CN104895795A - Multi-working condition hydraulic design method of centrifugal pump - Google Patents

Abstract

The invention provides a multi-working condition hydraulic design method of a centrifugal pump. The core concepts are that control of performance curves are achieved in two steps: firstly performance curves from zero flow to design condition flows are achieved by controlling the ratio Hr of the shut-off head and the design head; and secondly performance curves from the design condition flows to maximum flows are achieved by controlling the ratio Qr of the maximum flow and the design flow. For the method for controlling the Hr, in a certain range of specific speed, for different numbers of impeller blades and impeller exit arranging angles, according to the value of the specific speed, diameters and widths of current impeller exits are corrected and corresponding multiple terms of relation expressions are combined, wherein the specific speed is a known quantity, thereby achieving hydraulic design. For the method for controlling the Qr, in a certain range of specific speed, for different numbers of impeller blades and impeller exit arranging angles, according to the value of the specific speed, by fully considering the ratio of inter-blade total area of impeller exits and complement area of a pumping chamber, corresponding multiple terms of relation expressions are united, wherein the specific speed is a known quantity, thereby achieving hydraulic design.

Description

A kind of centrifugal pump multi-operating mode Hydraulic Design Method

Technical field

The present invention relates to a kind of centrifugal pump Hydraulic Design Method, particularly a kind of centrifugal pump multi-operating mode Hydraulic Design Method.

Background technique

At present, the high-efficiency hydraulic design method of Centrifugal Pumps in China, still theoretical based on velocity-coefficient method and similar Design, adopt the theoretical method combined with experience, the coefficient in most of formula is all rule of thumb to certain limit more, cannot choosing coefficient exactly; Or some coefficient needs to be selected by chart.Therefore, the selectable blindness design of band easily causes the uncertainty of water-power performance parameter like this.

Multi-operating mode Hydraulic Design Method has had some scholars or engineer to study, the main contents of its research mainly contain several types: one carries out multi-operating mode the Hydraulic Design by existing CFD software and algorithm software, its major character designs by software, lacks engineer applied; Two is the multi-operating mode the Hydraulic Designs for multistage pump, and its major character is undertaken combining by different hydraulic model and reaches the object of multi-operating mode the Hydraulic Design, and its shortcoming is mainly for the multi-operating mode the Hydraulic Design of multistage pump.

At present, mainly rely on experience design to the multi-operating mode Hydraulic Design Method of single stage centrifugal pump, its design result, with a large amount of unpredictability, therefore, is carried out controlled multi-operating mode the Hydraulic Design to centrifugal pump and is quite necessary.

Summary of the invention

For solving existing centrifugal pump when carrying out the Hydraulic Design, cannot accurately control performance curve Changing Pattern and do not reach the object of multi-operating mode the Hydraulic Design, the invention provides a kind of controllable centrifugal pump multi-operating mode Hydraulic Design Method.Essential core thought of the present invention is: the control of performance curve be divided into two stages to realize, one be from zero delivery to design conditions flow between performance curve mainly through controlling to close the ratio H of dead point lift and rated lift _rrealize; Two is mainly through controlling the ratio Q of peak rate of flow and design discharge from the performance curve between design conditions flow and peak rate of flow _rrealize.

Control H _rmethod mainly within the scope of certain specific speed, for different impeller blade number and impeller outlet laying angle, according to the size of specific speed, on basis to existing impeller outlet diameter, impeller outlet width correction, the corresponding many-termed relation formula taking specific speed as known quantity by simultaneous realizes the Hydraulic Design requirement; Control Q _rmethod mainly within the scope of certain specific speed, for different impeller blade numbers and blade angle, according to the size of specific speed, mend on the basis of area ratio after the gross area and pumping chamber between impeller outlet blade taking into full account, the corresponding many-termed relation formula taking specific speed as known quantity by simultaneous realizes the Hydraulic Design requirement.

