Global modelling of fire protection performance of intumescent coating under different cone calorimeter heating conditions

Fire Safety Journal 50 (2012) 51–62

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Global modelling of fire protection performance of intumescent coating under different cone calorimeter heating conditions Y. Zhang a, Y.C. Wang a,n, C.G. Bailey a, A.P. Taylor b a b

School of Mechanical, Aerospace and Civil Engineering, University of Manchester, UK Leighs Paints, Bolton, UK

a r t i c l e i n f o

abstract

Article history: Received 4 February 2011 Received in revised form 20 December 2011 Accepted 7 February 2012 Available online 3 March 2012

This paper presents a mathematical model to simulate the expansion process and global behaviour of intumescent coating applied to a steel plate under different cone calorimeter heating conditions. A mathematical expression has been found to relate the local rate of expansion of intumescent coating to the local rate of mass loss, rate of temperature change and temperature. Comparing the recorded expansion process of intumescent coating under cone calorimeter heating exposure, this modelling method has been found to give accurate results of the expansion–time relationship for the product tested. The thermal conductivity of expanding intumescent coating was modelled based on treating intumescent coating as a homogeneous porous media. The predicted steel temperatures were found to be in excellent agreement with experimental results from the cone calorimeter tests with different steel plate thicknesses and intumescent coating thicknesses under two different heat fluxes. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Intumescent coating Heat and mass transfer Modelling Fire protection Cone calorimeter

1. Introduction Structural steel is widely used in modern structural construction all over the world. It is an important and prime requirement of building regulations for steel-framed buildings to have sufficient fire resistance and one way to achieve this requirement is to apply passive fire protection to the structural steel [1]. Thin film intumescent coatings have become the dominant choice for passive fire protective materials because of their many advantages including: flexibility and ease of usage for both on- and offsite applications, light-weight, thin and attractive appearance, and high standard finish. Intumescent coating is inert at room temperature but intumesces up to 100 times its initial thickness when exposed to heat, forming a cellular charred layer of low conductivity foam. The foam layer protects the substrate steel from a fire, reduces the rate of temperature rise in the steel, and prolongs its load bearing capacity. The assessment of fire protective intumescent coatings is generally performed by means of standard fire resistance tests [2], which is an unrealistic fire scenario due to the temperature– time relationship of the fire being fixed and forever increasing in temperature with time. There is now a demand from the structural fire engineering community to consider more realistic fire conditions, in which the fire temperature–time relationship is

n

Corresponding author. E-mail address: [email protected] (Y.C. Wang).

0379-7112/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2012.02.004

defined in terms of the geometry of the compartment, available ventilation, amount of combustible material and the characteristics of the compartment boundaries. Intumescent coating is a reactive material and its thermal properties are dependent on the heating condition and hence on the type of fire exposure. Therefore, the thermal properties of intumescent coatings, particularly thermal conductivity, obtained from standard fire tests may not be consistent and reliable under a different set of fire exposure conditions. On the other hand, it is not feasible, or cost effective, to conduct numerous fire tests under different realistic fire exposure conditions. Therefore, developing a modelling approach, in which different fire exposure conditions can be incorporated, is preferred. The expansion of intumescent coating under heat is rather complicated, involving a complex mixture of gas, liquid and solid phases and with many variables being extremely difficult to measure. To date, the majority of previous research studies into the behaviour of intumescent coatings have been experimental based and mainly focused on understanding the effects of different formulations to help manufacturers develop products to pass the standard fire resistance rating test [3–5]. Very few studies have been conducted to investigate the performance of intumescent coatings under different fire conditions, with very limited success in modelling. The modelling efforts may be classified into three types according to the level of complexity. (1) At the simplest level, without considering the complex physical and chemical behaviour of intumescent coating [6,7], a simple

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Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

Nomenclature A a C Ctrap d e E h H K m n P Q R t T W x y Y g_

pre-exponential factor (s  1) unit surface area (m2) specific heat capacity (J K  1kg  1) trapped gas coefficient bubble size (m) emissivity activation energy (kJ mol  1) convection heat transfer coefficient (W m  2) heat of pyrolysis per unit mass of material (J kg  1) reaction rate constant mass (kg) number of elementary layers in the coating gas pressure (Pa) cone calorimeter heat flux (kW m  2) universal gas constant (J mol  1 K  1) time (s) temperature (K) mean gas molecular weight coordinate along coating thickness (m) coordinate along steel thickness (m) mass fraction mass flow rate of gas per unit area (kg s  1 m  2)

