A method for designing axial length of water turbine skirt based on statistical analysis of operating conditions

Abstract

The application provides a water turbine skirt axial length design method based on operation condition statistical analysis, and belongs to the technical field of hydraulic machinery design and manufacturing. The method solves the problem that the prior art regards the water turbine as an ideal device operating under a fixed condition, and completely ignores the basic fact that the blade angle dynamically changes with external conditions. The method comprises the following steps: collecting historical operation data of a target water turbine in a specific period, statistically analyzing the blade angle in the historical operation data, and determining a high-weight blade angle interval; for the blade angle in the high-weight blade angle interval, determining the projection position of the minimum gap point between the blade outer edge and the inner wall of the runner chamber in the axial direction, obtaining the axial position change range of the sealing key point, and recording the axial coverage interval; and determining the front end position and the rear end position of the skirt in the axial direction according to the axial coverage interval. The method is mainly used in the field of water turbine design.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic machinery design and manufacturing technology, and in particular relates to a method for designing the axial length of the turbine skirt based on statistical analysis of operating conditions. Background Technology

[0002] Hydropower turbines are core power equipment that converts the energy of water flow into mechanical energy, and their operating efficiency and stability directly affect the economic benefits of hydropower stations. In propeller turbines, the annular gap between the outer edge of the runner blades and the stationary inner wall of the runner chamber is called the blade tip clearance. During operation, due to the pressure difference between the working surface and the back surface of the blades, the high-pressure side fluid leaks through this gap to the low-pressure side, forming a blade tip leakage flow. This leakage flow not only does no work, resulting in energy loss, but also interferes with the mainstream water flow, causing eddies and pressure pulsations. It is one of the key reasons for the decline in turbine efficiency, unstable operation, cavitation erosion, and even increased vibration and noise of the unit.

[0003] To suppress tip leakage, a raised annular sealing structure, known as a skirt, is typically installed on the inner wall of the runner chamber along the circumference corresponding to the blade's rotation trajectory. Its function is to create a near-contact or minimally sized dynamic seal between the blade tip and the fixed wall surface, increasing the flow resistance of the leakage path and thus significantly reducing leakage flow. Therefore, the rational design of the skirt's axial length is crucial for balancing sealing effectiveness with friction loss and optimizing the unit's performance across all operating conditions.

[0004] However, the traditional skirt design method commonly used in the industry has fundamental flaws. This method is essentially a static design based on the rated operating point. During the design process, the optimal operating condition of the turbine at rated head and rated output is typically used as the single design input to determine the position of minimum tip clearance at a fixed blade angle, and the axial coverage range of the skirt is set accordingly. This design approach implicitly assumes that the unit will operate stably at the rated operating point for a long period.

[0005] In reality, influenced by both the seasonal variations in natural river flow and the real-time regulation of power grid load, the operating head, load, and associated blade angle of a hydroelectric turbine unit continuously fluctuate within a wide range, forming a complex dynamic operating condition spectrum. For example, during the high-flow period, the unit may operate under high load and large blade angle; while during the dry season or low-load peak shaving, it may operate under low load and small blade angle. Traditional static design methods are severely out of sync with these dynamic operating requirements, leading to a mismatch between design conditions and actual operating conditions, and causing a series of performance and reliability problems. First, under partial load conditions, if the actual blade rotation angle is less than the design angle, the minimum clearance point at the blade tip will shift towards the inlet edge. In this case, if the skirt length is insufficient, its leading edge may not cover this critical point, causing a short circuit in the leakage flow, seal failure, and a significant decrease in unit efficiency. Taking a certain axial-flow turbine as an example, under 60% load conditions, when the skirt length is shortened by 15% compared to the optimal value, the blade tip leakage flow increases by approximately 22%, efficiency decreases by approximately 1.8 percentage points, and the low-pressure area on the back of the blade expands by approximately 30%. Conversely, if the actual blade rotation angle is greater than the design angle, the critical point shifts towards the outlet edge, and insufficient coverage at the rear end of the skirt will also lead to leakage control failure.

