1. 前言
1. Preface
离心泵内实际的流动是三维、粘性、非定常的流动，空间任何一点的状态都是随时间变化的。国内外的大量实验和理论研究表明，水泵内非定常流动影响着叶片载荷、效率特性等各方面的性能。其中，空化和动静干涉是引起水泵内部压力脉动的两个主要因素。
The actual flow in a centrifugal pump is three-dimensional, viscous and unsteady flow, and the state of any point in space varies with time. A large number of experiments and theoretical studies at home and abroad have shown that unsteady flow in the pump affects the performance of blade load, efficiency and so on. Among them, cavitation and static interference are two main factors that cause pressure pulsation inside the pump.
与空化相关的压力脉动，对水力系统的稳定性、系统运行安全有很大影响，人们也对此展开了大量研究。目前空化流场中压力脉动的研究已涉及到多种装置系统，如反向磁盘[1]，灌排双向立式泵装置[2]、蝶形阀[3]、喷嘴[4]、诱导轮[5]、离心泵[6]和水轮机[7]等。基于大量研究可发现，汽蚀对压力脉动的影响（除叶频或轴频外）主要体现在两个方面，一是出现低频成分，周华[8]、王泽军[9]和李胜才[10]等通过试验得出低频压力脉动是空化发生的伴生现象。二是可能出现高频脉冲成分，是指空泡溃灭和回弹再生所发射的脉冲，在空化压力脉动中以高频分量的形式出现。通常空泡在破裂的过程中不但出现“噼啪”噪音，而且形成所谓的空化脉动，空化脉动诱导生成高频压力脉冲[11]。
The pressure pulsation related to cavitation has a great influence on the stability of the hydraulic system and the safety of the system, and a great deal of research has been carried out. At present, the research on the pressure pulse in the cavitation flow field have been related to various devices such as disk system, reverse [1], and two-way vertical pump system [2], butterfly valve [3], [4], [5], nozzle inducer [6] centrifugal pump and turbine [7]. A large number of studies can be found based on the effect of cavitation on pressure pulsation (except leaf frequency or frequency axis) is mainly reflected in two aspects, one is the low frequency components, [8], Zhou Hua Wang Zejun [9] and Li Shengcai [10] from the test results, the low-frequency pressure pulsation phenomenon accompanied cavitation. Two possible components of high frequency pulse, the pulse emission refers to the bubble collapse and rebound in the regeneration of high frequency components in the form of cavitation pressure pulsation. In the process of bubble rupture is usually not only crackling noise, and the formation of the so-called generation of high frequency pulsating cavitation, cavitation induced by pulsating pressure pulse [11].
研究表明，离心泵内部的动静干涉是引起压力脉动的主要原因之一，文献[12,13,14]成功地捕捉了叶轮-蜗壳的动静干涉作用引起的流场非定常流动特性。潘中永等[15]认为动静干涉是导致泵内部流动不稳定的一个重要原因，这种流动不稳定性最明显的特征就是引起的内部压力脉动的主频与叶片通过频率相同。Parrondo Gayo等[16]测试了离心泵蜗壳圆周方向的压力脉动，揭示了流量和叶片/隔舌位置是引起脉动的主要原因，并指出最大脉动值出现在距离隔舌最近的位置和小流量工况时。文献[17,18,19]指出，离心泵内部的压力以叶片旋转频率发生周期性变化，且额定流量时的压力波动幅度比偏工况时要小。倪永燕[20]和耿少娟[21]等也采用商用软件对离心泵全流道内进行了非定常湍流模拟，研究进一步表明叶轮和隔舌的动静干涉对叶轮流道出口压力脉动影响显著。
The study shows that the dynamic and static interference in centrifugal pump is one of the main reasons for pressure pulsation. The [12,13,14] literature successfully captured the unsteady flow characteristics of impeller and volute due to the dynamic and static interference. Pan Zhongyong and other [15] think that the static and dynamic interference is an important reason for the unstable flow inside the pump. The most obvious feature of the flow instability is that the main frequency of the internal pressure fluctuation is the same as the blade passing frequency. Parrondo Gayo and [16] tested the pressure pulsation in the circumferential direction of the centrifugal pump volute, and revealed that the main cause of the pulsation was the flow rate and the position of the blade / tongue, and pointed out that the maximum pulsation occurred at the nearest location and small flow condition. Document [17,18,19] points out that the pressure inside the centrifugal pump varies periodically with the rotation frequency of the blades, and the amplitude of pressure fluctuation at rated flow is smaller than that under the partial conditions. Ni Yongyan [20] and Geng Sao [21] also used commercial software to simulate unsteady turbulent flow in the whole flow passage of centrifugal pump. Further research shows that the dynamic and static interference of impeller and tongue tongue has significant influence on the outlet pressure pulsation of impeller.
