CN106870248B - A kind of hydraulic turbine draft cone makes a call to the determination method of 4 hole sites - Google Patents
A kind of hydraulic turbine draft cone makes a call to the determination method of 4 hole sites Download PDFInfo
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- CN106870248B CN106870248B CN201710110917.0A CN201710110917A CN106870248B CN 106870248 B CN106870248 B CN 106870248B CN 201710110917 A CN201710110917 A CN 201710110917A CN 106870248 B CN106870248 B CN 106870248B
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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
-
- 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
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- 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
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Abstract
The invention proposes a kind of determination methods that hydraulic turbine draft cone makes a call to 4 hole sites, including carrying out numerical simulation calculation using method for numerical simulation, obtain draft cone low-pressure area range, tail water vortex rope detail section is observed using high-speed photography imaging system, determine the nascent place of vortex rope, implement punching measure according to the place that vortex rope is come into being, the punching measure is to make a call to 4 holes to draft cone, the draft cone for making a call to 4 holes is the draft cone along the draft cone axle center of short and straight type relative to perforation at 2 holes, again on the basis of the draft cone in 2 holes, in position relatively on the lower vertically to wearing 2 holes.The present invention solves the problems, such as vortex rope and relevant pressure pulsation problem in the UNSTEADY FLOW inside water turbine set in the prior art, especially draft tube.
Description
Technical field
The invention belongs to hydraulic turbine stability technical field, in particular to a kind of hydraulic turbine draft cone makes a call to 4 hole sites really
Determine method.
Background technique
In hydroelectric generation importance increasingly prominent today, hydroelectric station operation efficiency and hydraulic turbine operation stability are promoted
It is required that becoming especially prominent.In the factor for influencing the operation of hydraulic turbine internal stability, hydraulic factors are the most prominent, including rotary part
Stator-rotor interaction, the blade surface separation of flow, cavitation vortex tape and cavitation draft tube vortex rope between stationary parts etc..In the hydraulic turbine
In operation, these flow phenomenon majorities occur under the inclined operating condition for deviateing design conditions, can induce in corresponding flow field serious
Pressure fluctuation, pressure fluctuation and then dissemination cause vibration and the running noises of unit, even in water turbine units itself
Induce factory vibration.Pressure fluctuation is the main source for causing irregular operation and vibration noise.
Pressure fluctuation caused by three-dimensional flow field derives from many aspects, such as the runner entrance separation of flow, induction in the hydraulic turbine
Flow field will be propagated toward upstream and downstream both direction, cause the waterpower exciting of upstream components and components downstream；And inside runner, leaf road
Whirlpool is then the largest unstable source, and the generation of vortex tape is also frequently accompanied by cavitating flows, and caused pressure fluctuation will be straight herein
It connects on effect and runner, forms the vibration of high frequency；In components downstream, inside draft tube, cavitation vortex rope will be below draft cone
It generates, forms screw, these spiral vortex bands will periodically act on Taper Pipe section and ell section, and cause the vibration of components downstream
It is dynamic, and induce noise.Experiment shows that the running frequency of draft tube vortex rope is low-frequency vibration, caused under different flow operating modes
Vibration and noise are different, but in general, and the movement of tail water vortex rope is the movement of lowest frequency, because influencing caused by unit also most
Seriously.If the power station Yan Tan and the power station Li Jiaxia are within unit operation half a year with the time to 2 years, several water turbine units
Occurs the cracking of weld seam and blade and lower interannular weld seam between runner bucket and crown in succession.By dividing runner crackle reason
Analysis, discovery mainly manufacture and the reason of operation aspects, and intense pressure pulsations when operation are the direct factors for causing crackle.
In Francis turbine, draft tube vortex rope induce pressure fluctuation be cause vibration and noise it is main come
Source has had numerous researchs to carry out mechanism and develop to analyze to draft tube vortex rope at present, and has proposed and reduce or eliminate tail
The measure of water pipe vortex rope, as change the water flow movement state in draft tube, control vortex rope eccentricity, introduce appropriate damping or
The Hydraulic Design of runner is improved, however these measures can not effectively weaken pressure fluctuation, some can bring additional make an uproar instead
Sound.
Summary of the invention
The purpose of the present invention is to overcome the shortcomings of the existing technology with it is insufficient, a kind of hydraulic turbine draft cone is provided and makes a call to 4 hole locations
The determination method set solves the problems, such as vortex rope and relevant pressure arteries and veins in the UNSTEADY FLOW inside water turbine set, especially draft tube
Dynamic problem.
The purpose of the present invention is achieved through the following technical solutions: a kind of hydraulic turbine draft cone makes a call to the determination method of 4 hole sites,
Step 1 carries out numerical simulation calculation using method for numerical simulation, obtains draft cone low-pressure area range；
Step 2 is observed tail water vortex rope detail section using high-speed photography imaging system, determines the nascent ground of vortex rope
Side；
Step 3 implements punching measure according to the place that vortex rope is come into being, and the punching measure is to make a call to 4 holes to draft cone, described
The draft cone for making a call to 4 holes is draft cone along the draft cone axle center of short and straight type relative to perforation at 2 holes, then the draft cone in 2 holes
On the basis of, in position relatively on the lower vertically to wearing 2 holes.
Further, the numerical simulation calculation specifically: use unit speed n11With specific discharge Q11To describe to flow entirely
Flow operating mode in road changes the ambient pressure level in test by regulating device cavitation coefficient, cavitation factor, Toma coefficient σ, is opened by adjusting movable guide vane
It spends a and changes unit speed and specific discharge；
Unit speed n11Is defined as:
D in formula1--- the runner diameter of model turbine, unit m；
H --- model turbine tests head, unit m；
N --- the runner revolving speed in model turbine, unit r/min；
Specific discharge Q11Is defined as:
Q in formula --- overcurrent flow in model francis turbine runner, unit m3/s；
Plant cavitation coefficient σ is defined as:
H in formulava--- the vacuum values in model experiment circulation loop in tail tank, unit m；
Ha--- the head that local atmospheric pressure is converted into experiment, unit m；
Hs--- the draught-height of the hydraulic turbine in experiment, unit m；
Hv--- the head that the saturated vapor pressure under experimental temperature is converted into, unit m；
Calculate the inclined operating point parameter of small flow of numerical simulation are as follows: a=16mm, n11=80.4r/min, Q11=
0.486m3/ s, σ=0.258；
The pressure distribution that draft cone and tail water tube portion are determined according to the small inclined operating condition of flow, so that it is determined that low-pressure area model
It encloses.