Not only improve impeller internal mobility status with the impeller of the present invention's design, ensure that centrifugal pump is when operating point for design is constant, by control H _r, Q _rrealize the control to performance curve, finally realize the object of multi-operating mode the Hydraulic Design.Realize that above-mentioned purpose adopts technological scheme:

1. specific speed n _s, its formula is as follows:

$n_s=3.65n\frac{\sqrt{Q_d}}{{H_d}^{0.75}}$

In formula:

N _s-specific speed;

Q _d-operating point for design flow, cube meter per second;

N-wheel speed, rev/min;

H _d-operating point for design lift, rice;

2. close the ratio H of dead point lift and rated lift _r, its formula is as follows:

$H_r=\left\{\begin{array}{c}3\×{10}^{-9}{n_s}^5-1\×{10}^{-6}{n_s}^4-0.010{n_s}^2+0.796n_s+0.222(Z=3,{\mathrm{\β}}_2=17,n_s\≤130);\\ 5\×{10}^{-10}{n_s}^5-3\×{10}^{-7}{n_s}^4+5\×{10}^{-5}{n_s}^3-0.005{n_s}^2+0.560n_s+0.071(Z=4,{\mathrm{\β}}_2=20,n_s\≤170);\\ 3\×{10}^{-10}{n_s}^5-2\×{10}^{-7}{n_s}^4+3\×{10}^{-5}{n_s}^3-0.003{n_s}^2+0.427n_s+0.160(Z=5,{\mathrm{\β}}_2=23,n_s\≤195);\\ 6\×{10}^{-11}{n_s}^5-6\×{10}^{-8}{n_s}^4+2\×{10}^{-5}{n_s}^3-0.003{n_s}^2+0.372n_s+0.094(Z=6,{\mathrm{\β}}_2=25,n_s\≤220);\\ 2\×{10}^{-11}{n_s}^5-2\×{10}^{-8}{n_s}^4+1\×{10}^{-5}{n_s}^3-0.002{n_s}^2+0.292n_s+0.042(Z=7,{\mathrm{\β}}_2=27,n_s\≤230);\\ 4\×{10}^{-11}{n_s}^5-4\×{10}^{-8}{n_s}^4+1\×{10}^{-5}{n_s}^3-0.002{n_s}^2+0.266n_s-0.086(Z=8,{\mathrm{\β}}_2=28,n_s\≤240);\end{array}\right.$

In formula:

H _rthe ratio of-pass dead point lift and rated lift,

H _g-close dead point lift, rice;

H _d-operating point for design lift, rice;

β ₂-impeller outlet angle, °;

N _s-specific speed;

The number of blade of Z-impeller, sheet;

3. area ratio Y, its formula is as follows:

(a) when number of blade Z be 4 ~ 6, b ₂≤ b _2d≤ 1.1b ₂time;

$Y=\left\{\begin{array}{c}0.009n_s+0.035(50\%\≤Q_r\≤60\%,n_s\≤170);\\ 0.007n_s(40\%\≤Q_r\≤50\%,n_s\≤220);\\ 0.005n_s-0.011(30\%\≤Q_r\≤40\%,n_s\≤280);\end{array}\right.$

(b) when number of blade Z be 7 ~ 9,0.9b ₂≤ b _2d≤ b ₂time;

$Y=\left\{\begin{array}{c}0.009n_s+0.035(40\%\≤Q_r\≤50\%,n_s\≤170);\\ 0.007n_s(30\%\≤Q_r\≤40\%,n_s\≤220);\\ 0.005n_s-0.011(20\%\≤Q_r\≤30\%,n_s\≤280);\end{array}\right.$

In formula:

Y-area ratio;

N _s-specific speed;

Q _rthe ratio of-peak rate of flow and design discharge,

Q _d-operating point for design flow, cube meter per second;

Q _b-peak rate of flow, according to designing requirement according to (0.4 ~ 0.6) H _dcorresponding flow, cube meter per second;

4. impeller inlet diameter D ₁, its formula is as follows:

$D_1=k_1\sqrt[3]{Q_d/n}$

In formula:

D ₁-impeller inlet diameter, rice;

Q _d-operating point for design flow, cube meter per second;

N-wheel speed, rev/min;

