Pitt & Peters Dynamic Wake Model

An alternative dynamic wake model for axial flow conditions is based on work by Pitt and Peters, see (Pitt & Peters, 1981). The original Pitt & Peter’s equation has the following form:

\[ \begin{equation} \bscalar{dT} = \bscalar{2U_{0} a \dot{m} + U_{0} m_{A} \dot{a}} \end{equation} \]

with \(\bscalar{a}\) representing the axial induction factor, \(\bscalar{m_{A}}\) being the added mass term and \(\bscalar{U_0}\) describing the free stream velocity. The equation can be rewritten into dimensional form as:

\[ \begin{equation} \bscalar{2{\overline{v}}_{qsn}\delta\dot{m'}} = \bscalar{2{\overline{v}}_{n}\dot{\delta m'} + {\dot{\overline{v}}}_{n}\delta{m'}_{A}} \end{equation} \]

where \(\bscalar{\dot{m'}}\) represents the mass flow per unit length and \(\bscalar{v_{qsn}}\) denotes the quasi-steady axial induced velocity. The added mass for a disc with radius \(\bscalar{R}\) is found to be:

\[ \begin{equation} \bscalar{m_A} = \bscalar{\dfrac{8}{3} \rho R^3} \end{equation} \]

For a rotor with \(\bscalar{N_B}\) number of blades, the added mass per unit length can be computed as:

\[ \begin{equation} \bscalar{\dfrac{\partial m_{A}}{\partial r}} = \bscalar{{m'}_{A} = \frac{8}{N_B}\rho r^{2}} \end{equation} \]

The Pitt and Peters model does not have a rate of change of the tangential induction with respect to time. Therefore the tangential induction is found by iteration.

Last updated 30-08-2024