CN113569496B - Wet mode analysis method for rotating wheel of water turbine - Google Patents
Wet mode analysis method for rotating wheel of water turbine Download PDFInfo
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- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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Abstract
The invention discloses a wet mode analysis method of a turbine runner, which comprises the following steps: s1, determining an effective interval range of fluid affecting a wet mode of a rotating wheel, and dividing the fluid in the effective interval range into n layers along a rotating shaft of the rotating wheel, wherein n is more than or equal to 2 and n is a positive integer; s2, assuming each layer of fluid as a particle without volume, and acquiring an additional mass matrix Ma of the fluid on the surface of the rotating wheel; s3, calculating the inherent frequency omega wet of the rotating wheel wet mode. The method solves the problems of low calculation efficiency, poor model stability, fuzzy evaluation data selection and complexity existing in the prior art.
Description
Technical Field
The invention relates to the technical field of hydraulic turbine vibration characteristic analysis, in particular to a hydraulic turbine runner wet mode analysis method.
Background
The wet mode of the turbine runner is the inherent vibration characteristic of the turbine runner in water. Because of the large difference in density and viscosity between water and air, the wet mode omega of the rotor wheel Wet state And a dry mode omega Dry The difference (in natural vibration characteristics in air) is also large. In particular, the wet mode and the dry mode of the rotating wheel have the same and approximate mode shape, but the wet modeIs lower than the natural frequency of the dry mode. I.e. there is a reduction in the wet mode, defined as the attenuation coefficient, λ=ω Wet state /ω Dry 。
When the vibration-proof design of the turbine runner is carried out, the natural frequency of the runner is required to be wrong by the main excitation frequency of boiled water after flowing through the fixed guide vane, the movable guide vane and the runner. Therefore, after the main excitation frequency is determined, wet mode calculation needs to be performed on the designed rotating wheel, so that the comprehensive maximum resonance frequency of the rotating wheel is staggered from the main excitation frequency, and resonance is avoided.
The current practice is: (1) Calculating the dry mode of the rotating wheel, and multiplying the dry mode by an empirical attenuation coefficient lambda; (2) And (3) building a model of the water body around the rotating wheel, and binding the water on the surface of the rotating wheel to perform wet mode calculation. The scheme (1) has the following problems: because the attenuation coefficients of each step or any pitch diameter of the wet mode are different, the inherent frequency accuracy of the wet mode obtained by the method is poor, and the vibration resistance design of the rotating wheel cannot be effectively guided. The scheme (2) has the problems that the three-dimensional water is directly bound on the surface of the rotating wheel, so that the structural form of the rotating wheel can be changed, and the wet mode shape of the rotating wheel is changed to a certain extent; for rotating machinery similar to a water turbine, the method also generates redundant and irregular wet mode vibration characteristics, which is not beneficial to the design comparison of a dry mode and a wet mode and the determination of an attenuation coefficient lambda.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a wet mode analysis method for a turbine runner, which solves the problems of low calculation efficiency, poor model stability, fuzzy evaluation data selection and complexity in the prior art.
The invention solves the problems by adopting the following technical scheme:
a wet mode analysis method of a turbine runner comprises the following steps:
s1, determining an effective interval range of fluid affecting a wet mode of a rotating wheel, and dividing the fluid in the effective interval range into n layers along a rotating shaft of the rotating wheel, wherein n is more than or equal to 2 and n is a positive integer;
s2, assuming each layer of fluid to be a non-volume particle, obtaining an additional mass matrix M of the fluid on the surface of the rotating wheel a ；
S3, calculating the inherent frequency omega of the rotating wheel wet mode Wet state The calculation formula is as follows:
|K s -ω wet state 2 (M s +M a )|＝0， (1)
Wherein K is s For the rigidity matrix of the rotating wheel, M s Is a rotor quality matrix.
