CN106096196A - A kind of single blade impeller slip coefficient computational methods in the range of full flow - Google Patents
A kind of single blade impeller slip coefficient computational methods in the range of full flow Download PDFInfo
- Publication number
- CN106096196A CN106096196A CN201610489722.7A CN201610489722A CN106096196A CN 106096196 A CN106096196 A CN 106096196A CN 201610489722 A CN201610489722 A CN 201610489722A CN 106096196 A CN106096196 A CN 106096196A
- Authority
- CN
- China
- Prior art keywords
- coefficient
- formula
- beta
- outlet
- impeller
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- 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
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Computer Hardware Design (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Microelectronics & Electronic Packaging (AREA)
- Structures Of Non-Positive Displacement Pumps (AREA)
Abstract
The invention discloses the single blade impeller slip coefficient computational methods in the range of a kind of full flow, process is: obtain coefficient h according to B ü semann test0And cmCurve, during to z=1, extracts the h under the different angle of outlet0And cmDiscrete data;Define according to Wilslicenus separation, by h0And cmDiscrete data is divided into 2 parts, carries out Multiple Non-linear Regression Analysis for independent variable obtain h with outlet blade angle and import and export radius ratio0And cmComputing formula, and substitute into B ü semann slip coefficient theory solution formula thus establish the computing formula of single blade impeller slip coefficient under design conditions;In the computing formula of design conditions, introduce the impact of very big lift and the full flow variation coefficient unsteady characteristic and flow to consider Procedure of Single-channel Pump, finally set up the solution formula of single blade impeller slip coefficient in the range of full flow.The present invention can be precisely calculated the slip coefficient under any angle of outlet in the range of single blade impeller full flow, also provides theoretical basis for foundation high accuracy Procedure of Single-channel Pump energy predicting model.
Description
Technical field
The invention belongs to fluid machinery design field, be specifically related to the single blade impeller slip system in the range of a kind of full flow
Number calculating method.
Background technology
Sliding phenomenon is the factor needing emphasis to consider in turbomachine (compressor, pump and steam turbine etc.) design process.Though
So B ü semann is deduced the Theory Solution of slip coefficient under design conditions based on two dimension potential flow theories, but the method solves multiple
Miscellaneous, it is impossible to practical implementation.Calculating slip coefficient subsequent to convenient, B ü semann gives theory by test and solves public affairs
Coefficient h in formula0And cmImport and export the change curve of radius ratio with the number of blade, outlet blade angle and blade, but this trial curve is only given
Go out blade exit angle beta2BIt is result when 5 °, 10 °, 20 °, 40 °, 60 ° and 90 °, therefore can not solve under any angle of outlet
Impeller slip coefficient, has significant limitation in actual applications.Although follow-up Wiesner and Stodola et al. is to slip system
Number solution formula have also been made relevant research and achieves certain achievement, but is only applicable to leaf through these achievements of verification experimental verification
The rotating machinery of sheet number z >=2, for rotating machinery that the number of blade is 1 inapplicable, when solving single blade impeller slip coefficient
Relatively large deviation is there is with result of the test.Therefore, in the urgent need to developing a kind of computational accuracy height and the single blade impeller of Practical
Slip coefficient computational methods.
Up to now, there is not yet the open of the Procedure of Single-channel Pump slip coefficient solution formula in the range of full flow and report, this
The bright single blade impeller slip coefficient computational methods provided in the range of a kind of full flow.
Summary of the invention
It is desirable to provide the single blade impeller slip coefficient computational methods in the range of a kind of full flow, the present invention is at B ü
On the basis of semann slip coefficient theory solution formula is analyzed and is concluded, it is proposed that single blade impeller sliding in the range of full flow
The solution formula of coefficient.
For reaching object above, by the following technical solutions:
The different outlet angle betas that B ü semannn test during z=1 is obtained2BLower coefficient h0And cmDiscrete data carry
Take, and according to the definition of Wilslicenus separation, the curve under 2 coefficient difference angles of outlet is divided into 2 parts;
With outlet blade angle and import and export radius ratio as independent variable, use Multiple Non-linear Regression Analysis respectively to h0And cm
Two parts of curve are fitted obtaining the computing formula of the two, and substitute into B ü semannn slip coefficient theory solution formula from
And set up the computing formula of single blade impeller slip coefficient under design conditions;
Under design conditions in the computing formula of slip coefficient, introduce very big lift and full flow variation coefficient to consider list
Runner pump unsteady characteristic and the impact of flow, thus finally set up the slip coefficient in the range of single blade impeller full flow and solve
Formula.
