Greice S.L. Andreis

Bioethanol combustion based on a reduced kinetic mechanism

Bioethanol is a fuel additive or a fuel substitute that has the benefit of being cleaner and price competitive with gasoline. Therefore, we develop a reduced kinetic mechanism capable of modeling the ethanol combustion and the generation of the combustion products

Mixing and Turbulent Flows

\text{H}_{2}\text{O},~\text{CO}_{2},~\text{CO},~ \text{H}_{2},~ \text{C}_{2}\text{H}_{4}

Numerical Methods for Reactive Flows

and OH. Based on a mechanism composed by 372 reversible elementary reactions among 56 reactive species, we propose a reduction strategy to obtain an eight-step mechanism for the ethanol. The reduction strategy consists in estimating the order of magnitude of the reaction rate coefficients, defining the main chain, applying the steady-state and partial equilibrium hypotheses, and justifying the assumptions through an asymptotic analysis. The main advantage of the obtained reduced mechanism is the decrease of the work needed to solve the system of chemical equations proportionally to the number of elementary reactions present in the complete mechanism. Numerical tests are carried out for a jet diffusion flame of ethanol and the results compare well with available data in the literature.

Development of an analytical–numerical solution for a steady and axisymmetric turbulent jet diffusion flame for the hydrogen based on a reduced kinetic mechanism

This chapter presents the basic equations of fluid dynamics for reactive and nonreactive flows in Cartesian coordinates. The equations are based on the balance obtained for mass, momentum, and energy. It also presents the derivation of the equation for the mass fraction of the chemical species, and shows the terms to be added to the equations of momentum and energy. The reactive term is proportional to the species concentration and follows the Arrhenius kinetics. The set of equations is presented using Einstein notation, which allows simplification of writing the equations system, in order to facilitate the numerical implementation.

A REDUCED KINETIC MECHANISM FOR PROPANE FLAMES

This chapter presents the basics of mixing in turbulent flow, starting with the notion of mixture fraction. This formulation can be extended to flows with various mixture fractions, when the number of reactions is small. Following is presented the basics of turbulent flows, such as turbulence scales, and the averages of Reynolds and Favre, which are useful for writing the reactive Navier equations. Notions of turbulence and models for the turbulent viscosity to be used with large-eddy simulation (LES) are presented. LES is the preferred technique, because there are no conditions for solving realistic Reynolds numbers, encountered in practice, using direct numerical simulation techniques.

Solução via LES de chamas difusivas

In this chapter, some techniques are presented for obtaining reduced kinetic mechanisms as the Direct Relation Graph (DRG) the sensitivity analysis based on the eigenvalues and eigenvectors of the Jacobian matrix of the chemical system, and techniques such as Intrinsic Low Dimensional manifolds (ILDM), Reaction Diffusion manifolds (REDIM), and flamelet. For premixed flames, laminar burning velocity and the basic equations are obtained, and the length and time scales are discussed. In order to represent the flame front, the G equation is discussed. For diffusion flames, flamelet equations are presented with the introduction of the probability density function and the scalar dissipation rate. The Burke-Schumann solution and an analytical solution for jet diffusion flames and for plumes are also illustrated. Then, models are presented for reactive flows in porous media. Initially, we discuss the model of Darcy and appropriate equations for precipitation and dissociation of minerals without combustion. Finally, the equations are presented for combustion in porous media and a discussion about ion precipitation is made.

Analytical-numerical solution for turbulent jet diffusion flames of hydrogen

First, the Cartesian and generalized coordinate systems and the coordinate transformation are introduced. We also discuss the method of virtual boundaries and the need to introduce a forcing term to represent the geometry. Next, we present the formulation for low Mach number, valid for most cases of reactive flows. Then the large-eddy simulations formulation is discussed as an improvement of Reynolds averaged Navier-Stokes (RANS) formulation, which is less expensive than direct numerical simulations (DNS) formulation. Subsequently, for a reactive flow model, the equations of momentum, energy, enthalpy, and chemical species are written as a general equation, which is approximated by methods of finite difference, finite volume, and finite element, to be integrated by Runge-Kutta methods. After that, approximations of order 3 and 4 are given, as well as some compact schemes of order of approximation 6. Then, we discuss some of the main methods used in the flow solution such as Gauss-Seidel, simplified Runge-Kutta, tridiagonal matrix algorithm (TDMA), Newton, strongly modified implicit procedure (MSI), and LU-SSOR, which is an LU decomposition with the introduction of dissipation. Then, we indicate some methods for solving stiff systems of equations, such as Newton’s method and Rosenbrock’s method, which can be seen as a combination of the methods of Newton and Runge-Kutta. After that, the principal boundary conditions, such as permeable and impermeable wall, symmetry and cut, far field and periodic are given, which are common in jet diffusion flames, and in reactive flows in porous media. Finally, some techniques for the acceleration of convergence as local time-stepping, residual smoothing, and the multigrid technique are introduced. Moreover, some numerical implementation details and the analysis of uncertainties for the solution of reactive flows is discussed.