WO2019206008A1 - 混流式水轮机转轮叶片出口边修型方法 - Google Patents

混流式水轮机转轮叶片出口边修型方法 Download PDF

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Publication number
WO2019206008A1
WO2019206008A1 PCT/CN2019/083076 CN2019083076W WO2019206008A1 WO 2019206008 A1 WO2019206008 A1 WO 2019206008A1 CN 2019083076 W CN2019083076 W CN 2019083076W WO 2019206008 A1 WO2019206008 A1 WO 2019206008A1
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Prior art keywords
blade
trimming
edge
exit
arc
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PCT/CN2019/083076
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English (en)
French (fr)
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石清华
龚莉
李国元
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东方电气集团东方电机有限公司
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Publication of WO2019206008A1 publication Critical patent/WO2019206008A1/zh

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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B3/00—Machines or engines of reaction type; Parts or details peculiar thereto
    • F03B3/12—Blades; Blade-carrying rotors
    • F03B3/121—Blades, their form or construction
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B19/00—Single-purpose machines or devices for particular grinding operations not covered by any other main group
    • B24B19/14—Single-purpose machines or devices for particular grinding operations not covered by any other main group for grinding turbine blades, propeller blades or the like
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B11/00—Parts or details not provided for in, or of interest apart from, the preceding groups, e.g. wear-protection couplings, between turbine and generator
    • F03B11/04—Parts or details not provided for in, or of interest apart from, the preceding groups, e.g. wear-protection couplings, between turbine and generator for diminishing cavitation or vibration, e.g. balancing
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B3/00—Machines or engines of reaction type; Parts or details peculiar thereto
    • F03B3/02—Machines or engines of reaction type; Parts or details peculiar thereto with radial flow at high-pressure side and axial flow at low-pressure side of rotors, e.g. Francis turbines
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/20—Hydro energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
    • Y02P70/10—Greenhouse gas [GHG] capture, material saving, heat recovery or other energy efficient measures, e.g. motor control, characterised by manufacturing processes, e.g. for rolling metal or metal working

Definitions

  • the invention relates to the field of water turbines, in particular to a method for repairing the outlet side of a Francis turbine runner blade.
  • the resonance induced by the Karman vortex on the exit of the runner blade is a hydrodynamic vibration with extremely strong destructive force. Once this resonance occurs, the whistling sound occurs when the turbine is running, and a large area crack of the runner blade is caused in a short time.
  • the resonance induced by the Kamen vortex street at the exit of the Francis turbine runner blade usually occurs in the operating region where the runner has a high flow rate, i.e., typically occurs in the high load operating region of the Francis turbine.
  • the frequency of howling is high, and the frequency of howling increases as the turbine load increases. Therefore, in actual engineering, it is not difficult to accurately identify such resonance phenomena.
  • the root cause of the resonance is that the frequency of the exit vane vortex of the runner blade coincides with or is close to the natural frequency of the runner blade under water.
  • the unit is m/s; t is the width of the wake of the de-flow, the unit is m, and the width of the trail is the sum of the thickness of the exit edge of the blade, the thickness of the front boundary layer of the blade, and the thickness of the boundary layer on the back of the blade.
  • the Strouha number S is related to the Reynolds number, for the calculation of the Karman vortex frequency of the turbine runner blade outlet, the Struha number S can only use the laboratory results of the fluid around the plate or cylinder. Is an experience value. Therefore, it is still impossible to accurately calculate the frequency of the exit vane vortex in the rotor blade at the design stage of the runner blade.
  • the natural frequency of the runner blades under water is difficult to accurately quantify by modal analysis, which also brings new difficulties to the Karman vortex frequency and the underwater natural frequency of the runner blades. . Therefore, the current situation is that the remediation can be passively performed only after the Francis turbine is put into operation and it is confirmed that the rotor blade exit Karman vortex induced resonance occurs.
  • the most effective way to deal with this resonance problem is to improve the leakage frequency of the Kamen vortex street of the Francis turbine runner blade outlet by modifying the blade outlet edge profile to be staggered from the underwater natural frequency of the runner blade.
  • Another advantage of increasing the frequency of the exit of the runner vane vortex is that as the frequency of the Karman vortex street increases, the vortex energy will weaken, and the vortex street with little energy is difficult to provoke resonance.
  • the Chinese Patent Publication No. CN 97143455A discloses a method for mitigating the pressure pulsation hazard in the no-leaf zone of a mixed-flow pump-turbine, characterized in that it includes a work done on a mixed-flow pump-turbine.
  • the high-pressure side blades of the mixed-flow pump turbine runner are arranged obliquely so that the angle ⁇ between the inflow edge of the blade and the axis direction is not less than 15°; 2) the flow of the mixed-flow pump turbine is guaranteed On the basis of the requirements of the wheel and its blade strength, two or three blades are added, the purpose of which is to reduce the spacing of the high-pressure side channels of the runner to reduce the development space of the drift vortex.
  • the method for mitigating the pressure fluctuation of the no-leaf zone of the mixed-flow pump-turbine disclosed in the patent document is proposed on the basis of the pressure pulsation in the no-leaf zone, and can only alleviate the hazard of the pressure-free pulsation of the mixed-flow pump turbine without the blade zone, and cannot Prevent or eliminate the turbine whistling and runner blade cracks caused by the hydrodynamic resonance of the blade induced by the Kamen vortex on the runner exit.
  • the present invention provides a method for repairing the exit side of a Francis turbine runner blade.
  • the present invention can effectively prevent or eliminate the modification of the back side profile of the runner blade of the Francis turbine runner. Turbine howling and runner blade cracks caused by blade hydroelastic resonance induced by Karen vortex on the runner exit, thereby improving the structural integrity of the Francis turbine runner and the operational safety of the turbine.