thermal analysis is carried out to determine the temperature dependent effective thermal conductivity of the intumescent coating based on standard fire tests or cone calorimeter tests. These studies are restricted to specific fire conditions, together with specific steel and coating thicknesses. It would be grossly inaccurate to extrapolate the results from these studies to different applications. (2) At the most complicated level, intumescent coating behaviour may be studied from fundamental microscopic level of chemical reaction, individual bubble generation, growth, movement, interaction with other bubbles and collapse [8–10]. This type of study requires many assumptions which will be difficult to validate, extensive input data that will be difficult to quantify and extremely demanding computational effort which will not be practical to implement. So far this type of modelling has been limited to the early stage of intumescencing and has not been validated. (3) The study presented in this paper will follow an intermediate approach in which the focus is on measurable global chemical and physical quantities of intumescent coating, with the chemical reactions being coupled with thermal analysis [11–18]. An example of this approach was adopted by Di Blasi [11,12], in which the chemical reactions of an intumescent coating were described by three independent global reactions: melting, swelling and charring. The degradation of the intumescent coating components were described by the Arrhenius kinetic law and the volume expansion was associated with mass loss. The effects of endothermic/exothermic chemical reactions and the energy loss due to gas escaping were taken into consideration. This method is attractive because the complex chemical reactions and bubble mechanisms are simplified so the heat and mass transfer process can be calculated using global physical/chemical properties. All the existing intermediate level studies have many limitations, the most critical one being that an ‘expansion factor (ratio)’ should be provided as input to determine the final coating thickness. However, in reality, the expansion ratio spans a wide range and is the most singular important factor affecting the

Greek letters

b trapped gas ratio during swelling DH decomposition heat in an elementary layer Dt time step (s) Dxi (i¼1,n) thickness of coating element layer (m) Dy thickness of steel element layer (m)

e l

r s n

void fraction thermal conductivity (W m  1 K  1) density (kg m  3) Stefan–Boltzmann constant (W m  2 K  4) stoichiometric coefficient

Subscripts c coating C char g gas s solid S steel S1, S2, S3 reactive components G1, G2, G3 gas products from S1, S2, S3

thermal properties of intumescent coating [11–18]. Indeed, the expansion ratio should be a model output instead of a prescribed input. By introducing an empirical relationship based on mass loss, Griffin [18] proposed an alternative method. However it is not clear whether the relationship proposed by Griffin would be applicable for different fire scenarios, since only one fire condition was explored. This paper builds on the research of Di Blasi [11,12] and Yuan [19,20], but presents a new model to allow the intumescent coating expanding process to be accurately predicted for different heating conditions. Experimental validation of the model was performed using the authors’ test results from a cone calorimeter, which is an instrument widely adopted to measure many materials fire properties because it allows small-scale heating tests to be performed in a timely and cost-effective manner. Cone calorimeter can produce a stable heating source of different heat fluxes, thus allowing the effects of heating condition on intumescent coating to be investigated.

2. Theory and mathematical model It is generally accepted that intumescent coating is composed of three active components (acid source, blowing agent, and charring agent) bound in a binder polymer [21–23]. When exposed to a heating source, several reactions are triggered almost simultaneously but in an appropriate sequence. First the coating melts and forms a viscous fluid; the acid source breaks down to yield a mineral acid as a catalyst, which then takes part in the charring reaction to yield the carbon char and at the same time the blowing agent decomposes to release a large amount of gaseous products, part of which is trapped in the coating to cause the molten matrix to swell. As the temperature increases, the mixture is solidified; finally, the carbon char further oxidises leaving a residual protective multi-cellar insulating layer. The major assumptions in this model are (1) Heat and mass transfer occurs in one-dimension only, being vertical to the surface of substrate. Fig. 1 shows a schematic of the coating system, which consists of a steel substrate and an

Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

53

stage of expansion. As a result, the volume of char is proportional to the mass of S3. Because only a unit area is considered in the model, it is sensible to assume that the bubble size is proportional to the volume shrinkage. In other words, the mean bubble size is inversely proportional to the conversion of S3. In summary, the bubble size reaches the maximum (dmax) at the end of the expanding stage and gradually decreases at the charring stage (Eq. (6)). Individual bubble behaviour and the change in bubble number are not considered in this model   Y2 Y3 þ YC d ¼ d0 þ ðdmax d0 Þ 1 ð6Þ Y 2,0 Y 3,0

Fig. 1. Schematic of the coating system and the finite-difference grid.

intumescent coating exposed to heat source on one side and insulated from the other. (2) It is assumed that the coating is made of three components: acid source (S1), blowing agent (S2) and charring materials (S3) with initial mass fractions of Y10, Y20, and Y30, respectively. S3 is a combination of the charring agent and binding materials. The three components follow three independent reactions corresponding to melting (Eq. (1)), swelling (Eq. (2)) and charring and degrading (Eq. (3)). G1, G2 and G3 are volatile species from the reactions and SC is the final solid char residue K1

S1 !G1

ð1Þ

K2

S2 !G2

ð2Þ

K3

S3 !nc SC þvv G3

ð3Þ

(3) It is assumed that the internal pressure maintains atmospheric pressure (1 atm) and the expansion rate can be calculated by ideal gas law (Eq. (4)). At the char degradation stage, the thickness gradually shrinks, which is assumed to be linear to depletion of the charring materials (Eq. (5)). None of the existing models in literature considers shrinkage of the expanded intumescent char   @x bR @m2 @T ¼ ðT melt o T o T C Þ þ m2 T ð4Þ @t aP 0 W g @t @t xt ¼ ðxtDt þ Dt

