CN103104548A - Hydraulic unequal pump lift design method for gas-liquid two-phase nuclear main pump impeller - Google Patents

Abstract

The invention relates to a hydraulic design method of unequal heads of impellers of a gas-liquid two-phase flow nuclear main pump. Its characteristic is that when the theoretical lift of the infinite blade of the front cover of the blade outlet is smaller than the theoretical lift of the infinite blade of the rear cover, the theoretical lift of the limited blade of the front cover of the impeller outlet is equal to the theoretical lift of the limited blade of the rear cover. The gas-liquid mixed medium is considered in the head, and the main geometric parameters of the impeller are adjusted through certain constraints to meet the design requirements of the nuclear main pump impeller. The impeller designed by the invention can improve the gas-liquid mixed transportation capacity of the main nuclear pump impeller. Therefore, the safe and stable operation of the nuclear main pump under the condition of loss of water accident can be guaranteed.

Description

Hydraulic design method of unequal head impellers for gas-liquid two-phase flow nuclear main pump

Technical field

The invention relates to a hydraulic design method of unequal lifts for the impeller of a gas-liquid two-phase flow nuclear main pump, in particular to a method for front and rear of the impeller outlet when the theoretical lift of the infinite blade of the front cover plate of the blade outlet is smaller than the theoretical lift of the infinite blade of the rear cover plate. A hydraulic design method for the unequal head of the impeller of the main pump with the gas-liquid two-phase flow and the equal theoretical head of the cover plate finite blade.

Background technique

Since the 1980s, the safety of nuclear reactors has aroused people's great attention, thus promoting the research of gas-liquid two-phase pumps. When the coolant leaks in the reactor, as the pressure in the cooling system decreases, the coolant starts to boil, so that the cooling pump moves in a state of gas-liquid two-phase flow.

At present, there is no mature design method for gas-liquid two-phase flow pumps, and it cannot be designed more reliably based on given parameters such as flow, head, and speed like clean water pumps. The main requirement for a gas-liquid two-phase flow pump is to increase the gas-liquid mixing ratio of the medium it can transport.

Traditional impeller design methods presuppose that the theoretical head should be the same value for all streamlines within the impeller in order to avoid unwanted flow. At the same time, it is considered that the value of the outlet placement angle remains constant over the entire outlet edge. The static moment of each streamline is not the same, so it can be concluded that the correction coefficient also changes, and the speed of each streamline is also different, that is to say, the exit edge is not parallel to the rotating axis as assumed. Changing the static moment of a given streamline, that is, changing the length of the streamline, can modify the work reduction coefficient to some extent, but the possibilities are limited at this time. Generally, the streamline located on the front wall of the impeller blades should be lengthened, but this has a bad effect on the shape of the flow channel between the impeller inlet blades.

Changing the correction coefficient can also achieve a constant speed, but at this time the assumption that the placement angle of the blade outlet is constant along the blade outlet edge must be changed, so it is difficult to determine the position of the outlet edge. When the specific rotation number n _s <250, the exit edge is generally a straight line, and if the exit edge is approximately at right angles to the streamline, the exit edge should be concave. When the specific rotation number n _s >250, in order to improve the shape of the flow channel between the blades to some extent, the streamline can be moved relative to the impeller wall, at this time the outlet edge can no longer be kept parallel to the rotation axis, that is, the A method of obliquely arranging the outflow side of the impeller. As the specific speed increases, the inclination angle also increases. At this time, different impeller outlet diameters are used, that is, the diameter of the impeller outlet of the rear cover is smaller than the diameter of the impeller outlet of the front cover, which can reduce the recirculation area of the impeller outlet and reduce the The loss of hydrodynamic force makes the lift of the characteristic curve rise in the small flow area.

Due to the difference in static moments, curvature radii, and outlet edge positions of different streamlines in the impeller, the impeller designed according to the infinite number of blades and other lifts will have different lifts (Ht) at the blade outlet, resulting in turbulent flow at the outlet edge, reducing pump efficiency.