Further, vortex rope twist vortex rope under the inclined operating condition of small flow.
Detailed description of the invention
Fig. 1 is waterpower test experimental bed schematic diagram；
Fig. 2 is tachometric survey schematic diagram；
Fig. 3 is pressure fluctuation measuring point schematic diagram；
Fig. 4 is model runner (A1293) pictorial diagram；
Fig. 5 is that 0 hole (b) of draft cone (a) prototype of various configuration makes a call to 2 holes (c) and makes a call to 4 holes；
Fig. 6 be hydroturbine calculation geometrical model (a) prototype draft cone (b) make a call to 2 hole draft cones (c) make a call to 4 hole draft cones -0 degree
View (d) plays 4 hole draft cones -90 degree view；
Fig. 7 is that pressure in draft tube is distributed top view (0 hole of prototype, a=16mm, σ=0.258, n under inclined operating condition11=80.4r/
min)；
Fig. 8 is (0 hole of prototype, the a=16mm, σ=0.258, n of draft cone surface pressure distribution under inclined operating condition11=80.4r/
min)；
Fig. 9 is that pressure in draft tube distribution top view (makes a call to 2 holes, a=16mm, σ=0.258, n under inclined operating condition11=80.4r/
min)；
Figure 10 is that draft cone surface pressure distribution (makes a call to 2 holes, a=16mm, σ=0.258, n under inclined operating condition11=80.4r/
min)；
Figure 11 is that pressure in draft tube distribution top view (makes a call to 4 holes, a=16mm, σ=0.258, n under inclined operating condition11=80.4r/
min)；
Figure 12 is that draft cone surface pressure distribution (makes a call to 4 holes, a=16mm, σ=0.258, n under inclined operating condition11=80.4r/
min)；
Figure 13 is that pressure in draft tube is distributed top view (0 hole of prototype, a=28mm, σ=0.277, n under big flow operating condition11=
83.2r/min)；
Figure 14 is prototype draft cone draft tube vortex rope (0 hole of prototype, a=28mm, σ=0.277, n under big flow operating condition11=
83.2r/min)；
Figure 15 is (0 hole of prototype, the a=28mm, σ=0.277, n of draft cone surface pressure distribution under big flow operating condition11=
83.2r/min)；
Figure 16 is that pressure in draft tube distribution top view (makes a call to 2 holes, a=28mm, σ=0.277, n under big flow operating condition11=
83.2r/min)；
Figure 17 is that draft cone surface pressure distribution (makes a call to 2 holes, a=28mm, σ=0.277, n under big flow operating condition11=
83.2r/min)；
Figure 18 is that pressure in draft tube distribution top view (makes a call to 4 holes, a=28mm, σ=0.277, n under big flow operating condition11=
83.2r/min)；
Figure 19 is that draft cone surface pressure distribution (makes a call to 4 holes, a=28mm, σ=0.277, n under big flow operating condition11=
83.2r/min)；
Figure 20 is punching draft cone draft tube vortex rope (a=28mm, σ=0.277, n under big flow operating condition11=83.2r/
min)；
Figure 21 be under inclined operating condition pressure in draft tube pulsating energy amount distribution (0 hole of prototype makes a call to 2 holes, makes a call to 4 holes, a=16mm, σ=
0.258, n11=80.4r/min).
Specific embodiment
Technical solution in the embodiment of the present invention that following will be combined with the drawings in the embodiments of the present invention carries out clear, complete
Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
Embodiment in invention, every other reality obtained by those of ordinary skill in the art without making creative efforts
Example is applied, shall fall within the protection scope of the present invention.
The present invention provides a kind of determination method that hydraulic turbine draft cone makes a call to 4 hole sites,
Step 1 carries out numerical simulation calculation using method for numerical simulation, obtains draft cone low-pressure area range；
Step 2 is observed tail water vortex rope detail section using high-speed photography imaging system, determines the nascent ground of vortex rope
Side；
Step 3 implements punching measure according to the place that vortex rope is come into being, and the punching measure is to make a call to 4 holes to draft cone, described
The draft cone for making a call to 4 holes is draft cone along the draft cone axle center of short and straight type relative to perforation at 2 holes, then the draft cone in 2 holes
On the basis of, in position relatively on the lower vertically to wearing 2 holes.
The numerical simulation calculation specifically: use unit speed n11With specific discharge Q11To describe flowing in full runner
Operating condition changes the ambient pressure level in test by regulating device cavitation coefficient, cavitation factor, Toma coefficient σ, is changed by adjusting movable guide vane aperture a
Unit speed and specific discharge；
Unit speed n11Is defined as:
D in formula1--- the runner diameter of model turbine, unit m；
H --- model turbine tests head, unit m；
N --- the runner revolving speed in model turbine, unit r/min；
Specific discharge Q11Is defined as:
Q in formula --- overcurrent flow in model francis turbine runner, unit m3/s；
Plant cavitation coefficient σ is defined as:
H in formulava--- the vacuum values in model experiment circulation loop in tail tank, unit m；
Ha--- the head that local atmospheric pressure is converted into experiment, unit m；
Hs--- the draught-height of the hydraulic turbine in experiment, unit m；
Hv--- the head that the saturated vapor pressure under experimental temperature is converted into, unit m；
Calculate the inclined operating point parameter of small flow of numerical simulation are as follows: a=16mm, n11=80.4r/min, Q11=
0.486m3/ s, σ=0.258；
The pressure distribution that draft cone and tail water tube portion are determined according to the small inclined operating condition of flow, so that it is determined that low-pressure area model
It encloses.
Vortex rope twist vortex rope under the inclined operating condition of small flow.
