Computational turbulence modeling

Nullaswamy, M., Turbulence models and their applications to the predictions of internal flows, Computers and Eluids, 15, 151, 1987. 

HOTM AC/RAPTAD contains individual codes HOTMAC (Higher Order Turbulence Model for Atmospheric Circulation), RAPTAD (Random Particle Transport and Diffusion), and computer modules HOTPLT, RAPLOT, and CONPLT for displaying the results of the ctdculalinns. HOTMAC uses 3-dimensional, time-dependent conservation equations to describe wind, lempcrature, moisture, turbulence length, and turbulent kinetic energy. 

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. ... 

With LES we get much more information than with traditional time-averaged turbulence models, since we are resolving most of the turbulence. In Fig. T1.15 the computed u velocity is shown as a function of time in two cells one cell is located in the wall jet (Fig.. 15a), and the other cell is in the middle of the room (Fig. ll.lSh). It is found the instantaneous fluctuations are very large. For example, in the region of the wall jet below the ceiling where the time-averaged velocity u)/l] ) is typically 0.5, the instantaneous velocity fluctuations are between 0.2 and 0.9. In the middle of the room, which is a low-velocity region, the variation of u is much slower, i.e., the frequency is lower. 

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

The ability to resolve the dissipation structures allows a more detailed understanding of the interactions between turbulent flows and flame chemistry. This information on spectra, length scales, and the structure of small-scale turbulence in flames is also relevant to computational combustion models. For example, information on the locally measured values of the Batchelor scale and the dissipation-layer thickness can be used to design grids for large-eddy simulation (LES) or evaluate the relative resolution of LES resulfs. There is also the potential to use high-resolution dissipation measurements to evaluate subgrid-scale models for LES. 

The number of equations to be solved is, among other things, related to the turbulence model chosen (in comparison with the k-e model, the RSM involves five more differential equations). The number of equations further depends on the character of the simulation whether it is 3-D, 21/2-D, or just 2-D (see below, under The domain and the grid ). In the case of two-phase flow simulations, the use of two-fluid models implies doubling the number of NS equations required for single-phase flow. All this may urge the development of more efficient solution algorithms. Recent developments in computer hardware (faster processors, parallel platforms) make this possible indeed. 

Leaving aside the difficult question of whether this model holds for multiphase flows, we still have the problem of determining in terms of the computed properties of the flow. The reader should appreciate that choosing an effective viscosity for a multiphase flow is much more complicated than just adding a turbulence model as done in single-phase turbulent flows. Indeed, even for a case involving two fluids (e.g., two immiscible liquids) for which the molecular viscosities are constant, the choice of the effective viscosities is not obvious. For example, even if the mass-average velocity defined by... 

In order to model turbulent reacting flows accurately, an accurate model for turbulent transport is required. In Chapter 41 provide a short introduction to selected computational models for non-reacting turbulent flows. Here again, the goal is to familiarize the reader with the various options, and to collect the most important models in one place for future reference. For an in-depth discussion of the physical basis of the models, the reader is referred to Pope (2000). Likewise, practical advice on choosing a particular turbulence model can be found in Wilcox (1993). 

At this point, the next step is to decompose the velocity into its mean and fluctuating components, and to substitute the result into the left-hand side of (6.42). In doing so, the triple-correlation term (UiUjUk) will appear. Note that if the joint velocity PDF were known (i.e., by solving (6.19)), then the triple-correlation term could be computed exactly. This is not the case for the RANS turbulence models discussed in Section 4.4 where a model is required to close the triple-correlation term. 

Relative to Lagrangian composition PDF codes that use an LES description of the flow, the turbulence models used in velocity, composition PDF codes have a limited range of applicability. However, the computational cost of the latter for reacting flows with detailed chemistry will be considerably lower. 

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. 

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