CN114091368A - Method for identifying cavitation state of axial flow turbine - Google Patents

Method for identifying cavitation state of axial flow turbine Download PDF

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CN114091368A
CN114091368A CN202111265390.1A CN202111265390A CN114091368A CN 114091368 A CN114091368 A CN 114091368A CN 202111265390 A CN202111265390 A CN 202111265390A CN 114091368 A CN114091368 A CN 114091368A
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cavitation
axial flow
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water turbine
linearity
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冯建军
门羿
朱国俊
罗兴锜
吴广宽
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Xian University of Technology
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    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/28Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
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    • G01H1/003Measuring characteristics of vibrations in solids by using direct conduction to the detector of rotating machines
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    • G01MEASURING; TESTING
    • G01HMEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
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    • F05INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
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Abstract

The invention discloses a method for identifying the cavitation state of an axial flow water turbine, which is a method for acquiring vibration signals of the water turbine under different working conditions, obtaining a characteristic parameter Hurst index by analyzing a vibration signal MF-DFA of a draft tube of the axial flow water turbine, and identifying the cavitation state based on the linearity of the Hurst index.

Description

Method for identifying cavitation state of axial flow turbine
Technical Field
The invention belongs to the technical field of fluid machinery, and relates to a method for identifying the cavitation state of an axial flow type water turbine.
Background
Water energy is very important for realizing the double-carbon target in China. The water turbine is core mechanical equipment for water energy development, and cavitation has obvious influence on the performance of the water turbine. Cavitation can cause cavitation erosion which can lead to flaking or even perforation of metallic material on localized surfaces of the runner and certain flow components. When cavitation and cavitation erosion are serious to the extent of destroying normal water flow, the energy loss of the water turbine can be increased rapidly, and the efficiency and the output are greatly reduced. Therefore, the determination of the cavitation state of the water turbine in the operation process is very important. Because the internal flow state of the prototype water turbine is invisible, the cavitation judgment method of the prototype water turbine can judge until the cavitation is serious, the efficiency is rapidly reduced, the large-shaft throw is increased and the noise is increased, and the judgment of the cavitation state at the moment is meaningless. A prototype water turbine cavitation state determination method capable of determining a real-time cavitation state must be provided.
Disclosure of Invention
The invention aims to provide a method for identifying the cavitation state of an axial flow water turbine, which accurately judges the cavitation state of the water turbine by analyzing a vibration signal MF-DFA of a draft tube of the axial flow water turbine.
The invention adopts the technical scheme that the method for identifying the cavitation state of the axial flow turbine specifically comprises the following steps:
step 1, collecting a vibration acceleration signal of a water turbine by adopting a vibration acceleration sensor to obtain a time sequence x after sampling the vibration acceleration signal of the water turbinek
Step 2, utilizing the vibration signal sequence x of the water turbine collected in the step 1kConstructing a dispersion sequence Y (i) of vibration signals, i is 1,2,3, … …, N;
step 3, dividing the dispersion series Y (i) obtained in the step 2 into non-overlapping N with equal length ssA section for dividing the sequence Y (i) into non-overlapping N sections with equal length s from the tailsAn interval; finally obtaining 2NsA plurality of equal-length intervals;
step 4, fitting the mean square error F of each interval obtained in the step 3 by adopting a least square method2(s,v);
Step 5, trending off F2(s, v) taking the average to obtain a q-wave function: f (q, S) -Sh(q)
Step 6, performing linear fitting on the change relation of the q-order Hurst index along with the order q;
step 7, calculating linearity of the Hurst index and the order q of the draft tube vibration signal of the axial flow water turbine under different cavitation coefficients based on the fitting result of the step 6, taking the linearity of 0.501 as a standard for judging whether cavitation occurs, and if the linearity is more than 0.501, proving that cavitation occurs, otherwise, cavitation does not occur;
and 8, identifying the cavitation state of the water turbine based on the step 7.
The invention is also characterized in that:
the specific process of the step 2 is as follows:
constructing a dispersion sequence Y (i) of a vibration signal by using an MF-DFA method, wherein i is 1,2,3, … …, N;
Figure BDA0003326811650000031
Figure BDA0003326811650000032
the specific process of the step 4 is as follows:
and fitting the mean square error of each interval of the vibration signal by adopting a least square method:
