CN112065629A - Method for detecting clearance cavitation primary of through-flow turbine - Google Patents

Method for detecting clearance cavitation primary of through-flow turbine Download PDF

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CN112065629A
CN112065629A CN202010784118.3A CN202010784118A CN112065629A CN 112065629 A CN112065629 A CN 112065629A CN 202010784118 A CN202010784118 A CN 202010784118A CN 112065629 A CN112065629 A CN 112065629A
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runner
cavitation
turbine
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vibration
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CN112065629B (en
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冯建军
戈振国
朱国俊
吴广宽
罗兴锜
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Xian University of Technology
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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
    • 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
    • F03B11/008—Measuring or testing arrangements
    • 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

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  • Combustion & Propulsion (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Hydraulic Turbines (AREA)

Abstract

The invention discloses a method for detecting clearance cavitation primary of a through-flow turbine, which comprises the following steps: starting a model tubular turbine test system, adjusting the operation condition of the model tubular turbine to enable blades of a runner to be in a non-clearance cavitation state, collecting vibration acceleration signals of a runner chamber by adopting a laser vibration meter to obtain a time sequence after sampling the vibration acceleration signals of the runner chamber, intercepting the time sequence and converting the time sequence into frequency signals; determining blade passing frequency f of model through-flow turbine runnerpAmplitude A ofp(ii) a Acquiring acceleration signals of the vibration of the lower runner chamber with different cavitation coefficients; determining a cavitation coefficient corresponding to the clearance cavitation primary generation of the runner blade of the model tubular turbine; and closing the model tubular turbine test system. The invention solves the problem that the accurate judgment of the clearance cavitation inception of the runner blade of the through-flow turbine is greatly influenced due to the difference of an observer and an observation position in the prior art.

Description

Method for detecting clearance cavitation primary of through-flow turbine
Technical Field
The invention belongs to the technical field of water turbines, and relates to a method for detecting clearance cavitation primary of a through-flow turbine.
Background
The through-flow turbine is important hydraulic mechanical equipment for developing ocean tidal energy, and the safe and stable operation and performance optimization of the through-flow turbine relate to the efficient development and utilization of the tidal energy. However, through-flow turbines often experience clearance cavitation due to the local flow velocity increase and pressure decrease as the water flows through the tip clearance between the runner and the runner chamber. The flow phenomenon not only induces cavitation erosion, vibration and noise of the runner blades to further influence the safe and stable operation of the through-flow turbine, but also relates to various flow problems such as blade tip leakage vortex, blade tip separation vortex, multiphase flow and the like to deteriorate the performance of the through-flow turbine. For the judgment of the initial cavitation of the gap of the through-flow turbine, the traditional method mostly adopts artificial vision to check the state of the rotor blade with visible bubbles just appearing for judgment. The traditional observation method greatly influences the accurate judgment of observing the clearance cavitation initiation of the runner blade of the through-flow turbine due to the difference of an observer and an observation position. Therefore, it is important to develop a detection method for accurately measuring the cavitation initiation of the gap of the through-flow turbine.
Disclosure of Invention
The invention aims to provide a method for detecting clearance cavitation inception of a through-flow turbine, which solves the problem that in the prior art, the accurate judgment of the clearance cavitation inception of a runner blade of the through-flow turbine is greatly influenced due to different observers and observation positions.
The invention adopts the technical scheme that a through-flow turbine clearance cavitation primary detection method adopts a through-flow turbine test system, which comprises a water inlet pipe, a runner chamber and a tail water pipe which are sequentially communicated, wherein a bulb body and a movable guide vane are sequentially arranged in the water inlet pipe according to the water flow direction, the movable guide vane is connected with a runner, the runner is positioned in the runner chamber, a laser vibration meter is arranged on the outer side of the runner chamber, the laser vibration meter is electrically connected with a data acquisition system through a lead, and the method is implemented according to the following steps:
step 1, starting a model tubular turbine test system, and enabling water flow to sequentially pass through a water inlet pipe, a bulb body, a movable guide vane, a rotating wheel and a draft tube;
step 2, adjusting the operation condition of the model tubular turbine to enable the blades of the rotating wheel to be in a non-clearance cavitation state;
step 3, keeping the running condition of the model tubular turbine stable, collecting the vibration acceleration signals of the runner chamber by adopting a laser vibration meter, and sending the measured data to a data collection system to obtain the time sequence after sampling the vibration acceleration signals of the runner chamber;
step 4, intercepting the time sequence obtained by sampling the acceleration signal of the runner chamber vibration obtained in the step 3 to obtain the intercepted time sequence;
step 5, converting a time domain signal of the acceleration time sequence of the vibration of the runner chamber into a frequency signal by using fast Fourier transform;
step 6, determining blade passing frequency f of model tubular turbine runnerpAmplitude A ofp；
Step 7, repeating the steps 4-6 to acquire acceleration signals of the vibration of the lower runner chamber with different cavitation coefficients;
step 8, determining a cavitation coefficient corresponding to blade gap cavitation primary generation of a model tubular turbine runner;
and 9, closing the model tubular turbine test system.
