10 energy released

Chapter 10

Energy Release in Backdraft Table of Contents

1. Introduction.............................................................................. 269 2. The Energy Released in a Backdraft Deflagration .................... 269 2.1 The Total Energy Released inside the Enclosure.................. 271 2.2 Energy Stored inside the Enclosure at Time t...................... 271 2.3 Energy Lost through Leakages (Openings)........................... 272 2.4 Chemical Energy Available for Backdraft ............................ 272 3. Important Parameters in the Energy Equations........................ 273 3.1 両i : The Influence of Type of Combustion Reaction ............... 273 3.1.1 Stoichiometric Combustion Reaction.............................. 274 3.1.2 Combustion Developed With Lack of Oxygen ................ 274 3.1.3 Combustion Reaction Developed with Lack of Fuel ....... 274 3.2 Combustion Heat of Gases as Function of the Temperature 275 4. Validation ................................................................................. 277 4.1 Experimental Design ............................................................ 277 4.1 Compartment Fire Modeling................................................ 281

4.3 Results of the Simulation ..................................................... 282 5. Conclusion ................................................................................ 285

10. Energy Released in Backdraft

1. Introduction A fire burning in an under-ventilated condition can lead to a rapid flame spread such as backdraft. If backdraft happens, a great amount of energy is released inside and outside (fireball) the fire compartment.

The energy that can be released in a backdraft scenario is assumed to be equal to the energy of the unburnt gaseous mixture inside the compartment at the moment of ignition, tignition. However, this energy is not necessarily the actual one released in a backdraft deflagration because the combustion may not react stoichiometrically.

Therefore, the total available energy in a backdraft deflagration can be divided in three parts: • • •

Energy released inside the enclosure.

Energy released outside the enclosure creating a fireball.

Energy not combusted in the deflagration due to the lack of oxygen.

A model for obtaining these energies was developed. The validation of this model is also provided.

2. The Energy Released in a Backdraft Deflagration In any fire scenario, energy is supplied to the compartment from the beginning of the fire to the time t.

A part of this energy is consumed by the fire, another part is stored within the compartment and the rest is lost through the leakages in the compartment boundary, i.e. openings.

• • •

Group 1: Chemical energy consumed by fire.

Group 2: Chemical energy stored in the compartment.

Group 3: Chemical energy lost through leakages (openings).

The energy of Group 1 cannot be included in the available energy for backdraft deflagration because this energy has been already “used” (consumed) and there’s no more energy left. The energy of Group 3, even if it has not been consumed, cannot be included neither in the energy released in a backdraft deflagration because it has escaped from the compartment before ignition.

Therefore, the available energy for backdraft deflagration is the chemical energy stored inside the compartment at the time of ignition, tignition (Group 2). It represents the maximum energy possible to be released in backdraft deflagration.

269

10. Energy Released in Backdraft This energy can also be divided in three groups: • • •

Group 2.1: Chemical energy released inside the compartment.

Group 2.2: Chemical energy released outside the compartment, fireball.

Group 2.3: Chemical energy not consumed.

Figure 10-1 represents the energy distribution in a backdraft scenario.

Total Energy

Group 1

Group 2

Consumed by fire

Stored in enclosure

Group 3 Lost through leakages

At t = tignition Group 2.1 Consumed inside

Group 2.2 Consumed outside

Group 2.3 Not consumed

Figure 10-1: Layout of the available energy for backdraft

Figure 10-2 represents the chemical energy history for a compartment with a burner that releases unburnt gas at a constant flow, i.e. methane. The solid line indicates the total chemical energy that enters the compartment through the burner. It increases linearly due to the constant flow rate. The dashed line indicates the chemical energy that is stored within the compartment as a function of time. The total stored chemical energy is initially zero since the fire consumes all the chemicals released by the burner due to the complete combustion. Later on, when the combustion becomes incomplete due to the oxygen starvation, the accumulation of unburnt gases within the compartment starts to take place.

