Blog
Printer-friendly versionPDF version

I was recently traveling to a User Conference that CD-adapco held in Asia and spent a great deal of time staring out the window of various aircraft. With several hours to contemplate wings, I started thinking about boundary layers and how I have been simulating them. After reading “Boundary Layer Theory” by H. Schlichting, I had to double-check to make sure my designs were modeling the fluid phenomena near the wall correctly. What we design is far from well-known and validated fluid dynamics test cases. In fact, we invent some of the most unconventional products.

As I opened the simulations to validate my assumptions, I ran a search in the Steve Portal on “y+”. Alongside a “Spotlight on Turbulence”, outlining the turbulence modeling options available in STAR-CCM+, the search pointed me to this helpful article entitled “Plotting y+ and u+ profiles at a position on a wall” put together by an Application Engineer at CD-adapco: I followed the methodology outlined to display the boundary layer I was modeling. Thanks to this check, I learned that I have to tweak the prism layer discretization in a few simulations!

More importantly, thanks to this article, the next time I board an aircraft I will be able to enjoy the in-flight entertainment instead of thinking about y+’s again!


 

Plotting y+ and u+ profiles at a position on a wall

To illustrate the procedure, the flow around a NACA airfoil is analyzed. A point has been defined as a derived part on the lower surface by intersecting planes and surfaces.

The velocity profile normal to the wall is analyzed at this point.

Flow around a NACA airfoil

A local coordinate system is created at the point. First, the wall normal is extracted in a table:

  • Input parts: the derived part "point on surface"
  • Scalar: all components of the Area vector

This table consists of 6 columns and 1 row: Area, Area, Area, X,Y,Z

 

Create local coordinate system

The next step is to create a new Cartesian coordinate system "Cartesian 1" in Tools > Coordinate Systems:

  • origin : (X,Y,Z) from the previous table.
  • j Direction : (Area, Area, Area) from the previous table
  • i Direction : (-Area, Area, 0) is a possible vector perpendicular to the j Direction

Create a new Cartesian coordinate system

For an accurate positioning of the coordinate system, it is recommended to export the previous table as a csv file and to open the file that contains the data with all digits.

After that, a derived part is created by intersecting a plane normal to the Y direction of "Cartesian 1" and a plane in the streamwise direction.
To achieve this, select "Cartesian 1" as the Coordinate System when creating the derived part.

The intersection of the 2 planes produces a line section.

A threshold is then used to extract just a part of this line section near the wall:

Derived part created

 

The velocity profile can be plotted directly on the threshold, as illustrated in the following image. Here, the boundary layer can be seen:

 

Threshold from normal section

In order to plot the velocity in the dimensionless parameters u+ and y+, the following report and field functions must be written :

1. Maximum report:

  • name: WallShearStress
  • input parts: "point on surface"
  • scalar: "Wall Shear Stress Magnitude"

2. Field function:

  • name: Utau
  • definition: sqrt($WallShearStressReport/$Density)

In this procedure, the reference velocity is defined as a friction velocity based on the wall shear stress report. This can only be done once the wall shear stress in known. In practice, STAR-CCM+ computes the reference velocity prior to the computation of the wall shear stress, using turbulent quantities specific to the particular turbulence model.

3. Field function:

  • name : y+
  • definition : $Utau*$WallDistance*$Density/$DynamicViscosity

4. Field function:

  • name : u+
  • definition : mag( , 0, $$Velocity("Cartesian 1") ] )/$Utau

In the previous expression, the magnitude of the velocity parallel to the wall is required. In the local coordinate system, the direction i and k are parallel to the wall, therefore the magnitude of (Vx, 0, Vz) in the local coordinate system is chosen.

The field functions u+ and y+ can then be displayed in an X-Y plot using the threshold line section as an input part:

Viscous sublayer plot

In this plot, the viscous sublayer, transition layer, log layer and far field are visible. The y+ range for which the data points match the log layer correlation will depend on the Reynolds number.


 

For more helpful tips from Steve, log on to The Steve Portal.

Entry to the Steve Portal, CD-adapco's customer service center web-site, containing software downloads, knowledge base, and other useful links, is permitted to registered customers of CD-adapco. To become a CD-adapco customer, click here.

Brigid Blaschak
Communications Specialist
Stephen Ferguson
Communications Manager
Dr Mesh
Meshing Guru
Sabine Goodwin
Senior Engineer, Technical Marketing
Prashanth Shankara
Technical Marketing Engineer
Joel Davison
Product Manager, STAR-CCM+
Jean-Claude Ercolanelli
Senior Vice President, Product Management at CD-adapco
Bob Ryan
President Red Cedar Technology