F2(s,v),v=1,2,...,2m;
when v is 1,2, …, m:
Figure BDA0003326811650000033
when v is m +1, m +2, …,2 m:
Figure BDA0003326811650000034
in the formula, yv(i) Is the fitted polynomial of order r of the v-th segment.
In step 5, the function F (q, s) satisfies the following formula:
Figure BDA0003326811650000035
in step 6, the mean value F (q, s) of the q-order fluctuation function and the interval length s have the following relationship:
F(q,s)~Sh(q)
wherein h (q) is the Hurst index.
The invention has the beneficial effects that: the invention provides a method for identifying a cavitation state based on linearity of a Hurst index for the first time by collecting vibration signals of a water turbine under different working conditions. When the water turbine does not generate cavitation, the vibration signal of the water turbine is a nonlinear non-stationary time sequence, the linearity of the Hurst index is low, the linearity is high, and the linearity of the Hurst index is basically kept unchanged when the cavitation does not occur; when the tail water pipe is subjected to cavitation inception, the linearity of the Hurst index starts to increase, the linear relation starts to deteriorate, and when the cavitation coefficient is reduced again, the cavitation degree increases, the linearity is higher and higher, and the linearity is lower and lower, so that the linearity of the Hurst index and the order q and the cavitation coefficient have a certain rule, and the cavitation state can be identified based on the linearity of the Hurst index, and a cavitation inception point can be found.
Drawings
FIG. 1 is a diagram of vibration acceleration signals collected in the method for identifying cavitation state of an axial flow turbine according to the present invention;
FIG. 2 is a graph showing the relationship between the mean value F (q, s) of the q-order fluctuation function and the interval length s in the method for identifying the cavitation state of the axial flow turbine according to the present invention;
FIG. 3 is a graph showing the linearity of the Hurst index along with the change of the cavitation degree in the method for identifying the cavitation state of the axial flow water turbine.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a method for identifying the cavitation state of an axial flow turbine, which specifically comprises the following steps,
step 1, collecting a vibration acceleration signal of a water turbine by adopting a vibration acceleration sensor to obtain a time sequence x after sampling the vibration acceleration signal of the water turbinek(ii) a Fig. 1 shows a diagram of a vibration acceleration signal acquired by the present invention.
Step 2, utilizing the collected water turbine vibration signal type nonlinear non-stationary time sequence xk(k ═ 1,2,3 …, N), constructing a dispersion sequence y (i) of the vibration signals, i ═ 1,2,3, … …, N;
Figure BDA0003326811650000051
Figure BDA0003326811650000052
step 3, dividing the vibration signal Y (i) in the step 2 into non-overlapping N with equal length ssAnd each interval contains s data. If N cannot divide s exactly during the calculation, Y (i) will have a part of the data remaining, and the sequence is divided into non-overlapping N with equal length s for the accuracy and completeness of the calculated datasInterval, finally obtaining 2NsAnd a section with equal length contains all the data.
Step 4, fitting the mean square error of each interval of the vibration signal by adopting a least square method
F2(s,v),v=1,2,...,2m;
When v is 1,2, …, m:
Figure BDA0003326811650000053
when v is m +1, m +2, …,2 m:
Figure BDA0003326811650000054
in the formula, yv(i) Is the fitted polynomial of order r of the v-th segment.
Step 5, trending off F2(s, v) taking the average, we get the q-wave function: f (q, S) -Sh(q)Then, fitting the logarithm of the function F (q, s) with s, in the process, taking 6 intervals with the interval Scale being 16-1026 equal ratio, determining that the detrending polynomial order r is 2, and the q-order value of the weighted local change is [ -5, 5]And taking the order q as-5, 0 and 5 respectively as analysis display.
Figure BDA0003326811650000061
The mean value F (q, s) of the q-order fluctuation function has the following relationship with the interval length s:
F(q,s)~Sh(q)
wherein h (q) is the Hurst index.
As shown in fig. 2, it is a graph of the mean F (q, s) of the q-order fluctuation function of the present invention and the section length s.
Step 6, performing linear fitting on the change relation of the q-order Hurst index along with the order q;
and 7, calculating the linearity of the Hurst index and the order q of the draft tube vibration signal of the axial flow water turbine under different cavitation coefficients based on the fitting result of the step 6, and as shown in fig. 3, the linearity is a graph of the change of the linearity of the Hurst index along with the cavitation degree.
Linearity is a characteristic value of the degree of coincidence of a calibration curve approaching a prescribed straight line, and the formula of linearity is as follows:
Figure BDA0003326811650000062
Δ Ymax represents the maximum deviation of the calibration curve from the fitted line, and Y represents the percentage of full scale output.
And 8, identifying the cavitation state of the water turbine based on the step 7, wherein when the linearity is between 0.50 and 0.501, cavitation does not occur, when the linearity is more than 0.501, cavitation starts to occur, and when the cavitation degree increases again, the linearity is correspondingly and continuously increased.

