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離心泵水力設計

    離心泵水力設計的任務是確定葉輪、吸水室、壓水室和其他過流部件的幾何結構參數,生成過流部件的模型圖，其水力尺寸由設計要求決定，同時還要保證所設計的泵具有較高的水力效率、良好的空化性能和較好的水力穩定性。設計要求通常包括流量、揚程、轉速、泵汽蝕余量或裝置汽蝕余量、效率以及輸送介質的物理性質等。
    葉輪是離心泵的核心部件,泵的流量揚程、效率及空化性能都與葉輪的水力設計有著重要關系。設計葉片的任務，就是設計出符合流動規律的葉片形狀，為此需要研究液流在葉輪內的運動規律。由于液流在葉輪內的流動一般是復雜的非定常三維黏性湍流，通常要根據具體情況，合理采用某些假定以建立簡化的流動模型來求解。根據對流動情況的假設和簡化不同，葉輪水力設計的流動理論可分為一元流動理論、二元流動理論以及三元流動理論。
    (1)一元理論 :葉輪是由無窮多個厚度無限薄的葉片組成的，這樣葉輪內的流動就具有軸對稱的特點，即a/aqs = 0,流面是以葉輪軸線為旋轉軸的回轉面:同時假定軸面速度沿過水斷面是均勾分布的。因此，葉輪中任意一點的軸面速度只與過水斷面的位置有關，即Cm=Cm(q1)。

(2)二元理論:二元理論與一元理論的相同點是它也認為葉輪是由厚度無限薄的無窮多個葉片組成的，同樣認為葉輪內的流動具有軸對稱的特點，但與一元理論不同之處在于二元理論并不認為軸面速度沿著過水斷而是均勻分布的。根據這種假設，葉輪中任意一點的軸面速度不僅與過水斷面的位置有關，還與該點在過水斷面上的位置有關，即Cm=Cm(q1，q2)

(3)三元理論:三元理論在理論上最為嚴格，它不采用葉片無窮多假設，所以葉輪內的流動也不是軸對稱流動，每個軸面的流動各不相同。另外，沿同一過水斷面軸面速度也不是均勻分布的。軸面速度隨軸面、軸面流線、過水斷面形成的3個坐標的變化而變化.即Cm=Cm(q1，q2.q3)。這種方法通過在三維空間中求解流動方程來計算葉片形狀，能夠更準確地模擬葉輪內空間流動的特性。
    注意:q1表示軸面流動方向.q2表示過水斷面方向，q3表示圓周速度方向。如圖1-98所示。

常規的一元水力設計方法去是根據計算所得的葉輪基本尺寸:葉輪外徑、葉輪出口寬度、葉輪進口直徑以及輪轂直徑，參考相近比轉專速葉輪的圖紙，初步繪制葉輪的軸面投影圖，包括葉輪的進口邊、出口邊、輪轂和輪緣，再用”內切圓校驗法"檢查流道的過流斷面面積的變化規

律,如果變化規律不理想，則要修改輪轂和輪緣的形狀，反復修改，直到滿足要求。

采用二元流動理論進行水力設計時,首先通過計算得到主要尺寸參數以生成初始軸面流道輪廓，應用準正交線法繪制軸面流網，并檢驗其過流斷面面積分布是否合理，通過對軸面流場不斷進行迭代計算來調整軸面流道輪廓，使用逐點積分法對葉片骨線繪型，對葉片在軸面流線方向上進行加厚,最后利用“貝塞爾”曲線對葉片頭部進行修整以完成設計,其程序流程如圖1-99所示。

對于全三元問題.目前國內外發展較快的一種方法 是采用Clebsch公式來表示流場，葉輪內的流動為穩定的有旋流;將流場分解為平均流場和周期流場，周期流場中的周期流動變量用傅里葉級數沿周向展開，把三元問題轉化為無窮多個二元平面問題來求解。
    以下以設計某離心泵參數為例，詳述采用二元理論設計的各過程，該離心泵所需主要結構參數見表1- 15。

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Hydraulic design of centrifugal pump

The task of hydraulic design of centrifugal pump is to determine the geometric structure parameters of impeller, suction chamber, pressurized water chamber and other flow passage components, and to generate the model diagram of flow passage components. The hydraulic size of the flow passage components is determined by the design requirements. At the same time, it is necessary to ensure that the designed pump has high hydraulic efficiency, good cavitation performance and good hydraulic stability. Design requirements usually include flow, head, speed, NPSH of pump or device, efficiency and physical properties of conveying medium.