@x m3 þ m4 Þ @t m3,0

ð5Þ

(4) It is assumed that the mean bubble size is proportional to the conversion of S2 and inversely proportional to the conversion of S3. The swelling process is mainly due to gases released by the blowing agent (S2). Although the bubble size is also affected by temperature, a bubble typically expands more than 10 times within a relatively narrow temperature range (473–723 K). Therefore, the sharp increase in bubble size is more a result of gases released than temperature, which increases about 1.5 times during the expansion phase. The conversion of S3 refers to the mass depletion of S3 during the oxidation stage. The reaction of S3 mainly occurs after the char has expended. The porosity of an expanded char typically is more than 90% and its density approaches that of air and does not change too much at the later

(5) It is assumed that coating expansion occurs within a temperature range between a lower value and a higher value. Some researchers [14,22] have suggested that the temperature range of expansion is from Tmelt to TC, where Tmelt is the temperature at which the viscosity of the melting polymer is reduced to a level when the volatile products start to be trapped and cause expansion; TC is the temperature when char-forming starts and the viscosity of the coating becomes too high for it to expand. Ideally Tmelt and TC should be determined from viscosity measurements but unfortunately the state-of-the-art rheometers can only provide a qualitative estimation of these temperatures due to the fragile nature of the intumescent coating during expansion. As will be shown later in the paper, the initial expansion rate is very low so that Tmelt has little effect on the final expansion thickness of the coating. Therefore, a conservatively low temperature of Tmelt ¼150 1C will be used. In contrast, the final expanded thickness of the coating becomes very sensitive to the upper temperatures TC. In the research studies of Di Blasi [11,12] and Yuan [19,20], this upper temperature is not required. In their research, the maximum rate of expansion is assumed to be the same regardless of the local heating condition and is treated as an input value. Expansion stops when the maximum rate of expansion is reached. For a truly predictive model, the approach of Di Blasi [11,12] and Yuan [19,20] is not useful. Finding an appropriate TC was a key part of this research. When intumescent coating is heated, its temperature distribution, and hence the rate of temperature change, is non-uniform. This will affect the expansion process. Therefore, it is important that the upper temperature TC is defined by the local condition. Considering a thin layer of bubbles surrounded by intumescent coating, the expansion is mainly caused by gases released from S2 (Eq. (2)). According to the law of acceleration, the driving force generated can be written as Eq. (7). This driving force has to be balanced by the barrier force from viscosity and surface tension according to Young’s equation [24]. When the balance is broken, expansion stops and the gases retained within the bubbles are released to the outside environment, but leaving the bubble sizes as before gas release. It is assumed that this balance is broken when the driving force reaches the maximum, at this point the expansion stops and the temperature is TC. Combining Eqs. (4) and (7) produces Eq. (8). Further simplification by neglecting the second derivative terms leads to Eqs. (9) and (10) F ¼ m2

@2 x @t 2

ð7Þ

F ¼ m2

@2 T @m2 @T @2 m2 þT 2 þ 2m2 2 @t @t @t @t 2

ð8Þ

_

@2 T @2 m2  0 and 0 2 @t @t 2

‘F  2m2

@m2 @T when F-F max , @t @t

ð9Þ

T ¼ TC

ð10Þ

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Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

relationship was established  C trap ms,g T=ms,0 T 0 T b ¼ melt T

(6) Not all gases released are retained in the bubbles and cause expansion, otherwise, the rate of expansion of the intumescent coating would be in the range of hundreds of times of the original thickness, rather than in tens of times. In the research by Di Blasi [11,12] and Yuan [19,20], the amount of gas trapped is simply assumed to be a constant and is the same regardless of the local heating condition in different locations of the intumescent coating. To stop ‘over expansion’, these research studies assumed a maximum expansion rate as an input. Since the main objective of this research is to predict intumescent coating expansion, the method of Di Blasi [11,12] and Yuan [19,20] is not adequate. Finding an expression to quantify the amount of released gas, that is trapped within bubbles to cause expansion, was another key aspect of this research. It is assumed that only part of G2 is trapped and contributes to coating expansion, the other remaining gases escapes and travels through the matrix to the outside environment. The escaped gas does not participate in the swelling process but contributes to convective heat transfer. Use b to represent the trapped gas fraction of G2. At present, understanding of intumescent coating behaviour under heating is not sufficiently mature to allow an expression for b to be derived based on a sound scientific principle. Therefore, this research followed an intuitive and trial and error approach to find an expression for b. Initially, different fixed values of Tc were tried and different forms of b–T relationship (for example, constant, triangular, exponential) were explored. But this process was not able to produce predictive results that were in ‘consistent’ agreement with test results for different heating conditions, different coating and steel plate thicknesses. The effects of variable coating temperature, mass (and via mass the rate of heating) should be included in the b–T relationship. After an exhaustive process, the following empirical

