K-s turbulence model

In another class of models, pioneered by Elghobashi and Abou-Arab (1983) and Chen (1985), a particle turbulent viscosity, derived by extending the concept of turbulence from the gas phase to the solid phase, has been used. This is the so-called k—s model, where the k corresponds to the granular temperature and s is a dissipation parameter for which another conservation law is required. By coupling with the gas phase k—s turbulence model, Zhou and Huang (1990) developed a k—s model for turbulent gas-particle flows. The k—s models do not... 

The k-s turbulence model was developed and described by Launder and Spalding (1972). The turbulent viscosity, pt, is defined in terms of the turbulent kinetic energy, k, and its rate of dissipation, z. 

The renormalized k-s model of FLUENT is used to compute the Reynolds stress tensors r, and the effective properties for each phase. A k-s turbulence model is also used in [3] and [8]. A less CPU-consuming model based on mixture-lengths is used in [4],... 

Balance equations listed here are before time averaging. For more details of time-averaged two-phase balance equations, the reader is referred to Ranade and van den Akker (1994) and the FLUENT manual. Turbulence was modeled using a standard k-s turbulence model. Governing equations for turbulent kinetic energy, k and... 

Due to the importance of turbulence in spray systems, this topic is treated in some detail. It includes a summary of time averaging and spatial filtering, followed by a description of RANS and LES turbulence modeling. The RANS model that is presented is the k—s turbulence model, and the LES SGS models that are outlined include the Smagorinsky model and the one-equation subgrid scale (SGS) model. 

Table 19.3 k-s turbulence model constants. (C3 and Cj are for the compressible form)... 

For the k-s. turbulence model, the boundary conditions for the turbulent kinetic energy k and its dissipation rate b are specified as... 

It has been achieved through the processing of an array of data, obtained as the result of solving the equations describing the turbulent motion of a continuous medium, and using the K-s turbulence model (Equations 2.1-2.12) with the method of finite elements on a nonuniform calculation grid. 

Generally, the agreement is good between the measured and computed velocities. Standard k-s turbulence model suggest lower values than measured in the tank. 

As pointed out earlier in Chapter 3 and will be covered in more detail later on in this chapter, the flow in a rotary kiln is typically gas-solid turbulent flow with chemical reactions, mainly combustion. The building blocks behind the user-defined functions (UDF) in commercial CFD codes applied to rotary kiln combustion modeling consist of "renormalization group" (RNG) k-s turbulent model for gas phase and, in the case of pulverized combustion particles, the statistical (stochastic) trajectory model for homogeneous volatile and heterogeneous solid-phase char combustion. The underlying equations are discussed in the next section. 

Determining the value of the turbulent viscosity p, is the main scope of the turbulence model. In the classical k-s turbulence model, two transport equations are solved for the turbulent kinetic energy (k) and its dissipation rate (s) to calculate the turbulent viscosity ... 

Schwarz MP, Turner WJ (1988) Applicability of the standard k-s turbulence model to gas-stirred baths. Appl Math ModeU 12 273-279... 

Menter FR (1992), Improved two-equation k-s turbulence models for aerodynamic flows. NASA technical memorandum 103975... 

Numerical analysis of the gas inside the dynamic scmbber reduces to solving the Navier-Stokes equations [3]. For the solution of equations of Navier-Stokes equations with a standard (k-s)-turbulence model. To find the scalar parameters k and 8 are two additional model equations containing empirical constants [4, 5]. The computational grid was built in the grid generator ANSYS ICEM CFD. The grid consists of 1247 542 elements. 

Analysis of the heat transfer deterioration mechanism by numerical simulation using the k-s turbulence model is in ref. [112]. Transient and accident analysis code for fast reactors, SPRAT-F, and calculation of the Oka-Koshizuka heat transfer correlation for the safety analysis at supercritical pressure are described in ref. [113]. 

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