A numerical investigation of using vortex generators to improve a flush waterjet performance

The flow separation on the ramp side of the inlet duct is the main reason for the performance degradation of the waterjet propulsion system under low inlet velocity ratio (IVR) conditions. A micro ramp vortex generator (MRVG) is installed on the bottom of the ship before the inlet entrance to suppress the ramp flow separation and to reduce the inlet flow distortion and improve the efficiency of the waterjet propulsion pump. The influences of the vortex generator on the overall performance and internal flow fields are computed with CFD solver. The results show that under the IVR=0.5 condition, the MRVG device can suppress the flow separation on the ramp side of the inlet duct. It increases the uniformity coefficient of the inlet flow from 0.64 to 0.75, but decreases the total pressure recovery coefficient by 0.02. The total pressure distortion DC60 is reduced by 0.665. After the installation of the vortex generator, the thrust of the propulsion system is increased by 4.01%, and the propulsion efficiency is improved by 3.99%.


Introduction
A flush waterjet propulsor mainly consists of an axial pump, intake duct and rudder nozzle.Water enters the impeller through the intake duct, and accelerates in the nozzle.Thrust is generated by the increased fluid momentum through the device [1].Waterjet propulsion efficiency depends mainly on the pump efficiency, which is now close 90 percent at the design operation.But the overall efficiency of a jet thruster is 65% -70%[2], because the piping system including the intake duct consumes extra power.Especially when a ship is navigating at high speeds, serious distorted inlet flow before the pump lowers the device system performance significantly.
Bulten [3] concluded that the main causes of the circumferential non uniformity of the inlet velocity field are: the boundary layer on the ship bottom, the bends of flow channel, and the rotating shaft.In an operation of low inlet velocity ratio (IVR≤0.6),flow separation occurs on the intake ramp side which aggravates the uneven flow distribution.Axial flow velocity deviates from the designed inlet flow direction before the pump impeller.Distorted inlet flow reduces the pump hydrodynamic performance.Brandner and Walker[4] installed triangular vortex generators (VG) on the sloped side wall to induce co-rotating vortices to counteract the secondary flow generated in the bends.Anderson[5] proposed a ramp-type vortex generator with a height lower than the thickness of the boundary layer.He proposed optimal structural dimensions of the MRVG widely used.Numerical simulations by Huang[6] and low-speed wind tunnel experiments by Wang[7] have demonstrated that vane-type vortex generator at the bottom of the ship in front of the inlet tube can effectively inhibit the development of flow separation and obtain significant total pressure recovery to enhance the inlet efficiency.
In this paper, the MRVG flow control technique is used on an axial jet thruster to eliminate the flow separation in the inlet tube under low inlet ratio conditions.It is anticipated to reduce the additional drag at high inlet ratio conditions while improving the engineering reliability of the VG device.The paper investigates the impact of relevant parameters on inlet duct flow, jet pump characteristics and the overall waterjet thrust performance Results provide a theoretical basis for the application of VG flow control techniques to improve water jet performance.

Waterjet inlet model
The research object is a flush-type waterjet thruster which consists of three components: an axial pump, intake duct and nozzle pipe.The inlet diameter of the pump is 180mm.Pump has a rotor of 5 blades and a stator of 9 vanes.Pump rotates at 1450rpm.The inlet entrance is shaped of half oval and a rectangle.Its outlet is a round pipe connected to the pump face.The intake duct is inclined 25° to ship hull.Dimensions of the inlet and its surrounding flow domain are depicted in figure 1.The length, width and depth of the auxiliary flow domain are 10 times, 6 times and 4 times the pump impeller diameter respectively.

CFD boundary conditions
In this paper, the steady state flow simulation of CFX19.2 is used.The turbulence model is the SST-kω model.The pressure-velocity coupling adopts the SIMPLEC method.The fluid is water at 25°C.Solution residuals are given at 10 -6 .The inlet boundary is specified on the auxiliary fluid domain with Wieghardt's velocity profile which has an exponent of 9 and local boundary layer thickness of 75mm.Two side walls are set mirrored.Two free outlet boundaries are set in the auxiliary domain and pump outlet respectively.Free stream speed of ship movement is fixed u0=10m/s.Other surfaces of inlet pipe and ship hull are non-slip walls.Thruster operation is conditioned by specifying the IVR value which is resulted from the given mass flow rate at the intake pipe outlet.

