Reaction-progress vector initial/inlet conditions

Figure 5.7. When the initial and inlet conditions admit a linear-mixture basis, the molar concentration vector c of length K can be partitioned by a linear transformation into three parts a reaction-progress vector of length NT , a mixture-fraction vector of length Nmf and 0, a null vector of length K — Nr — Nmf. The linear transformation matrix depends on the reference...

Note that the reaction-progress vector in the first column is non-zero. Thus, as we suspected, the mixture-fraction basis is not a linear-mixture basis. The same conclusion will be drawn for all other mixture-fraction bases found starting from (5.118). For these initial and inlet conditions, a two-component mixture-fraction vector can be found however, it is of no practical interest since the number of conserved-variable scalars is equal to Nq,m = 1 (k e 0, 1, 2). In conclusion, although the mixture fraction can be defined for the... 

The dimensionless vector of reaction-progress variables Y is then defined to be null in the initial and inlet conditions, and obeys... 

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