Hydraulic turbine draft cone model experiment
Model experiment is to study the important method of flow behavior in the hydraulic turbine.In order to obtain the stream under the conditions of different draft cones
Field information and draft tube vortex rope information have carried out experiment measurement using model test of hydraulic turbine platform.
Rig for model test is located at Research Institute of Large Electrical Machinery hydraulic turbine research department, Harbin Electric Machine Co., Ltd., is one
High parameter, high-precision hydraulic machinery test stand can carry out pump turbine, large pump and Francis Turbine with High Rated Head
Correlation test.
The waterpower experimental apparatus for testing number test 6, test capability, the size of installable model, hydraulic performance
Test method and test water meet the requirement of IEC60193-1999.Content of the test specifically includes that the energy examination of the hydraulic turbine
Test, the test of cavitation test, runaway speed, pressure fluctuation test, differential pressure flow measurement test, axial force test, guide vane Hydraulic Moment test,
Tonifying Qi test, abnormal low water head test etc., in addition, the fluidised form observation system of testing stand equipment can be to the inside stream of hydraulic
State is observed.
As shown in Figure 1, being waterpower test experimental bed critical component schematic diagram.This is equipped with high performance kinetic pump, stands
Formula structure dynamometer motor, high voltage bearing stainless steel pipe-line system, electrically operated valve, vacuum pump, high-precision test equipment and its original
Position calibration system etc..The high-precision electric control system of testing stand carries out the power-equipments such as water supply pump and dynamometer motor quick
Control is adjusted with high-precision.The high-precision test equipment of testing stand equipment measures every test parameters.It is high performance
Data collection and precessing system is acquired and handles to data.
The main structure member of testing stand is as shown in table 1.
1 testing stand main structural components of table
Above equipment is done as described below:
Test speed: the revolving speed of experimental rig is realized by dynamometer motor, dynamometer motor silicon controlled rectification power source
Power supply, can do four quadrant running, i.e., in forward and reverse rotation, can do generator operation and can do motor running, therefore it
Can satisfy the hydraulic turbine, water pump, pump-turbine different tests device various operating condition of test requirement.
Test head and flow: highest test head is 100m, maximum stream flow 1.0m3/s。
Test water: the efficient water treatment facilities of testing stand equipment are filtered tap water, use after sofening treatment
In test.This four tests of the density of water, the viscosity of water, the gas content in water and steam pressure are primarily upon in test to use
The condition of water.
The measurement of atmospheric pressure: the atmospheric pressure of testing stand is measured using barometric pressure sensor, the atmospheric pressure
Measurement module every year in Heilongjiang Province, examined and determine by Weights and Measures Bureau, and calibration certificate is issued after assay approval.
The speed measuring system of hydraulic machinery test stand is made of the ruler disk that tests the speed that velocity sensor and the number of teeth are 120.
Speed probe is the MP-981 type speed probe of little Ye company, Japan production.The ruler disk that tests the speed is mounted on hydraulic turbine arbor
The relative position in portion, speed probe and the ruler disk that tests the speed is as shown in Figure 2.The speed measuring system can measure 10000r/min's
Revolving speed.The electric impulse signal that velocity-measuring system generates is directly entered data collection system and data processing software is calculated.
On this waterpower test experimental bed, will also carry out runner in the fluidised form of vortex tape and draft tube observation, this mainly by
High-speed photography imaging system is completed.
Fluidised form observation system is by the stroboscope of German DRELLO company, the fibre optic endoscopes of WOLF company, Germany, number
Word industrial camera, synchronous trigger controller and image acquisition and processing work station are constituted, and can carry out real-time fluidised form observation, still image
Acquisition and dynamic files in stream media generate.It, can be existing to runner bucket front, the back side separation of flow and vortex tape cavitation by the system
As being observed.
In addition, by the transparent Taper Pipe at model test apparatus, it can be to the outlet edge of runner using fluidised form observation system
The cavitation phenomenons such as karman vortex, cavitation inception, vortex rope are observed.The high-speed camera produced simultaneously using Olympus company into
The high-frequency information of row vortex rope captures.
The specification of fibre optic endoscopes is as follows: German WOLF company production, size φ 10mm × 300mm × DOV50/
80/90 °, multi-angle of view probe, diameter 10mm, the fixed optical cable of active length 300mm, 4m.
High-speed photography specification of equipment is as follows: Japanese Olympus company production, model i-SPEED 2, cmos sensor, point
800 × 600 valid pixel of resolution, frame rate reach as high as 33000fps, minimum 1fps, highest 1000fps under full resolution, fastly
Door 5 microsecond of speed.Camera external controller display device connects device using standard LVDS, and 26 needle MDR are connected with photographic equipment
It connects.
In order to which the hydraulic stability to model hydraulic is assessed, pressure fluctuation test is usually carried out, carries out pressure
Pulsation test is primarily to obtaining the pressure fluctuation relative magnitude and dominant frequency within the scope of specific run and determining reduction pressure
The optimal tonifying Qi mode of pulsation.
Pressure fluctuation is often used pressure pulsation sensor to measure.The installation requirement diaphragm of pressure pulsation sensor with
Runner is concordant.As shown in figure 3, being mixed-flow, axial fixed blade propeller water turbine formula and the general installation site of pump turbine.Thoroughly do away with IEC test mark
Standard, the position of 4 pressure-measuring-points is as follows at draft tube, and P1 is located at draft tube cone downstream side, and P2 is located at draft tube cone upstream
Side, P3 are located at spiral case inlet, and the sensor that P4 separately increases is located at Taper Pipe and ell, survey in addition, P5 is arranged between guide vane and runner
Point.
The 112A22 type dynamic pressure transducer that the measurement of pressure fluctuation is produced using U.S. PCB company, the sensor
Sensitivity 15mv/kPa, resolution ratio are less than 0.007kPa, frequency range 0.5-250kHz, and covering test machines can reach
Maximum overcurrent frequency, hydraulic pulse can quickly and accurately be responded.Testing stand high-speed data acquistion system is adopted with height
Sample rate is acquired the response signal of pressure pulsation sensor, and usual sample frequency is 4000Hz.