  • the blade exit side includes the upper, middle and lower sections integrally formed.
  • the lengths of the upper and lower sections are L 1 , and L 1 is the nominal diameter of the runner. -4%, the middle section is the repairing zone, the upper section and the lower section are non-repairing zones, and the smooth transition between the trimming zone and the non-repairing zone, the thickness of the exit edge of the blade before trimming is t 1 ;
  • the thickness of the exit edge of the blade is t 2
  • the thickness of the exit edge of the blade after trimming is 0.4-0.5 times of the thickness t 1 of the exit edge of the blade before trimming
  • the front profile of the blade and the back profile of the blade after trimming The angle ⁇ between the straight segments is 20-25°; after the trimming, the back profile of the blade and the back profile of the modified blade pass through the arc, and the radius R of the arc is the thickness t 1 of the exit edge of the trimmed blade. 4-7 times;
  • the thickness t 1 of the exit edge of the blade before trimming the thickness t 2 of the blade exit edge after trimming, the angle ⁇ between the blade front profile and the straight section in the back profile of the modified blade
  • the radius R of the arc is used to determine the final geometry of the blade exit side trimming, and the distance L 2 from the tangent point of the arc to the blade exit side of the trim front blade is determined;
  • the angle ⁇ between the blade front profile line and the straight line segment in the back profile line of the modified blade, the radius R of the arc and the arc and the back surface of the modified front blade The distance from the tangent point of the profile line to the exit edge of the blade L 2 determines the size of the sub-family template and the arc-shaped template on the back side of the blade, and is integrally formed and manufactured;
  • the two end points of the trimming area are drawn on the back edge of the blade exit before the trimming, and according to the thickness t 2 of the exit edge of the blade after the trimming, the edge of the blade exit is scribed to determine the shape after trimming.
  • the runner comprises an upper crown, a lower ring and a plurality of blades fixed between the upper crown and the lower ring.
  • the blades are spatially twisted and curved, and any two blades have the same geometrical size, and the plurality of blades are along the runner.
  • the circumferential direction is evenly arranged, the blade comprises an integrally formed blade body and a blade outlet edge, and the blade outlet edge comprises a blade outlet positive pressure edge and a modified front blade outlet back pressure edge.
  • the cutting out of the blade airfoil means that a blade airfoil is cut along a section perpendicular to the blade exit side 1, and the blade airfoil geometry is composed of a series of discrete point coordinates (Xp, Yp) and blades on the front side of the blade. A series of discrete point coordinates (Xs, Ys) on the back are determined.
  • the mother-child template comprises an integrally formed mother template and a sub-template.
  • the blade outlet side comprises an integrally formed upper section, a middle section and a lower section, and the lengths of the upper section and the lower section are both L 1 , L 1 is 3-4% of the nominal diameter of the runner, the middle section is a trimming zone, and the blade outlet side is
  • the upper crown and the exit and lower ring junction areas of the blade are usually high stress areas, and the upper and lower sections are non-retrofit areas, which can ensure the mechanical strength of the blade in the junction area and avoid blade crack generation; the blade exit side and the upper crown and the blade exit There are more or less welding residual stresses when welding between the side and the lower ring.
  • the upper and lower sections are non-retrofit zones, which can ensure the fatigue strength of the blade in the area; Adjust the angle of the exit edge of the blade through the sample and the scribe line until the size of the sample is satisfied; the arc on the back of the blade is ground until the size of the arc on the back of the blade is satisfied; this modification simplifies the repair process and manual work.
  • the amount is small and the repairing time is short; through the step ag, the back side profile of the Francis turbine runner blade exit side is modified, and the entire trimming area is only limited to the blade exit side back.
  • the small area is local, so it has no influence on the hydraulic performance such as efficiency and cavitation of the Francis turbine, and it does not affect the mechanical properties of the runner.
  • the turbine runner blades can be improved. Exporting the exit frequency of Kamen vortex street so as to be staggered from the underwater natural frequency of the runner blade; and increasing the frequency of the exit of the runner vane vortex street, the energy of the Karman vortex street will be weakened, and the energy of the Kamen vortex street is difficult.
  • the resonance is aroused, which can effectively prevent or eliminate the turbine whistling and runner blade cracks caused by the blade hydro-elastic resonance induced by the Karman vortex on the runner exit, thereby improving the structural integrity of the Francis turbine runner and the operation of the turbine. safety.
