(m

2 K)

t, s

1 2 3 4 5

Fig. 9. Heat transfer coefficient time histories for reference temperature determined in

different positions P of the thermocouples with the same indices shown in Figure 6: 1- in P1; 2 – in P2; 3 – in P3; 4 – in P4; 5 – in P6. pini= 4.25 bara; Twall = 300 K, ∆T0 = 12 K

0

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30

1 10 100

t, s

h, W

/(m

^2K

)

1

2

3

4

Fig. 10. Heat transfer coefficient time histories for volumetric average as reference

temperature at different initial pressure levels: 1– 2.1 bara; 2 – 4.25 bara; 3 – 8.4 bara; 4 – 12.6 bara; Twall = 300 K, ∆T0 = 12 K


The time curves behave very similar. Two regions of more or less constant heat transfer coefficient can be distinguished again. The results derived from the time histories of Figure 10 are plotted in Figures 11 and 12 for the early region (1-2 s) and the late part (10-100 s) in approximately a linear dependency of heat transfer coefficient on pressure. This was repeated for three temperature levels: 300, 500 and 800 K.

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p, bara

h, W

/(m

^2K

)

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0 5 10 15

p, bara

h, W

/(m

^2K

)

300 K

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800 K

Fig. 11. Calculated heat transfer coefficient at three temperature levels as a function of initial pressure at an early stage of cooling: at 1 s.

Fig. 12. Calculated heat transfer coefficient at three temperature levels as a function of initial pressure in a late stage of cooling: at 100 s.

0

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0 5 10 15 20 25 30ρρρρ, kg/m3

h, W

/(m

2 K)

Tcan = Tsph = 300 K, Psph = 1 barTcan = Tsph = 300 K, Psph = varTcan = Tsph = 400 K, Psph = varTcan = Tsph = 500 K, Psph = varTcan = Tsph = 300 K, Pcan = 0 bara, reverse jet

y = 0.9892x

R2 = 0.7994

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0 5 10 15 20 25 30

p, bara

h, W

/(m

2 K)

Tcan = Tsph = 300 K, Psph = 1 barTcan = Tsph = 300 K, Psph = varTcan = Tsph = 400 K, Psph = varTcan = Tsph = 500 K, Psph = varTcan = Tsph = 300 K, Pcan = 0 bara, reverse jetLinear (trendline)

Fig. 13. Measured heat transfer coefficient plotted as a function of density at various pressure and temperature levels. Data fitted to a straight line for each temperature.

Fig. 14. Measured heat transfer coefficient as a function of initial pressure at different temperature levels. All data fitted to one straight line, Deliverable No. 33 Add. A [6]

In Figures 13 and 14 the experimental points are plotted as given in Deliverable No. 33 Addendum A [6]. The scatter in data is relatively large but can be explained by the change in h over time. Usually late time periods were taken for the measurement of the ln (∆T – t) slope. In Figure 13 the trend of the influence of temperature as is seen in the calculations is only visible for the higher temperatures. In Figure 14 all data are fitted to one straight line which corresponds fairly well with the line of calculated values at 300 K for 100 seconds after the start of cooling in Figure 12. In conclusion it can be stated that the heat transfer from a self-heating gas to an outside wall can be reasonably well estimated from the experiments and calculations made.


4 Time duration to gas self-ignition, IDT 4.1 Low temperature part ( ≤≤≤≤ 700K) with n-butane as fuel Exothermic reactions generate heat and self-heating of the reactants occurs when only part of the heat is transferred to the surroundings. When the process is at constant pressure the heat generation rate is the product of enthalpy change –∆H and reaction rate, and for a constant volume process the product of change in internal energy –∆U and reaction rate Usually reaction rate increases exponentially with temperature as described by the Arrhenius equation, which in a simple form is written as:

dx/dt = x k exp(-E/RT) (10)

in which x = concentration of decomposing compound X, k is the rate constant, T is the reactant temperature, E is the activation energy, and R is the universal gas constant. The rate constant k can still be a weak function of temperature and may therefore, for a large temperature range, be written as ATn. A more extensive survey of the theory of ignition and gaseous fuel oxidation reactions is presented in Griffiths and Barnard [14]. If the overall reaction rate and heat generation can be lumped into a Arrhenius type of equation, a wealth of analytical models has been developed following Semenov, Frank-Kamenetzkii and Merzhanov. A well-known example for fitting experimental results of determination of ignition temperature T as a function of pressure p with A and B as constants, is the Semenov relation for thermal ignition:

ln (p/T) = A/T + B (11)

In a closed vessel where no heat losses occur and the reaction rate is not dependent on concentration (zero-order), given an initial temperature Ti the adiabatic induction time to ignition (at constant volume) is given by:

tad = {Cv/(–∆U)}{ RTi2/(E·k)}exp(E/RTi) (12)

where Cv is the heat capacity of the reaction mass. This represents the shortest time interval in which ignition can develop. When heat losses occur, the induction time increases depending on thermal conductivity and internal temperature gradients and heat transfer by convection near a wall. However, the importance of radical reactions in hydrocarbon oxidation processes must also be recognized, see e.g. [25, 26]. In particular at relatively low temperature these can accelerate and set off ignition, yet during a very substantial fraction of the overall induction time there is very little temperature change. The acceleration of reaction rate through this period is the result of the formation of alkyl peroxides and alkyl keto-peroxides which gradually accumulate a reservoir of active species as they decompose at increasing rates (575 K, 1 bara: 0.1 butyl peroxide and 0.2 mol% keto-peroxide). The decomposition occurs in a dramatically accelerating fashion (in the so called “degenerate chain branching” mode) aided by the accompanying temperature increase in the late stages of the induction period. The reactive hydroxyl (·OH) radicals play a crucial role in being produced in the decomposition and in initiating further reactions. A surge of these radicals leads to the phenomenon of cool flame which in the subsequent exothermic reactions increases temperature by tens to hundreds of degrees – although still far from the maximum possible temperature for complete combustion because the chemical conversion leads mainly to partially oxidised intermediate compounds However, this stage may bring conditions of temperature and pressure to a state in which further exothermic reactions can be induced in the complex mixture, principally through hydrogen peroxide decomposition as the hydroxyl radical producer, and leading to the final stage of ignition . An ignition process can therefore be two- or even multistage. Depending on conditions of pressure, temperature and heat loss a cool flame can be extinguished but the


burst can repeat itself a number of times. Oxidation can also take place as a slow process without a reaching this peak of activity (which is then of little concern as a combustion hazard but may be detrimental to the quality of a product from the chemical process). In Deliverables Nos. 5 [1], 29 [5], 30 [3] and 45-47 [15] more attention is given to details of these phenomena. A typical temperature-time history for the induction to a cool flame in n-butane is given in Figure 15. This curve was calculated in the same simulation run for 78% n-butane in oxygen as reported in Section 2.2. There the rate of heat production was shown in Figure 4. As can be seen the temperature increase for a large part of the induction time is small. Up to 700 seconds it is 0.04 K and at 1000 seconds still 1 K. During most of the induction period process can be called isothermal.

Figure 15. Example of calculated temperature time history in a simulation run with CHEMKIN, Aurora with the CNRS Nancy EXGAS derived model for a mixture of 78 mol% n-butane in oxygen initially at 4.1 bara and 500 K in a 20 l vessel with an assumed heat transfer coefficient of 4 W/(m2K) as described in Deliverable No. 29 [5]. The temperature increase up to 700 seconds is only 0.04 K and at 1000 seconds still only 1 K. The process is almost isothermal throughout this stage of reaction.

570

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870

970

1070

1170

1270

1370

1470

1570

0 2 4 6 8 10Time, s

T, K

h=0,2h=5h=40h=82

Figure 16. Simulation of a cool flame reaction in 9.5 mol% n-butane in air at 1 bara and at an initial temperature of 575 K based on detailed kinetics (further) developed in the Safekinex project by CNRS Nancy, Deliverable No. 35 [12]. The simulation is in a closed batch reactor of 20 l of uniform temperature at different levels of heat transfer at the wall, h in W/(m2K), simulating intensity of stirring. It can be concluded that heat loss has negligible effect on ignition delay. The effect of rate of heat loss becomes apparent from the height of the peak at ignition (two-stage) and the tangent of the slope of the cooling curve behind the peak.

450

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0 500 1000 1500

Time [s]

Tem

pera

ture

[K]


In the simulation there is a transition from the cool flame into explosion (two-stage ignition) with almost maximum heat output in the final jump in temperature and pressure (when the vessel is a closed volume), while in the experiments at this initial temperature the phenomena are much less violent and are limited to (repetitive) cool flame superposed on slow oxidation. Examples are shown in Deliverables Nos. 5 and 30 [1, 3].

0

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550 600 650 700 750 800 850

Temperature, K

IDT

, s

Experiments semi-open 500ml vessel

Calculation, full CNRS mechanism(Expl) (P=const)

Calculation, full CNRS mechanism(CF) (P=const)

Figure 17A. Induction time to cool flame and/or explosion in 9.5 mol% (rich) n-butane-air mixture at atmospheric pressure measured in semi-open, spherical 500 ml quartz glass vessel [1] and for comparison, calculated with detailed kinetic model developed in the Safekinex project by CNRS, Nancy. The best EXGAS derived model [12] shows a reactivity which at low temperature is too high (same ignition delay time at roughly 25 K lower temperature). The heat transfer coefficient, h, is taken as 1.5 W/(m2K). Expl = Explosion, CF = Cool Flame.

0

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25

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550 600 650 700 750 800 850

Temperature, K

IDT

, s

Experiments semi-open 200ml vesselExperiments closed 200ml vesselCalculation, full CNRS mechanism (Expl) (P=const)Calculation, full CNRS mechanism (CF) (P=const)

Figure 17B. The same as Figure 17A, but now for a 200 ml vessel in two versions: spherical semi-open quartz glass [1] and cylindrical, stainless steel closed [1, 2]. The difference between model and experiment below 700 K is as in the previous figure, but note the much better agreement above 750 K with the closed vessel experiments. (Calculation at constant pressure or constant volume did not show much difference). h= 1.5 W/(m2K); Expl = Explosion, CF = Cool Flame.


0

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15

20

25

30

500 550 600 650 700 750 800 850

Temperature, K

IDT

, s

Experiments 200 ml 10 bara

Calculation 200 ml,10 bara closed

Experiments 200 ml 1 bara

Figure 17C. Experiments with 9.7 mol% n-butane in air measuring Ignition Delay Times at 10 bara [1] in closed 200 ml cylindrical stainless steel vessels. In comparison CHEMKIN calculation results with the CNRS n-butane mechanism with h= 1.5 W/(m2K), and as a reference the experimental results at 1 bara closed vessel shown previously in Fig. 17B.

