Thin reaction zone

Figure 5.17. A laminar diffusion flamelet occurs between two regions of unmixed fluid. On one side, the mixture fraction is unity, and on the other side it is null. If the reaction rate is localized near the stoichiometric value of the mixture fraction st, then the reaction will be confined to a thin reaction zone that is small compared with the Kolmogorov length scale.

For infinitely fast kinetics, then, the temperature profiles form a discontinuity at the infinitely thin reaction zone (see Fig. 6.11). Realizing that the mass burning rate must remain the same for either infinite or finite reaction rates, one must consider three aspects dictated by physical insight when the kinetics are finite first, the temperature gradient at r = rs must be the same in both cases second, the maximum temperature reached when the kinetics are finite must be less than that for the infinite kinetics case third, if the temperature is lower in the finite case, the maximum must be closer to the droplet in order to satisfy the first aspect. Lorell et al. [22] have shown analytically that these physical insights as depicted in Fig. 6.15 are correct. 

Figure 6.3a shows the idealized sketch of concentration profiles near the interface by the 1 latta model, for the case of gas absorption with a very rapid second-order reaction. The gas component A, when absorbed at the interface, diffuses to the reaction zone where it reacts with B, which is derived from the bulk of liquid by diffusion. Ihe reaction is so rapid that it is completed within a very thin reaction zone this can be regarded as a plane parallel to the interface. The reaction product diffuses to the liquid main body. The absorption of CO2 into a strong aqueous KOH solution is close to such a case. Equation 6.21 provides the enhancement... 

For steady-state diffusion flames with thin reaction sheets, it is evident that outside the reaction zone there must be a balance between diffusion and convection, since no other terms occur in the equation for species conservation. Thus these flames consist of convective-diffusive zones separated by thin reaction zones. Since the stretching needed to describe the reaction zone by activation-energy asymptotics increases the magnitude of the diffusion terms with respect to the (less highly differentiated) convection terms, in the first approximation these reaction zones maintain a balance between diffusion and reaction and may be more descriptively termed reactive-diffusive zones. Thus the Burke-Schumann flame consists of two convective-diffusive zones separated by a reactive-diffusive zone. 

Equation (77) and (dT/dx) = Q+ = 0 provide first approximations to the results obtained by a more formal derivation of jump conditions across the thin reaction zone. Equation (56) applies on each side of the reaction zone in this three-zone problem. To the lowest order in the ZePdovich number, T remains constant for x > 0. The problem for x < 0 becomes identical to that described by equations (56)-(58), with the replacements E, = EJ 2R ... 

Combustion with a thin reaction zone (discussed earlier), where T =7 c=7 o+0/Cp, and for which the combustion velocity is determined by the adiabatic combustion temperature... 

From classic combustion theory (Zeldovich et ai, 1985), the following two conditions must be satisfied for a constant pattern combustion wave with thin reaction zone to be self-propagating ... 

Assuming the background gas species (i.e., the gas species which is not fuel, oxidizer, or product) is stagnant and that the reaction is confined to a thin reaction zone, the total mass-averaged gas mixture velocity,... 

We are interested in reaction-zone length because it appears to be the major parameter controlling detonation velocity in the nonideal detonation region. It appears that explosives with thick reaction zones have a larger effect on detonation-velocity/diameter and failure diameters than explosives with thin reaction zones. 

A steady-state is established—a thin reaction zone is embedded in a thicker diffusion /one (Figure 7..30 see Figure 7.29). over which reactant concentrations vary from bulk values tit the outer edges to low ones in the retiction zone. 

For a non-premixed flame, the relatively thin reaction zone is viewed as a collection of laminar flamelets subject to turbulence fluctuations. The chemical reactions within a flamelet can be treated as a locally one-dimensional phenomenon that depends on the fuel-oxidizer mixture. This mixture is expressed in terms of the mixture fraction... 

The immediate brick hot face was covered with a 1-2 mm thin reaction zone. Within this area the magnesia component is completely dissolved, only some chromite relics are still visible. Below the reaction zone a deep reaching infiltration and corrosion of the brick microstructure can be observed. The lowest infiltration of the brick microstructure was observed for RADEX 0X6 COMPACT and the highest for RADEX FM5 (see also Table I). 

In case of the alumina-chromia brick RESISTAL RK30SR (Fig. 5) infiltration of the microstructure can be traced over the whole polished section (0-20 mm fi-om the hot face). Nevertheless the highest microstructural changes were observed in the area 0-2 mm from the hot face. In that brick area pore filling infiltration, recrystallization of Cr-corundum bearing matrix, corrosion of Zr-mullite and formation of Mg-Fe-Al-Cr-oxide took place. The immediate hot face is covered with a 1-2 mm thin reaction zone. In the infiltrated brick microstructure cracks formed parallel but also vertical to the hot face can be observed. Cracks are partly filled with slag. 

The TAP theory developed up to now is linear and explains the many advantages of the Laplace-domain technique where obtaining exact and interpretable expressions is concerned. In the special case of TZTRs, it is possible to drop the requirement of linearity of the reaction and to reconstruct, purely from observed outlet fluxes, the temporal evolution of the concentrations and reaction rate in the thin reaction zones, without any a priori assumption of its linearity. The method used is called the Y procedure, in reference to the Cyrillic letter fl, an inverted R, for rate, which by a happy coincidence is also the first letter of the Roman surname of its inventor, G.S. Yablonsky. We consider the three-zone, TZTR (see Fig. 5.6), and write out the equations obtained from the zone transfer matrices as follows. 

In the thin reaction zone, the rate of consumption R satisfies... 

This concentration profile is illustrated in Fig. 2.31 as a fimction of the Thiele modulus 3>. From this diagram we note that when <1> is small, concentration profiles are fairly shallow, since the entire layer is being used. However when 4> is large, the concentration of substrate falls rapidly with distance into the polymer film. The reaction is essentially complete within a thin reaction zone (thickness 2fjt) near the polymer/solution interface. 

Daniele S, Mantzaras J, Jansohn P, Denisov A, Boulonchos K Flame front/turbulence interaction for syngas faeb in the thin reaction zones regime turbulent and stretched laminar flame speeds at elevated pressnres and temperatmes, J Fluid Mech 724 36-68, 2013. 

Bieniasz LK (1994) Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations. Part 4. The adaptive moving-grid solution of one-dimensional fast homogeneous reaction-diffusion problems with extremely thin reaction zones away from the electrodes. J Electroanal Chem 379 71-87... 

A constant average effective diffusivity and specific surface area may be used within the thin reaction zone. 

On the other hand, Avedesian and Davidson (33) suggested that O2 and CO bum rapidly in a very thin reaction zone surromding the particle. Carbon monoxide produced at the surface diffuses out toward the reaction zone while O2 from the main stream... 

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