The present invention is also characterized in that,
the time sequence obtained in step 4 after interception is: x (t) is a time sequence obtained by intercepting an acceleration signal of the vibration of the runner chamber of the model tubular turbine; s (t) is a time sequence after sampling of an acceleration signal of the vibration of the runner chamber of the model tubular turbine; w (t) is a window function, t being time.
The frequency signals obtained in step 5 are:
Figure BDA0002621298390000031
wherein the content of the first and second substances,
Figure BDA0002621298390000032
k is 0,1, …, N-1, N is the length of the time series x (t).
4. A flow turbine according to claim 3The detection method of cavitation inception is characterized in that in step 6 fp＝Zrn·fnWherein, in the step (A),
Figure BDA0002621298390000033
fpthe blade passing frequency of a model through-flow turbine runner is set; zrnThe number of the blades of the model through-flow turbine runner is set; f. ofnThe rotating frequency of a model tubular turbine runner is set; n is the rotating speed of the model tubular turbine runner, the frequency signal obtained in the step 5 is drawn into a frequency signal graph, and then the frequency signal graph is obtained according to fpLooking up the corresponding amplitude A in the frequency signal diagramp。
The step 7 specifically comprises the following steps: and (3) continuously reducing the cavitation coefficient sigma of the model through-flow turbine, adopting a laser vibration meter to collect acceleration signals of the runner chamber vibration under different cavitation coefficients, sending the acceleration signals to a data acquisition system, and then sequentially repeating the steps 4 to 6 until the obvious clearance cavitation phenomenon appears on the through-flow turbine runner blade, namely observing that continuous bubbles appear on the top of the through-flow turbine runner blade.
The step 8 specifically comprises the following steps: first order piecewise function fitted by least square method
Figure BDA0002621298390000034
Fitting step 6 through model through-flow turbine runner blade passing frequency fpAmplitude A ofpWith the variation trend of the cavitation coefficient sigma, then seeking the minimum mean square difference value and Q to obtain the intersection point of the first-order piecewise function according to the principle of least square method fitting function
Figure BDA0002621298390000035
Namely the position of the gap cavitation primary generation of the runner blade of the model through-flow turbine.
Piecewise function of first order
Figure BDA0002621298390000036
The formula of (1) is as follows:
Figure BDA0002621298390000037
in the formula:
Figure BDA0002621298390000038
is a first order piecewise function;
Figure BDA0002621298390000039
is the intersection of the first-order piecewise functions; a and a' are linear piecewise functions
Figure BDA00026212983900000310
The coefficient of the primary term; b and b' are linear piecewise functions
Figure BDA00026212983900000311
A medium constant term;
assuming test measurement data in a piecewise linear function
Figure BDA0002621298390000041
Intersection point
Figure BDA0002621298390000042
When is separated, is preceded by n1Measured data, followed by N0-n1Measurement data, N0For the number of iterations performed in step 7, the minimum squared difference value and Q are given by the following equation:
Figure BDA0002621298390000043
wherein i represents the ith repeated test in the step 7, x is an abscissa value of a coordinate axis, namely a value of the cavitation coefficient sigma, and y is an ordinate value of the coordinate axis, namely a passing frequency f of the bladepAmplitude A ofpThe value of (a) is,
Figure BDA0002621298390000044
is a function representing a fitted linear piecewise
Figure BDA0002621298390000045
The fitting value of the i-th repeated test is the fitting amplitude ApThe value of (a) is,
Figure BDA0002621298390000046
representing fitted linear piecewise function
Figure BDA0002621298390000047
The value of the cavitation coefficient σ at the ith iteration;
the minima are obtained by partial derivative of Q:
Figure BDA0002621298390000048
Figure BDA0002621298390000049
wherein the minimum value Q corresponds to
Figure BDA00026212983900000410
The value is a piecewise linear function
Figure BDA00026212983900000411
The point of intersection of the model tubular turbine runner blade clearance cavitation is the primary position.