270

10. Energy Released in Backdraft 45 40

Energy [MJ]

35 30 25

Chemical energy burnt+lost Total chemical energy

20 15

Chemical energy stored 10 5

Chemical energy burnt

Chemical energy lost

0 0

60

120

180

240

300

360

420

480

Time [s]

Figure 10-2: Chemical energy histories for the energy within the compartment

The difference between the supplied energy by the burner and the stored energy is a function of the energy consumed and the energy lost through leakage.

The analytical expressions of the above energies are developed by the author in the following sections. The terms employed in these expressions are explained in Section “2.4 Energy Available for Backdraft”.

2.1 The Total Energy Released inside the Enclosure The total energy released inside the enclosure is calculated by integrating the unburnt gaseous mixture released by the burning material in the pyrolysis process over the time, Eq. (10-1). It is expressed in MJ. E TotalEnergy =

∑ (∫

t

0

i

ɺ mixt ∆H i c (t, T)·mol in ψ i dt

)

(10-1)

2.2 Energy Stored inside the Enclosure at Time t The energy stored inside the enclosure at each time is calculated using Eq. (102). It is expressed in MJ.

EStored =

∑ ∆H (t, T)·mol i c

mixt stored

ψi

(10-2)

i

271

10. Energy Released in Backdraft

2.3 Energy Lost through Leakages (Openings) The energy lost through leakages during a period of time is given by Eq. (10-3), where t1 and t2 are the initial and final time of the period. It is expressed in MJ.

∑ (∫

E Lost =

i

t2

t1

ɺ mixt ∆H i c (t, T)·mol out ψ i dt

)

(10-3)

For t1 = 0 and t2 = t (for t ≤ tigntion), Eq. (10-3) gives the energy lost through the leakages or openings of the compartment. For t1 = tigntion and t2 = tflame, Eq. (103) gives the energy released outside the compartment (fireball).

2.4 Chemical Energy Available for Backdraft The maximum available energy for a backdraft scenario is calculated as a function of the ignition time. This energy is expressed as: E Back _ max =

∑ ∆H (t i c

ignition

, T)·mol mixt stored ψ i

(10-4)

i

Eback_max represents the maximum expected energy in a backdraft deflagration that can occur at time tignition. It consists of:

•

Energy released inside the compartment, E Back _in .

E Back _ in =

i

•

tflame

∑∫

tignition

ɺ mixt ∆H ic (T)·mol u → b ψ i ξ i dt

(10-5)

Energy released outside the compartment (fireball), E Back _ out .

E Back _out =

∑∫ i

•

tflame

tignition

ɺ umixt ∆Hci (T)·mol → v ψ i dt

(10-6)

Energy not consumed in the deflagration, E Back _ notconsumed .

E Back _ notconsumed = E Back _max − ( E Back _in + E Back _out )

(10-7)

Where: • • •

ɺ mixt mol in represents the amount of moles of gaseous mixture entering the compartment per unit of time, mol/s. mol mixt stored represents the total amount of moles of the gaseous mixture accumulated in the compartment at time t, in mol. ɺ mixt mol out represents the amount of moles of the gaseous mixture going out through the openings of the compartment per unit of time, in mol/s

272

10. Energy Released in Backdraft • • • • • • •

∆H ic (t, T) is the combustion heat of the fuel i at T K, expressed in kJ/mol. (See Section 3.2: “Combustion Heat of gases as Function of Temperature”). ψ i is the molar fraction of the fuel i in the gaseous mixture in the compartment, in %. ξi is a parameter that identifies the kind of combustion taking place. (See Section 3: “Important Parameters in the Energy Equations”). ɺ mixt mol u → b represents the moles of unburnt gas that become consumed inside the compartment per unit of time, expressed in mol/s. ɺ mixt mol u → v represents the moles of unburnt gas that go out through the openings per unit of time, expressed in mol/s. tflame is the time at which the flame of deflagration reaches the opening, in s. tignition is the time at which the ignition of the gaseous mixture occurs, in s.

ɺ mixt ɺ mixt ɺ u→b and m ɺ u→ v (See Chapter 9: “ Note: mol u → b and mol u → v are obtained from m Ignition of the Flammable Region: Backdraft Deflagration”).

