双吸泵空化性能改进

Improvement of cavitation performance of double suction pump

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前 言

Preface

基于经验的传统叶轮设计需要繁琐的模型试验，大大增加了设计成本和设计周期，制约了离心泵高空化性能优化设计的进一步发展[2] 。随着计算流体动力学( CFD) 技术在水力机械内部流场计算中应用日益广泛，CFD成为优化设计的重要工具。长期以来，国内外学者采用数值模拟的方法对水泵内部空化流动进行了很多研究[5,6]，并成功预测了空化临界点[7,8,9]和离心泵叶轮内发生的多区域空化流动现象等[10,11]。如Medvitz等[12]捕捉到了离心泵在偏流量工况的能量和扬程下降特性，Coutier Delgosha等[13]采用正压状态方程对3台离心泵进行定常空化流动计算，成功获取了泵的扬程下降曲线及空泡结构。

The traditional design of the traditional impeller based on experience needs tedious model test, which greatly increases the design cost and design cycle, which restricts the further development of the optimization design of the high altitude performance of the centrifugal pump [2]. As computational fluid dynamics (CFD) technology is applied more and more widely in the calculation of internal flow field of hydraulic machinery, CFD has become an important tool for optimization design. For a long time, many domestic and foreign scholars have studied the cavitation flow inside the pump by numerical simulation methods, and have successfully predicted the [10,11] of the cavitation critical point [7,8,9] and the multi area cavitation flow phenomenon in the impeller of the centrifugal pump. [12], such as Medvitz and so on, captured the energy and head drop characteristic of the centrifugal pump in the partial flow condition, and the [13] of Coutier Delgosha and so on uses the positive pressure state equation to calculate the constant cavitation flow of the 3 centrifugal pumps, and successfully obtained the head drop curve and the vacuole structure of the pump.

不难看出，上述离心泵的空化研究较多集中于对外特性的预测，目前对叶轮空化性能优化改进的相关工作虽然也做了不少，但仍有待于深入研究。本文应用汽液两相流混合模型基本方程，对一台比转速为100的双吸泵叶轮内部空化性能进行数值计算和分析，并通过修改叶轮入口直径、前盖板圆弧半径及叶片进口边形状来提升叶轮空化性能，旨在给出离心泵空化流计算中叶轮改进的合理建议。

It is not difficult to see that the cavitation research of the centrifugal pump is mostly focused on the prediction of external characteristics. Although many related work on the optimization of the cavitation performance of the impeller has been done, it still needs to be studied in depth. In this paper, the cavitation performance of a double suction pump impeller with a specific speed of 100 is numerically calculated and analyzed by using the basic equations of the mixture model of a steam liquid two phase flow. The cavitation performance of the impeller is improved by modifying the inlet diameter of the impeller, the radius of the arc of the front cover plate and the shape of the inlet edge of the blade. The purpose of this paper is to give the middle leaf of the cavitation flow calculation of the centrifugal pump. Reasonable suggestions for the improvement of the wheel.

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基本参数及网格划分

Basic parameters and grid partition

本文计算模型为一台双吸泵，流量 QO=7000m3/h，扬程H=55m，叶片数Z=6，转速n =740rpm。计算域由吸水室、叶轮及压水室组成。划分网格时采用非结构化四面体网格，并在叶片头部及尾部，压水室隔舌处进行加密，计算域见图1。进行网格无关性检查时，当扬程的相对误差低于0.5%便可认为网格对计算结果无影响，最后确定计算所采用的网格总数为240万。

The calculation model is a double suction pump, with a flow rate of QO=7000m3/h, a lift H=55m, a blade number of Z=6, and a speed of n =740rpm. The calculation domain consists of a suction chamber, an impeller and a water pressing chamber. The unstructured tetrahedral mesh is used to divide the grid, and is encrypted at the tongue head of the blade head and tail. The computational domain is shown in Figure 1. When the relative error of the lift is less than 0.5%, it is considered that the grid has no effect on the results of the calculation, and the total number of grids used in the calculation is 2 million 400 thousand.

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边界条件设定

Boundary condition setting

边界条件在入口设为总压，进口处水的体积分数设为1，气泡的体积分数设为０。出口边界设为质量出口以控制模型的流量。通过调节进口压力改变进口的有效空化余量，从而控制水泵内部空化发生的程度。

The boundary condition is set at the inlet as the total pressure. The volume fraction of water at the inlet is 1 and the volume fraction of the bubble is 0. The export boundary is set as a quality outlet to control the flow of the model. By adjusting the inlet pressure, the effective cavitation allowance of the inlet is changed to control the degree of cavitation inside the pump.

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空化模型及湍流模型

Cavitation model and turbulence model

空化计算应用均质多相模型和Zwart-Gerbe-Belamri空化模型来考虑空泡的生长与溃灭，介质的饱和蒸汽压力设置为3574Pa，空泡的平均直径为2*10-6m。湍流模型选用RNG模型，该模型最主要的优点为：考虑到壁面上大尺度分离的影响，能有效地处理高应变率及流线弯曲程度较大的流动，所以在预测流体机械中三维非定常流动，能得出很好的结果。

In the cavitation calculation, the homogeneous multiphase model and the Zwart-Gerbe-Belamri cavitation model are used to consider the growth and collapse of the vacuoles. The saturated vapor pressure of the medium is set to 3574Pa, and the average diameter of the cavitation is 2*10-6m. The RNG model is selected for the turbulence model. The main advantage of the model is that the high strain rate and the flow line with a larger streamline can be effectively treated considering the influence of the large scale separation on the wall. So the three-dimensional unsteady flow in the fluid machinery can be predicted with good results.

