A bionic anti-cavitation leading edge for pump-turbine

Cavitation is one of the most important technical indicators for assessing reversible pump-turbines. This article describes an anti-cavitation leading edge based on a bionic shape to reduce cavitation. The shape is based on 6 typical fish-like streamlined profiles analyzed in CFD simulations. The flow fields around the profiles were analyzed for different angles of attack to identify the one with the least flow separation and a flat pressure drop. A bionic runner was then built to give an anti-cavitation leading edge. Three-dimensional CFD simulations show that the anti-cavitation leading edge effectively inhibits local flow separation and reduce the pressure drop. Moreover, cavitation tests show that the bionic runner reduces the cavitation inception coefficients. Thus, this design reduces the number of cavitation bubbles and improves the cavitation performance. These results will improve safety and reduce costs and provide a reference for similar hydraulic machinery experiencing.


Introduction
Cavitation is a common dangerous phenomenon in hydraulic machinery, usually causing vibration, noise and damage.Cavitation more likely occurs at off-design conditions and, as a consequence, affects stability and safety.In general, the scale and occurrence of cavitation is associated with minimum pressure conditions.However, measurements of the minimum pressure are difficult in hydraulic machinery.Often, critical cavitation data is obtained by measuring the external characteristics.However, before the conditions reach the "critical cavitation" conditions, in the runner, the actual extent of the cavitation is already quite serious.In reversible pump-turbines, the cavitation coefficient in pump-mode is much greater that in turbine mode [1][2][3].This means that a pump-turbine working as a pump is more prone to cavitation.Reversible pump-turbines usually have higher speeds and heads than typical centrifugal pumps.Thus, reversible pump-turbines contain greater fluid energy and are more likely to experience large-scale cavitation with tremendous negative impacts.For pump-turbine units, the cavitation inception in pump-mode is often regarded as the crucial factor.Hence, reduction of cavitation inception is obviously important in engineering applications.
Cavitation inception is a discrete type of cavitation and, as the name implies, is the initial stage in the cavitation process [4].Individual travelling bubbles and cavities were observed photographically by Ceccio and Brennen [5].They pointed out that cavitation inception is related to the pressure and viscous mode of the flow field.The pressure drop caused by flow separation induces the cavitation.Arakeri [6] used the Schliren technique for flow visualization to show the existence of laminar boundary-layer separation upstream of the cavitation separation.The distance between the two separation locations strongly depends on the Reynolds number.Flow separation occurs when the boundary layer lifts off or separates from the surface due to the geometry [7,8].Patel and Sowle [7] discussed the relationship between flow separation and pressure drop as a function of pressure distribution around the airfoil.In addition, Achenbach [9] measured the pressure and skin friction coefficients around a cylinder.In most designs, the flow separation location can be identified once the pressure distribution is known.The cavitation location can then also be estimated.For a pump-turbine, the geometry effects leading to cavitation can be eliminated by adjusting the blade leading edge shape to reduce the adverse pressure gradient.Delaying flow separation and cavitation will enhance the safety and stability of pump-turbine units.Construction and repair costs will also be substantially reduced.
There are many examples of flow optimization based on bionic feature.Bechert et al [10] experimentally analyzed drag reduction on three-dimensional riblet surfaces inspired by shark skin structures.Barthlott and Neinhuis [11] studied self-cleaning surfaces to explore the "Lotus Effect".The lotus-like micro roughness surface has been widely used on aircraft.Ren et al [12] investigated the rough leading edge of an owl wing for airflow noise reduction.This bionic feature is also applicable to the blades of wind turbines.However, there are no accord reports applying bionic flow structures to reversible pump-turbines.
For pump-turbine runners, cavitation is associated with the leading edge shape.Several streamlined fish-like profiles are analyzed here using CFD model.The flow fields around these surfaces have been numerically simulated using two-dimensional CFD simulations.Then, the optimal profile shape was chosen as an anti-cavitation leading edge.This anti-cavitation leading edge was then used in an ordinary pump-turbine as a new bionic runner with three-dimensional CFD simulations and cavitation experiments on both the original model and the bionic model.The simulations and experiments verify the effect of the anti-cavitation leading edge on the cavitation.

