Critical Damkohler number

For the rectangular silo, we compute the corresponding critical Damkohler number,... 

Applying Equations (5.21) to the adiabatic time corresponding to the critical Damkohler number, and realizing for a three-dimensional pile of effective radius, r,. A 3 (e.g. Sc = 3.32 for a sphere for Bi —> oo), then we estimate a typical ignition time at 6 = Sc 3 of... 

From the boundary conditions, show the dimensionless parameters that the critical Damkohler number will depend on. 

The flame lift-off height, which is related to the ignition distance, was inversely affected by the excitation frequency. Since the flow time scale decreased with increasing frequency, the data were plotted as a function of the Damkohler number in Fig. 29.14, where the characteristic flow time scale was estimated by large-eddy turnover time as 1/17 and the characteristic chemical reaction time was computed using an ignition delay model [21] for ethylene jet. While the results did not show any evidence of critical Damkohler number, the range... 

As can be seen from Fig. 4.7, the kinetic tangent pinch point at the critical Damkohler number Dar = 0.166 has an important role for the topology of the maps. This is also reflected by the feasibility diagrams given in Fig. 4.8(a-c). In Fig. 4.8(c), the stable node branch at positive Damkohler numbers are collected from the singular point analyses of the reactive condenser (Fig. 4.8(a)) and the reactive reboiler... 

Figure 4.33 illustrates the PSPS and bifurcation behavior of a simple batch reactive distillation process. Qualitatively, the surface of potential singular points is shaped in the form of a hyperbola due to the boiling sequence of the involved components. Along the left-hand part of the PSPS, the stable node branch and the saddle point branch 1 coming from the water vertex, meet each other at the kinetic tangent pinch point x = (0.0246, 0.7462) at the critical Damkohler number Da = 0.414. The right-hand part of the PSPS is the saddle point branch 2, which runs from pure THF to the binary azeotrope between THF and water. 

Other criteria can be used to establish the extinction condition and that are partially equivalent to the critical Damkohler number. Such criteria are a critical mass transfer numbers (BCI) [21,32], critical mass flux of fuel [2,6,28] or critical temperatures (Ta) [2,5,29-31], The critical mass transfer number has a direct influence over the flame temperature, and thus, represents the link between the condensed phase (i.e., production of fuel) and the chemical time. The critical mass flux operates under the same principle, but assumes a consistent heat input. Combustion reactions generally have high activation energy, therefore, the reaction can be assumed to abruptly cease when the temperature reaches a critical value (Tcr). 

Again, there is a main transition at a critical Damkohler number, Da = Dac. For smaller values of Da the initial perturbation is quickly diluted and the activator decays to the C state, as in the bistable case. The same behavior is observed when the initial perturbation is not sufficiently large. For Da > Dac the perturbation grows as in the bistable case, forming a growing filament that eventually fills the whole system (in the closed flow case), or covers the unstable manifold of the chaotic saddle (in open flows). The filament consists now of a pulse of the C concentration, with a maximum close to the excited state, and accompanied by a smaller pulse of C2. In the closed... 

For n = 1, y can be calculated from (5.15). depends on the kinetic parameters (Da, n) as well as on thermodynamic parameters K, a) of the system. Fig. 5.8 illustrates how the minimum reflux ratio varies with the Damkohler number for different reaction orders n. Qualitatively, decreases hyperbolically with increasing Da number. Multiple pinch points are possible for negative reaction orders within a certain Da window due to multiple intersections of the reboUer operating line with the VLF line. At l mm = the critical Damkohler number, Da n, — tP (5.12) is recovered. At Da = the smallest possible reflux ratio R it is obtained, which only depends on thermodynamic parameters besides the product specification xP... 

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