  • Figure 1 is an axial view of a Francis turbine runner
  • Figure 2 is a schematic view of the blade airfoil perpendicular to the exit section of the blade before trimming
  • Figure 3 is a schematic view showing the geometrical dimensions of the exit edge of the blade after trimming
  • Figure 4 is a schematic view showing the structure of the blade exit side inspection inspection template
  • Figure 5 is a cross-sectional view of the exit side of the Francis turbine runner blade
  • Fig. 6 is a model test observation result of a front door vane exit Karman vortex of a middle and low head mixed flow turbine runner blade outlet trimming
  • Figure 7 is a model test observation result of a vane vortex at the outlet of a blade of a middle and low head Francis turbine runner blade after trimming;
  • the method for repairing the exit side of the Francis turbine runner blade comprises the following steps:
  • the blade exit side 1 comprises an integrally formed upper section, middle section and lower section, the length of the upper section and the lower section are both L 1 , L 1 is the nominal diameter of the runner 3%, the middle section is the repairing zone, the upper section and the lower section are non-repairing zones, and the smooth transition between the trimming zone and the non-repairing zone, the thickness of the exit edge of the blade before trimming is t 1 ;
  • the thickness of the exit edge of the blade is t 2
  • the thickness of the exit edge of the blade after trimming is 0.4 times of the thickness t 1 of the exit edge of the blade before trimming
  • the front profile of the blade 2 and the profile of the blade behind the modified profile 3 The angle ⁇ between the straight segments is 20°
  • the rear blade profile 3 and the modified front blade back profile 4 are transitioned through a circular arc
  • the radius R of the arc is the thickness t 1 of the exit edge of the trimming blade. 4 times;
  • the thickness t 1 of the exit edge of the blade before trimming, the thickness t 2 of the blade exit edge after trimming, the angle between the blade front profile 2 and the straight section in the back profile line 3 of the modified blade ⁇ and the radius R of the arc determine the final geometry of the blade exit edge 1 and determine the distance L 2 from the tangent point of the arc to the blade exit edge 1 of the modified blade front profile line 4;
  • the angle ⁇ between the blade front profile 2 and the straight section of the modified blade back profile line 3, the radius R of the arc and the arc and before the modification The distance L 2 from the tangent point of the blade back profile line 4 to the blade exit edge 1 determines the size of the mother template 11 , the sub-template 12 and the blade back arc template 13 , and is integrally formed and manufactured;
  • the two end points of the trimming area are drawn on the back edge 5 of the blade exit before the trimming, and according to the thickness t 2 of the exit edge of the blade after trimming, the edge of the blade exit 1 is scribed to determine the repair.
  • the method for repairing the exit side of the Francis turbine runner blade comprises the following steps:
  • the blade exit side 1 comprises an integrally formed upper section, middle section and lower section, the length of the upper section and the lower section are both L 1 , L 1 is the nominal diameter of the runner 3.5%, the middle section is the repairing zone, the upper section and the lower section are non-repairing zones, and the smooth transition between the trimming zone and the non-repairing zone, the thickness of the exit edge of the blade before trimming is t 1 ;
  • the thickness of the exit edge of the blade is t 2
  • the thickness of the exit edge of the blade after trimming is 0.45 times the thickness t 1 of the exit edge of the blade before trimming
  • the front profile line 2 of the blade and the back profile line 3 of the modified blade The angle ⁇ between the straight segments is 23°
  • the rear blade profile 3 and the modified front blade back profile 4 are transitioned by a circular arc
  • the radius R of the arc is the thickness t 1 of the exit edge of the trimming blade. 5 times;
  • the thickness t 1 of the exit edge of the blade before trimming, the thickness t 2 of the blade exit edge after trimming, the angle between the blade front profile 2 and the straight section in the back profile line 3 of the modified blade ⁇ and the radius R of the arc determine the final geometry of the blade exit edge 1 and determine the distance L 2 from the tangent point of the arc to the blade exit edge 1 of the modified blade front profile line 4;
  • the angle ⁇ between the blade front profile 2 and the straight section of the modified blade back profile line 3, the radius R of the arc and the arc and before the modification The distance L 2 from the tangent point of the blade back profile line 4 to the blade exit edge 1 determines the size of the mother template 11 , the sub-template 12 and the blade back arc template 13 , and is integrally formed and manufactured;
  • the two end points of the trimming area are drawn on the back edge 5 of the blade exit before the trimming, and according to the thickness t 2 of the exit edge of the blade after trimming, the edge of the blade exit 1 is scribed to determine the repair.
  • the runner comprises an upper crown 7, a lower ring 8 and a plurality of blades fixed between the upper crown 7 and the lower ring 8.
  • the blades are spatially twisted and curved, and any two blades have the same geometrical size and multiple
  • the blades are evenly arranged in the circumferential direction of the rotor, the blades comprising an integrally formed blade body 9 and a blade outlet edge 1 comprising a blade outlet positive pressure edge 10 and a modified front blade outlet back pressure edge 5.
  • the method for repairing the exit side of the Francis turbine runner blade comprises the following steps:
  • the blade exit side 1 comprises an integrally formed upper section, middle section and lower section, the length of the upper section and the lower section are both L 1 , L 1 is the nominal diameter of the runner 4%, the middle section is the repairing zone, the upper section and the lower section are non-repairing zones, and the smooth transition between the trimming zone and the non-repairing zone, the thickness of the exit edge of the blade before trimming is t 1 ;
  • the thickness of the exit edge of the blade is t 2
  • the thickness of the exit edge of the blade after trimming is 0.5 times of the thickness t 1 of the exit edge of the blade before trimming
  • the front profile line 2 of the blade and the back profile line 3 of the modified blade are The angle ⁇ between the straight segments is 25°
  • the rear blade profile 3 and the modified front blade back profile 4 are transitioned by a circular arc, and the radius R of the arc is the thickness t 1 of the exit edge of the trimming blade. 7 times;
  • the thickness t 1 of the exit edge of the blade before trimming, the thickness t 2 of the blade exit edge after trimming, the angle between the blade front profile 2 and the straight section in the back profile line 3 of the modified blade ⁇ and the radius R of the arc determine the final geometry of the blade exit edge 1 and determine the distance L 2 from the tangent point of the arc to the blade exit edge 1 of the modified blade front profile line 4;
  • the angle ⁇ between the blade front profile 2 and the straight section of the modified blade back profile line 3, the radius R of the arc and the arc and before the modification The distance L 2 from the tangent point of the blade back profile line 4 to the blade exit edge 1 determines the size of the mother template 11 , the sub-template 12 and the blade back arc template 13 , and is integrally formed and manufactured;
  • the two end points of the trimming area are drawn on the back edge 5 of the blade exit before the trimming, and according to the thickness t 2 of the exit edge of the blade after trimming, the edge of the blade exit 1 is scribed to determine the repair.
  • the runner comprises an upper crown 7, a lower ring 8 and a plurality of blades fixed between the upper crown 7 and the lower ring 8.
