CN105626574A - Hydraulic design method of high-lift axial flow pump impeller - Google Patents

Abstract

The invention relates to a hydraulic design method of a high-lift axial flow pump impeller. Main geometric parameters of the impeller are provided, and include a maximum thickness delta max of axial flow pump blades, a molded line radius R, an impeller blade number z, an impeller hub side cascade solidity Sh, an impeller rim side cascade solidity S0, a blade inlet placing angle beta 1, a blade outlet placing angle beta 2, a blade inlet axial surface speed vm1, a blade outlet axial surface speed vm2, a blade outlet peripheral component speed vu2, an impeller diameter D, an impeller hub ratio Rd, an impeller lift coefficient psi, an impeller inlet hub diameter d2, an impeller hub dispersion angle alpha, an impeller round nut height hb, a blade outlet placing angle coefficient K beta 2, a blade inlet placing angle coefficient K beta 1, selection of wing sections with different sections of blades and the like. The designed axial flow pump impeller improves both the impeller lift and the cavitation resistance of an axial flow pump, facilitates computer programming, and can replace traditional similar design method and speed coefficient method of the axial flow pump to a greater extent.

Description

A kind of high-lift axial-flow pump impeller Hydraulic Design Method

Technical field

The present invention relates to the method for design of the major part of a kind of propeller pump, in particular to the high-lift axial-flow pump impeller Hydraulic Design Method of one. This axial flow pump lift is higher and anti-cavitation performance is good, is applicable to agricultural irrigation, municipal administration plumbing, thermoelectricity, petrochemical enterprise and supplies water for periodical feeding, technique and the field such as regional water transfer, especially nuclear power field.

Background technology

Propeller pump is the one of vane pump, has and accounts for that structure is simple, floor space is little, flow is big and the characteristic such as efficiency height, and the specific speed of propeller pump is 500��1600, and its range of application also starts to expand to the field of other pump series products gradually at present.

Propeller pump is mainly applicable to agricultural drainage and irrigation, municipal administration plumbing, thermoelectricity, nuclear power, petrochemical enterprise etc. for fields such as periodical feeding, technique water supply and regional water transfer. And the flow height of current propeller pump, but lift is relatively low. Along with the development of new forms of energy, nuclear power application is more and more extensive, but also will become the mainstay of China's energy cause. But when considering large discharge at present, lift does not but reach requirement; When lift reaches requirement, flow is really less comparatively speaking. The pump that large discharge is high-lift thus is that nuclear power industry is badly in need of.

The Hydraulic Design Method of the axial-flow pump impeller of prior art does not provide the method for design of system, and the impeller lift designed is lower, and still to be depended on experimental formula to a great extent, operability is not strong, the undue experience relying on engineering technical personnel. It is difficult to meet high-lift and that anti-cavitation performance is good requirement, and it is difficult to accomplish computer programming application and computer aided design (CAD). Nowadays propeller pump is in nuclear power industry a popular domain, only relies on transformation impeller shape sometimes can not meet and improves its lift and anti-cavitation performance, it is necessary to does perfect further to the Hydraulic Design Method of axial-flow pump impeller.

Application number is disclose one " axial flow pump impeller vane " in the Chinese invention patent of No. 02133456.0, this invention relates to a kind of axial-flow pump impeller vane, this kind of method of design only gives the concrete implementing method of the parameter of impeller vane, other parameters still rely on the experience of engineering technical personnel, do not provide system, accurate method of design, and be difficult to accomplish computer programming application and computer aided design (CAD). Application number is the multi-state method of design that the Chinese invention patent of No. 201410481735.0 discloses a kind of multi-phase mixed delivering axial-flow pump impeller, the present invention relates to the multi-state method of design of a kind of multi-phase mixed delivering axial-flow pump impeller, the performance requriements of what parameters all of described axial wheel and multiple operating modes of described propeller pump is linked together. But this patent only relates to several parameters of axial-flow pump impeller, does not provide the method for design of the parameter of axial-flow pump impeller completely. The Chinese invention patent that application number is No. 201310744652.1 discloses a kind of Double-way axial flow pump impeller Optimization Design, the open a kind of Double-way axial flow pump impeller Optimization Design of the present invention, on the basis of tradition streamline method design axial-flow pump impeller, by the optimization of aerofoil profile and paddle wheel plane figure is improved reversible axial flow pump impeller performance, reach the object simultaneously improving reversible axial flow pump impeller adiabatic efficiency and anti-cavitation performance. This kind of method of design not only makes diagonal pumps impeller stdn and systematize, also meets water conservancy and public works to the requirement of diagonal pumps multiparameter operating mode. But, contriver does not provide the method for design system of the basic parameter of axial-flow pump impeller, accurate in that patent yet, still relies on original similar-design method and velocity-coefficient method to a great extent.