Contents of the invention

In order to overcome the deficiencies of the existing nuclear main pump impeller design method, the present invention provides a hydraulic design method of unequal lift for the gas-liquid two-phase flow nuclear main pump impeller. The geometric parameters of the impeller can be adjusted by using the impeller designed by the present invention to achieve The effect of coincidence between the designed performance curve of the nuclear main pump and the required performance curve. The invention firstly proposes a hydraulic design method with unequal head of impeller of gas-liquid two-phase flow core main pump. Through the research on the traditional centrifugal pump hydraulic design method, it is found that the traditional centrifugal pump hydraulic design method will lead to unsatisfactory flow at the outlet of the impeller blades. This invention adopts the unequal head method for the first time, and considers the gas-liquid transport of the nuclear main pump during the loss of water accident. Two-phase medium, carry out the hydraulic design of the nuclear main pump, improve the gas-liquid mixed transportation capacity of the nuclear main pump, and ensure the safe and stable operation of the nuclear reactor.

Technical scheme of the present invention:

Since each streamline in the impeller is different, this difference will cause the slip coefficient μ of each streamline in the impeller to be different, and the theoretical head H _{t ∞} of the infinite blade is considered to be equal, and the finite blade theory of each streamline in the actual impeller Head H _t is not equal. In the hydraulic design of the centrifugal pump, when the theoretical head H _t of the finite blades in the impeller is equal, the hydraulic loss is the smallest, and such a hydraulic design is the best design result. Based on the above-mentioned design theory, the present invention starts from the premise that the theoretical head H _t∞ of the infinite blades is not equal, and adjusts the slip coefficient by modifying the geometric parameters of the impeller to make the theoretical head H _t of the limited blades equal, so that the unequal head method can be used to check the core Main pump impeller for hydraulic design purposes. The basic method of unequal head hydraulic design is:

It can be seen from the basic formula of theoretical head H _t with limited number of blades that H _t is affected by parameters such as D ₁ , D ₂ , β ₁ , β ₂ , n, etc., but this is generated when the centrifugal force is not considered to make the liquid flow along the front cover Obtained when the outflow phenomenon occurs. If the viscosity of the fluid, the shedding phenomenon of the front cover plate and the jet-wake structure of the blade outlet are considered, H _t will also be affected by geometric parameters such as b ₁ , b ₂ , and n _s . The relationship between H _t and H _t∞ is established through the slip coefficient, but the existing centrifugal pump slip coefficient formulas are all calculated according to the centerline of the axial flow channel (that is, the average value), without considering the actual flow of each streamline different impacts. Therefore, it is first necessary to establish a formula that can calculate the slip coefficient of each streamline separately.

In actual engineering design, the centrifugal pump impeller is divided into 2 to 3 streamlines for design. In the present invention, the theoretical lift of the infinite number of blades at the blade outlet is linearly distributed, and the lift of the middle streamline is the average value of the lifts of the front and rear cover plates. Therefore, only the front and rear cover lifts are calculated in the following discussion. Comprehensively comparing the existing slip coefficient formulas, since the Stirling formula considers the influence of viscosity, the slip coefficient formula is improved on the basis of the Stirling formula. Considering the different slip coefficients of the front and rear cover plates, there is

Stirling (1983) proposed the following formula

$\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; ZL</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}}\frac{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

where ψ——head coefficient;

δ—coefficient, δ=1.473φ ^2.16 ;

φ——geometric parameter;

b ₁ , b ₂ —— impeller inlet and outlet width;

L _R ——blade chord length, $L_R=\frac{R_2-R_1}{\sin \left(\frac{{\mathrm{\&beta;}}_1+{\mathrm{\&beta;}}_2}{2}\right)}.$

where ψ _a , ψ _b ——lift coefficients of the front and rear cover plates, the expression is

δ _a , δ _b —— calculation coefficients of the front and rear covers, expressed as

φ _a , φ _b ——geometric parameters of the front and rear covers, expressed as

b ₁ , b ₂ —— impeller inlet and outlet width;

L _R ——blade chord length, the expression is

From the calculation formula of infinite blade theoretical lift, the infinite blade theoretical lifts H _ta∞ and H _tb∞ of the front and rear cover plates of the blade outlet can be calculated respectively. Right now