  • the blades are spatially twisted and curved, and any two blades have the same geometrical size and multiple
  • the blades are evenly arranged in the circumferential direction of the rotor, the blades comprising an integrally formed blade body 9 and a blade outlet edge 1 comprising a blade outlet positive pressure edge 10 and a modified front blade outlet back pressure edge 5.
  • the cutting out of the blade airfoil means that a blade airfoil is cut along a section perpendicular to the blade exit side 1, and the blade airfoil geometry is composed of a series of discrete point coordinates (Xp, Yp) and blades on the front side of the blade. A series of discrete point coordinates (Xs, Ys) on the back are determined.
  • the method for repairing the exit side of the Francis turbine runner blade comprises the following steps:
  • the blade exit side 1 comprises an integrally formed upper section, middle section and lower section, the length of the upper section and the lower section are both L 1 , L 1 is the nominal diameter of the runner 4%, the middle section is the repairing zone, the upper section and the lower section are non-repairing zones, and the smooth transition between the trimming zone and the non-repairing zone, the thickness of the exit edge of the blade before trimming is t 1 ;
  • the thickness of the exit edge of the blade is t 2
  • the thickness of the exit edge of the blade after trimming is 0.5 times of the thickness t 1 of the exit edge of the blade before trimming
  • the front profile line 2 of the blade and the back profile line 3 of the modified blade are The angle ⁇ between the straight segments is 25°
  • the rear blade profile 3 and the modified front blade back profile 4 are transitioned by a circular arc, and the radius R of the arc is the thickness t 1 of the exit edge of the trimming blade. 7 times;
  • the thickness t 1 of the exit edge of the blade before trimming, the thickness t 2 of the blade exit edge after trimming, the angle between the blade front profile 2 and the straight section in the back profile line 3 of the modified blade ⁇ and the radius R of the arc determine the final geometry of the blade exit edge 1 and determine the distance L 2 from the tangent point of the arc to the blade exit edge 1 of the modified blade front profile line 4;
  • the angle ⁇ between the blade front profile 2 and the straight section of the modified blade back profile line 3, the radius R of the arc and the arc and before the modification The distance L 2 from the tangent point of the blade back profile line 4 to the blade exit edge 1 determines the size of the mother template 11 , the sub-template 12 and the blade back arc template 13 , and is integrally formed and manufactured;
  • the two end points of the trimming area are drawn on the back edge 5 of the blade exit before the trimming, and according to the thickness t 2 of the exit edge of the blade after trimming, the edge of the blade exit 1 is scribed to determine the repair.
  • the runner comprises an upper crown 7, a lower ring 8 and a plurality of blades fixed between the upper crown 7 and the lower ring 8.
  • the blades are spatially twisted and curved, and any two blades have the same geometrical size and multiple
  • the blades are evenly arranged in the circumferential direction of the rotor, the blades comprising an integrally formed blade body 9 and a blade outlet edge 1 comprising a blade outlet positive pressure edge 10 and a modified front blade outlet back pressure edge 5.
  • the cutting out of the blade airfoil means that a blade airfoil is cut along a section perpendicular to the blade exit side 1, and the blade airfoil geometry is composed of a series of discrete point coordinates (Xp, Yp) and blades on the front side of the blade. A series of discrete point coordinates (Xs, Ys) on the back are determined.
  • the mother-child template includes the integrally formed mother template 11 and the sub-template 12.
  • the polished blade exit edge 1 is completely fitted with the mother template 11 and cannot be fitted with the sub-template 12, the geometry after the trimming is determined. The dimensions meet the requirements.
  • the exit edge of the blade includes an integrally formed upper section, a middle section and a lower section.
  • the lengths of the upper section and the lower section are both L 1 , L 1 is 3-4% of the nominal diameter of the runner, the middle section is a trimming zone, the blade exit side and the upper crown and
  • the blade exit and lower ring intersections are usually high stress zones, and the upper and lower sections are non-retrofit zones, which can ensure the mechanical strength of the blade in the junction zone and avoid blade cracking; the blade exit and upper crown and the blade exit side and bottom There are more or less welding residual stresses in the ring welding. There is a heat-affected zone in the junction area.
  • the upper and lower sections are non-repairing zones, which can guarantee the fatigue strength of the blade in this zone.
  • the model and the scribing adjust the angle of the exit edge of the blade until the size of the sub-model is satisfied; the arc of the back of the blade is ground until the arc-shaped template of the back of the blade is satisfied, and the modification mode simplifies the repair process and the manual workload is small.
  • the repairing time is short; through the step ag, the back side profile of the Francis turbine runner blade exit side is modified, and the entire trimming area is limited to the back of the blade exit side.
  • the domain is local, so it has no influence on the hydraulic performance such as efficiency and cavitation of the Francis turbine, and does not affect the mechanical performance of the runner.
  • the discharge frequency of the street is staggered with the underwater natural frequency of the runner blade; and the energy of the Karman vortex street will be weakened after the exit velocity of the runner vane vortex is increased, and the Karman vortex street with low energy is difficult to provoke resonance. Furthermore, it is possible to effectively prevent or eliminate turbine whistling and runner blade cracks caused by blade hydroelastic resonance induced by the runner exit Karman vortex street, thereby improving the structural integrity of the Francis turbine runner and the operational safety of the turbine.
  • Fig. 4 is a schematic view showing the structure of the blade exit side inspection type sample, in which the suffixes of R and t 2 are tolerances and the unit is mm.
