[Dave442]

Dear all,

I am trying to understand how wall shear stress components are calculated in CFX. I have carried out a steady-state analysis of incompressible laminar fluid flow over a flat plate and validated the solution against the Blasius solution. As far as I am aware (I could not find a definition in the theory manual) the components and magnitude of the wall shear stress vector are defined as follows:

Tx = [Nx*Mu*(2*Du/Dx)]+[Ny*Mu*(Du/Dy+Dv/Dx)]+[Nz*Mu*(Du/Dz+Dw/Dx)]

Ty = [Nx*Mu*(Dv/Dx+Du/Dy)]+[Ny*Mu*(2*Dv/Dy)]+[Nz*Mu*(Dv/Dz+Dw/Dy)]

Tz = [Nx*Mu*(Dw/Dx+Du/Dz)]+[Ny*Mu*(Dw/Dy+Dv/Dz)]+[Nz*Mu*(2*Dw/Dz)]

T = sqrt(Tx^2+Ty^2+Tz^2)

In CFX-post I have exported the following variables for a sample node located roughly halfway along the length of the plate:

Dynamic Viscosity = 8.90E-04
Normal X = 0.00E+00
Normal Y = -1.00E+00
Normal Z = 0.00E+00
Velocity u.Gradient X = -5.27E-02
Velocity u.Gradient Y = 4.13E+02
Velocity u.Gradient Z = 0.00E+00
Velocity v.Gradient X = -9.79E-06
Velocity v.Gradient Y = 5.93E-02
Velocity v.Gradient Z = 0.00E+00
Velocity w.Gradient X = 0.00E+00
Velocity w.Gradient Y = 0.00E+00
Velocity w.Gradient Z = 0.00E+00

Using these variables and the equations above I calculate the following values for the components and magnitude of the wall shear stress vector:

Tx = -3.68E-01
Ty = -1.06E-04
Tz = 0.00E+00
T = 3.67E-01

Unfortunately, when I compare the calculated values to those exported from CFX I notice some differences:

Tx = 3.67E-01
Ty = -1.21E-19
Tz = -4.84E-25
T = 3.67E-01

Although the magnitude comes out the same I am clearly getting something wrong. If anyone has a better idea of how the wall shear stress components are calculated I would really appreciate some advice.

Thanks,
Dave