Damkohler-number

S-shaped flame temperature response with Damkohler number exhibiting edge propagation characteristics. (From Kim, J. and Kim, J.S., Combust. Theory Model, 10, 21,2006.)... 

Furthermore, analytical solutions of premixed edges were studied and the dependence of edge speed with the Damkohler number was reported [61], in which the edge speed ranged from positive to negative values, in a similar fashion as nonpremixed edge flames. 

In any circumstances, it can be expected that and (5x are algebraic functions of turbulence length scale and kinetic energy, as well as chemical and molecular quantities of the mixture. Of course, it is expedient to determine these in terms of relevant dimensionless quantities. The simplest possible formula, in the case of very fast chemistry, i.e., large Damkohler number Da = (Sl li)/ SiU ) and large Reynolds Re = ( Ij)/ (<5l Sl) and Peclet numbers, i.e., small Karlovitz number Ka = sjRej/Da will be Sj/Sl =f(u / Sl), but other ratios are also quite likely to play a role in the general case. 

For a specific comparison of the two different reactor types, channels of 300 pm diameter were considered. The equivalent pellet size for that case is 675 pm. As a characteristic quantity, the conversion at the reactor exits was computed for different flow velocities and a range of Damkohler numbers spanning three orders of magnitude. The results for the two different reactor types obtained in such a way were practically indistinguishable. This suggests that the different reactors considered in this study are equivalent as far as chemical conversion is concerned. 

The parameter term (k x) which is called Damkohler Number I, is dimensionless and is now the single governing parameter in the model. This results in a model simplification because originally the three parameters, x, k and Cao. all appeared in the model equation. 

With all three programs, vary the Damkohler number. Da over a range from 1 to 500 and explain the results. Note that when Da no longer has any influence on the rate then mixing must be controlling... 

Da Second Damkohler number K l2 ID K = first-order reaction rate constant l = characteristic length D = diffusion coefficient... 

In order to implement the PDF equations into a LES context, a filtered version of the PDF equation is required, usually denoted as filtered density function (FDF). Although the LES filtering operation implies that SGS modeling has to be taken into account in order to capture micromixing effects, the reaction term remains closed in the FDF formulation. Van Vliet et al. (2001) showed that the sensitivity to the Damkohler number of the yield of competitive parallel reactions in isotropic homogeneous turbulence is qualitatively well predicted by FDF/LES. They applied the method for calculating the selectivity for a set of competing reactions in a tubular reactor at Re = 4,000. 

Where dissolution or precipitation is sufficiently rapid, the species concentration quickly approaches the equilibrium value as water migrates along the aquifer the system is said to be reaction controlled. Alternatively, given rapid enough flow, water passes along the aquifer too quickly for the species concentration to be affected significantly by chemical reaction. The system in this case is transport controlled. The relative importance of reaction and transport is described formally by the nondimensional Damkohler number, written Da. 

Now, if the system is observed over a distance scale L, the characteristic time frrans associated with advective transport is simply the time L/vx required for groundwater to traverse distance L. The Damkohler number, the ratio of the two characteristic times,... 

A notable aspect of this equation is that L appears within it as prominently as the rate constant k+ or the groundwater velocity vx, indicating the balance between the effects of reaction and transport depends on the scale at which it is observed. Transport might control fluid composition where unreacted water enters the aquifer, in the immediate vicinity of the inlet. The small scale of observation L would lead to a small Damkohler number, reflecting the lack of contact time there between fluid and aquifer. Observed in its entirety, on the other hand, the aquifer might be reaction controlled, if the fluid within it has sufficient time to react toward equilibrium. In this case, L and hence Da take on larger values than they do near the inlet. 

Fig. 27.2. Concentration of dissolved silica and the quartz dissolution rate along a quartz sand aquifer being recharged at left by rainwater, for the scenario considered in Figure 27.1. Results were calculated assuming a range of flow velocities rapid flow corresponds to a Damkohler number Da less than one, whereas Da is greater than one for slow flow.

Figure 27.2 shows the results calculated for velocities spanning this range. The simulations correspond to Damkohler numbers Da (see Chapter 21) much less than one for rapid flow, to much greater than one when flow is slow. At low Da, transport... 

In dimensionless terms, there is a critical value for S (Damkohler number) that makes ignition possible. From Equation (4.23), this qualitatively means that the reaction time must be smaller than the time needed for the diffusion of heat. The pulse of the spark energy must at least be longer than the reaction time. Also, the time for autoignition at a given temperature T is directly related to the reaction time according to Semenov (as reported in Reference [5]) by... 

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... 

---