  • Figure 6 is a model test observation result of a front and rear blade exit Karman vortex street of a middle and low head Francis turbine runner blade outlet
  • Fig. 7 is a middle and low head Francis turbine runner blade outlet trimming blade outlet

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Abstract

一种混流式水轮机转轮叶片出口边（1）修型方法，包括以下步骤：截出叶片翼型，确定叶片出口边（1）修型区域；修型后叶片背面型线（3）与修型前叶片背面型线（4）通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t1的4‑7倍；确定叶片出口边（1）修型最终几何尺寸；确定子母样板（11、12）的尺寸和叶片背面圆弧样板（13）尺寸并一体加工；在叶片出口边（1）上划线，确定修型后叶片出口背压边（6）最终位置；调整叶片出口边（1）角度直至满足子母样板（11、12）尺寸；修磨叶片背面圆弧，直到满足叶片背面圆弧样板（13）尺寸。该方法能预防或消除因转轮出口卡门涡旋诱发的叶片水力弹性共振所产生的水轮机啸声和叶片裂纹，提高混流式水轮机转轮的结构整体性和水轮机的运行安全性。

Description

混流式水轮机转轮叶片出口边修型方法 技术领域
本发明涉及到水轮机领域，尤其涉及一种混流式水轮机转轮叶片出口边修型方法。
背景技术
在混流式水轮机所有流动致振问题中，因转轮叶片出口卡门涡街诱发的共振是一种破坏力极强的水力弹性振动。这种共振一旦出现，水轮机运行时会出现啸声，并在很短时间内引起转轮叶片大面积裂纹。由混流式水轮机转轮叶片出口卡门涡街诱发的共振通常出现在转轮具有高流速的运行区，即通常出现在混流式水轮机的高负荷运行区。此外，啸声的频率高，且啸声的频率随着水轮机负荷的增加而增大。因此，在实际工程中，准确识别这种共振现象并不困难。
引起共振的根本原因是转轮叶片出口卡门涡街的频率与转轮叶片在水下的固有频率重合或相近。
混流式水轮机转轮叶片出口卡门涡街的频率可以用下列公式计算：
Figure PCTCN2019083076-appb-000001
式中，f k为卡门涡街频率，单位Hz；S为斯特鲁哈数，它与雷诺数有关，在反击式水轮机中，S＝0.18-0.24；W为叶片边界层外的相对速度，单位m/s；t为脱流的尾迹宽度，单位m，该尾迹宽度为叶片出口边厚度、叶片正面边界层厚度、叶片背面边界层厚度三者之和。就目前的技术而言，虽然通过转轮叶片流体动力学分析可以准确给出叶片边界层外的相对速度W，但要准确计算叶片出口边脱流的尾迹宽度t仍有难度。其次，由于斯特鲁哈数S与雷诺数相关，针对水轮机转轮叶片出口卡门涡街频率的计算，斯特鲁哈数S仍只能采用实验室对平板或圆柱等绕流体的实验结果，是一个经验值。因此，在转轮叶片设计阶段仍然无法准确计算出转轮叶片出口卡门涡街的频率。
此外，就目前的技术而言，转轮叶片在水下的固有频率还难于通过模态分析准确地定量确定，这也为错开卡门涡街频率与转轮叶片水下固有频率带来新的难度。因此，目前的情况是，只有在混流式水轮机投入运行后被确认确实出现了转轮叶片出口卡门涡街诱发共振时，才能被动的进行补救。
处理该共振问题最有效的方法是通过修型叶片出口边型线来提高混流式水轮机转轮叶片出口卡门涡街的泄出频率，以便与转轮叶片的水下固有频率错开。提高转轮叶片出口卡门涡街泄出频率的另一个好处是，卡门涡街频率一旦提高，涡街能量将减弱，能量小的涡街很难激起共振。
公开号为CN 97143455A，公开日为2017年09月08日的中国专利文献公开了一种减轻混流式水泵水轮机无叶区压力脉动危害的方法，其特征在于，包括对混流式水泵水轮机所做的以下两方面的优化：1)将混流式水泵水轮机转轮高压侧叶片倾斜布置，使叶片的进水边骨线与轴线方向的夹角Φ不小于15°；2)在保证混流式水泵水轮机转轮及其叶片刚强度要求的基础上再增加2～3个叶片，其目的是减小转轮高压侧叶道间距，以缩小脱流漩涡的发展空间。
该专利文献公开的减轻混流式水泵水轮机无叶区压力脉动危害的方法，是在无叶区压力脉动产生原因的基础上提出的，仅能够减轻混流式水泵水轮机无叶区压力脉动的危害，不能预防或消除因转轮出口卡门涡街诱发叶片水力弹性共振所产生的水轮机啸声和转轮叶片裂纹。
发明内容
本发明为了克服上述现有技术的缺陷，提供一种混流式水轮机转轮叶片出口边修型方法，本发明通过对混流式水轮机转轮叶片出口边背面型线进行修型，能够有效预防或消除因转轮出口卡门涡街诱发的叶片水力弹性共振所产生的水轮机啸声和转轮叶片裂纹，从而提高混流式水轮机转轮的结构整体性和水轮机的运行安全性。
本发明通过下述技术方案实现：
混流式水轮机转轮叶片出口边修型方法，其特征在于，包括以下步骤：
a、截出叶片翼型，确定叶片出口边的修型区域，叶片出口边包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的3-4％，中段为修型区，上段和下段为非修型区，修型区和非修型区之间光滑过渡，修型前叶片出口边厚度为t 1；
b、修型后叶片出口边厚度为t 2，修型后叶片出口边厚度是修型前叶片出口边厚度t 1的0.4-0.5倍；叶片正面型线与修型后叶片背面型线中的直线段之间的夹角θ为20-25°；修型后叶片背面型线与修型前叶片背面型线通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t 1的4-7倍；
c、根据叶片翼型、修型前叶片出口边厚度t 1、修型后叶片出口边厚度t 2、叶片正面型线与修型后叶片背面型线中的直线段之间的夹角θ和圆弧的半径R来确定叶片出口边修型的最终几何尺寸，并定出圆弧与修型前叶片背面型线的切点至叶片出口边的距离L 2；
