Improved Version of Cone Tools for Predictions of Room

MASTER'S THESIS

Improved Version of Cone Tools forPredictions of Room Corner Tests

Jon Moln Teike

Master of Science in Engineering TechnologyFire Engineering

Luleå University of TechnologyDepartment of Civil, Environmental and Natural Resources Engineering

Department of Civil, Mining and Environmental Engineering SP Fire Technology Luleå University of Technology SP Technical Research Institute of Sweden SE-971 87 Luleå Box 857 Sweden SE-501 15 Borås Sweden

Improved version of Cone Tools for predictions of Room Corner Tests

Jon Moln-Teike

I

Preface First of all, I would like thank all the staff working at the department of Fire Technology at SP

Technical Research Institute of Sweden for giving me a pleasant visit and interesting

conversations during the breaks.

I would like to give special thanks to:

Maria Hjolman, for helping me with the Cone Tools program despite her busy schedule

Joakim Albrektsson, for all help regarding Visual Basic and numerical calculations

Furthermore, I would like to thank my supervisor Ulf Wickström for all help and constructive

feedback during the course of the work. I have learned a lot thanks to him.

It has been a turbulent time for me with many life-changing events during the course of the

work. Even if some of these events have been more tragic than others, it has been a very

educational time in many respects.

I am very grateful to have such great friends and family which have supported me through

this period.

Luleå, Sweden, May 2011

Jon Moln-Teike

II

Abstract Room Corner Test (ISO 9705) is used for classification of surface materials and as a reference

scenario for a number of countries, such as the European Single Burning Item test. Due to the

cost of a Room Corner Test it is of interest to predict the course of the test before it is

performed.

By using the model from Wickström and Göransson, which use the time to ignition and the

complete heat release rate from a Cone Calorimeter test (ISO 5660), it is possible to predict a

Room Corner Test quite good. However, because of the complexity of the model there has

been a need for a program which simplifies the use of the model. The program is called Cone

Tools and has been used in the process of the work.

The aim of the report was to simplify the equation system of the burning area in Cone Tools

and, if possible, improve it. Tests were also performed to see whether the correction factor in

Cone Tools could be improved.

The burning area equations have been done linear to simplify the system. All tests were

conducted in Cone Tools 3.2.1 which has been recoded by the use of Visual Basic. The

current and the modified model were compared against nine different products heat release

rate curve to see which model that makes the best prediction.

The result was very interesting were the modified model did better or as good prediction in

most cases compared to the current model. Some products, such as Plywood and FR ESP,

were predicted very well by the modified model.

The correction factor between different irradiance levels in Cone Tools is very crude and it is

therefore of interest to improve it. This was done by using the same quadratic expression, as

in Cone Tools 3.2.1, but taking the heat loss from the surface into account. The result showed

that the current correction factor gave a better translation when comparing them against

different products.

Nine tests are quite few to determine if the modified model will work for a large number of

diverse products. Therefore, more test needs to be performed before the modified can be

accepted as a new and improved model. This is however a good start and shows that it is

possible to improve predictions of a Room Corner Test.

III

Sammanfattning Room Corner Test (ISO 9705) används för att brandklassa ytmaterial och som

referensscenario till ett antal länder, som Europas Singel Burning Item test. Då kostnaden för

ett Room Corner Test är högt är det därför intressant att predicera resultatet från ett sådant

test, för en viss produkt.

Genom att använda Wickström och Göranssons modell, som använder tid till antändning och

hela värmeutvecklings kurvan från ett Konkalorimeter test (ISO 5660), är det möjligt att

predicera ett Room Corner Test ganska bra. Då modellen är komplex finns det ett behov av ett

program som förenklar arbetet med den. Programmet som har tagits fram heter Cone Tools

och har använts i arbetet.

Målet med arbetet är att förenkla ekvationerna för den brinnande arean i Cone Tools och, om

möjligt, förbättra programmets predicering. Det har även gjorts ett antal tester för att se om

korrektionsfaktorn i Cone Tools är möjlig att förbättra.

För att förenkla ekvationerna för den brinnande arean har alla ekvationssteg gjorts linjära.

Alla tester har gjorts i Cone Tools, som har blivit omkodad med hjälp av Visual Basic. Den

nuvarande samt den förändrade modellen jämfördes med nio olika produkters

värmeutvecklings kurvor för att se vilken av dem som gav bäst predicering.

Resultatet blev väldigt intressant där den modifierade modellen gjorde bättre eller minst lika

bra prediceringar i de flesta fall jämfört med den nuvarande modellen. Vissa produkter, som

Plywood och FR ESP, predicerades väldigt bra av den modifierade modellen.

Korrektionsfaktorn mellan olika värmeflöden i Cone Tools är väldigt grov och kan därför vara

intressant att förbättra. Detta gjordes genom att använda samma kvadratiska uttryck som Cone

Tools 3.2.1 men räkna in värmeförlusterna hos ytan. Resultatet visade dock att den nuvarande

korrektionsfaktorn gav en bättre överensstämmelse mellan olika värmeflöden vid jämförelse

med olika produkter.

Nio test är ganska lite för att fastställa att den modifierade modellen ska funka för ett stort

antal produkter. Dessutom har ingen kategorisering, beroende på termiska egenskaper, av

produkterna gjorts. Fler test behövs därför göras för att den modifierade modellen ska kunna

accepteras. Detta är i alla fall en bra början och visar på att det är möjligt att förbättra

prediceringar av ett Room Corner Test.

IV

1 Introduction ........................................................................................................................ 1 1.1 Background ................................................................................................................. 1 1.2 Aim ............................................................................................................................. 2 1.3 Delimitations .............................................................................................................. 2 1.4 Method ........................................................................................................................ 2 1.5 Cone calorimeter ......................................................................................................... 3 Room Corner Test .................................................................................................................. 4 1.6 Cone Tools .................................................................................................................. 4

1.6.1 Flow chart over Cone Tools ............................................................................... 5 1.6.2 Translating data from the Cone Calorimeter test ................................................ 7 1.6.3 Burning area ....................................................................................................... 9

2 Result ................................................................................................................................ 11 2.1 Time to ignition translation ...................................................................................... 11

2.1.1 Deriving the equation ....................................................................................... 11 2.1.2 Testing the equation .......................................................................................... 13 2.1.3 Conclusions on translation of time to ignition .................................................. 17

2.2 Burning area RCT ..................................................................................................... 20 2.2.1 Theoretical approach ........................................................................................ 20 2.2.2 Derived equations ............................................................................................. 22 2.2.3 Confirming the authenticity .............................................................................. 24 2.2.4 Comparisons between calculated and measured HRR in the RCT .................. 30 2.2.5 Conclusions ...................................................................................................... 57

3 Discussions and conclusions ............................................................................................ 59 3.1 The correction factor ................................................................................................ 59 3.2 The burning area ....................................................................................................... 59 3.3 Source of error .......................................................................................................... 61 3.4 Further works ............................................................................................................ 62

4 Reference .......................................................................................................................... 63 Annex A ....................................................................................................................................... i Annex B ...................................................................................................................................viii Annex C ..................................................................................................................................... ix Annex D ................................................................................................................................... xix

V

Abbreviations

CC Cone Calorimeter

HRR Heat Release Rate

IRV Ignition Response Value

RCT Room Corner Test

SBI Single Burning Item

Roman letter

IIa Constant of 0.025 [s-1]

Va Constant of 0.1 [s-1]

A Burning area [m2]

c Specific heat capacity [J/kgK]

h Convective heat transfer coefficient [W/m2K]

k Thermal conductivity [W/mK]

q ′′& Corrected incident radiation [W/m2]

Coneq& ′′ Irradiance level, CC [W/m2]

Crq ′′& Incident radiation emitted from a surface [W/m2]

incq ′′& Incident radiation to a surface [W/m2]

totq ′′& Surface heat flux [W/m2]

25q& ′′ Incident heat flux of 25 000 [W/m2]

burnerQ Heat release from the burner [W]

oductQPr Heat release from the burning product [W]

totQ Total heat release from the RCT [W]

t Time of the RCT [s]

igt Time to ignition, RCT [s]

igConet Time to ignition, CC [s]

igStartt Start of the time to ignition, RCT [s]

spreadt Time when surface temperature reaches 335 oC [s]

xt When the critical surface temperature is reached [s]

10t Time in the RCT at 600 seconds [s]

VI

gT Gas temperature [K] or [oC]

igT Ignition temperature [K] or [oC]

iT Initial temperature [K] or [oC]

sT Surface temperature [K] or [oC]

Greek letters

α Constant (0.25) [-]

γ Proportionality factor [K/W2/5]

ε Surface emissivity [-]

correctionη Reduction coefficient [-]

η Dimension less time [-]

spreadη Dimension less time [-]

600η Dimension less time [-]

gasθ Gas temperature [K] or [oC]

sθ Surface temperature [K] or [oC]

ξ Correction factor [-]

Newξ New correction factor [-]

ρ Density [kg/m3]

σ Stefan-Boltzmann constant (5.67*10-8) [W/m2K4]

τ Dummy variable [-]

1

1 Introduction

1.1 Background It is very cost efficient to predict Room Corner Tests (RCT) and single burning item tests

(SBI). By using a complete heat release rate (HRR) curve and the time to ignition from a cone

calorimeter (CC) test the software program Cone Tools can do a quite good prediction.

However improvements can be made for an even better prediction which this report will

examine.

There are two important classing systems for wall and ceiling materials within the Euroclass

system. The first is the SBI which today is the main technique of testing the Euroclass A2 - D.

The second are the Room Corner Test (according to ISO 9705) which is used as a reference

scenario of the SBI. RCT have also been used as reference for the classification system of the

Japanese building code. Both tests are defined as large scale tests.

It is also common to use bench-scale tests as the Cone Calorimeter which is a small scale test

and can be used to understand and predict fire behaviour in materials.5

Room Corner Test according to ISO 9705 is a quite expensive test and it is therefore

interesting to find means of predicting material behaviour in this kind of test. Cone Tools

together with the time to ignition and the heat release rate curve derived from a Cone

Calorimeter test (according to ISO 5660) of a product can in some cases predict the scenario

of a Room Corner Test. Some products can however be hard to predict.

