Calculation of Wall Shear Stress
Tags wall shear stress
Tau_w = T.n
T = 2 * mu * e_ij
e_ij = 1/2 * (partial(u_i,x_j) + partial(u_j,x_i))
Tau_w = T.n - ((T.n).n)n
See this discussion for more details:
Unfortunately, in code documentation, wall shear stress is usually just defined as
t = T.n % This is the traction vector (T.n).n % This is the magnitude (scalar) of the normal component of the traction vector, which is usually close to zero ((T.n).n)n % This a vector pointing in the direction of the normal vector 'n' with magnitude (T.n).n
Tau_wall = T.n - ((T.n).n)n
T.n is also a fairly good estimate of wall shear stress in most cases.
I'm looking for more sources on this topic, so please let me know if you have any! I'll add them here as I collect them:
Meister et al. "Modelling and simulation of bottle rinsing". Pg. 1417, eqn. 11. International Journal of Food Science and Technology. 2012.
<- This article uses the definition 'T.n', which is the same one used by the OpenFOAM utility 'wallShearStress'! This is in reality wall traction without the normal contribution of pressure.
Matyka et al. "Wall orientation and shear stress in the lattice Boltzmann model", Appendix A, eqn. A.6. Computers and Fluids. 2013.
Stahl et al. "Measurements of wall shear stress with the lattice Boltzmann method and staircase approximation of boundaries", Appendix A, eqn. 36. Computers and Fluids. 2010.
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