For the defect of above-mentioned existence, the present inventor has invented a kind of high-lift axial-flow pump impeller Hydraulic Design Method, do not only give axial-flow pump impeller parameter system, accurate method of design, also solve the problem of propeller pump low lift and cavitation, improve axial flow pump lift and cavitation performance, extend work-ing life and the maintenance cycle of pump, the most important thing is to contribute to computer programming application and computer aided design (CAD), the original similar-design method of propeller pump and velocity-coefficient method can be replaced to a great extent.

Goal of the invention

Along with the fast development of China's economy and the minimizing day by day of global energy, how save energy has become the problem that people more and more pay close attention to. The domestic demand for pump series products is very big at present, and the 20%��25% of every annual electricity generating capacity all can consume on pump series products. How to realize propeller pump while ensureing large discharge, widen efficient district further, and lift can be improved, become the pressing problem of current propeller pump development. Existing method of design, Design Theory is quite different with actual model, it is very difficult to reach desired effect. It is an object of the invention to improve propeller pump lift, strengthen propeller pump anti-cavitation performance, increase life-span and the maintenance cycle of pump, to reduce the workload of maintenance personnel. Also contribute to computer programming application and computer aided design (CAD), the original similar-design method of propeller pump and velocity-coefficient method can be replaced to a great extent, and calculate more accurate, Design Theory and actual model are more met.

Summary of the invention

In order to solve the problem, the present invention provides a kind of axial-flow pump impeller Hydraulic Design Method. By improving the method for design of several important parameters of impeller, improve mobility status, it is to increase axial flow pump lift and cavitation performance.

Realizing the technical scheme that above-mentioned purpose adopts is:

(1) impeller lift coefficient ��

$\mathrm{\ψ}=0.8487e^{\[-{\left(\frac{n_s-912.2}{910.7}\right)}^2\]}+3.95e^{\[-{\left(\frac{n_s+5293}{3249}\right)}^2\]}---\left(1\right)$

In formula:

��-impeller lift coefficient;

n_s-specific speed;

(2) hub ratio R_d

$R_d=\frac{d_h}{D}=\frac{0.8234{\mathrm{\ψ}}^3-0.3658{\mathrm{\ψ}}^2+0.04459\mathrm{\ψ}+0.001323}{{\mathrm{\ψ}}^3-0.3382{\mathrm{\ψ}}^2+0.003165\mathrm{\ψ}+0.008626}---\left(2\right)$

In formula:

R_d-hub ratio;

d_h-impeller hub diameter, rice;

D-impeller diameter, rice;

��-impeller lift coefficient;

(3) impeller diameter D

$D=\{9.772e^{\[-{\left(\frac{n_s+2496}{3053}\right)}^2\]}-12.84e^{\[-{\left(\frac{n_s-2338}{1688}\right)}^2\]}\}\·\sqrt{\frac{1}{1-{R_d}^2}}\·\sqrt[3]{\frac{Q}{n}}---\left(3\right)$

In formula:

D-impeller diameter, rice;

n_s-specific speed;

R_d-hub ratio;

Q-design conditions flow, rice³/ the second;

N-design conditions rotating speed, rev/min;