[0006] Secondly, if the skirt is designed to be too long to cover a wider turning range in order to avoid the aforementioned problems, it will bring new negative effects. An excessively long skirt will unnecessarily increase the friction area with the water flow, resulting in continuous frictional losses in non-critical areas. More seriously, under high flow rates and large turning angles, an excessively long skirt may disrupt the streamline of the runner chamber wall, causing flow separation and violent vortices, thus deteriorating hydraulic performance. The disclosure materials indicate that when the skirt length is extended by 12% beyond the optimal value, flow separation occurs under 80% load conditions, leading to an efficiency decrease of up to 4.1 percentage points under low flow conditions. Studies have shown that the efficiency loss caused by the increased equivalent clearance due to improper skirt length is comparable to or even more severe than the actual increase in clearance.

[0007] Furthermore, the mismatch between the skirt length and the operating conditions can lead to unstable leakage flow at the blade tip, which can directly induce increased vibration and noise during unit operation and may promote cavitation erosion. All of these factors can accelerate the fatigue and damage of key equipment components, significantly shorten the overhaul cycle, and increase the maintenance costs and power generation losses of the power plant.

[0008] The fundamental flaw in existing technologies lies in the limitations of their design philosophy: they treat the turbine as an ideal device operating under fixed conditions, completely ignoring the basic fact that blade angles dynamically change with external conditions. More importantly, this method also fails to consider the time or energy weighting distribution of different operating conditions throughout the unit's entire lifecycle. In actual operation, certain operating conditions, such as the area near the optimal efficiency zone, may occupy the majority of operating time and power generation, while extreme operating conditions occur with extremely low probability. Traditional methods treat all operating conditions equally or focus only on a single rated point, failing to accurately match the skirt length to the core operating range that has the greatest impact on overall performance, thus making it difficult to achieve optimal comprehensive performance throughout the entire lifecycle. Summary of the Invention

[0009] In view of this, the present invention aims to propose a design method for the axial length of the turbine skirt based on statistical analysis of operating conditions, in order to solve the problem that the existing technology regards the turbine as an ideal device operating under fixed conditions, completely ignoring the basic fact that the blade angle changes dynamically with external conditions.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: a method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions, the method comprising: Step S1, Operational data acquisition and statistical analysis: Collect historical operating data of the target turbine within a specific period, perform statistical analysis on the blade angles in the historical operating data, and determine the high-weight blade angle intervals; Step S2, Determining the key position range: For the blade rotation angle within the high-weight blade rotation angle range, determine the axial projection position of the minimum gap point between the corresponding blade outer edge and the inner wall of the impeller chamber, and obtain the axial position variation range of the sealing key point, which is denoted as the axial coverage range. Step S3, axial length determination: Based on the axial coverage area, determine the front end position L1 and rear end position L2 of the skirt in the axial direction.

[0011] Furthermore, a preferred embodiment is proposed, wherein step S1 includes: Export historical operating data, including head, load, and blade angle, from the hydropower station monitoring system; The percentage of operating time and / or power generation in different blade rotation angle ranges is statistically analyzed. Based on the operating time ratio and / or power generation ratio, a weight threshold is set, and the minimum continuous angle interval that includes the rated operating blade angle and whose cumulative ratio reaches the weight threshold is determined by the peak domain accumulation method, which is used as the high-weight blade angle interval.

[0012] Furthermore, a preferred method is proposed, wherein the determination of the high-weight blade rotation angle using the peak neighborhood accumulation method includes: Calculate the overall contribution rate of each blade rotation angle interval, where the overall contribution rate is the average of the proportion of operating time to the proportion of power generation; The interval with the highest overall contribution rate is defined as the peak interval; Centered on the peak interval, adjacent intervals are successively included to the left and right until the newly formed continuous intervals meet the following conditions: the cumulative operating time ratio and the cumulative power generation ratio are not lower than the weight threshold, and the blade rotation angle under rated operating conditions is included.

[0013] Furthermore, a preferred embodiment is proposed: if the rated operating condition blade angle is not located within the initially determined peak range, the continuous range is continuously extended to the side containing the rated operating condition blade angle until the continuous range contains the rated operating condition blade angle.

