CN107191308A - A kind of Forecasting Methodology of mixed flow pump turbine complete characteristic curve - Google Patents
A kind of Forecasting Methodology of mixed flow pump turbine complete characteristic curve Download PDFInfo
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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
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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
- F03B13/00—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates
- F03B13/06—Stations or aggregates of water-storage type, e.g. comprising a turbine and a pump
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- 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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- 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
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/16—Mechanical energy storage, e.g. flywheels or pressurised fluids
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Abstract
The invention discloses a kind of Forecasting Methodology of mixed flow pump turbine complete characteristic curve, including：With reference to the characteristics of actual measurement method for complete characteristic curves of reversible pump turbine, the internal character analysis of amendment description flow omnicharacteristic and torque omnicharacteristic；Count the unit parameter of characteristic operating point on different specific speed method for complete characteristic curves of reversible pump turbine, the dominant functional relation set up between the unit parameter of each characteristic operating point and pump turbine optimum operating condition specific speed and relative opening of guide vane；The unit parameter of each characteristic operating point under different guide vane openings is obtained according to above-mentioned dominant functional relation, so that it is determined that the undetermined coefficient in the internal character analysis of amendment, obtains the prediction complete characteristic curve of any specific speed pump turbine.The complete characteristic curve error very little that this method prediction is obtained, therefore when carrying out rotary wheel model experiment, only a few features operating mode can be tested, instruct to accelerate model test process.
Description
Technical field
The present invention relates to Hydraulic Design field, and in particular to a kind of prediction side of mixed flow pump turbine complete characteristic curve
Method.
Background technology
With the sustained and rapid development of China's economic society, power network peak-valley difference increasingly increases, peak modulation capacity is not enough gradually into
In order to restrict the outstanding problem of China's power system development.And hydroenergy storage station is being solved as a kind of outstanding peak regulation instrument
Peak regulation pressure and improve intelligent grid operation that certainly the problem of dissolving of wind-powered electricity generation extensive development, nuclear power large-scale grid connection are brought
Effect in terms of flexibility and security can not be substituted.
However, different from conventional hydropower station, hydroenergy storage station change working is rapid, start and stop are frequent, water pump water wheels are added
The special bidirectional flow-through characteristic of machine so that the more conventional power station of Calculations of Hydraulic Transient in hydroenergy storage station is much more complex, from
And threaten the safety and stability in power station.Therefore, under the background of China's hydroenergy storage station Large scale construction, research water-storage electricity
The intrinsic characteristic of Hydraulic Transient of standing process, is of great significance to the safe and stable operation tool in power station.
The four-quadrant complete characteristic curve of pump turbine is the key element for studying hydroenergy storage station Hydraulic Transient process.
But feasibility study and concept phase in power station, because model test is not carried out or prototype is also unselected, often lack phase
The complete characteristic curve answered, the Preliminary design to hydroenergy storage station brings many difficulties, and applies mechanically close specific speed unit
Complete characteristic curve, in fact it could happen that the concept phase, which respectively adjusts, protects parameter and be satisfied by design requirement, and skill is when applying stage prototype and checking,
Some adjust protects the exceeded situation of parameter, causes error larger.Therefore, it is how accurately pre- before pump turbine is selected
Method for complete characteristic curves of reversible pump turbine is surveyed, with the transient process in initial analysis hydroenergy storage station unit and pressure pipeline, is instructed
Engineering design becomes important research direction.
Lack the feelings of method for complete characteristic curves of reversible pump turbine for hydroenergy storage station feasibility study and concept phase
Condition, when carrying out the calculating of hydroenergy storage station Calculations of Hydraulic Transient, it is common practice to apply mechanically head, single-machine capacity and specific speed
Close method for complete characteristic curves of reversible pump turbine.However, using the meter of the close pump turbine runner complete characteristic curve of specific speed
Although the result of calculation for calculating result and prototype runner complete characteristic curve is similar on waveform, calculating extreme value difference is larger, causes
Or pipe design intensity is bigger than normal during Preliminary design, investment is caused to increase；Pipe design intensity is less than normal, there is accident wind
Danger.Therefore, this way for applying mechanically head, single-machine capacity and the close method for complete characteristic curves of reversible pump turbine of specific speed can not be accurate
Instruct the Preliminary design of engineering in ground.
