Combustion reference velocity

Premixed flames are waves of combustion (for example, see [PRU 13]), whose reference velocity (that of the adiabatic planar flame) can quite easily be calculated on the basis of the thermodynamic characteristics of the constituent parts, as long as we are deahng with flames with high activation energy. Here, we shall limit ourselves to the study of the effects of gravity and of a centrifugal acceleration field on such flames, and primarily on their res dting frequency of oscillation. 

Airborne particulate matter may comprise liquid (aerosols, mists or fogs) or solids (dust, fumes). Refer to Figure 5.2. Some causes of dust and aerosol formation are listed in Table 4.3. In either case dispersion, by spraying or fragmentation, will result in a considerable increase in the surface area of the chemical. This increases the reactivity, e.g. to render some chemicals pyrophoric, explosive or prone to spontaneous combustion it also increases the ease of entry into the body. The behaviour of an airborne particle depends upon its size (e.g. equivalent diameter), shape and density. The effect of particle diameter on terminal settling velocity is shown in Table 4.4. As a result ... 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

The flow involves fuel, F, issuing from a central slot of width D with an oxidizer, O, co-flow with both streams at the reference temperature, Tq. A global single-step, irreversible, exothermic chemical reaction of the type F + rO —> (1 -f r)P with an Arrhenius reaction rate coefiicient is assumed. A hot layer of combustion products, P, at the inlet serves to separate the fuel and oxidizer streams and acts as an ignition source. The inlet conditions for the velocity, temperature, and composition are shown in Fig. 10.2. The ratio of the inlet velocities of the fuel to oxidizer streams is chosen as 4. Inlet velocity forcing is used to induce early roll-up and pairing of the jet shear layer vortices. 

The quantity, h, in Equation 5 is not likely to be greatly different from its value in a plane adiabatic combustion wave. Taking x as the coordinate normal to such wave, h becomes the integral of the excess enthalpy per unit volume along the x-axis, so that the differential quotient, dh/dx, represents the excess enthalpy per unit volume in any layer, dx. Assuming the layer to be fixed with respect to a reference point on the x-axis, the mass flow passes through the layer in the direction from the unbumed, w, to the burned, 6, side at a velocity, S, transporting enthalpy at the rate Sdh/dx. Because the wave is in the steady state, heat flows by conduction at the same rate in the opposite direction, so that... 

In a first approximation, for the dimensions of the radiating layers with which we must work, we may consider that each element of volume radiates independently of the others, and we thus have the conditions to which the calculations of the previous section refer. For mixtures of carbon monoxide, in which the flame velocity has been studied in detail, we carried out detailed calculations of the influence of radiation on the combustion temperature. 

Figure 5-23 has been used to correlate furnace performance data for a multitude of industrial furnaces and combustors. Typical operational domains for a variety of fuel-fired industrial furnaces are summarized in Table 5-7. The WSCC approach (or speckled furnace model) is a classic contribution to furnace design methodology which was first due to Hottel [op. cit.]. The WSCC model provides a simple furnace design template which leads to a host of more complex furnace models. These models include an obvious extension to a tanks-in-series model as well as multizone models utilizing empirical cold-flow velocity patterns. For more information on practical furnace design models, reference is made to Hottel and Sarofim (op. cit., Chap. 14). Qualitative aspects of process equipment have been treated in some detail elsewhere (Baukal, C. E., ed., The JohnZink Combustion Handbook, CRC Press, Boca Raton, Fla., 2001). 

If we consider a combustion wave as an infinite plane moving through a reaction system, then with respect to the plane itself considered as stationary the unburiied gases move toward it at a velocity while far behind it the burned gases leave with a velocity Vh- The difference in velocities is due to the difference in densities of the burned and unburned gases, p and pw. The law of conservation of mass requires that the mass flow rate across any surface be constant, so that, if v is the linear gas velocity at any point with reference to the stationary flame front, the mass velocity Th = pv constant at every point and, in particular, far from the flame front on either side... 

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