[0014] Furthermore, a preferred method is proposed, wherein in step S2, the specific method for obtaining the axial position variation range of the sealing key point is as follows: Establish a three-dimensional geometric model that includes the turbine chamber and blades; The blade is controlled to rotate continuously within the high-weight blade rotation angle range. Through motion simulation, the axial projection position of the minimum gap point between the outer edge of the blade and the inner wall of the impeller chamber is measured and recorded under different blade rotation angles. The axial projection positions corresponding to the lower limit angle and the upper limit angle of the high-weight blade angle range are respectively used as the start and end points of the axial coverage range.

[0015] Furthermore, a preferred embodiment is proposed, wherein step S2 further includes establishing the blade rotation angle θ. Axial position of the key sealing point The geometric relationship model is expressed as follows:

[0016] Where is the blade chord length; is the lower limit of the high-weighted turning angle interval; and is the upper limit of the high-weighted turning angle interval.

[0017] Furthermore, a preferred embodiment is proposed, wherein step S3, determining the front end position L1 and the rear end position L2 of the skirt edge, includes: The starting position of the axial coverage area is taken as the theoretical position L1 of the front end of the skirt, and the ending position of the axial coverage area is taken as the theoretical position L2 of the rear end of the skirt. In L1 理论 and L2 理论 Based on this, safety margins Δs are added to the front-end and back-end directions respectively to obtain the final L1 and L2, i.e., L1 = L1 理论 -Δs, L2=L2 理论 +Δs.

[0018] Furthermore, a preferred method is proposed, wherein the value of the safety margin Δs is determined based on at least one of the following factors: the machining tolerance of the blade and the skirt, the assembly clearance deviation of the impeller chamber and the blade, and the elastic deformation caused by hydraulic load during operation.

[0019] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions as described in any of the preceding claims.

[0020] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of a turbine skirt axial length design method based on statistical analysis of operating conditions as described above.

[0021] Compared with the prior art, the beneficial effects of the present invention are: This invention acknowledges the dynamic and random nature of turbine operating conditions, abandoning the practice of selecting a single operating point. By performing statistical analysis on historical operating data based on operating time or power generation contribution, the high-weight blade angle ranges with the greatest impact on performance throughout the entire life cycle are identified. Essentially, this step extracts the continuous, fluctuating operating data stream into discrete, critical design input ranges, ensuring statistical alignment between design objectives and actual operating requirements. Secondly, a precise relationship is established between the blade rotation kinematic model and the fixed geometry of the runner chamber. For the identified high-weight angle ranges, geometric analysis or motion simulation is used to find the axial positions of the key sealing points between the blade outer edge and the inner wall of the runner chamber at all angles within this range. These discrete key point positions collectively constitute a continuous axial coverage range. This step completes the critical mapping from the operating parameter space to the axial position space, providing direct geometric constraints for structural design. Finally, the theoretical axial coverage range obtained from the above mapping serves as the core basis for skirt length design. To ensure that the skirt can reliably perform its sealing function within the core operating range under uncertainties such as deformation during actual manufacturing, installation, and operation, a safety margin based on engineering experience is added to the boundary of the theoretical range. This ultimately determines the axial positions of the front and rear ends of the skirt, thus solving the long-standing mismatch problem between dynamic operating requirements and static structural design.

[0022] Because the axial length of the skirt is specifically designed to cover all critical sealing points within the unit's actual high-weight operating range, the skirt can always be aligned with and effectively seal the critical areas with the narrowest tip clearance and highest leakage risk during the unit's most critical operating periods. This fundamentally avoids leakage short circuits caused by insufficient coverage under non-rated operating conditions, or flow interference caused by excessive coverage, achieving precise and adaptive suppression of tip leakage flow.

[0023] The method proposed in this invention directly translates into improved hydraulic efficiency through effective control of tip leakage flow. Leakage losses are minimized within the main operating range; simultaneously, unnecessary friction and flow separation losses introduced in non-critical areas due to excessive skirt length are avoided. As illustrated in the explanatory materials, this method effectively prevents efficiency degradation caused by inappropriate length, enabling the unit to maintain near-optimal efficiency levels under realistic and diverse operating conditions, thereby significantly improving the weighted average efficiency.

