A method for suppressing hump characteristics of a pump-turbine based on split blade optimization

Abstract

The application discloses a water pump water turbine hump characteristic suppression method based on split blade optimization. The method establishes a prototype runner and a complete flow system model, split short blades are arranged between adjacent original long blades, a number-length ratio two-dimensional parameter space is constructed by means of blade number combination and a ratio of corresponding diameters of long blade and short blade outlet edges, a parameter non-monotonic response law and an effective interval are identified through first stage wide range scanning, second stage fine screening is carried out in the candidate interval, and an optimal coupling window is obtained; further, stability evaluation is carried out in combination with the flow-head characteristic in the hump area of the pump working condition, the internal flow field and the pressure pulsation, and target split blade configuration is determined on the basis of meeting the head and efficiency requirements. The application can take into account the hydraulic performance and the hump area operation stability, and improves the pertinence and efficiency of the split blade parameter optimization of the water pump water turbine.

Description

Technical Field

[0001] This invention relates to the field of pumped storage unit design technology, specifically to a method for suppressing the hump characteristics of a pump-turbine based on optimized splitter blades. Background Technology

[0002] Pumped storage power stations serve multiple functions, including peak shaving, frequency regulation, emergency backup, and promoting the integration of renewable energy. As the core energy conversion equipment of pumped storage units, the pump-turbine must consider both pump and turbine operating conditions. With the development of units towards higher head, larger capacity, and wider operating conditions, stability issues under off-design conditions are becoming increasingly prominent.

[0003] In the low-flow range of pump operation, the flow-head characteristic curve of the pump turbine may exhibit local non-monotonic changes, forming a hump characteristic. The flow within the hump region is significantly unsteady, and the flow matching relationship between the impeller passage, the bladeless zone, the guide vanes, and the tailrace pipe changes, easily leading to phenomena such as flow separation, backflow, vortices, rotational instability, and pressure pulsation, which in turn cause fluctuations in operating point, increased vibration, and increased noise.

[0004] Existing technologies have already controlled hump characteristics through different flow components. Invention patent CN114576065B discloses a pump-turbine runner with bending-torsional sweep characteristics. By changing the axial projection, cylindrical projection, and blade placement angle distribution of the high-pressure side of the main blades, the geometric design space of the main blades is expanded to improve the hump characteristics under pump conditions and the S-characteristics under turbine conditions. This solution mainly starts from the original geometry of the main blades. However, since the main blades bear the main energy conversion function, their geometric parameters are simultaneously constrained by factors such as efficiency, cavitation, and mechanical strength. Therefore, the ability to directly adjust the flow distribution within the runner's impeller passages and the dimensions of local flow channels remains limited.

[0005] Invention patent CN115199455A discloses a grooved draft tube and its usage method for suppressing the hump characteristics of a pump-turbine. By setting annularly distributed inner grooves on the inner wall of the draft tube cone, the water flow forms a jet to disrupt or suppress pre-swirl, thereby improving the flow pattern in the draft tube and reducing hump instability. This solution mainly acts on the draft tube region and can control pre-swirl, but it does not directly change the flow channel structure between adjacent blades of the runner. When the unstable flow in the hump region simultaneously involves velocity gradients, flow separation, wakes, and static-rotation interference within the runner blade passages, local control only in the draft tube region is still insufficient to directly regulate the flow inside the runner.

[0006] Splitter blades can re-divide the flow channel between adjacent main blades, altering the channel width, blade density, load distribution, and exit wake, thus possessing the potential to improve the flow inside the runner. However, the effect of splitter blades does not monotonically increase with increasing number or length. Too few splitter blades result in insufficient channel segmentation and rectification; too many reduce the flow area and increase frictional losses. Insufficient splitter blade length limits their guiding and constraining capabilities for the main flow; excessive length may alter the degree of blade passage blockage and load distribution. Therefore, there is a mutually restrictive coupling relationship between the number and length of splitter blades, and they cannot be simply selected as independent parameters.

[0007] Another shortcoming of existing technologies is that conventional structural optimization often uses design operating efficiency, head, or a single flow field index as the main evaluation criteria. However, hump characteristics are essentially the result of the combined effects of external characteristics and internal unsteady flow. Achieving high efficiency near the design flow rate does not necessarily mean that a scheme can simultaneously reduce vortices, backflow, and pressure pulsations in the hump region. Therefore, a systematic approach is still needed that can first identify an efficient coupling window of the splitter blade number-length ratio, and then perform secondary screening within that window based on the external characteristics, internal flow field, and pressure pulsations in the hump region.