And the horizontal distance between the measuring point of the laser vibration meter and the position corresponding to the runner chamber is L, and L is more than 0.5 m.
The invention has the beneficial effects that: the invention relates to a method for detecting clearance cavitation primary of a through-flow turbine, which firstly provides a method for passing frequency f on a runner blade by using an acceleration signal of runner chamber vibration of a runner chamber of a through-flow turbine through monitoring the acceleration signal of the runner chamber vibration of a model through-flow turbinepAmplitude A ofpThe method for determining the cavitation inception of the through-flow turbine runner blade gap along with the variation trend of the cavitation coefficient sigma. Before the occurrence of interstitial cavitation, fpAt an amplitude value ApSlowly increases with decreasing cavitation coefficient σ; at the top of the suction surface of the runner blade during the initial stage of clearance cavitationThe generated bubbles are very few, and the micro bubbles in the water play a role of buffering, so that the impact of water flow on the wall surface of the runner chamber is reduced, and the amplitude A of an acceleration signal of the vibration of the runner chamber when the runner blade passes through the frequency is reducedpAnd decreases. When the bubbles are further increased, the destruction of the bubbles causes an impact on the runner chamber, thereby increasing the vibration of the runner chamber. Therefore, at the initial stage of cavitation, the vibration acceleration signal passes through the rotor blade at the frequency fpAmplitude A ofpWith a local minimum.
Drawings
FIG. 1 is a schematic structural diagram of a through-flow turbine test system used in a method for detecting cavitation onset in a through-flow turbine according to the present invention;
FIG. 2 is a layout diagram of a laser vibration meter 7 in the method for detecting the initial cavitation of the gap in a tubular turbine according to the present invention;
FIG. 3 shows the transit frequency f of the runner blade in the method for detecting the clearance cavitation of the through-flow turbinepAt an amplitude value ApAnd (4) a trend graph along with the change of the cavitation coefficient sigma.
In the figure, 1, a water inlet pipe, 2, a bulb body, 3, a movable guide vane, 4, a rotating wheel, 5, a rotating wheel chamber, 6, a tail water pipe, 7, a laser vibration meter and 8, a data acquisition system.
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 detecting clearance cavitation inception of a through-flow turbine, which adopts a through-flow turbine test system, the structure of which is shown in figure 1, and comprises a water inlet pipe 1, a runner chamber 5 and a draft pipe 6 which are sequentially communicated, a bulb body 2 and a movable guide vane 3 are sequentially arranged in the water inlet pipe 1 according to the water flow direction, the movable guide vane 3 is connected with a runner 4, the runner 4 is positioned in the runner chamber 5, the outer side of the runner chamber 5 is provided with a laser vibration meter 7, the laser vibration meter 7 is electrically connected with a data acquisition system 8 through a lead, the horizontal distance between the measuring point of the laser vibration meter 7 and the position corresponding to the runner chamber 5 is L, L is more than 0.5m, as shown in figure 2, the measuring point of the laser vibration meter 7 is arranged at the outer side of the runner chamber 5, the horizontal distance is L,the laser vibration meter 7 adopts laser as a detection means, has non-invasive performance, is not influenced by a measuring distance, and can accurately measure a vibration acceleration signal; as shown in FIG. 3, the runner blade passing frequency fpAt an amplitude value ApThe trend of change with cavitation coefficient σ is: as the cavitation coefficient σ decreases, fpAt an amplitude value ApSlowly increasing and then decreasing to a local minimum value, wherein the corresponding cavitation coefficient is a cavitation initiation point, and f is the point of cavitation initiation along with the development of cavitationpAt an amplitude value ApThe method is obviously increased and specifically implemented according to the following steps:
step 1, starting a model tubular turbine test system, and enabling water flow to sequentially pass through a water inlet pipe 1, a bulb body 2, a movable guide vane 3, a rotating wheel 4 and a draft tube 6;
step 2, adjusting the operation condition of the model tubular turbine to enable the blades of the rotating wheel 4 to be in a non-clearance cavitation state;
step 3, keeping the running condition of the model tubular turbine stable, collecting the vibration acceleration signals of the runner chamber 5 by using a laser vibration meter 7, and sending the measured data to a data collection system 8 to obtain a time sequence after sampling the vibration acceleration signals of the runner chamber 5;