3. Important Parameters in the Energy Equations 3.1 ξi : The Influence of Type of Combustion Reaction The type of combustion that takes place in a backdraft deflagration has a very important role in the amount of energy released inside the compartment. The parameter ξi has been introduced in the Eq. (10-5) for expressing this influence.

Three different types of combustions are considered: • • •

Case 1; Stoichiometric combustion reaction. Section 3.1.1.

Case 2; Combustion developed with lack of oxygen. Section 3.1.2.

Case 3; Combustion developed with lack of fuel. Section 3.1.3.

For checking in which of these three cases the deflagration falls, the limiting reactant of the mixture must be identified. If the limiting reactant is the air (oxygen), the combustion reacts with lack of oxygen, however if the limiting reactant is the fuel, the combustion reacts with lack of fuel. In the latter situation, the energy released inside the compartment will be the maximum expected. A process for identifying the limiting reactant is given in Annex VI. The value of ξi according to the type of combustion for C-H-O containing fuels is commented in the sections below.

273

10. Energy Released in Backdraft

3.1.1 Stoichiometric Combustion Reaction All the unburnt gases of the mixture react until exhaustion. The parameter ξi takes the value of 1.0. In this case, neither fuel nor oxygen is found in the combustion products. ξi = 1.0

(10-8)

3.1.2 Combustion Developed With Lack of Oxygen The unburnt gases of the mixture are not able to react until exhaustion.

Unburnt gases are found in the combustion products but no oxygen. The value of the parameter ξi is given by the Eq. (10-9). i _ react

ξi =

mol deflagration mol itignition

(10-9)

react Where mol i_ is the quantity of the unburnt specie “i” that reacts in the tignition deflagration and mol itignition is the quantity of the unburnt gas “i” that is accumulated at ignition time. Both are given in mol. Annex VI shows how react mol i_ tignition is obtained for other species accumulated in the compartment and the available oxygen.

The excess of unburnt species i is given by the Eq. (10-10): excess i _react mol i_ = mol itignition − mol deflagration tignition

(10-10)

Where mol it_excess is the excess of the unburnt specie i, in mol. ignition

3.1.3 Combustion Reaction Developed with Lack of Fuel In this situation the unburnt gases of the mixture are able to react until exhaustion. Unburnt gases are not found in the combustion products only oxygen. The parameter ξi takes the value of 1.0. ξi = 1.0

(10-11)

This situation is assumed to happen in a fireball.

The excess of oxygen is given by Eq. (10-12): 2 _ excess 2 2 react molOtignition = molOtignition − molOdeflagration

(10-12)

274

10. Energy Released in Backdraft 2 _ excess Where molOtignition is the excess of the unburnt specie i, in mol. Annex VI shows O2 _ excess how mol tignition is obtained for the other accumulated species.

3.2 Combustion Heat of Gases as a Function of the Temperature All combustion reactions take place with a released of energy. It is obtained by means of the heat combustion heat. In literature, the combustion heat of a fuel is normally found at 25ºC, however this value is temperature dependent. Table (2-2) shows the combustion heats of some common fuels at 25ºC. However, in a backdraft scenario the gas temperature is often greater than 25º.

Higher temperatures than 25ºC mean higher values of combustion heat and as a consequence higher energy released.

Therefore, it is important to calculate the suitable combustion heat as a function of the gas temperature of the compartment at time tignition.

Let’s consider Eq. (10-13) the general form of representing chemical reactions, where a, b, c and d represent the quantity of moles of the gas species A, B, C and D, respectively. aA + bB → cC + dD

(10-13)

For calculating the combustion heat of unburnt gases at the temperature T higher than 25ºC, Eq. (10-14) is used, (Brizuela, 1999):

(

∆Hic (T) = c ∆Hf,C (To ) +

∫

(

T

To

) (

T

)

cp,C dT + d ∆H f,D (To ) + ∫ cp,DdT +

−a ∆Hf,A (To ) +

∫

T

To

) (

To

cp,A dT − b ∆Hf,B (To ) +

∫

T

To

)

cp,B dT (10-14)

where ∆Hf,i is the heat of formation of gas species “i”. Since the combustion heat of a fuel at 25ºC can be expressed as Eq. (10-15), Eq. (10-14) can be rewritten as Eq. (10-16) (Pérez Jiménez, C. 2004):