ð11Þ

The above relationship gives a value of 1 when expansion starts and decreases when the coating temperature increases. The proportion of gas trapped also decreases as more gases are released. This is sensible because when the coating temperature is high but the rate of heating is low, further gases are released but a diminishing amount of the gas released is trapped to cause coating expansion. In Eq. (11), Ctrap is introduced as a constant, depending on the intumescent coating material. This constant is assumed not to change under different heating conditions. Therefore, it can be evaluated experimentally. The starting temperature Tmelt is introduced into Eq. (11) since it is assumed that all the gas is trapped and participates in expansion when the expansion process starts. Other equations follow those defined by De Blasi and Yuan [11,12,20] and are listed in Table 1, which also presents the boundary conditions. The equations are solved using the finite difference method [11,12]. In the numerical method, the coating and the substrate are divided into many fine layers (for example, Dx¼0.1 mm and Dy¼1 mm) and a sufficiently fine time increment (typically Dt ¼0.01 s) is used. Fig. 1 shows an illustration of the finite-difference grid. The Fourier number is defined using Eq. (12). The time interval Dt and layer thickness Dx have to satisfy Eq. (13) to preserve the stability of the numerical calculation f¼

lDt

ð12Þ

rC Dx2

1 2 4 0 f

ð13Þ

Table 1 List of equations [11–12, 20]. Chemical kinetic equation

  Ej K j ¼ Aj exp  , RT

j ¼ 1,2,3

ð14Þ

Mass conservation @m1 ¼ m0,1 K 1 Y 1 , @t

@m2 @m3 @mC ¼ m0,2 K 2 Y 2 2 , ¼ m0,3 K 3 Y 3 , ¼ nc m0,3 K 3 Y 3 @t @t X@t@mj @mC @ms @mg ¼ ¼ þ @t @t @t @t j ms ¼ m0,1 Y 1 þ m0,2 Y 2 þ m0,3 Y 3 þ nc m0,3 Y 3 , mg ¼ m0 ms

Mass continuity

@mg @ðexrg Þ  @t @t

_ in _ out m g m g ¼ Solid phase volume xs ¼ x0 ð1e0 Þ State equation

ms , m0

e¼

r¼

W g P0 RT

Energy conservation inside coating

xxs , x

ð15Þ2ð18Þ ð19Þ ð20Þ2ð21Þ

ð22Þ

i ¼ 1,n

ð23Þ2ð24Þ ð25Þ

@ @T @ðmCTÞ ðl Þ ¼ þ DH @x @x @t @ðexrg Þ _ g TÞ @ðmCTÞ @T @ms @ðm ¼ ðms C s þ mg C g Þ þ Cg T þ Cg þ Cs T @t @t @x @t @t   X @mj DH ¼ Hj @t

ð26Þ ð27Þ ð28Þ

Energy conservation inside steel @ @T S @T S ðlS Þ¼ mS C @y @y @t

ð29Þ

Thermal conductivity of intumescent coating

ln ¼ ls lg

lg ls

2 3

2 3

e þ 1e

2

2

ð30Þ

3 3 ls ðe eÞ þ 1e þ e

4 0:717

lg ¼ lcond þ lrad , lcond ¼ 4:815  10 T Boundary and initial conditions

,

lrad ¼

2  4desT 3 3

@T ¼ Q esðT 4 T faire Þhconv ðTT 0 Þ @x _g @m @T S n @T ¼ 0, TS ¼ T, l ¼l At the substrate and coating interface : @x @x @x @T S ¼0 At the bottom of substrate : l @x At top coating surface :

ln

ð31Þ2ð33Þ ð34Þ ð35Þ2ð37Þ ð38Þ

Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

3. Experimental methods In order to check the theoretical method as described in the previous section, a large number of thermogravimetric analysis (TGA) and one set of cone calorimeter tests have been performed to provide experimental data for validation. The TGA tests were performed by the coating manufacturer (Leighs Paints) and the cone calorimeter tests were carried out at the University of Manchester. The cone calorimeter tests included combinations of different steel plate thicknesses, different intumescent coating thicknesses, and different heating rates. 3.1. TGA tests To determine the chemical kinetic properties of the coating, a series of TGA tests were performed at different heating rates (5, 10, 20 and 50 1C/min) under 150 ml/min air flow. The thermal

Table 2 Sample details for cone calorimeter tests. Sample IDn 65/50 kW/m2

Steel thickness (mm)

Target D.F.T. (mm)

Measure D.F.T. (mm)

A04H1/A04L1 A04H2/A04L2 A08H1/A08L1 A08H2/A08L2 A12H1/A12L1 A12H2/A12L2 B04H1/B04L1 B04H2/B04L2 B08H1/B08L1 B08H2/B08L2 B12H1/B12L1 B12H2/B12L2 C04H1/C04L1 C04H2/C04L2 C08H1/C08L1 C08H2/C08L2 C12H1/C12L1 C12H2/C12L2

5 5 5 5 5 5 10 10 10 10 10 10 20 20 20 20 20 20

0.4 0.4 0.8 0.8 1.2 1.2 0.4 0.4 0.8 0.8 1.2 1.2 0.4 0.4 0.8 0.8 1.2 1.2

0.48/0.35 0.48/0.37 0.7/0.9 0.82/1.0 1.6/1.25 1.65/1.3 0.28/0.5 0.3/0.5 0.7/0.85 0.81/0.83 1.5/1.1 1.6/1.2 0.55/0.54 0.62/0.55 0.83/1.1 0.77/1.0 1.24/1.5 1.23/1.6

n Sample ID¼ steel thickness (A: 5 mm, B: 10 mm, C: 20 mm)þ coating thickness (04, 08, 12 mm)þheat flux (H: 65 kW/m2 L: 50 kW/m2)þsample number (1, 2).

