Algebraic Reynolds stress model

Taulbee, D.B. 1992. An improved algebraic Reynolds stress model and corresponding nonlinear stress model. J. Physics Fluids A 4(11) 2555-61. 

Reynolds stress model, in which the unknown pw-w, is calculated directly by the modeled Eq. (1.23a). The advantage of this model is anisotropy and more rigorous, while its weakness is the need of much computer work. It is called standard Reynolds stress model. For reducing the computer load, a simplified model, called Algebraic Reynolds stress model, Eq. (1.24) is used instead of Eq. (1.23a). The accuracy of simplified model is comparable to the standard Reynolds stress model. 

Almost all modern CFD codes have a k - model. Advanced models like algebraic stress models or Reynolds stress model are provided FLUENT, PHOENICS and FLOW3D. Table 10-3 summarizes the capabilities of some widely used commercial CFD codes. Other commercially CFD codes can be readily assessed on the web from hptt//www.cfd-online.com This is largest CFD site on the net that provides various facilities such as a comprehensive link section and discussion forum. 

More advanced models, for example the algebraic stress model (ASM) and the Reynolds stress model (RSM), are not based on the eddy-viscosity concept and can thus account for anisotropic turbulence thereby giving still better predictions of flows. In addition to the transport equations, however, the algebraic equations for the Reynolds stress tensor also have to be solved. These models are therefore computationally far more complex than simple closure models (Kuipers and van Swaaij, 1997). 

Currently the widely used turbulence models are standard K-s model, RNG K-e model and the Reynolds stress model (RSM). Standard K-s model is based on isotropic turbulence model, its simulation result error of separator flow field is large (Shan Yongbo, 2005). RNG K-s model has improved with a standard K-s model, but there are still larger defects. To improve the cyclone vortex field strength prediction results a greater extent, algebraic stress turbulence model based... 

Similar to the standard Reynolds stress model, the algebraic model involves twelve variables and twelve model equations. The model is closed and solvable. 

Turbulence modeling capability (range of models). Eddy viscosity k-1, k-e, and Reynolds stress. k-e and Algebraic stress. Reynolds stress and renormalization group theory (RNG) V. 4.2 k-e. low Reynolds No.. Algebraic stress. Reynolds stress and Reynolds flux. k- Mixing length (user subroutine) and k-e. 

This type of model is usually referred to as an algebraic scalar-flux model. Similarmodels for the Reynolds-stress tensor are referred to as algebraic second-moment (ASM) closures. They can be derived from the scalar-flux transport equation by ignoring time-dependent and spatial-transport terms. 

The flow pattern is calculated from conservation equations for mass and mometum, in combination with the Algebraic Stress Model (ASM) for the turbulent Reynolds stresses, using the Fluent V3.03 solver. These equations can be found in numerous textbooks and will not be reiterated here. Once the flow pattern is known, the mixing and transport of chemical species can be calculated from the following model equation ... 

Computational experience has revealed that the two-equation models, employing transport equations for the velocity and length scales of the fluctuating motion, often offer the best compromise between width of application and computational economy. There are, however, certain types of flows where the k-e model fails, such as complex swirling flows, and in such situations more advanced turbulence models (ASM or RSM) are required that do not involve the eddy-viscosity concept (Launder, 1991). According to the ASM and the RSM the six components of the Reynolds stress tensor are obtained from a complete set of algebraic equations and a complete set of transport equations. These models are conceptually superior with respect to the older turbulence models such as the k-e model but computationally they are also (much) more involved. 

Wherever the convective and diffusive transport of Reynolds stresses are important (flows that are far from equilibrium), algebraic stress models may prove to be inadequate, and solution of the full transport equations of the Reynolds stresses may become necessary. Extensive efforts have been made to model the terms appearing in the exact transport equations of Reynolds stresses. The redistributive term has been the... 

The standard two-equation k-e model has been used for almost all of the simulations referred to in this chapter because it is the most tested and reliable turbulence model available. Although it will not give the amount of information that a mean Reynolds stress or an algebraic stress model will give, it requires an order of magnitude less CPU time and gives predictions of the mean velocities that are of comparable accuracy to the higher order models. 

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