The 903BO2 type dynamic pressure marking apparatus (essence that pressure pulsation sensor uses PCB company, the U.S. to produce before and after the test
Degree ± 0.2%FS) it is demarcated.
This waterpower test experimental bed, based on certain power station model turbine, hydraulic turbine maximum head 71m, minimum head
44m, rated head 57m.Model turbine runner (A1293) as shown in figure 4, the parameter of model runner and other important devices such as
Shown in table 2.
2 model runner major parameter of table
In order to carry out flow measurement to various forms of draft cones, the draft cone various configuration in test, packet is given below
The case where including 0 hole of prototype, making a call to 2 holes and make a call to 4 hole, as shown in Figure 5.
In model experiment, unit speed n is generallyd use11With specific discharge Q11Flow operating mode in full runner described, and if
Change the ambient pressure level in test, then needs regulating device cavitation coefficient, cavitation factor, Toma coefficient σ.Changed by adjusting movable guide vane aperture a
Unit speed and specific discharge.
Unit speed n11Is defined as:
D in formula1--- the runner diameter (low-pressure side) (m) of model turbine；
H --- model turbine tests head (m)；
N --- the runner revolving speed (r/min) in model turbine.
Specific discharge Q11Is defined as:
Q in formula --- overcurrent flow (m in model francis turbine runner3/s)。
For model measurement, plant cavitation coefficient has great influence for internal flow phenomenon.According to international electricity
- 60193 standard of work committee regulation, plant cavitation coefficient σ is defined as:
H in formulava--- the vacuum values (m) in model experiment circulation loop in tail tank；
Ha--- the head (m) that local atmospheric pressure is converted into experiment；
Hs--- the draught-height (m) of the hydraulic turbine in experiment；
Hv--- the head (m) that the saturated vapor pressure under experimental temperature is converted into.
According to being discussed above, using n11And Q11Carry out the operation operating condition of descriptive model experiment, as shown in table 3.These operating conditions
In, including small guide vane operating condition and big aperture operating condition, it can observe the tail water vortex rope of different shape, such as the helical vortex under small guide vane
Band, the column vortex rope under big aperture.
Table 3 tests measurement condition point parameter
Hydraulic turbine whole flow field three-dimensional simulation method
Geometric Modeling
In calculating, the full runner simulation of the hydraulic turbine has been used, and for the ease of numerical value calculating, has increased entering into spiral case
Mouth section part, import is round entrance, is exported as elbow of draft tube outlet.
Zoning is based on overall geometry model, it comprises volute inlet section, spiral case, fixed guide vane, movable guide vane, turns
7 parts such as wheel, draft tube and ell.
For this calculating, main Geometrical change component is draft cone, and Fig. 6 gives experimental study and numerically modeling
Used in different shaping draft cone, including do not punch prototype draft cone, make a call to 2 hole draft cones and make a call to 4 hole draft cones.
Above-mentioned prototype draft cone is the draft cone of short and straight type, and the draft cone for making a call to 2 holes is the structure of opposite perforation along axle center
Type, the draft cone for making a call to 4 holes construct on the basis of making a call to 2 hole, in position relatively on the lower vertically to wearing 2 holes.
Grid setting
In order to preferably adapt to flow complicated 3D Flow Field Calculation in the full runner of the hydraulic turbine, to each portion of above-mentioned geometric configuration
Part has carried out grid dividing respectively, and the grid of different components is attached in calculating using interface, corresponding grid letter
Breath is as shown in table 4.
Each component gridding information of the full runner of table 4
Flowing domain to calculate grid is that structured grid and unstructured grid mix, under 7,000,000 quantity grids, Ke Yiman
The demand that sufficient numerical value calculates.
Numerical method
For full fluid flow on channel numerical simulation, this research is calculated using commercial CFD software ANSYS, is solved using CFX
Device is solved.CFX is the limited bulk discrete method based on finite element, uses 24 point interpolations to hexahedral mesh unit, and
Simple finite volume method is only with 6 point interpolations.It is calculated using multi-node parallel, difference scheme uses higher-order forms.
Calculating convergence criterion is residual error 10-5, Steady Flow calculating is first carried out, then using Steady Flow result as initial fields, into
Row Unsteady flow computation.Since component each in full runner is using the method for constructing grid respectively, so on sound interface
It needs to transmit using data, i.e., between movable guide vane and runner basin, uses Frozen between runner and draft tube basin
And Rotor series interface combines.In addition, being described in the processing of flow field wall area using Wall-function.
Boundary condition setting
It is arranged according to the operating condition of model experiment, numerical simulation takes identical calculating operating condition.
Given runner low-pressure side diameter D1After model experiment head H, the unit speed n that is provided according to experiment condition11、
Movable guide vane aperture a can obtain specific discharge Q by combined characteristic at this time11.Therefore from n11And Q11It sets out, has:
Actual speed:
Actual flow:
If the cross-sectional area at spiral case inlet is S, inlet velocity are as follows:
V=Q/S (6)
In addition, needing to be arranged draft tube outlet pressure in numerical simulation according to plant cavitation coefficient σ calculating formula above.
According to above content, the boundary condition in numerical value calculating is provided that
Entrance: using volute inlet extension as entrance, using mass flow condition for import, at the same be arranged reference pressure, just
The parameters such as beginning turbulence intensity.
Outlet: being flowing outlet with ell outlet, and using pressure export condition, which is provided by above-mentioned cavitation conditions,
It is provided with absolute pressure numerical value.
Wall surface: all solid wall surfaces are all made of no slip boundary condition, and near wall region flowing carries out mould using Wall-function
It is quasi-.
Governing equation
Consider that the flowing in the full runner of the hydraulic turbine is incompressible Three-dimensional Flow, and ignore the energy exchange with the external world, then
Governing equation includes continuity equation and the equation of momentum.
Continuity equation (when incompressible, density p does not change with space at any time):
The equation of momentum:
When solving the full runner Three-dimensional Flow of the hydraulic turbine, average flow field calculation is carried out using Reynolds average method (RANS), and
Corresponding turbulence model is set to carry out eddy stress closing.In the present invention, closing turbulence model uses k- ω SST (stress shearing mould
Type) model, which is got up standard k-ε model and k- ω models coupling using mixed function, is contained and is turned to twist and shear choosing
?.The model equation of k- ω SST is as follows.