K ₁-impeller inlet correction factor, k ₁=0.13C ^0.513;

C-cavitation specific speed, $C=\frac{5.62n\sqrt{Q_d}}{\mathrm{NPS}{H}_r^{0.75}};$

Q _dthe flow of-design conditions, cube meter per second;

NPSH _r-necessary NPSH, rice;

5. impeller outlet diameter D ₂, its formula is as follows:

$D_2=\frac{84.7k_{u2}{H_d}^{0.5}}{n}$

In formula:

D ₂-impeller outlet diameter, rice;

H _d-operating point for design lift, rice;

N-wheel speed, rev/min;

K _u2-outlet peripheral velocity coefficient;

6. export peripheral velocity coefficient k _u2, its formula is as follows:

$k_{u2}=\left\{\begin{array}{c}5\×{10}^{-12}{n_s}^3-2\×{10}^{-9}{n_s}^2+0.001n_s+0.975,Z(3-4);\\ 5\×{10}^{-12}{n_s}^3-2\×{10}^{-9}{n_s}^2+0.001n_s+0.935,Z(5-6);\\ 5\×{10}^{-12}{n_s}^3-2\×{10}^{-9}{n_s}^2+0.001n_s+0.910,Z(7-8);\end{array}\right.$

In formula:

K _u2-outlet peripheral velocity coefficient;

N _s-specific speed;

The number of blade of Z-impeller, sheet;

7. impeller outlet width calculated value b ₂, its formula is as follows:

$b_2=k_{b2}\sqrt{\frac{k_{m2}{Q}_d}{\mathrm{\π}{v}_{m2}}}$

In formula:

B ₂-impeller outlet width calculated value, rice;

K _b2-impeller outlet width correction factor, k _b2=5.798n _s ^-0.35;

Q _d-operating point for design flow, cube meter per second;

V _m2the vertical component of-impeller outlet absolute velocity, meter per second;

K _m2-outlet axis plane velocity coefficient;

8. export axis plane velocity coefficient k _m2, its formula is as follows:

$k_{m2}=\left\{\begin{array}{c}-8\×{10}^{-11}{n_s}^4+5\×{10}^{-8}{n_s}^3-1\×{10}^{-5}{n_s}^2+0.002n_s-0.015,Z(3-4);\\ -4\×{10}^{-11}{n_s}^4+3\×{10}^{-8}{n_s}^3-8\×{10}^{-6}{n_s}^2+0.001n_s-0.002,Z(5-6);\\ 3\×{10}^{-12}{n_s}^4-2\×{10}^{-9}{n_s}^3-1\×{10}^{-6}{n_s}^2+0.017,Z(7-8);\end{array}\right.$

In formula:

K _m2-outlet axis plane velocity coefficient;

N _s-specific speed;

The number of blade of Z-impeller, sheet;

9. spiral case eighth section area F ₃its formula is as follows:

F ₃＝Y(D ₂π-ZS _u)b _2dsinβ ₂

In formula:

F ₃-spiral case eighth section area, square metre;

Y-area ratio;

D ₂-impeller outlet diameter, rice;

The number of blade of Z-impeller, sheet;

S _u-blade circumferential thickness, rice;

B _2dthe final selected value of-actual impeller outlet width, rice;

β ₂-impeller outlet angle, °;

The invention has the beneficial effects as follows: improve the mobility status in impeller, ensure that centrifugal pump is when operating point for design is constant, by control H _r, Q _rrealize the object of multi-operating mode the Hydraulic Design.

Accompanying drawing explanation

Fig. 1 is the flow-lift curve in the hydraulic performance curve of the present invention's example

Fig. 2 is the impeller axial plane figure of one embodiment of the invention.

Fig. 3 is the impeller blade key plan of same embodiment.

Fig. 4 is the volute throat schematic diagram of same embodiment.

In Fig. 1: H _g-close dead point lift, H _d-operating point for design lift, Q _d-design discharge, Q _b-1.3Q _d

Fig. 2: 1. front shroud of impeller, 3. back shroud of impeller, D ₁-impeller inlet diameter, D ₂-impeller outlet diameter, b ₂-impeller outlet width.

