Work Per Cycle

This report type is available only when Harmonic Balance Flutter motion is activated.

It has its own properties but is subject to the report node’s pop-up menu.

This report computes the work done by the fluid on the structure (or the boundary surfaces selected). The work per cycle is computed as:

where the summation is over all the faces of the boundary surface, $T$ is the time period, and ${\hat{q}}_f^0$ is the mean of the integrand ${\hat{q}}_f^{*}$ (which represents the power at each time level) over all the time levels. The power at each time level is computed as:

where $p_f^{*}$ is the time level pressure at the face, $D$ is the pseudo-spectral time derivative operator, ${\mathbf{x}}_f^{*}$ is the time level displacement of the face, ${\mathbf{v}}_f^{*}=D{\mathbf{x}}_f^{*}$ is the time level velocity of the face, and ${\mathbf{a}}_f^{*}$ is the time level face area.

A negative value of the converged work-per-cycle shows that the blade is dynamically stable and does not flutter.