[0024] The method proposed in this invention provides a stable and controlled flow field at the blade tip clearance, which can significantly reduce pressure pulsation, eddy currents, and cavitation caused by unstable leakage flow. This directly leads to a reduction in unit vibration and noise levels, creating favorable conditions for improved cavitation performance. The improved operating environment effectively delays damage to key components such as the runner and runner chamber caused by cavitation and fatigue, thereby extending the overhaul cycle and service life of the equipment.

[0025] The combined effects of these technologies ultimately translate into significant economic benefits. Continuous efficiency improvements directly increase power generation revenue; reduced vibration and cavitation lower maintenance frequency and costs; and improved equipment reliability ensures power plant availability. This invention, through a pre-optimization design method, achieves synergistic optimization of the two key economic indicators—power generation revenue and maintenance costs—throughout the entire lifecycle of the turbine, thereby enhancing the overall economic efficiency of the power plant. Attached Figure Description

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions, as described in this invention. Figure 2 This is a schematic diagram illustrating the definition of the axial length parameters L1 and L2 of the skirt as described in this invention. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0028] Implementation Method 1, see [link] Figure 1This embodiment describes a method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions. This method addresses the problem in existing technologies that treat turbines as ideal devices operating under fixed conditions, completely ignoring the fundamental fact that blade angles dynamically change with external conditions. Step S1, Operational data acquisition and statistical analysis: Collect historical operating data of the target turbine within a specific period, perform statistical analysis on the blade angles in the historical operating data, and determine the high-weight blade angle intervals; Step S2, Determining the key position range: For the blade rotation angle within the high-weight blade rotation angle range, determine the axial projection position of the minimum gap point between the corresponding blade outer edge and the inner wall of the impeller chamber, and obtain the axial position variation range of the sealing key point, which is denoted as the axial coverage range. Step S3, axial length determination: Based on the axial coverage area, determine the front end position L1 and rear end position L2 of the skirt in the axial direction.

[0029] Step S1 in this embodiment includes: Export historical operating data, including head, load, and blade angle, from the hydropower station monitoring system; The percentage of operating time and / or power generation in different blade rotation angle ranges is statistically analyzed. Based on the operating time ratio or power generation ratio, a weight threshold is set, and the minimum continuous angle interval that includes the rated operating blade angle and whose cumulative ratio reaches the weight threshold is determined by the peak domain accumulation method. This interval is then used as the high-weight blade angle interval.

[0030] Furthermore, the determination of the high-weight blade rotation angle using the peak neighborhood accumulation method includes: Calculate the overall contribution rate of each blade rotation angle interval, where the overall contribution rate is the average of the proportion of operating time to the proportion of power generation; The interval with the highest overall contribution rate is defined as the peak interval; Centered on the peak interval, adjacent intervals are successively included to the left and right until the newly formed continuous intervals meet the following conditions: the cumulative operating time ratio and the cumulative power generation ratio are not lower than the weight threshold, and the blade rotation angle under rated operating conditions is included.

[0031] Furthermore, if the rated operating condition blade angle is not located within the initially determined peak range, the continuous range is continuously extended to the side containing the rated operating condition blade angle until the continuous range contains the rated operating condition blade angle.

[0032] In step S2 of this embodiment, the specific method for obtaining the axial position variation range of the sealing key point is as follows: Establish a three-dimensional geometric model that includes the turbine chamber and blades; The blade is controlled to rotate continuously within the high-weight blade rotation angle range. Through motion simulation, the axial projection position of the minimum gap point between the outer edge of the blade and the inner wall of the impeller chamber is measured and recorded under different blade rotation angles. The axial projection positions corresponding to the lower limit angle and the upper limit angle of the high-weight blade angle range are respectively used as the start and end points of the axial coverage range.

