A partially submerged propeller theory was developed by employing a singularity distribution method. Unsteady pressure doublets and pressure sources represented the blade camber and blade-and-cavity thickness respectively. The induced velocities were derived by reducing the formula to a lifting-line configuration. The free-surface effect was considered by use of the image method. The induced velocities contained the singular integrals of 5th order, which are usually numerical unstable. An effort was made to derive numerically stable formulae from these singular equations by applying a method similar to the induction-factor method of Morgan & Wrench (1965) and Lerbs (1952) used for steady-state fully wetted propeller problems. These new formulae are not only applicable to the present partially submerged ventilated propeller problem, but also to general unsteady subcavitating and cavitating propeller problems such as propeller starting-up and non-periodic loading problems. By combining the two-dimensional water entry-and-exit theory of Wang (1979), the thrust and torque coefficients were calculated for representative partially submerged propellers and favourably compared with the experimental data.
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