I studied a thesis about a axial turbine and but i didn't understood the bold part of following sentences. What is the exact meaning of "dot product of the pressure and viscous force coefficients on each face with the specified force vector"? This thesis is performed by using Fluent.
*The forces coefficients (CA and CT) on blade surface were calculated by summing the dot product of the pressure and viscous force coefficients on each face with the specified force vector.
I am unsure of the context of you question but perhaps this will give some insight.
There is a pressure and viscous stress contribution to the force on a boundary. This force can be calculated from the Navier-Stokes equations by:
$$F=\int_{V}\left[\boldsymbol{\nabla}p+\mu\triangle\boldsymbol{v}\right]dV$$
Rewriting this slightly to:
$$F=\int_{V}\boldsymbol{\nabla}\cdot\left[p\boldsymbol{I}+\mu\boldsymbol{\nabla}\boldsymbol{v}\right]dV$$
We can transform this integral to a surface integral using the divergence theorem:
$$F=\int_{S}\left[p\boldsymbol{I}+\mu\boldsymbol{\nabla}\boldsymbol{v}\right]\cdot\boldsymbol{n}dS$$
where $n$ is the unit normal vector to the boundary.