[0008] Therefore, the technical problems that need to be solved in this field are: how to establish a coupling matching relationship between the number and length ratio of the splitter blades to avoid local optima caused by single-factor optimization of the number or length; how to identify candidate windows with good energy performance from a large parameter space; and how to further combine the flow rate, head characteristics, internal flow structure and pressure pulsation characteristics in the hump region to determine the target configuration that is truly suitable for hump suppression in pump operation from the candidate windows. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method for suppressing the hump characteristics of pump-turbines based on the coupled optimization of the number and length ratio of splitter blades. This method does not treat the number or length of a single splitter blade as an independent optimization object. Instead, it establishes a two-dimensional parameter combination of the number ratio and length ratio, identifies its non-monotonic response law and candidate high-efficiency intervals through a wide-range scan, performs a localized refined search on the candidate intervals, and further combines the external characteristics of the hump region, internal flow field, and pressure pulsation for stability screening, thereby obtaining a target splitter blade configuration that balances energy performance and hump region stability.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: a method for suppressing the hump characteristics of a water pump turbine based on optimized flow divider blades, specifically comprising: Step S1: Establish a prototype water pump turbine runner and a complete flow system model. Establish a computational domain for the complete flow system, including the volute, fixed guide vanes, movable guide vanes, runner, and tailrace pipe. Based on the prototype runner, establish a runner model with splitter blades. The splitter blades are positioned between adjacent original blades, forming a combined long and short blade flow channel.

[0011] Step S2: Define the coupling parameter for the number and length ratio of the splitter blades. The quantity ratio is determined by the original number of long blades and the number of short splitter blades, with the ratio 'a' of the diameters corresponding to the outlet edges of the long and short blade ribs used as the length ratio parameter. Preferably, the number of long blades is equal to the number of short splitter blades, and quantity ratio schemes of 4 long and 4 short, 5 long and 5 short, 6 long and 6 short, 7 long and 7 short, and 8 long and 8 short are established sequentially.

[0012] Step S3 involves performing a first-stage wide-range parameter scan. Multiple length ratios 'a' are set for each quantity allocation, forming a two-dimensional parameter matrix of quantity-length ratio. Numerical calculations are performed under uniform head, flow rate, rotational speed, guide vane opening, and boundary conditions to obtain efficiency and other hydraulic performance parameters for both pump and turbine operating conditions. Based on the variation of efficiency with length ratio under different quantity allocations, and the increase in efficiency with quantity at the same length ratio, the unimodal characteristics of the quantity effect and the effective range of the length effect are identified.

[0013] Step S4: Determine the first candidate interval and perform a second-stage refined screening. Based on the first-stage scanning results, the region with a high length ratio and good overall hydraulic performance of the two operating modes is determined as the first candidate interval. Within this interval, the length ratio step size is reduced, and different quantity ratios are recombined for refined calculation to obtain the optimal coupling window for the quantity-length ratio.

[0014] Step S5: Perform secondary stability screening in the hump region. For the parameter combination and prototype impeller within the preferred coupling window, conduct steady-state and transient numerical simulations at multiple typical flow points in the hump region of the pump operating conditions. Compare the flow-head relationship, efficiency, pressure field, velocity field, streamlines, turbulent kinetic energy, and vortex structure. Compare the pressure pulsation dominant frequency, harmonics, and amplitude using the time-domain signal and fast Fourier transform results from the pressure monitoring points.

[0015] Step S6: Determine the target hump suppression configuration. Based on meeting the design head and efficiency requirements, the target flow splitter blade number and length ratio are determined from the preferred coupling window using the following screening conditions: reduction of the hump area, weakening of the abnormal slope of the characteristic curve, flow separation and vortex reduction in the impeller and adjacent areas, and reduction of pressure pulsation amplitude. Based on this, the target impeller structure for suppressing the hump characteristics of the water pump turbine is obtained.

[0016] Let D be the diameter corresponding to the exit edge of the long blade skeletal line. LThe diameter corresponding to the outlet edge of the shunting short blade rib line is D. S Then the length ratio parameter 'a' is expressed as: a = D L / D S (1); In a preferred embodiment, the length ratio 'a' of the first-stage wide-range scan is successively set to 9 / 10, 8 / 10, 3 / 4, 13 / 20, 11 / 20, and 1 / 2, forming a two-dimensional parameter matrix with five quantity ratios ranging from 4 long and 4 short to 8 long and 8 short. Calculation results show that, with a fixed length ratio, as the number of blades increases, the efficiency generally exhibits a non-monotonic pattern of first increasing and then decreasing or tending to saturate, indicating that there is an upper limit to the increase in the number of blades. With a fixed quantity ratio, a larger length ratio is generally beneficial to improving pump efficiency. Based on this pattern, the region where 'a' is not less than 0.8 can be considered as the key region for subsequent refined screening.

