Numerical analysis of a waterjet propulsion system

A waterjet propulsion system is used to propel ships, using a pump which produces a high speed jet. A standard waterjet installation can be divided into an inlet, a pump and a nozzle. For manoeuvring and reversing purposes an additional steering device can be integrated into the installation. The development of waterjet propulsion systems has made significant progress over the last few decades. Nowadays, commercial fast-ferries reach velocities of 50 knots, which is about 90 km/h. The theory to describe waterjet propulsion systems is derived from open propeller theory. The prediction of the thrust of a propeller is based on the momentum balance of a streamtube control volume. This thrust is then transferred though the shaft of the propeller to the hull of the ship. In contrast, for a waterjet propulsion system, forces are transferred to the hull not only through the shaft but also through the solid surface of the installation. A critical review learns that some assumptions made for open propellers are not valid for waterjets. The inflow to the waterjet pump is non-uniform. This results in a blade loading that varies during an impeller revolution. The cause and the effects of this non-uniform inflow have been investigated. Four contributing factors are identified for the development of a non-uniform velocity distribution just upstream of the pump. As a first cause, the water is ingested from below the the hull of the ship, where a boundary layer with a non-uniform velocity distribution is present. Even at normal operating conditions, the water is subsequently retarded in the inlet, which results in an increase of the nonuniformity. Finally, the inflow passes the bend in the inlet and the protruding shaft which add to the increase in non-uniformity. It is concluded that the nonuniformity is the result of the accumulated vorticity in the flow. Due to this vorticity, a stable velocity distribution is found, and the typical velocity distribution is more or less independent of the actual design of the inlet. The investigations are based on numerical analyses of the flow through the complete waterjet installation. Selection of the numerical method is based on the capability to capture typical flow phenomena in a waterjet installation: high Reynolds number, time-dependency, and incompressible flow in a partially rotating frame of reference. Due to the high level of non-uniformity of the inflow, the ability to generate and transport vorticity in the flow is an important requirement, as well as the possibility to take into account the flow phenomena in the tip clearance region between the rotating blades and the stationary housing. A Reynolds averaged Navier-Stokes (RANS) method is chosen to perform all numerical analyses. The Reynolds-stresses are obtained using the twoequation k-e turbulence model. This turbulence model is known to produce an error near a stagnation point. An estimation of the influence of this error on the prediction of thrust and torque shows that the actual deviations are acceptable. The numerical models of both the waterjet inlet and the mixed-flow pump are validated with available experimental data. Results of calculations of the waterjet inlet flow are compared with measurements of static pressure along the inlet and with the total pressure and velocity distribution at the impeller plane. Agreement between the CFD results and the experimental data is good for all calculated conditions. The flow phenomena in a waterjet inlet are characterised by the inlet velocity ratio (IVR), which is the ratio of the ship speed and the pump speed. The shape and location of the streamtube of the ingested water is determined with aid of a concentration scalar. This enables the visualisation of the streamtube and the calculation of the mass averaged inflow velocity. In this way the wake fraction of the waterjet installation is determined accurately. It is shown that the actual shape of the streamtube depends on IVR. The CFD calculations of the mixed-flow pump are validated with experimental data for the pump head and the shaft power. The calculations are performed with a quasi-steady multiple frame of reference (MFR) method and a fully transient moving mesh method. Differences between predicted head and power in both methods are small. The fully transient moving mesh calculations with a uniform inflow velocity distribution provide the unsteady excitation forces on the impeller due to rotor-stator interaction. It is found that the magnitude of the radial interaction force depends on the flow rate though the pump. The influence of the non-uniform velocity distribution to the pump is investigated as well. The deviation in pump performance is limited to a few Numerical analysis of a waterjet propulsion system 191 percent for the calculated conditions. The influence on radial forces is far greater, however. An additional mean component of the radial force is found, the magnitude and direction of which are related to the flow rate and the level of non-uniformity. The origin of this mean force is an unbalanced torque on the impeller blades, due to a variation of the angle of attack during a revolution. Both validated numerical models of the inlet and the pump are combined to form the complete waterjet installation. Results of the calculations of the complete unit are compared with the results of the standard waterjet performance prediction and selection software of Wärtsilä Propulsion Netherlands BV. Good agreement is found for the prediction of flow rate, thrust and torque of the installation. Two methods to determine the thrust are used: (i) the integration of the axial force component on the solid wall and (ii) the application of a simplified version of the integral momentum balance equation. The latter method is generally applied by ship building companies. A clear deviation between the two methods is found for higher ship speeds. Analysis of the net force in vertical direction reveals a significant lift force at high speeds. It is concluded that the method based on the momentum balance for the streamtube control volume, has some short-comings. The deviation increases for higher ship speeds. The numerical results confirm the hypothesis that the simplified method to describe waterjet installations is not correct. This can be partly attributed to the neglect of the influence of the hull in the vicinity of the waterjet inlet and partly to the neglect of the contributions of the pressure distribution acting on the stream tube.