In Fig. 3: 3. blade, β ₂-blade outlet angle, θ-subtended angle of blade, S _u-blade circumferential thickness.

In Fig. 4: 4. throat's position view.

Embodiment

Designing requirement: design conditions flow is 0.02801 cube of meter per second, design conditions lift is 50 meters, and design conditions must net positive suction head be 4 meters, and rotating speed is 2960 revs/min, closing dead point lift is 65 meters, peak rate of flow is lift flow 0.03675 cube of meter per second corresponding when being 25 meters.

(1) $n_s=3.65n\frac{\sqrt{Q_d}}{{H_d}^{0.75}}=3.65\×2960\×\frac{\sqrt{0.02801}}{{50}^{0.75}}=96.2$

(2) closing dead point lift according to designing requirement is 65 meters, and design conditions lift is 50 meters, obtains

$H_r=\frac{H_g-H_d}{H_d}\×100\%=\frac{65-50}{50}\×100\%=30\%$

By

$H_r=\left\{\begin{array}{c}3\×{10}^{-9}{n_s}^5-1\×{10}^{-6}{n_s}^4-0.010{n_s}^2+0.796n_s+0.222(Z=3,{\mathrm{\β}}_2=17,n_s\≤130);\\ 5\×{10}^{-10}{n_s}^5-3\×{10}^{-7}{n_s}^4+5\×{10}^{-5}{n_s}^3-0.005{n_s}^2+0.560n_s+0.071(Z=4,{\mathrm{\β}}_2=20,n_s\≤170);\\ 3\×{10}^{-10}{n_s}^5-2\×{10}^{-7}{n_s}^4+3\×{10}^{-5}{n_s}^3-0.003{n_s}^2+0.427n_s+0.160(Z=5,{\mathrm{\β}}_2=23,n_s\≤195);\\ 6\×{10}^{-11}{n_s}^5-6\×{10}^{-8}{n_s}^4+2\×{10}^{-5}{n_s}^3-0.003{n_s}^2+0.372n_s+0.094(Z=6,{\mathrm{\β}}_2=25,n_s\≤220);\\ 2\×{10}^{-11}{n_s}^5-2\×{10}^{-8}{n_s}^4+1\×{10}^{-5}{n_s}^3-0.002{n_s}^2+0.292n_s+0.042(Z=7,{\mathrm{\β}}_2=27,n_s\≤230);\\ 4\×{10}^{-11}{n_s}^5-4\×{10}^{-8}{n_s}^4+1\×{10}^{-5}{n_s}^3-0.002{n_s}^2+0.266n_s-0.086(Z=8,{\mathrm{\β}}_2=28,n_s\≤240);\end{array}\right.$

Known: to work as Z=5, β ₂=23 °, n _sthe value of Hr corresponding when≤195 is about 30%, therefore, determines Z=5, β ₂=23 °;

$Q_r=\frac{Q_b-Q_d}{Q_d}\×100\%=\frac{0.03675-0.02801}{0.02801}\×100\%=31.2\%$

(3) by result of calculation Z=5, n before _s=96.2 is known:

$Y=\left\{\begin{array}{c}0.009n_s+0.035(50\%\≤Q_r\≤60\%,n_s\≤170);\\ 0.007n_s(40\%\≤Q_r\≤50\%,n_s\≤220);\\ 0.005n_s-0.011(30\%\≤Q_r\≤40\%,n_s\≤280);\end{array}\right.$

Known: Y=0.47, consider Q _r=30% is lower limit, therefore gets b _2d=b ₂;

(4) be 4 meters from design conditions necessary NPSH:

$C=\frac{5.62n\sqrt{Q_d}}{\mathrm{NPS}{H}_r^{0.75}}=\frac{5.62\×2960\×\sqrt{0.02801}}{4^{0.75}}=984.3$

k ₁＝0.13C ^0.513＝0.13×984.3 ^0.513＝4.46

round 0.094 meter;