[0017] In a further preferred embodiment, length ratios of 40 / 50, 42 / 50, 43 / 50, 44 / 50, 45 / 50, 46 / 50, 47 / 50, and 48 / 50 are set within the range of a = 0.80 to 0.96, and then recombined with quantity ratios ranging from 4 long and 4 short to 8 long and 8 short. Detailed results show that under pump operating conditions, the efficiency corresponding to most length ratios exhibits a single-peak distribution with the quantity ratio, with a relatively obvious high-efficiency zone forming near the 5 long and 5 short ratio. The optimal quantity ratio for turbine operating conditions can shift towards the 6 long and 6 short ratio, indicating that the optimal requirements for the quantity-length ratio are not entirely consistent between the two operating modes.

[0018] Based on the energy performance characteristics of both operating modes, a value of 45 / 50 to 48 / 50, combined with a ratio of 5 long and 5 short pumps, can serve as a preferred candidate coupling window when the pump operating condition is the primary reference. This candidate window is used to narrow down the search range for subsequent hump region stability evaluation. The target hump suppression configuration still needs to be further determined based on the flow-head characteristics, internal flow field, and pressure pulsation results, thereby avoiding directly equating the highest efficiency scheme with the optimal hump suppression scheme.

[0019] Compared with the prior art, the beneficial effects of the present invention include: (1) The present invention optimizes the ratio of the number and length of the splitter blades as two-dimensional parameters that are coupled together. It can identify the non-monotonic matching law that increasing the number is not necessarily better and increasing the length is not an independent determination of performance, thus avoiding local optima caused by single-factor optimization.

[0020] (2) The present invention adopts a hierarchical optimization route of “wide range scanning - candidate interval identification - local refinement - secondary screening of hump area”, which can first use energy performance to quickly eliminate obviously unfavorable parameter combinations, and then concentrate computing resources to analyze high-value parameter areas, thereby improving optimization efficiency.

[0021] (3) The calculation results of this invention show that when the length ratio is high, the reasonable quantity ratio can form a balance between flow channel division, rectification effect, flow area and friction loss; when the quantity is too large, the efficiency tends to saturate or decrease, which reflects the coupling matching relationship between quantity and length ratio, and provides verifiable parameter basis for target impeller configuration.

[0022] (4) This invention does not take the highest efficiency as the only goal, but further combines the flow-head characteristics, pressure pulsation and internal flow field of the hump region within the preferred coupling window for screening, which helps to avoid the situation where efficiency is improved but the unsteady flow in the hump region is not improved synchronously.

[0023] (5) The present invention can improve the velocity gradient, load distribution and outlet wake by re-dividing the impeller flow channel by splitting the flow blade, reduce local flow separation, secondary flow and large-scale vortex, and select a configuration with lower pressure pulsation through secondary stability evaluation, thereby improving the operating stability of the pump in the hump area.

[0024] (6) The parameterized optimization method formed by the present invention can be used for the design of the runner of a new pumped storage unit, and can also be used for the retrofit of the runner of an existing unit while keeping the volute, guide vanes and tailrace pipe basically unchanged. Attached Figure Description

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a comparison chart of pump operating efficiency under different ratios in the first stage of this invention embodiment; Figure 3 This is a comparison chart of turbine operating efficiency under different ratios in the first stage of this invention embodiment; Figure 4 This is a comparison chart of pump operating efficiency under different ratios in the second stage of this invention embodiment; Figure 5 This is a comparison chart of turbine operating efficiency under different ratios in the second stage of this invention embodiment; Figure 6 This is a comparison diagram of the original impeller and the flow-diverting blade impeller structures of this invention; Figure 7 This is a schematic diagram of the parametric design of the flow divider blades of the present invention. Detailed Implementation

[0027] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. It should be understood that the following embodiments are used to illustrate the technical concept and implementation process of the present invention, and are not intended to limit the scope of protection of the present invention. For pump-turbines of different models, specific speeds, heads and capacities, the quantity ratio, length ratio, calculation conditions and screening range can be adjusted accordingly according to their actual operating parameters. As long as the technical approach of using the coupling screening of the number and length ratio of the splitting blades and combining the external characteristics of the hump region, the internal flow field and pressure pulsation for secondary evaluation is adopted, the present invention can be implemented.

[0028] Example 1 This embodiment takes a pump-turbine of a pumped storage power station as the research object. A complete flow system including the volute, fixed guide vanes, movable guide vanes, runner, and draft tube is established. To ensure comparability between different flow-splitting blade schemes, the geometry of the volute, fixed guide vanes, movable guide vanes, and draft tube remains unchanged, except for the number and length ratio of the flow-splitting blades inside the runner. Figure 6 As shown, the prototype runner adopts a uniformly distributed original long blade structure; the runner with splitting blades sets splitting short blades between adjacent original long blades, so that the long blades and splitting short blades are arranged alternately along the circumferential direction.

