wallShearStress in OpenFOAM

May 08, 2017

The wall shear stress, $\tau_w$ , is given by:

$\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$

Where $\mu$ is the dynamic viscosity, $u$ is the flow velocity parallel to the wall and $y$ is the distance to the wall.

The SI unit of wall shear stress is pascal ( $Pa$ ), which is identical to $\frac{kg}{m\cdot s^2}$ .

The skin friction coefficient, $C_f$ , is defined by:

$C_f \equiv \frac{\tau_w}{\frac{1}{2} \, \rho \, U_\infty^2}$

Where $\tau_w$ is the local wall shear stress, $\rho$ is the fluid density and $U_\infty$ is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet).

Incompressible Flow

Laminar
In OpenFOAM, wallShearStress usually is in "kinematic pressure", namely in "m2/s2". It doesn't take into account the density of the fluid. So, you should multiply by rho to reach tau.

tau = (wallShearStress) rho*

or with wallGradU utility

tau = (wallGradU) mu*

You can use the Calculator filter in ParaView to multiply the "wallShearStress" field by the density value.

Turbulence

$\tau_w = \nu_{eff} \frac{\partial U}{\partial y}$

Compressible Flow

You must run "wallShearSress -compressible" with that flag in place.

Laminar

wallShearSress -compressible

Turbulence
wallShearStress -compressible:

tau_w = -(mu + mut) * (wallGradU)

$\tau_w = \mu_{eff} \frac{\partial U}{\partial y}= \rho \nu_{eff} \frac{\partial U}{\partial y}$

Refs [1]

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