It specifically comprises the following steps that
1, B ü semannn during z=1 is tested the outlet angle beta obtained2BCoefficient h under 0~90 °0And cmExtract,
And according to the definition of Wilslicenus separation by the h under the different angles of outlet0And cmCurve is divided into 2 parts, horizontal component and curve
Part.
(A) coefficient h under the different angles of outlet that B ü semannn test during z=1 is obtained0And cmExtract, do respectively
Go out h0With R1/R2, cmWith R1/R2Graph of relation;
(B) define according to Wilslicenus separationBy under the difference angle of outlet
H0And cmCurve is divided into 2 parts such as level and curve;
2, radius ratio R is imported and exported with outlet blade angle and impeller1/R2For independent variable, Multiple Non-linear Regression Analysis is used to divide
Other to h0And cmTwo parts of curve are fitted obtaining the computing formula of the two, and substitute into B ü semannn slip coefficient theory and ask
Solution formula thus set up the computing formula of single blade impeller slip coefficient under design conditions.
(A) to R1/R2When=0, export angle beta2BAt 0~90 ° of lower h0Discrete data extract, and define R1/R2=0
Time h0For h0_max, use nonlinear regression analysis to h with the angle of outlet for independent variable0_maxIt is fitted, i.e. establishes h0_max's
Mathematic(al) representation.
(B) h is set up0And cmThe mathematical model of first paragraph curve, h0-R1/R2And cm-R1/R2The first paragraph of curve chart is one
Horizontal line section, and h0And cmEqual, it is h0_max, then R can be obtained1/R2<RεlimitTime h0And cmMathematic(al) representation:
h0=cm=h0_max (2)
(C) import and export radius ratio as independent variable with outlet blade angle and impeller, use Multiple Non-linear Regression Analysis to h0-
R1/R2And cm-R1/R2The Part II of curve chart is fitted, then obtain R1/R2>RεlimitTime, h0And cmCurve Part II
Mathematic(al) representation;
N=0.5sin β2B 2-sinβ2B+1.2 (6)
Wherein: m and n is respectively h0-R1/R2And cm-R1/R2The convex-concave coefficient of second segment curve;
(D) formula (1) and (2) or (3) and (5) are substituted into following B ü semannn slip coefficient theory solution formula,
Set up the computing formula of single blade impeller slip coefficient under design conditions.
In formula: φthFor theoretical flow coefficient, for impeller outlet axis plane velocity vm2With peripheral speed u2Ratio, i.e. φth=
vm2/u2。
3, increase very big lift in the solution formula of slip coefficient represents that item is to consider the impact of unsteady characteristic.
(A) h is understood by impeller lift computing formula (8) under the B limited number of blade of ü semann0When taking maximum, impeller lift is maximum, i.e.
h0It is taken as h0_maxTime impeller lift maximum.
Wherein,Meansigma methods for impeller outlet axis plane velocity;HthFor theoretical head;
Therefore by the h by formula (7) right side molecule Section 10Use h0_maxReplace the impact considering lift maximum,
Obtain consider unsteady characteristic time design conditions under single blade impeller slip coefficient solution formula:
In formula:
τ2For blade exit excretion coefficient,Wherein su2For the circumferential thickness of impeller outlet blade, D2For leaf
Wheel outlet diameter.
(B) based on formula (9), according to the test data of single channel centrifugal pump, with blade exit angle beta2BIt is from becoming with flow-rate ratio
Amount, uses Multiple Non-linear Regression Analysis to set up the computing formula of single blade impeller full flow slip coefficient:
In formula: γ is full flow variation coefficient, computing formula is
Wherein:For discharge coefficient,For the discharge coefficient under optimum operating condition.
It is an advantage of the current invention that:
1, method based on Multiple Non-linear Regression Analysis, establishes h0And cmMathematics computing model, it is achieved that arbitrarily leaf
Under the sheet angle of outlet, single blade impeller slip coefficient solves;
2, the single blade impeller slip coefficient computing formula set up considers the impact of flow, can accurately calculate single channel
Slip coefficient in the range of centrifugal pump full flow, relative to original computation model, existing single blade impeller slip coefficient calculates
The calculating deviation of model only has 5.05%, fully meets engineer applied requirement;
3, the single blade impeller slip coefficient computational methods set up are for setting up single channel centrifugal pump energy characteristics prediction mould
Type provides the foundation, thus can realize single channel centrifugal pump multi-state Hydraulic Optimizing Design.
Accompanying drawing explanation
Fig. 1 is a kind of flow chart based on the single blade impeller slip coefficient computational methods in the range of full flow.
