Space flame calculation

Figure 2. Space and time scales in the gedanken flame calculation. A naive direct solution of the problem could take 3000 years of computer time. The calculation should be possible in 100 sec.

For 2D and 3D dynamic simulations such on-line reduction are very computationally costly. A less CPU time intensive approach is to pre-define the combustion domains or zones in which a certain sub-set of the detailed mechanism is used. This is often used for diffusion flame calculations where the domains can be defined by the fuel rich and the fuel lean zones. Hence, schemes that find the smallest chemical sub-set locally in time or space have been proposed e.g. by Schwer et al. (Schwer et al., 2003)). Here each computational cell was assigned a certain sub-mechanism based on a set of physical criteria such as temperature, pressure, species concentrations etc. For highly turbulent flames where these criteria can change rapidly and steeply from cell to cell, this method can be demanding. A single criterion was therefore proposed by Lovas et al. (Lovas et al., 2010), where the sub-mechanism was chosen based on mixture fraction alone. This approach will act as example of implementation of adaptive... 

Various calculations of reacting flows, such as perfectly stirred reactors [12], laminar flames [13,14], turbulent flames [15,16], and hypersonic flows [17] have verified the approach presented above. Due to space limitation we shall only present one example, namely a premixed laminar flat flame calculation [13]. It provides a nice, simple test case for the verification of the model. The specific example is a syngas (40 Vol. % CO, 30 Vol. % H2, 30 Vol. % N2)-air system at p = 1 bar, and with a temperature of 290 K in the unburnt gas. The fuel/air ratio is 6/10. The influence of simplified transport models is described elsewhere [13]. Here, for the sake of simplicity, only systems with equal diffusivity shall be considered. In this case a three-dimensional manifold with enthalpy and two reaction progress variables as parameters has been calculated, i.e. the chemistry has been simpli-... 

Step 6 Calculate the location of the flame center, which is treated as the source of all radiation from the flame. Only flames bent over by the wind are considered, since for nearly vertical flames (calm air) the effective center of flame radiation is higher off the ground and therefore not limiting for spacing purposes. 

The cooling effect of the channel walls on flame parameters is effective for narrow channels. This influence is illustrated in Figure 6.1.3, in the form of the dead-space curve. When the walls are <4 mm apart, the dead space becomes rapidly wider. This is accompanied by falling laminar burning velocity and probably lowering of the local reaction temperature. For wider charmels, the propagation velocity w is proportional to the effective flame-front area, which can be readily calculated. On analysis of Figures 6.1.2b and 6.1.3, it is evident that the curvature of the flame is a function of... 

Of course, this is unacceptable. Ideally such a simple calculation should take about 100 seconds (See Figure 3). What are needed are numerical algorithms which have the resolution in time and space only where it is required. Furthermore, these algorithms should be optimized to take advantage of what is known about the physics and chemistry of the problem. This will be discussed further below where it is shown how the application of various numerical algorithms can be used to reduce this flame system to a tractable computational problem. 

In flames, the ratio of concentration sensitivity vs. space variable (distance) functions, where the sensitivities are calculated with respect to any two parameters, are found to be the similar for all concentrations and temperatures of the model. This phenomenon is called the self-similarity of sensitivity functions [70,71]. The reason is that in flames the temperature is the dominant variable and any perturbation in the system affects the concentration-distance functions mainly through the changes induced in the temperature [72]. 

Catalytic reactions were carried out with 2 g catalyst placed in a fixed-bed continuous-flow reactor at the gas space velocity (F/W) of 1440 ml/g h under the reaction pressure of 200 KPa. The products were withdrawn periodically from the outlet of the reactor and analyzed by gas chromatography with a 4 m long squalane column and detected by a hydrogen flame ionization detector. The conversion and selectivity were calculated on the carbon number basis. 

We now wish to derive the potentials due to an electron with charge —e moving with uniform velocity v along the x axis of the inertial flame S introduced in the previous section, i.e. the electron is at rest in the S frame (see figure 3.1). Suppose that we wish to calculate the potentials at the field point (x, y, z) at time t = 0 in S. By (3.183) this corresponds to the space-time point (x, y, z, t ) in S where... 

Figure 16.2.2. Head-space injection of the gaseous sample into the duoniatographic system. Typical chromatogram of class 1 solvents using the conditions described for System A (European Pharmacopoeia method). Flame-ionization detector calculation of H/h for 1,1,1-trichloroethane.

Fig. 6.5 (a) 2D and ID manifolds for the hydrogen flame example. Starting from any point in phase space, the trajectories (dotted lines) quickly approach the 2D manifold (mesh stffface) and then the ID manifold (bold line) and move along it towards the equilibrium point. Reprinted with permission from Davis and Tomlin (2(X)8b). Copyright (2008) American Chemical Society, (b) The collapse of reaction trajectories onto a 2D intrinsic low-dimensional manifold or ILDM (black mesh) for an wo-octane—air system plotted in a projection of the state space into CO2—H2O—H2 concentration coordinates. ID ILDM (purple symbols), OD ILDM (equilibrium, red circle). The coloured lines are homogeneous reactor calculations for different fuels. Reprinted from (Blasenbrey and Maas 2000) with permission from Elsevier... 

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