[0033] Step S2 in this embodiment further includes establishing the blade rotation angle. Axial position of the key sealing point The geometric relationship model is expressed as follows:

[0034] Where is the blade chord length; is the lower limit of the high-weighted turning angle interval; and is the upper limit of the high-weighted turning angle interval.

[0035] In step S3 of this embodiment, determining the front end position L1 and the rear end position L2 of the skirt includes: The starting position of the axial coverage area is taken as the theoretical position L1 of the front end of the skirt, and the ending position of the axial coverage area is taken as the theoretical position L2 of the rear end of the skirt. In L1 理论 and L2 理论 Based on this, safety margins Δs are added to the front-end and back-end directions respectively to obtain the final L1 and L2, i.e., L1 = L1 理论 -Δs, L2=L2 理论 +Δs.

[0036] Furthermore, the value of the safety margin Δs is determined based on at least one of the following factors: the machining tolerance of the blade and the skirt, the assembly clearance deviation of the impeller chamber and the blade, and the elastic deformation caused by hydraulic load during operation.

[0037] Implementation Method 2, see below Figure 2 This embodiment describes a complete implementation of the turbine skirt axial length design method based on statistical analysis of operating conditions described in Embodiment 1, including: By analyzing the unit's historical operating data, the system identifies the operating range that has the greatest impact on the performance throughout the entire life cycle, and directly converts this operating characteristic into the axial geometric parameters of the skirt.

[0038] First, historical operating data of the target turbine within a specific period is collected, including key operating parameters such as head, load, and blade angle. Based on the operating time distribution and power generation contribution, high-weight angle intervals are scientifically identified, and the actual variation range of blade angles is determined. Second, a precise blade motion geometry model is established, considering various boundary conditions in actual operation. The variation law of the characteristic position of the blade tip clearance corresponding to the high-weight angle interval is systematically analyzed to determine the key position intervals that need to be covered, providing a direct basis for axial length design. Finally, axial length optimization is determined. That is, based on the boundary values ​​of the key position intervals, the front end position L1 and the rear end position L2 of the skirt are directly determined. The values ​​of L1 and L2 ensure complete coverage of all key positions corresponding to the high-weight operating intervals.

[0039] The design method proposed in this embodiment will be described in detail below: Step 1: Run data acquisition and in-depth analysis Operational data for the unit over the most recent two complete hydrological years were exported from the power plant monitoring system to obtain valid data records. Statistical analysis yielded detailed statistical results on the blade angle distribution, as shown in Table 1.

[0040] Table 1. Statistical Table of Blade Rotation Angle Distribution Range

[0041] Table 1 provides statistics on the operating time and power generation ratio of each turning interval, which helps to identify the turning intervals of high-weight blades.

[0042] In this embodiment, the blade rotation angle +12° corresponding to the rated operating condition is first found, which falls within the range of +10° to +15°.

[0043] The weight threshold α = 0.8 is set. The high-weight interval is determined by the peak domain accumulation method. The determination principle is: on the premise of ensuring that the rated operating point is included, the interval is taken as the center and expanded to the left and right sides simultaneously to find the smallest continuous turning angle interval in which the cumulative operating time ratio and the cumulative power generation ratio both reach α.

[0044] (1) Determine the peak range Calculate the overall contribution rate of each interval. = (Time percentage + Power generation percentage) / 2: -5°~+5°: = (5.8 + 4.5) / 2 = 5.15% +5°~+10°: = (23.1 + 22.8) / 2 = 22.95% +10°~+15°: = (40.0+41.5) / 2 = 40.75% (maximum value, including the rated point) +15°~+20°: = (28.2+28.9) / 2 = 28.55% +20°~+25°: = (2.9 + 2.3) / 2 = 2.60% Therefore, the peak value range is +10° to +15°, which already includes the rated operating point.

[0045] (2) Expand to both sides Centered on the peak interval, adjacent intervals are successively included to the left and right, and the cumulative time percentage and cumulative power generation percentage are recalculated for each interval included.

[0046] Initial range: +10°~+15°; cumulative time percentage = 40.0%; cumulative power generation percentage = 41.5%; neither reached α=0.8.