Mesh-independent verification
Hybrid grid topology is used to mesh the complex flow domain.A small box of non-structural mesh covers the VG zone.The inlet is a transitional pipe from oval-rectangle to a circular with shaft and is divided into 4 zones for meshing.Since the flow asymmetry to the pump face, the whole pump including 5 blades and 9 vanes is meshed by Turbogrid H-I grid. Figure 4 shows that the mesh-independent verification of pump impeller and intake duct.For the pump flow, when the grid number of one blade passage is more than 890K, the rate of change of the mass flow rate at the outlet of the monitoring point is less than 1%.For the intake flow, the optimum number of grids is 5.44M by the variation of ξ and Φ is less than 1%.

Result and discussion
The inlet velocity ratio (IVR) is an important parameter that characterizes the operating state of a water jet propulsion device.In this paper, numerical simulations are used to analyze the VG effects on the flow field and the overall performance at the design operating condition (IVR=0.5).

Improved thruster performance
When the waterjet pump works, the non-uniform inlet flow to the rotating impeller induces varied blade incidence at different peripheral and radial positions.Figure 6 compares the calculated pump efficiency and head under different operating conditions.The pump has its top efficiency at the flow rate of Q/Q0=0.9, but its top head at Q/Q0=0.6.It is a general characteristic of axial pump.For all operation conditions, a pump in a thruster has a lower head and efficiency than its proto machine.In a thruster installed with MRVG device, pump has small but evident improvements of head and efficiency.It is interesting to note that VG does not change the shape of performance characteristic curves.Improvement is larger for low flow rates than high flow rates.It implies that VG affects the pump performance in a given operation range of low flow rate.

Figure 6. Pump head and efficiency curves.
Table 1 summarizes the inlet performance parameters which are average-calculated in the PF plane.The uniformity and pressure recovery coefficients are increased for more uniformed flow.The DC60 factor is reduced for less distortion of total pressure.These parameter variations verify the positive effect of MRVG control on the inlet flow behaviour.The propulsion efficiency of a thruster is made up of two parts: the pump efficiency and the pipe system efficiency.Improvement of pump performance will advocate thruster performance.Figure 7 shows the comparison of the thruster performance with and without MRVG device.
All the performance indicators have been improved by MRVG.The thrust, which is the key parameter for measuring the performance of a waterjet propeller, has been increased by 4.01%.
The waterjet efficiency ηd and pump efficiency ηp increased by 3.99% and 3.77%, respectively.We conjectured that the addition of the MRVG reduces the intake duct distortion of the water jet propulsion pump and reduces piping losses.

Effect on pump inlet distortion
Pump operation depends on its inflow incidence to each blade section along the blade height.Normally, blade to blade incidence is designed close to the airfoil's top lift before stalling.Any deviation from the designed incidence leads to lift reduction and drag increase for a raised incidence.Given fixed impeller rotation speed, incidence is affected by the actual axial velocity component, assuming axial inflow to the pump inlet.
Figure 10 shows the relative inflow angle before the pump rotor at 50% span.Uniform inlet flow angle has a regular nearly constant angle with a small fluctuation due to the downstream stator.But in a pump with a inlet bend, the incidence varies along the peripheral pitch line.It is obvious that MRVG reduces the variance.MRVG alleviates the difference from the proto pump design, but not absolutely solved the problem of inlet distortion.Figure 11 and 12 shows the distributions of turbulent kinetic energy through the pump impeller and at 50% span.The wake core of flow separation is highly turbulent and occupies 1/5 of rotor inlet face.It flows through a rotor passage and extends over two vane channels.Since the impeller is rotating, the actual wake covers wider vane cascade and disturbs the exit jet flow.Much loss is then generated due to the mixing of wakes behind the guide vane.Vortex generators reduce the size of separation wake before the pump inlet.The wake is driven through the impeller within one passage.Its wake "street" is more narrow than in baseline thruster.It is easy to conclude that the vane exit flow is much uniform to raise the jet flow momentum.

Conclusions
This paper numerically the MRVG effects on the performance and flow field of a waterjet thruster.Suppressing inlet flow distortion of axial velocity is regarded as the predominant reason to improve thrust.Main conclusions are following: (1) Installation of the vortex generator pair improves the uniformity of the outlet flow in an inlet bend, because it delays the flow separation on the inlet ramp side.Under the designing condition, the uniformity is raised from 0.64 to 0.75.The total pressure distortion is reduced from 1.32 to 0.64.The performance of the intake duct is significantly improved (2) The inlet distorted flow affects the performance of the water jet pump and finally the device thrust.Installed MRVG reduces the distortion.Under the design conditions, the head, efficiency and thrust of the water jet propulsion pump were increased by 4.5%, 4.1% and 7.99%, respectively, and the thrust and propulsion efficiency of the water jet thruster were increased by 4.01% and 3.99%, respectively.
(3) Vortex generator affects not only the flow performance of intake duct, but also the flow inside pump impeller and outlet guide vane.At off design working conditions, the penalty of MRVG on pump flow is negligible because VG height is controlled less than local boundary layer thickness.

