CN106096196A - A kind of single blade impeller slip coefficient computational methods in the range of full flow - Google Patents

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 c_mCurve, during to z=1, extracts the h under the different angle of outlet₀And c_mDiscrete data；Define according to Wilslicenus separation, by h₀And c_mDiscrete 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 c_mComputing 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

A kind of single blade impeller slip coefficient computational methods in the range of full flow

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 c_mImport 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 beta_2BIt 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 obtained_2BLower coefficient h₀And c_mDiscrete 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 c_m 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 obtained_2BCoefficient h under 0～90 °₀And c_mExtract, And according to the definition of Wilslicenus separation by the h under the different angles of outlet₀And c_mCurve 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 c_mExtract, do respectively Go out h₀With R₁/R₂, c_mWith R₁/R₂Graph of relation；

(B) define according to Wilslicenus separationBy under the difference angle of outlet H₀And c_mCurve 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 c_mTwo 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 beta_2BAt 0～90 ° of lower h₀Discrete data extract, and define R₁/R₂=0 Time h₀For h_{0_max}, use nonlinear regression analysis to h with the angle of outlet for independent variable_{0_max}It is fitted, i.e. establishes h_{0_max}'s Mathematic(al) representation.

$h_{0\_max}=1-\frac{1}{1+\[2-(0.5-16{\mathrm{sin\β}}_{2B}+10.5{\sin }^2{\mathrm{\β}}_{2B}){\mathrm{sin\β}}_{2B}\]\left(\frac{1}{4{\mathrm{\πsin\β}}_{2B}}\right)}---\left(1\right)$

(B) h is set up₀And c_mThe mathematical model of first paragraph curve, h₀-R₁/R₂And c_m-R₁/R₂The first paragraph of curve chart is one Horizontal line section, and h₀And c_mEqual, it is h_{0_max}, then R can be obtained₁/R₂<Rε_limitTime h₀And c_mMathematic(al) representation:

h₀=c_m=h_{0_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 c_m-R₁/R₂The Part II of curve chart is fitted, then obtain R₁/R₂>Rε_limitTime, h₀And c_mCurve Part II Mathematic(al) representation；

$h_0=(1-\frac{1}{1+\&lsqb;2-(0.5-16{\mathrm{sin\&beta;}}_{2B}+10.5{\sin }^2{\mathrm{\&beta;}}_{2B}){\mathrm{sin\&beta;}}_{2B}\&rsqb;\left(\frac{1}{4{\mathrm{\&pi;sin\&beta;}}_{2B}}\right)})\&lsqb;1-{\left(\frac{R_1/R_2-{\mathrm{R\&epsiv;}}_{\lim it}}{1-{\mathrm{R\&epsiv;}}_{\lim it}}\right)}^m\&rsqb;---\left(3\right)$

$m=0.02+\frac{1}{\frac{1.3}{2{\mathrm{\&pi;sin\&beta;}}_{2B}}+\frac{1.3}{2\mathrm{\&pi;}}{\mathrm{sin\&beta;}}_{2B}+(1-\frac{3.8}{2\mathrm{\&pi;}})}---\left(4\right)$

$c_m=1-\left(\frac{1}{1+\&lsqb;2-(0.5-16{\mathrm{sin\&beta;}}_{2B}+10.5{\sin }^2{\mathrm{\&beta;}}_{2B}){\mathrm{sin\&beta;}}_{2B}\&rsqb;\left(\frac{1}{4{\mathrm{\&pi;sin\&beta;}}_{2B}}\right)}\right)\&lsqb;1-{\left(\frac{R_1/R_2-{\mathrm{R\&epsiv;}}_{\lim it}}{1-{\mathrm{R\&epsiv;}}_{\lim it}}\right)}^n\&rsqb;---\left(5\right)$

N=0.5sin β_2B ²-sinβ_2B+1.2 (6)

Wherein: m and n is respectively h₀-R₁/R₂And c_m-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: φ_thFor theoretical flow coefficient, for impeller outlet axis plane velocity v_m2With peripheral speed u₂Ratio, i.e. φ_th= v_m2/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 h_{0_max}Time impeller lift maximum.

$H_{th}=h_0\&times;\frac{{u_2}^2}{g}-\frac{h_0}{c_m}\&times;\frac{u_2\&times;\stackrel{\&OverBar;}{v_{m2}}}{g}{\mathrm{cot\&beta;}}_{2B}---\left(8\right)$

Wherein,Meansigma methods for impeller outlet axis plane velocity；H_thFor theoretical head；

Therefore by the h by formula (7) right side molecule Section 1₀Use h_{0_max}Replace 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 s_u2For 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 beta_2BIt 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 c_mMathematics 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=1_mWith R₁/R₂Change curve.