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0 5 10 15 20 25

Time [min]

Tem

pera

ture

[K]

0

0,05

0,1

0,15

0,2

0,25

Mol

e fra

ctio

n O

2

Temperature [K]

Mole fraction O2

Mole fraction O2experimental

Figure 18. Model calculation with detailed EXGAS kinetics of temperature-time history of self-ignition of 78% n-butane and 22% oxygen at 4.1 bara and 500 K in a 20 l steel vessel [5]. If performed at 38.5 K lower temperature (461.5 K) the calculation synchronised with the measured consumption of oxygen (diamonds). Heat transfer coefficient is assumed to be 4 W/(m2K). If low temperature oxidation is active, acceleration of reaction takes place via the radical chain branching process and much less as a result of self heating, so heat loss has only limited influence on ignition delay time. This is illustrated in Figure 16 showing simulation results with 9.5% n-butane in air at 1 bara. In Figures 17A and B and 18 comparisons are shown of simulations with experiments at quite different conditions2. In all cases the kinetic model below 650 K behaves as if it is too

2 Although the IDT in the simulation can be determined according to the tangential method as done in the experiment, because the highest rate of increase of temperature in the simulation is always near the maximum temperature (steep temperature jump), for simplicity IDT is taken as calculated by the default in the program being the time to reach the initial temperature plus 400 K.


reactive. To obtain the same IDT-value the simulation has to be run at about 25 K (Figures 17 A and B respectively) and 38.5 K (Figure 18) lower than the experiments were done. The experimental results at low temperature, such as in Figures 17A and B have been obtained by TU Delft in semi-open glass flasks in different volumes (100, 200 and 500 ml), but have been reproduced rather accurately at BAM in 200 ml closed steel vessels. This confirms that the rate of heat loss does not play a significant role. It is therefore probable that the model indeed over emphasises the reactive. Recently, Frolov et al. [16] simulated the 78% n-butane in oxygen experiment with an alternative butane oxidation model. To reproduce the experimental result they assumed slow decomposition of butyl hydroperoxide and hydrogen peroxide respectively into oxygen and butane water to simulate the termination of reactive intermediates on soot particles and walls:

C4H9O2H → C4H10 + O2 (a) H2O2 → H2O + 0.5O2 (b)

The effective activation energies E1 and E2 of reactions (a) and (b) were assumed zero, while the corresponding pre-exponential factors were taken equal to k1 = k2 = k = 80 s-1, hence at a temperature independent low rate representing mass transport types of processes. When these two reactions were included in the SAFEKINEX scheme for the test at 500 K presented in Figure 18 the temperature difference reduced from 38.5 to 6.5 K. This appears to be the first numerical investigation of surface destruction of this type in the low temperature oxidation region. In the oxidation mechanism after formation of a butyl radical followed by molecular oxygen addition in the oxidation mechanism, butyl hydroperoxide can be formed via external H-abstraction. Alternatively an intramolecular H-abstraction yields a butyl hydroperoxy radical to which further oxygen addition occurs leading to butyl ketohydroperoxide, C3H7COOOH, see e.g. Deliverable No. 35 [12]. On the basis of CHEMKIN calculations it turned out that taking out the internal H-abstraction part of reaction at 500 K does not change the outcome much, while in contrast blocking the external branch makes a marked difference and delays the cool flame occurrence significantly. At a higher temperature the internal branch becomes increasingly influential. At 550 K the two branches have a similar quantitative contribution, but at 650 K the internal branch is predominant. In addition, when in analogy of reactions (a) and (b) a decomposition of butyl keto-hydroperoxide was assumed at 575 K, even with a rate constant as low as 6 s-1, the discrepancy for IDT between numerical simulation and experiment disappears. A small error in the value of a rate constant in the scheme or a termination at the wall can therefore account for the mismatch. Wall effects will be addressed further in the next section. At higher pressure, molecular collision frequencies go up and the lowest temperature at the which cool flame occurs decreases considerably, as is shown in Figure 17C, while also in small volumes much longer induction times become possible (at 10 bara in 200 ml at 543 K IDT becomes 100 s). Figures 17A, B and C and Figure 18 also show the strong effect of initial temperature on the IDT value. At lower temperature IDT lengthens, such that at 500 K and 4.1 bara for 78 mol% n-butane in oxygen the IDT becomes as long as 20 minutes. The relation between IDT and temperature can be approximated with an exponential function in a so-called Semenov plot (log IDT vs. 1/T), although this name is used too for describing the relation between log p and 1/Tign. If the process of ignition would be thermal rather than chain branching and nearly isothermal the relation IDT versus T may also take the form of Equation (12), which has the advantage of including the heat capacity, heat of reaction and


rate dependence on pressure. If the following values3 are substituted: E = 153 kJ/mol K (36.5 kcal/mol K), k = 3.3·1011

·p0.5 and at atmospheric pressure -∆Q = 2·105 J/m3 or rather 2.95·105 J/kg (the overall reaction heat effect -∆Q calculated by integration over time of a CHEMKIN, Aurora run output of the rate of heat generation is at 560 K of this order of magnitude) the measured IDT values in the LTOM region for the 9.5% n-butane in air at atmospheric pressure (C=Cp) are reasonably well reproduced, see Figure 19A. For the calculations use can be made of the spreadsheet of Appendix I. For this range of conditions the relation can therefore be used for engineering purposes. The measured IDT value for a 78% n-butane mixture in oxygen at 500 K and 4.06 bara is about 1300 seconds [5]. With the values as above (C=Cv, but same heat effect per unit of mass) an IDT-value is found of 1370 s. At higher pressure and longer ignition delay times prediction by this relation becomes worse. This is true for the 9.7% n-butane mixtures in air at 10 bara (C=Cv), as shown in Figure 19B, of which the experimental values have been reported in Deliverables Nos. 5 and 33 [1, 2]. To produce Figure 19B the heat release per unit of mass has been reduced by a factor of 3. Also it seems that the apparent activation energy at the higher pressure and lower temperature becomes higher (roughly 50 rather than 36.5 kcal/mol). In other words at lower temperatures the experimental IDT becomes relatively longer. An explanation can be sought in the slower production of organic peroxides or the decomposition as mentioned before, although one would expect the latter to be less influential at higher pressure or in a larger vessel.

05

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Temperature [K]

Igni

tion

Del

ay T

ime

[s]

Measured points

Calculated exponential

Poly. (Calculatedexponential)

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500 520 540 560 580 600

Temperature [K]

Igni

tion

Del

ay T

ime

[s] Experiment 6.3 l

Calculated

Experiment 200 ml

Poly. (Calculated)

Figure 19A: Fit by a 6-degree polynomial of IDT points calculated with Equation 8 at 10 K temperature intervals with the parameter values quoted in the text above for an atmospheric 9.5% n-butane mixture in air, in comparison with the measurements in a 200 ml vessel reported in Deliverable No. 5 [1].

Figure 19B: Fit by a 6-degree poly-nomial of IDT points calculated with Eq. 8 with the same parameter values as for Fig. 19 A for 9.7% n-butane mixture in air, at a pressure of 10 bara in comparison with the measurements in 6.3 and 0.2 l steel vessels reported in Deliverables Nos. 33 and 5 [2, 1].

In conclusion it is clear that heat loss does not much affect the time of occurrence of a cool flame. Prediction of ignition delay time on simulation of full kinetics in a perfectly stirred batch reactor underestimates measured values at lower temperature and higher pressure. To a lesser extent the same is true for a simple engineering type of equation.

4.2 Higher temperature part (> 700 K) At higher temperature where the intermediate mechanism (ITOM) becomes important, i.e. for n-butane above 700 K, it was thought that heat loss might have more effect on IDT. 3 Suggested in personal communication by Frolov, Basevich and Borisov (Semenov Institute, Moscow) September 2006


Examining the experimental findings as reproduced in Figure 20A seems to strengthen that interpretation. The IDT-values near 760 K seem to strongly increase with decreasing volume. In Figure 20B temperature-time histories are plotted of AIT tests near 760 K. In 100 and 200 ml vessels the wall temperature has been 761 K, but in the 500 ml one it was 750 K. Ignition delay times τT for a 9.5% n-butane in air mixture. P = 1 atm.

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Ambient Temperature [K]

Igni

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Del

ay T

ime

[s]

500 ml

200 ml

100 ml

Figure 20A. Induction time versus ambient temperature showing the Negative Temperature Coefficient (NTC)-diagrams for the AIT tests in semi-open 100, 200 and 500 ml flasks with 9.5 mol% n-butane in air at atmospheric pressure. (IDT open squares between 730 and 770 K with 100 ml vessel was determined by hand), Deliverable No. 5 [1]. In the region CF Cool Flame resulted, partly superposed on SO, Slow Oxidation, and finally EXPL explosion.

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Time [s]

Tem

pera

ture

[K]

T4 500 mlT5 500 mlTwall 500 mlT4 200 mlT5 200 mlTwall 200 mlT4 100 mlT5 100 mlTwall 100 ml

Figure 20B. Temperature-time history of AIT test in 500ml flask at 750 K and in 200 and 100 ml at 761 K with 9.5 mol% n-butane in air at atmospheric pressure. The start of the experiment with the injection of the mixture was at about 4.5 s on the time line. The test in the 100 ml flask did not explode but showed only slow oxidation with a maximum temperature at 160 s. Back extrapolation from the point of the maximum rate of temperature rise resulted in the IDT value shown in Figure 10a of about 40 s. The centre temperature T4 starts higher but remains lower in the explosion peak than the temperature near the top T5. The peak of the 500 ml test would therefore have come out at 760 K a few seconds earlier and with a higher temperature maximum. In general with smaller volume the peak, sometimes accompanied by audible and visual effects, comes later and is less pronounced. In the 100 ml

CF

CF on SO

SO EXPL


volume an explosion does not develop; the reaction takes place as a long duration slow oxidation with a maximum temperature rise of less than 5 K after about 160 seconds. It is only that the tangent projection method for determining IDT at the intersection with the base line [1] produces the corresponding duplicate test points of 37.5 and 42.5 seconds in Figure 20A. However, in the simulation with CHEMKIN neither area-to-volume ratio, nor heat transfer coefficient has much effect on induction time, although the effect is greater than that observed below 700 K. This could already have been noted when comparing calculated IDT values versus temperature above 700 K for 500 ml in Figure 17A with those for 200 ml in Figure 17B. Induction time is

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pe

ratu

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500 ml200 ml

100 ml

Figure 21. Calculated temperature-time histories at 760 K wall temperature of 9.5 mol% n-butane in air with the CNRS mechanism at atmospheric pressure with an extremely high heat transfer coefficient of 100 W/(m2K) for three different vessel volumes: 500, 200 and 100 ml. As can be noticed heat loss has only a minor influence on induction time, but has an effect on the temperature reached.

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Time [s]

Tem

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[K]

Twall 761T4 761T5 761Twall 852

T4 852T5 852

Figure 23. Temperature-time histories of AIT tests at 761 K and 852 K in semi-open 100 ml flask with 9.5 mol% n-butane in air at atmospheric pressure. The experiment at 852 K shows that also in the 100 ml flask at higher temperature explosion is possible. Typical for sudden reactions either cool flame or explosion, is the peak becoming highest near the top of the vessel and not in the centre of vessel.


not strongly affected. On the other hand maximum temperature decreases with volume as shown clearly when comparing calculated T-t histories at 760 K wall temperature presented in Figure 21 for the three volumes at relatively high heat loss: that is, in semi-open vessel (pressure constant) and very high heat transfer coefficient of 100 W/(m2K). However, the induction times remain much shorter than those measured and even for the 100 ml volume there is in the calculation still a considerable heat production peak at the end of the process.

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Te

mp

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h=0.9 W/(m2K)h=10 W/(m2K)h=50 W/(m2K)

h=100 W/(m2K)

Figure 22A. Results of calculated tempera-ture-time histories with 9.5 % n-butane in air in a semi-open 200 ml vessel at 4 different heat loss levels at 760 K.

Figure 22B. Results of calculated temperature-time histories with 9.5 % n-butane in air in a closed 200 ml vessel at 4 different heat loss levels at 760 K.