Because of the introduction of the fluid additional mass matrix Ma on the surface of the rotating wheel, the Ma replaces the three-dimensional distribution characteristic of the water body in the actual calculation process, the calculation model is simplified, the volume of the calculation model is reduced, the calculation efficiency is improved, the oscillation characteristic of a fluid-solid coupling interface is eliminated, and the calculation stability is improved. In addition, as the fluid is replaced by the Ma matrix without volume, the geometric characteristics of the calculation model and the dry mode calculation model have better consistency when the wet mode calculation is carried out, the derivation of irregular wet modes is avoided, and the selection, judgment and evaluation of runner mode data in engineering application are facilitated. The technical scheme solves the problems of low calculation efficiency, poor model stability, fuzzy and complicated evaluation data selection in the prior art.
As a preferred technical solution, in step S2, the calculation formula for obtaining the additional mass matrix Ma of the fluid on the surface of the rotor is:
wherein X, Y and Z are the spatial coordinate values of the X axis, the Y axis and the Z axis of any point of the rotating wheel in a three-dimensional rectangular coordinate system, i is the layer number of the fluid, i=1, 2 and …, n is a positive integer, ρ is the density of the fluid, and ze i For the initial coordinate value of the ith layer fluid in the Z axis, zs i For the termination coordinate value of the i-th layer fluid in the Z axis, R is the maximum radius of a certain integral surface in the i-th layer fluid, and D is the integral area of the rotating wheel in the coordinates (x, y) of the certain integral surface.
The formula is convenient for calculating the additional mass matrix Ma of the fluid on the surface of the rotating wheel, and when in actual use, the center of gravity of the rotating wheel is taken as the origin, a three-dimensional rectangular coordinate system is established, but the inconsistency of the origins of the three-dimensional rectangular coordinate system is selected, and the calculation result of the additional mass matrix Ma of the fluid on the surface of the rotating wheel is not influenced.
As a preferred technical scheme, the method further comprises the following steps:
s4, omega of step S3 Wet state Taking the attenuation coefficient lambda of the first 3-order mode of the rotating wheel to evaluate the accuracy.
And the accuracy evaluation is carried out on the attenuation coefficient lambda, so that the technical evaluation on the whole analysis method is convenient, and the accuracy of the analysis result is verified.
In a preferred embodiment, in step S4, if the attenuation coefficient λ corresponds to formula (3), ω of step S3 is considered as ω Wet state The calculation result of (2) is accurate; otherwise, returning to the step S1;
wherein m is r M is the total weight of the rotating wheel w Is the total weight of the fluid within the effective interval of the fluid.
The quantitative verification is carried out on the attenuation coefficient lambda, so that the accuracy assessment of the attenuation coefficient lambda is more accurate, and the technical assessment of the whole analysis method is more convenient.
As a preferred technical solution, step S3 includes the following steps:
s31, analyzing the stiffening effect of the stress of the rotating wheel by considering the influence of the rotating speed and the fluid pressure on the rigidity of the rotating wheel to obtain a rigidity matrix K for stiffening and improving the stress of the rotating wheel r ；
S32, rigidity matrix K which is rigidized and lifted by utilizing rotating wheel stress r Matrix K of rigidity of counter-rotating wheel s Make corrections to K in equation (1) s Corrected to K s ' make K s '＝K s +K r ；
S33, utilizing the corrected runner stiffness matrix K s ' calculating the inherent frequency omega wet of the runner wet mode, wherein the calculation formula is as follows:
|(K s +K r )-ω wet state 2 (M s +M a )|＝0， (4)。
Stiffness matrix K lifted by wheel stress rigidization r Matrix K of rigidity of counter-rotating wheel s Further improves the natural frequency omega of the wet mode of the rotating wheel Wet state The accuracy of the system ensures that the analysis is more accurate and practical, the wet mode of the turbine runner is more convenient to analyze, the design and performance improvement of the turbine runner are more convenient, and the like.
In a preferred embodiment, in step S1, the fluid in the effective area is divided into n layers along the rotation axis of the rotor according to the degree of twisting of the rotor blades and/or the axial height of the rotor.
The degree of twist of the rotor blades and/or the rotor axial height are taken into account, thereby facilitating a more scientific determination of the effective interval range of the fluid affecting the rotor wet mode.