This can depend on a fire retardant surface, joints in the product, if the product cracks and /or

melts when exposed to heat.5

For products with normal combustion pattern, like wood, it will be much cheaper to test in a

Cone Calorimeter and thereafter use Cone Tools.5

Cone Tools is an old program and the equations are hard to follow and have been empirical

derived. This paper will therefore test if Cone Tools will make better predictions by adjusting

equations of the burning area and correction factors between the CC test and the RCT

according to new theories.

2

1.2 Aim The aim of the report is to improve and simplify the prediction of the Cone Tools program.

This will be done by testing theoretical derived equations. The report intends to give a clearer

description on how the equations in Cone Tools are used to predict a Room Corner Test.

1.3 Delimitations Both equations current used in Cone Tools and the newly derived uses semi-infinite

properties. It is then possible to express the thermal response by the thermal inertia (kρc).3

All test are assumed to be homogeneous i.e. there are no variations in the product, neither for

the Cone Calorimeter test nor the Room Corner Test.

This thesis will only examine the Room Corner Test part of Cone Tools. The report has

mainly investigated the heat release rate of the predicted RCT, the time to ignition and the

correction factor in Cone Tools.

There are different variables which by some extent have been derived empirical in Cone

Tools. This report has only investigated how the area changes and how the time to ignition is

translated from the Cone Calorimeter test. The different variables used to test the correction

factor are done by changing the emissivity, ignition temperature of the material and by using

different incident radiations for the Cone Calorimeter heater.

1.4 Method Literature and scientific papers where collected from SP and from recommendations of

Professor Ulf Wickström. The literature was thoroughly examined to achieve a deeper

understanding about theory relating thermal ignition. All calculations, except for those made

by Cone Tools, have been made in excel.

Cone Tools (version 3.2.1) have been used to calculate the predicted heat release rate curve

for a RCT.

Visual basic 6.0 (version 8176) has been used to change the code in Cone Tools. The ordinary

code structure has been thoroughly reviewed by comparing it to equations from the report of

Wickström and Göransson.3 The new code structure, with newly derived equations, has then

been tested against the current Cone Tools code. This is due to the complexity of the code

structure in Cone Tools which makes it important to see that nothing, which was not intended,

was changed when recoding the program.

3

All data for the test in this report have been derived from the SP database and results from

two different tests which was conducted by SP.7, 8, 9

Several discussions with Ulf Wickström and Maria Hjolman have been done during the

course of the work.

Nine products have been used to test the improved Cone Tools. All products which have been

used are from the Eurefic (European Reaction to Fire Classifications) program.

1.5 Cone calorimeter The Cone Calorimeter is used for small-scale tests, see figure

1. The aim with a Cone Calorimeter is to measure time to

ignition, smoke production, weight loss and how large the heat

release rate is of the burning specimen. The heat release rate is

derived by measuring the oxygen depletion from the test. This

is done by collecting the fumes from the specimen in a duct. In

the duct there is an instrument which is measuring the heat

release rate of the product. The method is used with a

specimen which is 100 mm by 100 mm. The incident radiation

from the heater can vary between 10 - 100 kW/m2. If the

specimen is easy to ignite a lower heat flux is more desirable

and some product may need quite high irradiance level to

ignite at all.5

Figure 1 arrangement of a Cone Calorimeter test.

4

Room Corner Test According to ISO 9705 a product will be tested

during 20 minutes, the first ten minutes the burner

will have an output of 100 kW and thereafter 300

kW, to see how it behaves in a fire. The burner is

placed in the corner of the room. The test room has

an internal length of 3.6 m, width of 2.4 m, height

of 2.4 m and opening with a width of 0.8 and a

height of 2.0 m (see figure 2). Test products shall

cover the ceiling and three walls. The room is

ventilated and over the door opening a duct is

placed to collect all the gases. By measuring the

oxygen depletion from the fumes it is possible to

receive the heat release rate of the test.3, 5

1.6 Cone Tools The software program Cone Tools is coded in Visual Basic by the Swedish National Testing

and Research Institute (SP). It is used to predict the behaviour of different materials in SBI or

Room Corner Tests based on Cone Calorimeter test data. To achieve a prediction the program

need the time to ignition (tig) and the complete heat release rate curve ( Coneq ′′& ) as a function of

time from a Cone Calorimeter test. The predications are often quite good. There are however

problems regarding the structure and the code of Cone Tools.

Equations which are used to predict a RCT heat release rate (HRR) have been derived from

Wickström Göranssons model.3, 4 These equations are also problematic due to their

appearance. It is hard to see how the equations are thought to work. The equations is

empirical derived and have therefore an uncertain theoretical yield.

Different materials such as product with fire retardant, melts when heated or cracks will be

difficult to predict with Cone Tools due to irregularities which make them much more

complex to describe. 3, 5

Figure 2: Setup of a Room Corner Test with transparent walls and ceilings.

5

There are three basic assumptions, according to Wickström and Göranssons, which need to be

made before using the program:

• The rate of growth of the burning area and the heat release rate are decoupled.

• The burning area growth rate is proportional to the ease of ignition. This can also be

defined as the inverse of the ignition time on a small scale.

• The heat release rate per unit area at each point in the SBI test is the same as in a small

scale (Cone Calorimeter test).3

Cone Tools are coded to calculate the burning area up to 32 m2. The program will end when

the test reaches 2000 kW. However progressions up to 1000 kW when flashover occurs is the

most interesting part when used to class products in the Euroclass system. 1

Heat release rate over 1000 kW can be interesting to see how strong the flashover will

become i.e. how steep the gradient of the curve would be.11

1.6.1 Flow chart over Cone Tools There are a number of variables which must be derived in Cone Tools. A flow chart has been

made to give a better overview of the functions in Cone Tools, see figure 3. This report will

investigate the correction factor of the time to ignition and the burning area growth. These

two steps will be described more thoroughly below.

First data from the Cone Calorimeter test has to be translated to the same type of incident

radiation used in Cone Tools which is 25 kW/m2. The equations used in Cone Tools for RCT

are according to Wickström and Göransson model.3 They use a six step description of the

burning area, see figure 4. The burning area depends on the heat flux from the burner and the

surface temperature on the product. It is also described in dimension less time.

Due to the first assumption the heat release rate and the burning area are decoupled. Both are

varying by time which gives a superposition, in an alternative form it can also be described as

an integral. This integral is called Duhamel’s superposition integral. The superposition will

finally give a prediction of the heat release rate curve of a RCT. A more comprehensive

description of each step to predict the heat release rate in a RCT can be seen in annex A.3

There are other models for example Östman and Tsantaridis model which makes good

predictions on flashover. The prediction is best for product were flashover occurs within ten

minutes. However the model of Wickström and Göransson has still an overall better

prediction.1

6

Figure 3: Flow chart over the Cone Tools function to predict the HRR of a RCT.

Cone Calorimeter

Time to ignition (CC) Heat release rate (CC)

Correction factor (Time to ignition)

Time to ignition (CC) (At 25 kW/m2)

Heat release rate (CC) (At 25 kW/m2)

Burning Area (t/tig) (Flashover)

Burning Area (t/tig) (No flashover)

Heat release rate (RCT) Duhamel’s superposition integral

∑=

−•∆=N

iiNioduct qAQ

1Pr

Room Corner Test

Surface temperature

>335oC <335 oC

Correction factor (Heat release rate)

7

1.6.2 Translating data from the Cone Calorimeter test If the Cone Calorimeter test was not conducted at an irradiance level of 25 kW/m2 ( 25q ′′& ),

which Cone Tools uses, the data needs to be translated. This is done bye using a correction

factor, see equation (2). Equation (1) and (3) are used to translate the time to ignition and the

heat release rate to the right irradiance level in Cone Tools:

ξ•= igConeig tt (1)

Where

2

25

′′′′

=q

qCone

&

&ξ (2)

Where tig is the time to ignition for the RCT, ξ is the correction factor and tigCone is the time to

ignition from the Cone Calorimeter test. The heat release rate of the Cone Calorimeter test is

defined as Coneq ′′& .

31

25

′′′′

•′′=′′Cone

Cone qq

qq&

&&& (3)

Where q ′′& is the corrected heat release rate for the Room Corner Test.5

Cone Tools change the time as well when the ignition time will start counting.

When calculating the start of ignition (tigStart) in the RCT, following formula is used

4

ξ•= igCone

igStart

tt (4)

For example a Cone Calorimeter test with a tigCone of 20 seconds and an incident heat flux of

35 kW/m2 would be translated to following values:

8

Using equation (1) and equation (2)

st ig 392,392535

202

≈=

•=

The time to ignition when calculating the area in the RCT is therefore 39 seconds.

Using equation (2) in equation (4)

st igStart 108.942535

202

≈=

•=

The ignition time i.e. when the burning area equation starts to increase, for the RCT starts

growing after ten seconds.

For irradiance levels of 50 kW/m2 or more the HRR curve for the RCT will start growing at

the same time or later compared to the ignition time of the Cone Calorimeter test. If the

incident heat flux is lower than 50 kW/ m2 in the Cone Calorimeter test, the HRR curve will

start earlier.

9

1.6.3 Burning area The burning area in Cone Tools is based on Wickström and Göranssons experimental derived

functions. The progress in the Room Corner Test can be explained in six different steps as

showed in figure 4.3

Figure 4: A simplification of the different steps which can occur in a Room Corner Test. The steps are thought to resemble different outcomes in a RCT. The first step starts when the material starts to ignite i.e. time to ignition. This is usually a

quite slow progress and will only affect the area behind the flames from the burner. The

maximum area for this function is when it reaches 2 m2 then it will either grow exponential

towards a flashover (step II) or stay within the area of the burner (step III). According to

Wickström and Göransson Step II will occur if the surface temperature reaches 335 degrees

Celsius. For more information regarding the surface temperature go to annex A. If flashover

does not occur the burning area will stay within the area affected by the burner (where the

heats flux from the burner pyrolisates the material) until the burner effect increases to 300 kW

after ten minutes. When the effect is increased the procedure will be the same as in the first

step but with a steeper angel because the room has been heated and will therefore ignite in a

10

greater rate. The function in step IV will reach a maximum area of 5 m2, if the surface

temperature is less than 335 oC. Four of the steps are described in Annex A.3

11

2 Result

2.1 Time to ignition translation The Cone Tools program is based on Cone Calorimeter tests using an irradiance level of 25

kW/m2. However it is common to use other heat flux level due to poor repeatability or that

the materials tested would not ignite. The Cone Tools have therefore a scaling equation to

translate tig from other heat fluxes to tig for an incident heat flux of 25 kW/m2 which the

program is based on. The equation is very crude and has been derived empirical and the

material assumed with semi finite properties, see equation (2).5 The equation neglects the

emitted radiation and convection loss which according to theory should render in errors.

