### 4.2.7. Guidelines for Mesh Generation

One of the most essential issues for the optimal performance of turbulence models is the proper resolution of the boundary layer. In this section, two criteria are suggested for judging the quality of a mesh:

- Minimum spacing between nodes in the boundary layer

- Minimum number of nodes in the boundary layer

These are simple guidelines for the generation of meshes that satisfy the minimal requirements for accurate boundary layer computations.

#### 4.2.7.1. Minimum Node Spacing

The goal is to determine the required near wall mesh spacing, , in terms of Reynolds number, running length, and a target value. This target value depends on the flow type and the turbulence model in use (that is, on the near-wall treatment in use). See Scalable Wall Functions and Automatic Near-Wall Treatment for Omega-Based Models in the CFX-Solver Theory Guide for more information.

##### 4.2.7.1.1. Determination of the Near Wall Spacing

The estimates will be based on correlations for a flat plate with a Reynolds number of:

| (4–13)

with characteristic velocity and length of the plate .

The correlation for the wall shear stress coefficient, , is given by White [14]:

| (4–14)

where is the distance along the plate from the leading edge.

The definition of for this estimate is:

| (4–15)

with being the mesh spacing between the wall and the first node away from the wall.

Using the definition

| (4–16)

can be eliminated in Equation 4–15 to yield:

| (4–17)

can be eliminated using Equation 4–14 to yield:

| (4–18)

Further simplification can be made by assuming that:

where is some fraction.

Assuming that , then, except for very small Re x, the result is:

| (4–19)

This equation allows us to set the target value at a given location and obtain the mesh spacing, for nodes in the boundary layer.

#### 4.2.7.2. Minimum Number of Nodes

##### 4.2.7.2.1. Goal

A good mesh should have a minimum number of mesh points inside the boundary layer in order for the turbulence model to work properly. As a general guideline, a boundary layer should be resolved with at least:

| (4–20)

where N normal, min is the minimum number of nodes that should be placed in the boundary layer in the direction normal to the wall.

##### 4.2.7.2.2. Formulation

The boundary layer thickness can then be computed from the correlation:

| (4–21)

to be:

| (4–22)

The boundary layer for a blunt body does not start with zero thickness at the stagnation point for . It is, therefore, safe to assume that is some fraction of , say 25%. With this assumption, you get:

| (4–23)

You would, therefore, select a point, say the fifteenth off the surface (for a low-Re model, or 10th for a wall function model) and check to make sure that:

| (4–24)

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