(4) vane inlet axis plane velocity v is not revised_m��

${v_m}^{\′}={v_{m1}}^{\′}={v_{m2}}^{\′}=\left[\begin{array}{c}4.07+0.117cos\left(0.0016n_s\right)+0.0266sin\left(0.0016n_s\right)\\ +0.0382\cos \left(0.0032n_s\right)+0.032\sin \left(0.0032n_s\right)\end{array}\right]\·\frac{Q}{D^2\mathrm{\π}(1-R_d^2)}---\left(4\right)$

In formula:

v_m1'-do not revise vane inlet axis plane velocity, rice/second;

v_m2'-do not revise blade exit axis plane velocity, rice/second;

n_s-specific speed;

Q-design conditions flow, rice³/ the second;

D-impeller diameter, rice;

R_d-hub ratio;

(5) vane inlet axis plane velocity v_m1, blade exit axis plane velocity v_m2

$v_{m_1}=v_{m_2}=\frac{{n_s}^2+6.766n_s+0.6544}{0.98{n_s}^2-8.612n_s+0.625}\·{v_m}^{\′}---\left(5\right)$

In formula:

v_m1-vane inlet axis plane velocity, rice/second;

v_m2-blade exit axis plane velocity, rice/second;

n_s-specific speed;

(6) blade exit place peripheral compoent of velocity v_u2

$v_{u_2}=(3.84{n_s}^{-0.8787}-0.00349)\·Dn---\left(6\right)$

In formula:

v_u2-blade exit place the peripheral compoent of velocity, rice/second;

n_s-specific speed;

D-impeller diameter, rice;

N-design conditions rotating speed, rev/min;

(7) impeller hub side leaf grating dense degree S_h

$S_h=\frac{l}{t_h}=0.1815e^{\[-{\left(\frac{n_s-398.1}{595.1}\right)}^2\]}+1.161e^{\[-{\left(\frac{n_s-9088}{18510}\right)}^2\]}---\left(7\right)$

In formula:

S_h-impeller hub side dense the degree of leaf grating;

L-aerofoil profile chord length, rice;

t_h-impeller hub side pitch, rice;

n_s-specific speed;

(8) wheel rim side leaf grating dense degree S₀

$\begin{array}{c}{S}_0=\frac{l}{t_0}=0.7537+0.095cos\left(0.026n_s\right)+0.1748\sin \left(0.026n_s\right)\\ -0.017\cos \left(0.052n_s\right)+0.08\sin \left(0.052n_s\right)\end{array}---\left(8\right)$

In formula:

S₀-wheel rim side dense the degree of leaf grating;

L-aerofoil profile chord length, rice;

t₀-wheel rim side pitch, rice;

n_s-specific speed;

(9) vane inlet laying angle COEFFICIENT K_��1

$K_{{\mathrm{\β}}_1}=\frac{1.268\×{10}^{-6}{n_s}^4-0.0036{n_s}^3+22.95{n_s}^2+0.15n_s+0.0726}{{n_s}^2+19.44n_s-0.98}---\left(9\right)$

In formula:

K_��1-vane inlet laying angle coefficient;

n_s-specific speed;

(10) blade exit laying angle COEFFICIENT K_��2

$K_{{\mathrm{\β}}_2}=60.32+0.014cos\left(0.0036n_s\right)-0.22sin\left(0.0036n_s\right)+0.048cos\left(0.0072n_s\right)-0.011sin\left(0.0072n_s\right)---\left(10\right)$

In formula:

K_��2-blade exit laying angle coefficient;

n_s-specific speed;

(11) vane inlet laying angle ��₁

${\mathrm{\β}}_1=\arctan \frac{K_{{\mathrm{\β}}_1}\·v_{m_1}}{2.72sin(0.00116n_s+0.4637)+1.7sin(0.0015n_s+3.28)\·D_{i}n}---\left(11\right)$

In formula:

��₁-vane inlet laying angle, degree;

K_��1-vane inlet laying angle coefficient;

n_s-specific speed;

D_i-different cross section impeller diameter, rice;