[0047] Simultaneously, the coverage extends to the left and right, encompassing +5° to +10° (23.1% of time, 22.8% of power generation); and +15° to +20° (28.2% of time, 28.9% of power generation): After expansion, the coverage range is +5° to +20°, with a cumulative time share of 91.9% and a cumulative power generation share of 93.2%. Both indicators have exceeded the α value, and the rated point remains within this range, so the expansion stops.

[0048] (3) Check if it can be shrunk The interval +5° to +20° has a width of 15°. After removing the left-hand +5° to +10° interval, the cumulative time percentage is 68.2% and the cumulative power generation percentage is 70.4%, both less than the α value. Similarly, after removing the right-hand interval, the cumulative time percentage and cumulative power generation percentage do not meet the α value, indicating that the interval cannot be contracted.

[0049] (4) Determine the high-weight interval The final coverage angle range is +5° to +20°. This range accounts for 91.9% of the cumulative operating time and 93.2% of the cumulative power generation, and includes the rated operating point +12°. This range carries more than 80% of the unit's operating time and more than 80% of its power generation, making it a critical area affecting the performance throughout its entire life cycle.

[0050] General rule explanation: For different generating units, if the rated operating point is not within the initially determined peak range, priority should be given to expanding to include the rated point. That is, during the expansion process, regardless of whether the cumulative percentage has reached the threshold, as long as the rated point has not yet been included, it is necessary to continuously expand to the side (or both sides) containing the rated point until the rated point is covered. The finally determined range must simultaneously satisfy: cumulative percentage ≥ α and the rated point... Interval.

[0051] Step 2: Blade motion trajectory analysis and axial coverage range determination The purpose of this step is to continuously rotate the blade within the high-weight angle range to find the axial distribution range of the part where the outer edge of the blade is closest to the inner wall of the impeller chamber (i.e., the key sealing point). This range is the axial range that the skirt must cover.

[0052] (1) Definition of key position For any turning angle The critical location is defined as the projection of the point where the normal clearance between the outer edge profile of the blade and the inner wall of the impeller chamber is smallest at that turning angle onto the blade axial direction (i.e., the direction of the unit axis). This point is also called the sealing critical point, as it is the part through which leakage flow is most likely to pass at the blade tip, and the skirt must effectively cover it.

[0053] (2) Geometric description of the blade's motion trajectory The outer edge of the blade is considered as a spatial curve. When the blade rotates continuously within the high-weighted rotation angle range [+5°, +20°] determined in step 1, each point on its outer edge sweeps a trajectory in space, and the set of all trajectories constitutes the motion envelope surface of the blade tip.

[0054] For the objective of determining the axial length of the skirt, the most important question is: where do the points on the outer edge of the blade that are closest to the inner wall of the impeller chamber (i.e., the key sealing points) fall axially throughout the entire movement?

[0055] (3) Numerical acquisition of key sealing points For any fixed rotation angle There exists a point on the outer edge of the blade with the minimum radial distance to the inner wall of the impeller chamber, which is called the sealing critical point at that angle. This embodiment uses a geometric method: an assembly model of the impeller chamber and the blade is established in 3D CAD software, and the minimum clearance position at each angle is directly measured using a motion simulation module. The axial position of the sealing critical point at each end angle is then read.

[0056] (4) Establishment of geometric relations To quantitatively describe the blade rotation angle Axial position of the key sealing point Based on the relationship between the blade outer edge profile and the generatrix of the runner inner wall, the following simplified geometric model is established: Define the axial position of the key sealing point With blade angle It approximately satisfies a linear relationship:

[0057] in: This is the chord length of the leaf blade; , These are the lower and upper limits of the high-weighted corner interval, respectively (in this embodiment) =+5°, =+20°); , These are the proportional coefficients from the sealing key points at the lower and upper limits of the corner to the water inlet edge, respectively.

