7.3 Gas-Phase Chemistry Solver

The mass conservation equation representing gas-phase

reactions is given as

γˆ ϕ i

t

chem

= γˆ Rϕi

(ϕ 1,ϕ 2, ...,ϕ N ) + γˆ Sϕ i

, (36)

where Rϕi and Qϕi represent chemistry reactions and

source terms, respectively, and N is the total number of

species in the chemical mechanism. Although various units

could be used in the solution of gas-phase chemistry

problems, the use of parts per million by volume is

convenient for numerical reasons since the magnitude of the

values for trace gases is small. Because the computational

grid is constant for the duration of a synchronization time

step, the Jacobian and species density in γˆ ϕ i of Eq. (36)

can be decoupled, and the density of a trace gas species

converted to volumetric (or molar) mixing ratio units. This

leads to the following conservation equation for gas-phase

chemistry in terms of the time-rate of change of the

volumetric mixing ratio for each species:

where m i = q i (Mair / Mi ) is used as the definition of the

volumetric or molar mixing ratio, and Rˆ m i = Rϕi / ρ and

Qˆ mi

= Q ϕ

i / ρ represent chemistry reactions and source

terms in molar mixing ratio. In the remainder of this

section, the over bars will be dropped for simplicity.

By using the kinetics laws for elementary reactions and by

applying a mass balance to each species, the equation for the

rate of change of each species concentration can be derived

for a single cell:

In Eqs. (38a-d), Pi represents the production of species i,

Limi represents the chemical loss of species i, υ

i,l is the

stoichiometric coefficient for species i in reaction l, and rl is

the rate of chemical reaction l. The sum l = 1...Ii , in Eq.

(38c) is over all reactions in which species i appears as a

product, and in Eq. (38d) l = 1...Ji is over all reactions in

which species i appears as a reactant.

The rate of chemical reaction l can be expressed as the

product of a rate constant kl and a term that is a function of

the concentration of the reactions. For elementary reactions,

the concentration dependent term is the product of the

reactant concentrations. In terms of mixing ratios, the rate

of reaction l (rl ) takes one of the following forms:

p37

n1051 - n1052 - n1053 - n1054 - n1055 - n1056 - n1057 - n1058 - n1059 - n1060 - n1061 - n1062 - n1063 - n1064 - n1065 - n1066 - n1067 - n1068 - n1069 - n1070 - n1071 - n1072 - n1073 - n1074 - n1075 - n1076 - n1077 - n1078 - n1079 - n1080 - n1081 - n1082 - n1083 - n1084 - n1085 - n1086 - n1087 - n1088 - n1089 - n1090 - n1091 - n1092 - n1093 - n1094 - n1095 - n1096 - n1097 - n1098 - n1099 - n1100

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