V_m1-vane inlet axis plane velocity, rice/second;

N-design conditions rotating speed, rev/min;

(12) blade exit laying angle ��₂

${\mathrm{\β}}_2=\arctan \frac{K_{{\mathrm{\β}}_2}\·v_{m_2}}{\[3.13+0.0098\cos \left(0.0029n_s\right)+0.0083\sin \left(0.0029n_s\right)\]\·(D_{i}n-k_{{\mathrm{\β}}_2}{v}_{u_2})}---\left(12\right)$

In formula:

��₂-blade exit laying angle, degree;

K_��1-vane inlet laying angle coefficient;

v_m2-blade exit axis plane velocity, rice/second;

n_s-specific speed;

D_i-different cross section impeller diameter, rice;

N-design conditions rotating speed, rev/min;

v_u2-blade exit place the peripheral compoent of velocity, rice/second;

(13) impeller vane number z

Z=111-0.06514n_s-190.1S₀+1.18��10^-5n_s ²+0.05042n_s��S₀+89.05S₀ ²(13)

In formula:

Z-impeller vane number;

n_s-specific speed;

S₀-wheel rim side dense the degree of leaf grating;

(14) maximum blade thickness ��_max

${\mathrm{\δ}}_{max}=\[0.0133+0.0017cos\left(0.019H\right)-0.00043sin\left(0.019H\right)\]\·D\sqrt{H}---\left(14\right)$

In formula:

��_max-maximum blade thickness, rice;

H-design conditions lift, rice;

D-impeller diameter, rice;

(15) type line radius R

$R=\{0.52e^{\[-{\left(\frac{D-0.078}{5.41}\right)}^2\]}+0.024e^{\[-{\left(\frac{D-1.67}{0.485}\right)}^2\]}\}\·\frac{l}{sin\left(\frac{{\mathrm{\β}}_2-{\mathrm{\β}}_1}{2}\right)}---\left(15\right)$

In formula:

R-type line radius, rice;

D-impeller diameter, rice;

L-aerofoil profile chord length, rice;

��₂-blade exit laying angle, degree;

��₁-vane inlet laying angle, degree;

(16) impeller inlet place hub diameter d₂

d₂=[-0.0281ln (n)+0.81704] d_h(16)

In formula:

d₂-impeller inlet place hub diameter, rice;

H-design conditions lift, rice;

d_h-impeller hub diameter, rice;

(17) impeller hub spread angle ��

$\mathrm{\α}=2\arctan \left(\frac{d_h-d_2}{(0.73912\·H^{-0.08078})\·d_h}\right)---\left(17\right)$

In formula:

��-impeller hub spread angle, degree;

d₂-impeller inlet place hub diameter, rice;

H-design conditions lift, rice;

d_h-impeller hub diameter, rice;

(18) impeller round nut height h_b

h_b=(0.000002H²-0.00002H+0.38014)��d₂(18)

In formula:

h_b-impeller round nut height, rice;

d₂-impeller inlet place hub diameter, rice;

H-design conditions lift, rice;

(19) airfoil cross sectional shape

X < (D-d_hDuring)/2, the aerofoil profile that cross-sectional shape adopts thickness bigger;

X > (D-d_hDuring)/2, cross-sectional shape adopts lift coefficient relatively big, relatively partially thin aerofoil profile.

In formula:

X-blade distance hub side length.

According to above-mentioned steps, it is possible to obtain a kind of relative system, the method for design of accurate impeller significant parameter.

Axial-flow pump impeller main geometric parameters is determined by above-mentioned method of calculation, comprise axial-flow pump impeller lift coefficient, hub ratio, impeller diameter, vane inlet axis plane velocity, blade exit axis plane velocity, the blade exit place peripheral compoent of velocity, the impeller hub side dense degree of leaf grating, the wheel rim side dense degree of leaf grating, blade exit laying angle coefficient, vane inlet laying angle coefficient, vane inlet laying angle, blade exit laying angle, impeller vane number, maximum blade thickness, type line radius impeller inlet place hub diameter, impeller hub spread angle, impeller round nut height and different section forms, it is different from tradition additive method and velocity-coefficient method, more can guarantee the mutual coupling of hydraulic part size, calculate more accurate, Design Theory and actual model are more met, and be more conducive to computer application and programming.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention is further described.