As a preferable technical solution, in step S1, the range of n is selected as follows: n is more than or equal to 4 and less than or equal to 12.
The range of n is selected as follows: n is more than or equal to 4 and less than or equal to 12, so that the accurate analysis result is conveniently obtained, the workload and the data processing amount are simultaneously considered, the method also accords with application scenes of numerous runner wet mode analysis, and the analysis is more efficient while the application scenes are wide.
In a preferred embodiment, in step S1, the fluid within the effective interval is divided into layers with the same height along the rotation axis of the rotor.
Compared with the method that the fluid in the effective interval range is divided into the layers with the non-identical heights along the rotating shaft of the rotating wheel, the accuracy of the analysis result of the layering method is the same as or equivalent to that of the method that the fluid in the effective interval range is divided into the layers with the non-identical heights along the rotating shaft of the rotating wheel, so that the calculation amount is reduced conveniently, and the complexity of the wet mode analysis of the rotating wheel is reduced.
As a preferred solution, the fluid is selected to be a liquid or a gas.
The fluid can be liquid or gas, can be pasty substances, and can also be gas or vaporized substances with larger specific gravity, so that the fluid has wider applicable range.
As a preferred technical scheme, the fluid is water.
The water turbine runner works in water as a common working condition, and the selection mode is suitable for a wide range of wet mode analysis scenes of the water turbine runner.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, as the additional mass matrix Ma of the fluid on the surface of the rotating wheel is introduced, in the actual calculation process, ma replaces the three-dimensional distribution characteristic of the water body, the calculation model is simplified, the volume of the calculation model is reduced, the calculation efficiency is improved, the oscillation characteristic of a fluid-solid coupling interface is eliminated, and the calculation stability is improved. In addition, as the fluid is replaced by the Ma matrix without volume, the geometric characteristic of the calculation model and the dry mode calculation model have better consistency when the wet mode calculation is carried out, the derivation of an irregular wet mode is avoided, and the selection, judgment and evaluation of the runner mode data in engineering application are facilitated; the problems of low calculation efficiency, poor model stability, fuzzy evaluation data selection and complexity in the prior art are solved;
(2) The method carries out accuracy assessment on the attenuation coefficient lambda, and is convenient for carrying out technical evaluation on the whole analysis method so as to verify the accuracy of the analysis result;
(3) The invention quantitatively verifies the attenuation coefficient lambda, so that the accuracy evaluation of the attenuation coefficient lambda is more accurate, and the technical evaluation of the whole analysis method is more convenient;
(4) The rigidity matrix K is lifted through the stress rigidization of the rotating wheel r Matrix K of rigidity of counter-rotating wheel s Further improves the natural frequency omega of the wet mode of the rotating wheel Wet state The accuracy of the system ensures that the analysis is more accurate and practical, the wet mode of the turbine runner is more convenient to analyze, the design and performance improvement of the turbine runner are more convenient, and the like;
(5) The invention considers the torsion degree of the runner blade and/or the axial height of the runner, thereby being convenient for more scientifically determining the effective interval range of the fluid affecting the wet mode of the runner;
(6) The invention selects the range of n as follows: n is more than or equal to 4 and less than or equal to 12, so that the accurate analysis result is conveniently obtained, the workload and the data processing amount are simultaneously considered, the application scene of the wet mode analysis of a plurality of rotating wheels is met, the application scene is wide, and meanwhile, the analysis is more efficient;
(7) In step S1 of the present invention, the fluid in the effective interval range is divided into each layer with the same height along the rotating shaft of the rotating wheel, and compared with the fluid in the effective interval range is divided into the layers with the different heights along the rotating shaft of the rotating wheel, the accuracy of the analysis result of the layering method is the same as or equivalent to the analysis result of the fluid in the effective interval range is divided into the layers with the different heights along the rotating shaft of the rotating wheel, which is convenient for reducing the calculation amount and also reduces the complexity of the wet mode analysis of the rotating wheel;
(8) The fluid can be liquid or gas, can be pasty substances, and can also be gas or vaporized substances with larger specific gravity, so that the fluid range suitable for the invention is wider;
(9) The method selects the fluid as water, and the turbine runner works in the water as a common working condition, so that the selection mode is suitable for a wide range of wet mode analysis scenes of the turbine runner.
