CN107153753B - Method for estimating basic parameters of mixed-flow water turbine - Google Patents

Method for estimating basic parameters of mixed-flow water turbine Download PDF

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CN107153753B
CN107153753B CN201710493690.2A CN201710493690A CN107153753B CN 107153753 B CN107153753 B CN 107153753B CN 201710493690 A CN201710493690 A CN 201710493690A CN 107153753 B CN107153753 B CN 107153753B
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董宏成
蒋登云
田迅
孙文彬
刘丁
王辉
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PowerChina Chengdu Engineering Co Ltd
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Abstract

The invention relates to a water turbine, and provides a method for estimating basic parameters of a mixed-flow water turbine, which is used for estimating the basic parameters of the mixed-flow water turbine. The basic parameters of the water turbine to be estimated comprise specific speed nsUnit speed n11And unit flow rate Q11The method of the invention comprises the following steps: determining the specific rotating speed of the francis turbine to be estimated, and recording the specific rotating speed as ns(ii) a Determining the maximum applied water head of the francis turbine to be estimated, wherein the maximum applied water head is recorded as HmaxAnd judging HmaxThe range in which it is located; according to HmaxThe estimation formula of the corresponding range estimates basic parameters, and the formula is as follows: when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure DDA0001332112280000011
Figure DDA0001332112280000012
when 100m is more than HmaxWhen the thickness is less than or equal to 200m, ns＝2191.5Hr ‑0.5007，
Figure DDA0001332112280000013
Q11＝1.0642Ln(ns) -4.7812; when 200m is more than HmaxWhen the particle size is less than or equal to 300m,
Figure DDA0001332112280000014
n11＝1.2874ns 0.7878，Q11＝0.7821Ln(ns) -3.3718; when H is presentmaxWhen larger than 300m, ns＝3609.2Hr ‑0.6189，n11＝37.207ns 0.1186，Q11＝0.3652Ln(ns) -1.4009. The invention is suitable for mixed-flow water turbines and can better meet the requirements of new hydropower engineering.