step 4, intercepting the time sequence obtained after the acceleration signal of the vibration of the runner chamber 5 obtained in the step 3 is sampled, wherein the time sequence obtained after interception is as follows: x (t) is a time sequence obtained by intercepting an acceleration signal of the vibration of the model turbine runner chamber 5; s (t) is a time sequence after sampling of an acceleration signal of the vibration of the runner chamber 5 of the model tubular turbine; w (t) is a window function, t refers to time;
step 5, converting a time domain signal of the time series of the acceleration of the vibration of the runner chamber 5 into a frequency signal by using fast fourier transform, wherein the frequency signal is:
Figure BDA0002621298390000061
wherein the content of the first and second substances,
Figure BDA0002621298390000062
k is 0,1, …, N-1, N is the length of time series x (t);
step 6, determining the blade passing frequency f of the model tubular turbine runner 4pAmplitude A ofp，fp＝Zrn·fnWherein, in the step (A),
Figure BDA0002621298390000063
fpthe blade passing frequency of a model tubular turbine runner 4 is set; zrnThe number of the blades of the model through-flow turbine runner 4 is shown; f. ofnThe rotating frequency of the model tubular turbine runner 4 is set; n is the rotating speed of the model tubular turbine runner 4, the frequency signal obtained in the step 5 is drawn into a frequency signal graph, and then the frequency signal graph is obtained according to fpLooking up the corresponding amplitude A in the frequency signal diagramp；
And 7, repeating the steps 4-6 to acquire the vibration acceleration signals of the lower runner chamber 5 with different cavitation coefficients, which specifically comprises the following steps: continuously reducing the cavitation coefficient sigma of the model through-flow turbine, acquiring acceleration signals of the runner chamber vibration by adopting a laser vibration meter under different cavitation coefficients, sending the acceleration signals to a data acquisition system, and then sequentially repeating the steps 4 to 6 until obvious clearance cavitation phenomena appear on the blades of the through-flow turbine runner 4, namely observing that continuous bubbles appear on the blade top of the through-flow turbine runner 4;
step 8, determining a cavitation coefficient corresponding to blade gap cavitation primary generation of the model tubular turbine runner 4; first order piecewise function fitted by least square method
Figure BDA0002621298390000071
Fitting step 6 through model through-flow turbine runner blade passing frequency fpAmplitude A ofpWith the variation trend of the cavitation coefficient sigma, then seeking the minimum mean square difference value and Q to obtain the intersection point of the first-order piecewise function according to the principle of least square method fitting function
Figure BDA0002621298390000072
Namely the position of cavitation primary generation at the gap of the model through-flow turbine runner;
piecewise function of first order
Figure BDA0002621298390000073
The formula of (1) is as follows:
Figure BDA0002621298390000074
in the formula:
Figure BDA0002621298390000075
is a first order piecewise function;
Figure BDA0002621298390000076
is the intersection of the first-order piecewise functions; a and a' are linear piecewise functions
Figure BDA0002621298390000077
The coefficient of the primary term; b and b' are linear piecewise functions
Figure BDA0002621298390000078
A medium constant term;
assuming test measurement data in a piecewise linear function
Figure BDA0002621298390000079
Intersection point
Figure BDA00026212983900000710
When is separated, is preceded by n1Measured data, followed by N0-n1Measurement data, N0For the number of iterations performed in step 7, the minimum squared difference value and Q are given by the following equation:
Figure BDA00026212983900000711
wherein i represents the ith repeated test in the step 7, x is an abscissa value of a coordinate axis, namely a value of the cavitation coefficient sigma, and y is an ordinate value of the coordinate axis, namely a passing frequency f of the bladepAmplitude A ofpThe value of (a) is,
Figure BDA00026212983900000712
is a function representing a fitted linear piecewise
Figure BDA00026212983900000713
The fitting value of the i-th repeated test is the fitting amplitude ApThe value of (a) is,
Figure BDA0002621298390000081
representing fitted linear piecewise function
Figure BDA0002621298390000082
The value of the cavitation coefficient σ at the ith iteration;
the minima are obtained by partial derivative of Q:
Figure BDA0002621298390000083
Figure BDA0002621298390000084
wherein the minimum value Q corresponds to
Figure BDA0002621298390000085
The value is a piecewise linear function
Figure BDA0002621298390000086
The point of intersection of the model tubular turbine runner blade clearance cavitation primary position;
and 9, closing the model tubular turbine test system.