Claims (5)

1. A method for identifying the cavitation state of an axial flow turbine is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1, collecting a vibration acceleration signal of a water turbine by adopting a vibration acceleration sensor to obtain a time sequence x after sampling the vibration acceleration signal of the water turbinek
Step 2, utilizing the vibration signal sequence x of the water turbine collected in the step 1kConstructing a dispersion sequence Y (i) of vibration signals, i is 1,2,3, … …, N;
step 3, dividing the dispersion series Y (i) obtained in the step 2 into non-overlapping N with equal length ssA section for dividing the sequence Y (i) into non-overlapping N sections with equal length s from the tailsAn interval; finally obtaining 2NsA plurality of equal-length intervals;
step 4, fitting the mean square error F of each interval obtained in the step 3 by adopting a least square method2(s,v);
Step 5, trending off F2(s, v) taking the average to obtain a q-wave function: f (q, S) -Sh(q)
Step 6, performing linear fitting on the change relation of the q-order Hurst index along with the order q;
step 7, calculating linearity of the Hurst index and the order q of the draft tube vibration signal of the axial flow water turbine under different cavitation coefficients based on the fitting result of the step 6, taking the linearity of 0.501 as a standard for judging whether cavitation occurs, and if the linearity is more than 0.501, proving that cavitation occurs, otherwise, cavitation does not occur;
and 8, identifying the cavitation state of the water turbine based on the step 7.
2. The method for identifying the cavitation state of the axial flow turbine as claimed in claim 1, wherein: the specific process of the step 2 is as follows:
constructing a dispersion sequence Y (i) of a vibration signal by using an MF-DFA method, wherein i is 1,2,3, … …, N;
Figure FDA0003326811640000021
Figure FDA0003326811640000022
3. the method for identifying the cavitation state of the axial flow turbine as claimed in claim 2, wherein: the specific process of the step 4 is as follows:
fitting the mean square error of each interval of the vibration signal by using a least square method
F2(s,v),v=1,2,...,2m;
When v is 1,2, …, m:
Figure FDA0003326811640000023
when v is m +1, m +2, …,2 m:
Figure FDA0003326811640000024
in the formula, yv(i) Is the fitted polynomial of order r of the v-th segment.
4. The method for identifying the cavitation state of the axial flow turbine as claimed in claim 3, wherein: in step 5, the function F (q, s) satisfies the following formula:
Figure FDA0003326811640000025
5. the method for identifying the cavitation state of the axial flow turbine as claimed in claim 4, wherein: in step 6, the mean value F (q, s) of the q-order fluctuation function and the interval length s have the following relationship:
F(q,s)~Sh(q)
wherein h (q) is the Hurst index.
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CN115048746A (en) * 2022-07-05 2022-09-13 西安理工大学 Method for calculating vibration probability density curve of rotating wheel of full-through-flow turbine

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