55

gravimetric analyser used was TA instrument SDT 2000 with simultaneous DSC/TGA. Alumina pans were used to hold the samples. The samples were made from thoroughly dried coating, which was ground to powder and then compressed in the pan to form a thin layer of sample in full contact with the pan. The initial samples weighed about 7 mg and the temperature range was from 30 1C to 1000 1C. The recorded data were processed using the software supplied with the TGA. 3.2. Cone calorimeter test sample preparation The substrates used were 100 mm  100 mm steel plates with three different thicknesses of 5, 10 and 20 mm. They were coated by a commercially available water based intumescent coating (Firetex, Leighs Paints, UK). A blade coating method was used to apply the coating: coating was applied to the steel plate and a blade was placed above the plate at the desired height, depending on the required dry film thickness (DFT), and then moved over the substrate to remove any excess coating. The target DFTs were 0.4, 0.8 and 1.2 mm. Samples were dried at ambient temperature for at least 48 h until thoroughly dried. The DFTs of each specimen were measured using a digital thickness gauge and are listed in Table 2. 3.3. Cone calorimeter tests Fig. 2 shows the experimental setup for the cone calorimeter tests and an example of the sample before, during and after the test. Each test sample was exposed to a cone calorimeter (standard version, Fire Testing Technology) for about 60 min. The air flow in the cone calorimeter was 24 L/min, similar to that used for TGA tests. Two nominal radiant heat fluxes of 50 and 65 kW/m2 were used in the tests, the radiant power being measured at 50 mm below the cone heater. Heat flux at different positions below the centre of the cone heater was measured using a Gardon-type Medtherm heat flux metre to quantify the heat flux change during coating expansion. The steel plate temperature was monitored with two thermocouples fixed on to the back of steel plate. The edge and bottom of the steel plate were in contact with a layer of 100 mm thick mineral wool to minimise heat loss to the surrounding environment. The temperature in the mineral

Fig. 2. (a) Experimental setup for the cone calorimeter test, (b) samples before test, (c) during test, and (d) after test.

56

Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

wool was monitored by a thermocouple placed at 50 mm below the steel plate. The test sample was placed in a height-adjustable stand under the cone heater. The in situ coating expansion process

was filmed using a camcorder. The video images were then processed by a Matlab image processing technique to track the expansion process and the expanded coating thickness profile.

Table 3 Kinetic properties and other parameters used in the model, literature values are from Refs. [11] (n) or [20] (y).

4. Experimental results and comparison with predictions

Kinetic parameters A1 (s  1) E1 (kJ/mol) A2 (s  1) E2 (kJ/mol) A3 (s  1) E3 (kJ/mol) Y1,0 Y2,0 Y3,0

nc ng H1 (kJ/kg) H2 (kJ/kg) H3 (kJ/kg)

4.1. TGA test results

Other parameters 300 54 2  106 110 5.0 60 0.28 0.17 0.55 0.65 0.35  1256n  1256n 9789n

1.884 y 0.48 y 1.0 y 0.345  10  3 y 37.68  10  3 y 1400.0 y 7850.0 y 1.0 y 30  10  3n 20.0n 1 423 1.0  10  4 3.5  10  3

Cc (kJ/kg/K) Cs (kJ/kg/K) Cg (kJ/kg/K) lc (Kw/mK) ls (Kw/mK) rc (kg/m3) rs (kg/m3) e Wg (kg/mol) h (kW/m2) Ctrap Tmelt (K) db (m) df (m)

The TGA tests were performed in air. According to research studies by others, the main effects of the atmosphere (air or N2) to which intumescent coatings are exposed to are during the oxidation stage of pyrolysis. In the early expanding stage, air is not involved in the reaction so has little influence on the expansion process. For example, Griffin et al. [18,25] found that the effects of atmospheric oxygen content mainly occurred when J the coating temperature was greater than 540 C. Jimenez et al. [26] also found that there was no significant diffidence between degradation of intumescent coatings whether in air and nitrogen at the early stage.

90 Simulated mass loss Experimental mass loss Experimental mass loss rate Simulated mass loss rate

80

0.5 0.4

70 0.3 60 0.2

50 40

0.1

30

0.0 0

200

400 600 Temp /°C

800

70 65 60 55 50 45 40 35

1000

10

Fig. 3. Comparison between simulated and the experimental curves of TGA.

110

20

30 40 50 60 70 Distance below cone heater /mm

Fig. 5. Variation of radiant heat flux with height.

a. Start with 7.7 mg samples ( ~7 mm3)

Mass loss Driving force

b. 215°C no significant expansion, sample softened

100

0.03

c

c. 410°C Sample expanded to ~70 mm3

90 80

e. 456°C Maximum volume was ~120 mm3

0.02

70 f. 630°C Sample shrinked to ~80 mm3

60

30 0

200

Char formation

40

Intumescence

g.1000°C Volume was ~40 mm3

50 Melting

Mass loss /%

d. 420°C Sample expanded to ~100 mm3

Driving force

Mass Loss /%

80

75 Heat Flux /kW/m2

90

Mass Loss Rate /%/s

100

50 kW/m2 (nominal) 65 kW/m2 (nominal)

85

0.6

d

e

0.01 f

Degradation

400 600 800 Temperature /°C

0.00 1000

1200

Fig. 4. Qualitative behaviour of intumescent coating at different stages of reaction.

g

80

90

Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

57

3mm

Sample A04L2, exposed to 50 kW/m2, initial coating thickness 0.4 mm.

