Chemical source term reaction rate functions

Note that because the columns of T happen to be orthogonal, the linear transformation matrix results in a diagonal form for MT. The reaction rate functions in the transformed chemical source term then act on each of the transformed scalars individually.21... 

Chemical reactions for which the rank of the reaction coefficient matrix T is equal to the number of reaction rate functions R, (i. e 1,..., I) (i.e., Nr = I), can be expressed in terms of / reaction-progress variables Y, (i. e 1,...,/), in addition to the mixture-fraction vector . For these reactions, the chemical source terms for the reaction-progress variables can be found without resorting to SVD of T. Thus, in this sense, such chemical reactions are simple compared with the general case presented in Section 5.1. 

As discussed in Section 5.1, the chemical source term can be written in terms of reaction rate functions A>, f0). These functions, in turn, can be expressed in terms of two nonnegative functions, (5.6), corresponding to the forward and reverse reactions ... 

In the reaction region the chemical source terms appear. The structure of this region is illustrated in Fig. 25.3, where it is seen that the limit 6 < p, < e is the one considered here. All three of these small parameters are related to appropriate Damkohler numbers [44]. The RRA analysis [44] results in predictions of peak temperature as a function of strain rate, shown in Fig. 25.4. The excellent agreement here is important for being able to calculate contaminant production with good accuracy. Figure 25.5 shows the sufficient agreement obtained for important radicals as well. 

The photodissociation rate coefficients are included as source and sink terms in a system of time-dependent continuity equations for the atmosphere. Modem values for vertical (eddy) diffusion and solar photon flux are utilized. The system of 2nd-order ordinary differential equations is solved by integration, and yields chemical species abundances as a function of time and altitude. The isotope atmospheric chemistry includes only SO2 isotopologue photodissociation reactions and production of SO isotopologues. Additional isotopic reactions such as SO2 oxidation by OH, SO photolysis, SO disproportionation during self-reaction, and SO dimmer formation, have been neglected. My objective here is to focus only on SO2 photolysis as a S-MIF mechanism. 

It can happen that our information is limited and the detailed chemical components balance not needed. Then only heat and mass balances are set up see Section 5.4. A typical example is a heat exchanger network. In the equations (5.7.11), the quantities (5.7.9) are approximated as functions of temperature only, say h (T ) in stream j. Formally, we can consider in addition certain source terms s n) in some nodes n e T , for example due to heats of reactions, a priori assessed or regarded as unknown p2U ameters to be computed from the set of constraints (given measured values of mass flowrates and temperatures). For example in a heat exchanger network, P ) = (P-Tq) is the sensible heat of stream y, with temperature P, specific heat cj, and reference temperature. We introduce the vectors hs of components hi, j e, and h of components for j 6 J (5.4.8), then the vectors (5.4.9) of components hi (j e J ) and h (5.4.10) of components for j e J the quantity /ij = is the heat flowrate in material stream j, with heat content factor hi. Finally s is the vector of components s(n), n g T . Then the heat and mass balance is represented by the equations (5.4.6). Again, the heat transfer rates through dividing walls can be eliminated by summation of the two scalar equations in (5.7.11), viz. the n]-th... 

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