∆Hic (To ) = c∆Hf,C (To ) + d∆Hf,D (To ) − a∆Hf,A (To ) − b∆Hf,B (To )

(10-15)

Therefore, T

T

T

T

To

To

To

To

∆H ic (T) = ∆H ic (To ) + c ∫ cp,C dT + d ∫ cp,DdT − a ∫ cp,A dT − b ∫ cp,B dT

(10-16)

Above cp,i is the specific heat (at constant pressure) of the gas species “i”. Its value is found in the literature for a great number of chemical substances as a function of the temperature. Figure 10-3 represents the values of the specific heat for common gases found in a fire situation (O2, H2, N2, H2O, CO and CO2), in a range of temperatures between 298 and 1600 K. The analytical expressions

275

10. Energy Released in Backdraft of the specific heat for each gas species have been obtained by assuming a polynomial equation of degree 1 or 2 (see Annex VI).

O2

14

H2

13

N2

12

H2O

[Cal/mol K]

15

11

CO2

10

CO

9 8 7 6 5 200

400

600

800

1000

1200

1400

1600

1800

[K]

Figure 10-3: Specific heat of selected fuels as a function of the temperature.

Figure 10-4 represents the values of the combustion heat for methane (CH4), hydrogen (H2) and carbon monoxide (CO) in a range of temperatures between 300 and 800 K. 2500 2250

CH4

H2

CO

2000

[kJ/molK]

1750 1500 1250 1000 750 500 250 0 300

350

400

450

500

550

600

650

700

750

800

Temperature [K]

Figure 10-4: Variation of the combustion heat as function of the temperature.

276

10. Energy Released in Backdraft As a representative case, a rise of 25% in the combustion heat of methane is obtained by increasing the initial temperature of 300K to 500K.

4. Validation To validate our model, the obtained results using it are compared with the values given by Fleischmann, 1993. Fleischmann obtained an estimation of the energy by means of an energy budget in the compartment, based on the amount of mass exchange through the opening from the time of opening to the time the propagated flames reach the opening.

4.1 Experimental Design Figure 10-5 shows a schematic of the compartment, its internal dimensions and the locations of the instrumentation. The characteristics of the process and how the tests have been carried out are explained in Section 6.1 of Chapter 5. Note that the opening is a centered window (0.4 m x 0.4 m).

Burner

1.2 m

1.2 m TC tree

2.4 m Pressure relief panel Opening hatch

Bidirectional probes

Leakage vent

Figure 10-5: Schematic of the Fleischmann compartment. Centered window opening.

277

10. Energy Released in Backdraft Experiments were conducted using a 70kW fire source. Burn times ranged from 415 s to 535 s. In these experiments the flame died out about 150 s.

Table 10-1 represents the results of the 11 tests carried out. Column 1 is the experiment number. Columns 2 and 3 are the burner characteristics, i.e., the burner flow rate and the time the burner gas is flowing. Columns 4-6 are the calculated lower layer temperatures, the upper layer temperatures, and the layer heights at opening. Columns 7-8 give the total mass that flows into and out of the compartment after hatch opening and prior to ignition, respectively.

Columns 9-10 give the total mass that flows into and out of the compartment after opening and prior to flames exiting the compartment.

Table 10-2 gives a summary of the calculated energies. Column 1 is the experiment number. Columns 2-5 are the compartment species concentration at opening for O2, CO, CO2 and HC, respectively. Column 7 represents the chemical energies stored in the compartment when the compartment was opened. Column 8 gives the energy that flows out of the compartment prior to backdraft ignition. The energy that flows out of the opening between the compartment ignition and the flames existing the opening is given in column 9.

Column 10 gives the amount of energy burned in the compartment assuming that all the available oxygen is consumed. Column 11 gives the energy that is not burned there. Column 12 gives the amount of energy that is available for the fireball.

A combustion efficiency of 1.0 was supposed in these results.