Bionic information extraction
2.1.1.Bionic profile modeling.Fish spend a considerable amount of their lifetime swimming and therefore are expected to do that efficiently.Natural selection will have favored shapes that reduce the energy needed for acceleration and sustained swimming [13].A fish can be divided into parts by the three virtual body axes shown in Figure 1.The body sections defined by axes A-A' and B-B' divide the fish into right-and-left parts with the same volume and weight.The right-and-left parts form a streamlined body shape along the horizontal surface which from the point of view of the fish, more easily pushes the water aside to allow the fish to swim.Hertel [14] conducted wind tunnel tests to measure the drag force on different fish shapes to identify the relationship between the drag force and the width-length ratio D/L.
Six typical streamlined fish shapes [14] are shown in Table 1.This study presents a series of CFD simulations to calculate the flow field around these bionic profiles for an anti-cavitation leading edge.The CFD simulations used a structured quadrilateral mesh for the fluid domain with refinement in the near wall region.A grid independence study was conducted with from 50,000 to 200,000.Elements.The differences in the results for meshes having more than 150,000 elements were less than 0.3% and the calculated y + was less than 50.Thus, further calculations used meshes elements with about 150,000.As an example, the fluid domain and mesh for profile A are shown in Figure 2. The commercial software ANSYS CFX was used to obtain a steady solution to the incompressible Reynolds averaged Navier-Stokes equations [15].The SST k-ω model proposed by Menter [16] was used as the turbulence model.The domain boundaries consisted of a velocity inlet, a pressure outlet, a no slip wall for the airfoil and two open boundaries for the top and bottom.This boundary type allowed water to flow into or out of the domain and is only supplied in ANSYS CFX.The inlet velocity was 1 m/s with angles of attack of 0, 5 and 10 degrees.The pressure outlet boundary was a static pressure of 0 Pa.
where p is the pressure, p∞ and V∞ are the reference pressure and velocity, and ρ is the density of 998 kg/m 3 .The reference values were acquired at the reference point located 2 m upstream from the leading edge.Figure 4 shows the Cp curves for all the profiles at 0 and 10 degree angles of attack.These curves only contain the pressure data on the low-pressure surface.
The pressure-velocity contours and the pressure coefficient curves lead to the following rules.At the 0 degree angle of attack, the minimum pressure coefficients, Cpmin, for profiles A, B and C are much lower than those for D, E and F. The pressure drop trends are then much flatter for D, E and F. Furthermore, the Cpmin locations of A, B and C are closer to the leading edge because the flow separated earlier.As with stall, the separation location becomes closer to the leading edge with increasing angle of attack.At the 10 degree angle of attack, the Cpmin locations for profiles D, E and F were further forward than those of A, B and C due to thinner profile thickness.However, the Cpmin of D, E and F were still larger.In conclusion, Table 2 shows Cpmin and the corresponding relative chord lengths, Ls, where Cpmin occurs for both 0 and 10 degree angles of attack.  2 rule out profiles A, B and C due to their low Cpmin.Profile F, even with the highest Cpmin, would not be selected because its excessively thin profile thickness might cause flutter.Profiles D, E had similar geometries and pressure distributions.E was slightly superior to D in both the Cpmin and Ls.Thus, profile E was selected as the geometry for the anti-cavitation leading edge.

Simulation and model experiment
After extracting the optimal shape from the bionic information, an anti-cavitation leading edge was built based on an existing runner whose outside diameter, D1, was 468 mm.The procedures is shown in Figure 5.The runner domain was a single periodic channel with hexahedral structural meshes.In the grid independence study, the total number of elements was increased from about 1,000,000 to 2,000,000.The differences in the CFD for these two meshes were less than 0.5% and the y + were all less than 30 with additional near wall grid refinement.Therefore, the total number of elements for the mesh used in the calculations was about 1,076,000.The domain and mesh for the bionic runner are shown in Figure 7.The cavitation inception tests were conducted on a typical hydraulic machinery test rig for the same flow conditions as in the 3D simulation.A photograph and schematic of the experiment are shown in Figure 8. NPSHa is the effective net positive suction head and NPSHr is the required net positive suction head.NPSHa depends only on the equipment and the ambient conditions.A bigger NPSHa means that cavitation is less likely to happen。NPSHr depends on the internal flow characteristics in the machine and indicate whether cavitation will occur.NPSHr is hard to measure because the minimum pressure in the runner is difficult to measure.NPSHr can be measured by lowering the ambient pressure with a vacuum pump to cause cavitation at the given flow rate and head conditions.At that moment, NPSHa and NPSHr would be equal and the current net positive suction head, NPSHca, can be easily measured for the cavitation inception data.NPSHca can be expressed as: where ρ is the density of water, g is the acceleration of gravity, pv is the vapour pressure, pS and VS denote the pressure and velocity on the reference plane.As shown in Figure 8, the reference plane was set at the pump-mode inlet, so the reference pressure and velocity data were acquired at the draft tube inlet.Then, the cavitation bubbles were observed using high-speed camera through the reflected image from the blade.A "3 bubbles" criterion was used to identify cavitation inception with the flow rate, reference velocity and recorded pressure after the camera showed about three cavitation bubbles.The flow coefficient, Cφ, and the cavitation coefficient, Cσi, were then calculated to plot the Cφ-Cσi cavitation inception graph.The flow coefficient, Cφ, is expressed as: where ρ is the density of water, ω is the angular speed, R2 is the outer radius of the runner and Qm is the mass flow rate.Cσi is modified to be: where H is the head for the whole unit and NPSHca is as defined in Equation ( 2).

