Wall Quantities
flow_props computes near-wall quantities directly from the CFD dataset and grid geometry.
Wall Shear Stress
The wall shear stress is evaluated as:
\[
\tau_w = \mu_w \left.\frac{\partial u}{\partial \eta}\right|_w
\]
The current implementation uses a one-sided second-order finite-difference approximation at the wall.
Skin-Friction Coefficient
\[
C_f = \frac{\tau_w}{\tfrac{1}{2}\rho_\infty u_\infty^2}
\]
This requires freestream density and velocity.
Wall Heat Flux
\[
q_w = -k_w \left.\frac{\partial T}{\partial \eta}\right|_w
\]
As with shear stress, the wall-normal derivative is approximated with a one-sided finite-difference stencil.
Stanton Number
The package reports:
\[
St = \frac{q_w}{\rho_\infty u_\infty c_p (T_\infty - T_w)}
\]
This is a practical working definition for the current package implementation.