The content of the invention
The technical problems to be solved by the invention are existing hydroenergy storage station Calculations of Hydraulic Transient computational methods, because of set
Cause error larger with head, single-machine capacity and the close method for complete characteristic curves of reversible pump turbine of specific speed, it is impossible to refer to exactly
The problem of leading engineering Preliminary design.
In order to solve the above-mentioned technical problem, the technical solution adopted in the present invention is to provide a kind of mixed flow pump turbine
The Forecasting Methodology of complete characteristic curve, comprises the following steps：
With reference to actual measurement method for complete characteristic curves of reversible pump turbine the characteristics of, amendment description flow omnicharacteristic and torque omnicharacteristic it is interior
Characteristic analytic theory；
The unit parameter of characteristic operating point on different specific speed method for complete characteristic curves of reversible pump turbine is counted, each feature work is set up
Dominant functional relation between the unit parameter and pump turbine optimum operating condition specific speed and relative opening of guide vane of condition point；
The unit parameter of each characteristic operating point under different guide vane openings is obtained according to above-mentioned dominant functional relation, so that it is determined that
Undetermined coefficient in the internal character analysis of amendment, obtains the prediction complete characteristic curve of any specific speed pump turbine.
In the above-mentioned technical solutions, the calculation of the internal character analysis of description flow omnicharacteristic and torque omnicharacteristic
Specially：
When pump turbine stable operation under hydraulic turbine condition and pump operating condition, pass through the stream to stream interface in the middle of runner
Fast triangle is analyzed, the relation between flow, rotating speed and torque when obtaining pump turbine stable operation, Yi Jiliu
Relation between amount, rotating speed and head；
By introducing unit speed, specific discharge and units of torque, above-mentioned relation formula is converted, description stream is just obtained
Measure the internal character analysis of omnicharacteristic and torque omnicharacteristic.
In the above-mentioned technical solutions, unit speed is introducedSpecific dischargeIt is single
Position torque M1'=M/D1 3H, hydraulic turbine condition efficiency etaT=1-STQT 2/ H=1-STQ1′2D1 4With pump operating condition efficiency etaP=(1+
SPQ1′2D1 4)-1, then specific discharge of the pump turbine in hydraulic turbine condition and pump operating condition stable operation, unit speed and
Relation between units of torque is：
M′1T=αTQ′1T 2-βTQ′1Tn′1T
M′1P=-αPQ′1P 2+βPQ′1Pn′1P
aTn′1TQ′1T-bTn′1T 2+cTQ′1T 2=1
-aPn′1PQ′1P+bPn′1P 2-cPQ′1P 2=1
According to actual measurement complete characteristic curve feature, the operating point that specific discharge is zero in complete characteristic curve, its specific torque
And be not zero, therefore above-mentioned formula is modified to：
M′1T=αTQ′1T 2-βTQ′1Tn′1T+γT
M′1P=-αPQ′1P 2+βPQ′1Pn′1P+γP
Wherein, subscript T represents hydraulic turbine condition, i.e. centripetal flow operating mode；Subscript P represents pump operating condition, i.e. centrifugal flow
Operating mode；n1′、Q1' and M1' it is respectively unit speed, specific discharge and units of torque；η is hydraulic efficiency；N, Q and M are respectively water
Pump turbine rotating speed, flow and axle power square；D1For runner diameter；H is head or lift；S is loss coefficient；αT、βT、γT、aT、
bT、cTFor the coefficient related with hydraulic turbine condition parameter to unit geometric parameter；αP、βP、γP、aP、bP、cPFor with unit geometric parameters
The number coefficient related to pump operating condition parameter.