Drawings
FIG. 1 is a schematic illustration of the present invention for determining the effective interval range of a fluid affecting the wet mode of a rotor;
FIG. 2 is a schematic illustration of fluid stratification in accordance with the present invention;
FIG. 3 is a schematic illustration of the wheel of the present invention fully immersed in a fluid;
FIG. 4 is a schematic illustration of a portion of a rotor having a portion exposed to the outside of the fluid;
FIG. 5 is a dry mode shape cloud for example 3 of the present invention;
FIG. 6 is a cloud of wet mode shapes in example 3 of the present invention
Fig. 7 is a graph showing the natural frequency contrast of the dry mode, wet mode, and wet mode (considering stress stiffening) of the first 4 pitch diameter mode in example 3 of the present invention.
The reference numerals and corresponding part names in the drawings: 1. 2 movable guide vanes, 2 bottom rings, 3 lower rings of rotating wheels, 4 blades, 5 top covers, 6 main shafts, 7, runner crown, 11, runner, 12, fluid, 31, runner lower ring end face.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
Example 1
As shown in fig. 1 to 7, a wet mode analysis method for a turbine runner includes the following steps:
s1, determining an effective interval range of fluid affecting a wet mode of a rotating wheel, and dividing the fluid in the effective interval range into n layers along a rotating shaft of the rotating wheel, wherein n is more than or equal to 2 and n is a positive integer;
s2, assuming each layer of fluid as a particle without volume, and acquiring an additional mass matrix Ma of the fluid on the surface of the rotating wheel;
s3, calculating the inherent frequency omega of the rotating wheel wet mode Wet state The calculation formula is as follows:
|K s -ω wet state 2 (M s +M a )|＝0， (1)
Wherein K is s For the rigidity matrix of the rotating wheel, M s Is a rotor quality matrix.
Because of the introduction of the fluid additional mass matrix Ma on the surface of the rotating wheel, the Ma replaces the three-dimensional distribution characteristic of the water body in the actual calculation process, the calculation model is simplified, the volume of the calculation model is reduced, the calculation efficiency is improved, the oscillation characteristic of a fluid-solid coupling interface is eliminated, and the calculation stability is improved. In addition, as the fluid is replaced by the Ma matrix without volume, the geometric characteristics of the calculation model and the dry mode calculation model have better consistency when the wet mode calculation is carried out, the derivation of irregular wet modes is avoided, and the selection, judgment and evaluation of runner mode data in engineering application are facilitated. The technical scheme solves the problems of low calculation efficiency, poor model stability, fuzzy and complicated evaluation data selection in the prior art.
As shown in fig. 1, in actual use, when determining the effective interval range of the fluid affecting the wet mode of the wheel, the effective interval range of the fluid affecting the wet mode of the wheel may be determined as a set of the following ranges: a movable vane tail vaneless region (indicated by an arrow at A); the area below the lower end surface of the top cover (indicated by an arrow at B); fluid in the space of the end face +0.1R area (R is the radius of the inner wall of the outlet of the lower ring of the rotating wheel) of the lower ring of the rotating wheel. In fig. 1, the structures and areas of the movable guide vane 1, the bottom ring 2, the runner lower ring 3, the blades 4, the top cover 5, the main shaft 6, the upper crown 7, the end face 31 of the runner lower ring, etc. show the effective interval range for determining the fluid affecting the runner wet mode.
Fig. 2 shows the fluid in the effective interval along the rotation axis of the rotor, and the horizontal dashed line in fig. 2 shows a layering line for dividing the fluid in the effective interval into n layers along the rotation axis of the rotor.