3mm

Sample B12H1, exposed to 65 kW/m2, initial coating thickness 1.2 mm. Fig. 6. Examples of bubble formed after cone tests.

Table 3 presents the chemical kinetic data derived from TGA tests and Fig. 3 compares the experimental mass loss and mass loss rate curves with the simulated results using the kinetic data in Table 3 and Eqs. (14)–(19). The proposed Arrenhius equations are sufficiently accurate and the derived chemical kinetic parameters have successfully captured the major features of the different reaction stages of the intumescent coating. A qualitative study of the different reaction stages of the intumescent coating was conducted by stopping the TGA tests at different temperatures and estimating the consequent sample volumes. As Fig. 4 shows, the results are consistent with the assumptions of this research which divide the reactions of intumescent coating into four stages: Stage I: melting, no significant expansion; Stage II: blow agent decomposition, rapid expansion of coating; Stage III: char forming, maximum expansion around the maximum mass loss rate of S2, consistent with the assumption for Eq. (10); Stage IV: shrinking corresponding to decomposition of char. As shown in Fig. 4, the first three stages are quite distinct from each other but the rates of mass of mass loss for the third and forth stages are similar, thus justifying the assumption that charring and degradation are treated as one reaction in this model.

Table 4 Summary of comparison between predicted and measured thickness of samples exposed to 65 kW/m2. Sample ID

Final thickness (mm)/expansion ratio

Predicted thickness (mm)/expansion ratio

Difference (%)

A04H1 A04H2 A08H1 A08H2 A12H1 A12H2 B04H1 B04H2 B08H1 B08H2 B12H1 B12H2 C04H1 C04H2 C08H1 C08H2 C12H1 C12H2

21/44 20/42 26/39 34/42 31/19 32/19 13/46 16/54 26/39 32/40 38/25 40/25 21/37 27/42 24/30 25/32 35/28 33/27

20.5/43 20.5/43 25.6/38 28.1/35 37.4/23 38.5/23 13.5/48 14.9/50 25.6/38 30.2/38 37.6/25 43.1/27 19.8/35 25.4/40 29.7/37 26.5/34 32.3/26 32.3/26

 2.4 2.5  1.5  17.4 20.6 20.3 3.8  6.9  1.5  5.6  1.1 7.7  5.7  5.9 23.8 6  7.7  2.1

4.2. Cone test data Due to radiant heat flux change at different heights below the cone calorimeter, the heat flux on the expanding coating surface was different. Fig. 5 shows the distribution of measured heat flux at different distances below the centre of the cone heater, ranging from 15 mm to 80 mm (to cover all possible final positions of top coating surface). The distribution is approximately linear. As shown in Table 2, a large number of tests were performed covering all combinations of heat flux, steel thickness and coating thickness. Each test was repeated. However, due to space limitation, except for the expansion rate, detailed duplicate test results will not be presented here. Table 3 also lists other physical properties of the coating and the substrate, among them, the constant (Ctrap) and the maximum bubble size (dmax) were obtained from cone calorimeter tests. The value of Ctrap was determined by trial and error to achieve the best agreement between predictions and test results. This is

considered acceptable because the objective of this research is to develop a practical method that can allow the fire protection performance of intumescent coating to be predicted for different heating conditions. As long as the prediction method is consistently applicable for different heating conditions, it is considered that the predictive model has captured the main influential parameters in the correct way. Otherwise, the value of Ctrap would be different for different testing conditions. To calculate the thermal conductivity of the expanding intumescent coating, the dominating bubble size dmax should be determined throughout the expansion process of the coating. As shown in Eq. (6), the bubble size is a function of the mass conversion of S2 and S3. The maximum bubble size dmax was measured from samples which had just gone through the intumescence stage but had not suffered shrinkage due to degradation. Fig. 6 shows some examples of bubbles formed at the coating

Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

Table 5 Summary of comparison between predicted and measured thickness of samples exposed to 50 kW/m2. Difference (%)

22/63 20/54 38/42 36/36 48/38 46/35 25/50 24/48 38/47 38/46 41/37 39/33 20/37 19/35 39/35 38/38 40/27 42/26

17.3/48.6 19.4/51.4 32.6/35.6 34.1/34 32.9/26.4 36.2/27.7 21.6/42 21.6/42 29.8/35.3 29.2/34.9 30.3/27.3 32.4/26.7 21.8/40.7 23.1/41.8 35.1/31.8 33.5/33 35.0/23.3 38.3/23.8

 22.7 5  15.8  5.6  31.2  21.7  16  12.5  9.1  23.7  26.8  17.9 10 21.1  10.2  13.2  12.5  9.5

30 500

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2500

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40

A08H1

35

Steel Temperature /°C

600

surfaces after different fire exposures. Most expanded chars were too fragile to allow the inside bubble size to be examined. However, some chars formed from the low irradiance (50 kW/m2) test samples were relatively firm. They were broken off for inside examination of the char. The bubbles inside the char had similar size to those at the surface. The maximum bubble size (dmax) was set at 3.5 mm, which is the same as measured by Yuan for the same intumescent coating [19,20].