Therefore functions which takes radiation and convection loss, for a surface, into account

should give better translation between heat fluxes. This hypothesis will be examined below.

2.1.1 Deriving the equation Using the general theoretical expression of the total heat flux should give a more accurate

translation between heat fluxes (see equation (5)). Because the temperature is to the fourth

power, tig needs to be solved numerical. However it has been found that it is possible to get

quite good similarity with equation (6) by reducing a portion of the incoming irradiance.6, 10

Equation (6) will be tested first to see if it can give a better translation than Cone Tools

current procedure. This is done by comparing the two different equations with real measured

values on different heat fluxes and materials. Below is a theoretical walkthrough to achieve a

translation equation to 25 kW/m2.

In general the total heat transferred by radiation and convection to a surface can be written as

( ) ( )sgsinctot TThTqq −+−′′=′′ 4σε && (5)

Where ε is the emissivity, Incq ′′& is the incident radiation to the surface, σ is the Stefan-

Boltzmann constant (5.67*10-8 W/ (m2K4)), Ts is the surface temperature, h is the heat transfer

coefficient and Tg is the gas temperature.

12

With a weighted constant n which is 0.6 for thick solids, the total heat flux can also be

described as.9

Crinctot qqq ′′−′′=′′ &&& ηε (6)

The reduced heat flux Crq ′′& can be described as follows

)(4iggigCr TThTq −−=′′ εσ& (7)

Tig is the ignition temperature of the material which is an important factor in the fire

progression. Equation (7) in equation (6) gives

( )( )iggiginctot TThTqq −−−′′=′′ 4εσηε && (8)

The equation is based on empirical observations but have a quite good yield. 10

By using equation (8) it should be possible to get more precise translation between different

heat fluxes from a theoretical point of view, compared to current basic equation (2) in Cone

Tools.

Time to ignition (tig) can be written as10

( ) 2

4

′′

−•=

tot

iigig q

TTckt

&

ρπ (9)

Putting equation (6) in equation (9) gives:

( ) 2

4

′′−′′

−•=

crinc

iigig qq

TTckt

&& ηερπ

(10)

Then the same material properties (kρc) between the different heat flux levels in equation (10)

are assumed. Then it is possible to express tig as

13

( ) 221

4

′′≈

′′−′′

−•=

totcrinc

iigig qqq

TTckt

&&& ηερπ

(11)

Equation (6) in equation (11) gives

2

1

′′−′′=

crincig qq

t&& ηε

(12)

Assuming a linear similarity between incident heat flux levels of the Cone Calorimeter gives:

2525

ig

qig

newnew

qig

ig t

ttt

incinc ′′′′

=→=&&

ξξ

(13)

ξnew is the correction value between the irradiance level of 25 kW/m2 and all other heat fluxes.

Equation (12) in equation (13) gives:

2

252

25

2

25

1

1

−′′′′

−′′′′

=

′′−′′′′−′′

=

′′−′′

′′−′′=

ηε

ηε

ηεηε

ηε

ηεξ

Cr

inc

Cr

Crinc

Cr

Cr

Crincnew

qqqq

qqqq

qq

qq

&

&

&

&

&&

&&

&&

&&

This gives 2

25

−′′′′

−′′′′

=ηε

ηεξ

Cr

inc

Crnew

qqqq

&

&

&

&

(14)

2.1.2 Testing the equation Table 1 show all values which have been use to test the response of the hypothesis. These

values have been derived in discussions with professor Wickström.11

14

Table 1 all values used to test the response of the hypothesis is shown. The incq ′′& values will be used in an interval between 15 - 75 kW/m2. The prefix column describes the variation of the emissivity and the ignition temperature when plotted in figure 5.

Prefix Values Property Prefix

25q ′′& 25 kW/m2K -

incq ′′& 15,…, 75 kW/m2K -

ε 0.8, 0.9, 1.0 - H8, H9, H1

η 0.6 - -

h 12 W/m2K -

Tig 350, 400, 450 0C 350, 400, 450

Tg 20 0C -

Figure 5 shows the results for different properties compared with the current value in Cone

Tools which is the red dotted line. The graphs y-axis has been logarithmic to give a better

overview. As can be seen in figure 5 all test values are quite close to each other. The ignition

temperature has the largest impact between the curves which suggest that all other variations

can be neglected. The two H-value (“H8 450” and “H1 350”) for the ignition temperature of

450 oC with emissivity of 0.8 and 350 oC with an emissivity of 1.0 will be used to test against

experimental values. This because they are the two most extreme values and if the

experimental data is between these two values, further studies will be made.

Relation between differen heat flux levels and a heat flux of 25 kW

0,01

0,1

1

10

0 10000 20000 30000 40000 50000 60000 70000 80000

Heat flux (kW/m2)

ξH8 350

H8 400

H8 450

H9 350

H9 400

H9 450

H1 350

H1 400

H1 450

Cone Tools

Figure 5: The relation between different results from the values in table. ξ is the correction value between the irradiance level of 25 kW/m2 and other heat fluxes (see equation (2) and equation (14)). 8, 9 and 1 represents the emissivity which is 0.8 for H8, 0.9 for H9 and 1.0 for H1. Number 350, 400 and 450 is the different ignition temperature in degree Celsius.

15

15 types of products have been used to be able to test if the new equations will give a better

translation than the current one. The products are described in table 2 with the time to ignition

(in seconds) for different incident radiations.

Table 2: Different products with ignition time (in seconds) of irradiance levels 25, 35, 50 and 75 kW/m2. If more than one time to ignition was available for certain irradiance level the mean value between those was taken.

Product/ Ignition time for 25 kW/m2

35 kW/m2

50 kW/m2

75 kW/m2

(t)

a Textile wall covering

157 51.0 26.0 - s

b Plywood HPL 20 mm

134 51.0 21.5 - s

c Polystyrene

38.0 22.0 14.0 - s

d Mineral Wool faced (CDK07509_EUREFIC7)

16.0 10.0 7.00 - s

e PUR rigid

208 42.0 24.0 - s

f Painted paper plasterboard

134 104 45.7 21.0 s

g Plastic faced Steel sheet

82.5 78.0 34.0 - s

h FR EPS

116 52.5 28.5 - s

i FR particle board (Type B1, EUREFIC6)

68.5 41.0 19.5 - s

j Mineral Wool faced (CDK7113_EUREFIC7)

10.5 7.00 4.50 - s

k FR particle board (CDK9307_EUREFIC9)

34.0 24.5 17.0 - s

l Plywood

- 103 44.0 21.0 s

m PMMA

- 60.0 30.0 - s

n Painted gypsum

- 260 131 31.7 s

o Plywood HPL 16 mm

- 55.0 28.3 12.3 s

In figure 6, 7 and 8 the experimental values for some different materials are compared with

the current equations in Cone Tools and the two extreme values derived from equation (14)

with n= 0.6, emissivity 0.8 and 1.0 along with ignition temperature of 350 oC and 450 oC.

The Y-axis is the “ξ” value which describes the relation between 25 kW/m2 and an irradiance

level of 35 kW/m2, in figure 6, and 50 kW/m2

, in figure 7. Figure 8 describes the relation

16

between 35 and 50 kW/m2. The experimental values have been derived from SP database and

two other tests, also conducted by SP.1, 3, 5 The blue dots in the graphs are the real weighted

values between the two different heat fluxes. If there was more than one tig for an incident

heat flux level the mean between the values were used.

The results show that the best prediction of the two tested equations is the current one in Cone

Tools 3.2.1. This contradicts the hypotheses which were made in this report. The Cone Tools

formula can probably be improved and this shows that it is more complex than at first

thought.

35 kW/m2 to 25 kW/m2

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

a b c d e f g h i j k

ξ

Experiment

Cone Tools

H8 450

H1 350

Figure 6: The result of the two chosen test value, the Cone Tools value and the different products. The straight lines are theoretical values and the dotted are measured values of different products. ξ is the correction factor for a Cone Calorimeter test with an irradiance level of 35 kW/m2 which are translated to an irradiance level of 25 kW7m2.

17


0

2

4

6

8

10

12

a b c d e f g h i j k

ξ

Experiment

Cone Tools

H8 450

H1 350



0

0,1

0,2

0,3

0,4

0,5

0,6

a b c l m n o

ξ

ExperimentCone ToolsH8 450H1 350


2.1.3 Conclusions on translation of time to ignition The Cone Tools 3.2.1 formula (see equation (2)) gives a quite good translation and is easy to

understand. The result suggests that equation (2) is predicting the translation best. The results

18

show that a lower η (less heat loss) gives better prediction. The prediction algorithm in Cone

Tools has no heat loss at all (η=0 i.e. not introduced at all) which also gives the best result.

The linearity between heat fluxes can be discussed; when plotting measured time to ignition

values for different heat fluxes and materials (see figure 9) there are some of the curves which

look more linear than quadratic. Products with low ignition times seem to have a more linear

expression. Meanwhile products with longer ignition times have a more quadratic look. The

number of measured points is few which make it hard to draw any conclusions and further test

could show a different relationship between different heat fluxes. If the relation between

different irradiance levels is expressed in a different way than quadratic, the hypotheses

would maybe give a more accurate translation than the current approach has showed.

According to Hansen and Hovde1 this depends on the type of product. Some product may

have a more linear appearance because of their thermal properties. For example thick products

can have the same characteristics as thin solids and therefore have a more linear appearance,

which make the quadratic correction flawed.1

Equation (14) has been derived through the use of numerical solution in theoretical manner10

and therefore could render in errors. It may be possible to get a better result with the more

theoretical right equation (5) by solving it numerically.

The measured ignition time from the Cone Calorimeter test is often very crude. It is done by

observing when the product starts to ignite which can be hard to see. This can result in huge

errors, especially for products with short times to ignition.1 A larger amount of values or

another means of obtaining the time to ignition in a more accurate way is therefore needed.

The tests have been conducted for Cone Calorimeter tests with a heat flux between 25 - 50

kW/m2 and it is uncertain if the incident heat fluxes outside this interval have the same yield.