B ü semann coefficient h when Fig. 2 is z=10With R1/R2Change curve.
B ü semann coefficient c when Fig. 3 is z=1mWith R1/R2Change curve.
H when Fig. 4 is z=10_maxWith outlet angle beta2BChange curve.
Fig. 5 is result of calculation and the result of the test of impeller slip coefficient.
Detailed description of the invention
Embodiment:
When Fig. 2 is z=1, export angle beta2BIt is 5 °, 10 °, 20 °, 40 °, 60 °, the coefficient h of 90 °0Extract, make respectively
h0With R1/R2Graph of relation;
Angle beta is exported when Fig. 3 is z=12BIt is 5 °, 10 °, 20 °, 40 °, 60 °, the coefficient c of 90 °mExtract, make respectively
cmWith R1/R2Graph of relation;
When Fig. 4 is z=1, to R1/R2H when=00Discrete data extract, and define h now0For h0_max, make
H0_max-β2BGraph of a relation;
With a specific speed nsAs a example by the Procedure of Single-channel Pump of=140, its design conditions performance parameter is: flow Qd=220m3/
H, lift Hd=20m, rotating speed n=1474r/min;Main structure parameters is: impeller inlet diameter Dj=125mm, impeller outlet are straight
Footpath D2=300mm, blade exit angle beta2B=16 °, blade exit width b2=100mm.It is respectively adopted formula (9) and (10) to this
The slip coefficient of impeller of pump calculates, and uses experimental test result to calculate slip coefficient, wherein the calculating knot of formula (9) simultaneously
Fruit is not for consider the slip coefficient μ that changes in flow rate affectsth, the result of calculation of formula (10) is to consider the sliding of changes in flow rate impact
Coefficient μ.Result of calculation and result of the test are shown in that Fig. 5, Fig. 5 are μ-flow-rate ratio q* graph of a relation, q*=Q/Qopt, Q is under different operating mode
Flow, QoptFor the flow under optimum operating condition.
As seen from Figure 5, slip coefficient is gradually reduced along with flow increases, sliding in the range of design conditions and efficiently district
Coefficient is in the range of 0.4~0.58;Do not consider the slip coefficient μ that changes in flow rate affectsthVery big with test gap, maximum deviation
It is 47.2%;Add the slip coefficient μ after slip coefficient full flow variation coefficient γ, with test value, there is preferable concordance,
Large deviation is only 5.05%.
Therefore the single blade impeller slip coefficient computational methods that the present invention sets up can accurately calculate single blade impeller and entirely flow
Slip coefficient in weight range.
Claims (4)
1. the single blade impeller slip coefficient computational methods in the range of a full flow, it is characterised in that comprise the steps of
(1) B ü semann during z=1 is tested the outlet angle beta obtained2BCoefficient h under 0~90 °0And cmExtract, and foundation
The definition of Wilslicenus separation is by the h under the different angles of outlet0And cmCurve is divided into 2 parts, horizontal component and curved portion;
(2) with outlet blade angle and import and export radius ratio R1/R2For independent variable, use Multiple Non-linear Regression Analysis respectively to h0
And cmTwo parts of curve are fitted obtaining the computing formula of the two, and substitute into B ü semann slip coefficient theory and solve public affairs
Formula, sets up the computing formula of single blade impeller slip coefficient under design conditions;
(3), under design conditions in the computing formula of slip coefficient, very big lift and full flow variation coefficient are introduced to consider list
The unsteady characteristic of runner pump and the impact of flow, finally set up the slip coefficient in the range of single blade impeller full flow and solve public affairs
Formula.
2., according to the single blade impeller slip coefficient computational methods in the range of a kind of full flow described in claim 1, it is special
Levy and be: in described step (1), B ü semann during z=1 is tested the outlet angle beta obtained2BCoefficient h under 0~90 °0And cm
Extract, and according to the definition of Wilslicenus separation by the h under the different angles of outlet0And cmCurve is divided into 2 parts, horizontal part
Dividing and curved portion, it specifically comprises the following steps that
(A) B ü semann during z=1 is tested the outlet angle beta obtained2BCoefficient h under 0~90 °0And cmExtract, do respectively
Go out h0With R1/R2、cmWith R1/R2Graph of relation;
(B) define according to Wilslicenus separationBy the h under the different angles of outlet0
And cmCurve is divided into 2 parts such as level and curve.