[0029] Each flow component has its own fluid domain established and then assembled as a whole. Under pump operation, the fluid enters from the tailrace pipe side and flows sequentially through the impeller, moving guide vanes, fixed guide vanes, and volute. Fluid interfaces are set between the computational domains to achieve continuous transmission of pressure, velocity, and turbulence variables. After model assembly, duplicates, geometric interferences, flow channel breaks, and unclosed areas are checked to ensure the continuity and integrity of the computational domains.

[0030] The preferred computational grid is a structured hexahedral mesh. Mesh independence was verified for different mesh sizes, with head and efficiency as the primary criteria. As the number of mesh elements increases, the computational results gradually stabilize; when the mesh size reaches approximately 6.25 million elements, further increasing the mesh size has a relatively small impact on head and efficiency. Therefore, this embodiment uses a mesh model of approximately 6.5 million elements for subsequent steady-state and transient calculations to balance computational accuracy and computational resource consumption.

[0031] The computational medium is water, treated as an incompressible fluid. The Reynolds-averaged governing equations are used to describe the internal flow, and the SST k-ω model is employed for turbulence. A pressure inlet is used, and a mass flow rate outlet is used. A rotating computational domain is set up in the impeller region, while other flow components are stationary domains. Data exchange between these domains is achieved through interfaces. The pressure-velocity coupling uses the SIMPLEC algorithm, and the governing equations are discretized using a second-order precision scheme. The residual convergence accuracy is set to 10. -6 .

[0032] Steady-state calculations first obtain the head, efficiency, pressure field, velocity field, streamlines, and turbulent kinetic energy distribution for each operating condition, and use the converged steady-state flow field as the initial condition for transient calculations. The time step for transient calculations is set to the time corresponding to 3° rotation of the impeller, with 20 internal iterations per time step, continuously calculating 30 rotations of the impeller to obtain stable periodic pressure signals and unsteady flow processes.

[0033] To verify the reliability of the numerical model, multiple operating conditions were selected on both sides of the design flow rate, and the numerically calculated flow-head and flow-efficiency curves were compared with the experimental results. The overall trend of the numerical results and experimental results is consistent, with the maximum head error being approximately 1.22% and the maximum efficiency error being approximately 3.27%. This indicates that the established numerical model can well reflect the external characteristics and internal flow laws of the pump-turbine, and can be used for subsequent optimization of the splitter blade parameters and pressure pulsation analysis.

[0034] Example 2 To establish the coupling relationship between the number and length ratio of the splitter blades, this embodiment first performs a wide-range two-dimensional parameter scan. Using the original number of long blades N... L and the number of short shunting blades N S To form a quantity ratio, and to make N L =N S Five different quantity ratios are set in sequence: 4 long and 4 short, 5 long and 5 short, 6 long and 6 short, 7 long and 7 short, and 8 long and 8 short, as shown in Table 1.

[0035] The length of the splitter blades is characterized by the ratio of the diameters corresponding to the exit edges of the long and short blade ribs. For example... Figure 7 As shown, let the diameter corresponding to the exit edge of the long blade skeletal line be D. L The diameter corresponding to the outlet edge of the shunting short blade rib line is D. S The length ratio parameter a is determined according to formula (1). In the first stage, a is set to 9 / 10, 8 / 10, 3 / 4, 13 / 20, 11 / 2 and 1 / 2 respectively, forming a total of 30 combinations of quantity-length ratio. The mass flow rate of the pump is set to 379 kg / s and the mass flow rate of the turbine is set to 350 kg / s; the same boundary conditions, rotational speed, guide vane opening and solution settings are used for each scheme.

[0036] Table 1 Design Scheme for the Quantity-Length Ratio of Diverter Blades in the First Stage

[0037] Table 2 Efficiency of the first-stage impeller pump with splitter blades

[0038] Table 3 Efficiency of the turbine with split-flow blades in the first stage

[0039] As shown in Table 2, under a fixed length ratio, the pump efficiency does not continuously increase with the increase in the number of blades, but rather exhibits a pattern of first increasing and then decreasing or gradually approaching saturation. Taking a=9 / 10 as an example, the pump efficiency increases from 91.33% with 4 long and 4 short blades to 91.87% with 5 long and 5 short blades, and then decreases to 91.43% with 6 long and 6 short blades, 90.82% with 7 long and 7 short blades, and 90.28% with 8 long and 8 short blades, respectively. This change indicates that increasing the number of splitting blades can enhance the flow channel segmentation and rectification effect, but as the number of blades continues to increase, the reduction in flow area and the increase in friction loss gradually become dominant, causing the efficiency to drop from its peak.

[0040] With a fixed ratio, the length proportion of the splitter blades also shows a significant impact. Taking a 5-long-5-short configuration as an example, when 'a' increases from 1 / 2 to 9 / 10, the pump efficiency increases from 87.90% to 91.87%. A larger length proportion helps to enhance the guidance and constraint of the splitter blades on the mainstream and makes the geometric correspondence between the long and short blades more continuous. When the splitter blades are short, the asymmetric flow channel formed by the long and short blades is more obvious, and low-speed zones and flow separation are more likely to occur near the inlet of the splitter blades, resulting in additional hydraulic losses.