19

Ignition time for different Irradiance levels and materials

0

50

100

150

200

250

25 30 35 40 45 50 55 60 65 70 75Heat flux level (kW/m2)

Tim

e to

ign

itio

n (s

)

a b c

d e f

g h i

j k l

m n o

Figure 9: Time to ignition of different products at irradiance level between 25 and 75 kw/m2.

20

2.2 Burning area RCT The burning area for RCT in Cone Tools 3.2.1 has, as said before, been derived empirical.

First step is to make the burning area more understandable in Cone Tools. Thereafter

rearrange the expression so that all equations are expressed in dimension less time (t/tig) which

from a theoretical point of view should be accurate.3 The new equations have been derived by

looking at different HRR curves for RCT and burning area curve in the report of Wickström

and Göransson.4

Due to the complexity of the burning area curves all equations will be linear. This is a

simplification of the reality and because it is an overall simplification of the system this

should be acceptable. So a linear curve can probably give a good prediction and are

furthermore easier to understand. This assumption is therefore made to simplify the system as

much as possible which is one of the aspirations with this report.

2.2.1 Theoretical approach All products are assumed to emit the same HRR per unit area which makes small and large

scale tests similar. This is however a simplification and should be consider cautiously. The

same three assumptions, according to Wickström and Göransson, are also assumed here (see

chapter 1.7). Then it is possible to describe the burning area as a function of dimension less

time (t/tig).3

To give a better approach of the work the same type of schematic picture will be followed as

shown in figure 4. See figure 10 for the new approach and equations.

All fire starts slowly; because the product needs to be heated first to reach the ignition

temperature (receive enough energy). Depending on how much energy received and the

material properties of the product the course will go faster or slower. So when the product

eventually ignites the process will go slow, as in equation (16).

An experiment was conducted by Kokkala where different heat fluxes, from a burner with 100

kW and 160 kW, in a room without a ceiling were measured. The result showed different

incident heat flux levels at different places on a wall. This is because the burner irradiance is

distributed differently along the affected surface. This suggests that the area will start to burn

earlier in some places than others. The tests were done without ceiling which can make it hard

to apply the results on a RCT.2 However, this shows that the burning area will grow

continuously if the incident heat flux is distributed equally over the affected area.

21

The burning area will continue to grow until it reaches the edge of the area which receives

energy i.e. were the irradiance level is not enough to make the product burn. Maximum area

should be different depending on material properties but is here simplified so that all products

have a maximum of 2 m2, which is the same assumed area behind the burner, according to

Wickström and Göransson.3 This assumption could be too high according to Kokkala.2 The

ceiling in the RCT should however give an increase of the burning area, how much is hard to

say.

If the burning product release enough energy to start pyrolis the area around it will continue to

grow and lead to an uncontrolled course i.e. it will lead to flashover (see equation (19)).

Flashover occurs when the total heat release rate reaches 1000 kW in the Room Corner Test.3

The surface temperature is the depending ratio for a product to lead to flashover. The critical

value for the surface temperature is assumed to be 335 oC and is derived in the same way as in

Cone Tools 3.2.1, see annex A for a more comprehensive review of the function of the surface

temperature. If the product has a surface temperature below 335 oC the burning area will

continue to increase until it reaches 2 m2 and will be the same until the effect of the burner is

increased after ten minutes.

When the effect of the burner is increased to 300 kW it will be the same lapse as when the

product started to burn, either it reaches a limited area or it will lead to flashover (if the

surface temperature reaches 335 oC). Because the room is already heated and the effect from

the burner is raised to 300 kW the burning area will grow much quicker compared to the

growth of the first equation step. Furthermore the product can receive enough energy to have

an ongoing process which would lead to flashover. The progression of the flashover curve

(see equation (19)) is assumed to be the same for both before and after the effect of the burner

is raised. Because the room has been heated the flashover curve should have a bigger gradient.

However it is possible that products which go to flashover after ten minutes have a larger

thermal inertia which can give an opposite effect on the progression of the curve.11

The maximum growth of the burning area, unless flashover occurs, is assumed to be 5 m2.

This area can, as said before, be too high.2

22

Figure 10: A schematic view of the new derived burning area equations. Each step is represented by an equation except the two constants which is 2 m2 before ten minutes of the RCT and 5 m2 after.

2.2.2 Derived equations Equations in this chapter have been derived from test data of products which have been tested

with both a Cone Calorimeter test and a HRR curve for a measured RCT of the same product.

The burning area curves from the report of Wickström and Göransson have been examined to

see the progression of the burning area. These curves have been derived ocular and are

therefore very uncertain.4

All tests have been conducted in Cone Tools which been reprogrammed to desired equations

by the use of Visual Basic. The changed variables are the burning area and the maximum

burning area.

All equations concerning burning area are expressed in terms of the parameter η which is

defined as the dimension less time.

23

ξη

•==

igConeig tt

tt

(15)

Time t is the RCT time and tig is time to ignition at an irradiance level of 25 kW/m2. tigCone and

the correction factor ξ is the same as in Cone Tools 3.2.1 due to better yield, as was concluded

before (see chapter 2.1.3).

The burning area will be described in three different forms, compared to Cone Tools 3.2.1

which have four. These equations apply to certain time intervals, areas and surface

temperatures. Table 3 describes each equation and in what context it applies.

For a more schematic picture over the equations see figure 10.

Table 3: The new derived equations for the modified model of Cone Tools. Step Equation Limit 1 ( )αηη −•= 0.3)(A

Where α is a constant of 0.25

0< t < 600 s

0 m2 < A(η) < 2 m2

(16)

2 ( ) 0.2)(18)( 600 +−−•= αηηηA Where

αξ

η −•

=igConet

600600

600 < t <1200 s

2 m2 < A(η) < 5 m2

(17) (18)

3 ( ) )()(15)( spreadspread AA ηαηηη +−−•= Where

αξ

η −•

=igCone

spreadSpread t

t

0 < t < 1200 s

Surface temperature > 335oC

(19) (20)

Equation (17) has an added area of 2 m2 because equation (16) will end at this area.

The surface temperature will reach 335 oC at time tspread. A(ηspread) is the burning area just

before the critical value of the surface temperature is reached. Cone Tools are using the same

area one second (time step) before equation (19) starts to apply.

The new equations (equation (16) and equation (17)) have a 25 % less gradient compared to

the same equations steps in Cone Tools. Equation (19) is harder to compare because of the

difference in the equation.

24

2.2.3 Confirming the authenticity Due to the complexity of changing existing program codes, which can give unexpected and

undesired results, in Cone Tools there is a need to investigate these errors further. Several

fictitious tests have been conducted to make sure that no errors have occurred. The test has

been done with both the new coding in Cone Tools and the current one to be able to see what

differs.

The visual basic code is shown in annex B. Only a fraction of the code structure is showed

due to copyright policy but should give a good view on how the code is thought to work. As

can be seen in the code there is four equations, because the former Cone Tools used four. But

two of those have been made identical which is the flashover curve before and after ten

minutes. This is done because if one of the equations is deleted some other functions in the

program would lose their ability.

The fictitious tests have been done in a excel spread sheet with different HRR made as hat

profiles, see figure 11. A test with several hat profiles, like a pyramid, has also been done.

Example of a hat profile

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200

Time (s)

HR

R (

kW/m

2 )

Figure 11: An example of a complete heat release rate curve of a fictitious Cone Calorimeter test. The varying variables in the analyse is the time to ignition, the heat release rate in the fictive

Cone Calorimeter test, different time span of the hat profile and different irradiance levels in

the Cone Calorimeter test.

25

To determine the legitimacy of the burning area equations, together with the same data

derived from Cone Tools 3.2.1, the result of the surface temperature, the burning area and the

RCT heat release rate have been investigated for each test. Two tests are shown below and the

rest are described in annex C.

Test I

The test has following input

Time to ignition (Cone calorimeter) 300 s

Incident heat flux (Cone calorimeter) 50 kW/m2

HRR (Cone calorimeter) 200 kW/m2

Flashover:

New equation 761 s

Cone Tools 721 s

The heat release rate for the Cone Calorimeter test is described in figure 12 which show a hat

profile i.e. a sudden and constant HRR. In this test the HRR is 200 kW/m2 during 600

seconds.

HRR Cone Calorimeter

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200

Time (s)

HR

R (

kW

/m2 )

Figure 12: A fictitious HRR curve of a Cone Calorimeter test. By using the heat release curve described in figure 12 and the time to ignition, calculated by

Cone Tools, a heat release curve for a RCT can be drawn (figure 13).

26

Heat release rate RCT

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200

Time (s)

HR

R (

kW)

New equation

Cone Tools

Figure 13: Predicted HRR for a RCT by Cone Tools with the current burning area equations and the new ones. Cone Tools reach flashover before the new equation which can be interesting to note. Figure 13 shows the predicted HRR curve of the fictitious Cone Calorimeter data from both

the new equations and the current Cone Tools system. As can be seen the current Cone Tools

curve is slightly steeper and reaches flashover a bit earlier than with the new equations. When

looking at the burning area, see figure 14, it becomes quite clear where the two curves differ.

When the surface temperature of 335 oC is reached for the two curves, at approximately 950

seconds, the current Cone Tools starts to get an exponential appearance. However the new

equations have a clearly linear appearance with a steeper gradient. This shows very clearly the

intended difference between the two equations and confirms the new code.

Burning area

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200

Time (s)

Bu

rnin

g a

rea

(m2 )

New equation

Cone Tools

Figure 14: The predicted burning area of the fictitious test. This shows very clearly the difference of the current equations and the new.

27

Both curves have quite similar surface temperature during the time (see figure 15). A peculiar

occurrence is when the RCT reach ten minutes and increases the output from the burner to

300 kW. At this time both curves make a dip which seems odd. The reason behind this event

is because the constant γ changes from 50 K/W2/5 to 35 K/W2/5.

The small difference between the two curves depends on the changed burning area.

Surface temperature

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200

Time (s)

Tem

per

atu

re (

oC

)

New equation

Cone Tools

Figure 15: The predicted surface temperature from both the new and the current program. Observe the sudden temperature drop of both curves at 600 seconds, when the burner effect is raised to 300 kW.

Test II

The test has following input

Time to ignition (Cone calorimeter) 100 s

Incident heat flux (Cone calorimeter) 25 kW/m2

HRR (Cone calorimeter) 300 kW/m2

Flashover:

New equation 80 s

Cone Tools 90 s

In this test the HRR from the Cone Calorimeter test is 300 kW/m2 and during 400 seconds.

The hat profile is described in figure 16.

