Review of thrust prediction method based on momentum balance for ducted propellers and waterjets

Equations for thrust calculation of ducted propellers and waterjet propulsion systems are derived from the theory of open propellers. The streamtube of an open propeller shows contraction upstream and downstream of the propeller, with a strength depending on the propeller loading. The contraction of the streamtube in a waterjet propulsion unit is governed by the geometry of the installation. This paper presents the analyses of the development of the streamtube of a waterjet and a ducted propeller. Determination and visualization of the streamtubes is accomplished with a commercial CFD method. Development of the streamtube is analyzed in streamwise direction and as a function of the loading of the waterjet or the ducted propeller. It is proven that the ducted propeller has a fixed ratio between the velocity through the nozzle and the velocity downstream. This is comparable to the behavior of a waterjet, and consequently different from an open propeller. Thrust of the propulsion unit can be determined from a direct summation of all wall forces or from summation of the different terms of a momentum balance. The pressure, which acts on the streamtube surface, is neglected in this calculation, according to generally accepted theory. Comparison of both methods shows deviations for some operating conditions, which is attributed to the neglect of the pressure forces. It is concluded that the pressure forces on the streamtube of both ducted propellers and waterjet propulsion systems should not be neglected a priori.