Added Mass and Damping of Vibrating Propellers

Abstract

A general analysis of the added mass and damping of a marine propeller in all modes of rigid body vibration is presented. This derivation assumes that the pressure distribution on a propeller blade due to a unit heave oscillation or unit pitch oscillation about the midchord point can be obtained by two_dimensional thin foil theory, lifting_line theory, or lifting_surface theory. These results show that eighteen coefficients are needed to completely characterize the added mass and damping of a propeller. The use of two_dimensional thin foil theory and lifting_line theory to obtain the pressure distribution on a propeller blade due to a unit heave oscillation or unit pitch oscillation are reviewed. These results have been utilized in the PRAMAD computer program which calculates the added mass and damping of a vibrating propeller. This program incorporates approximate lifting-surface corrections which were obtained by regressing the ratio of lifting_surface and lifting-line results for a matrix of four_bladed Wageningen B-Series propellers. Results are presented for sensitivity studies performed using the PRAMAD program to show the effects of advance coefficient, vibration frequency, blade number, and skew on propeller added mass and damping. Preliminary design equations are presented for the estimation of all eighteen added mass and damping coefficients of 4-, 5-, 6-, and 7_bladed Wageningen B_Series propellers.