Turbulent solutal convection model

The present model approach has combined three equations to predict the onset of cellular growth during freezing of natural waters (i) constitutional supercooling from morphological stability theory, (ii) an exact diffusive solute redistribution and (iii) an intermittent turbulent solutal convection model. The main results are ... 

The next step is to introduce the limiting effect of convection into the problem. A solution based on a nonlinear turbulent boundary layer model has been given by Foster It states that the critical time C at the onset of convection is given as... 

When a solute is transferred from a solid into a high-pressure gas, it is then taken downstream in the bulk fluid by convective transport. Depending on turbulence, the solute may travel further by other mass-transport mechanisms such as dispersion. Dispersion spreads the solute axially and radially in a cylindrical stet. Eaton and Akgerman [30] considered both axial and radial effects in a model for the desorption of heavy organics, from carbon, by a dense gas. 

The first approach is the discretization of the convection and the diffusion operators of the PDEs, which gives rise to a large (or very large) system of effective low-dimensional models. The order of these low-dimensional models depend on the minimum mesh size (or discretization interval) required to avoid spurious solutions. For example, the minimum number of mesh points (Nxyz) necessary to perform a direct numerical simulation (DNS) of convective-diffusion equation for non-reacting turbulent flow is given by (Baldyga and Bourne, 1999)... 

While the work of Lin et al. is interesting in that it tries to model convective turbulence from first principles, it still contains arbitrary parameters (four) and approximations that cast doubts on the reliability of the results. Specifically, the height of the nebula H had to be chosen arbitrarily since the model as constructed by Lin et al. gives rise to a degenerate set of solutions for H. The arbitrariness in the choice of H... 

Modeling particulate transport, or various process phases, has been attempted only relatively recently. Sayre (20) gave a very sound basis for further work by using a momentum solution of the two-dimensional convection-diffusion equation characterizing particle transport when additional terms for sedimentation, bed adsorbance, and re-entrainment (erosion) are included. He showed, with extensive hypothetical calculations, which hydrodynamic parameters are important and how they could be quantified. He was also able to show that his concept of bed adsorbance and re-entrainment requires further elucidation and indicated that there might be a turbulence effect on the sedimentation step. Hahn et al. 

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. 

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