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Tables 4 and 5 compare the predicted and measured final thickness for all the tests under cone calorimeter heat flux 65 and 50 kW/m2, respectively. The measured expansion ratios (final thickness/initial thickness) spanned a wide range from 20 to 60 under different experimental conditions. This wide range has been correctly predicted by the model. The difference between the predicted and experimental results is mostly less than 10% with the maximum difference about 30%. Bearing in mind the simplicity of the model and the complexity of intumescent coating behaviour, this margin of error is considered small and the prediction results excellent. In particular, the proposed model is based on local conditions of intumescent coating. Except for the Ctrap value, other constants used in the model can be easily measured. The value of Ctrap is not directly measureable, but can be obtained by calibrating the model against a small set of test results. The most important issue is that the Ctrap value is independent of the testing condition. Figs. 7–12 compares the measured and predicted time profiles of steel temperature and expansion thickness for different experimental conditions. In most cases, agreement between the modelling and test results is excellent for both the expansion thickness and steel temperature. In particular, the different stages of behaviour of intumescent coating are accurately calculated across the entire ranges of heating rate, intumescent coating thickness and steel plate thickness. This indicates that the main hypotheses (start and stop temperatures, trapped gas function) are appropriate. The different test samples under different experimental conditions experienced different degrees of reduction in thickness. This stage of behaviour has been predicted with good accuracy by the model and confirms the assumption that the expansion thickness is a function of depletion of the charring material (Eq. (5)).

30

500

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4.3. Comparison between experimental and prediction results

Expansion Thickness /mm

Predicted thickness (mm)/E.R.

35

Expansion Thickness /mm

A04L1 A04L2 A08L1 A08L2 A12L1 A12L2 B04L1 B04L2 B08L1 B08L2 B12L1 B12L2 C04L1 C04L2 C08L1 C08L2 C12L1 C12L2

Final thickness (mm)/ expansion ratio (E.R.)

A04H1

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Sample ID

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Fig. 7. Comparison of predicted and measured steel temperatures (shapes) and expansion thickness profiles (lines) for 5 mm steel thickness exposed to heat flux 65 kW/m2.

4.4. Sensitivity study results The theoretical model requires input data of Ctrap and dmax. The value of dmax can be directly measured. However, due to variation in bubble size, the value of dmax cannot be determined with great precision. The value of Ctrap does not have a specific physical meaning and can only be obtained by calibration of the theoretical model against a small number of tests. In addition, the

Y. Zhang et al. / Fire Safety Journal 50 (2012) 51–62

10 Test Modelling Test Modelling

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Fig. 8. Comparison of predicted and measured steel temperatures (shapes) and expansion thickness profiles (lines) for 10 mm steel thickness exposed to heat flux 65 kW/m2.

trapped gas ratio (Eq. (11)), in which the value of Ctrap is used, is based on conceptual and intuitive reasoning but does not have the backing of precise analysis based on a fundamental theory. To ensure that the theoretical model is consistently applicable under different conditions, it is important that the prediction results are not sensitive to small changes in these two values. This has been checked by a sensitivity study.

Steel Temperature /°C

500

Expansion Thickness /mm

Steel Temperature /°C

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Fig. 9. Comparison of predicted and measured steel temperatures (shapes) and expansion thickness profiles (lines) for 20 mm steel thickness exposed to heat flux 65 kW/m2.

Fig. 13 shows the effects of changing the value of Ctrap on prediction results. Changes of 720% in Ctrap value gave a very small mean difference ( o2%) in the predicted steel temperature. The corresponding changes in predicted thickness prediction were; 11% 73% and 13% 74%, respectively. Due to the large effect of Ctrap on the value of b, the predicted expansion thickness is more sensitive to changes in Ctrap. However, changing the expansion thickness has the opposite effect in changing the

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35

Test Modelling Test Modelling

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5 0

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Fig. 10. Comparison of predicted and measured steel temperatures (shapes) and expansion thickness profiles (lines) for 5 mm steel thickness exposed to heat flux 50 kW/m2.

Fig. 11. Comparison of predicted and measured steel temperatures (shapes) and expansion thickness profiles (lines) for 10 mm steel thickness exposed to heat flux 50 kW/m2.

coating thermal conductivity through its influence on changing the bubble size, thus greatly reducing the sensitivity of the predicted steel temperature to Ctrap. Since it is the steel temperature, not the coating thickness, that is of the ultimate interest, the level of sensitivity reported here is entirely acceptable. Of course, if an order of magnitude change is made to the value of Ctrap, there will be large changes to the predicted steel temperature. For example, changing the value of Ctrap from 1.0 to 0.1, both

the predicted coating thickness and steel temperature profiles are significantly affected, as shown in Fig. 13. Fig. 14 shows that changing the value of dmax by 720%, there is negligible change to the resulting predicted coating thickness (o1%) but the change in predicted steel temperature is slightly more noticeable ( o3%) due to direct effect of bubble size on coating thermal conductivity. However, the effect on steel temperature is still very small.