As a preferred embodiment, in step S2, an additional mass matrix M of the fluid on the rotor surface is obtained a The calculation formula of (2) is as follows:
wherein X, Y and Z are the spatial coordinate values of the X axis, the Y axis and the Z axis of any point of the rotating wheel in a three-dimensional rectangular coordinate system, i is the layer number of the fluid, i=1, 2 and …, n is a positive integer, ρ is the density of the fluid, and ze i For the initial coordinate value of the ith layer fluid in the Z axis, zs i For the termination coordinate value of the i-th layer fluid in the Z axis, R is the maximum radius of a certain integral surface in the i-th layer fluid, and D is the integral area of the rotating wheel in the coordinates (x, y) of the certain integral surface.
The formula is convenient for calculating the additional mass matrix Ma of the fluid on the surface of the rotating wheel, and when in actual use, the center of gravity of the rotating wheel is taken as the origin, a three-dimensional rectangular coordinate system is established, but the inconsistency of the origins of the three-dimensional rectangular coordinate system is selected, and the calculation result of the additional mass matrix Ma of the fluid on the surface of the rotating wheel is not influenced.
As a preferred technical scheme, the method further comprises the following steps:
s4, toOmega of step S3 Wet state Taking the attenuation coefficient lambda of the first 3-order mode of the rotating wheel to evaluate the accuracy.
And the accuracy evaluation is carried out on the attenuation coefficient lambda, so that the technical evaluation on the whole analysis method is convenient, and the accuracy of the analysis result is verified. In actual use, the formula λ=ω can be used Wet state Omega Dry and combine with |K s -ω Dry 2 M s The attenuation coefficient λ is calculated by =0.
In a preferred embodiment, in step S4, if the attenuation coefficient λ corresponds to formula (3), ω of step S3 is considered as ω Wet state The calculation result of (2) is accurate; otherwise, returning to the step S1;
wherein m is r M is the total weight of the rotating wheel w Is the total weight of the fluid within the effective interval of the fluid.
The quantitative verification is carried out on the attenuation coefficient lambda, so that the accuracy assessment of the attenuation coefficient lambda is more accurate, and the technical assessment of the whole analysis method is more convenient.
As a preferred technical solution, step S3 includes the following steps:
s31, analyzing the stiffening effect of the stress of the rotating wheel by considering the influence of the rotating speed and the fluid pressure on the rigidity of the rotating wheel, and obtaining a rigidity matrix Kr of stiffening and lifting of the stress of the rotating wheel;
s32, rigidity matrix K which is rigidized and lifted by utilizing rotating wheel stress r Matrix K of rigidity of counter-rotating wheel s Make corrections to K in equation (1) s Corrected to K s ' make K s '＝K s +K r ；
S33, utilizing the corrected runner stiffness matrix K s ' calculate the natural frequency ω of the wet mode of the wheel Wet state The calculation formula is as follows:
|(K s +K r )-ω wet state 2 (M s +M a )|＝0， (4)。
Stiffness matrix K lifted by wheel stress rigidization r Matrix K of rigidity of counter-rotating wheel s Further improves the natural frequency omega of the wet mode of the rotating wheel Wet state The accuracy of the system ensures that the analysis is more accurate and practical, the wet mode of the turbine runner is more convenient to analyze, the design and performance improvement of the turbine runner are more convenient, and the like.
Example 2
As further optimization of embodiment 1, this embodiment includes all the technical features of embodiment 1, as shown in fig. 1 to 7, and in addition, this embodiment further includes the following technical features:
in a preferred embodiment, in step S1, the fluid in the effective area is divided into n layers along the rotation axis of the rotor according to the degree of twisting of the rotor blades and/or the axial height of the rotor.
The degree of twist of the rotor blades and/or the rotor axial height are taken into account, thereby facilitating a more scientific determination of the effective interval range of the fluid affecting the rotor wet mode.
As a preferable technical solution, in step S1, the range of n is selected as follows: n is more than or equal to 4 and less than or equal to 12.
The range of n is selected as follows: n is more than or equal to 4 and less than or equal to 12, so that the accurate analysis result is conveniently obtained, the workload and the data processing amount are simultaneously considered, the method also accords with application scenes of numerous runner wet mode analysis, and the analysis is more efficient while the application scenes are wide.
