CE 808 : Structural Fire Engineering Ch 3. FIRE AND HEAT V. Kodur, Professor Dept of Civil and Env. Engineering Michigan State University

Ch 3. FIRE AND HEAT Fuels Combustion Fire Initiation Pre-flashover Fires t-squared Fires Basics of Heat Transfer CE 808 – Chapter 3

Fuels - Materials Material available as fuel are part of the building structure, lining materials, or contents of the building All materials are hydrocarbons, their molecules consisting mainly of carbon & atoms, with the addition of oxygen, nitrogen & others in some cases Heat release rates (HRR) from combustion depend on the nature of the burning material, the size of the fire, and the amount of air available calorific value CE 808 – Chapter 3

Fuels - Calorific Value The calorific value or heat of combustion is the amount of heat released during complete combustion of a unit mass of fuel Most solid, liquid and gaseous fuels have a calorific value between 15 and 50 MJ/kg Net calorific values Hc (MJ/kg) for a range of common fuels See distributed Table (Table 3.1 in Text Book) For materials containing moisture the effective calorific value Hc,n (MJ/kg) is Hc,n = Hc (1 - 0.01 mc) - 0.025 mc mc is the moisture content given by mc = 100 md / (100 + md) md is the moisture content as percentage of dry weight CE 808 – Chapter 3

Fuels - Calorific Value For typical dry wood fuel with a moisture content of md = 12% and Hc = 19 MJ/kg mc = 10.7% and Hc,n = 16.7 MJ/kg Max. possible energy, E (MJ), that can be released when fuel burns is the energy contained in the fuel, & is given by: E = M Hc,n M is the mass of the fuel (kg) CE 808 – Chapter 3

Fuels – Fire Load Fire load in buildings is usually expressed as Fire Load Energy Density (FLED) per floor area For each room, FLED - ef (MJ/m2 floor area) is given by: ef = E/Af Af is the floor area of the room Some references express fire load as energy density per total room bounding surfaces - et (MJ/m2 total room surface area) is given by: et = E/At At is the total area of the bounding surfaces of the room (floor, ceiling and walls, including window openings) CE 808 – Chapter 3

Fuels – Fire Load ef is larger than et by the ratio At/Af It is important to know which fuel load density is being used in any given situation Major errors can be caused if the distinction is not clear Results of several fuel load surveys are shown in tables distributed (Appendix B in textbook) CE 808 – Chapter 3

Fuels – Fire Load Design fire loads should be determined in a similar way to design loads (earthquake load vs. extreme likely design fire scenario) should reflect almost the max. fire load expected in building life Both fixed and moveable fire loads should be included Should be less than 10% probability being exceeded in 50 Yrs When fire load is determined from representative surveys, the design load should be the 90-percentile value of surveyed loads (about 1.65 to 2.0 the average value) Therefore, the recommended design fire load is twice the average values given in tables distributed (Appendix B in textbook) CE 808 – Chapter 3

Fuels – Heat Release Rate (HRR) For a fire, the average HRR - Q (MW) is given by: Q = E/t E is the total energy contained in the fuel (MJ) t is the duration of the burning (s) CE 808 – Chapter 3

Combustion - Chemistry Combustion of organic material is a chemical reaction involving oxidation of hydrocarbons to produce water vapour and carbon dioxide Exothermic reaction For example, the chemical reaction for the complete combustion of propane is: C3H8 + 5O2  3CO2 + 4H2O However, in many fires, incomplete combustion occurs leading to production of CO or carbon as soot particles CE 808 – Chapter 3

Combustion - Phase Change & Decomposition Gases can mix with air to burn directly without any phase change Solid and liquid fuels must be converted to the gaseous phase before they can burn Some solid fuels melt when heated Some other fuels, thermally decompose with a transition directly from solid to gaseous phase Ex: thermally decomposition of wood Referred to as pyrolysis for wood CE 808 – Chapter 3

Combustion - Flame Temperature The max. temp. reached in a flame is known as the adiabatic flame temp. Adiabatic flame temp. may be reached in a small region in the flame centre Average temp. of the flame will be considerably less CE 808 – Chapter 3

