Mean heat release rate

The values of laminar flame speeds for hydrocarbon fuels in air are rarely greater than 45cm/s. Hydrogen is unique in its flame velocity, which approaches 240cm/s. If one could attribute a turbulent flame speed to hydrocarbon mixtures, it would be at most a few hundred centimeters per second. However, in many practical devices, such as ramjet and turbojet combustors in which high volumetric heat release rates are necessary, the flow velocities of the fuel-air mixture are of the order of 50m/s. Furthermore, for such velocities, the boundary layers are too thin in comparison to the quenching distance for stabilization to occur by the same means as that obtained in Bunsen burners. Thus, some other means for stabilization is necessary. In practice, stabilization... 

The absolute overpressure is different from the overpressure of a safety valve which is expressed in terms of gauge pressures. It was originally recommended by Leung131 that the arithmetic mean be used for the heat release rate per unit mass ... 

When using the method, it is essential that the heat release rate per unit mass due to the runaway reaction, q, is measured in an suitable calorimeter (see Annex 2) which simulates the external heat input. If this is not the case, then q can be underestimated since the external heating means that the degree of conversion of the reaction is less (and the reaction rate higher) at any given temperature compared with the adiabatic situation. 

From the technology of combustion we move to the molecular mechanism of flame propagation. We shall give a molecular-kinetic expression for the heat release rate by calculating the frequency v of collisions of fuel molecules with other molecules (v is proportional to the molecular velocity and inversely proportional to the mean free path), further taking into account that only a small (1/j/) part of all collisions are effective. The quantity 1/v—the probability of reaction taken with respect to a single collision— depends on the activation heat of an elementary reaction event, as well as on the fraction of all molecules comprised of those radicals or atoms by means of which the reaction occurs. The molecular-kinetic expression for the coefficient of thermal conductivity follows from formulas (1.2.4) and (1.2.3). 

Heat cannot be directly measured. In most cases heat measurement is made indirectly by using temperature measurement Nevertheless, there are some calorimeters able to measure directly the heat release rate or thermal power. Calorimetry is a very old technique, which was first established by Lavoisier in the 18th century. In the mean time, a huge choice of different calorimeters, using a broad variety of designs and measurement principles, were developed. 

Therefore the sensitivity usually ranges between 2 and 20Wkg 1. This heat release rate corresponds to a temperature increase rate of about 4 to 40 °C hour-1 under adiabatic conditions. This also means that an exothermal reaction is detected at a temperature where the time to explosion (TMRJ) is in the order of magnitude of one hour only. 

The Semenov criterion means that for a cooling medium temperature above 10 °C, the initial heat release rate of the reaction cannot be removed by the cooling system. This delivers a broad enough margin for performing the reaction with a cooling system temperature below this level. This is a static criterion. 

The Villermaux criterion and the Da/Si criterion are dynamic stability criteria, meaning that with a cooling medium temperature above the limit level, 20 resp. 30 °C, the reactor will be operated in the instable region and present the phenomenon of parametric sensitivity. If instead of B12, B is used, both criteria lead to the same result. This should not be surprising since they derive from the same heat balance considerations, that is, the heat release rate of the reaction increases faster with temperature than the heat removal does. 

Thus, there are two reasons for modifying the process the maximum heat release rate of the reaction and the accumulation of reactants are too high. There are different means for solving the problem first is to increase the feed time (Figure 7.8), the second to increase the reaction temperature (Figure 7.9). This worked example is continued in Section 7.8.2. 

For cases where the secondary reaction plays a role (class 5), or if the gas release rate must be checked (classes 2 or 4), the heat release rate can be calculated from the thermal stability tests (DSC or Calvet calorimeter). Secondary reactions are often characterized using the concept of Time to Maximum Rate under adiabatic conditions (TMRad). A long time to maximum rate means that the time available to take risk-reducing measures is sufficient. However, a short time means that the... 

An alternative method graphically determines the slope in an Arrhenius plot The natural logarithm of the heat release rate is plotted as a function of the reciprocal temperature (in K). Hence, it can be verified that the points obtained are on a straight line, meaning that they follow Arrhenius law and the slope corresponds to the ratio E/R that delivers the activation energy. In Figure 11.5, the abscissa is... 

Consider lkg/s of coal that is combusted with an adequate amount of air (approximately zero exergy contribution). The rate at which exergy flows into the system is therefore 23,583 kW. The combustion releases heat, namely, at a rate of 21,860 kW at a temperature T. Since we have created a heat source at temperature T, it is straightforward to compute the work potential (exergy) of this heat source. All we need to do is multiply the heat release rate (21,860 kW) by the Carnot factor 1 - (T0/T). This means that if the combustion takes place at temperature T = 1200 K for a fluidized bed reactor (Table 9.1), the efficiency of the combustion alone is combustion = (21,860/23,583) [1 - (T0/T)] = 0.93 [1 - (T0/T)] = 0.93 [1 - (298.15/1200)] = 0.7 This means that already 30% of the maximum work has been lost We summarize this simplified analysis in Figure 9.15. 

They found the heat release rate to be proportional to the product [H] [O21 [H2O], and the dependence of H on pressure and mass flow to be also consistent with the removal of H by reaction (iv). Similar conclusions about the recombination were reached by Getzinger and Schott [181] from shock tube experiments, in which OH concentrations were measured and used to calculate total radical concentrations by means of the partial equilibrium assumption. 

Caprio et al. [18] measured heat release rates from i-butane oxidation at 100 kPa in the reactant mixture [i-C4Hio] [O2] [N2] = 1 2 1 (Fig. 6.6). A considerably higher heat release rate than that from propane occurred in this system despite the lower partial pressure of reactant. It seems likely that the differences in residence times in the respective experiments is contributory since variations in the heat release rate from i-butane oxidation were obtained when the mean residence time was changed [18]. However, Lignola et al. [47] showed that, at constant tres, the heat release rate from primary reference fuel mixtures, comprising i-CgHig and n-C7H16, depended on the proportions of the fuel components (Fig. 6.6). 

Further research should be conducted toward establishing a better means to categorize the true fire hazard of all flammable and combustible liquids. The flash point, and in some cases boiling point, are measured values that are used for the current classification system. Additional properties, such as viscosity, dissolved combustible solids, and heat of combustion or heat release rate data should be included in a more comprehensive system. 

These heats of reaction become perceptible in practice in high heat release rates, which is of safety technical significance. But two further special effects have to be accounted for in polymerization reactions. These are on one hand an extraordinary dynamics in the thermal power, which means very strong time dependent changes in the second derivative of the total heat output with respect to time, and on the other hand an enormous dynamic change in the physicochemical properties of the reaction mixture in the course of the reaction. The reaction system has to be adequately designed and safety technically evaluated in respect to both effects. 

In this model, the current due to convective motion of the melt has been neglected, because the magnetic Reynolds number for this system is of the order of 10, which means that the charge transported by convection is much smaller than the diffusive current. The electric field intensity, E, can be used to calculate the local heat release rate in the slag or bullion by Joule heating according to the equation ... 

The heat release rate is equal to the Heat Release Parameter (HRP) times the net heat flux [Eq. (53.22)]. Decrease in the HRP value would decrease the heat release rate. The HRP value can be decreased by decreasing the heat of combustion and/or increasing the heat of gasification by various chemical and physical means. An examination of the data in Table 53.9 for heat of combustion show that introduction of oxygen, nitrogen, sulfur, halogen, and other atoms into the chemical structures of the polymers reduces the heat of combustion. For example, the heat of combustion decreases when the hydrogen atoms attached to... 

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