In a preferred embodiment, in step S1, the fluid within the effective interval is divided into layers with the same height along the rotation axis of the rotor.
Compared with the method that the fluid in the effective interval range is divided into the layers with the non-identical heights along the rotating shaft of the rotating wheel, the accuracy of the analysis result of the layering method is the same as or equivalent to that of the method that the fluid in the effective interval range is divided into the layers with the non-identical heights along the rotating shaft of the rotating wheel, so that the calculation amount is reduced conveniently, and the complexity of the wet mode analysis of the rotating wheel is reduced.
As a preferred solution, the fluid is selected to be a liquid or a gas.
The fluid can be liquid or gas, can be pasty substances, and can also be gas or vaporized substances with larger specific gravity, so that the fluid has wider applicable range.
As a preferred technical scheme, the fluid is water.
The water turbine runner works in water as a common working condition, and the selection mode is suitable for a wide range of wet mode analysis scenes of the water turbine runner.
It is worth to be noted that, for wet mode calculation including larger curved surface structure besides the turbine runner, the above technical scheme is also applicable;
it is worth to say that, for the wet mode calculation of the simple structure of the surface characteristics except the rotating wheel of the water turbine, the layering of the water body can be reduced, even the layering is not performed;
it is worth noting that for structures where the structure is not completely surrounded by fluid, only the mass of fluid needs to be added to the surface of the fluid; the technical scheme of the invention is still applicable. For example, if the rotor has a portion exposed to the outside of the fluid, only the wet mode of the portion of the rotor immersed in the fluid may be analyzed. In fig. 3, the positional relationship of the runner 11, the fluid 12 illustrates the structure in which the runner 11 is fully immersed in the fluid 12; in fig. 4, the positional relationship between the rotor 11 and the fluid 12 shows a structure in which a part of the rotor 11 is exposed to the outside of the fluid 12.
Example 3
As shown in fig. 1 to 7, this example provides a more refined embodiment on the basis of example 1 and example 2.
The wheel resonance is not only related to the natural frequency but also to the mode shape corresponding to the respective natural frequency. Only if the vector direction of excitation is the same as the mode shape and the excitation frequency is near the natural frequency of the rotor, the rotor will resonate. The hydraulic excitation frequency induced by hydraulic interference between the turbine runner blade and the guide vane can be expressed by the following formula:
n×Z s ×f 0 ±K×f 0 ＝m×Z r ×f 0 ， (5)
wherein Z is s Representing the number of guide vanes; k represents a rotating radial segmentThe number of points; m is more than or equal to 0 and m can be any integer; n is more than or equal to 0 and can be any integer; z is Z r Representing the number of the runner blades; f (f) 0 Indicating the frequency conversion.
Z s 、Z r And f 0 Is a known parameter. The corresponding K value can be obtained by equation (5). The frequency corresponding to the pitch diameter K is f k The maximum excitation frequency of the rotating wheel is nZ s f 0 . To prevent resonance, f should be designed to k Relative nZ s f0 has a safety margin of 10% or more. Therefore, vibration analysis of the rotating wheel should comprehensively consider the vibration mode and frequency of the corresponding pitch diameter.
By the wet mode calculation method, the inherent frequency and the mode shape of the wet mode of the rotating wheel can be obtained. Comparing the dry mode and wet mode of the runner in fig. 5 and 6, it can be seen that the vibration rule of the runner in air and water is almost consistent with the same pitch diameter.
The natural frequency of the rotor in water is less than the natural frequency in air, as shown in fig. 7, due to the mass of the body of water and damping. Meanwhile, after the wet mode calculation method is used for calculation, the mode shape of the wet mode of the rotating wheel is kept consistent after the stress rigidization effect is considered, but the natural frequency is slightly improved, and the improvement ratio of the natural frequency of the mode with the first 4 pitch diameter is not more than 2.5%.
As described above, the present invention can be preferably implemented.
