skin friction coefficient and y+
 

I think there is a problem with the way SU2 calculates y+ or the skin friction coefficient. The values are not consistent with each other. I am using version 7.0.4

I am looking at the boundary layer of a Mach 6 nozzle. I used the following equation to calculate y+ for compressible flow as found in Viscous Fluid Flow (White):

y+ = y*sqrt(rho_inf*cfx/rho_w/2)*U_inf*rho_w/mu_w

where cfx is the skin friction coefficient in x as output by SU2. I checked this y+ value with the y+ value that is output by SU2. The values are several orders of magnitude off.

I first calculated velocity (U) by multiplying the Mach number by the speed of sound:

U = Mach*a
a = sqrt(gamma*R*T) where gamma and R are constant

I tried again with the velocity calculated by the momentum divided by the density. I got the same result.

My contour plots and values of other variables are reasonable and expected.

Does SU2 calculate the y+ value differently or is this a bug in the coding?

This is what the code does:
FrictionVel = sqrt(fabs(WallShearStress)/Density);
YPlus[iMarker][iVertex] = WallDistMod*FrictionVel/(Viscosity/Density);

Which is equivalent to what you have provided you use rho_inf and U_inf consistently with how the friction coefficient was computed.
The reference values SU2 uses are printed in the beginning of the simulation on a large table.

Just to clarify are you using the "cf_x" as output by SU2 (i.e. x-component of skin friction) or did you calculate the skin friction along the tangential direction to find the new y+ value?

I used the x-component of skin friction that SU2 output

You should be using the skin friction coefficient tangential to the wall. Using the x component works when the flow is only along x like channels or flat plates. You can perhaps try to use the x-component only for a flat plate to check. In general, the wall shear stress in the y+ formula refers to shear stress along the wall and not only the x-component.



The calculation in SU2 is in the Friction_Forces routine of this file https://github.com/su2code/SU2/blob/.../CNSSolver.cpp