Turbulent Thermal Diffusivity Model

Turbulent Thermal Diffusivity Model Table 2.1 Model constants of Eq. (2.10) by different aufhcn ... 

The turbulent thermal diffusivity t is calculated by using the T — Zf two-equation model ... 

The turbulent thermal diffusivity at can also be calculated by using two-equation model as shown in Fig. 7.5, in which, similar to the turbulent mass diffusivity Dj, the t reaches almost steady condition after traveling a distance about 50-fold of the effective catalyst diameter from the entrance and decreases sharply afterward. 

The turbulent viscosity i/j is determined using the WALE model [330], similar to the Smagorinski model, but with an improved behavior near solid boundaries. Similarly, a subgrid-scale diffusive flux vector Jfor species Jk = p (uYfc — uYfc) and a subgrid-scale heat flux vector if = p(uE — uE) appear and are modeled following the same expressions as in section 10.1, using filtered quantities and introducing a turbulent diffusivity = Pt/Sc], and a thermal diffusivity Aj = ptCp/Pr. The turbulent Schmidt and Prandtl numbers are fixed to 1 and 0.9 respectively. 

Uniform Fluid Properties. Analyses of turbulent boundary layers experiencing surface transpiration employ a hierarchy of increasingly complex models of the turbulent transport mechanisms. Most of the analyses, supported by complementary experiments, have emphasized the transpiration of air into low-speed airstreams [110-112], Under these conditions, the fluid properties in the boundary layer are essentially constant, and the turbulent boundary layer can be described mathematically with Eqs. 6.170 and 6.179. In addition, when small quantities of a foreign species are introduced into the boundary layer for diagnostic purposes or by evaporation, the local foreign species concentration in the absence of thermal diffusion is given by... 

Great efforts are needed even in a laboratory to achieve a homogeneous spatial distribution of the concentrations, temperature and pressure of a system, even in a small volume (a few mm or cm ). Outside the confines of the laboratory, chemical processes always occur under spatially inhomogeneous conditions, where the spatial distribution of the concentrations and temperature is not uniform, and transport processes also have to be taken into account. Therefore, reaction kinetic simulations frequently include the solution of partial differential equations that describe the effect of chemical reactions, material diffusion, thermal diffusion, convection and possibly turbulence. In these partial differential equations, the term f defined on the right-hand side of Eq. (2.9) is the so-called chemical source term. In the remainder of the book, we deal mainly with the analysis of this chemical source term rather than the full system of model equations. 

Physical and numerical models are created describing the d3mamics of turbulent combustion in heterogeneous mixtures of gas with polydispersed particles. The models take into account the thermal destruction of particles, chemistry in the gas phase, and heterogeneous oxidation on the surface influenced by both diffusive and kinetic factors. The models are validated against independent experiments and enable the determination of peculiarities of turbulent combustion of polydispersed mixtures. 

The evaluation of these statistical second moments is the goal of turbulence models. These models fall into two categories. First are models in which the turbulent fluxes are expressed in the same functional form as their laminar counterparts, but in which the molecular properties of viscosity, thermal conductivity, and diffusion coefficient are supplemented by corresponding eddy viscosities, conductivities, and diffusivities. The primary distinction is the recognition that the eddy coefficients are properties of the turbulent flow field, not the... 

The first analysis of the wrinkled flame structure was carried out by Barenblatt, Zeldovich and Istratov (1962) but in the diffusive-thermal model where the gas expansion effects i) and ii) are neglected. This model was extensively used these ten last years to culminate in the derivation by G. Sivashinsky (1977) of a non linear differential equation for the flame motion describing a self turbulizing behavior of the cellular structures (Michelson 6e Sivashinsky 1977). The main interest of this model is to provide us with a simple framework for studying systematically all the d3mamical effects that can possibely be produced by the diffusion of heat and mass. The asymptotic technique applied to solve this model in the limit of large values of the Zeldovich number is presented in the paper of Jou 1 in 6e Clavin (1979)... 

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