Comparison of the simulation results at constant pressure and constant volume in Figures 22A and B reveals that closing a vessel has a noticeable effect on (calculated) explosion phenomena. Simulations have been carried out at four extents of heat transfer coefficient. The peaks become higher and earlier when the volume is closed (no work is exerted). It shall be concluded that although differences are there, they are quantitatively limited. This is consistent with the earlier noted finding that heat loss has more influence than below 700 K. Experimentally in the semi-open 100 ml flask at higher initial temperature, explosion peaks do develop, as illustrated by the test at 852 K presented in Figure 23, where in contrast to 760 K a reaction peak occurs instead of a slow oxidation. Pressure has a relative strong effect on reducing the induction time. At 700 and 800 K induction time reduces from 0.4 and 2.1 seconds respectively at atmospheric level to 0.02 and 0.03 seconds at 10 bara, whereas the H2O2 concentration just before reaching the temperature peak of 1650 - 1730 K goes through a maximum of up to 0.7 mol%. Instead of the progressively accelerated decomposition of accumulating organic peroxides as butyl hydroperoxide and butyl ketohydroperoxide as ‘fuel’ for chain branching and the occurrence of the cool flame phenomenon as in the low temperature oxidation mechanism (LTOM), now hydrogen peroxide build-up and decomposition can lead to hot ignition. An analysis is given by Griffiths et al. [17] about the role of H2O2 as an intermediate and the complex pathways in which the very reactive ·OH and the slower reacting HO2· radicals act at both sides of reaction equations. An illustration of the change in mechanism is shown by. the open squares near the abscissa of Figure 17B above 700 K, indicating that the cool flame mechanism in these cases is still weakly present but loses effect almost immediately after the start of the oxidation. The accumulating hydrogen peroxide is totally consumed in the final

P = constant V = constant


temperature jump4. At 750 K, just before the peak, the calculated H2O2 concentration is 0.63 mol% and at 800 K 0.41 mol%. The calculated time to ignition at temperatures just above 700 K is of the order of a few seconds and short relative to the experimentally measured IDT in AIT experiments at atmospheric pressure: e.g. at 750 K 30 s in 100 ml, 20 s in 200 ml and 10 s in 500 ml; as appears from Figure 20A for the experiments and the calculated ‘No wall effect’ column of Table 2. Table 2. Calculated induction periods, IDT in seconds, for the 9.5 mol% n-butane in air mixture at 750 K and at pressures of 1, 2 and 10 bara, taking account of wall effects, h = 1.5 W/(m2K).

Vessel type Experiment No wall effect Cat. I Cat. II T peak CatII, K 100 ml glass 30 3.1 14.0 1890.0 956 200 ml glass 20 3.1 10.0 198.0 1346 500 ml glass 10 3.0 6.0 14.5 1652

200 ml steel 1 bara 5 2.7 9.5 178.0 1840 200 ml steel 2 bara 0.5 0.6 0.7 1985 200 ml steel 10 bara Ca. 1 0.1 0.1 0.1 2051

It is known that the hydroperoxy HO2· radicals are relatively long living. In smaller vessel the ratio of wall surface area to volume increases, radicals can travel a smaller distance to reach a wall and surface termination reactions are more favoured, even though molecular mean free paths are short at atmospheric pressure. Even though molecular mean free paths are short at atmospheric pressure the species of lower reactivity are able to sustain multiple collisions in the gas phase without reaction, and so can migrate to the wall. As part of the SAFEKINEX project some work5 has been done to investigate this effect. In Appendix IV a brief communication paper of this work is given. In line with the assumptions made in this paper a number of calculations have been performed for the vessels relevant in the experimental part of the project. All vessels were assumed spherical (The calculation serves just to obtain an order of magnitude impression). Acidic material (Category I as defined in Appendix IV) and salt and metal oxides (Category II, with a much stronger effect) are known to decompose HO2· radicals and H2O2 to inert products The rates follow from the product kwd (kw is rate constant in s-1, d = diameter vessel in m) with values of respectively 10.7 and 0.05 m/s. Category I corresponds with the first value; category II with both. Category I is certainly relevant for glass; category II is relevant to steel. However in the experimental tests no special care was taken to clean and pacify the glass or metal surfaces (other than the “ageing” process that occurs with repeated experiments). So, the glass may be contaminated to some degree with Category II substances. The activity of the stainless steel surface of the 200 ml vessel with respect to metal oxides is unknown and may be low. Calculation results at an initial temperature of 750 K are collected in Table 2 for semi-open (closed by perforated stopper) quartz glass vessels, 100, 200 and 500 ml and closed stainless steel 200 ml. For comparison experimental time values estimated from Figure 20A are given in the second column. The column on the far right shows, as a measure of the strength of the end-effect – the explosion- the maximum temperature reached with Category II wall activity. The figures indicate that wall effects seem to be rather strong in the range of volumes of the

4 This jump is associated with the so called blue flame phenomenon which because of the immediate further development to hot flame will mostly not be discernible as such. 5 This contribution is based on the Ph.D. study of F. Buda, which is gratefully acknowledged.


AIT test set-up (100 – 500 ml). The stronger the wall effect, the slower the process of oxidation and the lower the temperature reached in the peak, since heat loss is effective over a larger time period. The deviations can easily explain the experimental results. Also striking is the reducing effect of pressure. Doubling pressure to 2 bar almost suppresses wall effects completely. This can be explained by the many bimolecular reactions with oxygen in which HO2· radicals are produced. At increased pressure as a result of the higher production of HO2· radicals the decomposition at a wall does not have a sufficiently significant effect on concentration to compete effectively with the accelerating effect of chain branching. AIT should therefore certainly not be determined in open vessels. Table 3 shows that the wall effect is not influenced heavily by heat transfer, as is to be expected from the results without wall effect taken into account. Table 3. Calculated induction periods, IDT in seconds, for the 9.5 mol% n-butane in air mixture at various values of the heat transfer coefficient, h, at 750 K and in a semi-open 100 ml quartz glass vessel at atmospheric pressure, taking account of wall effects

h W/m2K No wall effect/ s Category I/ s Category II/ s T peak Cat II/ K 1.5 3.1 14.0 1890 956.0 15.0 3.9 15.3 1890 751.4 45.0 4.8 17.0 1890 750.5

It is also interesting to see the effects over the temperature range of interest between 700 and 825 K. Results of these calculations are given in Table 4. It therefore appears that even the shape of the IDT versus temperature profile as seen in Figure 20A is reproduced taking into account wall effects. Table 4. Calculated induction periods, IDT in seconds, for the 9.5 mol% n-butane in air mixture at various temperatures and in a semi-open 100 ml quartz glass vessel at atmospheric pressure, taking account of wall effects, h = 1.5 W/(m2K).

T wall/ K Experiment/ s No wall effect/ s Cat, I/ s Cat. II/ s T peak Cat II/ K 700 1 0.4 0.4 0.5 1632

725 10

1.5 2.9 SO, max at 55 s

749

750 30 3.1 14.0 1890 956 775 35 2.8 12.3 2420 986 800 25 2.1 6.8 379 1526 825 10 1.4 3.3 11.5 1688

There may however be a further explanation for the difference experiment versus simulation not taking into account wall termination effects. The much longer ignition times in the experiments may be still attributed also to heat losses, but in a different way than just a higher heat transfer at the wall of the vessel. In Figure 20B it can be seen that the temperature initially near the top of the vessel, hence the inlet of the flask, is lower than in the centre. This temperature difference is between 5 and 10 K. The pocket with the higher temperature will start reacting, will further increase in temperature and become buoyant, but will then subsequently mix with cooler parts and the hydrogen peroxide produced will be diluted and/or decomposed. This could therefore exhaust the necessary build-up of active peroxide to trigger off the final runaway and it tends to slow the oxidation process. The open nature of the test set-up in glass enhances the dilution. The 200 ml closed steel vessel experiments follow in the low temperature region the glass vessel results quite precisely. On the contrary at temperatures just beyond the NTC these tests cover the simulations and the larger 500 ml


glass test results better than the 200 ml semi-open glass ones. The simulations in Figures 22A and B point in the same direction but are less pronounced than in actual AIT tests. At 760 K the highest temperature reached is still near the top of the glass vessel. At even higher temperature the induction become so short that the highest temperature in the explosion is definitely the centre. A more accurate approach of induction time in a semi-open set-up is not possible without taking into account the temperature and concentration gradients. This is beyond reach of the computational tools for the time being. In conclusion the following can be stated:

• Determination of the ignition delay time shall be performed in a closed vessel and not an open one, with sufficient large diameter or at sufficient high pressure to avoid wall effects.

• Determination of the ignition temperature shall be performed at a fixed ignition delay time.

4.3 The effect of mixture composition Calculations of IDT have been made for three n-butane-air mixture compositions. As compositions have been chosen the stoichiometric one (3.1 mol%), rich near the upper explosion limit (9.5 mol%) with which all AIT tests with n-butane have been done, and very rich, a factor three above the upper explosion limit (30 mol%). This reflects too the range of compositions covered experimentally with a number of other fuels such as methane and ethylene (Deliverable No. 33 Addendum B [20]) and propane (Deliverable No. 13 [27]). In Table 5 the results have been summarised for a closed vessel of 200 ml (constant volume) at an initial pressure of 1 bara with a heat transfer coefficient of 1.5 W/(m2K) at three initial temperatures (Ti). For constant pressure (semi-open vessel) the IDT values are slightly larger (2-10%), except for the stoichiometric mixture at low temperature (50% larger). Table 5: Calculation results of ignition delay time and final temperature for various compositions at constant volume (200 ml) at 1 bara initial pressure.

Molar fractions of mixture Ti = 575 K Ti = 650 K Ti = 800 K n-C4H10 O2 N2 IDT, s Tf, K IDT, s Tf, K IDT, s Tf, K 0.031 0.204 0.765 5.6 2638 0.4 2661 4.2 2688 0.095 0.190 0.715 4.7 1794 0.3 1900 1.95 1982 0.300 0.147 0.553 3.6 1042 0.2 1073 0.9 1128

The influence of composition on IDT is not very strong but increases with temperature. In Figure 24 calculated temperature-time profiles are shown at an initial temperature of 800 K. So, in fact one does not notice from the qualitative shape of the curves a passing of the upper explosion limit line. The most energetic mixture (stoichiometric) produces the longest induction time. With increase in fuel content IDT becomes shorter. The final effect depends even more on composition. The final temperature reached, diminishes with increasing hydrocarbon content as a result of gradually less complete combustion (and heat release). The profiles of temperature-time at the lowest temperature of 575 K are still from low-temperature oxidation with formation of organic peroxides, then “jump-wise” to reaching maximum temperature followed by a slow decay due to heat loss. At 650 and 800 K for the fuel richest composition the profile becomes a more smooth self-heating process as shown in Figure 24. This pattern appears even more pronounced in experiments as e.g. shown in Deliverable No. 13 [27] for propane. In the experiments by natural convection temperature gradients form and as a result the temperature increase when reaction is slow, is more gradual, while in the very


rich mixtures due to entrainment of air into the flask partial explosions of pockets of mixture in the explosion range can occur.

500

1000

1500

2000

2500

3000

0 1 2 3 4 5

Time, s

Tem

pera

ture

, K

3.1% C4H10-air9.5% C4H10-air30.0% C4H10-air

Fig.24: Temperature-time profiles of self-heating process of various n-butane mixtures with air calculated for a closed 200 ml vessel at an initial temperature of 800 K and 1 bara initial pressure.