278

Run number

Fuel flow [kW]

Burner time [s]

Tu [K]

Tl [K]

hl [m]

t= ti m out [kg]

m int= ti [kg]

t= tfl m out [kg]

m int= tfl [kg]

P3EXP 82 P3EXP 79 P3EXP 77 P3EXP 85 P3EXP 81 P3EXP 76 P3EXP 86 P3EXP 83 P3EXP 78 P3EXP 80 P3EXP 84

70 72 72 70 72 75 70 72 74 73 70

415 415 415 415 475 475 475 535 535 535 535

360 364 362 363 359 356 361 355 354 357 354

382 384 381 384 375 374 378 369 368 371 368

0.48 0.45 0.46 0.48 0.46 0.44 0.46 0.45 0.46 0.49 0.46

0.271 0.400 0.550 0.68 0.390 0.531 0.66 0.400 0.540 0.650 0.72

0.35 0.62 0.74 0.93 0.57 0.79 0.96 0.62 0.81 0.95 1.13

* 1.57 1.63 1.67 1.15 1.56 1.62 1.70 1.20 1.31 1.47

* 0.62 0.75 0.94 0.57 0.80 0.96 0.62 0.81 0.95 1.13

Table 10-1: Summary of the 11 window experiments reporting the burner characteristics, layer temperatures, height and mass flow into and out of the compartment.

Run number P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP

82 79 77 85 81 76 86 83 78 80 84

YO2 [%]

YCO [%]

YCO2 [%]

YHC [%]

0.11 0.003 0.05 0.15 0.11 0.003 0.05 0.17 0.11 0.003 0.05 0.18 (0.17) (0.002) (0.03) (0.02) 0.11 0.003 0.05 0.18 0.11 0.003 0.05 0.19 (0.16) (0.002) (0.04) (0.03) 0.11 0.003 0.05 0.18 0.11 0.003 0.05 0.2 0.11 0.003 0.05 0.2 (0.15) (0.002) (0.04) (0.04)

ES [KJ]

EI [KJ]

EF [KJ]

EO [KJ]

EFB [KJ]

EN [KJ]

Pmax [Pa]

14430 16590 17470 15260 17280 18720 18130 17450 19390 18990 19840

2030 3400 4950 5440 3510 5040 6270 3600 5080 6500 7920

0 4860 4270 3020 6670 4360 3500 5670 2720 2530 2850

6220 4030 5300 4810 3260 4570 4960 3790 5280 5540 5770

8210 12550 12170 10450 14020 14150 13180 13660 14110 13450 14080

6180 4290 2950 1990 3840 4750 3410 4390 6310 4420 3310

2 13 9 14 22 82 115 189 258 213 102

Table 10-2: Summary of the energy accounting reporting the species concentration at compartment opening, the energy stored in the compartment at opening, the energy which exist in the compartment prior to ignition, the energy that exists in the compartment after ignition and before flames exit the compartment, the energy released in the compartment by the backdraft and the energy that is available for fireball and the maximum pressure reached.

10. Energy released in backdraft phenomenon

4.1 Compartment Fire Modeling The input data used in the simulation are the following: • • •

The model assumes that the fire develops in one zone.

All the partitions of the compartment consist of one layer of gypsum and one layer of ceramic blanket. The properties are summarized in Chapter 5: “Combustion Products in Fires”.

Three openings are considered. The first one corresponds to the opening hatch, the second one corresponds to the pressure relief vent and the third one is introduced for considering other leakages in the compartment. Their dimensions and initial states are summarized in Table 10-3.

Opening Hatch Pressure relief vent Leakage vent

Initial state Close Open Open

Final state Open Close Open

Sill [m] 0.4 0.0 0.0

Soffit [m] 0.800 0.125 0.005

Width [m] 0.400 0.125 0.090

Table 10-3: Dimensions and initial state of the openings.

The hatch opening changes from closed to open 5.0 seconds after the burner is switched off. The burner time is shown in Table 10-1. The pressure relief vent is closed 5.0 s before the burner time. OZone does not allow using circular vents. Therefore, to simulate this vent a rectangular one with equivalent area is considered. The leakage vent has been defined considering a gap of 0.20 mm in the edges of openings.

