Turbulence k-e model

Another detailed method of determining pressures is computational fluid dynamics (CFD), which uses a numerical solution of simplified equations of motion over a dense grid of points around the building. Murakami et al. and Zhoy and Stathopoulos found less agreement with computational fluid dynamics methods using the k-e turbulence model typically used in current commercial codes. More advanced turbulence models such as large eddy simulation were more successful but much more costly. ... 

Hunt and Kulmala have solved the full turbulent fluid flow for the Aaberg system using the k-e turbulent model or a variation of it as described in Chapter 13— the solution algorithm SIMPLE, the QUICK scheme, etc. Both commercial software and in-house-developed codes have been employed, and all the investigators have produced very similar findings. 

An appropriate model of the Reynolds stress tensor is vital for an accurate prediction of the fluid flow in cyclones, and this also affects the particle flow simulations. This is because the highly rotating fluid flow produces a. strong nonisotropy in the turbulent structure that causes some of the most popular turbulence models, such as the standard k-e turbulence model, to produce inaccurate predictions of the fluid flow. The Reynolds stress models (RSMs) perform much better, but one of the major drawbacks of these methods is their very complex formulation, which often makes it difficult to both implement the method and obtain convergence. The renormalization group (RNG) turbulence model has been employed by some researchers for the fluid flow in cyclones, and some reasonably good predictions have been obtained for the fluid flow. 

In comparison with Bakker and Van den Akker (1994b) and Venneker et al. (2002), Khopkar et al. (2005) applied a more sophisticated two-fluid approach including a standard k-e turbulence model. Using the incorrect snapshot approach due to Ranade (2002), their simulation results (for gas flow numbers being 4 times higher than those of Bakker and Van den Akker, 1994b) still exhibit major discrepancies with respect to experimental data. One of the... 

RANS simulations usually exploiting some k-e turbulence model, intended for global information on the average flow field and the global transport phenomena in full-scale process equipment, with additional output (of limited confidence level) on spatial distributions of k and e ... 

Pironneau, O., and B. Mohammadi. 1994. Analysis of the k-e turbulence model. Paris Mason Editeur. 

The Fluent code with the RSM turbulence model, predict very well the pressure drop in cyclones and can be used in cyclone design for any operational conditions (Figs. 3, 5, 7 and 8). In the CFD numerical calculations a very small pressme drop deviation were observed, with less than 3% of deviation at different inlet velocity which probably in the same magnitude of the experimental error. The CFD simulations with RNG k-e turbulence model still yield a reasonably good prediction (Figs. 3, 5, 7 and 8) with the deviation about 14-20% of an experimental data. It considerably tolerable since the RNG k-e model is much less on computational time required compared to the complicated RSM tmbulence model. In all cases of the simulation the RNG k-< model considerably underestimates the cyclone pressme drop as revealed by Griffiths and Boysan [8], However under extreme temperature (>850 K) there is no significant difference between RNG k-< and RSM model prediction. 

The K-E turbulence model discussed above, which is often termed the k-e model because of the symbols originally used for K and E, contains a number of empirical constants. Typically assumed values for these constants are ... 

The K-E turbulence model discussed above only applies when e v. This will not be true near the wall. The most common way of dealing with this problem is to assume that there is a universal velocity distribution adjacent to the wall and the K-E turbulence mo del is then only applied outside of the region in which this wall region velocity distribution applies. Alternatively, more refined versions of the K-E turbulence model have been developed that apply under all conditions, i.e., across the entire boundary layer. 

A k-e turbulence model was proposed by Yang (1992) to simulate the flow field in circulating fluidized beds, consisting of the following equations ... 

Jenne, M. and Reuss, M. (1999), A critical assessment on the use of k-e turbulence model for simulation of the turbulent liquid flow induced by a Rushton turbine in baffled stirred tank reactor, Chem. Eng. ScL, 54, 3921-3941. 

Sokolichin, A. and Eigenberger, G. (1999), Applicability of standard k-e turbulence model to the dynamic simulation of bubble columns, Chem. Eng. Sci., 54, 2273-2284. 

Stapleton KW, Guentsch E, Hoskinson MK, Finlay WH. On the suitability of k-e turbulence modelling for aerosol deposition in the mouth and throat a comparison with experiment. J Aerosol Sci 2000 31 739-749. 

In general CFD models show a good applicability for risk assessments in urban areas however, their results can differ depending on turbulent closure models and other assumptions. Many CFD models, based on the RANS equations, use the standard k-e turbulence models (originally developed for hydro-dynamical engineering problems), which are violated in complex flow in street canyons and have to be improved and further verified. LES models show substantially better correspondence with measurement data in urban areas and have good perspectives in future, but they are more expensive computationally, and therefore, their usage is limited. 

Shimizu, Y and Tsujimoto, T. (1994) Numerical analysis of turbulent open-channel flow over a vegetation layer using a k-e turbulence model, J. Hydroscience and Hydraulic Engineering, 11(2), 57-67. 

In this subsection an overview of the various formulations of the k — e turbulence models applied to multiphase flows is given. 

The given k — e turbulence model formulation has been used to determine the turbulence of the continuous phase in two-phase bubbly flow by several investigators on bubble columns (e.g., [65, 127]) and on stirred tank reactors (e.g., [49]). 

In most gas-particle flow situations occurring in fluidized bed reactors, a standard k — e turbulence model is used to describe the turbulence in the continuous phase whereas a separate transport equation is formulated for the kinetic energy (or granular temperature) of the particulate phase [122, 42, 41, 165, 84, 52]. Further details on granular flows are given in chap 4. 

Johansson SH, Davidson L, Olsson E (1993) Numerical Simulation of Vortex Sheadding Past Triangular Cylinders at High Reynolds Number Using a k-e Turbulence Model. Int J Numer Methods Fluids 16 859-878... 

Lo [51] simulated two- and three phase isothermal non-reacting stirred tanks with two downward pumping 45o pitched -blade disc turbines and one curved-blade impeller at the bottom. Four or six baffles were placed at equal distance around the vessel wall. An Eulerian multiphase-population balance (MUltiple-SIze-Group, MUSIG) model was used as implemented in CFX. Turbulence of the continuous phase was modeled by the standard k-e turbulence model, and an algebraic relation was used for the particle induced eddy vis-... 

Menter FR (1992) Improved Two-Equation k-e Turbulence Models for Aerodynamic Flows. NASA Technical Memorandum 103975... 

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