28


0

100

200

300

400

500

600

0 200 400 600 800 1000 1200

Time (s)

HR

R (

kW/m

2 )

Figure 16: A fictitious HRR curve of a Cone Calorimeter test. From the HRR in the fictitious Cone Calorimeter test together with an ignition time of 100

seconds a HRR for a RCT is predicted as can be seen in figure 17.

Heat release rate (RCT)

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200

Time (s)

HR

R (

kW)

New equation

Cone Tools

Figure 17: Predicted HRR for a RCT by Cone Tools with the current burning area equations and the new. An interesting observation is that the new equations reach flashover before the Cone Tools 3.2.1 does. The heat release curves look almost the same except of the form. The Cone Tools 3.2.1 have a

more rounded character meanwhile the new curve looks more pointed. This is due to the

different area curves were Cone Tools use a polynomial equation when reaching the critical

value of the surface temperature while the new one only use linear curves which make it more

uneven. The difference compared with the first test is that the new equation reaches flashover

before the Cone Tools. This is because the equation for flashover before ten minutes is steeper

29

in the beginning than its counterpart. This can also be seen when looking at the burning area

(see figure 18).

Burning area

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200

Time (s)

Bu

rnin

g a

rea

(m2 )

New equation

Cone Tools

Figure 18: The predicted burning area of the fictitious test of the current and the new program code. The surface temperature can be seen in figure 19. Both curves are very similar and show only

small deviations between the old and the new. This depends on the effect of the changed

burning area equations.

Surface temperature

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200

Time (s)

Tem

per

atu

re (

oC

)

New equation

Cone Tools

Figure 19: The predicted surface temperature from both the new and the current program. No deviations, except when it reaches it maximum area, have been found in all tests which

have been conducted. Because the new curve is less gradient as the one in Cone Tools 3.2.1

when reaching a surface temperature of 335 oC after ten minutes it will progress under a

longer time. This can in some extreme cases make the program reach its maximum burning

30

area, which is 32 m2. However it has only been observed when the HRR for the RCT exceeds

1400 kW.

It is of course possible that errors have been missed. However it is quite unlikely, especially

when real test measurement, which is presented below, shows good results.

2.2.4 Comparisons between calculated and measured HRR in the RCT Nine different products with measured HRR curves from Room Corner Tests have been

compared with a predicted RCT HRR curve from both the Cone Tools 3.2.1 and the modified

version of Cone Tools. All Cone Calorimeter test data, for each product, available from the

SP Database have used as input to Cone Tools 3.2.1 and the new code to predict the HRR

curve. All Cone Calorimeter and Room Corner Test data have been derived from the Eurefic

tests.8 Each CC test and RCT is linked by a number in the SP database, for example “Eurefic

2” which is plywood of an certain quality. This number is showed in the title of each product

used from the database.

All steps in the schematic figure 10 are represented by the tested products. This shows that the

modified Cone Tools can predict all steps very well. Furthermore the assumed area growth

functions of time over time to ignition in the Cone Calorimeter in the modified Cone Tools

are much more comprehensible compared to the current functions. They contained time

variables of different dimensions. The new formula will make it easier to make new

improvements. All equations are now described in the same way, dimension less time (η), and

therefore easier to follow.

To avoid errors from the measurement of the time to ignition in the CC tests the time to

ignition has been determined when the HRR exceeds 50 kW/m2. Some of the figures can also

be found in annex D.

All time to flashover for the measured RCT and the predicted from Cone Tools 3.2.1 and the

modified Cone Tools, by the use of CC test data, is shown in table 4. Only products and CC

test data which have lead to flashover is registered in the table.

31

Table 4: Time to flashover of the tested products. The measured flashover time is compared with predicted time to flashover from the modified Cone Tools and Cone Tools 3.2.1, with the use of different CC test data. Test Product Flashover

RCT Flashover prediction Modified Cone Tools

Flashover prediction Cone Tools 3.2.1

RCT Plywood 150 s CC Plywood 1 at 25 kW/m2 142 s 165 s CC Plywood 2 at 25 kW/m2 152 s 176 s CC Plywood 3 at 35 kW/m2 102 s 125 s CC Plywood 4 at 50 kW/m2 175 s 207 s CC Plywood 5 at 50 kW/m2 117 s 139 s CC Plywood 6 at 50 kW/m2 161 s 192 s CC Plywood 7 at 50 kW/m2 121 144 s

RCT FR ESP 80.0 s CC FR ESP 1 at 25 kW/m2 88.0 s 102 s CC FR ESP 2 at 25 kW/m2 91.0 s 104 s CC FR ESP 3 at 50 kW/m2 68.0 s 77.0 s CC FR ESP 4 at 35 kW/m2 76.0 s 87.0 s CC FR ESP 5 at 35 kW/m2 76.0 s 87.0 s CC FR ESP 6 at 50 kW/m2 69.0 s 78.0 s CC FR ESP 7 at 35 kW/m2 213 s 257 s CC FR ESP 8 at 50 kW/m2 227 s 266 s CC FR ESP 9 at 50 kW/m2 218 s 258 s

RCT Painted paper plasterboard No flashover for this product RCT Melamine face No flashover for this product RCT Plastic faced steel sheet No flashover for this product RCT Textile wall covering 660 s CC Textile wall covering 1 at 35 kW/m2 632 s 633 s CC Textile wall covering 2 at 35 kW/m2 644 s 641 s CC Textile wall covering 3 at 50 kW/m2 628 s 629 s CC Textile wall covering 6 at 50 kW/m2 108 s 156 s

RCT PVC wall carpet 655 s CC PVC wall carpet 1 at 50 kW/m2 638 s 636 s CC PVC wall carpet 2 at 50 kW/m2 780 s 750 s CC PVC wall carpet 3 at 50 kW/m2 734 s 714 s CC PVC wall carpet 4 at 25 kW/m2 N/A 1100 s CC PVC wall carpet 6 at 35 kW/m2 106 s 148 s CC PVC wall carpet 7 at 35 kW/m2 115 s 156 s CC PVC wall carpet 8 at 50 kW/m2 117 s 634 s

RCT FR particle board b1 630 s CC FR particle board b1 1 at 50 kW/m2 627 s 626 s CC FR particle board b1 6 at 50 kW/m2 83.0 s 128 s

RCT Polyurethane foam 195 s CC Polyurethane foam 1 at 50 kW/m2 251 s 287 s CC Polyurethane foam 2 at 50 kW/m2 258 s 301 s CC Polyurethane foam 3 at 35 kW/m2 806 s 777 s

32

Plywood (Eurefic 2)

The plywood product which has been tested has a thickness of 12 mm and a density of 600

kg/m3. One measured HRR curves in the RCT and seven CC tests have been used when

evaluating the modified Cone Tools and comparing it with Cone Tools 3.2.1. The result can

bees seen in figure 20-26 were the green curves are the measured, the blue curves are the

modified Cone Tools and the red curves are Cone Tools 3.2.1. As can be seen in the figures

the modified Cone Tools have a very good fit compared to the HRR curves of the measured

RCT. In four of the Cone Calorimeter tests the modified Cone Tools have a better prediction

and in three Cone Tools 3.2.1 has a better prediction. All CC tests which have been used for

Plywood are shown in respectively figure were they are used. As can be seen all curves have

similar appearance which gives a strong suggestion that measurements of the CC tests are

quite accurate. The different irradiance levels correlate with each other which also give the

measured values a good yield.

Figure 20: With the use of the CC data (the small figure), Cone Tools 3.2.1 and the modified Cone Tools have predicted the two measured HRR curves of a RCT. The Modified model gives a very good prediction.

33

Figure 21: Predicting the HRR curve of Plywood with the use of a CC test data. The modified Cone Tools have a very good prediction.

Figure 22: Predicted HRR curve from Cone Tools 3.2.1 and the modified model. Cone Tools 3.2.1 have the best prediction with this CC test.

34

Figure 23: Predicting the HRR curve of Plywood with the use of a CC test data. The modified Cone Tools have a quite good prediction.

Figure 24: Predictions of a measured RCT with plywood by the use of Cone Tools 3.2.1 and the modified Cone Tools.

35

Figure 25: Predicting the HRR curve of a RCT with the use of Cone Tools 3.2.1 and the modified Cone Tools model. The modified model has a good prediction.

Figure 26: Predicting the HRR curve of a RCT with the use of Cone Tools 3.2.1 and the modified model.

FR ESP on Calcium Silicate board (Eurefic 11)

The fire retardant expandable polystyrene (ESP) is placed on a Calcium Silicate board and

have a thickness of 25 mm and a density of 34 kg/m3. One measured RCT and nine CC test

have been used for this product. The result is shown in Figure (27 - 32) and three of the CC

test results are shown in annex D.

36

All figures show a very good fit of the blue curves (the modified Cone Tools) compared to the

measured HRR curve. The Red curves (Cone Tools 3.2.1) have a quite good fit when looking

at time to flashover (1000 kW) were it do a better prediction in some cases. However, the red

curves have a quite bad fit overall.

The HRR from the different CC data have the same pattern except for the three tests in

appendix D. The reason behind this is uncertain but may depend on different measurement

procedures or the property of these products is somewhat different.

Figure 27: Predictions of the modified Cone Tools (blue) and Cone Tools 3.2.1(red).The modified model have predicted the HRR Curve from the measured test well.

37

Figure 28: The prediction of the modified Cone Tools is quite good with the use of the HRR of the CC test (the purple curve).

Figure 29: Predicting the measured HRR curve (green) with the use of Cone Tools 3.2.1(red) and the modified Cone Tools (blue).

38

Figure 30: Cone Tools 3.2.1 and the modified Cone Tools predictions of a FR ESP, placed on a Calcium Silicate board, product. The prediction shows very clearly the difference between the two models. The modified is considerable more gradient and therefore fits the measured HRR curve (green) better.

Figure 31: Predictions of the modified Cone Tools and Cone Tools 3.2.1). The modified Cone Tools have a very good fit compared to the measured HRR curve.

39

Figure 32: Predictions of the modified Cone Tools and Cone Tools 3.2.1. Cone Tools 3.2.1 have a very good prediction of the flashover and the modified have the same gradient as the measured HRR curve.

Painted paper plasterboard (Eurefic 1)

The painted paper plasterboard used in the tests has a thickness of 12 mm. One RCT test

measurement and nine CC tests have been used for this product.