•

• • • • • •

The considered species are carbon dioxide (CO2), carbon monoxide (CO), water (H2O), nitrogen (N2), oxygen (O2) and methane (CH4). For the CO yields, the correlations Eq. (5-26)-(5-27)-(5-28) given in Chapter 5: “Combustion Products in Fire” are chosen. For the other species Eq. (520)-(5-21)-(5-22)-(5-23) are used with an average yields coefficients of B = 0.9.

The fire source was a flowing methane gas burner, 0.09 m2. The combustion heat of methane is considered to be 50.0 kJ/g.

The flame is imposed to die out at 150 s from the beginning of the fire.

The combustion heat for CO and H2 is 283 and 242 kJ/mol, respectively.

The burning speed in the deflagration is 0.44 m/s, (stoichiometric value of methane) The discharge coefficient is supposed to be 0.6. χ is calculated using Eq. (9-11) of Chapter 9: “Ignition of the Flammable Region: Backdraft Deflagration”. γu and γb are the stoichiometric values of methane, 1.38 and 1.18, respectively.

281

10. Energy released in backdraft phenomenon

4.3 Results of the Simulation Table 10-4 represents the mass species accumulated inside the compartment at ignition time. Column 1 is the run name. Columns 2-7 give the mass of species accumulated at ignition time. Column 8 gives the total mass accumulated in the compartment at ignition time.

Run number

mO2 [kg]

mCO [kg]

P3EXP 82 P3EXP 79 P3EXP 77 P3EXP 85 P3EXP 81 P3EXP 76 P3EXP 86 P3EXP 83 P3EXP 78 P3EXP 80 P3EXP 84

0.36 0.44 0.51 0.52 0.45 0.45 0.50 0.45 0.46 0.51 0.50

0.022 0.019 0.018 0.014 0.018 0.018 0.015 0.017 0.017 0.015 0.014

mCO2 [kg] 0.14 0.14 0.11 0.09 0.11 0.11 0.10 0.10 0.11 0.10 0.11

mHC [kg] 0.3 0.25 0.22 0.19 0.31 0.30 0.22 0.30 0.31 0.22 0.21

mN2 [kg]

mH2O [kg]

masstotal [kg]

2.06 2.13 2.22 2.29 2.14 2.13 2.24 2.15 2.19 2.29 2.25

0.114 0.107 0.083 0.073 0.091 0.091 0.079 0.086 0.091 0.085 0.083

3.01 3.10 3.17 3.19 3.13 3.11 3.16 3.12 3.18 3.23 3.17

Table 10-4: Mass species (O2, CO, HC, N2, H2O) accumulated in the compartment at ignition time according to OZone simulation.

The maximum pressure, Pmax, simulated in OZone is approximately 1.4 bar for all the cases. A great difference between this pressure and the ones obtained in the experiments is noted (see Table 10-2).

The reasons for this difference are: •

•

The energy model is based on the results of the deflagration model of Chapter 9. It assumes a well-stirred situation. That is not true in backdraft and this hypothesis affects seriously the maximum pressure inside the compartment.

The input data describing the burning speed, the expansion coefficient, etc are for the stoichiometric mixture CH4+Air. These values must be updated according the real concentration in the compartment and the different types gas species.

282

10. Energy released in backdraft phenomenon

Table 10-5 shows the computed energies. Column 1 is the run name. Columns 25 show the available energy for backdraft deflagration, the energy consumed inside and outside the compartment and the energy not consumed. Columns 6-7 give the values of the energy used for comparison together with the non consumed energy.

Columns 6 and 7 are obtained using Eq. (10-17) and Eq. (10-18). The reason for using these equations is based on the fact that the energies (ES, EI, EF, EO, EFB) obtained in Table 10-2 have different definitions to those obtained in the Table 10-5 ( E Back _ max , E Back _in , E Back _ out , E Back _ notconsumed ).

