Average rates of heat release

In view of the results just given, we might guess that local average rates of chemical heat release in turbulent diffusion flames are calculable in some fashion from P(Z). However, this is not possible even in principle for equilibrium flows. As equilibrium is approached, the chemical production terms in the equations for species conservation become indeterminate, involving differences of large numbers that cancel (for example, see Section B.2.5.2). A more circuitous route is therefore needed to find the average rate of heat release [15], [20], [27], [28]. The necessary expressions will be developed here. 

Near conditions of chemical equilibrium, averages involving are best computed from the right-hand side of equation (44). Under assumptions 1, 2, and 3 of Section 1.3 and the approximation of equal binary diffusion coefficients, equation (44) becomes 

In view of equation (1-1) and equation (3-71), the quantity in the square brackets in equation (46) vanishes. Therefore, in a turbulent flow under the given approximations, the local, instantaneous rate of production of species i per unit volume is  

Multiplication by heats of formation and summation over i provides a similar expression for the local, instantaneous rate of heat release. 

By introducing the heat of formation per unit mass for each species i at temperature T(Z), say /if, we may express the local, instantaneous rate of heat release per unit volume as g so that the average rate of 

---

Leung s method (as given in equation (6.5) below) is applicable if all the above assumptions are true. Assumption (d) above, regarding the use of an average rate of heat release, tends to be the most limiting in terms of the maximum difference that can be allowed between the relief pressure and the maximum pressure. The absolute overpressure (often referred to simply as the "overpressure") has been sometimes used to characterise this. This is given by ... 

Average rate of heat release (Av. RHR, 3 min) is the average value of heat release during the period between ignition and three minutes after ignition. This is thought to correlate best with the heat release in a room burn situation, where not all of the material is ignited at the same time. 

The Cone calorimeter yields smoke results which have been shown to correlate with those from full scale fires [10, 15-18]. The concept of a combined heat and smoke release measurement variable for small scale tests has been put into mathematical terms for the cone calorimeter smoke parameter (SmkPar) [10]. It is the product of the maximum rate of heat release and the average specific extinction area (a measure of smoke obscuration). The correlation between this smoke parameter and the smoke obscuration in full scale tests has been found to be excellent [10]. The corresponding equation is ... 

Note TTI, time to ignition PHRR, peak of heat release rate MAHRE, maximum average rate of heat emission THR, total heat release EHC, effective heat of combusion TSR, total smoke released. 

The mechanism of sound amplification by heat release was understood by Rayleigh [51]. Qualitatively, if we erroneously neglect any velocity changes just to get a quick result, then equation (10) is = pp /(2y) and equation (4-54) is Dp/Dt — a Q/(CpT where Q denotes the rate of heat release per unit volume multiplying the second equation by p /y and averaging over a cycle, by use of the first equation, we obtain... 

Fig. 71. Average temperature distribution over the combustion zones of the mixture Nb+xB, rate of heat release

Smoke parameter The product of the average specific extinction area and the peak rate of heat release. This parameter indicates the amount of smoke generated MW/kg... 

The rate of heat release during the Initial stages of fire exposure is considerably less, however, for treated wood than for untreated wood. Brenden (56), using the FPL rate of heat release method, obtained a maximum heat release rate of 611 Btu per square foot per minute for untreated 3/4-lnch Douglas-flr plywood, with an average release rate of 308 Btu per square foot per minute for the first 10 minutes. Fire-retardant-treated Douglas-fir plywood, with 3.6 pounds per cubic foot dry chemical and a reported flame spread of 25 to 28, had a maximum heat release rate of 132 Btu per square foot per minute at 42 minutes and an average rate of 16 Btu per square foot per minute for the first 10 minutes. 

The effect of the additives on the oxygen index of PMMA, PS and nylon-6, 6 has also been measured. [227). The results are shown in Table 5.5. The trend in oxygen index response for PMMA and PS is similar to the trend in the peak and average heat release rate data from the cone calorimeter. Scung reports similar results fo r polypropylene with additives or fillers, in their comparison between cone calorimeter and traditional tests (oxygen index, glow wire test, etc.) [229]. The correlation is very poor, however, between the LOI and rate of heat release for nylon-6,6 with silica gel / KjCOj additives. 

Rate of heat release Average value of heat release rate during a specified period of time. This value correlates with heat release in a room bum situation where all of the material is not ignited at the same time kW/m ... 

---