[0041] Table 3 shows that the response of the turbine operating condition to the quantity-length ratio is not exactly the same as that of the pump operating condition. For example, when a=9 / 10, the turbine operating condition achieves the highest efficiency of 92.08% at the 6 long and 6 short position, while the pump operating condition achieves the highest efficiency at the 5 long and 5 short position under the same length ratio.

[0042] like Figure 2 and Figure 3 As shown, two fundamental patterns can be identified through the first-stage wide-range scan: First, there is a significant non-monotonic effect in the quantity ratio; appropriately increasing the number of blades is beneficial to improving flow, but the performance benefits decrease after exceeding a certain number. Second, regions with a high length ratio are generally more conducive to pump energy performance. Based on these patterns, the region where a ≥ 0.8 is determined as the key area for the second-stage refined search.

[0043] Example 3 After identifying the high length ratio region in the first stage, the length ratio is further refined to identify a narrower matching window between the quantity and length ratio. In this embodiment, eight length ratios are set: a=48 / 50, 47 / 50, 46 / 50, 45 / 50, 44 / 50, 43 / 50, 42 / 50, and 40 / 50. These are then combined with five quantity ratios: 4 long 4 short, 5 long 5 short, 6 long 6 short, 7 long 7 short, and 8 long 8 short, resulting in 40 refined schemes.

[0044] Table 4. Refined Design Scheme for the Second-Stage Runner with Split Blades

[0045] Table 5. Efficiency of the second-stage impeller pump with splitter blades under operating conditions.

[0046] Table 6 Efficiency of the turbine with split-flow blades in the second stage

[0047] Table 5 shows that under pump operating conditions, when a = 48 / 50 and 47 / 50, the 5-long-5-short configuration achieves efficiencies of 91.86% and 91.70%, respectively; when a = 45 / 50, the efficiency reaches 91.83%. For most length ratios, the efficiency exhibits a clear single-peak distribution with respect to the number of blades, with the peak value mainly located near the 5-long-5-short or 6-long-6-short configurations. This result further illustrates that there is a coupled matching relationship between the number parameters and the length parameters, and sustained benefits cannot be obtained simply by increasing the number of blades.

[0048] When the number increases to 8 long and 8 short pumps, the pump efficiency under different length ratios is concentrated in a narrow range of approximately 90.0% to 90.5%, indicating that the flow channel has been sufficiently divided at this point. As the number continues to increase, parameter adjustments gradually enter the saturation zone, and efficiency differences are more affected by flow channel blockage and friction losses. This saturation phenomenon constitutes an important basis for judging the upper limit of the quantity ratio.

[0049] The response under turbine operating conditions is more complex. Table 6 shows that when a=45 / 50, the efficiency of the 6-long-6-short configuration reaches 89.69%, and when a=40 / 50, the efficiency of the 6-long-6-short configuration also reaches a relatively high value of 89.57%, indicating that the local optimum of the turbine operating condition can shift towards the vicinity of medium length and the 6-long-6-short configuration. This phenomenon further demonstrates that the geometric optimization directions of the pump and turbine operating conditions are inherently constrained. During design, coordination between the two operating modes is necessary based on the main technical objectives, rather than using the maximum efficiency at a single point under either condition as the sole selection criterion.

[0050] like Figure 4 and Figure 5 As shown, based on the two-dimensional parameter response laws of the first and second stages, when the hump problem under pump conditions is the main optimization object, while also considering the energy performance under turbine conditions, a value of 45 / 50 to 48 / 50, combined with a ratio of 5 long and 5 short components, can be determined as the preferred candidate coupling window. It should be noted that this window is used to narrow the parameter range for hump stability evaluation and is not directly equivalent to the final optimal hump suppression configuration; the final structure still needs to be determined through secondary evaluation of the external characteristics of the hump region, internal unsteady flow, and pressure pulsation.

[0051] Example 4 After obtaining the preferred candidate coupling window, the prototype impeller and candidate split-blade impellers are selected for full characteristic calculation of pump operation. The design flow rate and typical flow points in the hump region are determined based on the flow-head curve of the prototype machine, and at least the low-flow-depth operation, the operation before and after the hump region, and the design operation are covered.

[0052] First, compare the flow-head and flow-efficiency curves of each scheme. For the pump operating conditions in the hump region, focus on observing the degree of local non-monotonicity of the head curve, whether the negative slope range narrows, and the efficiency change at the same flow rate. If a parameter combination has high efficiency in the constant flow screening stage, but its flow-head curve still shows obvious abnormal inflections, it will not be considered as the final target configuration.