(5) by result of calculation Z=5, n before _s=96.2 is known:

k _u2＝5×10 ^-12n _s ³-2×10 ^-9n _s ²+0.001n _s+0.935＝1.031

round 0.21 meter;

(6) by result of calculation Z=5, n before _s=96.2 is known:

k _b2＝5.798n _s ^-0.35＝5.798×96.2 ^-0.35＝1.173

k _m2＝-4×10 ^-11n _s ⁴+3×10 ^-8n _s ³-8×10 ^-6n _s ²+0.001n _s-0.002＝0.04345

round 0.010 meter;

(7) from result of calculation before:

F ₃＝Y(D ₂π-ZS _u)b _2dsinβ ₂

＝0.47×(0.21×3.14-5×0.0068)×0.010×sin23

=0.00115 square metre

In the design process, the selection of other coefficient needs to carry out coefficient according to concrete actual conditions and chooses, as subtended angle of blade θ needs to choose etc. according to casting and clear husky difficulty or ease situation.

Above, that makes with reference to embodiment for the present invention illustrates, but the present invention is not limited to above-described embodiment, also comprises other embodiment in concept of the present invention or variation.

Claims (5)

1. a centrifugal pump multi-operating mode Hydraulic Design Method, is characterized in that: the control of performance curve be divided into two stages to realize: (a) from zero delivery to design conditions flow between performance curve mainly through controlling the ratio H closing dead point lift and rated lift _rrealize, embodying relation is:

$H_r=\left\{\begin{array}{c}3{\×10}^{-9}{n_s}^5-1\×{10}^{-6}{n_s}^4-{{0.010n}_s}^2+{0.796n}_s+0.222(Z=3,{\mathrm{\β}}_2=17,n_s\≤130);\\ 5{\×10}^{-10}{n_s}^5-3\×{10}^{-7}{n_s}^4+5\×{10}^{-5}{n_s}^3-{{0.005n}_s}^2+{0.560n}_s+0.071(Z=4,{\mathrm{\β}}_2=20,n_s\≤170);\\ 3{\×10}^{-10}{n_s}^5-2\×{10}^{-7}{n_s}^4+3\×{10}^{-5}{n_s}^3-{{0.003n}_s}^2+{0.427n}_s+0.160(Z=5,{\mathrm{\β}}_2=23,n_s\≤195);\\ 6\×{10}^{-11}{n_s}^5-6\×{10}^{-8}{n_s}^4+2\×{10}^{-5}{n_s}^3-{{0.003n}_s}^2+{0.372n}_s+0.094(Z=6,{\mathrm{\β}}_2=25,n_s\≤220);\\ 2\×{10}^{-11}{n_s}^5-2\×{10}^{-8}{n_s}^4+1\×{10}^{-5}{n_s}^3-{{0.002n}_s}^2+{0.292n}_s+0.042(Z=7,{\mathrm{\β}}_2=27,n_s\≤230);\\ 4\×{10}^{-11}{n_s}^5-4\×{10}^{-8}{n_s}^4+1\×{10}^{-5}{n_s}^3-{{0.002n}_s}^2+{0.266n}_s+0.086(Z=8,{\mathrm{\β}}_2=28,n_s\≤240);\end{array}\right.$

In formula:

H _rthe ratio of-pass dead point lift and rated lift, %;

H _g-close dead point lift, rice;

H _d-operating point for design lift, rice;

β ₂-impeller outlet angle, °;

N _s-specific speed;

The number of blade of Z-impeller, sheet;

(b) from the performance curve between design conditions flow and peak rate of flow mainly through controlling the ratio Q of peak rate of flow and design discharge _rrealize, embodying relation is:

(1) when number of blade Z is 4 ~ 6, b ₂≤ b _2d≤ 1.1b ₂time;

$Y=\left\{\begin{array}{c}{0.009n}_s+0.035(50\%{\≤Q}_r\≤60\%,n_s\≤170);\\ {0.007n}_s(40{\%\≤Q}_r\≤50\%,n_s\≤220);\\ {0.005n}_s-0.011(30{\%\≤Q}_r\≤40\%,n_s\≤280);\end{array}\right.$

