Unclustered Meshes

Spacing = .1horizontal 0.05 vertical

Coarse Mesh:

Along X: 200

Along Y: 130

The Mesh is clustered at the Wall, Inlet and Outlet.

Along X: 450

Along Y: 120

In this Case the Wall is clustered only at the Wall.

Coarse Case:

Solver: Density Based, Implicit, Steady, Axisymetric, Absolute Velocity Formulation and Green-Guass cell based Gradient Problem.

This is Energy problem and the Turbulance model used for the problem is Spalart-Allmaras.

Fine Case: Density based, Implicit, Steady, Axisymetric, Absolute Velocity Formulation and Green- Guass cell based Gradient problem

The Turbulance model used for this is k-epsilon Standard method.

The convergence criteria was reduced to 10^-5 in this case.

Case 3

Case1

Unclustered Coarse Mesh

Clustered Coarse Mesh

Clustered Fine Mesh

Case 2

Unclustered Coarse Mesh

Clustered Coarse Mesh

Clustered Fine Mesh

Case 3

Unclustered Coarse Mesh

Clustered Coarse Mesh

Clustered Fine Mesh With Turbulent Flow

Case3 Clustered Fine Mesh With Laminar Flow

The Reynolds-averaged approach to turbulence modeling requires that the Reynolds stresses in Equation  12.2-4 be appropriately modeled. A common method employs the Boussinesq hypothesis [ 142] to relate the Reynolds stresses to the mean velocity gradients:

(12.2-5)

The Boussinesq hypothesis is used in the Spalart-Allmaras model, the - models, and the - models. The advantage of this approach is the relatively low computational cost associated

with the computation of the turbulent viscosity, . In the case of the Spalart-Allmaras model, only one additional transport equation (representing turbulent viscosity) is solved. In the case of the - and - models, two additional transport equations (for the turbulence kinetic energy,

, and either the turbulence dissipation rate, , or the specific dissipation rate, ) are solved,

and is computed as a function of and . The disadvantage of the Boussinesq hypothesis as

presented is that it assumes is an isotropic scalar quantity, which is not strictly true.

The alternative approach, embodied in the RSM, is to solve transport equations for each of the terms in the Reynolds stress tensor. An additional scale-determining equation (normally for ) is also required. This means that five additional transport equations are required in 2D flows and seven additional transport equations must be solved in 3D.

In many cases, models based on the Boussinesq hypothesis perform very well, and the additional computational expense of the Reynolds stress model is not justified. However, the RSM is clearly superior for situations in which the anisotropy of turbulence has a dominant effect on the mean flow. Such cases include highly swirling flows and stress-driven secondary flows.