Turbulence reaction model

We will revisit this topic in Section III when discussing CFD models for mixing-sensitive reactions. Note that while the discussion above applies to RANS turbulence models, the method can be extended to LES by integrating over the SGS wavenumbers (i.e., starting at kc). 

The focus of the remainder of this chapter is on interstitial flow simulation by finite volume or finite element methods. These allow simulations at higher flow rates through turbulence models, and the inclusion of chemical reactions and heat transfer. In particular, the conjugate heat transfer problem of conduction inside the catalyst particles can be addressed with this method. 

Unlike Lagrangian composition codes that use two-equation turbulence models, closure at the level of second-order RANS turbulence models is achieved. In particular, the scalar fluxes are treated in a consistent manner with respect to the turbulence model, and the effect of chemical reactions on the scalar fluxes is treated exactly. 

A detailed reaction scheme dedicated to biomass combustion was used the SKG03 reaction mechanism [25]. The simulations were performed with the FLUENT flow solver using the realizable k-e model for turbulence modeling. 

The SGS turbulence model employed is the compressible form of the dynamic Smagorinsky model [17, 18]. The SGS combustion model involves a direct closure of the filtered reaction rate using the scale-similarity filtered reaction rate model. Derivation of the model starts with the reaction rate for the ith species, to i", which represents the volumetric rate of formation or consumption of a species due to chemical reaction and appears as a source term on the right hand side of the species conservation equations ... 

M 39] [P 37] The Reynolds-stress model describes best the experimental findings out of three turbulent models investigated (see Figure 1.105) [41]. Then, the model was used for predictions of the mixing efficiency as determined by an azo-type parallel reaction. It was found that the wall thickness has no major influence, whereas the channel depth, as expected, has an influence, affecting the shearing. 

Complicated Reactions and Flow. The ideal turbulence model must deal with multiscale effects within the subgrid model. If there is a delay as velocity cascades to the short wavelength end of the spectrum due to chemical kinetics or buoyancy, for example, the model must be capable of representing this. Otherwise bursts and intermittency phenomena cannot be calculated. 

A 2-D CFD model has been set up using FLUENT4.5 in a joint EU JOULE project with FLUENT and ALSTOM. As turbulence models the k- model and Reynolds Stress model (RSM) have been applied. As chemistry models a chemical equilibrium model has been applied and on the other hand two models describing finite reaction chemistry, i.e. the laminar flamelet model and the reaction progress variable model. The comparison between experiments and the numerical results from the three chemistry models show that the chemical equilibrium model is sufficient to predict the combustion of LCV gas at elevated pressures, since deviation from chemical equilibrium is small due to the fast reactions. Hence no improvements are expected and have been observed from kinetically limited models. The RSM with constants Cl and C2 in the pressure-strain term proposed by Gibson and Younis [17] seems to yield the best predictions, however, the influence of the type of turbulence model (RSM or k- e) on the species concentrations and temperature predictions is not very large. 

Turbulence is the most complicated kind of fluid motion. There have been several different attempts to understand turbulence and different approaches taken to develop predictive models for turbulent flows. In this chapter, a brief description of some of the concepts relevant to understand turbulence, and a brief overview of different modeling approaches to simulating turbulent flow processes is given. Turbulence models based on time-averaged Navier-Stokes equations, which are the most relevant for chemical reactor engineers, at least for the foreseeable future, are then discussed in detail. The scope of discussion is restricted to single-phase turbulent flows (of Newtonian fluids) without chemical reactions. Modeling of turbulent multiphase flows and turbulent reactive flows are discussed in Chapters 4 and 5 respectively. 

Homogeneous, isotropic turbulence cannot be assumed in the free jets. The authors in [541], therefore, utilized the Phoenics program (CHAM Ltd.) in connection with the slower diazotization reaction. The constants of the /c/e-turbulence model are adapted to well-known pictures of flow patterns and the turbulent Schmidt number determined to be Scturb = 1. It thereby succeeds in achieving the best description of the decoloration length. 

Wang Y, Komori S, Chung MK (1997) A Turbulence Model for Gas-Solid Two-Phase Flows. Journal of Chemical Engineering of Japan 30(3) 526-534 Whitaker S (1987) Mass Transport and Reaction in Catalyst Pellets. Transport... 

Turbulence models are generally limited to fully developed high-Reynolds number flows. Gas-phase flows are normally characterized by 5c 1, while for liquid phase flows, 5c > 1. The value of this Damkohler number indicates the relative rates of the mixing and chemical reaction rate time scales. Reactive flows might thus be divided into three categories Slow chemistry (Da/ -C 1), fast chemistry (Da/ 1), and finite rate chemistry (Da/ 1). 

A proper closure strategy for the reaction rate thus depends on the ratio of the rate of reactions and the rate of mixing. In the previous case, considering very slow reactions the concentration fluctuations decay to zero before the reactions occur and no turbulence modeling is needed. The other extreme involves infinitely fast reactions so that local instantaneous chemical equilibrium prevails everywhere in the mixture. If the rate constant is very large k oo), the reaction rate can only be finite when c.4Cb - - c c 0. 

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