When in the above-mentioned technical solutions, by the fundamental equation of pump turbine and to hydraulic turbine condition at runner
The analysis of flow velocity triangle, obtains pump turbine under hydraulic turbine condition during stable operation, between flow, rotating speed and torque
Relational expression is：
During due to hydraulic turbine condition there is following relation in torque and shaft power：
Simultaneous above-mentioned formula, the relational expression that can be obtained between flow, rotating speed and head is：
Wherein, subscript 1,2 represents runner inlet and outlet respectively；γ is fluid severe；G is acceleration of gravity；To be wide etc. related to stream interface in the middle of hydraulic turbine condition runner import and export current angle and runner import and export
Coefficient；b1And b2Guide vane height and outlet of rotary wheel axis plane projection width are represented respectively；α1And β2Respectively stator outlet stream angle and
Outlet of rotary wheel current angle；The π n/60 of ω=2 are angular velocity of rotation；R is stream interface radius；P is shaft power.
Stream when in the above-mentioned technical solutions, according to the fundamental equation of pump turbine and to pump operating condition at runner
The analysis of fast triangle, the relation between flow, rotating speed and torque when obtaining pump operating condition stable operation is：
Relation between flow, rotating speed and head is：
Wherein, b is and the geometric parameter such as stream interface in the middle of pump operating condition runner import and export current angle and runner import and export is wide
The coefficient related to duty parameter；For outlet of rotary wheel intermediate flow radius surface under pump operating condition.
In the above-mentioned technical solutions, when pump turbine stable operation under hydraulic turbine condition and pump operating condition, according to
The moment of momentum theorem, the fundamental equation that can obtain pump turbine is respectively：
Wherein, subscript T, P represents hydraulic turbine condition and pump operating condition respectively；Subscript 1,2 represents runner import and gone out respectively
Mouthful；VuFor the circumferential components of mass flow absolute velocity.
The analysis of flow velocity triangle when in the above-mentioned technical solutions, by hydraulic turbine condition at runner, can be obtained：
Above-mentioned formula is substituted into formulaIn, can obtain above-mentioned hydraulic turbine condition down-off,
Relational expression between rotating speed and torque；Wherein, VmFor flow rate on axial surface；U is runner peripheral speed.
The present invention has advantages below：
(1) the characteristics of combining actual measurement method for complete characteristic curves of reversible pump turbine, have modified description flow omnicharacteristic and torque is entirely special
The internal character analysis of property；
(2) unit parameter of characteristic operating point on different specific speed method for complete characteristic curves of reversible pump turbine can be calculated, is tied
Close the internal character analysis of amendment, may be implemented in pump turbine it is selected before, accurately predict the complete of pump turbine
Characteristic curve；The complete characteristic curve of prediction can for ancillary works Preliminary design, be hydroenergy storage station operation safety
Design considerations is provided, conventional sleeve head, single-machine capacity and the close method for complete characteristic curves of reversible pump turbine error of specific speed is overcome
Larger deficiency；
(3) due in the case of the unit parameter of known all characteristic operating point collection, predicting what is obtained using this method
Complete characteristic curve error very little, therefore when carrying out rotary wheel model experiment, only a few features operating mode can be tested, instruct
Accelerate model test process.
Brief description of the drawings
Fig. 1 is a kind of Forecasting Methodology flow chart of mixed flow pump turbine complete characteristic curve in the present invention；
The flow velocity triangle that Fig. 2 imports and exports for hydraulic turbine condition runner in the present invention；
Fig. 3 is each characteristic operating point distribution on most excellent aperture line in the present invention；
Fig. 4 is the relation between the unit parameter and optimal specific speed of characteristic operating point O points in the present invention；
Fig. 5 is O in the present inventioniRelation between the relative unit parameter and relative opening of guide vane of point set；Fig. 6 is the present invention
The complete characteristic curve of middle actual measurement and theoretical prediction is contrasted；
Fig. 7 is the transient process contrast based on prototype omnicharacteristic and prediction omnicharacteristic in the present invention.
Embodiment
In order to solve existing hydroenergy storage station Calculations of Hydraulic Transient computational methods, because apply mechanically head, single-machine capacity with
And the close method for complete characteristic curves of reversible pump turbine of specific speed causes error larger, it is impossible to instruct asking for engineering Preliminary design exactly
Topic.The present invention proposes a kind of Forecasting Methodology of mixed flow pump turbine complete characteristic curve, is stablized using current in runner
The speed triangle of flowing, sets up the mathematical modeling of description pump turbine omnicharacteristic, and combine each feature on complete characteristic curve
The unit parameter of operating mode point set and specific speed and the statistical relationship of guide vane opening, so as to realize method for complete characteristic curves of reversible pump turbine
Theoretical prediction.