4.4 The small chain hydrocarbons C 1-C3 n-Butane as a fuel is representative for the higher alkanes. In the later stages of the SAFEKINEX project also AIT tests with methane, ethylene and finally with propane have been carried out. Also the oxidation kinetics of these fuels has been modeled. A detailed report on the development of the C1 – C3 kinetic model is given in Deliverable No. 26 [18]. This includes an analysis of the available knowledge on C1 – C3 kinetics as well as an extensive description of the course that was taken in the development of the C1 – C3 kinetic

model. The most important criteria discussed in Deliverable No. 26 are the number and type of species, the reactions and reaction rate constants, and the thermodynamic and transport data. The validation of the model is described in Deliverable No. 34 [19]. The new C1 – C3 model, known as Konnov Safekinex, is suited for describing the pyrolysis, slow oxidation and ignition reactions as occur in the low temperature problems investigated in the project. It consists of 360 species and 2701 reactions and it also includes hydrogen combustion. It is designed to be applicable at temperatures between 550 and 1600 K and pressures up to 50 bara. A number of results with methane and ethylene in comparison with experiments taken from Deliverable No. 33 Addendum B [20] are shown in the Figures 25A and B, 26A and B and 27A and B. The experimental results on the surface look similar to those of n-butane with an NTC-like transition at a certain temperature, although the temperature level of the apparent discontinuity in IDT as a function of temperature is 200 K higher for methane and 50 K for ethylene. However there is no occurrence of cool flame as with n-butane. Slow oxidation is the more common process at low temperature. At temperatures above the discontinuity, the conversion peak becomes sharply steeper. In case of ethylene, the slow oxidation phenomenon starts immediately after injection and does not yield a measurable IDT. Above the discontinuity with the two compositions 14 mol% methane and 19 mol% ethylene in air, both just within the explosion range, explosion takes place with audible and visual consequences. For ethylene there was one point of the BAM 200 ml steel vessel self-ignition trials, which could serve for comparison and which shows a good agreement between both


types of tests. At higher concentrations slow oxidation prevails unless initial temperature becomes higher and explosion-like phenomena occur. This will be thermal explosion of the reacting mixture with probably flame in part of the volume due to air entrainment as shown also clearly in the later tests with propane (Fig.29A to H).

0

10

20

30

40

50

60

70

700 800 900 1000 1100 1200

Temperature (K)

IDT

(s)

14% CH4-air,experiments

Calculated

0

5

10

15

20

25

600 650 700 750 800

Temperature (K)

IDT (s

)

19% C2H4-air, AITexperiments

19% 200 ml closedsteel BAM, 1.3 bara

Calculated

Fig. 25A. Auto-ignition experimental results in the 500 ml glass vessel with 14 mol% methane in air in comparison with simulation applying the Konnov Safekinex C1-C3 model.

Fig. 25B. Auto-ignition experimental results in the 500 ml glass and 200 ml steel vessel with 19% ethylene-air in comparison with simulation applying the Konnov Safekinex C1-C3 model.

790

800

810

820

830

840

850

860

0 50 100 150 200Time [s]

Tem

pera

ture

[K]

M53 T4

M53 T5

860

880

900

920

940

960

980

1000

0 50 100 150 200

Time [s]

Tem

pera

ture

[K] M33 T4

M33 T5

Fig. 26A. Temperature-time history with 14% methane in air at 837 K initial temperature level, showing slow oxidation, IDT 18.7 s

Fig. 26B. Temperature-time history with 14% methane in air at 917 K initial tempe-rature level, showing explosion after 12.2 s

Fig. 27A. Temperature-time history with 19% ethylene in air at 744 K initial temperature level, showing slow oxidation

Fig. 27B. Temperature-time history with 19% ethylene in air at 755 K initial tempe-rature level, showing explosion after 17.4 s

700

720

740

760

780

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820

0 50 100 150 200

Time [s]

Tem

pera

ture

[K] E16 T5

E16 T4

700

750

800

850

900

950

0 50 100 150 200

Time [s]

Tem

pera

ture

[K]

E25 T5

E25 T4


The calculations with the Konnov Safekinex mechanism (360 species, 2701 reactions) take into account many details of the oxidation mechanism, but take relatively long to perform. The oxidation processes typically develop hydrogen peroxide first, which subsequently decomposes. So, there is no question of low but rather of intermediate temperature oxidation. As appears from Figure 25A in case of methane just as with n-butane calculated induction times are systematically shorter than the ones experimentally observed. Caron et al. [28] studied the system methane-air at elevated initial pressures up to 55 bara, initial temperatures of 620 to 720 K and methane concentrations up to 85 mol% in a 8 l autoclave. They define a reaction producing a significant temperature increase but lower than 200 oC accompanied by a pressure increase lower than 2 as a ‘cool flame’. If the temperature increase is larger than 200 oC they define the reaction as ‘auto-ignition’. At lower pressure and higher fuel concentration rather ‘cool flames’ are found than ‘auto-ignitions’. Whether it is really justified to make this sharp distinction and to call here the weaker temperature and pressure rises cool flame is questionable. As has been explained before for obtaining cool flame organic peroxide chemistry is active and the nature of the cool flame phenomenon occurring in case of e.g. n-butane is flash-like. It is more radical explosion than thermal. Below a temperature of 600 K n-butane readily produces cool flame. At that temperature methane does not show much sign of reaction, but at a temperature when it starts to react simulation shows hydrogen peroxide is formed. Also in case of ethylene as a fuel hydrogen peroxide dominates as reactant typical for intermediate temperature oxidation. The thermal nature of acceleration mechanism becomes stronger. Depending on conditions by self-heating temperature increases, hydrogen peroxide concentration builds up further and self reinforcing radical oxidation reactions follow, till finally almost jump-wise a maximum temperature is reached and all hydrogen peroxide is consumed. So, there seems rather a gradual change in final effect than a discontinuity. It also may be a misnomer to use in all cases the term ignition delay time, since it is often a merely an induction time to a thermal climax event, which is surely not the initiation of a propagating flame since it occurs with fuel concentrations far above the upper explosion limit. The last series of AIT- experiments performed have been with propane. In Deliverable No. 13 [27] the results have been reported in more detail than of previous tested fuels, since with increasing experience details gained significance. One series has been carried out with 12 mol% propane in air and another with 40 mol%. The first is just above the upper explosion limit and the latter percentage was inspired by a series of recently reported experiments by Norman et al. [21]. A summary of results and a selection of single test results are shown in Figures 28 and 29A to H. In Figure 30 an overview is presented of the results of the four fuels investigated in the SAFEKINEX project in the AIT test at comparable conditions. In general it can be concluded that the phenomena experimentally observed with propane are in between n-butane and methane. Simulation showed that at low temperature (600 K) a significant intermediate product consists of organic peroxides such as propylhydroperoxide (CH3)2CHOOH, while at the moment close to the final jump the hydrogen peroxide concentration is a thousand times smaller than of propylhydroperoxide. At an initial temperature of 700 K the picture has changed again towards hydrogen peroxide as the dominant intermediate as has also been put forward by Griffiths et al. [17] and others.


0

10

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70

80

90

600 650 700 750 800 850 900Initial temperature, K

IDT

, s

12% propane in air40% propane in air12% propane in air*40% propane in air*

* IDT up to other phenomenon (multiple cool flames, for example) begins after slow oxidation

Fig. 28. Ignition delay time versus initial (ambient) temperature for 12% and 40% propane-air mixtures at constant pressure of 1 bara in semi-open vessel of 500 ml quartz-glass.

Open dots – IDT to first temperature increase (slow oxidation phenomenon or explosion); Closed dots – IDT to second rapid temperature increase (multiple cool flame phenomenon on

underlying slow oxidation).

320

330

340

350

360

370

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390

0 50 100 150 200 250Time, s

Tem

per

atu

re, o C

Series1Series2Series3

12% 370C #2 a)

300

320

340

360

380

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420

0 20 40 60 80 100 120Time, s

Tem

pera

ture

, o C

T1T4T5

40% 370C #3 b)

400

405

410

415

420

425

430

435

440

0 50 100 150 200 250Time, s

Te

mpe

ratu

re, o C

T1T4T5

12% 430C #2 c)

370

380

390

400

410

420

430

440

450

0 50 100 150 200 250Time, s

Tem

per

atu

re, o C

T1T4T5

40% 430C #3 d)


450

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550

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800

0 10 20 30 40 50 60 70 80Time, s

Tem

per

atu

re, o C

T1T4T5

12% 500C #1 E)

450

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510

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550

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0 10 20 30 40 50 60Time, s

Te

mp

erat

ure

, o C

T1T4T5

40% 500C #2 F)

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0 20 40 60 80 100 120 140Time, s

Tem

per

atu

re, o C

T1T4T5

12% 610C #3 G)

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620

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660

680

700

0 10 20 30 40 50 60Time, s

Tem

pera

ture

, o C

T1T4T5

40% 610C #1 H)

Figures 29A to H. Sample individual AIT test results with propane at various temperature levels, A and B 642 K, C and D 696 K, E and F 768 K and G and H 882 K; at two mixture compositions, 12.0 mol% row left (A, C, E and G), and 40.0 mol% row at right (B, D, F, and H); 500 ml quartz glass vessel, 1 bara. A and B are classified as multiple cool flame superposed on slow oxidation, C and D as slow oxidation, E and F as explosion with highest temperature near the top of the flask, and G and H as explosion with highest temperature in the centre. In case of G a second explosion takes place 50 seconds after injection due to entrainment of fresh air. Simulations of propane oxidation were explored also at the conditions of some of the low-temperature oxidation tests under elevated pressure published by Norman et al. [21]. Their measured induction times range from 200 to 1400 seconds at temperatures between 250 and 300 oC (523 – 573 K) and pressures up till 16 bara in a 8 l vessel. Their results are shown for comparison in Figure 31. The same discrepancy occurs, as we have seen before with n-butane and methane at low temperatures. The calculated IDT for a volume of 8 litres and a heat transfer coefficient of 5 W/(m2.K) 3 bara pressure and 550 K (275 oC) is 13.5 seconds whereas the measured value is close to 800 s. At 6 bara the calculated value is 9.1 s versus the measured one of 100 s. At higher pressures the time necessary for a computation increases rapidly and the tolerances on the iteration have to be put tighter. As has been shown by Fairweather et al [22], some of the discrepancy for propane combustion may be attributed to inaccurate assignments of thermochemical parameters to some of the more complex intermediate species.


0

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80

90

550 600 650 700 750 800 850 900 950 1000

Temperature, K

Indu

ctio

n tim

e, s

methane 14%ethene 19%propane 12%n-butane 9.5%

Figure 30. Overview of experimental results of the determination of induction time (IDT) as a

function of initial temperature (oven) in Auto-ignition test (AIT) set-up in a semi-open (atmospheric) 500 ml quartz glass vessel for the four hydrocarbon fuels investigated at

comparable concentration in air with respect to the upper explosion limit.

Figure 31. Ignition delay times measured by Norman et al. [21] with 40 mol% propane in air in a 8 l vessel. Like we have seen for n-butane at higher pressure ignition can take place at lower temperature but delays become much longer. The dot at 3 bara near the abscissa represents the calculation result at that condition with the full Konnov Safekinex mechanism.

4.5 Simulations with strongly reduced mechanisms In Deliverable No. 38 [29] the Leeds group has proposed reduced or skeleton mechanisms for hydrocarbon oxidation kinetics. In two reduction steps a 1st skeleton mechanism and a 2nd one was derived. The usefulness and reliability of the mechanisms was demonstrated by comparing e.g. experimental values of ignition temperatures with ones calculated by the full, the 1st and the 2nd skeleton mechanisms. In the following for n-butane and propane the 2nd reduced skeleton mechanism was used to calculate ignition delay times. Results in comparison with the full mechanisms are given for n-butane and propane in Figures 32 and 33A and B respectively. Konnov Safekinex was applied as the full mechanism for propane.


The conclusion so far is that the skeleton mechanisms behave quite well. There is a systematic deviation over the whole range of calculated values to a lower value produced by the 2nd skeleton mechanism. The gain in computation time can be quite large also with the CHEMKIN software. For example in case of propane at the lowest temperature of 525 K the computation time with the full mechanism was 37 minutes and 23 seconds, whereas with the 2nd skeleton it was 6 seconds!

0,001

0,01

0,1

1

10

100

1000

500 600 700 800 900 1000 1100

Temperature, K

IDT

, s

C4H10 p=1, full mechp=1, skeleton2p=10, full mechp=10, skeleton2

Figure 32: Calculated ignition delay times (logarithmic scale) for 9.5% n-butane in air at 1 bara constant pressure in a 200 ml vessel, 1.5 W/(m2K) heat transfer coefficient, and at 10 bara in a closed 200 ml vessel, both with the full mechanism and the 2nd skeleton one.