d、根据修型后叶片出口边厚度t 2、叶片正面型线与修型后叶片背面型 线中的直线段之间的夹角θ、圆弧的半径R和圆弧与修型前叶片背面型线的切点至叶片出口边的距离L 2，确定子母样板和叶片背面圆弧样板的尺寸，并一体成型加工制造；
e、根据L 1的值在修型前叶片出口背压边上划出修型区的两个端点，根据修型后叶片出口边厚度t 2，在叶片出口边上划线，确定修型后叶片出口背压边的最终位置；
f、从叶片背面打磨叶片出口边，通过子母样板和划线调整叶片出口边的角度直至满足子母样板的尺寸；
g、修磨叶片背面圆弧，直到满足叶片背面圆弧样板尺寸。
所述步骤a中，转轮包括上冠、下环和固定于上冠与下环之间的多个叶片，叶片为空间扭曲曲面状，任意两个叶片几何尺寸相同，多个叶片沿转轮圆周方向均匀布置，叶片包括一体成型的叶片本体和叶片出口边，叶片出口边包括叶片出口正压边和修型前叶片出口背压边。
所述步骤a中，截出叶片翼型是指沿垂直于叶片出口边1的断面截出一段叶片翼型，叶片翼型的几何尺寸由叶片正面一系列离散点坐标(Xp，Yp)和叶片背面一系列离散点坐标(Xs，Ys)确定。
所述步骤f中，子母样板包括一体成型的母样板和子样板，当打磨后的叶片出口边与母样板完全嵌合且与子样板不能嵌合时，判定修型后几何尺寸符合要求。
本发明的有益效果是：
本发明，叶片出口边包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的3-4％，中段为修型区，叶片出口边与上冠以及叶片出口边与下环交接区通常为高应力区，上段和下段为非修型区，能够保障叶片在交接区的机械强度，避免叶片裂纹产生；叶片出口边与上冠以及叶片出口边与下环焊接时或多或少存在焊接残余应力，在该交接区存在热影响区，上段和下段为非修型区，能够保障该区域叶片的疲劳强度；从叶片背面打磨叶片出口边，通过子母样板和划线调整叶片出口边的角度直至满足子母样板的尺寸；修磨叶片背面圆弧，直到满足叶片背面圆弧样板尺寸；这种修型方式简化了修型工艺，人工工作量小，修型时间短；通过步骤a-g，对混流式水轮机转轮叶片出口边背面型线进行修型，整个修型区域仅局限在叶片出口边背面很小的区域，是局部的，因此对混流式水轮机的效率、空化等水力性能没有任何影响，也不会对转轮的机械性能产生影响；修型后，能够提高混流式水轮机转轮叶片出口卡门涡街的泄出频率，以便与转轮叶片的水下固有频率错开；且提高转轮叶片出口卡门涡街泄出频率后，卡门涡街能量将减弱，能量小的卡门涡街很难激起共振，进而能够有效预防或消除因转轮出口卡门涡街诱发的叶片水力弹性共 振所产生的水轮机啸声和转轮叶片裂纹，从而提高混流式水轮机转轮的结构整体性和水轮机的运行安全性。
附图说明
下面结合说明书附图和具体实施方式对本发明作进一步的具体说明：
图1为混流式水轮机转轮轴面图；
图2为修型前垂直于叶片出口边断面上的叶片翼型示意图；
图3为修型后的叶片出口边的几何尺寸示意图；
图4为叶片出口边修型检查样板结构示意图；
图5为混流式水轮机转轮叶片出口边划线图；
图6为一中低水头混流式水轮机转轮叶片出口边修型前叶片出口卡门涡街的模型试验观察结果图；
图7为一中低水头混流式水轮机转轮叶片出口边修型后叶片出口卡门涡街的模型试验观察结果图；
图中标记：1、叶片出口边，2、叶片正面型线，3、修型后叶片背面型线，4、修型前叶片背面型线，5、修型前叶片出口背压边，6、修型后叶片出口背压边，7、上冠，8、下环，9、叶片本体，10、叶片出口正压边，11、母样板，12、子样板，13、叶片背面圆弧样板。
具体实施方式
实施例1
混流式水轮机转轮叶片出口边修型方法，包括以下步骤：
a、截出叶片翼型，确定叶片出口边1的修型区域，叶片出口边1包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的3％，中段为修型区，上段和下段为非修型区，修型区和非修型区之间光滑过渡，修型前叶片出口边厚度为t 1；
b、修型后叶片出口边厚度为t 2，修型后叶片出口边厚度是修型前叶片出口边厚度t 1的0.4倍；叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ为20°；修型后叶片背面型线3与修型前叶片背面型线4通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t 1的4倍；
c、根据叶片翼型、修型前叶片出口边厚度t 1、修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ和圆弧的半径R来确定叶片出口边1修型的最终几何尺寸，并定出圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2；
d、根据修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ、圆弧的半径R和圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2，确定母样板11、子样板12和叶片背面圆弧样板13的尺寸，并一体成型加工制造；
e、根据L 1的值在修型前叶片出口背压边5上划出修型区的两个端点，根据修型后叶片出口边厚度t 2，在叶片出口边1上划线，确定修型后叶片出口背压边6的最终位置；
f、从叶片背面打磨叶片出口边1，通过子母样板和划线调整叶片出口边1的角度直至满足子母样板的尺寸；
g、修磨叶片背面圆弧，直到满足叶片背面圆弧样板13的尺寸。
实施例2
混流式水轮机转轮叶片出口边修型方法，包括以下步骤：
a、截出叶片翼型，确定叶片出口边1的修型区域，叶片出口边1包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的3.5％，中段为修型区，上段和下段为非修型区，修型区和非修型区之间光滑过渡，修型前叶片出口边厚度为t 1；