The present invention is described in detail with reference to specification drawings and specific embodiments.
The embodiments of the invention provide a kind of Forecasting Methodology of mixed flow pump turbine complete characteristic curve, as shown in figure 1,
Comprise the following steps：
S1, when pump turbine stable operation under hydraulic turbine condition and pump operating condition, by stream interface in the middle of runner
Flow velocity triangle analyzed, the relation between flow, rotating speed and torque when obtaining pump turbine stable operation, and
Relation between flow, rotating speed and head.
S2, introducing unit speed, specific discharge and units of torque, are converted into description flow complete by the relational expression in step S1
The internal character analysis of characteristic and torque omnicharacteristic, and actual measurement complete characteristic curve feature is combined, correct internal character analysis.
The unit parameter of characteristic operating point, sets up each spy on S3, statistics different specific speed method for complete characteristic curves of reversible pump turbine
Levy the dominant functional relation between the unit parameter of operating point and pump turbine optimum operating condition specific speed and relative opening of guide vane.
S4, based on the internal character analysis corrected in step S2, and under the different guide vane openings obtained according to step S3
The unit parameter of each characteristic operating point, then can determine that the undetermined coefficient in the internal character analysis corrected in step S2, so that
Obtain the prediction complete characteristic curve of any specific speed pump turbine.
Above-mentioned steps S1 realization principle is specific as follows：
When pump turbine stable operation under hydraulic turbine condition and pump operating condition, according to the moment of momentum theorem, it can be derived from
The fundamental equation (Eulerian equation) of pump turbine is respectively：
Wherein, subscript T represents pump turbine operating mode, i.e. centripetal flow operating mode；Subscript P represents pump turbine operating mode,
That is centrifugal flow operating mode；Subscript 1,2 represents runner inlet and outlet respectively；M is axle power square；γ is fluid severe；Q is to enter to turn
Flow in wheel；VuR is velocity moment；VuFor the circumferential components of mass flow absolute velocity；R is stream interface radius；H is head or raised
Journey；η is hydraulic efficiency；ω is angular velocity of rotation；G is acceleration of gravity.
Analyzed by the flow velocity triangle to stream interface in the middle of hydraulic turbine condition runner shown in Fig. 2, can by formula (1) and
V in formula (2)u1And Vu2It is written as：
Wherein, Vm1And Vm2Respectively runner inlet and outlet flow rate on axial surface；b1And b2Respectively guide vane height and runner goes out
Mouth axis plane projection width；α1And β2Respectively stator outlet stream angle and outlet of rotary wheel current angle.
Formula (5) and formula (6) are substituted into formula (1), can be obtained：
Simultaneously as during the hydraulic turbine there is following relation in torque and shaft power：
Wherein, P is shaft power；The π n/60 of ω=2 are angular velocity of rotation；N is rotating speed.
Simultaneous formula (7) and formula (8), can be obtained：
Formula (7) and formula (9) are respectively flow, rotating speed and torque of the pump turbine in hydraulic turbine condition stable operation
Between relation, and the relation between flow, rotating speed and head.Similarly, by analyzing flow velocity during pump operating condition at runner
Triangle, it is also possible to obtain the relation between flow, rotating speed and torque of the pump turbine in pump operating condition stable operation, with
And the relation between flow, rotating speed and head.Then the fundamental equation of pump turbine can be exchanged into：
Wherein,For with hydraulic turbine condition runner import and export current angle and runner import and export intermediate flow
The wide coefficient for waiting geometric parameter related to duty parameter in face；B be with pump operating condition runner import and export current angle and runner into and out of
Stream interface is wide in the middle of mouthful waits the geometric parameter coefficient related to duty parameter；For stream interface in the middle of outlet of rotary wheel under pump operating condition half
Footpath；ηT=(HT-STQT 2)/HT=1-STQT 2/HTFor hydraulic turbine condition efficiency；ηP=HP/(HP+SPQP 2)=(1+SPQP 2/HP)-1For
Pump operating condition efficiency；S is loss coefficient.