Results and Discussion
The lowest pressure coefficient, Cpmin, was found from the CFD simulations.was nondimensionalized based on a reference plane set at the runner inlet for the reference velocity and pressure.Cφ and Cpmin for the 9 flow rate conditions are shown in Figure 9.The lowest pressure coefficient, Cpmin, changed greatly with increasing flow rate.The variation can be divided into three stages.At small flow rates, Cpmin gradually decreased.As the flow rate increased, the angle of attack gradually tended to zero at the leading edge which reduced the local pressure drop and increased Cpmin to a maximum near the design point.For flow rates larger than the design flow rate, the angle of attack increased again which aggravated the flow separation and quickly reduced Cpmin.The pressure and velocity distributions at a blade span of 0.5 are shown in Figure 10 for flow rates of 145, 165 and 200 kg/s.For the original runner, the velocity increased and the pressure decreased suddenly near the leading edge due to the sharp geometry.However, the bionic runner had just a gentle decline because of the streamlined leading edge.In general, for the same working conditions, the bionic runner with the anti-cavitation leading edge had less flow separation and a higher Cpmin than the original runner.Thus, the anti-cavitation leading edge give the pump-turbine a greater safety margin.The simulation results are compared with experiment results in Figure 11 for a flow rate of 185 kg/s. in experiment, bubbles occurred near the leading edge and close to the shroud.For the same conditions, the lowest pressure regions given by the CFD model overlapped with the bubble locations.Thus, the geometry causes the local flow separation and increased pressure drop which result in cavitation.Altogether, nine sets of data were measured in the experiments with the data for the Cφ-Cσi curves compared in Figure 12.The curve for the original runner cross the operating range curves.Thus, cavitation will occur with the original runner, which is unsafe.However, for the bionic runner, Cσi were always lower than the plant cavitation coefficient, thus, cavitation was less likely to happen.The anticavitation leading edge reduced Cσi by an average of 16.44%, with a maximum Cσi reduction of 28.21%.Thus, the cavitation in the pump-turbine had significantly improved.

Conclusions
Bionic streamlined shapes were used to develop an anti-cavitation leading edge for a pump-turbine runner.CFD simulations were used to predict the pressure distribution.The cavitation coefficient was also measured experimentally.Comparison of the results showed that: (1) The runner geometry strongly impacts the flow distribution.A fish-like streamlined shape leads to a flat geometry that eliminates the adverse pressure gradient along the surface and delay the local flow separation.
(2) The leading edge radius of curvature is relatively large.They result is an abrupt transformation which adversely affects the cavitation inception.The anti-cavitation leading edge reduces the local flow separation and the pressure gradient by the streamlined shape.Therefore, the pump-turbine with the bionic anti-cavitation leading edge has a lower cavitation coefficient in the operating range.The reduced cavitation significantly enhances the operating safety and reduces the construction and repair costs.

Figure 1 .
Figure 1.Geometrical division and parameters in a fish.The top graph shows the three body axes,

Figure 2 .Figure 3 .
Figure 2. Mesh and boundary conditions.The left side boundary was a velocity inlet, the right side boundary was a pressure outlet, the top and bottom boundaries were open boundaries and the profile was a no slip wall.The inset shows a partial enlarged view of the grid refinement at profile leading edge.2.1.2.Analysis and shape selection.The CFD results in Figure3show the pressure contours and velocity vectors for the 0 and 10 degree angles of attack.The contours clearly show the minimum pressure region.The velocity vectors indicate the flow directions and reflect the local flow separation.The fluid flowed around the profile and separated from the surface near the leading edge.The minimum pressure region coincided with the separation location.Thus, the geometry, the pressure drop and the cavitation inception all correlate with each other.