3., according to the single blade impeller slip coefficient computational methods in the range of a kind of full flow described in claim 1, it is special
Levy and be: in described step (2), with outlet blade angle and import and export radius ratio R1/R2For independent variable, nonlinear multivariable is used to return
Return analysis respectively to h0And cmTwo parts of curve are fitted obtaining the computing formula of the two, and substitute into B ü semann slip system
Mathematics opinion solution formula, sets up the computing formula of single blade impeller slip coefficient under design conditions, and it specifically comprises the following steps that
(A) to R1/R2To outlet angle beta when=02BAt 0~90 ° of lower h0Discrete data extract, and define h now0For
h0_max, use nonlinear regression analysis to h with the angle of outlet for independent variable0_maxIt is fitted, i.e. establishes h0_maxMathematical expression
Formula:
(B) h is set up0And cmThe mathematical model of first paragraph curve, h0-R1/R2And cm-R1/R2The first paragraph of curve chart is horizontal line
Section, and h0And cmEqual, it is h0_max, then R can be obtained1/R2<RεlimitTime h0And cmMathematic(al) representation:
h0=cm=h0_max (2)
(C) import and export radius ratio as independent variable with outlet blade angle and impeller, use Multiple Non-linear Regression Analysis to h0-R1/R2
And cm-R1/R2The Part II of curve chart is fitted, then obtain R1/R2>RεlimitTime, h0And cmThe mathematics of curve Part II
Expression formula;
N=0.5sin β2B 2-sinβ2B+1.2 (6)
Wherein: m and n is respectively h0-R1/R2And cm-R1/R2The convex-concave coefficient of second segment curve;
(D) formula (1) and (2) or (3) and (5) substituting into following B ü semannn slip coefficient theory solution formula, foundation sets
The mathematic(al) representation of single blade impeller slip coefficient under meter operating mode:
In formula: φthFor theoretical flow coefficient, for impeller outlet axis plane velocity vm2With peripheral speed u2Ratio, i.e. φth=vm2/u2。
4., according to the single blade impeller slip coefficient computational methods in the range of a kind of full flow described in claim 1, it is special
Levy and be: in described step (3), the computing formula of design conditions introduces very big lift and flow-rate ratio to consider Procedure of Single-channel Pump
Unsteady characteristic and the impact of flow, finally establish single blade impeller slip coefficient in the range of full flow solves public affairs
Formula, it specifically comprises the following steps that
(A) the impeller lift computing formula under the limited number of blade of B ü semann:
Wherein,Meansigma methods for impeller outlet axis plane velocity;HthFor theoretical head;
H is understood by formula (8)0Take maximum impeller lift constantly maximum, i.e. h0It is taken as h0_maxTime impeller lift maximum;
Therefore can be by the h by formula (7) right side molecule Section 10Use h0_maxReplace, to consider the impact of lift maximum,
Thus obtain considering during unsteady characteristic the solution formula of single blade impeller slip coefficient under design conditions:
In formula: τ2Excretion coefficient is exported for impeller blade,Wherein su2Circumferential thickness for impeller outlet blade;D2
For impeller outlet diameter;
(B) based on formula (9), according to the performance test data of single channel centrifugal pump, with blade exit angle beta2BIt is from becoming with flow-rate ratio
Amount, uses Multiple Non-linear Regression Analysis to set up slip coefficient solution formula in the range of single blade impeller full flow:
In formula: γ is flow modificatory coefficient
Wherein:For discharge coefficient,For optimum operating condition down-off.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201610489722.7A CN106096196A (en) | 2016-06-28 | 2016-06-28 | A kind of single blade impeller slip coefficient computational methods in the range of full flow |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201610489722.7A CN106096196A (en) | 2016-06-28 | 2016-06-28 | A kind of single blade impeller slip coefficient computational methods in the range of full flow |
Publications (1)
Publication Number | Publication Date |
---|---|
CN106096196A true CN106096196A (en) | 2016-11-09 |
Family
ID=57214353
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201610489722.7A Pending CN106096196A (en) | 2016-06-28 | 2016-06-28 | A kind of single blade impeller slip coefficient computational methods in the range of full flow |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN106096196A (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN107102163A (en) * | 2017-04-26 | 2017-08-29 | 江苏大学 | A kind of pump endoparticle sliding velocity computational methods based on stream calculation in clear water |
CN110336830A (en) * | 2019-07-17 | 2019-10-15 | 山东大学 | A kind of ddos attack detection system based on software defined network |
