Algebraic Stress Model ASM

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). 

A cure against these longer CPU times is the Algebraic Stress Model (ASM) described by, e.g., Rodi (1984) and used and recommended by, e.g., Bakker (1992) and Bakker (1996). Most commercial codes do no longer support an ASM. 

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 ... 

Algebraic Stress Models (ASM) Accounts for anisotropy Combines generality of approach with the economy of the k-s model Good performance for isothermal and buoyant thin shear layers Restricted to flows where convection and diffusion terms are negligible Performs as poorly as k-e in some flows due to problems with s equation Not widely validated... 

In the algebraic stress model or ASM , the transport equations for the Reynolds stresses are rewritten as algebraic expressions by assuming that the transport of the stresses around the flow field is proportional to the transport of the turbulent kinetic energy, k. 

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. 

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. 

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