Description

Method for estimating basic parameters of mixed-flow water turbine
Technical Field
The invention relates to a water turbine, in particular to a method for estimating basic parameters of a mixed-flow water turbine.
Background
The water turbine is a machine which converts the mechanical energy of water flow into the mechanical energy of a rotating wheel in a hydropower station and enables the rotating wheel and a main shaft to continuously run by overcoming various resistances, is called as the heart of the hydropower station, has very important functions on the initial investment of hydropower engineering and the exertion of the economic benefits of a power plant after operation by reasonably selecting the parameters, and is important content of the design of the hydropower engineering.
Specific speed n of water turbinesThe method is a comprehensive index for measuring the energy characteristic, cavitation characteristic, operation stability, economy and advancement of the water turbine. The improvement of the specific rotating speed has important significance for improving the energy characteristic of the water turbine, reducing the unit manufacturing cost and the civil engineering investment of a factory building; but the improvement of the specific rotating speed is limited by the factors of the strength, the cavitation performance, the silt abrasion, the operation stability and the like of the water turbine. Therefore, how to reasonably determine the specific speed nsIs a very important content in the design of hydroelectric engineering. By calculation of formula
Figure BDA0001332112270000011
It is known that the variation range of the efficiency η (the francis turbine is generally 90% -95%) is limited, and only when the unit rotating speed n is used11And unit flow rate Q11When reasonably matched, the most suitable specific rotating speed n can be obtainedsValue and hydraulic turbine combination properties.
The current closest solution to the present invention to solve the above problems is: to obtain a basic parameter of the turbine-specific speed nsUnit speed n11And unit flow rate Q11There are generally two approaches. The method comprises the following steps: if parameters of a water turbine head, output and the like in the designed hydroelectric engineering are the same as or close to the designed and manufactured parameters of the water turbine, the basic parameters of the water turbine are estimated by using the model runner parameters and the comprehensive characteristic curve. Since the method is based onUnder the limit of the current technical conditions, it is difficult to fully and deeply test and study the characteristics of a certain existing model runner, so that the calculated specific speed n of the water turbinesUnit speed n11And unit flow rate Q11New requirements of hydropower engineering are generally difficult to meet; in particular to large, medium or special hydropower engineering, and a new runner is developed and researched by applying new technologies such as CFD and the like according to the specific conditions and the operation requirements of the engineering. The second method comprises the following steps: when there is no proper model runner data, the basic parameters of the turbine are estimated according to the statistical formula. The method estimates the basic parameters of the water turbine according to a statistical formula, so that the statistical formula is more at present, the water turbine parameter sample data based on each statistical formula is before the seventh and eighty years of the last century or in a certain water head section or in a certain output range, certain limitations exist, and the results calculated by different statistical formulas in the same hydroelectric engineering are different, some of the results are even greatly different, and the results cannot be correctly selected. Therefore, the requirements of hydropower engineering on continuous development of new technology, new materials, new processes, new structures and the like cannot be met by the first method and the second method, and the calculated specific rotating speed n of the water turbinesUnit speed n11And unit flow rate Q11It is also difficult to meet new requirements of hydroelectric engineering.
In recent years, the development of hydropower in China has attracted attention, plays an important role in adjusting energy structure, and has become a huge power for leading and promoting the development of hydropower in the world and a Chinese image which is reputable in the world after high-speed rails in China. By the end of 2014, the total installed capacity of Chinese hydropower breaks through 3 hundred million kilowatts, which accounts for about one fourth of the total amount of global hydropower installation, and the global hydropower installation is estimated to reach 20.5 hundred million kilowatts in 2050. In order to fully utilize the prior achievements and take the development strategy of going out one way and one way as a trigger to provide powerful technical support for the subsequent domestic and foreign hydroelectric engineering construction, the invention uses a large amount of water turbine parameters as sample data and tries to regress and count to obtain new basic parameter estimation of the water turbine by using the principle of least square method on the basis of collecting and collating a large amount of well-operated mixed-flow water turbine generator set data in domestic and foreign 30 yearsCalculating a formula to obtain a reasonable specific speed n of the water turbinesUnit speed n11And unit flow rate Q11The estimated value is used for meeting the new requirements of the hydropower engineering.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: a method for estimating basic parameters of a mixed-flow water turbine is provided, and the basic parameters of the mixed-flow water turbine are estimated.
In order to solve the problems, the invention adopts the technical scheme that: a method for estimating basic parameters of a mixed-flow water turbine comprises the following steps:
a. determining the rated water head of the francis turbine to be estimated, wherein the rated water head is recorded as Hr；
b. Determining the maximum applied water head of the francis turbine to be estimated, wherein the maximum applied water head is recorded as HmaxAnd judging HmaxThe range in which it is located; in the invention HmaxThe range where possible is shared by Hmax≤100m、100m＜Hmax≤200m、200m＜Hmax≤300m、HmaxMore than 300 m;
c. according to HmaxAnd (3) estimating the specific rotating speed by using a specific rotating speed estimation formula corresponding to the range, wherein the specific rotating speed is recorded as nsThe specific speed estimation formula is as follows:
when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure BDA0001332112270000021
when 100m is more than HmaxWhen the thickness is less than or equal to 200m, ns＝2191.5Hr -0.5007(4)；
When 200m is more than HmaxWhen the particle size is less than or equal to 300m,
Figure BDA0001332112270000022
when H is presentmaxWhen larger than 300m, ns＝3609.2Hr -0.6189(10)。
Further, the present invention also includes step dmaxCorresponding range unit speed estimation formula and the result obtained in step cnsEstimating a unit rotational speed, said unit rotational speed being denoted as n11The specific speed estimation formula of the range is as follows:
when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure BDA0001332112270000023
when 100m is more than HmaxWhen the particle size is less than or equal to 200m,
Figure BDA0001332112270000024
when 200m is more than HmaxWhen the particle size is less than or equal to 300m, n11＝1.2874ns 0.7878(8)；
When H is presentmaxWhen larger than 300m, n11＝37.207ns 0.1186(11)。
Further, the present invention also includes step emaxCorresponding range unit flow rate estimation formula and n obtained in step csEstimating the unit flow rate, said unit flow rate being denoted as Q11The specific speed estimation formula of the range is as follows:
when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure BDA0001332112270000031
when 100m is more than HmaxWhen the grain size is less than or equal to 200m, Q11＝1.0642Ln(ns)-4.7812 (6)；
When 200m is more than HmaxWhen the grain size is less than or equal to 300m, Q11＝0.7821Ln(ns)-3.3718 (9)；
When H is presentmaxWhen larger than 300m, Q11＝0.3652Ln(ns)-1.4009 (12)。
It should be noted that: n of water turbine in calculating unit rotation speed and unit flowsThe values solved by the values and the estimation equations (1), (4), (7) and (10) may sometimes differ a little because nsThe value is usually a value which is beneficial to calculating other subsequent parameters such as the synchronous rotating speed of the generator, for example, the synchronous rotating speed of the generator calculated according to the estimation value of the estimation formula is 99r/min, and the generator synchronously rotatesThe speed must be taken as 100r/min, n recommended by the generator standardsIf the value is taken, corresponding correction is needed; of course, n may be n as requiredsThe value is the value solved by the estimation formulas (1), (4), (7) and (10), so the person skilled in the art can select the value according to the needs.
The invention has the beneficial effects that: the invention collects and arranges a large amount of well-operated mixed-flow water turbine generator set data at home and abroad in nearly 30 years according to the maximum application water head H of the water turbinemaxDivide the data into Hmax≤100m、100m＜Hmax≤200m、200m＜Hmax≤300m、HmaxThe number of the mixed flow type water turbine is more than 300m, so that the mixed flow type water turbine has different performance characteristics corresponding to different water head ranges. Using least square method, using a large quantity of water turbine parameters as sample data, regression statistics to obtain basic parameters-specific speed n of mixed flow water turbine at four water head sectionss(m.kW), unit rotation speed n11(r/min) and unit flow rate Q11(m3The estimation formula of/s) is calculated and deduced in advance, a more reasonable basic parameter estimation method is creatively summarized for large and medium mixed-flow water turbines or mixed-flow water turbines with special requirements, new hydroelectric engineering requirements are better met, and powerful technical support is provided for the subsequent domestic and foreign hydroelectric engineering construction. And, the present invention is applicable regardless of the presence or absence of identical or similar water turbine models.
Detailed Description
The invention is further illustrated by the following examples.
The basic parameter statistical formula of the mixed-flow water turbine which is commonly adopted at present mainly comprises ①
Figure BDA0001332112270000032
②
Figure BDA0001332112270000041
③n11＝50+0.11ns，④
Figure BDA0001332112270000042
⑤Q11＝0.1134(ns/(50+0.11ns))2，⑥
Figure BDA0001332112270000043
The following equations (1) - (12) of the present invention and the commonly used statistical equations ① - ⑥ are applied to the sample data to obtain the error between the calculation result of each equation and the true value, and tables 1-5 are the comparison between several groups of sample data and the calculation error.
Table 1 several sets of sample data (turbine real parameters)
Figure BDA0001332112270000044
TABLE 2 comparison of the error of calculation of the formula of the present invention with the statistical formula commonly used at present (H)max≤100m)
Figure BDA0001332112270000045
TABLE 3 comparison of the error of calculation of the formula of the present invention with the currently commonly used statistical formula (100m < H)max≤200m)
Figure BDA0001332112270000046
TABLE 4 comparison of the error of calculation of the formula of the present invention with the currently commonly used statistical formula (200m < H)max≤300m)
Figure BDA0001332112270000047
Figure BDA0001332112270000051
TABLE 5 comparison of the error of calculation of the formula of the present invention with the statistical formula commonly used at present (H)max＞300m)
Figure BDA0001332112270000052
The calculation results in tables 2 to 5 show that the sum of squares of the errors obtained by the formulas (1) to (12) is minimum in each water head, namely the sum is optimal, and the method can be better applied to the selection of basic parameters of the mixed-flow water turbine in new hydropower engineering.
The foregoing describes the general principles and features of the present invention and, together with the general principles of the invention, further modifications and improvements thereto, may be made without departing from the spirit and scope of the invention as set forth in the appended claims.