CN111680372A (en) * | 2020-06-10 | 2020-09-18 | 大连海事大学 | One-dimensional calculation method considering working capacity of centrifugal fan impeller in natural prerotation |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN103994100A (en) * | 2014-05-07 | 2014-08-20 | 江苏大学 | Design method for spiral single-channel non-blocking centrifugal pump impeller |
CN104533829A (en) * | 2014-11-26 | 2015-04-22 | 江苏大学 | Diagonal flow pump impeller hydraulic design method |
KR101629005B1 (en) * | 2015-03-27 | 2016-06-10 | 한국생산기술연구원 | optimal design method of single channel pump impeller, single channel pump impeller and centrifugal pump designed by the method |
-
2016
- 2016-06-28 CN CN201610489722.7A patent/CN106096196A/en active Pending
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN103994100A (en) * | 2014-05-07 | 2014-08-20 | 江苏大学 | Design method for spiral single-channel non-blocking centrifugal pump impeller |
CN104533829A (en) * | 2014-11-26 | 2015-04-22 | 江苏大学 | Diagonal flow pump impeller hydraulic design method |
KR101629005B1 (en) * | 2015-03-27 | 2016-06-10 | 한국생산기술연구원 | optimal design method of single channel pump impeller, single channel pump impeller and centrifugal pump designed by the method |
Non-Patent Citations (1)
Title |
---|
丁剑: ""单流道离心泵非定常特性及水力设计方法研究", 《万方数据知识服务平台》 * |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN107102163A (en) * | 2017-04-26 | 2017-08-29 | 江苏大学 | A kind of pump endoparticle sliding velocity computational methods based on stream calculation in clear water |
CN107102163B (en) * | 2017-04-26 | 2019-08-27 | 江苏大学 | A kind of pump endoparticle sliding velocity calculation method based on stream calculation in clear water |
CN110336830A (en) * | 2019-07-17 | 2019-10-15 | 山东大学 | A kind of ddos attack detection system based on software defined network |
CN111680372A (en) * | 2020-06-10 | 2020-09-18 | 大连海事大学 | One-dimensional calculation method considering working capacity of centrifugal fan impeller in natural prerotation |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN104298869B (en) | A kind of fluid structurecoupling Numerical prediction method of elastic hydrofoil | |
Wu et al. | Investigation of pre-stall behavior in an axial compressor rotor—Part I: Unsteadiness of tip clearance flow | |
CN105868497B (en) | Tailwater tunnel Water turbine governing system simulation modeling method and model are risen in a kind of change of band | |
CN105956350B (en) | Modeling method for water exchange system of pump storage group | |
CN103047173B (en) | Method for obtaining high-efficiency low-noise impeller of centrifugal pump volute | |
Guo et al. | Analysis of viscosity effect on turbine flowmeter performance based on experiments and CFD simulations | |
CN106096196A (en) | A kind of single blade impeller slip coefficient computational methods in the range of full flow | |
Adhikari et al. | Computational analysis of part-load flow control for crossflow hydro-turbines | |
CN104636542A (en) | Method for predicting energy performance of pump through adjustable guide vane on basis of CFD | |
CN106372296B (en) | A kind of hydraulic turbine multimachine differential equation calculation method with common conduit | |
CN111400941A (en) | Numerical prediction method for internal reflux and reflux vortex cavitation of vane pump | |
CN111695269A (en) | Multi-time-interval electricity-gas comprehensive energy system state estimation method, system and device | |
Jakobsen et al. | CFD simulations of transient load change on a high head Francis turbine | |
CN102663241A (en) | Analog calculation method for transient power of water turbine under elastic water attack | |
CN114186506A (en) | Prediction method for full characteristic curve of centrifugal pump | |
CN104500150A (en) | Piecewise linear model for actuating mechanism of turbine speed controller and parameter acquisition method | |
Antonsen | Unsteady flow in wicket gate and runner with focus on static and dynamic load on runner | |
Shojaeefard et al. | Studying the impact of impeller geometrical parameters on the high-efficiency working range of pump as turbine (PAT) installed in the water distribution network | |
CN116561986A (en) | Pumped storage power station hydraulic oscillation analysis method, system and medium based on complex frequency domain equivalent circuit model | |
CN111625987B (en) | Turbulence model generation method based on deep learning | |
Fernando et al. | A comparative study between artificial neural network and linear regression for optimizing a hinged blade cross axis turbine | |
INGRANATA | Development, implementation and validation of a hydropower plant model with Francis turbine | |
Chen et al. | Optimization of two-stage closure law of turbine wicket gates and its application | |
He et al. | Nonlinear Correction and Temperature Compensation Method of Turbine Flowmeter Based on Neural Network | |
Dunca et al. | Discharge evaluation from pressure measurements by a genetic algorithm based method |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
RJ01 | Rejection of invention patent application after publication |
Application publication date: 20161109 |
|
RJ01 | Rejection of invention patent application after publication |