Figure 33 shows the result of one of the tests. The rest of the tests have the same prediction

curves as in figure 33 and are shown in annex D. All tests gives a good fit compared to the

real RCT curve. Both the modified Cone Tools and Cone Tools 3.2.1 have almost the same

prediction curves.

As can be seen in the figures there are no particular CC test data which is deviating from the

others.

40

Figure 33: Predicting HRR for a measured RCT by using the modified Cone Tools and Cone Tools 3.2.1. Melamine face placed on a Calcium Silicate board (Eurefic 4)

The Melamine face has been placed on a Calcium Silicate board and has a thickness of 0.9

mm and a density of 1400 kg/m3. Four CC tests and one measured RCT have been used for

this product.

Figure 34 show the result with the use of one of the CC tests. The other tests have the same

prediction curves as in figure 34 and are shown in annex D

All tests, both Cone Tools 3.2.1 and the modified Cone Tools have a good fit. The modified

Cone Tools may have a slightly better fit in some cases.

The HRR curves of the different CC tests have a quite good resemblance with each other.

41

Figure 34: Predictions of the fire behaviour of a Melamine face, placed on Calcium Silicate board, with the use of Cone Tools 3.2.1 and the modified model, compared with a real measured RCT. The HRR of the CC data is shown in the small figure.

Plastic faced steel sheet on mineral wool (Eurefic 5)

The plastic faced steel sheet has been placed on mineral wool. The thickness is 0.9 mm and

the product has a density of 640 kg/m3. One real RCT and five CC tests have been used for

this product.

Figure 35 shows the result with the use of one of the CC test data. The other four CC tests

have predicted the measured HRR from the RCT the same as in figure 35 and are shown in

annex D.

All predictions independent of CC test have a good fit.

42

Figure 35: The modified Cone Tools and Cone Tools 3.2.1 predictions compared with a measured RCT.

Textile wall covering on plasterboard (Eurefic 3)

The textile wall covering has been placed on plasterboard and has a thickness of 1 mm. Eight

CC tests and one measured RCT has been used for this product.

The predictions from the modified Cone Tools and Cone Tools 3.2.1, along with the real

measured RCT is shown in figure 36 - 43.

The HRR curves of the different CC tests are shown in the same figure as it is used.

There are three CC tests (Figure 36 - 38) which have predicted the real RCT curve quite good

by using both the modified model and Cone Tools 3.2.1. The Modified Cone Tools has a

declining curve in figure 36 - 38 and depends on its linearly appearance which is less extreme

compared to Cone Tools 3.2.1, which have polynomial appearance when the surface

temperature reaches 335 oC.

There are four CC test data which give a surface temperature below 335 oC for both the

modified Cone Tools and Cone Tools 3.2.1. This makes the curves decline and avoiding

going to flashover.

The CC test in figure 41 has lead to flashover before ten minutes for both the prediction

models. This is the only CC test which gives this value and it probably depends on that the

surface temperature barely reached 335 oC.

All CC tests have the same form which suggests that all tests have been conducted by

products with the similar properties.

43

The reason behind the different prediction result, depending on which CC data is used, could

be difference in material properties or that both Cone Tools 3.2.1 and the modified is within

the margins were the surface temperature barely reaches 335 oC or counter wise i.e. the

criteria for the prediction to lead to flashover is very close in all the cases..

Figure 36: Predictions of HRR from a textile wall covering RCT by the modified Cone Tools (blue) and Cone Tools 3.2.1 (Red).

Figure 37: Predicting a measured HRR curve by using CC data and the two predicting models. Note the decreasing gradient of the both model.

44

Figure 38: Predicting a measured HRR curve for a textile wall covering product, placed on plasterboard, with the use of Cone Tools 3.2.1 and the modified Cone Tools. Both predictions have a quite good fit to the measured HRR curve.

Figure 39: Predicting a measured HRR curve for a textile wall covering product, placed on plasterboard, with the use of Cone Tools 3.2.1 and the modified Cone Tools. None of the predictions managed to reach the surface temperature of 335 oC.

45

Figure 40: Predicting a measured HRR curve for a textile wall covering product, placed on plasterboard, with the use of Cone Tools 3.2.1 and the modified Cone Tools.

Figure 41: Predicting a measured HRR curve for a textile wall covering product with the use of Cone Tools 3.2.1 and the modified Cone Tools. Both predictions reached 335 oC before ten minutes.

46



47

PVC wall carpet on plasterboard (Eurefic 10)

The Polyvinyl chloride (PVC) wall carpet is placed on plasterboard and has a thickness of 0.9

mm. Eight CC tests and on real RCT have been used for this product.

The result of the prediction along with the real RCT is shown in figure 44 - 51.

The result shows several deviations from the real RCT. It is only two of Cone Tools 3.2.1

curves (figure 44 and figure 51) and one of the modified Cone Tools (figure 44) which gives a

good prediction.

All other tests predicts either a too early or to late flashover progression or no flashover at all.

The HRR curves of the CC tests in the figures may give some answers.

Two of CC tests (figure 47 and figure 48) have a quite different appearance (in the form of a

short spike) compared to all other HRR curves which have a longer declining progression.

This can for example depend on difference when the test was conducted or a different density

of the product compared to the others.

PVC melts when it burns which makes it a complex material and hard to predict. This could

also explain the big variations in the predictions.

Figure 44: Predictions of a RCT by the use of the modified Cone Tools (blue) and Cone Tools 3.2.1 (red).

48

Figure 45: Predictions of a RCT by the use of the modified Cone Tools and Cone Tools 3.2.1.

Figure 46: Predictions of a measured HRR curve for a PVC wall carpet product, placed on plasterboard, by the use of Cone Tools 3.2.1 and the modified Cone Tools.

49

Figure 47: Predictions of a measured HRR curve for a PVC wall carpet product, placed on plasterboard, by using of Cone Tools 3.2.1 and the modified Cone Tools.


50



51


FR particle board b1 (Eurefic 6)

The tested fire retardant particle board has a thickness of 16 mm and a density of 630 kg/m3.

One real RCT and six CC tests have been used for this product.

The result of the predictions is shown in figure 52 - 57. The results are similar to the one of

the Textile wall covering product were two predictions reaches flashover before ten minutes

and some did not reach flashover at all. Only one CC test did predict the real measured one.

Both the modified Cone Tools and Cone Tools 3.2.1 (in figure 52) had almost the same

prediction curve. However, the real RCT curve seems to be quite irregular after 1000 kW

which can depend on the fire retardant chemical.

The HRR curves of the CC tests show no irregularities which should suggest that all the tests

have the same properties.

The reason behind the different prediction results is uncertain and can depend on that the

criteria for flashover is within the interval of the different CC tests.

52

Figure 52: Predictions of a FR particle board, tested in a RCT, by the modified Cone Tools and Cone Tools 3.2.1.

Figure 53: Predictions of a measured HRR curve for a FR Particle board product by the use of Cone Tools 3.2.1 and the modified Cone Tools.

53



54


Figure 57: Predictions of a measured HRR curve for a FR Particle board product by the use of Cone Tools 3.2.1 and the modified Cone Tools. Plastic faced steel sheet on polyurethane foam (Eurefic 9)

The product is 1 mm thick and has a density of 160 kg/m3. Three CC tests and one RCT have

been used.

55

The result is shown in figure 58 – 60. The modified Cone Tools have a better prediction in

figure 58 and figure 59 compared to Cone Tools 3.2.1 and the gradient of the curves is about

the same for the two prediction models.

Both of the predictions models reached flashover after ten minutes in figure 60. Because

Cone Tools 3.2.1 is more gradient than the modified model after ten minutes it can sometimes

decline. This is because the HRR from the CC data has ended.

Figure 58: Predicting a measured RCT of plastic faced steel sheet on polyurethane foam with the use of Cone Tools 3.2.1 and the modified Cone Tools.

56



57

2.2.5 Conclusions The new equations for the area growth have

1. Been considerably simplified compared to the ones used in Cone Tools 3.2.1

2. Been defined in dimension less time

3. Improved the overall accuracy of the prediction of the HRR in a RCT

4. Been verified by the use of fictitious hat profiles

This will ease the continuously works and further improvements of the prediction

calculations.

No unpredicted changes in the Cone Tools code structure have been observed which makes

the result assured.

The test against measured values shows that a simplified linear equation system can predict a

RCT. The test also shows that the new equations make better predictions than the Cone Tools

3.2.1. In a couple of cases, as in plywood and FR EPS, the modified Cone Tools show very

good predictions. The new equations have predicted all nine products better or as good as the

current one which makes it very interesting. Even if further test needs to be done before it can

be confirmed that the new equations will make better predictions overall it is a very

interesting start.

An interesting observation which was done during the test was that the flashover curve for the

modified model was steeper than the current model before ten minutes and after ten minutes

the ordinary went to flashover before the modified. This is one of the reason why the modified

did much better predictions. It suggests that the flashover curve should be steeper before ten

minutes compared to after. This seems odd because the room is heated and the burner effect is

raised it should give a more rapid fire growth. The answer to this is uncertain but it could

depend on the thermal properties of products with this kind of course.

The modified Cone Tools are adapted against the HRR curve of measured Room Corner Test

data and it will therefore have some deviating setup as to the actual test. This is because the

HRR is derived in the smoke duct which means that the smoke have to travel a certain

distance before it is registered. This can be seen in the “Test data” curve in all real RCT in

this report were it takes a while before the HRR curve starts to incline. Because of this it

could be argued that the actually events of the HRR curve occurs some seconds before,

depending on the speed of the smoke and the ventilation, compared to the measured one. This

58

is probably a quite small flaw but should be considered if further improvements are to be

done.

One problem which has arisen during the course of the work is between which interval it is

interesting to see the heat release rate curve for the RCT. The Euroclass system is only

interested of the HRR between 0 and 1000 kW. The time to flashover is regarded as one of the

most important factor in a Room Corner Test.1 It can be of interest to predict the HRR curve

even further too see how the flashover progresses. This is hard to say and in this report the

HRR curve have been examined mainly up to 1000 kW.

Sometimes the modified Cone Tools reaches the burning area limit, of 32 m2, which makes

the HRR curve plain out. Because the new equations are linearly expressed compared to Cone

Tools 3.2.1 quadratic equation, when going towards flashover, it can sometimes make the

HRR curve to plain out earlier compared to Cone Tools 3.2.1. This have only been observed

at higher HRR levels (1400 kW and upwards) but is still a reason of concern.