Above-mentioned steps S2 realization principle is specific as follows：
Because complete characteristic curve is to characterize unit specific discharge, unit force under different guide vane openings under steady running condition
The cluster curve of correlation between square and unit speed, therefore introduce unit speedSpecific dischargeUnits of torque M1'=M/D1 3H、ηT=1-STQT 2/ H=1-STQ1′2D1 4And ηP=(1+SPQ1′2D1 4)-1,
Formula (10) is substituted into formula (13), can be converted：
M′1T=αTQ′1T 2-βTQ′1Tn′1T (1)
M′1P=-αPQ′1P 2+βPQ′1Pn′1P (2)
aTn′1TQ′1T-bTn′1T 2+cTQ′1T 2=1 (3)
-aPn′1PQ′1P+bPn′1P 2-cPQ′1P 2=1 (4)
According to actual measurement complete characteristic curve feature, the operating point that specific discharge is zero in complete characteristic curve, its specific torque
And be not zero, therefore formula (14) and formula (15) should be modified to：
M′1T=αTQ′1T 2-βTQ′1Tn′1T+γT (5)
M′1P=-αPQ′1P 2+βPQ′1Pn′1P+γP (6)
Wherein, n1' it is unit rotating speed (r/min)；D1 is runner diameter (m)；H is head or lift (m)；Q1' it is unit stream
Measure (m3/s)；M1' it is unit torque (Nm)；αT、βT、γT、aT、bT、cTIt is and geometric parameter and pump turbine operating mode ginseng
The related coefficient of number；αP、βP、γP、aP、bP、cPIt is the coefficient related with pump turbine duty parameter to geometric parameter.
Formula (16) and formula (17) determine centripetal flow operating mode (Q ' respectively1T＞ 0) and centrifugal flow operating mode (Q '1P＜ 0) when
Flow omnicharacteristic；Torque when formula (18) and formula (19) determine pump turbine operating mode and pump turbine operating mode respectively is entirely special
Property.Formula (16)~formula (19) is the mathematical modeling for describing pump turbine omnicharacteristic, the internal character analysis reason also referred to as corrected
By.
Due to only having three undetermined coefficients in above-mentioned each equation, therefore, as long as three spies in known correspondence operating mode area
A unit parameter is levied, convolution (16) is that can determine that above-mentioned undetermined coefficient to (19), so that theoretical prediction complete characteristic curve.
Above-mentioned steps S3 realization principle is specific as follows：
Every characteristic curve can regard the curve that each characteristic operating point of the timing of guide vane opening one is formed by connecting paragraph by paragraph as,
Therefore, if can each characteristic point of Accurate Prediction unit parameter, with reference to step S2 description complete characteristic curve mathematical modeling, just
Can the theoretical complete characteristic curve for drawing pump turbine.Fig. 3 show point of characteristic operating point on most excellent aperture line (τ=1)
Cloth.
Wherein, point C represents high-efficiency point in pump operating condition area I；Point B1 is that pump operating condition area I brakes area's II intersection points with water pump,
Its specific discharge is zero；Point A is water pump braking area II and hydraulic turbine condition area III intersection points, and its unit speed is zero；Point O is represented
Optimal operating condition point in pump turbine operating mode area III, its generating efficiency highest；Point R is runaway speed point, and its specific torque is
Zero；Point B2 is the intersection point that pump turbine brakes area IV and the pump condition area V that turns one's coat, and its specific discharge is zero.Due under each aperture
There is features described above point, so as to constitute complete characteristic curve characteristic operating point collection Ci、B1i、Ai、Oi、Ri、B2i(i represents guide vane opening
Sequence number).