b、修型后叶片出口边厚度为t 2，修型后叶片出口边厚度是修型前叶片出口边厚度t 1的0.45倍；叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ为23°；修型后叶片背面型线3与修型前叶片背面型线4通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t 1的5倍；
c、根据叶片翼型、修型前叶片出口边厚度t 1、修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ和圆弧的半径R来确定叶片出口边1修型的最终几何尺寸，并定出圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2；
d、根据修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ、圆弧的半径R和圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2，确定母样板11、子样板12和叶片背面圆弧样板13的尺寸，并一体成型加工制造；
e、根据L 1的值在修型前叶片出口背压边5上划出修型区的两个端点，根据修型后叶片出口边厚度t 2，在叶片出口边1上划线，确定修型后叶片出口背压边6的最终位置；
f、从叶片背面打磨叶片出口边1，通过子母样板和划线调整叶片出口边1的角度直至满足子母样板的尺寸；
g、修磨叶片背面圆弧，直到满足叶片背面圆弧样板13的尺寸。
所述步骤a中，转轮包括上冠7、下环8和固定于上冠7与下环8之间的多个叶片，叶片为空间扭曲曲面状，任意两个叶片几何尺寸相同，多个叶片沿转轮圆周方向均匀布置，叶片包括一体成型的叶片本体9和叶片出口边1，叶片出口边1包括叶片出口正压边10和修型前叶片出口背压边5。
实施例3
混流式水轮机转轮叶片出口边修型方法，包括以下步骤：
a、截出叶片翼型，确定叶片出口边1的修型区域，叶片出口边1包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的4％，中段为修型区，上段和下段为非修型区，修型区和非修型区之间光滑过渡，修型前叶片出口边厚度为t 1；
b、修型后叶片出口边厚度为t 2，修型后叶片出口边厚度是修型前叶片出口边厚度t 1的0.5倍；叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ为25°；修型后叶片背面型线3与修型前叶片背面型线4通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t 1的7倍；
c、根据叶片翼型、修型前叶片出口边厚度t 1、修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ和圆弧的半径R来确定叶片出口边1修型的最终几何尺寸，并定出圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2；
d、根据修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ、圆弧的半径R和圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2，确定母样板11、子样板12和叶片背面圆弧样板13的尺寸，并一体成型加工制造；
e、根据L 1的值在修型前叶片出口背压边5上划出修型区的两个端点，根据修型后叶片出口边厚度t 2，在叶片出口边1上划线，确定修型后叶片出口背压边6的最终位置；
f、从叶片背面打磨叶片出口边1，通过子母样板和划线调整叶片出口边1的角度直至满足子母样板的尺寸；
g、修磨叶片背面圆弧，直到满足叶片背面圆弧样板13的尺寸。
所述步骤a中，转轮包括上冠7、下环8和固定于上冠7与下环8之间的多个叶片，叶片为空间扭曲曲面状，任意两个叶片几何尺寸相同，多个叶片沿转轮圆周方向均匀布置，叶片包括一体成型的叶片本体9和叶片出口边1，叶片出口边1包括叶片出口正压边10和修型前叶片出口背压边5。
所述步骤a中，截出叶片翼型是指沿垂直于叶片出口边1的断面截出一段叶片翼型，叶片翼型的几何尺寸由叶片正面一系列离散点坐标(Xp，Yp)和叶片背面一系列离散点坐标(Xs，Ys)确定。
实施例4
混流式水轮机转轮叶片出口边修型方法，包括以下步骤：
a、截出叶片翼型，确定叶片出口边1的修型区域，叶片出口边1包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的4％，中段为修型区，上段和下段为非修型区，修型区和非修型区之 间光滑过渡，修型前叶片出口边厚度为t 1；
b、修型后叶片出口边厚度为t 2，修型后叶片出口边厚度是修型前叶片出口边厚度t 1的0.5倍；叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ为25°；修型后叶片背面型线3与修型前叶片背面型线4通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t 1的7倍；
c、根据叶片翼型、修型前叶片出口边厚度t 1、修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ和圆弧的半径R来确定叶片出口边1修型的最终几何尺寸，并定出圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2；
d、根据修型后叶片出口边厚度t 2、叶片正面型线2与修型后叶片背面型线3中的直线段之间的夹角θ、圆弧的半径R和圆弧与修型前叶片背面型线4的切点至叶片出口边1的距离L 2，确定母样板11、子样板12和叶片背面圆弧样板13的尺寸，并一体成型加工制造；
