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離心泵水力設(shè)計(jì)
離心泵水力設(shè)計(jì)的任務(wù)是確定葉輪、吸水室、壓水室和其他過(guò)流部件的幾何結(jié)構(gòu)參數(shù),生成過(guò)流部件的模型圖，其水力尺寸由設(shè)計(jì)要求決定，同時(shí)還要保證所設(shè)計(jì)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(wěn)定性。設(shè)計(jì)要求通常包括流量、揚(yáng)程、轉(zhuǎn)速、泵汽蝕余量或裝置汽蝕余量、效率以及輸送介質(zhì)的物理性質(zhì)等。
葉輪是離心泵的核心部件,泵的流量揚(yáng)程、效率及空化性能都與葉輪的水力設(shè)計(jì)有著重要關(guān)系。設(shè)計(jì)葉片的任務(wù)，就是設(shè)計(jì)出符合流動(dòng)規(guī)律的葉片形狀，為此需要研究液流在葉輪內(nèi)的運(yùn)動(dòng)規(guī)律。由于液流在葉輪內(nèi)的流動(dòng)一般是復(fù)雜的非定常三維黏性湍流，通常要根據(jù)具體情況，合理采用某些假定以建立簡(jiǎn)化的流動(dòng)模型來(lái)求解。根據(jù)對(duì)流動(dòng)情況的假設(shè)和簡(jiǎn)化不同，葉輪水力設(shè)計(jì)的流動(dòng)理論可分為一元流動(dòng)理論、二元流動(dòng)理論以及三元流動(dòng)理論。
(1)一元理論 :葉輪是由無(wú)窮多個(gè)厚度無(wú)限薄的葉片組成的，這樣葉輪內(nèi)的流動(dòng)就具有軸對(duì)稱的特點(diǎn)，即a/aqs = 0,流面是以葉輪軸線為旋轉(zhuǎn)軸的回轉(zhuǎn)面:同時(shí)假定軸面速度沿過(guò)水?dāng)嗝媸蔷捶植嫉摹Ｒ虼?，葉輪中任意一點(diǎn)的軸面速度只與過(guò)水?dāng)嗝娴奈恢糜嘘P(guān)，即Cm=Cm(q1)。
(2)二元理論:二元理論與一元理論的相同點(diǎn)是它也認(rèn)為葉輪是由厚度無(wú)限薄的無(wú)窮多個(gè)葉片組成的，同樣認(rèn)為葉輪內(nèi)的流動(dòng)具有軸對(duì)稱的特點(diǎn)，但與一元理論不同之處在于二元理論并不認(rèn)為軸面速度沿著過(guò)水?dāng)喽蔷?/span>勻分布的。根據(jù)這種假設(shè)，葉輪中任意一點(diǎn)的軸面速度不僅與過(guò)水?dāng)嗝娴奈恢糜嘘P(guān)，還與該點(diǎn)在過(guò)水?dāng)嗝嫔系奈恢糜嘘P(guān)，即Cm=Cm(q1，q2)
(3)三元理論:三元理論在理論上最為嚴(yán)格，它不采用葉片無(wú)窮多假設(shè)，所以葉輪內(nèi)的流動(dòng)也不是軸對(duì)稱流動(dòng)，每個(gè)軸面的流動(dòng)各不相同。另外，沿同一過(guò)水?dāng)嗝孑S面速度也不是均勻分布的。軸面速度隨軸面、軸面流線、過(guò)水?dāng)嗝嫘纬傻?/span>3個(gè)坐標(biāo)的變化而變化.即Cm=Cm(q1，q2.q3)。這種方法通過(guò)在三維空間中求解流動(dòng)方程來(lái)計(jì)算葉片形狀，能夠更準(zhǔn)確地模擬葉輪內(nèi)空間流動(dòng)的特性。
注意:q1表示軸面流動(dòng)方向.q2表示過(guò)水?dāng)嗝娣较?/span>，q3表示圓周速度方向。如圖1-98所示。
常規(guī)的一元水力設(shè)計(jì)方法去是根據(jù)計(jì)算所得的葉輪基本尺寸:葉輪外徑、葉輪出口寬度、葉輪進(jìn)口直徑以及輪轂直徑，參考相近比轉(zhuǎn)專(zhuān)速葉輪的圖紙，初步繪制葉輪的軸面投影圖，包括葉輪的進(jìn)口邊、出口邊、輪轂和輪緣，再用”內(nèi)切圓校驗(yàn)法"檢查流道的過(guò)流斷面面積的變化規(guī)
律,如果變化規(guī)律不理想，則要修改輪轂和輪緣的形狀，反復(fù)修改，直到滿足要求。
采用二元流動(dòng)理論進(jìn)行水力設(shè)計(jì)時(shí),首先通過(guò)計(jì)算得到主要尺寸參數(shù)以生成初始軸面流道輪廓，應(yīng)用準(zhǔn)正交線法繪制軸面流網(wǎng)，并檢驗(yàn)其過(guò)流斷面面積分布是否合理，通過(guò)對(duì)軸面流場(chǎng)不斷進(jìn)行迭代計(jì)算來(lái)調(diào)整軸面流道輪廓，使用逐點(diǎn)積分法對(duì)葉片骨線繪型，對(duì)葉片在軸面流線方向上進(jìn)行加厚,最后利用“貝塞爾”曲線對(duì)葉片頭部進(jìn)行修整以完成設(shè)計(jì),其程序流程如圖1-99所示。
對(duì)于全三元問(wèn)題.目前國(guó)內(nèi)外發(fā)展較快的一種方法 是采用Clebsch公式來(lái)表示流場(chǎng)，葉輪內(nèi)的流動(dòng)為穩(wěn)定的有旋流;將流場(chǎng)分解為平均流場(chǎng)和周期流場(chǎng)，周期流場(chǎng)中的周期流動(dòng)變量用傅里葉級(jí)數(shù)沿周向展開(kāi)，把三元問(wèn)題轉(zhuǎn)化為無(wú)窮多個(gè)二元平面問(wèn)題來(lái)求解。
以下以設(shè)計(jì)某離心泵參數(shù)為例，詳述采用二元理論設(shè)計(jì)的各過(guò)程，該離心泵所需主要結(jié)構(gòu)參數(shù)見(jiàn)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.