K equation:
ω equation:
Wherein, G, Г and Y respectively indicate respective generating item, effective diffusion term and dissipative term, and D indicates orthogonal diverging item, S
For the customized source item of user.
In addition, the model and standard k- ω model are the difference is that α∞Value, the parameter in standard k- ω model
For constant, and in k- ω SST model, α∞It is defined as follows:
α∞=F1α∞,1+(1-F1)α∞,2 (11)
Wherein have:
The cross-diffusion of k- ω SST model combination in ω equation, and turbulent viscosity considers turbulent flow and cuts and answers
The propagation of power.The advantage is that has preferable processing near wall region and main flow area, and model is without complicated nonlinear dampling
Function, thus it is more stable and accurate.
In order to analyze the influence and corresponding Pressure Fluctuation in Draft Tube information that full runner flow field flows draft tube, herein
4 pressure-measuring-points that -60193 standard of International Electrotechnical Commission has chosen draft tube region are analyzed, i.e., below Taper Pipe away from
From outlet of rotary wheel side 0.3D2Measuring point (Taper Pipe+the Y0.3D of left and right 2 at place2、-Y0.3D2) and draft tube and ell junction a left side
Right 2 measuring points (on the inside of ell, on the outside of ell).Pressure fluctuation measuring point having the same in model measurement and numerical simulation.
In the pressure fluctuation experiment of model measurement, collected measuring system is only voltage change signal, passes through voltage
Calibration and conversion after obtain pressure signal value.And in numerical value calculating, by the simulation in flow field, flow field letter will be directly obtained
Velocity fluctuation and pressure fluctuation signal value in breath, the pressure fluctuation acted on wall surface will be carried out directly with model experiment results
Compare.
In order to analyze the pressure fluctuation in time domain, need to obtain the amplitude information and frequency information of pressure fluctuation,
Simultaneously in order to do dimensionless processing to frequency, frequency multiplication f ' is defined, frequency multiplication f ' can be obtained by given frequency f divided by frequency is turned.From
Time-domain information is transformed into frequency domain information, needs by Fourier transformation:
Formula also becomes Fourier's direct transform above, can get the pulsation energy under each frequency of pressure fluctuation signal in this way
Information.
At certain frequency f, the amplitude of pressure fluctuation A calculating for decompositing signal is as follows:
R is the real part of frequency-domain function in formula, and I is imaginary part, and n is sampling number.
Since the geometry spacing between entrance edge of blade and movable guide vane is very close, the interference of the two high fdrequency component generation
By the raising for causing high frequency pressure pulsations amplitude, the interference effect can be such that pressure fluctuation is further magnified, and lead to operation stability
It is deteriorated.
Finally, the amplitude under each frequency is drawn on frequency domain axis, the frequency domain variation diagram of pressure fluctuation signal has just been obtained
Spectrum.
Hydraulic turbine flow field numerical value calculates
According to model experiment introduction, the present invention calculates the flow field under inclined operating condition, chooses two differences under aperture
Flow operating mode, specific duty parameter are as shown in table 5.
5 numerical value of table calculates operating point parameter
In above-mentioned operating condition, calculated for 3 kinds of different draft cone configurations, i.e. the geometry in 0 hole of prototype, 2 holes and 4 holes
Shape.It is pointed out that guide vane opening a=16mm close to optimal aperture line 17mm, unit speed n11=80.4r/min also connects
The unit speed value 74.5r/min of nearly optimum operating condition；Guide vane opening 28mm is close to power limit line, the measurement condition unit speed
Also higher, it is 83.2r/min.Therefore the 1st operating condition is the inclined operating condition of small flow, the 2nd operating condition is the inclined operating condition of big flow.
It is more smooth for the flowing inside runner about the runner flow field information under the conditions of low flow rate condition, but in leaf
There is streamline inflection in the inlet of piece suction surface, it is meant that flowing flow back, reflux generally mean that vortex appearance and
The presence of low-pressure area, so in this case, the cavitation band being easy to appear in impeller clearance, the i.e. presence of vortex tape.
In order to further illustrate the flow field situation in runner, from axial flow direction, three horizontal cross-sections are chosen to mention
Velocity field is taken, there is certain flow starts back in the entrance of blade suction surface, and back-flow velocity is larger, but impeller clearance
Downstream, flowing is more smooth and more uniform, and flowing circumferentially is gentle.Meanwhile when close to outlet edge, flowing velocity has become
Very little, because herein close to draft cone, therefore be the nascent place of vortex rope.
The small inclined operating condition lower tail water flow field comparative analysis of flow
Vortex rope in experiment under inclined operating condition occurs vibrating and coming into being change in location, first provides used here as method for numerical simulation
Pressure lowermost extent near draft cone.For the position punched in guiding experiment, inclined operating condition lower tail water pipe sections are provided first
Pressure distribution.In inclined operating condition (a=16mm, σ=0.258, n11=80.4r/min) under, Fig. 7 gives 0 hole draft cone of prototype
Draft tube partial pressure top view.
From figure 7 it can be seen that the pressure partially under operating condition in draft cone and draft tube partial cross sectional be distributed it is asymmetric, it is circumferential
Pressure distribution somewhere has minimum value.The pressure distribution on one week its surface of draft cone is provided separately below, such as Fig. 8 institute
Show.
From figure 8, it is seen that asymmetry also occurs in the pressure distribution of draft cone and draft tube partially circumferentially, draft cone is by going out
Oral area divides there are pressure minimum point, after the pressure is lower than local local pressure, that is, vortex rope occurs., it was also found that it should in experiment
Place is the place for generating vortex rope, but under the operating condition, the phenomenon that vortex rope moves up and down also occurs.In order to eliminate the phenomenon, in whirlpool
The nascent place of band, implements punching measure, it is therefore an objective to will balance the inside and outside water flow pressure of draft cone, utilize flow equilibrium shadow
Pressure distribution is rung, and then vortex rope position is further moved down, and reduces vortex rope up and down motion, while reducing its caused pressure arteries and veins
It is dynamic.