H when Fig. 4 is z=1_{0_max}With outlet angle beta_2BChange 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 beta_2BIt 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=1_2BIt is 5 °, 10 °, 20 °, 40 °, 60 °, the coefficient c of 90 °_mExtract, make respectively c_mWith R₁/R₂Graph of relation；

When Fig. 4 is z=1, to R₁/R₂H when=0₀Discrete data extract, and define h now₀For h_{0_max}, make H_{0_max}-β_2BGraph of a relation；

With a specific speed n_sAs a example by the Procedure of Single-channel Pump of=140, its design conditions performance parameter is: flow Q_d=220m³/ H, lift H_d=20m, rotating speed n=1474r/min；Main structure parameters is: impeller inlet diameter D_j=125mm, impeller outlet are straight Footpath D₂=300mm, blade exit angle beta_2B=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 affects_th, 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/Q_opt, Q is under different operating mode Flow, Q_optFor 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 affects_thVery 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 obtained_2BCoefficient h under 0～90 °₀And c_mExtract, and foundation The definition of Wilslicenus separation is by the h under the different angles of outlet₀And c_mCurve 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 c_mTwo 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 obtained_2BCoefficient h under 0～90 °₀And c_m Extract, and according to the definition of Wilslicenus separation by the h under the different angles of outlet₀And c_mCurve 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 obtained_2BCoefficient h under 0～90 °₀And c_mExtract, do respectively Go out h₀With R₁/R₂、c_mWith R₁/R₂Graph of relation；

(B) define according to Wilslicenus separationBy the h under the different angles of outlet₀ And c_mCurve 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 c_mTwo 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=0_2BAt 0～90 ° of lower h₀Discrete data extract, and define h now₀For h_{0_max}, use nonlinear regression analysis to h with the angle of outlet for independent variable_{0_max}It is fitted, i.e. establishes h_{0_max}Mathematical expression Formula:

$h_{0\_max}=1-\frac{1}{1+\&lsqb;2-(0.5-16{\mathrm{sin\&beta;}}_{2B}+10.5{\sin }^2{\mathrm{\&beta;}}_{2B}){\mathrm{sin\&beta;}}_{2B}\&rsqb;\left(\frac{1}{4{\mathrm{\&pi;sin\&beta;}}_{2B}}\right)}---\left(1\right)$

(B) h is set up₀And c_mThe mathematical model of first paragraph curve, h₀-R₁/R₂And c_m-R₁/R₂The first paragraph of curve chart is horizontal line Section, and h₀And c_mEqual, it is h_{0_max}, then R can be obtained₁/R₂<Rε_limitTime h₀And c_mMathematic(al) representation:

h₀=c_m=h_{0_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 c_m-R₁/R₂The Part II of curve chart is fitted, then obtain R₁/R₂>Rε_limitTime, h₀And c_mThe mathematics of curve Part II Expression formula；

$h_0=(1-\frac{1}{1+\&lsqb;2-(0.5-16{\mathrm{sin\&beta;}}_{2B}+10.5{\sin }^2{\mathrm{\&beta;}}_{2B}){\mathrm{sin\&beta;}}_{2B}\&rsqb;\left(\frac{1}{4{\mathrm{\&pi;sin\&beta;}}_{2B}}\right)})\&lsqb;1-{\left(\frac{R_1/R_2-{\mathrm{R\&epsiv;}}_{\lim it}}{1-{\mathrm{R\&epsiv;}}_{\lim it}}\right)}^m\&rsqb;---\left(3\right)$

$m=0.02+\frac{1}{\frac{1.3}{2{\mathrm{\&pi;sin\&beta;}}_{2B}}+\frac{1.3}{2\mathrm{\&pi;}}{\mathrm{sin\&beta;}}_{2B}+(1-\frac{3.8}{2\mathrm{\&pi;}})}---\left(4\right)$

$c_m=1-\left(\frac{1}{1+\&lsqb;2-(0.5-16{\mathrm{sin\&beta;}}_{2B}+10.5{\sin }^2{\mathrm{\&beta;}}_{2B}){\mathrm{sin\&beta;}}_{2B}\&rsqb;\left(\frac{1}{4{\mathrm{\&pi;sin\&beta;}}_{2B}}\right)}\right)\&lsqb;1-{\left(\frac{R_1/R_2-{\mathrm{R\&epsiv;}}_{\lim it}}{1-{\mathrm{R\&epsiv;}}_{\lim it}}\right)}^n\&rsqb;---\left(5\right)$

N=0.5sin β_2B ²-sinβ_2B+1.2 (6)

Wherein: m and n is respectively h₀-R₁/R₂And c_m-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: φ_thFor theoretical flow coefficient, for impeller outlet axis plane velocity v_m2With peripheral speed u₂Ratio, i.e. φ_th=v_m2/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:

$H_{th}=h_0\&times;\frac{{u_2}^2}{g}-\frac{h_0}{c_m}\&times;\frac{u_2\&times;\stackrel{\&OverBar;}{v_{m2}}}{g}{\mathrm{cot\&beta;}}_{2B}---\left(8\right)$

Wherein,Meansigma methods for impeller outlet axis plane velocity；H_thFor theoretical head；

H is understood by formula (8)₀Take maximum impeller lift constantly maximum, i.e. h₀It is taken as h_{0_max}Time impeller lift maximum；

Therefore can be by the h by formula (7) right side molecule Section 1₀Use h_{0_max}Replace, 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 s_u2Circumferential 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 beta_2BIt 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.