Claims (3)

1. A method for estimating basic parameters of a mixed-flow water turbine is characterized by comprising the following steps:
a. determining the rated water head of the francis turbine to be estimated, wherein the rated water head is recorded as Hr；
b. Determining the maximum applied water head of the francis turbine to be estimated, wherein the maximum applied water head is recorded as HmaxAnd judging HmaxThe range in which it is located;
c. according to HmaxAnd (3) estimating the specific rotating speed by using a specific rotating speed estimation formula corresponding to the range, wherein the specific rotating speed is recorded as nsThe specific speed estimation formula is as follows:
when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure FDA0002401270600000011
when 100m is more than HmaxWhen the thickness is less than or equal to 200m, ns＝2191.5Hr -0.5007；
When 200m is more than HmaxWhen the particle size is less than or equal to 300m,
Figure FDA0002401270600000015
when H is presentmaxWhen larger than 300m, ns＝3609.2Hr -0.6189。
2. The francis turbine basic parameter estimation method according to claim 1The method of calculation, characterized in that it further comprises a step dmaxCorresponding range unit rotating speed estimation formula and n obtained in step csEstimating a unit rotational speed, said unit rotational speed being denoted as n11The unit speed estimation formula of the range is as follows:
when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure FDA0002401270600000012
when 100m is more than HmaxWhen the particle size is less than or equal to 200m,
Figure FDA0002401270600000013
when 200m is more than HmaxWhen the particle size is less than or equal to 300m, n11＝1.2874ns 0.7878；
When H is presentmaxWhen larger than 300m, n11＝37.207ns 0.1186。
3. A francis turbine basic parameter estimation method according to claim 1 or 2, which further comprises step emaxCorresponding range unit flow rate estimation formula and n obtained in step csEstimating the unit flow rate, said unit flow rate being denoted as Q11The unit flow rate estimation formula of the range is as follows:
when H is presentmaxWhen the particle size is less than or equal to 100m,
Figure FDA0002401270600000014
when 100m is more than HmaxWhen the grain size is less than or equal to 200m, Q11＝1.0642Ln(ns)-4.7812；
When 200m is more than HmaxWhen the grain size is less than or equal to 300m, Q11＝0.7821Ln(ns)-3.3718；
When H is presentmaxWhen larger than 300m, Q11＝0.3652Ln(ns)-1.4009。
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CN112067181B (en) * 2020-09-15 2021-08-31 中国电建集团成都勘测设计研究院有限公司 Method for calculating specific rotating speed of single-stage reversible mixed-flow pump turbine
CN113591254B (en) * 2021-09-01 2023-04-28 中国电建集团成都勘测设计研究院有限公司 Calculation method for runaway rotational speed of water turbine bucket

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