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61

600

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20 15 10 Test Modelling Test Modelling

5

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Ctrap = 1.0 Ctrap = 1.2 Ctrap = 0.8 Ctrap = 0.1

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Expansion Thickness /mm

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50 650 600 550 500 450 400 350 300 250 200 150 100 50 0

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300 dmax =4.2 mm dmax = 3.5 mm dmax = 2.8 mm

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650 600 550 500 450 400 350 300 250 200 150 100 50 0

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Fig. 14. Effect of changing the maximum bubble size (dmax) on prediction results.

Expansion Thickness /mm

Steel Temperature /°C

Fig. 13. Effects of changing Ctrap on prediction results.

0

1000 1500 2000 2500 3000 3500 Time /t

Fig. 12. Comparison of predicted and measured steel temperatures (shapes) and expansion thickness profiles (lines) for 20 mm steel thickness exposed to heat flux 50 kW/m2.

5. Conclusions A theoretical model has been developed to predict the expansion of intumescent coating so as to allow temperature in the protected steel substrate to be calculated under different heating conditions. The model attempts to describe the global behaviour of intumescent coating and is based on previous research by Di Blasi [11,12] and Yuan [19,20]. However significant new developments have been made in this research so that the proposed model is truly predictive. These new developments

enable the intumescent coating expansion process to be predicted through the introduction of a trapped gas ratio (b, Eq. (11)) that is a function of the local temperature and rate of mass reduction. The start and finish conditions for coating expansion also represent significant advances from previous research studies. All the input data to the model are independent of the heating condition and can be either directly measured or indirectly obtained through calibration. The proposed model has been used to predict a large number of cone calorimeter tests covering a range of testing conditions, including coating thickness, steel plate thickness and heat flux. The predictive results have been shown to be highly accurate, in terms of both the coating expansion and steel temperature profiles at different times. The predictions captured the different critical timings of measurements under all heating and experimental conditions. In most cases, the predicted intumescent coating expansion rate is within 10% of the test results with a maximum difference of about 30%. Furthermore, the prediction results are not sensitive to two constants of the model that would be difficult to obtain precisely, Ctrap and dmax, suggesting that relative large inaccuracies ( 720%) in these values would still be acceptable. This paper has used cone calorimeter test results to validate the proposed model. The authors are currently conducting furnace fire tests under different fire exposure conditions. Further validation of the proposed model, using the proposed tests, will pave a pathway towards real performance based fire resistant

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design of structural steel protected with intumescent coating under different, and realistic, fire conditions.

Acknowledgements The research reported in this paper was supported by the UK’s Engineering Physical and Science Research Council through Grant EP/F060718/1. The authors would like to thank Mr. Jim Gorst and Mr. Jim Gee for their help with the tests. Intumescent coating was supplied free of charge by the collaborating coating manufacturer. References [1] CEN, ENV 1993-1-2, Eurocode 3, Design of Steel Structures, Part 1.2, General Rules—Structural Fire Design, BSI, London, 2005. [2] CEN, EN 13381-8, Test Methods for Determining the Contribution to the Fire Resistance of Structural Members, Part 8, Applied Passive Protection Products to Steel Member, BSI, London, 2010. [3] I. Vroman, S. Giraud, F. Salaun, S. Bourbigot, Polypropylene fabrics padded with microencapsulated ammonium phosphate: effect of the shell structure on the thermal stability and fire performance, Polym. Degrad. Stability 95 (9) (2010) 1716–1720. [4] M. Le Bras, M. Bugajny, J.M. Lefebvre, S. Bourbigot, Use of polyurethanes as char-forming agents in polypropylene intumescent formulations, Polym. Int. 49 (10) (2000) 1115–1124. [5] S. Bourbigot, M. Le Bras, S. Duquesne, M. Rochery, Recent advances for intumescent polymers, Macromol. Mater. Eng. 289 (6) (2004) 499–511. [6] J.B. Henderson, J.A. Wiebelt, M.R. Tant, A model for the thermal response of polymer composite-materials with experimental-verification, J. Compos. Mater. 19 (6) (1985) 579–595. [7] M. Bartholmai, R. Schriever, B. Schartel, Influence of external heat flux and coating thickness on the thermal insulation properties of two different intumescent coatings using cone calorimeter and numerical analysis, Fire Mater. 27 (4) (2003) 151–162. [8] K.M. Butler, Physical modeling of intumescent fire retardant polymers, Polym. Foams 669 (1997) 214–230. [9] K.M. Butler, H.R. Baum, T. Kashiwagi, Three-dimensional modeling of intumescent materials, in: Proceedings of the Antec ’96, Plastics—Racing into the Future, Society of Plastics Engineers, vol. 42, Indianapolis, IN, 1996, pp. 3063–3067.

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