STAR-CCM+ Technical Notes

STAR-CCM+ Wall Stress Function

The built-in STAR-CCM+ WallShearStress field function contains a component normal to the wall that is not zero in general, and therefore the function should more appropriately be called “WallStress.” A quick search of the internet in CFD forums reveals that this naming confusion exists in other CFD software packages as well. CD-adapco technical support has stated that the quantity “WallShearStress” is computed as tau.dA/|dA|, where dA is the area vector and tau is the stress tensor at the wall. In turbulent flows using wall functions, the tangential component of tau is subtracted off and replaced with the tangential component computed from wall functions.

User Field Functions to Obtain Normal and Tangential (Shear) Components of Wall Stress

Define a user field function with the following properties to obtain the normal component of wall stress:

Normal component of wall stress

Property	Value
Type	Vector
Dimensions	Stress
Function Name	sigmaW
Definition	dot($$WallShearStress,unit($$Area))*unit($$Area)

Define a user field function with the following properties to obtain the tangential (shear) component of wall stress:

Tangential component of wall stress

Property	Value
Type	Vector
Dimensions	Stress
Function Name	tauWS
Definition	$$WallShearStress - $$sigmaW

The magnitude of the wall shear stress vector, “tauWS,” can be obtained for use in the definition of other field functions by using the “mag” built in field function: “mag($$tauWS).” To create a scene containing a color plot of the scalar magnitude of the wall shear stress vector, go to the object tree for the scene: Displayers --> Scalar --> Scalar Field --> Property box --> Function --> tauWS --> Magnitude. This is basically the same procedure used for generating a scalar magnitude from any vector field function as quantity to plot.

To illustrate the differences in these quantities the various functions are plotted in the following figures for the case of flow under a small symmetric section of a flooded bridge deck where some of the flow is diverted down under the deck. The case is one with the deck 15 cm above the flat bed in 0.5 m deep water with 0.6 m/s inlet flow velocity and a smooth wall condition. For rough wall conditions typical for a sediment bed of sand, the shear stress would be considerably larger.

File:Vector WallShearStress.png Figure 1: Bed stress vector plot using the built in field function WallShearStress showing that the stress vector has a normal component pointing down in the region where flow is diverted down under the deck and a normal component pointing up in the region where flow is leaving the confined area under that deck.

The normal component sigmaW is plotted in Figure 2. The size of the vectors is scaled up to make them easily visible in the figure. Note that the maximum magnitude of the normal components in this case is a very small fraction of the wall stress vector magnitude: a maximum 0.08 Pa for the normal component compared to a maximum of about 1.2 Pa for the bed stress vector.

File:Vector sigma.png Figure 2: Normal component, sigmaW, of the built in field function WallShearStress along the bed. It’s maximum value is about 0.08 Pa compared to a maximum stress vector of about 1.2 Pa.

In Figure 3 a vector plot the user defined field function tauWS is shown with vectors that are clearly parallel to the flat bed. They are the shear component of the more general wall stress vector.

File:Vector tau.png Figure 3: Vector plot of the user field function tauWS showing that this wall shear stress function does yield vectors that are parallel to the wall.

In this case the maximum difference in magnitude between the build in WallShearStress function that has a component normal to the wall and the user defined function tauWS that is parallel to the wall is less than 1 percent. In flows that have stagnation points on a surface of interest, such as the down flow generated in front of pier obstruction, the normal stress on the bed will be more significant.

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