Combuston - Smouldering Combustion Smouldering is a flameless combustion Ex: burning of a cigarette Slower than flaming combustion & temp. are low & do not affect the structure Very hazardous, specially for sleeping occupants Smoke from smouldering combustion will activate smoke detectors but not heat detectors Smoldering fires – Ground Zero Fires CE 808 – Chapter 3

Fire Initiation - Ignition Ignition occurs when a combustible mixture of gases is heated to temp. that will trigger an exothermic reaction of combustion Ignition almost always requires external heat source Pilot ignition occurs in the presence of a flame or spark Auto-ignition causes a spontaneous ignition which is self heating within solid materials After ignition, initial fire spread occurs from the burning object to adjacent ones Flames tend to spread rapidly on surfaces having high temp. rate increase on exposure to heat flux CE 808 – Chapter 3

Fig. – HRR for furniture items Burning Objects If an object such as a furniture item is ignited and allowed to burn freely in the open, the HRR tends to increase exponentially as the flames get larger & they radiate more heat back to the fuel A peak HRR is usually reached, followed by steady- state burning and eventual decay Fig. – HRR for furniture items CE 808 – Chapter 3

Table: Burning rates for liquid and solid fuels Burning Objects Table: Burning rates for liquid and solid fuels CE 808 – Chapter 3

t-Squared Fires t-squared fires are characterized by a parabolic curve with the HRR proportional to the time squared The t-squared HRR is given by: Q = (t/k)2 = ( t)2 Q is HRR (MW), t is time (s), k is a growth constant (s/MW1/2),  is fire intensity coefficient (MW/s2) CE 808 – Chapter 3

Figure - t-squared fire (Calculation of HRR) t-Squared Fires Figure - t-squared fire (Calculation of HRR) characterized by parabolic curve with HRR proportional to the t2 used to calculate fire growth (design fires) in rooms in the pre-flashover phase CE 808 – Chapter 3

t-Squared Fires - Calculations Figure- HRR for a fire in office furniture with slow, medium and fast fire growth rates – (fire load of 3200 MJ) The peak HRR has been taken as 9MW The furniture item weighs 160kg with a calorific value of 20 MJ/kg, giving a total energy load of 3200 MJ, which is the area under each curve shown CE 808 – Chapter 3

Fire Spread to Other Items t-squared fires are generally used to describe the HRR for burning of a single object Fire can spread from the first burning object to a second object by flame contact or by radiant heat transfer The time to ignition of a second object depends on the intensity of radiation from the flame & distance between objects When the time to ignition of the second object has been calculated, the combined HRR can be added at any point in time to give the total HRR for these two, and subsequent objects This combined curve is the input design fire for room under consideration CE 808 – Chapter 3

Fire Spread to Other Items Fig - t-squared HRR (fire) separately & combined for two objects The first object burns with medium growth rate for 10 min, followed by 1 minute of steady burning at its HRR of 4.0 MW The second object ignites after 3 min, burning with fast growth rate for 4 min followed by steady burning at 2.5 MW for 2 min CE 808 – Chapter 3

Room Fires The t-squared design fires all assume open-air burning with unlimited ventilation, and no suppression by sprinklers or firefighters When these burning objects are in a room they burn differently, with the burning rate enhanced by radiation, but limited by the available ventilation The design fires are used as input to room fire models to calculate fire development CE 808 – Chapter 3

Heat Transfer - Conduction Conduction is the mechanism for heat transfer in solid materials factor in the ignition of solid surfaces, & in the fire resistance of barriers & structural members Thermal properties needed for heat transfer calculations in solid materials include: density,  (kg/m3), specific heat, Cp (J/kg-K), thermal conductivity, k (W/m-K), Also often needed are: thermal diffusivity,  = k/Cp (m2/s), and thermal inertia, kCp (W2s/m4K2) function of temp. CE 808 – Chapter 3

Heat Transfer - Conduction Table - Thermal properties of common materials CE 808 – Chapter 3

Heat Transfer - Conduction In the steady-state situation, heat transfer by conduction is given by: q" = k dT/dx q" is the heat flow per unit area (W/m2) k is the thermal conductivity (W/m-K) T is the temp. (oC or K) x is the distance in heat flow direction (m) CE 808 – Chapter 3