[0058] Substitute the CAD measurement results into: When hour, =0.28; when hour, =0.72. This linear relationship reflects the basic law that the sealing key point moves monotonically towards the water outlet as the rotation angle increases. It should be noted that this relationship is a simplified expression of the actual geometric features and is used to illustrate the principle of the invention; in actual engineering applications, the precise location of the sealing key point should be based on the results of three-dimensional CAD motion simulation.

[0059] (5) Calculation of axial coverage area Based on the above geometric relationship, the axial coverage range corresponding to the entire high-weight corner interval is uniquely determined by the two endpoint values: when When the angle is +5°, the key sealing point is located at 28%L from the water inlet edge of the blade. when At +20°, the key sealing point is located at 72%L from the water inlet edge of the blade.

[0060] because The axial position of the sealing critical point varies monotonically within the range (the axial position of the sealing critical point corresponding to the rated operating point +12° is between 28%L and 72%L). For any intermediate turning angle, the axial position of the sealing critical point must fall between 28%L and 72%L. Therefore, the axial coverage range is determined to be [28%L, 72%L].

[0061] The physical meaning of the above calculation results is that when the blade is continuously adjusted within the high-weight operating range, the "narrowest clearance channel" dynamically formed between the outer edge of the blade and the inner wall of the impeller chamber is always located within the range of 28%L to 72%L in the axial direction. Therefore, only when the axial coverage of the skirt completely includes this range can the tip leakage flow be effectively blocked throughout the entire high-weight operating range (including the rated operating point).

[0062] Step 3: Final determination of axial length Based on the axial coverage range [28%L, 72%L] obtained in step 2, the final axial length of the skirt is determined according to the following principles.

[0063] (1) Scope of theoretical coverage To ensure effective control of tip leakage flow throughout the high-weight operating range, the skirt must completely cover this axial range; that is, the theoretical position of the front end of the skirt (near the inlet side) should not be later than 28%L, and the theoretical position of the rear end of the skirt (near the outlet side) should not be earlier than 72%L.

[0064] Therefore, the theoretical length is: L1 理论 =28%L; L2 理论 =72%L (2) Engineering corrections and safety margins Actual manufacturing and installation involve uncertainties such as machining tolerances, assembly clearance deviations, and thermal and elastic deformation during operation. To compensate for these errors, a safety margin Δs is added on both sides of the theoretical range. The value of Δs needs to be comprehensively considered: 1) Machining tolerances for blades and skirts (±0.5%L in this embodiment); 2) Assembly clearance deviation between the runner chamber and the blade (±0.5%L in this embodiment); 3) Elastic deformation caused by hydraulic load during operation (±1%L in this embodiment).

[0065] Taking Δs = 2%L ensures complete coverage of the target range even under the most unfavorable combination of size chains. The corrected formula is: L1 = L1 理论 - Δs L2 = L2 理论 + Δs (3) Final determination Substitute the values: L1 = 28%L - 2%L = 26%L L2 = 72%L + 2%L = 74%L Therefore, the final axial length of the skirt hem is: The front end position L1 = 26%L (distance from the blade inlet edge); the rear end position L2 = 74%L (distance from the blade outlet edge), where L is the blade chord length.

[0066] This design ensures that the skirt completely covers critical locations (28%L to 72%L) within the main operating range (+10° to +20°), and provides a 2%L safety margin to compensate for various errors during manufacturing, installation and operation, thereby maintaining stable and reliable sealing performance throughout the entire life cycle.

[0067] The core technical advantages in the implementation of this embodiment are as follows: (1) Data-driven scientific design. The design is based entirely on actual operating data, and the basis for the design is sufficient and reliable; the statistical analysis methods are scientific and reasonable, and can accurately identify key operating ranges; (2) The process is simple and efficient. The core design can be completed in three clear steps, which greatly improves design efficiency; (3) Significant engineering value. The method has good versatility and is applicable to various types of water turbines.

[0068] This embodiment provides a novel technical approach for turbine skirt design and has significant engineering application value.

[0069] Implementation Method 3: This implementation method proposes a computer device, including a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions, as described in any one of Implementation Methods 1 to 2.