Tests to change both maximum area and surface temperature have been done but the other

values in the equations have been kept the same, because changes might result in various

complex errors in Cone Tools 3.2.1.

When the heat release starts to exceeds 1400 kW some of the prediction starts to become

unreasonable. This can be seen in the textile wall covering product, in figure 36 - 38, were the

“Modified” curves starts to decrease. This is due to its linearity with time of the area. In the

Cone Tools 3.2.1 the area increases according to a second degree relation with time. Cone

Tools 3.2.1 curve is also slowing down but after a longer time span and a at a higher heat

release rate.

Products as FR EPS, FR particle board and plastics like the PVC wall carpet have, as been

said before, a different behaviour in fire tests. These tests should be considered carefully due

to the complexity of the products. Especially the PVC wall carpet has been hard to predict.

59

3 Discussions and conclusions

3.1 The correction factor Because irradiance levels in CC tests can differ from 10 - 100 kW/m2 it is important to have a

program which can use all of these tests. The correction factor for the time to ignition used in

Cone Tools 3.2.1 does not take heat loss into consideration which should render in errors,

according to a theoretical approach (see equation (5) and (6)).

When testing the correction factor for the Cone Tools 3.2.1 and the newly derived from

equation (6) the Cone Tools 3.2.1 had the best predictions. The test was conducted from 15

products with irradiance levels of 25, 35 and 50 kW/m2. This was an unexpected result and

the explanation behind it is uncertain. From a theoretical point of view the derived equation

(6) should have been more accurate. There is however some factors which can affect this.

Material properties are an interesting factor when looking at fire behaviour. According to

Hansen and Hovde the material properties of a product can inflict the curve of the correlation

between different heat fluxes.1 It could therefore be interesting to investigate the correction

factor by looking at different material with the same thermally properties.

The equation used in the test was also a simplification of the reality. This can also be a source

of error and by using equation (5) could give a better result than the current used.

The quadratic corrections factor without regard to energy losses works well. It has of course

some deficiencies but compared to the overall simplification regarding the prediction of a

Room Corner Test it is a small error.

3.2 The burning area Cone Tools is a very good and simple program to predict behaviour in medium-scale tests.

This makes the program very practical with a wide range of users.

The program and the tools needed to use the program (time to ignition and the heat release

curve from a Cone Calorimeter test) are easy to understand. It is however more complex to

understand all equations which is needed to make the model work.

The result of the new equations for the burning area has been successful. It is more simplified

than the burning area equations in the current Cone Tools and has so far predicted equally- or

better results in most cases than the current. The nine tests show that the modified model can

give a better prediction.

60

This report has given a good view into the function of the burning area and how it works.

More aspects than the burning area are however governing the prediction of a Room Corner

Test. The surface temperature has a big part in the response of the progression and governs

when the equation should lead to flashover. This could probably be improved more and it may

also be possible that the Cone Tools would improve its predictions if it would be able to

change the critical value of the surface temperature depending on product.

Hansen and Hovde have modified the model of Wickström and Göransson by having three

different IRV (ignition response value) values depending on products.1 A single IRV value

(which was assumed to be 1250 tign3) was, according to Hansen and Hovde, a too big

assumption. The modified model was optimized by using statistical factorial design. The

result from their test showed an improvement of Wickström and Göranssons model.1 The

modified model along with the new derived burning equations could give an even better

prediction of Room Corner Tests.

The maximum area which is 2 m2 the first ten minutes of a RCT and then 5 m2, unless

flashover occurs, is also questionable. As was concluded before, the different products would

probably have different maximum area depending on the products (kρc) and furthermore the

area can have been exaggerated, according to Kokkala.2 This is also a part which can be

improved, as with the surface temperature, which would lead to better predictions in Cone

Tools, under the assumption that maximum area for each product could be changed. This

could maybe be done by looking at the thermal inertia of a product.

To be able to adjust both surface temperature and the maximum area it requires a deeper

understanding on what these factors depend on and a simple way of deriving them for each

product in an accurate manner.

Questions have arisen during the course of the work about which interval the predicted heat

release rate should be calculated within in Cone Tools. The Cone Tools program has been

created to predict the Euroclass of a product and therefore mainly interest in fire behaviour

within the HRR of 0 to 1000 kW. HRR below 1000 kW are therefore more prioritised even if

it in some cases can be interesting to see what happens after 1000 kW.

The use of a linear flashover curve in the modified model can be problematic compared with

real life fire behaviour. When a fire starts going towards flashover it accelerates and this

effect is hard to represent with a linear curve. But as most of the Cone Tools parts have been

more or less simplified a linear curve can work. However further improvements may be done

61

by the use of other functions, like polynomial or other quadratic equations, for the flashover

curve.

It is unsure if all types of product are represented (thermal resistant products, low/high density

product and so on) in the test and it is therefore a need for a more categorised approach. This

report has showed that it is still possible to improve the predictions of a Room Corner Test.

The burning area of the Cone Tools program is still a region which can be improved. By

testing more complex equation systems and even putting in an extra equation step, which take

the movement over the ceiling and downwards into account, could lead to very interesting

improvements.

3.3 Source of error All data have been retested and redone, some even several times. Tests have also been

performed to rectify the recoded Cone Tools code. This was done by testing simple fictitious

hat profiles and comparing them to the Cone Tools 3.2.1. The tests did not give any indication

of errors in the code and should therefore be seen as right.

There have been a huge set of data processed during the course of the work. Because of the

huge amount errors may occur. It is however quite unlikely that any huge error may have

occurred because of all the retests.

Cone Tools do not just predict the heat release rate for a RCT it has several more application

such as smoke spread and SBI prediction. This makes the code quite complex and moreover

there have been different programmers which have done the coding. This makes the code

really hard to understand and it is therefore possible that some unintended changes will occur

if you change something in the code. The test may not cover every aspect of the code and

even if it is unlikely errors may have occurred when Cone Tools were recoded.

None of the tested products have been categorised. This means that some products type may

be overrepresented and some not included at all.

62

3.4 Further works

The work of the burning area has still some missing pieces. A more comprehensive database

of Room Corner Tests (according to ISO 9705) and Cone Calorimeter data (according to ISO

5660) should be collected. This could confirm the results from this report and moreover give

opportunity to improve and test other models.

The maximum area behind the burner can be interesting to examine. If some similarities

between different products thermal inertia and the burning area behind the burner could be

found this could improve the prediction of Cone Tools.

An interesting research area is to see if products which went to flashover after ten minutes

have a less steep, or as steep or steeper curve compared to products which went to flashover

before ten minutes. The thermal inertia and the already heated room should have a quite large

effect on this aspect.

The Correction factor is still possible to improve. This can be done by looking deeper on the

material properties of products and by testing the, from a theoretical point of view, right

equation.

63

4 Reference

Literature [1] Hansen A. S. & Hovde P. R. (2002). Prediction of time to flashover in the ISO

9705 Room Corner Test based on Cone Calorimeter test results. Submitted to Fire and Materials, 2001. Revised 2002.

[2] Kokkala, K. (1993). Characteristics of a flame in an open corner of walls.

Proceedings from Interflame ´93: Oxford, England, ISBN 0 9516320 35. [3] Wickström, U. & Göransson, U. (1992). Prediction of Heat Release Rates of

Surface Materials in Large-scale Fire Test Based on Cone Calorimeter Results. Borås: SP Swedish National Testing and Research Institute. SP report 1992:22, ISBN 91-7848-340-9.

[4] Wickström, U. & Göransson, U. (1987). Full-scale/Bench-scale Correlations of

Wall and Ceiling Linings. Borås: SP Swedish National Testing and Research Institute. SP report 1988:11, ISBN 91-7848-097-3.

[5] Van Hees, P., Hertzberg, T. & Hansen, A. S. (2002). Development of a

Screening Method for the SBI and Room Corner using the Cone Calorimeter, Nordtest project 1479-00. Borås: SP Swedish National Testing and Research Institute. SP report 2002:11, ISBN 91-7848-904-0.

[6] Babrauskas, V. (2003). Ignition Handbook. Fire Science Publisher/ Society of

Fire Protections Engineers, Issaquah WA. Test data [7] Brandteknik, (1990). Konkalorimeterresultat från SP:s forsook I Eurefic project

#4. Borås: SP Swedish National Testing and Research Institute. [8] Hjolman, M. (2005). SP Fire Data Base. SP

Retrieved 2011-03-20, from http://www.sp.se/sv/index/services/firedb/Sidor/firedb.aspx

[9] SP Swedish National Testing and Research Institute (1995). Reduced data,

spread sheets and graphs, on wall insulation products, w1-w5 from tests according to ISO 9705 ISO 5660-1 DIN 53436 (modified). Borås: SP Swedish National Testing and Research Institute.

Notes [10] Wickström, Ulf. Unpublished lecture notes at Luleå University of Technology.

64

Private Conversation [11] Wickström, Ulf. The department of Fire Technology at SP Technical Research

Institute of Sweden and Luleå University of Technology.

i

Annex A Using Cone Tools

Cone Tools has a quite simple architectural design (see figure 61). Before any calculations

can be made the program need a heat release rate curve (time dependent) this is done by open

the file with the desired product. Cone Tools can interpret data by defining how the

measurement are structured in the file i.e. how colons are separated by “,” or some other

character. These interpretations are called “types”. There are already six different types when

installing Cone Tools but it is possible to make new or change types by clicking on the

“types” icon.

Figure 61: The Cone Tools software program. When the desired file is open Cone Tools will show the heat release rate curve for the Cone

Calorimeter test (see figure 62). Now it is time to start the calculation by pressing the

calculation icon. Calculation is done by defining the incident radiation and the time to ignition

(it is also possible to start the time to ignition when the incident heat flux reaches 50 kW/m2)

from the Cone Calorimeter test. It is also possible to have a more sensitivity analyze of the

time to ignition. Depending on the reliability of the Cone Calorimeter test data it can be

interesting to have an interval instead of a single value.

ii

Figure 62: Doing calculations in the Cone Tools program. The heat release rate for the RCT will be shown along with different results for RCT or SBI

(see figure 63). The calculation is possible to save which is saved in a excel document with all

the calculated values.5

Figure 63: Result of a predicted RCT in the Cone Tools program.

iii

Burning area

Below is the different burning area equations described.