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520 530 540 550 560 570 580 590 600 610

Temperature, K

IDT

, s

C3H8 p=3, fullp=3, skel2

Figure 33A: Calculated ignition delay times for 40.0% propane in air at 3 bara constant pressure in a 8 l vessel, 5 W/(m2K) heat transfer coefficient with the full Konnov Safekinex mechanism in comparison with the 2nd skeleton one.


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500 550 600 650 700 750 800 850 900Initial temperature, K

IDT

, s

12% C3H8-air exp.

12% C3H8-air exp, 2nd peak

12% C3H8-air calc. full

12% C3H8-air calc. skel2

Figure 33B: Calculated values of ignition delay time as a function of temperature of mixtures of 12 mol% propane in air at atmospheric pressure in a 500 ml vessel (heat transfer coefficient 1.5 W/(m2K)) on the basis of the full Konnov Safekinex mechanism – lower line, and the skeleton 2 mechanism –upper line, in comparison with the experimental values. However does exception confirm also here the rule? The odd one appeared to be propane at atmospheric pressure as shown in Figure 33B together with the experimental data already shown in Figure 28. No good explanation can be given. The detailed calculation results do not show a systematic deviation. The hydrogen peroxide concentration slowly builds up toward the end of the induction period and is then completely exhausted in the final temperature jump. At lower temperatures than shown in the graph (550 K with full; 625 K with skeleton 2) calculation did not produce a peak.

4.6 Alternative kinetic mechanisms and simulation s oftware An alternative mechanism for n-butane suited for low temperature oxidation simulation has been developed by Strelkova [23]. The mechanism was developed on the software infrastructure of Chemical Workbench (see Appendix II). It consists of 34 species and 48 reactions and is on the same chemical basis as the EXGAS derived model. An example calculation result is shown in Fig. 34. Also here at relatively low temperature the calculated IDT falls short of the measured value. Although in theory the kinetics as stored in the Chemical Work Bench data base CARAT can be converted to the CHEMKIN format and the other way around. In practice when importing other mechanisms, even in the CHEMKIN format, there appear problems of trivial nature resulting in solutions which not converge which are rather time consuming to resolve. Manual interaction and correction is needed. The robustness of the software is not ideal yet. The Help offered is not always clear and contains cryptic expressions. With COSILAB little experience was obtained but also there importation of mechanisms generated problems such as not checking for duplicates. CANTERA could not be implemented and run in the time available.


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30

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Temperature, K

IDT

, s

Experiments closed 200ml vessel

Skeletal mechanism (CWB) (V=const) (Expl)

Skeletal mechanism (CWB) (V=const) (CF)

Figure 34. 200 ml closed steel vessel experiments in comparison with the outcomes of the calculation of the 9.5 mol% n-butane in air mixture oxidation with the Strelkova skeletal mechanism [23] without heat loss on the Chemical Workbench software package (see Appendix II).


5 Characterisation of the conditions of natural conve ction enabling ignition 6

There exist numerous in-direct experimental observations (prior and during the SAFEKINEX project) indicating that an evolution of gaseous auto-ignition with its specific features inside a vessel (sphere, cylinder or else) is governed by not only a balance between the chemical heat release and thermal conductivity (as it was documented in the classical theory of Frank-Kamenetskii [30] for thermal explosion), but also by gravity and convection effects. To this can be added that compressibility and viscosity of the gas mixtures can have an impact too. Due to the complexities in performing direct experimental studies of the mentioned factors, especially with a high spatial and temporal resolution, a role of theoretical analysis and numerical simulation shall not be underestimated. Systematic reactive Computational Fluid Dynamics studies of gaseous thermal auto-ignition inside of a closed sphere were initiated and described in references [24, 31, 32] with taking explicitly into account gravity, convection, compressibility and viscosity effects.

5.1 Basic gas-dynamic flow patterns In [31] it was revealed that two basic gas-dynamic flow patterns and associated thermal heat transfer mechanisms can be delineated. Numerical simulations were performed for 2-dimensional geometry of the evolution of the gas-dynamic fields during auto-ignition of the

initially quiescent (velocity vector 0=iV�

), premixed exothermic reactive gas (initial

temperature 0

~T , initial density 0

~ρ , initial volume fraction of limiting reagent (chemical

reaction extent - 0) inside of a closed spherical vessel (radius 0Rɶ ) with a given temperature of

wall ( 0

~~TTa = ). Overall reaction rate and heat generation can be represented by a zero-order

Arrhenius type of equation (one-step kinetics). The following dimensionless parameters have been introduced: effective Froude (inverse Richardson or Rayleigh7) number -

)~~(~)

~~(~ 3

02

002

0 RgRgVFr ⋅=⋅= ν with gɶ gravitational acceleration vector, Prandtl number -

00~~Pr χν= , Arrhenius number - aETRAr

~)

~~( 0⋅= with Rɶ gas constant and aEɶ activation

energy. Further, use was made of the Frank-Kamenetskii number - chT ttFK ~~= , with

)~~~~(~

02

00 λρ Rct VT ⋅⋅= characteristic thermal time, and )~

)()~

(~

()~~~(~

000 rVch HTkArTct ∆⋅⋅⋅⋅⋅= ηϕρ

- characteristic chemical time, in which Vcɶ is specific heat capacity at constant volume, λɶ is

heat conductivity, 0 0( )k Tɶ ɶ is rate constant at initial temperature, *( ) (1 )mic cϕ = − with ic is

concentration and m chemical reaction order and rH~∆ chemical reaction enthalpy. Next is

Todes number - )~

*)()~

(~

()~~~( 000 rV HcTkArTcTd ∆⋅⋅⋅⋅⋅= ϕρ , dimensionless temperature

)~

()~~

( 00* ArTTTT ⋅−= and finally the effective Strouhal (Damköhler) number

Pr)()~~(~

)~)~~((

~ 2000 ⋅=⋅=⋅= γνν FKtRtRRSh chch , with νɶ is kinematic viscosity, γ ratio of

specific heats at constant pressure and volume and Pr is Prandtl number.

6 The following section has been part of a study in the framework of the Russian-Netherlands scientific cooperation, project NWO No. 046.016.012 2004-2006 cosponsored by Russian Foundation for Basic Research, projects 05-08-50115a and 05-08-33411a. It is work mainly carried out by Prof. A.V. Panasenko of TSNIIMASH under guidance of Professors I.A. Krillov and A.I. Lobanov. 7 Strictly speaking, a definition of the Rayleigh number, used at page 6 of this report (see formula (2)), is valid for stationary problems only, where temperature difference between two given specific spatial points is constant during natural convection. Use of the effective Froude number and Frank-Kamentskii number is more relevant for natural convection effect studies of a substantially non-stationary process of thermal auto-ignition.


a) b)

Figure 35. Snap-shots ( 1=t ) of the convective stream-lines for thermal auto-ignition with conductive-dominated heat removal ( 6.0=Fr , 065.01 =−Sh , 06.0=Td , =Ar 0.05). a) – FK=5, b) – FK=30

a) b)

Figure 36. Snap-shot ( 1=t ) of the convective stream-lines for thermal auto-ignition with convective-dominated heat removal ( 0006.0=Fr , 065.01 =−Sh , 06.0=Td , =Ar 0.05). a) – FK=5, b) – FK=11.


Along with a validation against the well known limit thermal explosion limit (reaction heat release- thermal conductivity balance as described in the framework of the Frank-Kamenetskii theory [30]; no gravitation field), two basic natural convection flow patterns, which are evolving during auto-ignition, were documented: a radial streamline pattern and a toroidal convection one. For large values of the effective Froude numbers, Fr (viscosity effects dominate over the gravitational ones) the chemical reaction heat release induces a radial convective flow from centre to the wall of the spherical vessel. The stream-lines (see Figure 35) are practically radial within the inner part of the vessel. Temperature iso-surfaces preserve a spherical symmetry. The location of the centres of the temperature iso-surfaces practically coincides with the vessel centre and does not depend on the value of the Frank-Kamenetskii number. Convective contribution to overall heat removal is small. Under super-critical conditions with the effective Froude number value below a certain threshold depending on the Frank-Kamenetskii number, buoyancy disturbs essentially both the stream-line and temperature fields. Here, the main feature of the stream-line structure is the onset of a large toroidal vortex (see Figure 36). During the auto-ignition process, this vortex is forming in the bottom part of the vessel and floating to the top. Intensity of the toroidal convective flow and its evolution depends on the Frank-Kamenetskii number. The higher the initial Frank-Kamenetskii number, the quicker the center of the temperature iso-sphere is moving away from the vessel center. Appearance of the well-defined toroidal convection within the vessel core results in the following changes: 1) shift of the dominating overall heat removal mechanism – from conduction-driven to convection-driven; 2) changes of the critical conditions for thermal explosion – in comparison with the classical thermal explosion theory.

5.2 Convection Effect on Induction Delay Time From Figure 37 it can be seen that a well developed convective flow reduces the ignition delay time, computed for the time history of the maximum temperature. The maximum temperature (over the vessel volume) was taken as a characteristic temperature suitable for comparison of thermal behaviour for the different initial conditions. However, in the real experiments, it is hardly possible to track accurately (in time and space) a location of the point with maximum temperature. In order to obtain spatially-averaged information, which can be obtained in experiments, a dependence upon time was computed of the Nusselt number averaged over the vessel surface aNu . The following definition was used:

∫∫=S

dsdn

dT

SaNu

1

heгe n is external normal to the spherical vessel surface, and S – the surface area. In Figure 38, the time profiles of the averaged Nusselt numbers are shown. In both cases ( FK = 7 and 11), time period to attain the maximum value of thermal flux from gas to vessel walls is shorter for situations, where well-defined convection takes place (Fr =0.0006). Interpretation of the observed interplay of the convection and auto-ignition is the following. For small values of the Froude number, even a small chemical heat release during the induction period results in substantial convective flow, ascending at symmetry axis. This enhances heat transfer from the ‘hot’ central region to the top inner part of the vessel in comparison with pure conduction, resulting in an overall larger reaction heat release and a faster local thermal runaway. Convection from the hottest central part plays the role of an “igniter” for the upper points, located near the top of the spherical vessel.


Figure 37. Characteristic time history of the maximum temperature Tmax inside of a spherical vessel for situations with thermal explosion taking place and a well-developed toroidal convection present (FK = 6)

Figure 38. Convective effect on induction delay time: Nusselt number averaged (over sphere volume) versus time.