H _th∞a ＝[(1-x ₂ )V _u2la u _2a -(1-x ₁ )V _u1la u _1a +x ₂ V _u2ga u _2a -x ₁ V _u1ga u _1a ]/g front cover

h _th∞a ＝[(1-x ₂ )V _u2lb u _2b -(1-x ₁ )V _u1lb u _1b +x ₂ V _u2gb u _2b -x ₁ V _u1gb u _1b ]/g rear cover

(11)

In the formula, x—mass gas fraction, x=m _g /m

m _g ——gas phase mass flow rate,

m ₁ ——liquid phase mass flow rate,

m—mass flow rate of gas-liquid mixed phase, m=m _g +m ₁ ,

V—circumferential component of absolute velocity,

u—peripheral speed.

According to the slip coefficient formula above and the calculation formula of the finite blade theoretical head H _t , the finite blade theoretical heads H _ta and H _tb of the front and rear shrouds of the blade outlet can be respectively determined. Right now

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ta</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&infin;</span>\mathrm{<span\; class="notranslate">\; a</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; tb</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&infin;</span>\mathrm{<span\; class="notranslate">\; b</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

If the infinite blade theoretical lift of the front cover plate of the blade outlet is smaller than the infinite blade theoretical lift of the rear cover plate, and the limited blade theoretical lifts of the front and rear cover plates of the impeller outlet are equal, then the following relation holds true

H _ta∞ <H _tb∞ (13)

H _ta =H _tb (14)

By adjusting the geometric parameters of the impeller to satisfy the equations (13) and (14), the theoretical head design with unequal number of infinite blades can be achieved, so as to achieve the purpose of equal theoretical head of finite blades.

Adjusting the geometric parameters of the impeller is actually a process of optimizing the design. The optimal design requires a good fit between the various geometric parameters of the impeller on the premise of satisfying the specified performance, so as to obtain the highest possible efficiency. The constraint range of the design variable has an important impact on the optimization result. If the design range of the variable is too narrow, the optimization point may be missed. If the value range is too large, it does not conform to the design law and manufacturing process of the pump. The range of values of the design variables is widened. The constraints in the optimal design process of the present invention are:

25°<β ₂ <60° (15)

$\mathrm{<span\; class="notranslate">\; 0.537</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.815</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; 8</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 12</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; 3.68</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 3.975</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

30°<β ₁ <40° (19)

$\frac{\mathrm{<span\; class="notranslate">\; 0.58</span>}\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g\; H</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 0.98</span>}\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; 3.5</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g\; H</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Fig. 1 is an axial sectional view of an impeller according to an embodiment of the patent of the present invention.

Fig. 2 is the impeller vane figure of the same embodiment (the impeller plane sectional view seen from the impeller front cover towards the impeller rear cover after the front cover of the impeller is removed).

In the figure: 1. Front cover of impeller, 2. Rear cover of impeller, 3. Width of impeller blade inlet, 4. Width of impeller blade outlet, 5. Outer circle diameter of impeller blade, 6. Impeller inlet diameter, 7. Blade inlet Placement angle, 8. Blade outlet placement angle, 9. Blade wrap angle, 10. Blade, 11. Blade working surface, 12. Blade back. In the figure, a, b, and c respectively represent the streamlines of the front cover, the streamlines of the rear cover, and the middle streamlines.

Detailed ways

Figures 1 and 2 together define the shape of the impeller for this embodiment. Like most centrifugal pump impellers, it has an impeller front cover (1) and an impeller rear cover (2), and is a closed impeller. In the figure, the convex surface of the blade (10) is the blade working surface (11), and the concave surface of the blade is the blade back surface (12). The present invention adjusts the geometric parameters of the impeller through the following relational formulas, the impeller blade inlet width b ₁ (3), the impeller blade outlet width b ₂ (4), the outer circle diameter D ₂ (5) of the impeller blade, and the impeller inlet diameter D ₁ (6), blade inlet placement angle β ₁ (7), blade outlet placement angle β ₂ (8), blade wrap angle ψ(9), the performance of the nuclear main pump in this embodiment meets the flow rate of the optimal efficiency working condition Q _BEP , the head H _BEP of the optimal efficiency condition, the requirement of the impeller speed n.