The invention relates to a method for detecting clearance cavitation inception of a through-flow turbine, which is characterized in that an acceleration signal of the vibration of a runner chamber of a model through-flow turbine is monitored, and the passing frequency f of the acceleration signal of the vibration of the runner chamber on a runner blade is utilizedpAmplitude A ofpDetermining whether the through-flow turbine runner blade occurs or not along with the variation trend of the cavitation coefficient sigmaAnd (4) cavitation in the gap. Before the occurrence of interstitial cavitation, fpAt an amplitude value ApSlowly increases with decreasing cavitation coefficient σ; at the beginning of interstitial cavitation, fpAt an amplitude value ApDecrease, local minima occur; with the development of cavitation, fpAt an amplitude value ApAnd the cavitation coefficient sigma is rapidly increased along with the continuous reduction of the cavitation coefficient sigma, so that the cavitation coefficient corresponding to the local minimum value is the cavitation initiation point.

Claims (8)

1. The utility model provides a detection method for through-flow turbine clearance cavitation inception, its characterized in that adopts through-flow turbine test system, including inlet tube (1) runner room (5), draft tube (6) that communicate in proper order, bulb body (2), activity stator (3) have set gradually according to the rivers direction in inlet tube (1), activity stator (3) are connected with runner (4), runner (4) are located runner room (5), the outside of runner room (5) is provided with laser vibrometer (7), laser vibrometer (7) are connected with data acquisition system (8) through the wire electricity, specifically implement according to following step:
step 1, starting a model tubular turbine test system, wherein water flow sequentially passes through a water inlet pipe (1), a bulb body (2), a movable guide vane (3), a rotating wheel (4) and a draft tube (6);
step 2, adjusting the operation condition of the model tubular turbine to enable the blades of the rotating wheel (4) to be in a non-clearance cavitation state;
step 3, keeping the running condition of the model tubular turbine stable, collecting the vibration acceleration signals of the runner chamber (5) by adopting a laser vibration meter (7), and sending the measured data to a data collection system (8) to obtain a time sequence after sampling the vibration acceleration signals of the runner chamber (5);
step 4, intercepting the time sequence obtained by sampling the acceleration signal of the vibration of the runner chamber (5) obtained in the step 3 to obtain the intercepted time sequence;
step 5, converting a time domain signal of the acceleration time sequence of the vibration of the runner chamber (5) into a frequency signal by using fast Fourier transform;
step 6, determining the blade passing frequency f of the model tubular turbine runner (4)pAmplitude A ofp；
Step 7, repeating the steps 4-6 to collect the vibration acceleration signals of the lower runner chamber (5) with different cavitation coefficients;
step 8, determining a cavitation coefficient corresponding to blade gap cavitation primary generation of the model tubular turbine runner (4);
and 9, closing the model tubular turbine test system.
2. The method for detecting cavitation inception of a tubular turbine as claimed in claim 1, wherein the time series obtained in step 4 after interception is: x (t) is a time sequence obtained by intercepting an acceleration signal of the vibration of the model turbine runner chamber (5); s (t) is a time sequence after sampling of an acceleration signal of the vibration of the runner chamber (5) of the model tubular turbine; w (t) is a window function, t being time.
3. The method for detecting the initial cavitation of the gap of the tubular turbine as recited in claim 2, wherein the frequency signals obtained in the step 5 are:
Figure FDA0002621298380000021
wherein the content of the first and second substances,
Figure FDA0002621298380000022
n is the length of the time series x (t).