5.3 Critical conditions for thermal explosion in a compressible gas The summary of the parametric computations is shown in Figure 39 where the boundaries for the critical phenomena (natural toroidal convection, thermal explosion), and their interplay is visualized in a two-dimensional phase plane ( 0/ FKFK , )1lg( Fr , where 0FK is the critical value8 of the Frank-Kamenetskii number as derived in the standard theory of thermal explosion [30]). Here a solid, red line represents a thermal bifurcation. Any phase point, located below the solid red line represents the conditions, which do not result in a thermal explosion. Any phase point, located above the solid, red line, represents the conditions which induce the thermal explosion. Accordingly, a dashed, black line represents a gas-dynamic bifurcation boundary (above – convection is absent, below – convection exists). The mentioned borders break the phase plane into three regions: region I – no explosion, no well-developed toroidal convection, only a weak radial convection is present; region II – thermal

8 This value is defined as the FK -number at which the rate of the (dimensionless) temperature increase is highest.


explosion, well-developed toroidal convection; region III – thermal explosion, no well-developed toroidal convection, only a weak

1

1,5

2

2,5

3

3,5

0 1 2 3

Lg(1/Fr)

FK/F

Ko

explosionboundary(above -Yes/below- No)

toroidalconvectionboundary(above -No/below -Yes)

III

II

I

Figure 39. Critical phenomena during thermal auto-ignition in compressible, viscous, thermally conductive gas. Region I – no explosion, toroidal convection. Region II – explosion, toroidal convection. Region III – explosion, no toroidal convection. 0FK - Critical value of

the Frank-Kamenetskii number according to classical theory of thermal explosion radial convection is present. For hazard analysis in case of engineering application, the boundary between the explosion and non-explosion regimes at the phase surface (FK, Fr) is approximated by the following formula:

)1291(108.2

14

0 FrFrFK

FK

⋅−⋅+=

−

the boundary between the well-defined (toroidal) convective and non-convective regimes can be approximated by the following formula:

)951(

103.11

3

0 FrFrFK

FK

⋅−⋅+=

−

The main goals of the reported study have been the following: 1) to extend the Frank-Kamenetskii’s thermal explosion framework in order to take into account explicitly the effects of gravity, convection, and viscosity for compressible reactive gaseous systems; 2) to define quantitatively the boundaries between the basic patterns of the thermal and gas-dynamic behaviour of the system under consideration in the phase space of key dimensionless parameters. This was realised by solving the full Navier-Stokes flow equations by rigidly non-dimensionalising the problem and solving the resulting equations by two-dimensional numerical simulations in a very fine mesh with a powerful computer by means of parallelization techniques; 3) to obtain engineering correlations for experiment planning and engineering applications, via fitting of the mentioned computed boundaries by simple analytical formulae.


6 Conclusions Summarising, if an estimate has to be given of the possibility of auto-ignition and the ignition delay time in a process flow at a given temperature and pressure on the basis of a kinetics model and a model of heat (and mass) transfer several problems have to be solved:

a. Within a certain residence time temperature, pressure and mixture composition have to be known. If conditions are such that low temperature oxidation takes place (n-butane, T < 700 K) heat loss seems not to be critical. Ignition delay is determined by the occurrence of cool flame caused through the progressively accelerated decomposition of accumulating organic peroxides. The maximum time to consider depends on pressure and temperature level. At low pressure it is no more than half a minute; at higher pressure fuels such as n-butane and propane can still self-ignite at even lower temperatures after 20 or more minutes. Also at a given temperature the induction time shortens considerably with an increase of pressure.

b. Present detailed kinetic models appear to behave too reactive at low temperature. They strongly underrate the measured induction times. Also they produce hot flame/explosion where tests show only cool flame or slow oxidation. The closest one coming in simulation of tests, is by adding to the model organic peroxide destruction reactions at low temperature. A simple overall approach, not taking into account this mechanism, is fitting the formula for the adiabatic induction period. Such a formula calculates the induction time for temperatures below those for the NTC region.

c. At higher temperature (n-butane > 700 K) and low pressure (atmospheric or lower) HO2· radicals and hydrogen peroxide decomposing at the wall of the vessel seem to influence the result rather strongly at atmospheric pressure and below and explain the increase of duration of induction for small vessels (5-10 cm diameter) as used in atmospheric AIT tests.

d. For the experimental set-ups (0.5 l and 20 l vessels) heat losses have been measured and calculated. When expressed in a heat transfer coefficient and a temperature difference between vessel centre and wall, natural convection changes the heat transfer coefficient in time and temperature difference. In simulation no temperature gradient can be handled yet by the batch reactor models (other than the simplest one-dimensional, pure conduction case, as discussed in Deliverable No. 38). In such case heat loss has a much less drastic effect on the ignition delay time than expected. However it is not certain how heat losses interfere when a faster reacting, warmer pocket of gas loses heat and active species to a surrounding gas of lower temperature.

e. The aim of auto-ignition tests is to determine ignition temperatures and ignition delay times. It is common understanding that ignition is followed by flame propagation. In many experiments however slow oxidation phenomena culminating in a final rapid rise in temperature occur with various fuels e.g. methane, ethylene and propane far outside the explosion range. This is confirmed by simulation. Kinetics simulation does not justify sharp distinction between cool flame and explosion in case of fuels other than n-butane and higher alkanes. A gradual shift of mechanism with temperature takes place. Explosion limit concentration does not show up as a discontinuity or even a steep change. Pressure increase varies with final temperature achieved. So, again an upper explosion limit should be determined on the basis of ability of the mixture to propagate flame.

f. Reduced kinetic models behave very well in predicting IDT in comparison with full ones.

g. Several software packages are available now for simulating stirred batch reactor processes. The most expensive one is at present still the best in performance. Portability of kinetic models developed on a certain software infrastructure to other packages is however still limited. Problems arise with stability and accuracy.


7 References 9 1. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 5, Report on

experimentally determined self-ignition temperature and the ignition delay time, January 2005.

2. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 33, Report on experiments needed for kinetic model development (high pressure), April 2006.

3. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 30, Report on experiments needed for kinetic model development (CVB approach), April 2005.

4. Pekalski, A.A., 2004, Theoretical and experimental study on explosion safety of hydrocarbons oxidation at elevated conditions, Dissertation, Delft University of Technology, 18 November, Delft, The Netherlands.

5. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 29, Report on intermediate species concentration during the ignition process, October 2005

6. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 33, Report on experiments needed for kinetic model development (high pressure), April 2006, Addendum A, Heat loss measurements explosion sphere, March 2006.

7. Carslaw H.S. and Jaeger J.C., Conduction of Heat in Solids, 2nd ed. Oxford Science Publications, 2003, p. 233 ISBN 0 19853368 3 (PbK)

8. Barnard J.A., Harwood, B.A.; Physical Factors in the Study of the Spontaneous Ignition of Hydrocarbons in Static Systems; Department of Chemical Engineering, University College, London, England; Combustion and Fame 22, 35-42 (1974)

9. Ten Holder, G. P., “The influence of the overall heat transfer coefficient on combustion phenomena of n-butane-air mixtures”, M.Sc Thesis, Delft University of Technology, May 2003.

10. Reaction design, San Diego CA., 2006, http://www.reactiondesign.com/ 11. Kee R.J., Landram C.S. and Miles J.C., “Natural Convection of a Heat-Generating Fluid

Within Closed Vertical Cylinders and Spheres”, Journal of Heat Transfer February 1976, p. 55- 61.

12. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 35, Validated detailed kinetic model for C4 - C10 hydrocarbons, May 2005.

13. Griffiths J.F. et al., private communication about work performed in the SAFEKINEX project framework, November 2006

14. Griffiths J.F. and Barnard J.A., Flame and Combustion, Chapman & Hall, 1995, ISBN 0 7514 0199 4.

15. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable Nos. 45-47, Workshop Teaching Material, November 2006.

16. Frolov, S. M., Basevich, V. Ya., Smetanyuk, V. A., Belyaev, A. A., & Pasman, H. J, 2006, Oxidation and combustion of fuel-rich n-butane–oxygen mixture in a standard 20-liter explosion vessel. European Conference on Computational Fluid Dynamics, ECCOMAS CDF, P. Wesseling, E. Oñate, J. Périaux (Eds), Egmond, 5–8 September 2006, The Netherlands.

17. Griffiths, J.F., Hughes, K.J. and Porter, R., 2005, The role and rate of hydrogen peroxide decomposition during hydrocarbon two-stage auto-ignition, Proc. Combust. Inst, 30 (1): 1083-1091.

18. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 26, Report on ongoing progress of C1 - C3 detailed kinetic model development, April 2004.

9 All Project SAFEKINEX Deliverables can be found on www.safekinex.org


19. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 34, Validated C1 - C3 kinetic oxidation model, October 2005.

20. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 33, Report on experiments needed for kinetic model development (high pressure), April 2006, Addendum B, Additional experiments on the self-ignition temperature and the ignition delay time: ETHENE and METHANE, February 2006

21. Norman F., Van den Schoor, F., Verplaetsen H., “Auto-ignition and upper explosion limit of rich propane-air mixtures at elevated pressures”, Journal of Hazardous Materials A137 (2006) 666-671.

22. Kevin J. Hughes, John F. Griffiths, Michael Fairweather and Alison S. Tomlin, Evaluation of models for the low temperature combustion of alkanes, Phys. Chem. Chem. Phys., 2006, 8, 3197 – 3210

23. Strelkova M.I., Kirillov I. A., Pasman H. J., Skeletal mechanism of n-butane oxidation, submitted to Physico-chemical Kinetics in Gas-Dynamics (in Russian); Strelkova M.I., Safonov A., Sukhanov L.P., Kirillov I.A., Potapkin B.V., Pasman H.J., First principles based estimation of the low temperature mechanism of n-butane oxidation, submitted to the 3rd Imternational Symp. on Non-Equilibrium Processes, Combustion and Atmospheric Phenomena, NEPCAP-2007, Dagomis, Russia 25-29 June, 2007

24. Kirillov I. A., Panasenko A V., Zaev I.A., Pasman H. J., Modeling of the Buoyancy Effects on Thermal Auto-Ignition of the Compressible Gas, submitted to J. Haz. Mat., Feb 2007

25. Rogers, R.L., 1979, Studies of the Combustion of Decane, Dissertation The City University, London; see also Cullis C.F., Hirschler M.M., and Rogers, R.L., 1982, The Cool Flame Combustion of Decane, Proc. Roy. Soc. London A382, 429-440.

26. Griffiths J.F., and Barnard J.A., 1996, Flame and Combustion, 3rd edition, Blockie Academic & Professional.

27. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 13, Report on Additional Experiments, May 2007.

28. Caron M., Goethals M., De Smedt G., Berghmans J., Vliegen S., Van ’t Oost E., van den Aarssen A., 1999, Pressure dependence of the auto-ignition temperature of methane/air mixtures, Journal of Hazardous materials A65, 233-244.

29. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 38, Reduced Kinetic Models for Different Classes of Problems, February 2007.

30. Frank-Kamenetskii D.A., Diffusion and Heat Transfer in Chemical Kinetics, (1967), Nauka, pp. 352

31. Kirillov I.A. Panasenko A.V., Pasman H.J. On convective flow dynamics during self-ignition of gas mixture in spherical vessel, Cosmonautics and Rocket Engineering, 2006, v.3(44), pp.150-156 (in Russian)

32. Kirillov I.A. Panasenko A.V., Pasman H.J. Effects of thermal conductivity, thermal convection and gravity on gas phase autoignition in a closed explosion sphere, poster at the 31st Int. Symp. on Combustion, Heidelberg, Germany, August 6-11, 2006

SAFEKINEX - Deliverable 18 - Model, software for calculation of AIT and its validation page 47 (59)

APPENDIX I

Appendix I. Excel sheet to calculate heat transfer coefficient and adiabatic induction time Picture of the Excel-sheet used to calculate values of Rayleigh and Grashof number, to derive the heat transfer coefficient from the Grashof number via a curve fitted to the graph produced by Kee et al. [11], and to calculate the induction time as if a thermal explosion under adiabatic conditions is taking place, given values of reaction rate constant and activation energy. For Excel sheet picture see next page

AP

PE

ND

IX I


Calculation of Rayleigh Number

Gr,mod = q g β( 2 r) 5 ρ 2 /( λ η 2 )

Fill in: 1. Temperature to calculate the specific heat, viscosity and thermal conductivity of the pure species q = heat production, W/m3 Nu–10

2. Mixture composition to calculate the mixture properties Nu = h*(2r) / λ ---->read from Fig. 2: 1,3

Input variables are in red , other parameter values in black and calculated output data in blue q Nu

300 11,28

yi yi Mix properties T [K] and p [bara]: 570 1 Ra/r3·∆∆∆∆T [m -3·K-1] 8,66E+06 Pr Gr,mod h'