$\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; ZL</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}}\frac{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; three</span>}<span\; class="notranslate">\; )</span>$

In the formula, ψ——head coefficient

δ—coefficient, δ=1.473φ ^2.16 ;

φ——geometric parameter;

b ₁ , b ₂ —— impeller inlet and outlet width;

L _R ——blade chord length, $L_R=\frac{R_2-R_1}{\sin \left(\frac{{\mathrm{\&beta;}}_1+{\mathrm{\&beta;}}_2}{2}\right)}$

H _th∞a ＝[(1-x ₂ )V _u2la u _2a -(1-x ₁ )V _u1la u _1a +x ₂ V _u2ga u _2a -x ₁ V _u1ga u _1a ]/g front cover

H _th∞a ＝[(1-x ₂ )V _u2lb u _2b -(1-x ₁ )V _u1lb u _1b +x ₂ V _u2gb u _2b -x ₁ V _u1gb u _1b ]/g rear cover

(twenty four)

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ta</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&infin;</span>\mathrm{<span\; class="notranslate">\; a</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; tb</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&infin;</span>\mathrm{<span\; class="notranslate">\; b</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 25</span>}<span\; class="notranslate">\; )</span>$

H _ta∞ ＞H _tb∞ (26)

H _ta =H _tb (27)

Restrictions:

25°＜ _β2 ＜60° (28)

$\mathrm{<span\; class="notranslate">\; 0.537</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.815</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 29</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; 8</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 12</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 100</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 30</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; 3.68</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 3.975</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 31</span>}<span\; class="notranslate">\; )</span>$

30°<β ₁ <40° (32)

$\frac{\mathrm{<span\; class="notranslate">\; 0.58</span>}\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g\; H</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 0.98</span>}\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; 3.5</span>}\sqrt[\mathrm{<span\; class="notranslate">\; 3</span>}]{\frac{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g\; H</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 33</span>}<span\; class="notranslate">\; )</span>$

According to the shape of the performance curve to be achieved according to the design requirements, adjust β ₂ between 25° and 60°. When the curve drops steeply, β ₂ takes a small value, and when the curve is flat, β ₂ takes a large value. In order to improve the gas-liquid mixed transport capacity of the impeller of the nuclear main pump, the largest possible outlet placement angle should be selected.

The hydraulic design method of gas-liquid two-phase flow nuclear main pump impeller with unequal head is adopted in this design, which can be applied to the transportation of gas-liquid two-phase flow during loss of water accidents.

In this embodiment, blade wrapping angle and number of blades can be selected and determined according to casting process requirements. While ensuring performance, more blades are selected, usually 4-7 blades.

Claims (5)

1. gas-liquid two-phase flow core main pump impeller does not wait the lift Hydraulic Design Method, according to core main pump performance being satisfied the flow Q of optimum efficiency operating mode _BEP, the lift H of optimum efficiency operating mode _BEP, the requirement of wheel speed n.It is characterized in that at the unlimited blade theoretical head of the front shroud of blade exit during less than the unlimited blade theoretical head of back shroud, the limited blade theoretical head of impeller outlet front shroud equates with the limited blade theoretical head of back shroud, and the core main pump is carried the gas-liquid two-phase medium when having considered loss of-coolant accident (LOCA), and regulate the impeller main geometric parameters by following formula and constraint conditio, to satisfy the Centrifugal Impeller Design requirement.