Figure 4 .
Figure 4. Pressure coefficients on the low pressure surfaces, (a) 0 degree angles of attack, (b) 10 degree angles of attack.The data in Table 2 rule out profiles A, B and C due to their low Cpmin.Profile F, even with the highest Cpmin, would not be selected because its excessively thin profile thickness might cause flutter.Profiles D, E had similar geometries and pressure distributions.E was slightly superior to D in both the

( 1 )
Select the top 75% of profile E, generate a relative length-thickness curve, and select the end width, Du. (2) Cut off the top 20% of the origin blade along the streamwise direction.(3) Use the rest with a top width, Dm, with Du from procedure 1 equal to 1.05 Dm to generate an anti-cavitation leading edge proportional to the original length-thickness rates.(4) Smoothly connect the anti-cavitation leading edge with the rest part of the blade.A CAD model of the bionic runner was then created.The original and the bionic runner profiles are compared in Figure6.

Figure 6 .
Figure 6.Comparison of the original and bionicrunner including the real model and the CAD model.Three-dimensional fluid domains were created for the bionic and original runners from CAD models.The runner domain was a single periodic channel with hexahedral structural meshes.In the grid independence study, the total number of elements was increased from about 1,000,000 to 2,000,000.The differences in the CFD for these two meshes were less than 0.5% and the y + were all less than 30 with additional near wall grid refinement.Therefore, the total number of elements for the mesh used in the calculations was about 1,076,000.The domain and mesh for the bionic runner are shown in Figure

Figure 7 .
Figure 7. Mesh for the periodic computational domain.The inset shows a partial enlarged view of the grid refinement at leading edge.The 3D numerical simulations used the incompressible Reynolds averaged Navier-Stokes equations with the SST k-ω turbulence model.The cavitation inception was based on the pressure drop with the simulations run without cavitation with a reference pressure of 1 Atm.The runner domain was set as rotating with a rotational speed of 1000 rpm.The domain boundaries consisted of a mass flow inlet, a pressure outlet, two rotating periodic interfaces and three no slip walls with 9 different conditions in the simulation.The flow through the whole runner Qv0 were 110, 125, 145, 155, 165, 185, 200, 210 and 225 kg/s.Thus, the mass flow rates at the inlet of a single channel, Qv, were set as one ninth of Qv0.A static pressure of 0 Pa was set at the pressure outlet boundary.The no slip walls included the hub, shroud and blade.The cavitation inception tests were conducted on a typical hydraulic machinery test rig for the same flow conditions as in the 3D simulation.A photograph and schematic of the experiment are shown in Figure8.NPSHa is the effective net positive suction head and NPSHr is the required net positive suction head.NPSHa depends only on the equipment and the ambient conditions.A bigger NPSHa means that cavitation is less likely to happen。NPSHr depends on the internal flow characteristics in the machine and indicate whether cavitation will occur.NPSHr is hard to measure because the minimum pressure in the runner is difficult to measure.NPSHr can be measured by lowering the ambient pressure with a vacuum pump to cause cavitation at the given flow rate and head conditions.At that moment, NPSHa and NPSHr would be equal and the current net positive suction head, NPSHca, can be easily measured for the cavitation inception data.NPSHca can be expressed as:

Figure 8 .
Figure 8. Photograph and schematic diagram of the cavitation inception experiment device, (a) photograph of the pump-turbine model, (b) schematic diagram of the whole test rig.

Figure 9 .
Figure 9.The variation of the flow coefficient, Cφ, and the lowest pressure coefficient, Cpmin.

Figure 10 .
Figure 10.Pressure and velocity distributions at a blade span of 0.5.The simulation results are compared with experiment results in Figure11for a flow rate of 185 kg/s. in experiment, bubbles occurred near the leading edge and close to the shroud.For the same conditions, the lowest pressure regions given by the CFD model overlapped with the bubble locations.Thus, the geometry causes the local flow separation and increased pressure drop which result in cavitation.Altogether, nine sets of data were measured in the experiments with the data for the Cφ-Cσi curves compared in Figure12.The curve for the original runner cross the operating range curves.Thus, cavitation will occur with the original runner, which is unsafe.However, for the bionic runner, Cσi were always lower than the plant cavitation coefficient, thus, cavitation was less likely to happen.The anticavitation leading edge reduced Cσi by an average of 16.44%, with a maximum Cσi reduction of 28.21%.

Figure 11 .
Figure 11.Comparison of the bubbles seen in the experiment and the lowest pressure region calculated in the CFD simulation.

Figure 12 .
Figure 12.The experiment data of cavitation coefficient Cσi.

Table 1 .
The streamlined fish shapes and geometry parameters.

Table 2 .
Lowest pressure coefficient and its position.