N2 (Nitrogen) 0,7900 0,7149 Molar mass MT=Σ yiMi [kg/mol] 3,16E-02 Vol. litre 0,50 0,86 6,27E+05 5,1

O2 (Oxygen) 0,2100 0,1900 density ρ = (pMT/RT) [kg/m3] 0,67 ∆T [K] 0,1

C4H10 (n-Butane) 0,1050 0,0950 heat cap. CpT=Σ yiCpi; Cv [J/mol·K] 4,39E+01 3,33E+01 8,66E+06 Ra log Ra

H20 (Water) 0,0000 0,0000 CpTmass; Cv [J/kg·K] 1389 1054 1,03E+02 2,01

CO (Carbon monoxide) 0,0000 0,0000 viscosity ηT=Σ yiηi [Pa·s]=[kg/ms] 2,76E-05 p [Pa] 1,00E+05

normalise! check 1,1050 1,0000 conductivity λT=Σ yiλi [W·mk] 0,044 g [m/s2] 9,81

Specific Heat Cp= A + B·T +C·T^2 + D·T^3 + E·T^4 [J/mol*K]

Tmin Tmax A B C D E γ [J/mol·K] [J/kg·K]

N2 300 1000 2,93E+00 1,49E-03 -5,68E-07 1,01E-10 -6,75E-15 1,40 30,00 1071,22

O2 300 1000 3,19E+00 1,57E-03 -6,91E-07 1,32E-10 -9,24E-15 1,40 32,31 1009,74

C4H10 300 1000 7,71E+00 2,78E-02 -9,62E-06 1,55E-09 -9,53E-14 1,20 172,08 2960,81

H20 300 1000 2,68E+00 3,10E-03 -9,31E-07 1,35E-10 -7,70E-15 1,20 34,65 1922,92

CO 300 1000 3,03E+00 1,44E-03 -5,63E-07 1,02E-10 -6,91E-15 1,40 30,62 1093,34

Viscosity η = A + B·T + C·T^2 [micropoise]

Tmin Tmax A B C η (25C) η (Tmin) η (Tmax) [micropoise] [Pa·s]

N2 150 1500 42,606 4,75E-01 -9,88E-05 175,52 111,67 533,12 281,26 2,81E-05

O2 150 1500 44,224 5,62E-01 -1,13E-04 201,85 126,04 633,08 327,85 3,28E-05

C4H10 150 1200 -4,946 2,90E-01 -6,97E-05 75,33 36,99 242,75 137,73 1,38E-05

H20 280 1073 -36,826 4,29E-01 -1,62E-05 89,68 82,07 404,97 202,44 2,02E-05

CO 68 1250 23,811 5,39E-01 -1,54E-04 170,95 59,78 457,31 281,22 2,81E-05

Thermal Conductivity λ = A + B·T + C·T^2 [W/m·K]

Tmin Tmax A B C λ (25C) λ (Tmin) λ (Tmax) [W/m·K]

N2 78 1500 0,00309 7,59E-05 -1,10E-08 0,02475 0,00895 0,0922 0,04279165

O2 80 1500 0,00121 8,62E-05 -1,33E-08 0,02571 0,00802 0,10042 0,04598337

C4H10 225 675 -0,00182 1,94E-05 1,38E-07 0,01625 0,00954 0,07423 0,0541304

H20 275 1073 0,00053 4,71E-05 4,96E-08 0,01898 0,01723 0,10811 0,04347213

CO 70 1250 0,00158 8,25E-05 -1,91E-08 0,02448 0,00726 0,0749 0,04241185

Molar mass Calculation of radius of sphere

M [kg/mol] Volume Radius Area π = 3,14159265

N2 0,02801 [ml] [cm^3] [m^3] [m] [m^2]

O2 0,03200 100 23,87 2,39E-05 0,0288 1,042E-02 Fit of Nusselt vs. Grashof

C4H10 0,05812 200 47,75 4,77E-05 0,0363 1,654E-02 Gr Log Gr Nu

H20 0,01802 500 119,37 1,19E-04 0,0492 3,046E-02 3,00E+04 4,47712125 0,03

CO 0,02801 20000 4774,65 4,77E-03 0,1684 3,563E-01 1,00E+05 5 0,17

4,00E+05 5,60205999 0,9

1,00E+06 6 1,8

Adiabatic induction time : 4,00E+06 6,60205999 3,5

t ad = {C /(–∆Q )}{ RTi2/(Ek)}exp(E /RTi) 1,00E+07 7 5

4,00E+07 7,60205999 9

p const = 0 C J/mol.K E kcal/mol n in p n 1,00E+08 8 12

otherwise 1 4,39E+01 36,5 0,5 4,00E+08 8,60205999 19

0 –∆Q J/kg k 1/s t ad s 1,00E+09 9 24

1,97E+05 2,95E+05 3,30E+11 25,2 4,00E+09 9,60205999 34

1,00E+10 10 44

4,00E+10 10,60206 60

r^3

3 2 /pRa g r C Tβ ρ λη= ∆ 23 /p

Rag C

r Tβ ρ λη=

∆

Nu-10 vs. mod. Gr

y = 5E-05x6 - 0,0005x5 + 0,0024x4 + 0,077x3 - 0,7239x2 + 1,5994x

R2 = 0,9998

0,01

0,1

1

10

100

4 5 6 7 8 9 10 11

modified Grashof

Nus

selt

-10

AP

PE

ND

IX I


APPENDIX II

Appendix II. Brief descriptions of the four curren t software packages for calculating ignition processes and lam inar flame. CHEMKIN 4.0.2 Reaction Design® is the exclusive developer and distributor of CHEMKIN® [AA1], the de facto standard for modeling of gas and surface-phase chemistry. As both a software developer and a services provider, Reaction Design focuses on reactor and combustor design and improvement. Engineers, chemists, and programmers have expertise that spans multi-scale engineering from the molecule to the plant. The collection of data is accumulated by Sandia National Laboratories over the period from 1980 to 1995. The data fits in this collection are based on a variety of sources, including JANAF Tables, NASA, and computational chemistry calculations performed at Sandia and elsewhere. This data set has been fixed and not updated in order to assure backwards compatibility and consistency with published CHEMKIN results. The CHEMKIN data format is a minor modification of that used by Gordon and McBride [AA2] for the Thermodynamic Database in the NASA Chemical Equilibrium code. However, CHEMKIN allows a different midpoint temperature for the fits to the properties of each chemical species. Additional extensions allowed by CHEMKIN for multiple temperature ranges and for very large molecular clusters. The format has become the de facto international standard for the description of reactions, thermodynamics, and transport properties. The CHEMKIN software enables the simulation of complex chemical reactions in order to predict how chemistry will affect overall process or device. CHEMKIN software consists of a suite of idealized reacting flow models that predict detailed chemical kinetics and reaction behavior. These models are designed to provide a compact description of transport phenomena and an unlimited description of chemistry details in a computationally efficient package. CHEMKIN can address gas-phase and gas-surface chemical kinetics in a variety of reactor models that can be used to represent the specific set of systems of interest. CHEMKIN is a commercial package.

COSILAB 2.0.2 SoftPredict® in Ruhr-Universität Bochum [AA3] is a subdivision of ROTEXO GmbH & Co. KG [AA4]. COSILAB is a general combustion simulation tool that can be used to simulate a variety of laminar flames including, in some cases, radiating flames, droplets and sprays. Under the COSILAB hood resides the RUN1DL laminar-flame and flamelet code. This code has been developed since the early eighties, and it has been used by numerous research groups worldwide. RUN1DL is a computer program for the numerical simulation of one-dimensional and "quasi one-dimensional" laminar flames. Moreover it provides reactor tools for a variety of geometries, including stirred reactors, plug flow reactors, calculation of ignition-delay times and many more. COSILAB supports all popular data formats for chemical reaction mechanisms, thermodynamic data and molecular transport data as well as CHEMKIN. A variety of different popular models for chemistry are implemented, including detailed mechanisms of elementary reactions, systematically reduced kinetic mechanisms, global one-step reaction models and the flame-sheet model for diffusion flames. Similarly, various popular models of thermodynamics and molecular transport are implemented, ranging from detailed


molecular models for thermal conductivities, dynamic viscosities and diffusion coefficients to simple constant-property models. The models implemented for chemistry, molecular transport and thermodynamics can be overwritten by a user’s own models. The programming languages Fortran, C or C++ can be used. Parts of the source code can be purchased, e.g., code that defines the discretized governing equations. Currently this is Fortran code. The user can modify, augment or eventually completely rewrite these portions of the code and hence adapt it to his particular physical problem at hand. COSILAB is a commercial program.

CANTERA CANTERA [AA5] by D. Goodwin (Stanford University) is a suite of object-oriented software tools for problems involving chemical kinetics, thermodynamics, and/or transport processes. The suite is designed to efficiently simulate problems with large elementary reaction mechanisms, and includes tools to model stirred reactor and stagnation flows with surface chemistry, to compute chemical equilibrium, and to generate reaction path diagrams automatically, among many others. It can be used on all common programs, and interfaces are provided for MATLAB, Python, C++, or Fortran. CANTERA is designed with the dual objectives of ease of use and high performance. It consists of a kernel written in C++ that provides the core numerical capabilities and is optimized for efficiency, and user interface package that provide an intuitive, high level way of interacting with the kernel. CANTERA is particularly useful for simulations with large, elementary reaction mechanism. It places no limit on the number of species and reactions, uses efficient algorithms to evaluate reaction rates of progress, and includes fully-implicit integrators and solves designed for use with stiff system of equations. The developer and project manager of CANTERA is David Goodwin. The first public release of the package as CANTERA 1.1, was in 2001. This package is still under development, new capabilities are still added. The input file is converted from CHEMKIN format input files to CTI files. A CANTERA input file may contain more than one phase specification, or may contain specifications of interfaces (surfaces). Several reaction mechanism files in this format are included in the CANTERA distribution, including ones that model high-temperature air, a hydrogen/oxygen reaction mechanism, and a few surface reaction mechanisms. CANTERA is freely-available software.

Chemical Workbench (CWB) Chemical Workbench is developed by “Kinetic Technology” (KINTECH) [AA6] which is a company taking a leading place among Russian software developers in the field of modelling physical and chemical processes. Chemical Workbench is a tool with easy-to-use graphical user interface (GUI) which helps the users to simulate, optimize, and design a wide range of thermodynamic and kinetic aspects of chemical processes and reactors for important industrial, research, or educational applications. Combustion and detonation waves, safety analysis, CVD, heterogeneous, and catalytic reactions and processes are the main areas of interest. The GUI permits the user to build his simulation model of the processes from universal reactor models by creating reactor chains containing


linked reactors objects. This option dramatically increases the program's capability to study physical and chemical processes. Chemical Workbench contains built-in, tightly integrated thermodynamic and kinetic databases. The databases can be used in two modes: first, as a source of data during input and formation of initial data and conditions for calculation, second, as an independent instrument for calculating various thermodynamic functions of matter and analyzing the data contained in the database. The following databases are available: The Molecular Properties Database, The Thermodynamic Properties Database, The Processes Database, The Mechanism’s Database. There are three ways for entering substance properties data to database: the user enters all information by himself (manual entering); information is extracted automatically from the Substances Database and converting CHEMKIN format input file to Database. A structure of input of initial data to database allows to add supplementary new data, as well as to adjust and delete information, what makes the application easily extendable with using Wizard program which allows users themselves easily to add new models. This package is a commercial product.

References: A1. http://www.reactiondesign.com A2. S. Gordon and B. J. McBride, Computer Program for Calculation of Complex Chemical

Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks and Chapman-Jouguet Detonations, NASA Report SP-273, 1971.