$\mathrm{\&phi;}=\frac{{2\mathrm{\&pi;R}}_2}{{\mathrm{ZL}}_R}\frac{b_2}{b_1}[{\sin \mathrm{\&beta;}}_2-\frac{R_1}{R_2}{\sin \mathrm{\&beta;}}_2]---\left(3\right)$

H _{Th ∞ a}=[(1-x ₂) V _U2lau _2a-(1-x ₁) V _U1lau _1a+ x ₂V _U2gau _2a-x ₁V _U1gau _1a]/g front shroud

H _{Th ∞ a}=[(1-x ₂) V _U2lbu _2b-(1-x ₁) V _U1lbu _1b+ x ₂V _U2gbu _2b-x ₁V _U1gbu _1b]/g back shroud

(4)

$\left\{\begin{array}{c}{H}_{\mathrm{ta}}={\mathrm{\&mu;}}_a{H}_{t\&infin;a}\\ H_{\mathrm{tb}}={\mathrm{\&mu;}}_b{H}_{t\&infin;b}\end{array}\right.---\left(5\right)$

H _ta∞＜H _tb∞ (6)

H _ta＝H _tb (7)

Constraint conditio:

25°＜β ₂＜60° (8)

$0.537{\left(\frac{n_s}{100}\right)}^{5/6}\sqrt[3]{\frac{Q}{n}}<b_2<0.815{\left(\frac{n_s}{100}\right)}^{5/6}\sqrt[3]{\frac{Q}{n}}---\left(9\right)$

$8{\left(\frac{n_s}{100}\right)}^{-0.5}\sqrt[3]{\frac{Q}{n}}<b_2<12{\left(\frac{n_s}{100}\right)}^{-0.5}\sqrt[3]{\frac{Q}{n}}---\left(10\right)$

$3.68\sqrt[3]{\frac{Q}{n}}<b_2<3.975\sqrt[3]{\frac{Q}{n}}---\left(11\right)$

30°＜β ₁＜40° (12)

$\frac{0.58Q}{4\sqrt[3]{\frac{Q}{n}}{K}_{m1}\sqrt{2\mathrm{gH}}}<b_1<\frac{0.98Q}{3.5\sqrt[3]{\frac{Q}{n}}{K}_{m1}\sqrt{2\mathrm{gH}}}---\left(13\right)$

In formula:

μ---slip coefficient;

ψ---head coefficient;

K _m1---correction factor;

δ---coefficient, δ=1.473 φ ^2.16

φ---geometric parameter;

L _R---the blade chord length, $L_R=\frac{R_2-R_1}{\sin \left(\frac{{\mathrm{\&beta;}}_1+{\mathrm{\&beta;}}_2}{2}\right)};$

b ₁, b ₂---impeller inlet/outlet width;

D ₁, D ₂---impeller inlet/outlet diameter;

β ₁, β ₂---impeller blade inlet/outlet laying angle;

N speed, rev/min;

Q---operating point for design flow, m3/s;

H---operating point for design lift, rice;

X---mass gas content rate, x=m _g/ m

m _g---gas phase mass flow,

m ₁---the liquid phase mass flow rate,

M---gas-liquid mixed phase mass flow rate, m=m _g+ m ₁,

The circumferential components of V---absolute velocity,

U---peripheral velocity.

2. gas-liquid two-phase flow core main pump impeller does not wait the lift Hydraulic Design Method as claimed in claim 1, it is characterized in that at H _{Ta ∞}＞H _{Tb ∞}The time, H _ta=H _tb, the hydraulic loss that produces in impeller is minimum, and such the Hydraulic Design is only best design result.

3. gas-liquid two-phase flow core main pump impeller as claimed in claim 1 does not wait the lift Hydraulic Design Method, it is characterized in that: the performance curve shape that will reach according to designing requirement, and with β ₂Adjust β when curve falls suddenly between 25 °～60 ° ₂Get the small value, β when curve is smooth ₂Get large value.For improving the gas-liquid delivery ability of core main pump impeller, should choose large as far as possible outlet laying angle.

4. gas-liquid two-phase flow core main pump impeller as claimed in claim 1 does not wait the lift Hydraulic Design Method, it is characterized in that: impeller blade import laying angle β ₁, adjust between 30 °～40 ° without the separation of flow by optimum efficiency point.

5. gas-liquid two-phase flow core main pump impeller as claimed in claim 1 does not wait the lift Hydraulic Design Method, subtended angle of blade and the number of blade can require to select to determine according to casting technique, in guaranteed performance, select the more number of blade, usually getting the number of blade is 4～7.

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