(2) when number of blade Z is 7 ~ 9,0.9b ₂≤ b _2d≤ b ₂time;

$Y=\left\{\begin{array}{c}{0.009n}_s+0.035(40\%{\≤Q}_r\≤50\%,n_s\≤170);\\ {0.007n}_s(30{\%\≤Q}_r\≤40\%,n_s\≤220);\\ {0.005n}_s-0.011(20{\%\≤Q}_r\≤30\%,n_s\≤280);\end{array}\right.$

In formula:

Y-area ratio;

Q _rthe ratio of-peak rate of flow and design discharge, %;

Q _d-operating point for design flow, cube meter per second;

Q _b-peak rate of flow, according to designing requirement according to (0.4 ~ 0.6) H _dcorresponding flow, cube meter per second.

2. centrifugal pump multi-operating mode Hydraulic Design Method as claimed in claim 1, is characterized in that: impeller inlet diameter D ₁determined by following relation:

$D_1=k_1\sqrt[3]{Q_d/n}$

In formula:

D ₁-impeller inlet diameter, rice;

N-wheel speed, rev/min;

K ₁-impeller inlet correction factor;

k ₁＝0.13C ^0.513

In formula:

C-cavitation specific speed;

$C=\frac{5.62n\sqrt{Q_d}}{{\mathrm{NPSH}}_r^{0.75}}$

In formula:

NPSH _r-necessary NPSH, rice.

3. centrifugal pump multi-operating mode Hydraulic Design Method as claimed in claim 1, is characterized in that: impeller outlet diameter D ₂determined by following relation:

$D_2=\frac{{84.7k}_{u2}{H_d}^{0.5}}{n}$

In formula:

D ₂-impeller outlet diameter, rice;

K _u2-outlet peripheral velocity coefficient, $k_{u2}=\left\{\begin{array}{c}{5{\×10}^{-12}{n_s}^3-2{\×10}^{-9}{n_s}^2+0.001n}_s+0.975,Z=(3-4);\\ {5\×{10}^{-12}{n_s}^3-2\×{10}^{-9}{n_s}^2+0.001n}_s+0.935,Z=(5-6);\\ 5\×{10}^{-12}{n_s}^3-2{\×10}^{-9}{n_s}^2+{0.001n}_s+0.910,Z=(7-8);\end{array}\right..$

4. centrifugal pump multi-operating mode Hydraulic Design Method as claimed in claim 1, is characterized in that: impeller outlet width b ₂determined by following relation:

$b_2=k_{b2}\sqrt{\frac{k_{m2}{Q}_d}{{\mathrm{\πv}}_{m2}}}$

In formula:

B ₂-impeller outlet width calculated value, rice;

K _b2-impeller outlet width correction factor, k _b2=5.798n _s ^-0.35;

V _m2the vertical component of-impeller outlet absolute velocity, meter per second;

K _m2-outlet axis plane velocity coefficient,

$k_{m2}=\left\{\begin{array}{c}-8{\×10}^{-11}{n_s}^2+5{\×10}^{-8}{n_s}^3-1{\×10}^{-5}{n_s}^2+{0.002n}_s-0.015,Z=(3-4);\\ -4\×{10}^{-11}{n_s}^4+3\×{10}^{-8}{n_s}^3-8{\×10}^{-6}{n_s}^2+{0.001n}_s-0.002,Z=(5-6);\\ 3{\×10}^{-12}{n_s}^4-2\×{10}^{-9}{n_s}^3-1\×{10}^{-6}{n_s}^2+0.017,Z=(7-8);\end{array}\right..$

5. centrifugal pump multi-operating mode Hydraulic Design Method as claimed in claim 1, is characterized in that: spiral case eighth section area F ₃determined by following relation:

F ₃＝Y(D ₂π-ZS _u)b _2dsinβ ₂

In formula:

F ₃-spiral case eighth section area, square metre;

S _u-blade circumferential thickness, rice;

B _2dthe final selected value of-actual impeller outlet width, rice.