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离心泵水力设计

    离心泵水力设计的任务是确定叶轮、吸水室、压水室和其他过流部件的几何结构参数,生成过流部件的模型图，其水力尺寸由设计要求决定，同时还要保证所设计的泵具有较高的水力效率、良好的空化性能和较好的水力稳定性。设计要求通常包括流量、扬程、转速、泵汽蚀余量或装置汽蚀余量、效率以及输送介质的物理性质等。
    叶轮是离心泵的核心部件,泵的流量扬程、效率及空化性能都与叶轮的水力设计有着重要关系。设计叶片的任务，就是设计出符合流动规律的叶片形状，为此需要研究液流在叶轮内的运动规律。由于液流在叶轮内的流动一般是复杂的非定常三维黏性湍流，通常要根据具体情况，合理采用某些假定以建立简化的流动模型来求解。根据对流动情况的假设和简化不同，叶轮水力设计的流动理论可分为一元流动理论、二元流动理论以及三元流动理论。
    (1)一元理论 :叶轮是由无穷多个厚度无限薄的叶片组成的，这样叶轮内的流动就具有轴对称的特点，即a/aqs = 0,流面是以叶轮轴线为旋转轴的回转面:同时假定轴面速度沿过水断面是均勾分布的。因此，叶轮中任意一点的轴面速度只与过水断面的位置有关，即Cm=Cm(q1)。

(2)二元理论:二元理论与一元理论的相同点是它也认为叶轮是由厚度无限薄的无穷多个叶片组成的，同样认为叶轮内的流动具有轴对称的特点，但与一元理论不同之处在于二元理论并不认为轴面速度沿着过水断而是均匀分布的。根据这种假设，叶轮中任意一点的轴面速度不仅与过水断面的位置有关，还与该点在过水断面上的位置有关，即Cm=Cm(q1，q2)

(3)三元理论:三元理论在理论上最为严格，它不采用叶片无穷多假设，所以叶轮内的流动也不是轴对称流动，每个轴面的流动各不相同。另外，沿同一过水断面轴面速度也不是均匀分布的。轴面速度随轴面、轴面流线、过水断面形成的3个坐标的变化而变化.即Cm=Cm(q1，q2.q3)。这种方法通过在三维空间中求解流动方程来计算叶片形状，能够更准确地模拟叶轮内空间流动的特性。
    注意:q1表示轴面流动方向.q2表示过水断面方向，q3表示圆周速度方向。如图1-98所示。

常规的一元水力设计方法去是根据计算所得的叶轮基本尺寸:叶轮外径、叶轮出口宽度、叶轮进口直径以及轮毂直径，参考相近比转专速叶轮的图纸，初步绘制叶轮的轴面投影图，包括叶轮的进口边、出口边、轮毂和轮缘，再用”内切圆校验法"检查流道的过流断面面积的变化规

律,如果变化规律不理想，则要修改轮毂和轮缘的形状，反复修改，直到满足要求。

采用二元流动理论进行水力设计时,首先通过计算得到主要尺寸参数以生成初始轴面流道轮廓，应用准正交线法绘制轴面流网，并检验其过流断面面积分布是否合理，通过对轴面流场不断进行迭代计算来调整轴面流道轮廓，使用逐点积分法对叶片骨线绘型，对叶片在轴面流线方向上进行加厚,最后利用“贝塞尔”曲线对叶片头部进行修整以完成设计,其程序流程如图1-99所示。

对于全三元问题.目前国内外发展较快的一种方法 是采用Clebsch公式来表示流场，叶轮内的流动为稳定的有旋流;将流场分解为平均流场和周期流场，周期流场中的周期流动变量用傅里叶级数沿周向展开，把三元问题转化为无穷多个二元平面问题来求解。
    以下以设计某离心泵参数为例，详述采用二元理论设计的各过程，该离心泵所需主要结构参数见表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.