E Back _ max = E S + E I

(10-17)

E FB = E Back _in + E Back _out + E I

(10-18)

Run Number P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP P3EXP

82 79 77 85 81 76 86 83 78 80 84

E Back _ max [kJ]

E Back _in [kJ]

E Back _ out [kJ]

E Back _ notconsumed [kJ]

Es [KJ]

EFB [KJ]

15452 12879 11323 9776 15886 15383 11306 15374 15880 11298 10796

2421 2935 3429 3511 3023 3016 3327 3037 3051 3391 3309

7531 6272 5510 4753 7731 7488 5499 7483 7730 5494 5255

5499 3671 2383 1510 5130 4879 2480 4852 5098 2411 2230

17482 16279 16273 15216 19396 20423 17576 18974 20960 17798 18716

11983 12607 13889 13705 14265 15544 15096 14121 15861 15386 16485

Table 10-5: Available energies for backdraft deflagration: consumed inside the compartment and consumed outside the compartment (fireball) computed by OZone.

A better agreement of results is found regarding the energies (see Figure 10-6 to Figure 10-8). The ES obtained in experiments is represented on the x-axis of Figure 10-6. The ES obtained by OZone simulations after correction with Eq. (10-17) is shown in the y-axis. The average relative deviation is 7%.

283

10. Energy released in backdraft phenomenon

22000 21000 20000

OZone [kJ]

19000 18000 17000 16000 15000 14000 13000 12000 12000

13000

14000

15000

16000

17000

18000

19000

20000

21000

22000

Experiments [kJ]

Figure 10-6: ES energy: test vs. OZone The experimental EFB is shown in the x-axis in Figure 10-7. The OZone EFB obtained after correction using Eq. (10-18) is given on the y-axis. The average relative deviation is 13%.

17000 16000 15000

OZone [kJ]

14000 13000 12000 11000 10000 9000 8000 8000

9000

10000

11000

12000

13000

14000

15000

16000

17000

Experiments [kJ]

Figure 10-7: EFB energy: test vs. OZone The experimental EN is shown in the x-axis in Figure 10-8. The OZone EN is given on the y-axis. The average relative deviation is 18%.

284

10. Energy released in backdraft phenomenon

7000 6000

OZone [kJ]

5000 4000 3000 2000 1000 0 0

1000

2000

3000

4000

5000

6000

7000

Experiments [kJ]

Figure 10-8: EN energy: test vs. OZone

5. Conclusion An energy model for calculating the energy released in a backdraft deflagration has been developed and implemented in OZone.

This model takes into account: • • • •

The initial conditions when the mixture combusts (pressure, temperature…).

The concentration of the species and their properties such as specific heat, molecular weight, combustion heat, etc.

The type of combustion that takes place inside and outside the compartment, i.e. stoichiometric, or combustion developed with lack or excess of oxygen.

The limiting reactant in the combustion.

Eleven backdraft tests have been modelled assuming to occur in a well-stirred situation. In addition, parameters such as the burning speed, expansion coefficient and specific heat ratios have been considered equal to those of a stoichiometric mixture.

Based on these hypotheses and regarding the energy released inside and outside the compartment and the energy not consumed, one may observe that OZone gives higher values of energy than the backdraft experiments. The maximum relative average deviation is found to be less than 20%.

285

10. Energy released in backdraft phenomenon

Regarding the maximum pressure, Pmax, reached in the compartment, higher values are found with OZone. This indicates that the hypotheses considered must be improved: • •

A well-stirred assumption does not accurately represent a backdraft deflagration.

Likewise, considering the explosion parameters such as γu, γb, Su and Ei equal to the stoichiometric values of methane does not produced accurate results.

Despite these errors, the results obtained by the model are on the side of safety results can be used as comparative values for assessing the risk and the intensity of the backdraft. For example, higher EBack_out creates a larger fireball diameter that can cause casualties, spread the fire to adjacent buildings or even cause structural damage, e.g., a fireball contained in a corridor will raise the pressure within the compartment.

286

10. Energy released in backdraft phenomenon

287

10. Energy released in backdraft phenomenon

Annex III -Molecular weight of a gaseous mixtureLet’s be ΨI, the molar fraction of the gas species “i”, and MWi its molecular weight.