A3. http://www.ruhr-uni-bochum.de A4. http://www.softpredict.com A5. http://www.cantera.org A6. http://www.kintech.ru


APPENDIX IV

Appendix III. Brief characterization of FLUENT CFD software CFD stands for Computational Fluid Dynamics. It is technology that enables to study the dynamics of fluids in flow. Using CFD, one can build a computational model that represents a system or device under investigation. Then one applies the fluid flow physics and chemistry to this virtual prototype, and the software will output a prediction of the fluid dynamics and related physical phenomena. Therefore, CFD is a sophisticated computationally-based design and analysis technique. CFD software gives the power to simulate flows of gases and liquids, heat and mass transfer, moving bodies, multiphase physics, chemical reaction, fluid-structure interaction and acoustics through computer modeling. Using CFD software, one can build a 'virtual prototype' of the system or device that wished to analyze and then apply real-world physics and chemistry to the model, and the software will provide images and data, which predict the performance of that design. At the core of any CFD calculation is a computational grid, used to divide the solution domain into number of elements where the problem variables are computed and stored. In FLUENT, unstructured grid technology is used, which means that the grid can consist of elements in a variety of shapes: quadrilaterals and triangles for 2D simulations, and hexahedra, tetrahedra, prisms, and pyramids for 3D simulations. These elements, created using automated controls in GAMBIT, FLUENT’s companion preprocessor, form an interlocking network throughout the volume where the fluid flow analysis takes place.

Fig. 1 Cell types.

FLUENT will solve the governing integral equations for the conservation of mass and momentum, and (when appropriate) for energy and other scalars such as turbulence and chemical species. In both cases a control-volume-based technique is used that consists of:

• Division of the domain into discrete control volumes using a computational grid. • Integration of the governing equations on the individual control volumes to construct

algebraic equations for the discrete dependent variables (“unknowns”) such as velocities, pressure, temperature, and conserved scalars.

• Linearization of the discretized equations and solution of the resultant linear equation system to yield updated values of the dependent variables.

Discretization of the governing equations can be illustrated most easily by considering the steady-state conservation equation for transport of a scalar quantity φ . This is demonstrated by the following equation written in integral form for an arbitrary control volume V as follows:

dVSAdAdV∫∫ ∫ +⋅∇Γ=⋅ φφ φυρφ

��

where ρ - density, υ� - velocity vector, A�

- surface vector,φΓ - diffusion coefficient forφ , φ∇ -

gradient of φ , φS - source of φ .

FLUENT's post processing tools can be used to generate meaningful graphics, animations and reports that make it easy to convey CFD results. Shaded and transparent surfaces, pathlines, vector plots, contour plots, custom field variable definition and scene construction are just some


of the post processing features that are available. Solution data can be exported to third party graphics packages, or to CAE packages for additional analysis.

Reference http://www.fluent.com/


APPENDIX IV

Appendix IV. A Tentative Modeling Study of the Effect of Wall Reactions on Oxidation Phenomena

P.A. GLAUDE*, F. BUDA, F. BATTIN-LECLERC

Département de Chimie-Physique des Réactions,

Nancy Université, CNRS, ENSIC,

1 rue Grandville, BP 20451, 54001 NANCY Cedex, France

Brief communication

Shortened running title :

EFFECT OF WALL REACTIONS ON OXIDATION PHENOMEMA

* E-mail : [email protected] ; Tel.: 33 3 83 17 51 01 , Fax : 33 3 83 37 81 20


Summary Simulations have been run to assess, when diffusion is neglected, the effect of tentative wall reactions on autoignition delay times and on a pressure-temperature diagram of oxidation phenomena in the case of n-butane. Two types of reactions depending of the type of wall coating have been considered for HO2 radicals with estimated rate constants. Simulations show a clear influence of these wall reactions on autoignition delay times, as well as on some ignition limits, for pressures below 1 atm. Keywords : wall effects, oxidation phenomena, HO2 radicals, autoignition, modeling.

Introduction Previous studies [B1, 2] have shown that the coating of the wall of the reactor can significantly influenced the position of the autoignition limit of hydrogen/oxygen and the limits between the different oxidation phenomena (slow reaction, cool flame, single or multiple stages autoignition) of organic compounds in a pressure-temperature diagram. For instance, Cherneskey and Bardwell [B3] have observed an increase of about 200 Torr (26 kPa) for the ignition limit at 623 K of an equimolar n-butane/oxygen mixture by just coating their silica reactor by a PbO layer. The purpose of this work is to define heterogeneous reactions, which could be of importance, and to qualitatively assess their effect on a detailed gas phase kinetic model of the oxidation of n-butane. Details about the writing of this detailed mechanism and its validation can be found in a recent paper [B4].

Definition of the wall reactions and their rate parameters According to previous work [B5-8], amongst the radicals present in oxidation conditions, only HO2 radicals would be sufficiently unreactive to diffuse to the surface and promote heterogeneous reactions. According to Cheaney et al. [B6], two categories of surfaces can be defined, each related to a specific heterogeneous reaction: ♦ Category I includes surfaces treated with acid and is related to reaction (W1):

HO2 + H+ → ½ H2O2 + ½ O2 + H+ (W1),

♦ Category II includes surfaces coated with salt or metal oxides and is related to reaction (W2):

HO2 + e- → ½ H2O + ¾ O2 + e- (W2). As predicted by these reactions, H2O2 was experimentally observed when the surfaces were of category I, but not for those of category II. Nevertheless, as the formation of H2O2 from the reaction between HO2 radicals and hydrocarbon molecules cannot be neglected, an additional reaction has been proposed for surfaces of category II [B6]:

H2O2 + e- → H2O + ½ O2 + e- (W3).

These three reactions are taken into account in our modeling study, with rate parameters estimated as explained thereafter, with the assumption of control by surface reactions, i.e. diffusion can be neglected. According to Blackmore [B9], when neglecting diffusion, the rate constant of the termination of radicals to the wall of a reactor is :

d

c

2

3k w

γ= for a spherical reactor d

ck w

γ= for a cylindrical reactor

with : γ : Probability of reaction on each collision,

c : Radicals average molecular velocity, which can be obtained from the kinetic

theory of gases (at an average temperature of 800 K, for c≈ 71700 cm.s-1for HO2 radicals and H2O2 molecules), d: Diameter of the reactor.


Results and discussion Figure 1 presents the influence of wall effects on simulated autoignition delay times for stoichiometric n-butane/air mixtures in an spherical reactor (10 cm diameter). Simulations were performed using SENKIN of CHEMKIN II [B10] and the gas-phase mechanism [B4] including no wall effect, reaction on surface of category I and reactions on surface of category II, respectively. For the reactions of HO2 radicals, we have assumed a low probability of reaction, γHO2, of 0.01. Zils et al. [B8] propose values of γHO2 between 0.017 and 0.062 according to the efficiency of treatment of the reactor with PbO. We have then obtained kw1 = kw2 equal to 107 s-1 and, kw3 = 0.5 s-1, assuming the same relationship for H2O2 molecules with a much lower probability of reaction, as they are not radicals, γH2O2 = 5x10-5. The figure shows that the effect of heterogeneous reactions depends strongly on pressure. At 5 bar, this effect is weak whatever the category of surface, whereas at 0.5 bar, the delay times are multiplied by a factor up to 10 when considering reaction on surface of category I and by a factor more than 1000 when considering reaction on surface of category II. As this simulation neglects diffusion, it certainly strongly overestimates the influence of heterogeneous reactions at high pressure. That involves that termination of free radicals at wall in high pressure applications, such as in engines, are certainly of very minor importance. Figure 2 displays simulated pressure/temperature diagrams of oxidation phenomena for equimolar n-butane/oxygen mixtures obtained under the conditions of Cherneskey and Bardwell [B3] with and without the two kinds of wall reactions. In this case, the reactor is cylindrical (6 cm diameter) and has been strongly treated involving a high probability of reaction: γHO2 = 0.06 and γH2O2 = 3x10-4, corresponding to kw1 = kw2 = 717 s-1 and kw3 = 3.6 s-1. The heat transfer coefficient at the pyrex wall has been taken equal to 30 W m-2 K-1. These diagrams were constructed automatically using a software developed at University of Leeds by Griffiths et al. [B11] and based on UNIX shell scripts to control the execution of a modified version of SPRINT in which the various non-isothermal behaviour i.e., ignition, cool flames, and slow reaction are characterised. This characterisation of the reaction modes is based on monitoring the temperature increase and temperature gradient within the simulated time. The diagram obtained without considering heterogeneous reactions is qualitatively similar to that experimentally observed [B3], even if quantitative differences are encountered for the position of some limits, e.g. the simulated minimum ignition temperature is about 515 K and the simulated pressure ignition limit above 550 K ranges between 100 and 250 Torr, whereas the experimental minimum ignition temperature is about 530 K and the experimental pressure ignition limit above 550 K varies between 250 and 300 Torr.

Simulations considering heterogeneous reactions do not show changes in the minimum ignition temperature as encountered by Cherneskey and Bardwell [B3], but display well an increase of the pressure ignition limit above 550 K. Below 550K, the influence of HO2 radicals is less important than that of alkylperoxy radicals (RO2) and wall reactions of these last radicals should probably be taken into account to reproduce a change in the minimum ignition temperature. The increase of the pressure ignition limit above 550 K ranges between 50 and 100 Torr below 670 K and is even larger at higher temperature. While the inhibiting effect of walls of category II is only slightly more pronounced than that of wall of category I below 670K, the difference is much more important at higher temperature, which was not experimentally observed [B3].


300

200

100

0Igni

tion

time

s (s

)

950900850800750700Temperature (K)

no wall effect Category I Category II/1000

(b)

0.5

0.4

0.3

0.2

0.1

0.0Igni

tion

time

s (s

)950900850800750700

no wall effect Category I Category II

(a)

Figure 1. Influence of wall effects on simulated autoignition delay times for stoichiometric n-butane/air mixtures for an initial pressure of (a) 5 bar and (b) 0.5 bar .

No Wall EffectCategory ICategory II

Ignition

Cool Flames

Slow Reaction

No Wall EffectCategory ICategory II

Ignition

Cool Flames

Slow Reaction

Figure 2. Influence of wall effects on the pressure/temperature diagram of oxidation phenomena for equimolar n-butane/oxygen mixtures (1 Torr = 0.13 kPa).

Acknowledgements Financial support of this work by the European Union within the “SAFEKINEX” Project EVG1-CT-2002-00072.


References B1. C. H. Bamford, C.F.H. Tipper, Gas phase combustion, Comprehensive Chemical Kinetic,

vol. 17., Elsevier (1977). B2. J.F. Griffiths, S.K. Scott, Prog. Energ. Combust. Sci., 13 (1987) 161-197 B3. M. Chernesky, J. Bardwell, Canad. J. Chem., 38 (1960) 482-492. B4. F. Buda, R. Bounaceur, V. Warth, P.A. Glaude, R. Fournet, F. Battin-Leclerc, Combust.

Flame 142 (2005) 170-186. B5. G.H.N. Chamberlain, D.E. Hoare, A.D. Walsh, Discus. Faraday Soc., 14 (1953) 89-97. B6. D.E. Cheaney, D.A. Davies, A. Davis, D.E. Hoare, J. Protheroe, A.D. Walsh, Proc.

Combust. Inst., 7 (1959) 183-187 B7. K.A. Sahetchian, A. Heiss, R .Rigny, J. Chim. Phys., 84 (1987) 27-32. B8. R. Zils, R. Martin, D. Perrin, Int. J. Chem. Kin., 30 (1998) 657-671. B9. D.R. Blackmore, J. Chem. Soc., Faraday Trans. 1, 74 (4) (1978) 765-775. B10. R.J. Kee, F.M. Rupley, J.A Miller, Sandia Laboratories Report, SAND 89 - 8009B (1993). B11. J.F. Griffiths, K.J. Hughes, R. Porter, private communication (2005).

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