Fig. 1 is axial-flow pump impeller axle axial plane figure.

Fig. 2 is axial-flow pump impeller plane blade-spacing diagram.

Embodiment

The present invention determines by following formula to comprise axial-flow pump impeller lift coefficient ��, hub ratio R_d, impeller diameter D, vane inlet axis plane velocity v_m1, blade exit axis plane velocity v_m2, blade exit place peripheral compoent of velocity v_u2, impeller hub side leaf grating dense degree S_h, wheel rim side leaf grating dense degree S₀, blade exit laying angle COEFFICIENT K_��2, vane inlet laying angle COEFFICIENT K_��1, vane inlet laying angle ��₁, blade exit laying angle ��₂, impeller vane number z, maximum blade thickness ��_max, type line radius R, impeller inlet place hub diameter d₂, impeller hub spread angle ��, impeller round nut height h_bDeng the section form that several parameters of impeller and blade are different.

This embodiment is at given design conditions flow Q, design conditions lift H, design conditions rotating speed n, calculates impeller hydraulic parameters:

$\mathrm{\&psi;}=0.8487e^{\&lsqb;-{\left(\frac{n_s-912.2}{910.7}\right)}^2\&rsqb;}+3.95e^{\&lsqb;-{\left(\frac{n_s+5293}{3249}\right)}^2\&rsqb;}---\left(1\right)$

$R_d=\frac{d_h}{D}=\frac{0.8234{\mathrm{\&psi;}}^3-0.3658{\mathrm{\&psi;}}^2+0.04459\mathrm{\&psi;}+0.001323}{{\mathrm{\&psi;}}^3-0.3382{\mathrm{\&psi;}}^2+0.003165\mathrm{\&psi;}+0.008626}---\left(2\right)$

$D=\{9.772e^{\&lsqb;-{\left(\frac{n_s+2496}{3053}\right)}^2\&rsqb;}-12.84e^{\&lsqb;-{\left(\frac{n_s-2338}{1688}\right)}^2\&rsqb;}\}\&CenterDot;\sqrt{\frac{1}{1-{R_d}^2}}\&CenterDot;\sqrt[3]{\frac{Q}{n}}---\left(3\right)$

${v_m}^{\&prime;}={v_{m1}}^{\&prime;}={v_{m2}}^{\&prime;}=\left[\begin{array}{c}4.07+0.117cos\left(0.0016n_s\right)+0.0266sin\left(0.0016n_s\right)\\ +0.0382\cos \left(0.0032n_s\right)+0.032\sin \left(0.0032n_s\right)\end{array}\right]\&CenterDot;\frac{Q}{D^2\mathrm{\&pi;}(1-R_d^2)}---\left(4\right)$

$v_{m_1}=v_{m_2}=\frac{{n_s}^2+6.766n_s+0.6544}{0.98{n_s}^2-8.612n_s+0.625}\&CenterDot;{v_m}^{\&prime;}---\left(5\right)$

$v_{u_2}=(3.84{n_s}^{-0.8787}-0.00349)\&CenterDot;Dn---\left(6\right)$

$S_h=\frac{l}{t_h}=0.1815e^{\&lsqb;-{\left(\frac{n_s-398.1}{595.1}\right)}^2\&rsqb;}+1.161e^{\&lsqb;-{\left(\frac{n_s-9088}{18510}\right)}^2\&rsqb;}---\left(7\right)$

$\begin{array}{c}{S}_0=\frac{l}{t_0}=0.7537+0.095cos\left(0.026n_s\right)+0.1748sin\left(0.026n_s\right)\\ -0.017\cos \left(0.052n_s\right)+0.08\sin \left(0.052n_s\right)\end{array}---\left(8\right)$

