Reacting flow

Temperature gradient normal to flow. In exothermic reactions, the heat generation rate is q=(-AHr)r. This must be removed to maintain steady-state. For endothermic reactions this much heat must be added. Here the equations deal with exothermic reactions as examples. A criterion can be derived for the temperature difference needed for heat transfer from the catalyst particles to the reacting, flowing fluid. For this, inside heat balance can be measured (Berty 1974) directly, with Pt resistance thermometers. Since this is expensive and complicated, here again the heat generation rate is calculated from the rate of reaction that is derived from the outside material balance, and multiplied by the heat of reaction. 

Damkdhler (1936) studied the above subjects with the help of dimensional analysis. He concluded from the differential equations, describing chemical reactions in a flow system, that four dimensionless numbers can be derived as criteria for similarity. These four and the Reynolds number are needed to characterize reacting flow systems. He realized that scale-up on this basis can only be achieved by giving up complete similarity. The recognition that these basic dimensionless numbers have general and wider applicability came only in the 1960s. The Damkdhler numbers will be used for the basis of discussion of the subject presented here as follows ... 

Kee, R.J., Coltrin, M.E., and Glarborg, R, Chemically Reacting Flow Theory and Practice, John Wiley Sons, Hoboken, New Jersey Inc., 2003. 

DNS results are usually considered as references providing the same level of accuracy as experimental data. The maximum attainable Reynolds number (Re) in a DNS is, however, too low to duplicate most practical turbulent reacting flows, and hence, the use of DNS is neither to replace experiments nor for direct comparisons— not yet at least. However, DNS results can be used to investigate three-dimensional (3D) features of the flow (coherent structures, Reynolds stresses, etc.) that are extremely difficult, and sometimes impossible, to measure. One example of such achievement for nonreacting... 

This section presents a variety of reacting flows computed with the LES methodology. The cases presented in this study were chosen, because each features a different aspect of turbulent combustion and also addresses a specific technical difficulty. 

Fox, R.O. (2003) Computational Models for Turbulent Reacting Flows, Cambridge University Press. 

Numerical computations of reacting flows are often difficult owing to the different time-scales involved and the highly non-linear dependence of the reaction rate on concentrations and temperature. The solution of the species concentration equations in combination with the momentum and the enthalpy equation generally requires an iterative procedure such as the one outlined in Section 1.3.4. A rough sketch of the numerical structure of a stationary reacting-flow problem is given as... 

Commenge et al. extended the one-dimensional model of reacting flows to include Taylor-Aris dispersion, i.e. they considered an equation of the form... 

Van Vliet, E., Derksen, J. J., and Van den Akker, H. E. A., Numerical Study on the Turbulent Reacting Flow in the Injector Region of an LDPE Tubular Reactor . Proceedings of the 12th European Conference on Mixing, Bologna, Italy, pp. 719-726 (2006). 

In chemical reacting systems, the Reynolds number of the flow is not the only source of computational challenges. Indeed, even for laminar reacting flows the chemical source term can be extremely stiff and tightly coupled to the diffusive transport terms. Averaging, as done above to treat turbulent flows, does not... 

The reaction rates Rt will be functions of the state variables defining the chemical system. While several choices are available, the most common choice of state variables is the set of species mass fractions Yp and the temperature T. In the literature on reacting flows, the set of state variables is referred to as the composition vector [Pg.267]

Let Yrj denote the mass fractions of the K chemical species describing the reacting flow. By definition, KYa—. Assuming that the chemical species are numbered such that the major species (e.g., reactants) appear first,2 followed by the minor species (e.g., products), we can define a linear transformation by... 

The NDF is very similar to the PDFs introduced in the previous section to describe turbulent reacting flows. However, the reader should not confuse them and must keep in mind that they are introduced for very different reasons. The NDF is in fact an extension of the finite-dimensional composition vector laminar flow where the PDFs are not needed, the NDF still introduces an extra dimension (1) to the problem description. The choice of the state variables in the CFD model used to solve the PBE will depend on how the internal coordinate is discretized. Roughly speaking (see Ramkrishna (2000) for a more complete discussion), there are two approaches that can be employed ... 

As a first example of a CFD model for fine-particle production, we will consider a turbulent reacting flow that can be described by a species concentration vector c. The microscopic transport equation for the concentrations is assumed to have the standard form as follows ... 

CFD models for turbulent multiphase reacting flows do not solve the laminar two-fluid balances (Eqs. 164 and 165) directly. First, Reynolds averaging is applied to eliminate the large-scale turbulent fluctuations. Using Eq. (164) as an example, we can apply Reynolds averaging to find (with pg constant)... 

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