Figure 1 .Figure 2 .
Figure 1.CFD model of waterjet thruster.A pair of vortex generators is mounted 1D ahead of the leading edge of the inlet entrance and is symmetrical about the center line.The height of the MRVG is typically 20%-40% of the local boundary layer thickness.Huang[8] analyzed this inlet flow field and determined that flow separation occurred on the inlet ramp side when IVR<0.7 condition.For all the conditions

Figure 3 .
Figure 3. Mesh topology.Figure4shows that the mesh-independent verification of pump impeller and intake duct.For the pump flow, when the grid number of one blade passage is more than 890K, the rate of change of the mass flow rate at the outlet of the monitoring point is less than 1%.For the intake flow, the optimum number of grids is 5.44M by the variation of ξ and Φ is less than 1%.

Figure 4 .
Figure 4. Verification of mesh independence.Validation of CFD method is a important step before we analyze the MRVG effect on the inlet flow behavior.Since we look at the inlet flow, we compared our computation with the experiment ofBrandner[4]  for available static pressure distribution on the inlet ramp wall shown in Figure5.In whole, CFD predicts well the distribution except near the shaft where is disturbed by the shaft wake.It is believed that it does not affect the PF flow field and hence the inlet distortion behavior before the pump rotor.Present CFD model and calculation method is reliable to predict the device performance.

Figure 5 .
Figure 5. Static pressure coefficient distributions on the inlet ramp side.

Figure 7 .
Figure 7.Comparison of thruster performance under designing condition.

Figure 8 Figure 8 .
Figure 8.Total pressure contours and velocity vectors in PF plane.Figure9shows that the dimensionless velocity contours and streamlines in the meridional plane of the intake duct.The fluid in the proto inlet separates near the duct ramp side due to adverse pressure gradient.MRVG delays the separation and reduces the reversed flow region.The flow separation on the ramp side is suppressed in the bend corner which is significantly smaller than in the baseline duct.

Figure 9 .
Figure 9. Dimensionless velocity cloud and streamlines in longitudinal section in intake pipe.

Figure 10 .
Figure 10.Circumferential distributions of relative inlet flow angle at 50% span.Figure11and 12 shows the distributions of turbulent kinetic energy through the pump impeller and at 50% span.The wake core of flow separation is highly turbulent and occupies 1/5 of rotor inlet face.It flows through a rotor passage and extends over two vane channels.Since the impeller is rotating, the actual wake covers wider vane cascade and disturbs the exit jet flow.Much loss is then generated due to the mixing of wakes behind the guide vane.Vortex generators reduce the size of separation wake before the pump inlet.The wake is driven through the impeller within one passage.Its wake "street" is more narrow than in baseline thruster.It is easy to conclude that the vane exit flow is much uniform to raise the jet flow momentum.

[ 1 ]
Wang L X 2021 Water Jet Propulsion Technology and Engineering Design National Defence Industry Press [2] Jung K H, Kim K C and Yoon S Y 2006 Investigation of Turbulent Flows in a Waterjet Intake Duct Using Stereoscopic PIV Measurements Journal of Marine Science and Technology 11 Pp 270-278 [3] Willem N B H 2006 Numerical analysis of a waterjet propulsion system Technische University Eitndhoven [4] Brandner P A and Walker G J 2007 An Experimental Investigation into the Performance of a Flush Water-jet Inlet Journal of Ship Research 51(01) Pp 1-21 [5] Anderson B H, Tinapple J and Surber L 2006 Optimal Control of Shock Wave Turbulent Boundary Layer Interactions Using Micro-Array Actuation aiaa journal [6] Huang C L, Dai R and Pan Z W 2021 Numerical study on the effect of vortex generator on the flow field in water jet propulsion inlet pipe Journal of Engineering Thermophysics 42(09) Pp 2298-2304 [7] Wang Z J, Huang C L and Chen L 2023 Experimental study of vortex generator to suppress the total pressure distortion of water jet propeller inlet pipe Chineses journal of Hydrodynamics 38(02):270-277 [8] Huang C L, Chen L and Wang Z L 2022 Numerical study of vortex generator-controlled water jet thruster inlet pipe flow separation.Journal of Propulsion Technology, 43(07)447-456 [9] Zhou Y Y 2023 Study on the application of VG and VGJ to inhibit flow separation in the inlet pipe of flat inlet water jet thruster Shanghai University of Science and Technology

Table 1 .
Variation of inlet performance parameters.