$K_{{\mathrm{\&beta;}}_1}=\frac{1.268\&times;{10}^{-6}{n_s}^4-0.0036{n_s}^3+22.95{n_s}^2+0.15n_s+0.0726}{{n_s}^2+19.44n_s-0.98}---\left(9\right)$

$K_{{\mathrm{\&beta;}}_2}=60.32+0.014cos\left(0.0036n_s\right)-0.22sin\left(0.0036n_s\right)+0.048cos\left(0.0072n_s\right)-0.011sin\left(0.0072n_s\right)---\left(10\right)$

${\mathrm{\&beta;}}_1=\arctan \frac{K_{{\mathrm{\&beta;}}_1}\&CenterDot;v_{m_1}}{2.72sin(0.00116n_s+0.4637)+1.7sin(0.0015n_s+3.28)\&CenterDot;D_{i}n}---\left(11\right)$

${\mathrm{\&beta;}}_2=\arctan \frac{K_{{\mathrm{\&beta;}}_2}\&CenterDot;v_{m_2}}{\&lsqb;3.13+0.0098\cos \left(0.0029n_s\right)+0.0083\sin \left(0.0029n_s\right)\&rsqb;\&CenterDot;(D_{i}n-K_{{\mathrm{\&beta;}}_2}{v}_{u_2})}---\left(12\right)$

Z=111-0.06514n_s-190.1S₀+1.18��10^-5n_s ²+0.05042n_s��S₀+89.05S₀ ²(13)

${\mathrm{\&delta;}}_{max}=\&lsqb;0.0133+0.0017cos\left(0.019H\right)-0.00043sin\left(0.019H\right)\&rsqb;\&CenterDot;D\sqrt{H}---\left(14\right)$

$R=\{0.52e^{\&lsqb;-{\left(\frac{D-0.078}{5.41}\right)}^2\&rsqb;}+0.024e^{\&lsqb;-{\left(\frac{D-1.67}{0.485}\right)}^2\&rsqb;}\}\&CenterDot;\frac{l}{sin\left(\frac{{\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1}{2}\right)}---\left(15\right)$

d₂=[-0.0281ln (H)+0.81704] d_h(16)

$\mathrm{\&alpha;}=2\arctan \left(\frac{d_h-d_2}{(0.73912\&CenterDot;H^{-0.08078})\&CenterDot;d_h}\right)---\left(17\right)$

h_b=(0.000002H²-0.00002H+0.38014)��d₂(18)

Formal at blade section, different cross sections adopts different air foil shapes, x < (D-d_hDuring)/2, the aerofoil profile that cross-sectional shape adopts thickness bigger; X > (D-d_hDuring)/2, cross-sectional shape adopts lift coefficient relatively big, relatively partially thin aerofoil profile.

The present invention adopts exact formulas design method to carry out waterpower design, pump lift and anti-cavitation is greatly improved, has good economic benefit, be more conducive to the Program Appliance of computer. Owing to the method for design of the present invention is different from tradition additive method and velocity-coefficient method, the mutual coupling of the size of hydraulic part more can be guaranteed. And calculate more accurate, Design Theory and actual model are more met.

Above, it is the concrete explanation that patent of the present invention is made with reference to embodiment, but the present invention is not limited to above-described embodiment, also comprises other embodiments within the scope of present inventive concept or variation.

Claims (9)

1. a high-lift axial-flow pump impeller Hydraulic Design Method, it is provided that the main geometric parameters of impeller, comprises axial flow pump blade inner maximum gauge ��_max, type line radius R, impeller vane number z, impeller hub side leaf grating dense degree S_h, wheel rim side leaf grating dense degree S₀, vane inlet laying angle ��₁, blade exit laying angle ��₂, vane inlet axis plane velocity v_m1, blade exit axis plane velocity v_m2, blade exit place peripheral compoent of velocity v_u2, impeller diameter D, hub ratio R_d, impeller lift coefficient ��, impeller inlet place hub diameter d₂, impeller hub spread angle ��, impeller round nut height h_b, blade exit laying angle COEFFICIENT K_��2, vane inlet laying angle COEFFICIENT K_��1, blade different cross section the selection of aerofoil profile, it is characterised in that: be applicable to following relation between impeller geometric parameter and pump operating point for design performance perameter:

$R=\{0.52e^{\&lsqb;-{\left(\frac{D-0.078}{5.41}\right)}^2\&rsqb;}+0.024e^{\&lsqb;-{\left(\frac{D-1.67}{0.485}\right)}^2\&rsqb;}\}\&CenterDot;\frac{l}{sin\left(\frac{{\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1}{2}\right)}---\left(1\right)$

${\mathrm{\&delta;}}_{max}=\&lsqb;0.0133+0.0017cos\left(0.019H\right)-0.00043sin\left(0.019H\right)\&rsqb;\&CenterDot;D\sqrt{H}---\left(2\right)$

Z=111-0.06514n_s-190.1S₀+1.18��10^-5n_s ²+0.05042n_s��S₀+89.05S₀ ²(3)

In formula:

R-type line radius, rice;

D-impeller diameter, rice;

��₂-blade exit laying angle, degree;

��₁-vane inlet laying angle, degree;

H-design conditions lift, rice;

��_max-maximum blade thickness, rice;

n_s-specific speed;

Z-impeller vane number;

S₀-wheel rim side dense the degree of leaf grating.

2. according to right (1) requirement, vane inlet laying angle ��₁, blade exit laying angle ��₂Design formula:

${\mathrm{\&beta;}}_2=\arctan \frac{K_{{\mathrm{\&beta;}}_2}\&CenterDot;v_{m_2}}{\&lsqb;3.13+0.0098cos\left(0.0029n_s\right)+0.0083sin\left(0.0029n_s\right)\&rsqb;\&CenterDot;(D_{i}n-K_{{\mathrm{\&beta;}}_2}{v}_{u_2})}---\left(4\right)$

${\mathrm{\&beta;}}_1=\arctan \frac{K_{{\mathrm{\&beta;}}_1}\&CenterDot;v_{m_1}}{2.72\sin \left(0.00116n_s+0.4637\right)+1.7\sin \left(0.0015n_s+3.28\right)\&CenterDot;D_{i}n}---\left(5\right)$

In formula:

K_��2-blade exit laying angle coefficient;

v_m2-blade exit axis plane velocity, rice/second;

D_i-different cross section impeller diameter, rice;

N-design conditions rotating speed, rev/min;

v_u2-blade exit place the peripheral compoent of velocity, rice/second;

K_��1-vane inlet laying angle coefficient;

v_m1-vane inlet axis plane velocity, rice/second.

3. according to right (1) requirement, impeller hub side leaf grating dense degree S_h, wheel rim side leaf grating dense degree S₀Design formula:

$S_h=\frac{l}{t_h}=0.1815e^{\&lsqb;-{\left(\frac{n_s-398.1}{595.1}\right)}^2\&rsqb;}+1.161e^{\&lsqb;-{\left(\frac{n_s-9088}{18510}\right)}^2\&rsqb;}---\left(6\right)$

$\begin{array}{c}{S}_0=\frac{l}{t_0}=0.7537+0.095cos\left(0.026n_s\right)+0.1748sin\left(0.026n_s\right)\\ -0.017\cos \left(0.052n_s\right)+0.08\sin \left(0.052n_s\right)\end{array}---\left(7\right)$

In formula:

S_h-impeller hub side dense the degree of leaf grating;

L-aerofoil profile chord length, rice;

t_h-impeller hub side pitch, rice;

t₀-wheel rim side pitch, rice.