4. The method for detecting cavitation inception of gap in tubular turbine as set forth in claim 3, wherein f in step 6 isp＝Zrn·fnWherein, in the step (A),
Figure FDA0002621298380000023
fpthe blade passing frequency of a model tubular turbine runner (4) is set; zrnThe number of the blades of the model through-flow turbine runner (4) is set; f. ofnThrough-flow turbine runner as model(4) The rotational frequency of (c); n is the rotating speed of the model tubular turbine runner (4), the frequency signal obtained in the step 5 is drawn into a frequency signal graph, and then the frequency signal graph is obtained according to fpLooking up the corresponding amplitude A in the frequency signal diagramp。
5. The method for detecting the initial cavitation of the gap of the tubular turbine as recited in claim 4, wherein the step 7 is specifically as follows: and (3) continuously reducing the cavitation coefficient sigma of the model through-flow turbine, adopting a laser vibration meter to collect acceleration signals of the runner chamber vibration under different cavitation coefficients, sending the acceleration signals to a data acquisition system, and then sequentially repeating the steps 4 to 6 until obvious clearance cavitation phenomena appear on the blade of the through-flow turbine runner (4), namely observing that continuous bubbles appear on the blade top of the through-flow turbine runner (4).
6. The method for detecting the initial cavitation of the gap of the tubular turbine as recited in claim 5, wherein the step 8 is specifically as follows: first order piecewise function fitted by least square method
Figure FDA00026212983800000314
Fitting step 6 through model through-flow turbine runner blade passing frequency fpAmplitude A ofpWith the variation trend of the cavitation coefficient sigma, then seeking the minimum mean square difference value and Q to obtain the intersection point of the first-order piecewise function according to the principle of least square method fitting function
Figure FDA00026212983800000313
Namely the position of cavitation primary generation at the gap of the model through-flow turbine runner.
7. The method of claim 6, wherein the linear piecewise function is used to measure clearance cavitation onset of a turbine
Figure FDA00026212983800000315
The formula of (1) is as follows:
Figure FDA0002621298380000031
in the formula:
Figure FDA0002621298380000032
is a first order piecewise function;
Figure FDA0002621298380000033
is the intersection of the first-order piecewise functions; a and a' are linear piecewise functions
Figure FDA0002621298380000034
The coefficient of the primary term; b and b' are linear piecewise functions
Figure FDA0002621298380000035
A medium constant term;
assuming test measurement data in a piecewise linear function
Figure FDA0002621298380000036
Intersection point
Figure FDA0002621298380000037
When is separated, is preceded by n1Measured data, followed by N0-n1Measurement data, N0For the number of iterations performed in step 7, the minimum squared difference value and Q are given by the following equation:
Figure FDA0002621298380000038
wherein i represents the ith repeated test in the step 7, x is an abscissa value of a coordinate axis, namely a value of the cavitation coefficient sigma, and y is an ordinate value of the coordinate axis, namely a passing frequency f of the bladepAmplitude A ofpThe value of (a) is,
Figure FDA0002621298380000039
is a function representing a fitted linear piecewise
Figure FDA00026212983800000310
The fitting value of the i-th repeated test is the fitting amplitude ApThe value of (a) is,
Figure FDA00026212983800000311
representing fitted linear piecewise function
Figure FDA00026212983800000312
The value of the spatio-temporal coefficient σ at the i-th iteration;
the minima are obtained by partial derivative of Q:
Figure FDA0002621298380000041
Figure FDA0002621298380000042
wherein the minimum value Q corresponds to
Figure FDA0002621298380000043
The value is a piecewise linear function
Figure FDA0002621298380000044
The point of intersection of the model tubular turbine runner blade clearance cavitation is the primary position.
8. The method for detecting the initial cavitation of the gap of the tubular turbine as recited in claim 1, characterized in that the horizontal distance L between the measuring point of the laser vibration meter (7) and the position corresponding to the runner chamber (5) is greater than 0.5 m.
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CN114091368A (en) * 2021-10-28 2022-02-25 西安理工大学 Method for identifying cavitation state of axial flow turbine
CN115370522A (en) * 2022-09-09 2022-11-22 中国长江电力股份有限公司 Test method for simulating real machine fault on model water turbine

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