Fig. 9 further provides inclined operating condition and makes a call to tail water flow field plane pressure distribution top view under the conditions of 2 holes.Figure 10 is further
It provides draft cone surface pressure distribution under inclined operating condition and (makes a call to 2 holes, a=16mm, σ=0.258, n11=80.4r/min), it should be noted that
, the pressure that Fig. 9 and Figure 10 are provided is distributed threshold value and Fig. 7 and Fig. 8 is consistent.As can be seen that after punching, draft cone
It is obviously improved with draft tube partial interior pressure.And the difference of the maxima and minima of pressure distribution becomes smaller.
In Figure 10, draft cone surface pressure distribution on circumferencial direction is given.As can be seen that the stress level around punching
Also there is promotion.Meanwhile comparing and two arranging the pressure size difference schemed can be seen that around the punching on relative position up and down, this is
Since tail water vortex rope is the reason generated from side.
Predictably, after pressure distribution improvement near draft cone, the form of tail water vortex rope should also become
Change, while its pressure fluctuation will also change.
Continue with the distribution of tail water partial pressure and the draft cone surface pressure distribution provided in the case of making a call to 4 holes.
Figure 11 is tail water partial pressure distribution when making a call to 4 hole.As can be seen that making a call under the conditions of 4 holes, pressure in draft tube is distributed water
It is flat further to be promoted, while the difference of the maxima and minima of pressure also becomes smaller.The pressure distribution of same sluicing poppet surface
As shown in figure 12, the stress level for punching surrounding has promotion.As it can be seen that punching under inclined working condition for stress level
Promotion plays positive effect, and the gradient of pressure distribution is also slowed down.
The punching measure of influence in order to further illustrate to(for) flowing, is given below the vortex rope situation of change under inclined operating condition:
When vortex rope shape extracts, identical vorticity criterion is used under three kinds of configurations, using identical cavitation pressure
Determine void volume score.Compare three kinds of situations and can be seen that firstly, with punching measure implementation, leaf road inside runner
Whirlpool gradually decreases, and void volume becomes smaller, and vortex structure becomes fine crushing；Secondly, the whirlpool from draft cone region, below draft cone
The nascent region of band, cavitation whirlpool volume are obviously reduced.The reduction of cavitation site, facilitate reduce vortex rope itself oscillation and
Bounce has positive effect for reducing pressure fluctuation.
Vortex rope after above-mentioned punching induces pressure fluctuation level, can provide, can obtain in subsequent pressure fluctuation calculating
To the pressure fluctuation obviously weakened.
Big flow optimum operating condition lower tail water flow field comparative analysis
Under the inclined working condition of small flow, it can be seen that punching measure substantially reduces stress level, this is given below and arranges
Apply the performance under big flow operating condition.Optimum operating condition is farther out in the operating condition, however it remains vortex rope, only different shapes is presented in vortex rope
State.
In the inclined operating condition of big flow (a=28mm, σ=0.277, n11=83.2r/min) under, Figure 13 gives 0 hole of prototype and lets out
Water cone draft tube partial pressure top view.As can be seen that the pressure distribution of draft cone and draft tube partially circumferentially has well
Symmetry, low-pressure area are located at draft cone peripheral part, this part is the nascent place of vortex rope.
Figure 14 gives the vortex rope point shape under the operating condition, shows column vortex rope.In turn, the pressure of sluicing poppet surface point
Cloth is presented in Fig. 15, and is upwarded pressure distribution including one week 4 side of draft cone.As can be seen that in one Zhou Fang of draft cone
Upwards, low-pressure area is present in the place of draft cone outlet, and here, pressure is lower than after local pressure for vaporization, will generate cavitation
Vortex rope.This and pressure distribution are consistent.
Nearly optimum operating condition is given below and makes pressure in draft tube distribution and draft cone surface pressing score under the conditions of 2 hole draft cones
Cloth.As shown in FIG. 16 and 17, although the pressure distribution of draft cone outlet changes, but still it is symmetrical, and its stress level
It is promoted.Identical trend can also observe under the conditions of making a call to the draft cone in 4 holes, as shown in Figure 18 and Figure 19.
Although above-mentioned pressure distribution is similar, with the implementation of punching measure, stress level has promotion, this will affect the work
The vortex rope shape of condition.Figure 20 has given under nearly optimum operating condition, makes a call to 2 holes and plays the draft cone vortex rope distribution in 4 holes.
In the case of above two draft cone, the straight vortex rope of elongated column is presented in tail water cavitation, and cavitation band is smaller.And with
It punches number to increase, cavitation band becomes smaller, this is the vortex rope variation basic condition under big flow operating condition.Simultaneously it can also be seen that punching
Later, the cavitation whirlpool distribution at outlet of rotary wheel is obviously reduced, and is only a small amount of concentrate on around draft cone outlet.This should be by
The flow regime of vortex rope is changed in punching measure.
Under the above conditions, there are still stronger cyclone structures in draft tube, but vortex rope form is relatively stable, also has one
Fixed pressure fluctuation.
Pressure fluctuation calculated result under inclined operating condition
Under big flow operating condition, unit generally operates in that the chance at this is smaller or runing time is shorter.It is primarily upon below
Pressure fluctuation under the small inclined operating condition of flow.
When pressure fluctuation calculates, the stable state Three-dimensional simulation under the operating condition is carried out first, and waiting flows into sufficiently
State of development and then the numerical simulation for carrying out transient state with every 1 ° of the rotation of runner for material calculation, while monitoring pressure fluctuation water
It is flat.
The inclined operating condition of small flow (a=16mm, σ=0.258, n is given below11=80.4r/min) lower three kinds of draft cone configurations
Under pressure fluctuation as a result, for 4 measuring points result it is as shown in figure 21, pressure fluctuation used Fourier variation carry out
Frequency domain converts, and corresponding energy density function (PSD) distribution under each frequency is provided in figure.
As can be seen from Figure 21, under inclined operating condition, the pressure fluctuation level on the right side of Taper Pipe is minimum, and on the left of Taper Pipe, ell
The horizontal equal highest of pressure fluctuation on the outside of inside and ell.After implementing punching measure, with the increase of punching quantity, pressure arteries and veins
Dynamic energy is gradually reduced, this is consistent with the development trend of pressure distribution and vortex rope in flow field.