The pump turbine model runner complete characteristic curve sample that 10 sets of specific speeds differ greatly is collected, unit head exists
Between 100~700m, cover high, medium and low drop, using each characteristic operating point unit parameter of Least Square Regression Analysis with most
Excellent operating mode specific speed nS(parameter of comprehensive characterization pump turbine characteristic) and relative opening of guide vane τ (τ=Ω/Ω0, Ω0Represent
Guide vane opening during generating efficiency highest) functional relation.Fig. 4 show the O points unit parameter (unit turn that regression analysis is obtained
Speed, specific discharge and specific torque) functional relation between optimum operating condition specific speed.Fig. 5 show what regression analysis was obtained
OiFunctional relation between point set relative unit parameter and relative opening of guide vane.
The governing equation of foundation is as follows：
n′1Oi=(75.4688+0.0782nS)×(-0.0742τ2+0.4353τ+0.6402) (20)
Q′1Oi=0.0855nS 1.6707×(-0.2243τ2+1.2241τ-0.0005) (21)
M′1Oi=0.1401nS 1.5870×(-0.4410τ2+1.4661τ-0.0267) (22)
Using same method, other characteristic operating point collection unit parameters and optimum operating condition specific speed and stator can be set up
The functional relation of relative opening degree.
The embodiment of the present invention is specifically implemented as follows：
The optimum operating condition specific speed of certain known hydroenergy storage station unit is nS=83.1 (mkW), according to the present invention's
Contrast of the complete characteristic curve that content and principle prediction are obtained with surveying complete characteristic curve is as shown in Figure 6.It can be seen that
The complete characteristic curve variation tendency that theoretical prediction and actual measurement are drawn is basically identical, and also maintains in small guide vane higher consistent
Property.
Also with prediction complete characteristic curve and prototype complete characteristic curve respectively to simultaneously " two machines send out nominal output, dash forward
Removal of load, stator normal switching-off " operating mode is calculated, and obtained tune protects Parameters variation process such as Fig. 7, adjusts the extreme value pair for protecting parameter
Than result such as table 1.From Fig. 7 and table 1 as can be seen that method proposed by the present invention it is more traditional apply mechanically head, single-machine capacity and
The way error of the close unit complete characteristic curve of specific speed is smaller, can effectively improve concept phase hydroenergy storage station waterpower
The computational accuracy of transient process, important data supporting is provided for the Preliminary design in power station.
The removal of load operating mode of table 1 difference runner characteristic comparing result
The present invention is calculated suitable for feasibility study and the Calculations of Hydraulic Transient of concept phase hydroenergy storage station, tool
Body is, under prototype complete characteristic curve unknown situation, and any specific speed mixed-flow type method for complete characteristic curves of reversible pump turbine is managed
By prediction, be hydroenergy storage station aqueduct structure design, the arrangement of hydraulic structure, unit and spiral case strength check and
Power station stable operation etc. provides information and foundation.
The present invention is not limited to above-mentioned preferred forms, anyone structure change made under the enlightenment of the present invention,
The technical schemes that are same or similar to the present invention, each fall within protection scope of the present invention.
Claims (7)
1. a kind of Forecasting Methodology of mixed flow pump turbine complete characteristic curve, it is characterised in that comprise the following steps：
With reference to the characteristics of actual measurement method for complete characteristic curves of reversible pump turbine, the internal characteristic of amendment description flow omnicharacteristic and torque omnicharacteristic
Analytic theory；
The unit parameter of characteristic operating point on different specific speed method for complete characteristic curves of reversible pump turbine is counted, each characteristic operating point is set up
Unit parameter and pump turbine optimum operating condition specific speed and relative opening of guide vane between dominant functional relation；
The unit parameter of each characteristic operating point under different guide vane openings is obtained according to above-mentioned dominant functional relation, so that it is determined that amendment
Internal character analysis in undetermined coefficient, obtain the prediction complete characteristic curve of any specific speed pump turbine.
2. the method as described in claim 1, it is characterised in that the internal character analysis of description flow omnicharacteristic and torque omnicharacteristic
Theoretical calculation is specially：
When pump turbine stable operation under hydraulic turbine condition and pump operating condition, pass through the flow velocity three to stream interface in the middle of runner
It is angular to be analyzed, the relation between flow, rotating speed and torque when obtaining pump turbine stable operation, and flow, turn
Relation between speed and head；
By introducing unit speed, specific discharge and units of torque, above-mentioned relation formula is converted, description flow is just obtained complete
The internal character analysis of characteristic and torque omnicharacteristic.