上述研究虽然使我们对空化和动静干涉引起的流场不稳定流动有了一定的理解，但二者相结合对水泵脉动的影响仍有待于深入研究。计算以一台在现场运行ns=270的双吸泵为例，对其在设计工况（1.0Qo）下，倒灌1m时的非定常空化流场进行压力脉动分析，旨在探寻该水泵振动的主要来源并给出有效的改进建议。
Although the above research makes us understand the unsteady flow field induced by cavitation and dynamic interference, the influence of the two combinations on the pump pulse needs to be further studied. Taking a double suction pump running on site as an example, the pressure pulsation of unsteady cavitating flow field under ns=270 design condition (1.0Qo) is analyzed, aiming at exploring the main source of the pump vibration and giving effective suggestions for improvement.
2. 计算模型
2. calculation model
2.1 基本参数及网格划分
2.1 basic parameters and grid partition
该比转速ns=270型双吸泵，其流量Qo=2900m3/h，扬程H=15m，叶片数Z=6，转速n=990rpm，NPSHr=5.2m。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，最后确定网格总数为255万。
This ratio speed ns=270 double suction pump has the flow rate of Qo=2900m3/h, the lift H=15m, the number of blade Z=6, the speed n=990rpm, and the NPSHr=5.2m. The computational domain consists of a water suction chamber, a impeller and a water pressure chamber. The unstructured tetrahedral mesh is used when dividing the grid, and in the head and tail of the blade, the pressure water chamber is encrypted at the tongue, and 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 calculation results, and the total number of grid is 2 million 550 thousand.
2.2 边界条件设定
2.2 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。
The boundary conditions are set at the entrance to the total pressure. The volume fraction of the water at the inlet is set to 1, and the volume fraction of the bubble is set to 0. The exit boundary is set up as the quality exit to control the flow of the model.
2.3 空化模型及湍流模型
2.3 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。
Cavitation calculation application of homogeneous multiphase model and Zwart-Gerbe-Belamri model to consider the growth and collapse of cavitation bubbles, medium saturation vapor pressure is set to 3574Pa, the average diameter of the cavity is 2*10-6m. The turbulence model used RNG model, the main advantage of this model is: considering the effect of wall on large scale separation, can effectively deal with the flow of high strain rate and streamline bending degree is bigger, so in the prediction of 3D fluid machinery in unsteady flow, can obtain very good results.
3. 计算结果分析
Analysis of 3. calculation results
压力脉动分析中测点的选择非常关键，这关系到计算结果是否能正确地反映泵内脉动的真实情况。本次计算中吸水室布置了如图2所示的5个压力监测点，用于掌握叶轮进口水流的流态信息；在压水室沿水流方向布置了如图3所示的4个压力监测点；叶轮出口布置了2个测点如图3所示。
The selection of the measuring point in the pressure pulsation analysis is very important, which is related to whether the calculation results can correctly reflect the real situation of the pulsation in the pump. In this calculation, the suction chamber is equipped with 5 pressure monitoring points shown in Figure 2, which are used to grasp the flow pattern information of the impeller inlet flow, and 4 pressure monitoring points are shown in Figure 3 as shown in the flow chamber, and 2 measuring points at the outlet of the impeller are shown in figure 3.
3.1压力脉动结果分析
Analysis of 3.1 pressure pulsation results
计算所用双吸泵的轴频，叶频。图4和图5分别给出一个旋转周期内吸水室及压水室各监测点的压力脉动时域、频域图。可以看出，各测点压力脉动呈规律性变化且脉动主频均为6（叶频），说明吸水室与压水室内的压力波动主要是由旋转叶轮和静止蜗壳的相互作用引起的。图6给出了三个旋转周期内叶轮出口监测点SS1、PS1的压力脉动时域、频域图。不难发现，叶轮出口压力脉动的主频为（转频）及2，且该位置处脉动幅值相对水泵其他部位都较大。国际上认为压力脉动合理的标准是：脉动保证值的范围应在出口压力值的±3%之内。该研究中，叶轮出口及隔
The axial frequency and frequency of the double suction pump used are calculated. Figure 4 and figure 5 give a time domain and frequency domain diagram of pressure pulsation for each monitoring point in a rotating chamber and a pressurized water chamber respectively. It can be seen that the pressure pulsation at each measuring point is regular and the pulsation frequency is 6 (Ye Pin), which indicates that the pressure fluctuation in suction chamber and pressure chamber is mainly caused by the interaction between the rotary impeller and the static volute. Figure 6 shows the time and frequency domain diagrams of pressure pulsation of SS1 and PS1 at the exit monitoring points of the impeller at three rotating cycles. It is not difficult to find that the main frequency of the pressure pulsation at the outlet of the impeller is (frequency conversion) and 2, and the amplitude of the pulsation at this position is larger than that of the other parts of the pump. The international standard of pressure pulsation is that the range of the guaranteed value of the pulsation should be within the range of 3% of the pressure value of the outlet. In this study, the outlet and septum of the impeller