Step I (When the product starts to ignite)

According to Wickström and Göransson

10.4)( −

•=

igtt

tA (21)

Step II (If the fire spreads (temperature reaches 335 oC) between 0 to 600 s)

( )

−•+•=

ig

xII t

ttaAtA

2

0 1)( (22)

Where A0 is the area burning behind the flames, aII is a constant of 0.0025 s-1 and tx is the

same inclination as equation (21).

.

Step IV (The burner effect is increased to 300 kW)

( )10

242)( tt

ttA

ig

−•+= (23)

The fourth step will start after ten minutes and hence t10 is equal to 600 s. Because the area

burning already are 2 m2 (which is assumed as a maximum in step I) when the irradiance level

is increased it has to be included in the equation.

Step V (If the fire spreads (temperature reaches 335 oC) between 600 to 1200 s)

( )

−•+•=

ig

xV t

ttaAtA

2

1 1)( (24)

A1 is the area behind the burner which is 5 m2 and av is a constant of 0.1 s-1.

iv

Heat release rate for the predicted RCT

The total heat release rate (Qtot) consist of the heat release from the burner (Qburner), which is

known, and the heat release from the burning product (Qproduct).

oductburnertot QQQ Pr+= (25)

Heat release from the product is dependent on the burning area which has been described

earlier. Due to constant change in the burning area Qproduct can only be obtained by super

positioning. The one used is called Duhamel’s superposition integral. This gives following

expression

∑=

−•∆=N

iiNioduct qAQ

1Pr (26)

With the Duhamel´s superposition integral the equation can be written as

( ) τττ dtqAQt

oduct ∫ −′=0

Pr )( (27)

Where τ is a dummy variable. However it is more preferable to use equation (26) when

calculating.

Surface temperature

The surface temperature is an important factor when predicting a RCT. As said before it is

critical for an uncontrolled progression (with the critical value of 335 degree Celsius) i.e. if

the sequence leads to flashover or not.3

The temperature of a surface depends on the temperature of combustible gasses passing over

it and also the thermal properties of the surface. The thermal properties of the surface are

assumed to solitary depend on the ignition time from the Cone Calorimeter test.

The gas temperature is assumed to depend on the sum (Qtot) of the heat release rate from the

burner and the burning area of the tested product.3

v

5/2totgas Q•= γθ (28)

Where γ is an empirical derived constant which, according to Wickström and Göransson, are

chosen to be 50 K/W2/5 for a burner rate of 100 kW and 35 K/W2/5 when the burner rate is 300

kW in the RCT. Equation (28) can be compared to McCaffrey’s plume equation for free

flames which also described the Qtot with a power of 2/5. Because of the ceiling in the RCT a

higher value could be considered.3

The response function η are, according to Wickström and Göransson, assumed to use

thermally thick properties and can therefore be expressed in thermal inertia (kρc). The thermal

inertia is proportional to the time to ignition from a Cone Calorimeter test, according to

Wickström and Göransson.3

Another expression has also been made for the thermal inertia. Instead of kρc the response

function will be described as IRV (ignition response value). IRV is also assumed to be

proportional to the ignition time of a Cone Calorimeter test with an irradiance level of 25

kW/m2. The inertia of wood has been assumed to represent a standard value of IRV which is.

IRV = 1250* tig (29)

IRV can be obtained from other irradiance levels by using the same scaling as is shown in

equation (29).

The response function expressed for semi-infinite bodies and which are exposed to a constant

gas temperature (which have been derived from Holman and Carslaw) can, according to

Wickström and Göransson, be described as

−==

ττθθ

η terfc

t

gas

sresponse exp1 (30)

Where

2hIRV

=τ (31)

vi

The heat transfer convection coefficient, h, is assumed to be 50 W/m2K when doing numerical

calculations. This has been deemed reasonable, according to Wickström and Göransson, for a

point near the burner plume. With a derived time dependent gas temperature it is possible to

obtain the surface temperature by superposition which follows the same procedure as equation

(26).3

( ) ∑=

−•=N

i

iNigs t

1

ηθθ (32)

Duhamel’s principle

The Duhamel’s superposition integral is a linear causality system. It can be resemble by

having a linear expression and putting it in a “box” which is concealed (see figure 64). On the

other side of the box the linear expression has been changed but the expression is the same.

This is the basic principle of superposition.

Figure 64: Basic principle of superposition.

The Duhamel’s superposition integral is a technique to solve linear inhomogeneous equations.

Two different variables vary by time, in this case the burning area and the heat release rate, to

derive the energy release. When the area is burning it will spread depending on material

properties and geometric variations. The area will burn during different time spans. The heat

release will also vary during the course. Figure 65 is an example on how the Duhamel’s

superposition integral is thought to work. The principle of this method is to sum all responses

of each time increment.

)( xt −ϑ

)( xt −ψ

vii

Figure 65: An example of the principle of the Duhamel’s superposition integral.

viii

Annex B Below is the code structure of the burning area in the modified Cone Tools. The code is

incomplete due to copyright policy. As can se in the code there is four definitions of the

equation meanwhile the modified model only use three (because of only one flashover

equation). This depends on the complexity to erase the fourth which would give problems

through the whole code structure. So instead of deleting it the flashover equation is defined

the same in two places instead.

Private Sub Areafun(Limit As Integer, i As Integer, Area() As Double, Limitmod As Double, _ Limitvalue As Double, Tigncc As Double, Alfa As Double) Dim Tign14 As Integer Dim Slope As Double, Rtign14 As Double Rtign14 = Tigncc / 4 Tign14 = CInt(Rtign14) Rtign14 = CDbl(Tign14) Slope = 3 / Tigncc If (i <= Tign14) Then Area(i) = 0 Else If (Limit = 0 And i <= 600) Then Area(i) = Slope * (i - Rtign14) ' detta är 3*(t/(tig*4)) If (Area(i) > 2) Then Area(i) = 2 Else If (Limit >= 1 And i <= 600) Then Area(i) = Area(Limit) + ((i / Tigncc) - (Limit / Tigncc)) * 15 If (Area(i) > 32) Then Area(i) = 32 Else If (Limit = 0) Then Area(i) = 2 + (i - 600) * Slope * 6 If (Area(i) > 5) Then Area(i) = 5 Else Area(i) = Area(Limit) + ((i / Tigncc) - (Limit / Tigncc)) * 15 If (Area(i) > 32) Then Area(i) = 32 End If End If End If End If End Sub

ix

Annex C Below is all other test which has been done to confirm the authenticity of the modified model.

This has been done by comparing it to Cone Tools 3.2.1. Every test has been examined by

looking at the HRR, Burning area and the surface temperature curve.

The test data from the Cone Calorimeter are fictitious.

Test III tig = 100 s Incident heat flux (Cone Calorimeter) = 50 kW/m2

HRR (Cone Calorimeter) = 300 kW/m2 Flashover: New equation 355 s Cone Tools 361 s


0

100

200

300

400

500

600

0 200 400 600 800 1000 1200

Time (s)

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Figure 66: The heat release rate curve of the fictitious Cone Calorimeter test.


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Figure 67: Prediction of a RCT from the fictitious Cone Calorimeter test. Both the new and the current model are presented.

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Burning area

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Cone Tools

Figure 68: The burning area for the two different models.

Surface temperature

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Cone Tools

Figure 69: The surface temperature of the two different models. Test IV tig = 100 s Incident heat flux (Cone Calorimeter) = 75 kW/m2


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Cone Tools


Burning area

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Cone Tools


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Surface temperature

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Tem

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New equation

Cone Tools

Figure 73: The surface temperature of the two different models. Test V tig = 600 s Incident heat flux (Cone Calorimeter) = 50 kW/m2



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New equation

Cone Tools


Burning area

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Cone Tools


Surface temperature

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Cone Tools

Figure 77: The surface temperature of the two different models.

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Test VI tig = 300 s Incident heat flux (Cone Calorimeter) = 50 kW/m2



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Burning area

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Cone Tools


Surface temperature

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Cone Tools

Figure 81: The surface temperature of the two different models. Test VII tig = 700 s Incident heat flux (Cone Calorimeter) = 50 kW/m2


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Cone Tools


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Cone Tools


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Surface temperature

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New equation

Cone Tools

Figure 85: The surface temperature of the two different models. Test VIII tig = 50 s Incident heat flux (Cone Calorimeter) = 50 kW/m2

HRR (Cone Calorimeter) = 400 kW/m2 (max) Flashover: New equation 313 s Cone Tools 326 s


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Heat release rate

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Cone Tools


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Figure 89: The surface temperature of the two different models.

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Annex D Below are all the rest of the CC data for the different products shown. FR ESP Three of the CC data have a different HRR curve compared to the others of the same product

(see figure 90– 92).

Because there are three with the same sort of curve it is unlikely that there are errors in the

measurement. The curves are of different heat fluxes which also show that it is probably no

major flaws in the measurements. The reason behind this can depend on different thermal

properties of these products compared to the others such as another type of fire retardant,

different thickness or density.

Figure 90: Predictions of a measured HRR curve for a FR ESP product by the use of Cone Tools 3.2.1 and the modified Cone Tools.

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Figure 91: Predictions of a measured HRR curve for a FR ESP product by the use of Cone Tools 3.2.1 and the modified Cone Tools.

Figure 92: Predictions of a measured HRR curve for a FR ESP product by the use of Cone Tools 3.2.1 and the modified Cone Tools. Painted paper plasterboard All different CC data gives the same result. Both Cone Tools 3.2.1 and the modified Cone Tools predict the measured HRR curve in all cases.

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Figure 93: Predictions of a measured HRR curve for a painted paper plasterboard product by the use of Cone Tools 3.2.1 and the modified Cone Tools.


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Figure 99: Predictions of a measured HRR curve for a painted paper plasterboard product by the use of Cone Tools 3.2.1 and the modified Cone Tools. Melamine face All different CC data gives the same result. Both Cone Tools 3.2.1 and the modified Cone Tools predict the measured HRR curve in all cases.

Figure 100: Predictions of a measured HRR curve for a melamine face product by the use of Cone Tools 3.2.1 and the modified Cone Tools.

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Plastic faced steel sheet All different CC data gives the same result. Both Cone Tools 3.2.1 and the modified Cone Tools predict the measured HRR curve in all cases.

Figure 103: Predictions of a measured HRR curve for a plastic faced steel sheet product by the use of Cone Tools 3.2.1 and the modified Cone Tools.


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Documents

Improved Version of Cone Tools for Predictions of Room