3. method as claimed in claim 2, it is characterised in that introduce unit speedSpecific dischargeUnits of torque M '1=M/D1 3H, hydraulic turbine condition efficiency etaT=1-STQT 2/ H=1-STQ1 ′2D1 4And water
Pump condition efficiency etaP=(1+SPQ1 ′2D1 4)-1, then unit of the pump turbine in hydraulic turbine condition and pump operating condition stable operation
Relation between flow, unit speed and units of torque is：
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<mi>n</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>b</mi>
<mi>T</mi>
</msub>
<msup>
<msubsup>
<mi>n</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>c</mi>
<mi>T</mi>
</msub>
<msup>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mn>2</mn>
</msup>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>-</mo>
<msub>
<mi>a</mi>
<mi>P</mi>
</msub>
<msubsup>
<mi>n</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>b</mi>
<mi>P</mi>
</msub>
<msup>
<msubsup>
<mi>n</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mn>2</mn>
</msup>
<mo>-</mo>
<msub>
<mi>c</mi>
<mi>P</mi>
</msub>
<msup>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mn>2</mn>
</msup>
<mo>=</mo>
<mn>1</mn>
</mrow>
According to actual measurement complete characteristic curve feature, the operating point that specific discharge is zero in complete characteristic curve, its specific torque is not
It is zero, therefore above-mentioned formula is modified to：
<mrow>
<msubsup>
<mi>M</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>&alpha;</mi>
<mi>T</mi>
</msub>
<msup>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mn>2</mn>
</msup>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mi>T</mi>
</msub>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<msubsup>
<mi>n</mi>
<mrow>
<mn>1</mn>
<mi>T</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>&gamma;</mi>
<mi>T</mi>
</msub>
</mrow>
<mrow>
<msubsup>
<mi>M</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>&alpha;</mi>
<mi>P</mi>
</msub>
<msup>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mi>P</mi>
</msub>
<msubsup>
<mi>Q</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<msubsup>
<mi>n</mi>
<mrow>
<mn>1</mn>
<mi>P</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>&gamma;</mi>
<mi>P</mi>
</msub>
</mrow>
Wherein, subscript T represents hydraulic turbine condition, i.e. centripetal flow operating mode；Subscript P represents pump operating condition, i.e. centrifugal flow operating mode；
n′1、Q′1With M '1Respectively unit speed, specific discharge and units of torque；η is hydraulic efficiency；N, Q and M are respectively water pump water wheels
Machine rotating speed, flow and axle power square；D1For runner diameter；H is head or lift；S is loss coefficient；αT、βT、γT、aT、bT、cTFor
The coefficient related with hydraulic turbine condition parameter to unit geometric parameter；αP、βP、γP、aP、bP、cPFor with unit geometric parameter and water
The related coefficient of pump condition parameter.
4. method as claimed in claim 3, it is characterised in that by the fundamental equation of pump turbine and to the hydraulic turbine
The analysis of flow velocity triangle during operating mode at runner, obtains pump turbine under hydraulic turbine condition during stable operation, flow, turn
Speed and torque between relational expression be：
<mrow>
<msub>
<mi>M</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;Q</mi>
<mi>T</mi>
</msub>
</mrow>
<mi>g</mi>
</mfrac>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>cot&alpha;</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;b</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>cot&beta;</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;b</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>Q</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>&omega;r</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;Q</mi>
<mi>T</mi>
</msub>
</mrow>
<mi>g</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>aQ</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>&omega;r</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</mrow>
1
During due to hydraulic turbine condition there is following relation in torque and shaft power：
<mrow>
<msub>
<mi>M</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>P</mi>
<mi>&omega;</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;Q</mi>
<mi>T</mi>
</msub>
<msub>
<mi>H&eta;</mi>
<mi>T</mi>
</msub>
</mrow>
<mi>&omega;</mi>
</mfrac>
</mrow>
Simultaneous above-mentioned formula, the relational expression that can be obtained between flow, rotating speed and head is：
<mrow>
<msub>
<mi>H&eta;</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>&omega;</mi>
<mi>g</mi>
</mfrac>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>cot&alpha;</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;b</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>cot&beta;</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;b</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>Q</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>&omega;r</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>=</mo>
<mfrac>
<mi>&omega;</mi>
<mi>g</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>aQ</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>&omega;r</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</mrow>
Wherein, subscript 1,2 represents runner inlet and outlet respectively；γ is fluid severe；G is acceleration of gravity；To be wide etc. related to stream interface in the middle of hydraulic turbine condition runner import and export current angle and runner import and export
Coefficient；b1And b2Guide vane height and outlet of rotary wheel axis plane projection width are represented respectively；α1And β2Respectively stator outlet stream angle and
Outlet of rotary wheel current angle；The π n/60 of ω=2 are angular velocity of rotation；R is stream interface radius；P is shaft power.