The molecular weight of a gaseous mixture is defined as follows: MWmixt =

∑ MW ·ψ i

()

i

i

-Limiting reactant: ExampleLet us consider the combustion reaction between methane and oxygen. The reaction can be represented by the equation: CH 4 + 2O2 → CO2 + 2H2O

()

This balanced reaction equation indicates that one mol of CH4 would react with two moles of O2. Thus, if you have 2 moles of CH4, 4 moles of O2 will be required. If there is an excess of moles of O2 (more than 4), they will remain unreacted, some will remain as an excess reactant, and the CH4 is a limiting reactant. It limits the amount of the product that can be formed.

··Polynomial equation for specific heat of O2, H2, N2, CO, H2O, CO2

cp,O2 = -4·106 T2 + 0.0128T + 25.802

for O2.

()

cp,H2 = 2·10-6 T2 - 0.0004T + 28.913

for H2.

()

cp,N2 = 0.0051T + 27.403

for N2.

()

cc,CO = 0.0053T + 27.5

for CO.

()

cp,H2O = 0.0111T + 29.959

for H2O.

()

for CO2.

()

−5

cp,CO2 = −10 T + 0.042T + 26.475 2

Where T is give in [K] and cp is obtained in [J/molK].

··Percentage of unburnt species reacting in a deflagration·· In a combustion reaction with lack of oxygen, not all the unburnt products react until exhaustion.

Let’s explain how the oxygen is shared among the unburnt products with an example. Let’s suppose a mixture formed of methane, dioxide carbon, monoxide

10. Energy released in backdraft phenomenon

carbon, hydrogen, water, oxygen and nitrogen. The molar fractions in the compartment of the species are indicated below: ψi Molar fraction

CH4 [%] 13.6

CO2 [%] 1.65

CO [%] 0.15

H 20 [%] 7

O2 [%] 13.5

H2 [%] 0

N2 [%] 64

First of all, the stoichiometric reaction of each unburnt gas must be established, where the value before the O2 is represented in this section as Xi: CH 4 + 2O2 → products ( H2O,CO2 )

()

CO + 1 2 O2 → products ( H2O, CO2 )

()

H2 + 1 2 O2 → products ( H2O,CO2 )

()

Then, the ratio specie-mixture is calculated according to Eq. () and Eq. (): mol total = molO2 + mol i ϕi =

()

mol i mol total

()

Resolving for CH4: mol total = molO2 + molCH4 = 2 + 1 = 3

ϕi = 100

molCH4 mol total

()

= 33.33

()

Table x shows the results for every species.

Eq. () Eq. () Eq. ()

MolesTotal [mol] 3.0 1.5 1.5

Moles of i 1 1 1

Moles of O2 2 0.5 0.5

ϕunburnt [%] 33.3 66.6 66.6

ϕoxygen [%] 66.6 33.3 33.3

molOi 2 required 27.20 0.075 0.000

Assuming 100 mol of mixture, the required oxygen for a stoichiometric combustion is obtained as: molO2 required =

∑ mol i

i O2 required

= 100∑ ψ i ·X i i

()

10. Energy released in backdraft phenomenon

Column 7 shows the required oxygen for the species present in the mixture.

This data is needed when trying to share in equality the mol of oxygen present in the initial mixture. It is done according to: mol

i O2 → unburnt

=

molO2 _mixture ·molOi 2 required

()

molO2 required

Once molOi 2 →unburnt has been obtained, the moles of unburnt species that react is given by:

mol

i_ react deflagration

=

molOi 2 →unburnt

i_ react

2

Moles of i in mixture 13.45

molOi 2 →unburnt [mol] 13.46

mol deflagration [mol] 6.730

0.5

0.05

0.037

0.074

0.5

0.00

0.000

0.000

Xi [--]

Eq. () Eq. () Eq. ()

()

Xi

Eq. () is used for obtaining the excess of oxygen, 2 _ excess 2 2 react molOtignition = molOtignition − molOdeflagration

()

2 _ excess molOtignition = 13.5 − (13.45 + 0.05 ) = 0.0

()

Eq. () is used for obtaining the excess of oxygen, excess _react mol i_ = mol itignition − mol ideflagration tignition

()

4 _excess molCH = 13.6 − 13.45 = 0.15 tignition

()