Heat Transfer - Conduction For transient heat flow, a 1-D heat transfer by conduction is given by: 2T/x2 = 1/ T/t t is time (s) &  is thermal diffusivity (m2/s) Materials with low  conduct more heat than materials with high  Equations can be extended to 2-D and 3-D Heat transfer Eqns. by conduction can be solved using: simple formulae use of design charts numerical analysis Refer to textbook for more information on calculation methods CE 808 – Chapter 3

Heat Transfer - Convection Convection is heat transfer by the movement of fluids, either gases or liquids Heat transfer by convection is an important factor in flame spread and in upward transport of smoke and hot gases to the ceiling or out of the window from a room fire Convective heat transfer is usually taken to be directly proportional to the temp difference between 2 materials as q"=hT q" (W/m2) heat flow per unit area h is the convective heat transfer coefficient (W/m2K) T is the temp. difference betn. surface of solid & fluid (oC or K) A typical value of h for fire-exposed str elements is 25 W/m2K CE 808 – Chapter 3

Heat Transfer - Radiation Radiation is the transfer of energy by waves is very important in fires because it is the main mechanism for heat transfer from: flames to fuel surfaces, hot smoke to building objects, & a burning building to an adjacent building The radiant heat flux q" (W/m2) at a point on a receiving surface is given by q" =  e  Te4  - Configuration or view factor e - Emissivity of the emitting surface  - Stefan-Boltzmann constant (5.67 x 10-8 W/m2K4) Te - Absolute temp. of the emitting surface (K) CE 808 – Chapter 3

Heat Transfer - Radiation The resulting heat flow q" (W/m2) from the emitting surface to the receiving surface is: q" =    (T e4 - T r4) Tr - absolute temperature of the receiving surface (K), and  - resultant emissivity of the two surfaces (range from 0 to 1), given by:  = 1 / (1/e + 1/r -1) r - emissivity of the receiving surface The view factor  is a measure of how much of the emitter is seen by the receiving surface CE 808 – Chapter 3

Heat Transfer - Radiation In the case of 2 parallel surfaces, view factor, , can be expressed as  = 1/90 [ x/1+x2 tan-1(y/1+x2) + y/1+y2 tan-1(x/1+y2)] x=H/2r, y=W/2r, H and W are height & width of rectangular source Fig – View factor - Emitting & receiving surfaces CE 808 – Chapter 3

Example 3.1 (a) Calculate the average HRR when 200 kg of paraffin wax burns in half an hour Mass of fuel M = 200 kg Calorific value Hc = 46 MJ/kg Energy contained in the fuel E = M Hc = 200 x 46 = 9200 MJ Time of burning t = 1800 s HRR Q = E/t = 9200/1800 = 5.11 MW CE 808 – Chapter 3

Example 3.1 (b) Calculate the fuel load energy density in an office 5 m x 3 m containing 150 kg of dry wood and paper & 75 kg of plastic mater-ials. Assume calorific values of 16 MJ/kg & 30 MJ/kg respectively. Mass of wood Mwood = 150 kg Calorific value Hc,wood = 16 MJ/kg Energy contained in the wood Ewood = M Hc = 150 x 16 = 2400 MJ Mass of plastic Mplastic = 75 kg Calorific value Hc,plastic = 30 MJ/kg Energy contained in plastic, Eplastic = M Hc = 75 X 30 = 2250 MJ Total energy in fuel E = Ewood + Eplastic = 2400 + 2250 = 4650 MJ Floor area Ar = 5 x 3 = 15m2 Fuel load energy density ef = E/Af = 4650/15 = 310 MJ/m2 CE 808 – Chapter 3