5. method as claimed in claim 3, it is characterised in that according to the fundamental equation of pump turbine and to plugman
The analysis of flow velocity triangle during condition at runner, the pass between flow, rotating speed and torque when obtaining pump operating condition stable operation
It is to be：
<mrow>
<msub>
<mi>M</mi>
<mi>P</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;Q</mi>
<mi>P</mi>
</msub>
</mrow>
<mi>g</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mi>&omega;</mi>
<msup>
<msub>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msub>
<mi>bQ</mi>
<mi>P</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
Relation between flow, rotating speed and head is：
<mrow>
<msub>
<mi>H</mi>
<mi>P</mi>
</msub>
<mo>=</mo>
<mi>H</mi>
<mo>/</mo>
<msub>
<mi>&eta;</mi>
<mi>P</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>&omega;</mi>
<mi>g</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mi>&omega;</mi>
<msup>
<msub>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msub>
<mi>bQ</mi>
<mi>P</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
Wherein, b is and geometric parameter and the work such as stream interface in the middle of pump operating condition runner import and export current angle and runner import and export is wide
The related coefficient of condition parameter；For outlet of rotary wheel intermediate flow radius surface under pump operating condition.
6. the method as described in claim 4 or 5, it is characterised in that when pump turbine is in hydraulic turbine condition and pump operating condition
During lower stable operation, according to the moment of momentum theorem, the fundamental equation that can obtain pump turbine is respectively：
<mrow>
<msub>
<mi>M</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;Q</mi>
<mi>T</mi>
</msub>
</mrow>
<mi>g</mi>
</mfrac>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>H</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<msub>
<mi>H&eta;</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>&omega;</mi>
<mi>g</mi>
</mfrac>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>M</mi>
<mi>P</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;Q</mi>
<mi>P</mi>
</msub>
</mrow>
<mi>g</mi>
</mfrac>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>P</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>H</mi>
<mi>P</mi>
</msub>
<mo>=</mo>
<mi>H</mi>
<mo>/</mo>
<msub>
<mi>&eta;</mi>
<mi>P</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>&omega;</mi>
<mi>g</mi>
</mfrac>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>P</mi>
</msub>
</mrow>
Wherein, subscript T, P represents hydraulic turbine condition and pump operating condition respectively；Subscript 1,2 represents runner inlet and outlet respectively；Vu
For the circumferential components of mass flow absolute velocity.
7. method as claimed in claim 4, it is characterised in that flow velocity triangle during by hydraulic turbine condition at runner
Analysis, can be obtained：
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>m</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>cot&alpha;</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>Q</mi>
<mi> </mi>
<msub>
<mi>cot&alpha;</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;r</mi>
<mn>1</mn>
</msub>
<msub>
<mi>b</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
</mrow>
2
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>u</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>m</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>cot&beta;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>&omega;r</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<mi>Q</mi>
<mi> </mi>
<msub>
<mi>cot&beta;</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;r</mi>
<mn>2</mn>
</msub>
<msub>
<mi>b</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
</mrow>
Above-mentioned formula is substituted into formulaIn, above-mentioned hydraulic turbine condition down-off, rotating speed can be obtained
Relational expression between torque；Wherein, VmFor flow rate on axial surface；U is runner peripheral speed.
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