e、根据L 1的值在修型前叶片出口背压边5上划出修型区的两个端点，根据修型后叶片出口边厚度t 2，在叶片出口边1上划线，确定修型后叶片出口背压边6的最终位置；
f、从叶片背面打磨叶片出口边1，通过子母样板和划线调整叶片出口边1的角度直至满足子母样板的尺寸；
g、修磨叶片背面圆弧，直到满足叶片背面圆弧样板13的尺寸。
所述步骤a中，转轮包括上冠7、下环8和固定于上冠7与下环8之间的多个叶片，叶片为空间扭曲曲面状，任意两个叶片几何尺寸相同，多个叶片沿转轮圆周方向均匀布置，叶片包括一体成型的叶片本体9和叶片出口边1，叶片出口边1包括叶片出口正压边10和修型前叶片出口背压边5。
所述步骤a中，截出叶片翼型是指沿垂直于叶片出口边1的断面截出一段叶片翼型，叶片翼型的几何尺寸由叶片正面一系列离散点坐标(Xp，Yp)和叶片背面一系列离散点坐标(Xs，Ys)确定。
所述步骤f中，子母样板包括一体成型的母样板11和子样板12，当打磨后的叶片出口边1与母样板11完全嵌合且与子样板12不能嵌合时，判定修型后几何尺寸符合要求。
叶片出口边包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的3-4％，中段为修型区，叶片出口边与上冠以及叶片出口边与下环交接区通常为高应力区，上段和下段为非修型区，能够保障叶片在交接区的机械强度，避免叶片裂纹产生；叶片出口边与上冠以及叶片出口边与下环焊接时或多或少存在焊接残余应力，在该交接区存在热影响区，上段和下段为非修型区，能够保障该区域叶片的疲劳强度；从 叶片背面打磨叶片出口边，通过子母样板和划线调整叶片出口边的角度直至满足子母样板的尺寸；修磨叶片背面圆弧，直到满足叶片背面圆弧样板尺寸，这种修型方式简化了修型工艺，人工工作量小，修型时间短；通过步骤a-g，对混流式水轮机转轮叶片出口边背面型线进行修型，整个修型区域仅局限在叶片出口边背面很小的区域，是局部的，因此对混流式水轮机的效率、空化等水力性能没有任何影响，也不会对转轮的机械性能产生影响；修型后，能够提高混流式水轮机转轮叶片出口卡门涡街的泄出频率，以便与转轮叶片的水下固有频率错开；且提高转轮叶片出口卡门涡街泄出频率后，卡门涡街能量将减弱，能量小的卡门涡街很难激起共振，进而能够有效预防或消除因转轮出口卡门涡街诱发的叶片水力弹性共振所产生的水轮机啸声和转轮叶片裂纹，从而提高混流式水轮机转轮的结构整体性和水轮机的运行安全性。
图4为叶片出口边修型检查样板结构示意图，图中R和t 2的后缀为公差，单位为毫米。
图6为一中低水头混流式水轮机转轮叶片出口边修型前叶片出口卡门涡街的模型试验观察结果图；图7为一中低水头混流式水轮机转轮叶片出口边修型后叶片出口卡门涡街的模型试验观察结果图；修型方案中，t 2＝0.43t 1，θ＝25°，R＝4.6t 1。从图6和图7的对比可以看出，叶片出口边修型后，完全消除了转轮叶片出口的可见卡门涡街，效果显著。

Claims (4)

  1. 混流式水轮机转轮叶片出口边修型方法，其特征在于，包括以下步骤：
    a、截出叶片翼型，确定叶片出口边(1)的修型区域，叶片出口边(1)包括一体成型的上段、中段和下段，上段和下段的长度均为L 1，L 1为转轮标称直径的3-4％，中段为修型区，上段和下段为非修型区，修型区和非修型区之间光滑过渡，修型前叶片出口边厚度为t 1；
    b、修型后叶片出口边厚度为t 2，修型后叶片出口边厚度是修型前叶片出口边厚度t 1的0.4-0.5倍；叶片正面型线(2)与修型后叶片背面型线(3)中的直线段之间的夹角θ为20-25°；修型后叶片背面型线(3)与修型前叶片背面型线(4)通过圆弧过渡，圆弧的半径R为修型前叶片出口边厚度t 1的4-7倍；
    c、根据叶片翼型、修型前叶片出口边厚度t 1、修型后叶片出口边厚度t 2、叶片正面型线(2)与修型后叶片背面型线(3)中的直线段之间的夹角θ和圆弧的半径R来确定叶片出口边(1)修型的最终几何尺寸，并定出圆弧与修型前叶片背面型线(4)的切点至叶片出口边(1)的距离L 2；
    d、根据修型后叶片出口边厚度t 2、叶片正面型线(2)与修型后叶片背面型线(3)中的直线段之间的夹角θ、圆弧的半径R和圆弧与修型前叶片背面型线(4)的切点至叶片出口边(1)的距离L 2，确定母样板(11)、子样板(12)和叶片背面圆弧样板(13)的尺寸，并一体成型加工制造；
    e、根据L 1的值在修型前叶片出口背压边(5)上划出修型区的两个端点，根据修型后叶片出口边厚度t 2，在叶片出口边(1)上划线，确定修型后叶片出口背压边(6)的最终位置；
    f、从叶片背面打磨叶片出口边(1)，通过子母样板和划线调整叶片出口边(1)的角度直至满足子母样板的尺寸；
    g、修磨叶片背面圆弧，直到满足叶片背面圆弧样板(13)的尺寸。
  2. 根据权利要求1所述的混流式水轮机转轮叶片出口边修型方法，其特征在于：所述步骤a中，转轮包括上冠(7)、下环(8)和固定于上冠(7)与下环(8)之间的多个叶片，叶片为空间扭曲曲面状，任意两个叶片几何尺寸相同，多个叶片沿转轮圆周方向均匀布置，叶片包括一体成型的叶片本体(9)和叶片出口边(1)，叶片出口边(1)包括叶片出口正压边(10)和修型前叶片出口背压边(5)。
  3. 根据权利要求1所述的混流式水轮机转轮叶片出口边修型方法，其特征在于：所述步骤a中，截出叶片翼型是指沿垂直于叶片出口边(1)的 断面截出一段叶片翼型，叶片翼型的几何尺寸由叶片正面一系列离散点坐标(Xp，Yp)和叶片背面一系列离散点坐标(Xs，Ys)确定。
  4. 根据权利要求1所述的混流式水轮机转轮叶片出口边修型方法，其特征在于：所述步骤f中，子母样板包括一体成型的母样板(11)和子样板(12)，当打磨后的叶片出口边(1)与母样板(11)完全嵌合且与子样板(12)不能嵌合时，判定修型后几何尺寸符合要求。
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