[0070] Implementation Method 4: This implementation method proposes a computer-readable storage medium storing a computer program. When the computer program is run by a processor, it executes the steps of a turbine skirt axial length design method based on statistical analysis of operating conditions, as described in any one of Implementation Methods 1 to 2.

[0071] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0072] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0073] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure and not to limit its protection scope. Although this disclosure has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading this disclosure, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the pending claims.

Claims

1. A method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions, characterized in that, The method includes: Step S1, Operational data acquisition and statistical analysis: Collect historical operating data of the target turbine within a specific period, perform statistical analysis on the blade rotation angle in the historical operating data, and determine the high-weight blade rotation angle interval; Step S2, Determining the key position range: For the blade rotation angle within the high-weight blade rotation angle range, determine the axial projection position of the minimum gap point between the corresponding blade outer edge and the inner wall of the impeller chamber, and obtain the axial position variation range of the sealing key point, which is denoted as the axial coverage range. Step S3, axial length determination: Based on the axial coverage area, determine the front end position L1 and the rear end position L2 of the skirt in the axial direction.

2. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 1, characterized in that, Step S1 includes: Export historical operating data, including head, load, and blade rotation angle, from the hydropower station monitoring system; The percentage of operating time and power generation in different blade rotation angle ranges were statistically analyzed. Based on the operating time ratio or power generation ratio, a weight threshold is set, and the minimum continuous angle interval that includes the rated operating blade angle and whose cumulative ratio reaches the weight threshold is determined by the peak domain accumulation method. This interval is then used as the high-weight blade angle interval.

3. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 2, characterized in that, The determination of the high-weighted blade rotation angle using the peak neighborhood accumulation method includes: Calculate the overall contribution rate of each blade rotation angle interval, where the overall contribution rate is the average of the proportion of operating time to the proportion of power generation; The interval with the highest overall contribution rate is defined as the peak interval; Centered on the peak interval, adjacent intervals are successively included to the left and right until the newly formed continuous intervals meet the following conditions: the cumulative operating time ratio and the cumulative power generation ratio are not lower than the weight threshold, and the blade rotation angle under rated operating conditions is included.

4. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 3, characterized in that, If the rated operating condition blade angle is not located within the initially determined peak range, the continuous range is continuously extended to the side containing the rated operating condition blade angle until the continuous range contains the rated operating condition blade angle.

5. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 1, characterized in that, In step S2, the specific method for obtaining the axial position variation range of the sealing key point is as follows: Establish a three-dimensional geometric model that includes the turbine chamber and blades; The blade is controlled to rotate continuously within the high-weight blade rotation angle range. Through motion simulation, the axial projection position of the minimum gap point between the outer edge of the blade and the inner wall of the impeller chamber is measured and recorded under different blade rotation angles. The axial projection positions corresponding to the lower limit angle and the upper limit angle of the high-weight blade rotation angle range are respectively used as the start and end points of the axial coverage range.

6. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 5, characterized in that, Step S2 further includes establishing the blade rotation angle. Axial position of the key sealing point The geometric relationship model is expressed as follows: Where is the blade chord length; is the lower limit of the high-weighted turning angle interval; and is the upper limit of the high-weighted turning angle interval.

7. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 1, characterized in that, In step S3, determining the front end position L1 and the rear end position L2 of the skirt includes: The starting position of the axial coverage area is taken as the theoretical position L1 of the front end of the skirt, and the ending position of the axial coverage area is taken as the theoretical position L2 of the rear end of the skirt. In L1 理论 and L2 理论 Based on this, safety margins Δs are added to the front-end and back-end directions respectively to obtain the final L1 and L2, i.e., L1 = L1 理论 -Δs, L2=L2 理论 +Δs.

8. The method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions according to claim 7, characterized in that, The value of the safety margin Δs is determined based on at least one of the following factors: the machining tolerance of the blade and the skirt, the assembly clearance deviation between the runner chamber and the blade, and the elastic deformation caused by hydraulic load during operation.

9. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a method for designing the axial length of a turbine skirt based on statistical analysis of operating conditions as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of a turbine skirt axial length design method based on statistical analysis of operating conditions as described in any one of claims 1-8.

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