In addition, the pressure fluctuation energy on the inside of ell and on the outside of ell declines the most obvious, energy as punching quantity increases
Enough drop to 1/2 or so of original level.This illustrates that punching measure really plays a significant role the inhibition of pressure fluctuation.
Finally, it can be seen that the Energy distribution on the outside of ell also occurs compared with multi -components at upper frequency, although this illustrates
At dominant frequency, pressure fluctuation occupies most energy, but still has very important contribution at upper frequency.It is available,
If being superimposed all pressure fluctuation energy, then the pressure fluctuation energy in ell outside is highest in 4 measuring points, this
Experiment measurement with back is consistent.But since the population value of pressure fluctuation energy is decline, unit after punching
Noise when operation will be substantially reduced, and also having obtained experiment confirms.
Turbine draft tube flow field experimental study
The inclined operating condition of small flow is mainly selected in experiment, has carried out energy and efficiency experiment first.
The energy and efficiency experiment parameter of the different draft cone configurations of table 6
As shown in table 6, under inclined operating condition operation, turn frequency about 18.6Hz, the dominant frequency of tail water vortex rope is 0.242 relative to frequency is turned
Times, this is almost the same under three kinds of draft cone configurations.Efficiency is derived according to energy, it is known that whole efficiency changes after punching
Very little only has a little reduction when making a call to 2 hole, and is increased instead making a call to 4 holes.Variation and the pressure fluctuation variation of efficiency should have
Relationship, pulsation energy reduce, and energy loss then reduces, and efficiency is then promoted.
As can be seen that punching measure will not influence the overall operation efficiency of unit substantially, therefore very little is influenced on Energy Test.
It may be speculated that punching measure only will affect the downstream part flow field in full runner, it will make the speed arteries and veins in draft tube flow field
Dynamic and pressure fluctuation reduces, and such noise also accordingly reduces.Therefore it is a kind of effective measures of Local application cavitation optimization.
Experimental analysis will be carried out to draft tube flow field below.Laboratory facilities are model experiment, in transparent tail water tube portion, are adopted
Flowing and the shooting of vortex rope are carried out with the method for high-speed photography, prototype draft cone draft tube vortex rope evolution timing is observed.
Under above-mentioned operating condition, cavitation vortex rope runs one week about 216ms, it is known that tail water vortex rope frequency is about 4.5Hz.
Helical form is presented in vortex rope under the operating condition, revolves around draft cone center.Examining vortex rope operation timing can
To find out, the vortex rope in 36ms, 96ms and 108ms has 2 to 3 bursts of thinner vortex rope to overlap, and its around itself
Helical center is also in rotation.Also, also there is the phenomenon that moving up and down along sluicing poppet surface in the initial position of vortex rope.
A plurality of thin vortex rope generates the related of the position that come into being with vortex rope at draft cone, has low on sluicing poppet surface
Nip zone is larger, then is easy to appear many places cavitation inception region.And numerical simulation also indicates that, 0 hole of prototype is let out under the operating condition
Water cone surface bottom portion has many places vortex rope to come into being point, it is seen then that numerical simulation result and experiment meet preferably.
In addition, can reasonably speculate has: the public affairs of vortex rope if considering contribution of the cavitation vortex rope for pressure fluctuation energy
Turn to contribute to the dominant frequency of pressure fluctuation, and itself rotation around helical center then contributes to the higher-frequency energy of pressure fluctuation.
High fdrequency component of the Francis turbine without the pressure fluctuation of leaf area is unobvious, and the ratio that amplitude accounts for mixing amplitude is smaller.
Without the pressure fluctuation of leaf area, there is also the multiple frequence components of blade passing frequency, and high frequency arteries and veins all in all is presented without the pressure fluctuation of leaf area
Dynamic feature.For punching measure, it is possible to reduce dominant frequency energy, be also possible to reduce higher-frequency energy, or also having can
It can reduce simultaneously.
In order to systematically analyze the influence punched to pressure fluctuation, different sluicing are given below under the inclined working condition of small flow
The vortex rope evolution condition of cone.Vortex rope evolution timing when observation makes a call to 2 holes and makes a call to 4 hole respectively.As can be seen that for letting out after punching
Water cone even disappears (making a call to 4 holes) although being substantially reduced in the region of the local cavitation inception of draft cone outlet and (making a call to 2 holes), by
In the presence of punching, using hole as starting point, there is comparatively fine vortex rope, instead of the coarse spiral vortex of 0 hole draft cone of prototype
Band.And with the application of punching measure, the phenomenon that vortex rope moves up and down, weakens or eliminates, especially when making a call to 4 hole, originally relatively slightly
Spiral vortex band be dispersed very thin single vortex rope, and almost disappear at some moment.
It should be pointed out that under the conditions of above-mentioned punching, although the volume of cavitation is reduced, but it can be seen that sometimes
There are still thinner dual vortex rope, i.e. the cavitation energy under high frequency state still remains, will be according on pressure fluctuation frequency spectrum
Old higher-frequency peak value exists.
Finally, to (a=28mm, σ=0.277, n under the inclined operating condition of big flow11=83.2r/min) vortex rope form seen
It surveys, it can be seen that under the inclined operating condition of big flow, regardless of draft cone configuration, column is presented in vortex rope form, and its diameter becomes
Change very much not.But from the point of view of vibration and noise observation in experiment, the noise level for punching draft cone is relatively low.In addition, above-mentioned whirlpool
The shape of band and the result of numerical simulation are consistent.
Pressure fluctuation in draft tube of water turbine analysis
While vortex rope develops and observes, the monitoring of pressure fluctuation has also been carried out.Experiment, will according to the method for model experiment
Pressure probe is embedded to draft tube wall surface, to detect flow field effect and the pressure value on draft tube wall surface, and records it at any time
Situation of change.The pressure fluctuation experimental result of 4 monitoring points is analyzed below.