[0053] Secondly, the pressure, velocity, streamlines, and turbulent kinetic energy distributions at the runner's mid-section and flow surface are analyzed, with a focus on the low-velocity region, recirculation region, and local vortices near the suction surface of the main blades and the short splitter blades. The influence of the splitter blades on the flow channel velocity gradient, blade load, and wake width is analyzed. A reasonable number-to-length ratio can make the flow channel segmentation between long and short blades more uniform, reduce the local adverse pressure gradient, and weaken the flow separation near the inlet of the splitter blades.

[0054] Further analysis of the pressure, velocity, and turbulent kinetic energy distributions in the bladeless region between the runner and the movable guide vanes, the movable guide vane flow channel, the fixed guide vane flow channel, and the volute region is conducted to determine the impact of the splitter blades on the circumferential non-uniformity of the flow rate during the transition from the runner to the stationary flow channel. For the tailrace region, the focus is on comparing the inlet pre-swirl, low-velocity region, large-scale vortices, and regions of concentrated turbulent kinetic energy. If the candidate design can achieve a more uniform velocity distribution at the runner outlet and reduce the pre-swirl intensity entering the tailrace, it will help to weaken the downstream development of large-scale vortices.

[0055] By jointly evaluating external characteristics and internal flow fields, schemes that only have good energy performance at the design point but insufficient improvement in flow in the hump region can be eliminated, thereby further converging the high-efficiency coupling window into a candidate configuration for hump stability.

[0056] Example 5 Transient calculations were performed based on candidate configurations for hump stability, and pressure monitoring points were deployed in different regions of the pump-turbine. Monitoring points DT1–DT11 were deployed in the draft tube region; several typical monitoring points were set in the runner flow channel; monitoring points GV1–GV12 were deployed in the movable guide vane flow channel; monitoring points SV1–SV16 were deployed in the fixed guide vane flow channel; and monitoring points SC1–SC11 were deployed in the volute. These monitoring points were used to simultaneously acquire the dynamic-static interference of the runner, the non-uniformity of flow in the guide vane region, and the transient pressure changes caused by draft tube vortices.

[0057] The pressure time-domain signals at each monitoring point were dimensionless and the frequency domain spectrum was obtained using Fast Fourier Transform. The dominant frequency, harmonics, and amplitude variations of the prototype runner and different candidate splitter blade schemes were compared in each monitoring region. The analysis examined both the dynamic and static interference components corresponding to the blade frequency and its harmonics, and also focused on low-frequency pressure fluctuations caused by backflow, rotational instability, and large-scale vortices.

[0058] The prototype runner easily generates strong large-scale vortices and circumferential non-uniform flow in the hump region, and its pressure fluctuations can propagate from the runner region to the guide vanes and tailrace. By adopting a reasonable ratio of the number to length of the splitting blades, the flow rate within the channel is redistributed, the velocity gradient and local flow separation are weakened, and the runner outlet wake and pre-swirl intensity decrease, thereby reducing the pressure pulsation amplitude in some monitoring areas. The dominant frequency in the pressure spectrum can still be represented by the blade frequency and its harmonics, but the corresponding frequency amplitude can decrease due to the weakening of the static-rotation interference.

[0059] The final configuration selection is not based on the minimum amplitude of a single monitoring point, but rather on a comprehensive consideration of the characteristics outside the hump region, the flow field in key areas, and pressure pulsations at multiple locations. Under the condition of meeting the head and efficiency requirements, the parameter combination with a reduced negative slope range, weakened large-scale vortices in the runner and tailrace, and generally low pressure pulsations at key monitoring locations is preferred.

[0060] Example 6 The fundamental reason for the coupling effect caused by the number and length ratio of the splitter blades lies in the fact that the flow channel segmentation strength, blade guiding effect, flow area, and wall friction loss all jointly affect the energy conversion inside the runner. When the number of splitter blades is small, the flow channel between adjacent long blades is still relatively wide, resulting in large local velocity gradients and load differences, and the weakening effect of the splitter blades on secondary flow and wake is limited. As the number increases, the flow channel width decreases, the circumferential flow distribution becomes more uniform, and efficiency and flow stability can be improved.

[0061] As the number of splitter blades continues to increase, the flow channel becomes excessively segmented, the flow area decreases, wetted perimeter and friction increase, and the local blockage effect intensifies, leading to saturation or even a decrease in efficiency improvement. Therefore, there is an appropriate range for the number of splitter blades related to their length ratio. Longer splitter blades can intervene in the mainstream guidance earlier, making the density change between long and short blades smoother, reducing sudden load changes and trailing edge asymmetric shedding; when the splitter blades are too short, the constraint on the mainstream is insufficient, and low-speed vortices are more likely to form at their inlet positions.