Impeller is the core component of centrifugal pump. The flow head, efficiency and cavitation performance of the pump are closely related to the hydraulic design of the impeller. The task of blade design is to design the blade shape which accords with the flow law. Therefore, it is necessary to study the movement law of liquid flow in the impeller. Because the fluid flow in the impeller is generally complex unsteady three-dimensional viscous turbulence, it is usually necessary to adopt some reasonable assumptions to establish a simplified flow model according to the specific situation. According to the different assumptions and simplifications of flow conditions, the flow theory of impeller hydraulic design can be divided into one-dimensional flow theory, two-dimensional flow theory and three-dimensional flow theory.

(1) It is assumed that the flow velocity of the impeller is infinite along the axis of the blade, i.e., the flow velocity of the impeller is infinite along the axis of the blade. Therefore, the axial velocity at any point in the impeller is only related to the position of the water passing section, that is, CM = cm (Q1).

(2) Binary theory: the same point between the two-dimensional theory and the one-dimensional theory is that it also considers that the impeller is composed of infinitely thin blades, and that the flow in the impeller is axisymmetric. However, the difference between the two-dimensional theory and the one-dimensional theory is that the axial velocity is not uniformly distributed along the water break. According to this assumption, the axial velocity at any point in the impeller is not only related to the position of the flow section, but also to the position of the point on the cross-section, that is, CM = cm (Q1, Q2)

(3) Three dimensional theory: the three-dimensional theory is the most rigorous in theory, it does not use the assumption of infinite blades, so the flow in the impeller is not axisymmetric, and the flow in each axial surface is different. In addition, the velocity along the same section is not uniform. The axial velocity changes with the changes of the three coordinates formed by the axial plane, the axial streamline and the cross-section, i.e. cm = cm (Q1, Q2. Q3). By solving the flow equation in three-dimensional space to calculate the blade shape, this method can more accurately simulate the flow characteristics in the impeller.

Note: Q1 is the axial flow direction, Q2 is the direction of flow section, Q3 is the direction of circumferential velocity. As shown in Figure 1-98.

The conventional one-dimensional hydraulic design method is based on the calculated basic impeller dimensions: impeller outer diameter, impeller outlet width, impeller inlet diameter and hub diameter. Referring to the drawings of similar specific speed impeller, the axial plane projection diagram of impeller is preliminarily drawn, including the inlet edge, outlet edge, hub and flange of the impeller, and then the "inscribed circle calibration method" is used to check the flow passage cross section Area gauge

If the change law is not ideal, the shape of hub and flange should be modified repeatedly until the requirements are met.

When the two-dimensional flow theory is used for hydraulic design, Firstly, the main dimension parameters are calculated to generate the initial axial flow channel contour, and the quasi orthogonal line method is used to draw the axial flow network, and whether the distribution of the flow cross-section area is reasonable. The axial flow field is adjusted by iterative calculation of the axial flow field. The blade bone line is drawn by the point by point integration method, and the blade is thickened in the axial streamline direction, Finally, "Bessel" curve is used to trim the blade head to complete the design. The program flow is shown in Fig. 1-99.

For the full three-dimensional problem, Clebsch formula is used to express the flow field, and the flow in the impeller is stable with swirling flow; the flow field is divided into average flow field and periodic flow field, and the periodic flow variables in periodic flow field are expanded along the circumference by Fourier series, and the three-dimensional problem is transformed into infinite two-dimensional plane problems to solve.

The following takes the design of a centrifugal pump parameters as an example to detail the design process using binary theory. The main structural parameters of the centrifugal pump are shown in table 1-15.