To initial pressure ambient experiment data carry out Fourier's variation, can directly under inclined operating condition pulse Energy distribution into
Row analysis.The small inclined working condition experimenting of flow the result shows that, punching measure implement after, the integral level of pressure fluctuation is all declined,
On the outside of ell, dominant frequency amplitude is reduced by up to.For the pressure-measuring-point (+Y0.3D2 ,-Y0.3D2) of Taper Pipe part, after punching,
The pulsation energy of higher-frequency is decreased obviously, and is disappeared in the operating condition for making a call to 4 holes.
In addition, the experimental results showed that, before punching, the pressure fluctuation energy on the outside of ell is maximum, its amplitude after punching
Decline the most significant.Compare with numerical simulation result, experimental result demonstrate well numerical simulation as a result, pressure fluctuation
Integral level have decline after punching, also illustrate that the measure punched on draft cone is effective.
In order to carry out quantitative explanation to the energy of pressure fluctuation, it is given below under different operating conditions for different sluicing wimble structures
Obtain ambient experiment data.According to IEC testing standard, mixing double-amplitude amplitude (peak-to-peak value) is used to the assessment of pressure fluctuation
Δ H/H is indicated.As shown in table 7,8,9 and 10, on the outside of respectively Taper Pipe+Y0.3D2, Taper Pipe-Y0.3D2, ell inside and ell
The pressure fluctuation characteristic data of measuring point.
As can be seen that spiral vortex band is more stable in small flow inclined operating condition, dominant frequency and the ratio for turning frequency are about 0.24,
With the increase of punching quantity, pulsation peak-to-peak value constant interval is little.Variation is significantly more the pressure under the inclined operating condition of big flow
Power pulsation, in addition on the inside of ell, in punching configuration, dominant frequency is substantially reduced remaining measuring point with the ratio for turning frequency, and dominant frequency reduces
Value is greater than 1/2 times of prototype draft cone operating condition.Also, the reduction of dominant frequency has likely via the decrease and disappearance of vortex rope in experiment
It closes, some moment, has the discontinuous phenomenon of vortex rope in draft tube.Particularly, for making a call to the operating condition in 4 holes, in all sluicing
It bores in configuration, the energy peak-to-peak value of dominant frequency, which has, to be substantially reduced, it is seen then that punching measure is effective.
Taper Pipe+Y0.3D under the different operating conditions of table 7 and draft cone configuration2The pressure fluctuation characteristic of point
Taper Pipe-Y0.3D under the different operating conditions of table 8 and draft cone configuration2The pressure fluctuation characteristic of point
The pressure fluctuation characteristic of ell inside measuring point under the different operating conditions of table 9 and draft cone configuration
Under the different operating conditions of table 10 and draft cone configuration on the outside of ell measuring point pressure fluctuation characteristic
In addition, it should be noted that when movable guide vane aperture increases, the dominant frequency pulsation of draft tube inlet and ell outlet
Peak-to-peak value decreases, this means that the corresponding high fdrequency component of pressure fluctuation becomes readily apparent from.In order to further determine beating
Energy magnitude behind hole is here summed it up first three order frequency (f1, f2, f3) energy of pressure fluctuation, whole for characterizing
Physical efficiency amount, as shown in table 11.As can be seen that first three rank energy summation reduces as punching quantity increases.On the whole, it punches
Measure has positive effect for the generation and relevant pressure pulsation that weaken vortex rope.
First three order frequency energy feature Δ H/H (%) of pressure fluctuation under the different draft cone configurations of table 11
The determination method for making a call to a kind of hydraulic turbine draft cone provided by the present invention 4 hole sites above, has carried out detailed Jie
It continues, used herein a specific example illustrates the principle and implementation of the invention, and the explanation of above embodiments is only
It is to be used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, according to this hair
Bright thought, there will be changes in the specific implementation manner and application range, in conclusion the content of the present specification should not manage
Solution is limitation of the present invention.
Claims (3)
1. a kind of determination method that hydraulic turbine draft cone makes a call to 4 hole sites, it is characterised in that:
Step 1 carries out numerical simulation calculation using method for numerical simulation, obtains draft cone low-pressure area range；
Step 2 is observed tail water vortex rope detail section using high-speed photography imaging system, determines the nascent place of vortex rope；
Step 3 implements punching measure according to the place that vortex rope is come into being, and the punching measure is to make a call to 4 holes to draft cone, described to make a call to 4
The draft cone in hole is the draft cone along the draft cone axle center of short and straight type relative to perforation at 2 holes, then the basis of the draft cone in 2 holes
On, in position relatively on the lower vertically to wearing 2 holes.
2. according to the method described in claim 1, it is characterized by: the numerical simulation calculation specifically: use unit speed
n11With specific discharge Q11Flow operating mode in full runner is described, passes through regulating device cavitation coefficient, cavitation factor, Toma coefficient σ and changes environment pressure in test
Power is horizontal, changes unit speed and specific discharge by adjusting movable guide vane aperture a；
Unit speed n11Is defined as:
D in formula1--- the runner diameter of model turbine, unit m；
H --- model turbine tests head, unit m；
N --- the runner revolving speed in model turbine, unit r/min；
Specific discharge Q11Is defined as:
Q in formula --- overcurrent flow in model francis turbine runner, unit m3/s；
Plant cavitation coefficient σ is defined as:
H in formulava--- the vacuum values in model experiment circulation loop in tail tank, unit m；
Ha--- the head that local atmospheric pressure is converted into experiment, unit m；
Hs--- the draught-height of the hydraulic turbine in experiment, unit m；
Hv--- the head that the saturated vapor pressure under experimental temperature is converted into, unit m；
Calculate the inclined operating point parameter of small flow of numerical simulation are as follows: a=16mm, n11=80.4r/min, Q11=
0.486m3/ s, σ=0.258；
The pressure distribution that draft cone and tail water tube portion are determined according to the small inclined operating condition of flow, so that it is determined that low-pressure area range.
3. according to the method described in claim 2, it is characterized by: vortex rope twist vortex rope under the inclined operating condition of small flow.
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| CN201461204U (en) * | 2009-07-03 | 2010-05-12 | 武汉大学 | Novel runner cone |
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