Modeling and Simulation of Reactive Flows
Numerical methods have evolved in recent decades, more intensely from the 1980s. However, this development cannot be compared with the development that occurred with computers. Virtually every 3 years, a new computer becomes obsolete.
While the solution of incompressible flows has been more frequent, both numerically and analytically, the compressible flow solution is usually obtained through numerical methods. The compressibility adds nonlinearities to the system equations, which makes it hard to obtain analytical solutions. In this context, the solution of reactive streams becomes even more complex.
Reactive flows are complex, both at low or high temperature, because the formulation typically adds to the Navier-Stokes equations a significant number of nonlinear equations due to reactions.
The combustion of hydrogen, for example, includes about 20 elementary chemical reactions and 8 species. So, eight equations, one for each species, would be added to the equations of nonreactive flow. Even for such a simple mechanism, the numerical solution is complex.
For methane combustion, one has about 300 elementary reactions among some tens of chemical species. Biofuels such as methanol and ethanol involve a similar number of elementary reactions as for methane. Complex fuels such as n-heptane and iso-octane involve hundreds of chemical species and thousands of elementary chemical reactions. For diesel and biodiesel there are thousands of chemical species and tens of thousands of elementary reactions.
Reactions that occur in aqueous media involve numerous minerals in the subsoil, about 4000, and tens of solutes. Of these, about 30 minerals and 15 solutes are themost important. Because the reactions in aqueous media are much faster than those occurring with the minerals, aqueous reactions are considered to be in equilibrium (occurring faster) in the subsoil.
Simplifications of chemical kinetics generally become an alternative. Small mechanisms of a low number of species are often reduced using the assumptions of steady-state and partial equilibrium. Large mechanisms are reduced using a combination of techniques such as direct relation graph (DRG), to obtain a skeleton mechanism and techniques based on the sensitivity analysis of the eigenvalues and eigenvectors of the Jacobian matrix of the chemical system to obtain a reduced mechanism.
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