Example 3.2 A room in a storage building has 2000 kg of polyethylene covering the floor. Calculate the HRR & duration of burning after the roof collapses in a fire. The room is 6.0 m by 10.0 m. Use the open-air burning rates from Table 3.2 in textbook. Mass of polyethylene M = 2000 kg Calorific value Hc = 43.8 MJ/kg Energy content of fuel E = M Hc = 2000 x 43.8 = 87600 MJ Surface burning rate q = 0.031 kg/s/m2 (Table 3.2) Floor area Af = 6.0x10.0 = 60.0m2 Specific HRR Qs = qHc = 0.031 x 43.8 = 1.36 MW/m2 Total HRR Q =Qs Af = 1.36x60 = 81.6 MW Duration of burning t = E/Q = 87600/81.6 = 1074 sec = 18 min. CE 808 – Chapter 3

Example 3.3 (a) Calculate the HRR for 160 kg of office furniture with an average calorific value of 20 MJ/kg, if it burns as a 'fast' t2-fire with a peak HRR of 9.0 MW. Mass of fuel M = 160 kg Calorific value Hc = 20 MJ/kg Energy contained in fuel E = M Hc = 160 x 20 = 3200 MJ Growth factor for fast fire k = 150 s/MW Peak HRR Qp = 9.0 MW Time to reach peak heat release t1 =kQp= 150x9 = 450s Energy released in time t1 E1 = t1 Qp/3 = 450 x 9/3 = 1350MJ E1 < E so there is steady burning CE 808 – Chapter 3

Example 3.3 Energy released in steady burning E2 = E - E1 = 3200 -1350 = 1850 MJ Duration of steady burning tb = E2 / Qp = 1850/9 = 206 s See Fig. for HRR curve for this “fast” fire CE 808 – Chapter 3

Example 3.3 (b) Repeat calculations in (a) for a 'slow' t2 fire growth rate. Growth factor for slow fire k = 600 s/MW Time to reach peak HRR t1 = kQp = 600 x 9 = 1800s Energy released in time t1 E1 = t1 Qp/3 = 1800 x 9/3 = 5400 MJ E1 > E, so fire does not reach steady-burning time for all fuel to burn tm =(3E k2)1/3 = (3 X 3200 X 6002)1/3 = 1512s Heat release at time t1 Qm = (tm/k)2 = (1512/600)2 = 6.3 MW See Fig 3.5 in textbook for HRR curve (shown as the 'slow' fire) CE 808 – Chapter 3

Example 3.4 (a) Calculate the steady-state heat transfer through a 150 mm thick concrete wall if the temperature on the fire side is 800°C & the temperature on the cooler side is 200°C. Wall thickness x = 0.15m Temperature difference T = 800 - 200 = 600°C = 600 K Temperature gradient dT/dx = 600/0.150 = 4000 K/m Thermal conductivity k = 1.0 W/m-K (from Table 3.4 in textbook) Heat transfer q" = k dT/dx = 1.0 x 4000 = 4000 W/m2 = 4 MW/m2 CE 808 – Chapter 3

Example 3.4 (b) Calculate the convective heat transfer coefficient on the cool side of the wall if the ambient temperature is 20°C and all the heat passing through the wall is carried away by convection. Temperature of wall Tw = 200°C Ambient temperature Ta = 20°C Temperature difference T = Tw- Ta = 200-20 = 180°C= 180K Heat transfer q" = 4000 W/m2 Convective heat transfer Coefficient h = q” / T = 4000/180 = 22.2 W/m2K CE 808 – Chapter 3

Example 3.5 Calculate the radiant heat flux from a window in a burning building to the surface of an adjacent building 5.0 m away. The window is 2.0 m high by 3.0 m wide and the fire temperature is 800°C. Assume an emissivity of 0.9. Emitter height H = 2.0 m Emitter width W = 3.0 m Distance from emitter r = 5.0 m CE 808 – Chapter 3

Example 3.5 Height ratio x = H/2r = 2/(2 x 5) = 0.20 Width ratio y = W/2r = 3/(2 x 5) = 0.30 Configuration factor  = 1/90 [x/1+x2 tan-1(y/1+x2) + y/1+y2 tan-1(x/1+y2)] = 0.0703 Emitter temperature T = 800°C = 1073K Emissivity  = 0.9 Stefan-Boltzmann constant  = 5.67x10-8 W/m2K4 Radiant heat flux q” =    T4 = 0.0703 x 0.9 x 5.6 x 10-8 x 10734/1000 = 4.69 kW /m CE 808 – Chapter 3