All of the features disclosed in all of the embodiments of this specification, or all of the steps in any method or process disclosed implicitly, except for the mutually exclusive features and/or steps, may be combined and/or expanded and substituted in any way.
The foregoing description of the preferred embodiment of the invention is not intended to limit the invention in any way, but rather to cover all modifications, equivalents, improvements and alternatives falling within the spirit and principles of the invention.
Claims (7)
1. The wet mode analysis method of the turbine runner is characterized by comprising the following steps of:
s1, determining an effective interval range of fluid affecting a wet mode of a rotating wheel, and dividing the fluid in the effective interval range into n layers along a rotating shaft of the rotating wheel, wherein n is more than or equal to 2 and n is a positive integer;
s2, assuming each layer of fluid to be a non-volume particle, obtaining an additional mass matrix M of the fluid on the surface of the rotating wheel a ；
S3, calculating the inherent frequency omega of the rotating wheel wet mode Wet state The calculation formula is as follows:
|K s -ω wet state 2 （M s +M a ）|=0，（1）
Wherein K is s For the rigidity matrix of the rotating wheel, M s Is a runner quality matrix;
in step S2, an additional mass matrix M of the rotor surface fluid is obtained a The calculation formula of (2) is as follows:
wherein X, Y and Z are the spatial coordinate values of the X axis, the Y axis and the Z axis of any point of the rotating wheel in a three-dimensional rectangular coordinate system, i is the layer number of the fluid, i=1, 2 and …, n is a positive integer, ρ is the density of the fluid, and ze i For the initial coordinate value of the ith layer fluid in the Z axis, zs i For the termination coordinate value of the ith layer fluid in the Z axis, R is the maximum radius of a certain integral surface in the ith layer fluid, and D is the integral area of the rotating wheel in the coordinates (x, y) of the certain integral surface;
the method also comprises the following steps:
s4, omega of step S3 Wet state Taking the attenuation coefficient lambda of the first 3-order mode of the rotating wheel to carry out accuracy evaluation;
in step S4, if the attenuation coefficient λ satisfies the formula (3), ω in step S3 is considered Wet state The calculation result of (2) is accurate; otherwise, returning to the step S1;
wherein m is r M is the total weight of the rotating wheel w Is the total weight of the fluid within the effective interval of the fluid.
2. The method for analyzing the wet mode of the runner of the water turbine according to claim 1, wherein the step S3 comprises the steps of:
s31, analyzing the stiffening effect of the stress of the rotating wheel by considering the influence of the rotating speed and the fluid pressure on the rigidity of the rotating wheel to obtain a rigidity matrix K for stiffening and improving the stress of the rotating wheel r ；
S32, rigidity matrix K which is rigidized and lifted by utilizing rotating wheel stress r Matrix K of rigidity of counter-rotating wheel s Make corrections to K in equation (1) s Corrected to K s ' ， Let K s '=K s +K r ；
S33, utilizing the corrected runner stiffness matrix K s ' calculate the natural frequency ω of the wet mode of the wheel Wet state The calculation formula is as follows:
|（K s +K r ）-ω wet state 2 （M s +M a ）|=0，（4）。
3. A method according to claim 1 or 2, wherein in step S1, the fluid in the effective interval is divided into n layers along the rotation axis of the runner according to the degree of twisting of the runner blades and/or the axial height of the runner.
4. A method for analyzing wet mode of a runner of a water turbine according to claim 3, wherein in step S1, a range of n is selected as follows: n is more than or equal to 4 and less than or equal to 12.
5. The method according to claim 4, wherein in step S1, the fluid in the effective interval range is divided into layers with the same height along the rotation axis of the runner.
6. The method of claim 1, wherein the fluid is selected from the group consisting of liquid and gas.
7. The method of claim 6, wherein the fluid is water.
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| CN108763628A (en) * | 2018-04-13 | 2018-11-06 | 西北工业大学 | The design method and device of multispan functionally gradient fluid conveying pipe |
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| CN105257066A (en) * | 2015-10-23 | 2016-01-20 | 西华大学 | Cylinder structure capable of resisting fluid vortex-induced vibration |
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