4. according to right (2) requirement, vane inlet axis plane velocity v_m1, blade exit axis plane velocity v_m2, blade exit place peripheral compoent of velocity v_u2Design formula:

${v_m}^{\&prime;}={v_{m1}}^{\&prime;}={v_{m2}}^{\&prime;}=\left[\begin{array}{c}4.07+0.117cos\left(0.0016n_s\right)+0.0266sin\left(0.0016n_s\right)\\ +0.0382\cos \left(0.0032n_s\right)+0.032\sin \left(0.0032n_s\right)\end{array}\right]\&CenterDot;\frac{Q}{D^2\mathrm{\&pi;}(1-R_d^2)}---\left(8\right)$

$v_{m_1}=v_{m_2}=\frac{{n_s}^2+6.766n_s+0.6544}{0.98{n_s}^2-8.612n_s+0.625}\&CenterDot;{v_m}^{\&prime;}---\left(9\right)$

$v_{u_2}=(3.84n_s^{-0.8787}-0.00349)\&CenterDot;Dn---\left(10\right)$

In formula:

v_m1'-do not revise vane inlet axis plane velocity, rice/second;

Q-design conditions flow, rice³/ the second.

5. according to right (1), (2), (4) requirement, impeller diameter D design formula:

$D=\{9.772e^{\&lsqb;-{\left(\frac{n_s+2496}{3053}\right)}^2\&rsqb;}-12.84e^{\&lsqb;-{\left(\frac{n_s-2338}{1688}\right)}^2\&rsqb;}\}\&CenterDot;\sqrt{\frac{1}{1-{R_d}^2}}\&CenterDot;\sqrt[3]{\frac{Q}{n}}---\left(11\right)$

In formula:

R_d-hub ratio.

6. according to right (5) requirement, hub ratio R_d, impeller lift coefficient �� design formula:

$R_d=\frac{d_h}{D}=\frac{0.8234{\mathrm{\&psi;}}^3-0.3658{\mathrm{\&psi;}}^2+0.04459\mathrm{\&psi;}+0.001323}{{\mathrm{\&psi;}}^3-0.3382{\mathrm{\&psi;}}^2+0.003165\mathrm{\&psi;}+0.008626}---\left(12\right)$

$\mathrm{\&psi;}=0.8487e^{\&lsqb;-{\left(\frac{n_s-912.2}{910.7}\right)}^2\&rsqb;}+3.95e^{\&lsqb;-{\left(\frac{n_s+5293}{3249}\right)}^2\&rsqb;}---\left(13\right)$

In formula:

d_h-impeller hub diameter, rice.

7. according to right (1) requirement, impeller inlet place hub diameter d₂, impeller hub spread angle ��, impeller round nut height h_bDesign formula:

d₂=[-0.0281ln (H)+0.81704] d_h(14)

$\mathrm{\&alpha;}=2\arctan \left(\frac{d_h-d_2}{\left(0.73912\&CenterDot;H^{-0.08078}\right)\&CenterDot;d_h}\right)---\left(15\right)$

h_b=(0.000002H²-0.00002H+0.38014)��d₂(16)

In formula:

d₂-impeller inlet place hub diameter, rice;

��-impeller hub spread angle, degree;

h_b-impeller round nut height, rice.

8. according to right (2) requirement, blade exit laying angle COEFFICIENT K_��2, vane inlet laying angle COEFFICIENT K_��1Design formula:

$K_{{\mathrm{\&beta;}}_2}=60.32+0.014cos\left(0.0036n_s\right)-0.22sin\left(0.0036n_s\right)+0.048cos\left(0.0072n_s\right)-0.011sin\left(0.0072n_s\right)---\left(17\right)$

$K_{{\mathrm{\&beta;}}_1}=\frac{1.268\&times;{10}^{-6}{n_s}^4-0.0036{n_s}^3+22.95{n_s}^2+0.15n_s+0.0726}{{n_s}^2+19.44n_s-0.98}---\left(18\right)$

9., according to right (1) requirement, the cross-sectional shape of blade adopts different section forms:

X < (D-d_hDuring)/2, the aerofoil profile that cross-sectional shape adopts thickness bigger;

X > (D-d_hDuring)/2, cross-sectional shape adopts lift coefficient relatively big, relatively partially thin aerofoil profile;

In formula:

X-blade distance hub side length.