Enclosure Fire Dynamics Chapter 1: Introduction Chapter 2: Qualitative description of enclosure fires Chapter 3: Energy release rates, Design fires Chapter 4: Plumes and flames Chapter 5: Pressure and vent flows Chapter 6: Gas temperatures (Chapter 7: Heat transfer) Chapter 8: Smoke filling (Chapter 9: Products of combustion) Chapter 10: Computer modeling Each course unit represents breaking down the problem into individual pieces

Overview Post-flashover fires (0,5 – 3 hours of fire) Pre-flashover fires (~ first 0-20 minutes of fire) Goal: Save human lives Energy balance Heat transfer coefficients Calculate gas temp Tg (t) by MQH method Post-flashover fires (0,5 – 3 hours of fire) Goal: Structural fire protection Calculate Tg by method of Magnusson et al Calculate Tg by Eurocode method

Concern is damage to people This is often viewed by fire fighters and they assume it is flashover As the fuel needs to flow longer to mix with sufficient oxygen for combustion, the flames appear to elongate as it travels to find sufficient oxygen to burn

Concern now becomes damage to building

Importance of knowing compartment temperature Life Safety Structural fire protection Results in vent mass flows Spread of smoke away from fire Heating of fuel Activation of detection systems Impact on suppression By fire department or sprinklers

Look at two cases: Pre-flashover Post-flashover Conditions changing with time (short) Derive energy balance based on design fire Two zone model Post-flashover Much longer time frame Conditions generally more steady One zone model Few calculation methods apply to both

Pre-flashover compartment temperature with the MQH method Method of McCaffrey, Quintiere and Harkleroad (MQH) Conservation of energy relation (balance) for a ventilated compartment Temperature is a function of dimensionless variables Experiments used to derive constants Allows simple solution without a computer

Start by looking at an energy balance for a compartment Other terms that we are missing (assume very small) Radiation through opening Energy accumulation in hot gas layer We will use the energy balance again in more detail in Chapter 8

Energy lost through openings (1st term on right hand side) We know: From Chapter 5, calculate vent mass flow: Ideal gas law: But HN is not known, so we write Hn is a function of Tg, Q, Ao and Ho. This function can also take up the constants Also, W Ho^3/2 is the same as Ao Ho^1/2

Energy loss to compartment (2nd term on right hand side) Heat is lost to boundaries by convection and radiation This energy is then conducted into the solid walls, ceiling and floor Define an effective heat conduction factor, hk,to represent all boundaries AT is the boundary surface area without openings AT is the boundary surface area

Effective heat conduction (transfer) coefficient, hk Calculations based on thermal penetration time, tp tp is the time for the unexposed temp to increase to 15% of exposed side temp

Two cases Thermally thin and thermally thick behavior Thermally thin case represents steady heating Thick case represents storing heat Methods in EFD for combining different thickness boundaries and for different materials Thus the effective heat transfer coef is a function of fire duration and material properties and thickness

Put the two parts together Solving for temperature difference is possible, but difficult in this form Express temperature rise with dimensionless variables, then correlate with experiment

Dimensionless temperature Dimensionless from dividing by Ta Substitute in function for mass flow rate Temperature change now given as a function of two groups

Finding function for temperature change Represent function using a power law Values for C, N and M from experiment 100+ tests with different fuels and linings Varied size of room, openings

Correlation of data C = 1.63 N = 2/3 M = -1/3 Calculation starts to over predict temperature above 500 C

Result of correlation Assuming standard properties: LHS Terms First: Ratio of energy released to energy convected Second: Ratio of energy lost to energy convected

Limitations on method Transient and steady fire growth with temperature rise of 20 – 600 oC Method predicts average temperature Mass flows through ventilation openings Two way flow established (after filling period) Well mixed upper layer with uniform temp Compartment not too large or too long (such as a corridor) Test: Height < 2.7 m Area < 12 m2 Fuel controlled burning Heat released inside compartment HRR not growing too fast If fuel controlled, are flames allowed to extend outside compartment? If flames extend outside compartment, it is necessary to modify the HRR to represent burning inside the compartment

Predicting HRR for flashover Set Tg = ~ 500 °C => solve for QFlashover MQH method

Overview Post-flashover fires (0,5 – 3 hours of fire) Pre-flashover fires (~ first 0-20 minutes of fire) Goal: Save human lives Energy balance Heat transfer coefficients Calculate gas temp Tg (t) by MQH method Post-flashover fires (0,5 – 3 hours of fire) Goal: Structural fire protection Calculate Tg by method of Magnusson et al Calculate Tg by Eurocode method

Now look at post-flashover fires Structural design for fire How will we know what the thermal exposure will be over the life of the building? This should be familiar from passive fire protection course What does dashed line represent? HRR changes when fuels move or when ventilation openings are altered, for example

International time-temperature curves Curves are intended to represent maximum exposure that reasonably will not be exceeded over the life of the building

Time-temperature curves NPD=Norwegian petroleum directorate – hydrocarbon fire curve ISO 834 curve on right

Measured compartment temperatures as a function of fuel load density Number in ( ) is fraction of one wall open for ventilation

Standard time-temperature curve (ISO 834) Intended to represent maximum temperatures observed during complete burnout of compartment contents Furnace testing of structural elements follows time-temperature curve Failure also includes allowing fire spread Is this curve conservative? What does it not take into account? Due to rapid rise in temperature, it represents a very severe exposure. It may not be conservative for some occupancies Standard time-temp curve does not take into account Decay Compartment geometry Ventilation openings Fuels Thermal properties

Options for time-temperature curves Use standard time-temperature curve ISO 834 Calculate a design specific time-temperature curve This will be the majority of what remains of this chapter Magnusson et al method Babrauskas method Eurocode method

Background material Enclosure surface area, At [m2] Fire load, Q [MJ] Now includes openings Fire load, Q [MJ] Energy released from all fuels in compartment Fire load density, Q”t [MJ/m2] Q”t = fire load density based on total enclosure surface area, At Surface area used for pre-flashover fires did not include openings

Opening factor and multiple openings Also a function of fuel load and interior surface area Ao = area of opening Ho = height of opening More on this in units 5 and 6

Result, Magnusson method Time-temperature curve is a function of: Fuel load density, Q”t Opening factor, Thermal properties of compartment Solutions given for one type of construction, corrected by Kf factor

Method of Magnusson and Thelandersson Collected many experimentally measured temperatures Numerically solved conservation of energy equation

Final form of Magnusson time-temperature curves

Method of Babrauskas (See page 3-140 in SPFE [2nd]) Factors account for physical phenomenon

Eurocode parametric fire exposure method Heating phase Cooling phase Advantage of natural log function is that you can take the derivative of them easily

Decay period results (400 MJ/m2) Curves of Magnusson, ISO 834, Eurocode and Pettersson Eurocode drops temp down too fast Less agreement during decay period of fires due to complexity of prediction (involves many factors)

Use of models Due to difficulties in estimating compartment fire temperatures, computer models are often used to solve conservation of energy equations The equations given in this unit are good for making initial estimates A lot of money can be saved if temperature is calculated instead of using ISO 834 curve Modeling makes transient calculations much easier.

Any questions? Next unit – Conservation equations