It is also useful to evaluate the stress component along the velocity direction. This is accomplished by evaluating the force density, which is applied on a small surface that is perpendicular to the velocity. If is the unit direction along the velocity, the stress component along the velocity direction can be evaluated formally as

(30–19)

Ansys Polyflow solves a more simple (but equivalent) form of this equation:

(30–20)

where is the velocity vector. Dividing by the square of the velocity magnitude is necessary, since the quantity depends only on the direction of the velocity field, and not explicitly upon its magnitude.

Clearly this quantity can be evaluated if the velocity field is nonzero. It is important to note that this quantity is not objective; indeed, a superimposed rigid motion can affect it. However, if the velocity boundary conditions are carefully selected, for a steady-state flow, this quantity provides extra-stress information along path lines.

If the total stress component along the velocity direction is needed, you can add the pressure contribution as follows:

(30–21)

You can obtain this value using a custom field function in CFD-Post. See the CFD-Post documentation for details.