[0062] The two types of effects mentioned above are mutually restrictive, meaning that the optimal number of blades corresponding to different length ratios is not exactly the same. The single-peak distribution, quantity saturation, and optimal point shifts between the two operating modes observed in the first and second stage calculations all indicate a non-monotonic coupling relationship between the number of splitter blades and the length ratio. Therefore, this invention does not select the maximum or minimum value from a single parameter, but first determines a two-dimensional candidate coupling window, and then completes the final selection using the hump region stability index.

[0063] Within the data range of this embodiment, a = 45 / 50 to 48 / 50 and 5 long and 5 short constitute a preferred candidate window with pump operating conditions as the primary reference. In actual engineering, several parameter combinations can be selected in this window and its adjacent area to perform full-flow external characteristics and transient stability calculations, and the target configuration can be determined based on the hump area range, abnormal slope, flow field separation degree, and pressure pulsation results. Since the target configuration depends on the specific unit geometry and operating parameters, the above candidate window is used to illustrate the implementation of the present invention and does not exclude the occurrence of adjacent but numerically different coupled windows in other types of pump-turbine systems.

[0064] Example 7 For newly constructed pumped storage power stations, a prototype runner model can be established after the preliminary hydraulic design of the pump turbine is completed. The candidate window for the number-length ratio of the splitter blades can be obtained through the two-stage parameter scanning method of this invention. Then, a secondary evaluation of the full characteristics and pressure pulsation in the hump region is performed. The final determined target splitter blade parameters are used for the hydraulic finalization of the runner. This allows for simultaneous consideration of efficiency and low-flow stability during the design phase, reducing the number of modifications required based solely on design efficiency.

[0065] For units already in operation that experience pump instability in the hump zone, the basic structures of the volute, fixed guide vanes, movable guide vanes, and tailrace pipe can remain unchanged. Only a parametric model of the splitter blades needs to be established for the original runner. Based on the actual head, speed, guide vane opening, and flow range, a new two-dimensional parameter space with a quantity-length ratio is established. The same wide-range scanning-refined screening-hump stability evaluation process is used to obtain the modification plan, thereby reducing the scope of modification and improving the design's specificity.

[0066] For pump-turbines of different models, specific speeds, and capacities, the quantity ratio, length proportion range, and fine-tuning step size can be changed. However, it is preferable to keep the structure and calculation conditions of each scheme consistent except for the parameters of the splitter blades, to ensure that the comparison results reflect the quantity-length ratio coupling relationship. After the final scheme is verified by model tests or field operation data, it can be used for engineering manufacturing and modification.

[0067] The above embodiments illustrate the main implementation process of the present invention. Those skilled in the art, without departing from the core technical concept of the present invention, can make equivalent adjustments to the number of flow divider blades, length ratios, numerical solution software, mesh generation methods, number of pressure monitoring points, and specific evaluation conditions, all of which can be considered as implementation methods of the present invention.

Claims

1. A method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades, characterized in that, Includes the following steps: S1. Establish a prototype runner of the water pump turbine and a complete flow system model including the volute, fixed guide vanes, movable guide vanes, runner and tailrace pipe. Based on the prototype runner, establish a runner model with splitting short blades, with the splitting short blades set between adjacent original long blades. S2. The number of blades is combined with the number of original long blades and the number of spur short blades. The ratio of the diameters corresponding to the exit edges of the bone lines of the original long blades and the spur short blades is used as the length ratio parameter. The combination of the number of blades and the length ratio parameter are combined to form a two-dimensional parameter space of number-length ratio. S3. Perform a wide-range parameter scan in the two-dimensional parameter space. Under the same operating mode, use the same head, flow rate, speed, guide vane opening and boundary conditions for numerical calculation of each parameter combination to obtain the efficiency and other hydraulic performance parameters under pump and turbine operating conditions. Based on the law of efficiency change with length ratio parameter under different blade number combinations and the law of efficiency change with blade number under the same length ratio parameter, identify the non-monotonic characteristics of blade number effect and the effective range of length ratio parameter. S4. Based on the results of the first stage wide-range parameter scanning, the region with a high length ratio and good comprehensive hydraulic performance of pump and turbine operating conditions is identified as the first candidate interval. Within the first candidate interval, the step size of the length ratio parameter is reduced, and different combinations of blade numbers are recombined for the second stage of fine calculation to obtain the optimal coupling window of the number-length ratio. S5. For the optimal parameter combination within the coupling window and the prototype impeller, steady-state and transient numerical simulations are carried out at multiple typical flow points in the hump region of the pump operating condition. The flow-head relationship, efficiency, pressure field, velocity field, streamline, turbulent kinetic energy and vortex structure are compared. Based on the time domain signal of the pressure monitoring point and the results of fast Fourier transform, the pressure pulsation dominant frequency, harmonic frequency and amplitude are compared. S6. Based on meeting the design head and efficiency requirements, the target blade number combination and target length ratio parameters are determined from the preferred coupling window using the following screening conditions: reduction of the hump area, weakening of the abnormal slope of the flow-head characteristic curve, weakening of flow separation and vortex in the impeller and adjacent areas, and reduction of pressure pulsation amplitude. This is to obtain the target impeller structure for suppressing the hump characteristics of the pump turbine pumping conditions.

2. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, The diversion short blades are arranged circumferentially between two adjacent original long blades, so that the original long blades and the diversion short blades form a long and short blade combination flow channel; when comparing different parameter combinations, except for the number of original long blades, the number of diversion short blades and the length ratio parameters, the geometry of the volute, fixed guide vanes, movable guide vanes and tailrace pipe remains consistent.

3. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, The length ratio parameter is determined according to the following formula: a=D L / D S ; D L D represents the diameter corresponding to the exit edge of the original long blade skeletal line. S The diameter corresponding to the outlet edge of the spur blade rib line.

4. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, The first stage of wide-range parameter scanning includes: setting multiple different combinations of blade numbers and setting multiple different length ratio parameters for each combination of blade numbers, so that the combination of blade numbers and the length ratio parameters are cross-combined to form a two-dimensional parameter matrix; comparing the efficiency with the length ratio parameter under the same combination of blade numbers and the efficiency with the number of blades under the same length ratio parameter, in order to identify the single-peak effect or saturation effect corresponding to the increase of the number of blades and the effective performance range corresponding to the length ratio parameter.

5. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 4, characterized in that, Based on the results of the first-stage wide-range parameter scanning, the parameter region with a high length ratio and good comprehensive hydraulic performance under both pump and turbine operating conditions is identified as the key search area for the second-stage refined calculation. Within the key search area, the step size of the length ratio parameter is reduced, and it is recombined with different blade number combinations to obtain a local high-performance matching region of quantity-length ratio.

6. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 5, characterized in that, Based on the efficiency response patterns of pump and turbine operating conditions obtained from the second-stage refined calculations, an optimal coupling window that takes into account the energy performance of both operating modes is determined from the local high-performance matching region. The optimal coupling window is used to narrow down the parameter range for subsequent stability evaluation in the hump region, and the highest efficiency of a single parameter combination is not used as the basis for determining the final target runner structure.

7. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, Based on the flow-head curve of the prototype pump turbine, determine the design flow rate and typical flow points in the hump region of the pump operating conditions, and at least cover the low-flow-depth operating conditions, the operating conditions before and after the hump region, and the design operating conditions; compare the flow-head curves and flow-efficiency curves of the prototype runner and the candidate runners in the optimal coupling window, evaluate the range of the hump region, the degree of local non-monotonicity of the head curve, and the changes in abnormal slopes, and exclude parameter combinations that, although having high efficiency, still have obvious abnormal inflections in the flow-head curve.

8. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, The internal flow field of the prototype runner and candidate runners is evaluated. The internal flow field evaluation includes analyzing the pressure field, velocity field, streamlines, turbulent kinetic energy, and vortex structure in the runner region, and analyzing the pressure, velocity, or turbulent kinetic energy distribution in at least one of the following regions: the bladeless region between the runner and the moving guide vanes, the moving guide vanes, the fixed guide vanes, the volute, and the draft tube. Among these, the evaluation focuses on the low-velocity region, recirculation region, local vortices, velocity gradient, wake, and the changes in flow non-uniformity at the runner outlet and pre-swirl at the draft tube inlet near the suction surface of the original long blades and the split short blades.

9. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, Pressure monitoring points were arranged at multiple locations in the runner channel, the movable guide vane channel, the fixed guide vane channel, the volute, and the tailrace pipe to acquire transient pressure time-domain signals from each monitoring point. The transient pressure time-domain signals were dimensionless and the frequency domain spectrum was obtained using fast Fourier transform. The dominant frequency, harmonics, and amplitude of pressure pulsations in different monitoring areas of the prototype runner and the candidate runner were compared. At the same time, the rotational-static interference components corresponding to the blade frequency and its harmonics, as well as the low-frequency pressure fluctuations caused by backflow, rotational instability, and large-scale vortices, were evaluated.

10. The method for suppressing the hump characteristics of a pump-turbine based on optimized flow divider blades according to claim 1, characterized in that, Under the condition of meeting the design head and efficiency requirements, the blade number combination and length ratio parameters corresponding to the candidate runner that simultaneously meet the following conditions relative to the prototype runner are determined as the target blade number combination and target length ratio parameters: the range of the pump operating hump area is reduced; the abnormal slope of the flow-head characteristic curve is weakened; the flow separation and vortex in the runner and adjacent areas are weakened; and the overall pressure pulsation amplitude at key pressure monitoring locations is reduced.

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