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计算结果分析

Analysis of calculation results

首先对双吸泵进行单相流场数值模拟，并以该计算结果为初始值，添加空化模型进行空化两相流计算。

First, the single-phase flow field of the double suction pump is numerically simulated, and the cavitation model is used to calculate the cavitation two-phase flow.

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原始叶轮空化性能预测

Prediction of cavitation performance of the original impeller

图2给出了数值计算所得扬程下降曲线。NPSHa值根据下式计算：

Figure 2 shows the head decline curve obtained from numerical calculation. The NPSHa value is calculated according to the following formula:

（1）式中:分别为叶轮进口压力，Pa；为工作介质密度，kg/m3；g为重力加速度，m/s2；为计算域进口断面的绝对速度，m/s2；相应温度下水的汽化压力，单位为Pa，文中主要在300K时取3574Pa。

(1) in the type: the inlet pressure of the impeller, Pa, for the working medium density, kg/m3; G as the gravity acceleration, m/s2; the absolute velocity of the import section of the calculation domain, m/s2; the vaporization pressure of the water at the corresponding temperature, the unit is Pa, and 3574Pa is taken mainly in 300K.

空化计算收敛的标准通常以进出口流量差（允许的最大流量差≤0.4%）及残差曲线衡量，求解过程中不同空化余量下的流动收敛性都较好。可以看出：NPSH值逐渐减小的过程中，扬程也相应出现下降。

The convergence of cavitation calculation is usually measured by the difference of the flow difference of the import and export (maximum allowable flow difference less than 0.4%) and the residual curve, and the convergence of the flow in the solution is better under the different cavitation allowance. It can be seen that in the process of decreasing NPSH value, the lift also decreases correspondingly.

(a)给出了数值计算所得叶轮内空泡的分布（黄色区域为空泡，汽相体积分数等值面取5％），可见空化主要发生在叶片吸力面头部靠前盖板附近，并向流道中心延伸。图3(b)所示现场拍摄的图片中，叶片金属表面几乎在相同位置显现蜂窝状，这主要由空泡溃灭引起局部高速水流打击金属而使其表面疲劳破坏形成，这些蜂窝孔一般与外部相通，且大多数坑槽与都与金属表面垂直。上述分析不难说明计算所采用的空化流数值方法在捕捉空泡现象时具有一定的准确性。

(a) the distribution of cavitation in the impeller is given (the yellow area is vacuole, the vapor phase volume fraction is 5%), and the cavitation mainly occurs near the front cover of the blade suction surface and extends to the center of the flow channel. In the pictures taken in Figure 3 (b), the metal surface of the blade appears almost at the same position in the same position. This is mainly caused by the collapse of the local high-speed water flow against the metal caused by the collapse of the vacuoles, which generally communicate with the outside, and most of the pit grooves are perpendicular to the metal surface. The above analysis is not difficult to explain that the cavitation flow numerical method used in the calculation has certain accuracy in capturing the cavitation phenomenon.

工程上规定：能量参数下降某一百分数( 1～3％) 时的NPSH值为水力机械的空化余量的临界值，记为 NPSHcr。现取扬程下降3％的点为临界空化余量，得到允许空化余量[12]。

The engineering stipulates that the NPSH value of a certain percentage (1 ~ 3%) of the energy parameter is the critical value of the cavitation allowance of the hydraulic machinery, which is recorded as NPSHcr. The critical cavitation allowance is 3%, and the allowable cavitation allowance is [12].

NPSH=NPSHcr+k

NPSH=NPSHcr+k

（2）式中k取0.3 。该水泵的NPSHcr=6.8m（图2中工况D），因而选用的双吸泵空化余量NPSH=7.1m。综合看来，该水泵的空化性能略差。实际应用中，通常采用修整叶片头部的方法来改善水泵的空化性能，具体做法是将叶片头部背面修薄，原理是减低叶片进口的水流速度和叶轮进口排挤，从而提高泵的抗空化能力。此外，采用耐空化材料，如铜合金、合金铸钢等，也不失为一种提高叶轮空化性能的可行之法。

(2) the K in the formula takes 0.3. The NPSHcr=6.8m of the pump (D in Figure 2), and the NPSH=7.1m of the double suction pump is chosen. In a comprehensive view, the cavitation performance of the pump is slightly poor. In practical application, the method of dressing the head of the blade is usually used to improve the cavitation performance of the pump. The concrete method is to trim the back of the head of the blade. The principle is to reduce the flow velocity of the inlet of the blade and the inlet and squeeze of the impeller, so as to improve the cavitation resistance of the pump. In addition, cavitation resistant material, such as copper alloy and alloy cast steel, is also a feasible method to improve the cavitation performance of the impeller.

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改进方案空化性能预测

Improved prediction of cavitation performance

影响水泵汽蚀性能的主要因素包括叶轮进口几何形状、叶片进口边形状、进出口安放角及流道形状等。因而，要改善一台水泵自身的空化性能，应重

The main factors affecting the cavitation performance of the pump include the geometry of the impeller inlet, the shape of the blade inlet, the angle of inlet and outlet, and the shape of the runner. Therefore, to improve the cavitation performance of a pump, it should be heavy.