Compressiblesimulationofrotor

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1、Compressible simulation of rotor-stator interaction in pump-turbines可压缩的转子的模拟定子相互作用在泵涡轮机Abstract. This work investigates the influence of water compressibility on pressure pulsationsinduced by rotor-stator interaction (RSI) in hydraulic machinery, using the commercial CFDsolver ANSYS-CFX. A pipe flo

2、w example with harmonic velocity excitation at the inlet planeis simulated using different grid densities and time step sizes. Results are compared with avalidated code for hydraulic networks (SIMSEN). Subsequently, the solution procedure isapplied to a simplified 2.5-dimensional pump-turbine config

3、uration in model scale with anadapted speed of sound. Pressure fluctuations are compared with numerical and experimentaldata based on prototype scale. The good agreement indicates that the scaling of acoustic effectswith an adapted speed of sound works well. Finally, the procedure is applied to a 3-

4、dimensional pump configuration in model scale. Pressure fluctuations are compared with results from prototype measurements. Compared to incompressible computations, compressible simulations provide similar pressure fluctuations in vaneless space, but pressure fluctuations inspiral case and penstock

5、may be much higher. With respect to pressure fluctuation amplitudesalong the centerline of runner channels, incompressible solutions exhibit a linear decreasewhile compressible solutions exhibit sinusoidal distributions with maximum values at half thechannel length, coinciding with analytical soluti

6、ons of one-dimensional acoustics.摘要。这工作调查水的压缩系数的影响在压力脉动促使由转子定子相互作用(相对强弱指数)在液压机械，使用广告差价合约解算器优化设计手册都会利用氟类材料。一个管道流动例子同和音的速度激发在进口机被模拟使用不一样的格密度，时间步大小。结果被比较avalidated但只有基因编码性状液的网络(simsen).ubsequently，解决步骤被适用于一个简化2。5维水泵水轮机组态在模型比例尺同一个适应声速。压力波动被比较数值，实验数据以原型为依据规模。良好协议表明那音响效果的规模同一个适应声速工作好。终于，程序被适用于一个3尺寸的的抽水机组态

7、在模型比例尺。压力波动被比较由于原型尺寸。比喻为不可压缩的计算，可压缩的模拟提供类似压力波动在vaneless空间，然而压力波动在蜗壳，闸门可高得多。关于压力波动振幅沿着中心线的亚军渠道，不可压缩的解展览一个直线下降而可压缩的解展览正弦的分配同最大估价格为一半通道长度，重合同善于分析的解的一维的声学。1. IntroductionFlow in hydraulic machinery is known to be unsteady. Pressure fluctuations induced by rotor-stator interaction (RSI) may be a major so

8、urce of vibration and fatigue. Extensive literature is available on RSI and unsteady flow in hydro turbines (e.g. 1-7). For many standard CFD applications, water compressibility does not play an important role and may be therefore neglected. However, typical RSI excitation frequencies of 50 to 200 H

9、z correspond to acoustic wavelengths of approximately 5 to 30 m, see wavelength-frequency dependence in Fig. 1. Hence, the acoustic wavelength in water may be in the range of prototype component dimensions. In such cases, acoustic resonance may occur, and acoustic effects may amplify pressure pulsat

10、ions and may cause high amplitude structural vibrations. Therefore, it is important to study compressibility effects on pressure fluctuations induced by RSI in hydraulic machinery. It is desired to perform hydraulic CFD in prototype scale. However, the Reynolds number is very high, and consequently

11、neither compressible nor incompressible CFD simulations can resolve boundary layers properly.On the other hand, most hydraulic tests and measurements are based on model scale. Therefore, it is necessary and useful to perform CFD simulations of hydro turbines generally in model dimensions, but hydro-

12、acoustic effects predicted in model scale should be valid for prototype machinery. As incompressible CFD does not consider the physics of acoustic phenomena, the transposition of computed pressure pulsations from the computational model to prototype conditions may be not physical for some parts of t

13、he turbine. Acoustic effects in hydraulic model scale tests are also not transposable to prototype size machinery. In contrast, compressible CFD simulations in model scale with adapted speed of sound (to scale acoustic effects) may be a good solution.1. 说明流入液压机械被知道是非定常。压力波动促使由转子定子相互作用(相对强弱指数)可一个主要源的

14、振动和疲劳。广泛的文学可用的在相对强弱指数，非定常流入桥梁水文计算程序涡轮机(e。g。1-7)。对许多标准差价合约应用，水的压缩系数不要起重要作用，可因此忽视。然而，典型相对强弱指数激发50的频率200赫兹符合声约的波长530米，见波长频率依赖性如图1。故，听觉的波长在水可能在范围原型元件尺寸。在这种情况下，声共振可能发生，音响效果可能放大压力脉动，可能原因高振幅构造的的振动。因此，是很重要的学习可压缩性影响压力波动促使由相对强弱指数在液压机械。它被愿望演出液差价合约在原型规模。然而，雷诺数非常高，所以既不可压缩的也不不可压缩的差价合约模拟能解决边界层妥善。另一方面，非常液测试和尺寸被基于模型

15、比例尺。因此，它是需，有用演出差价合约桥梁水文计算程序的模拟涡轮机通常在模型维，然而桥梁水文计算程序音响效果预测在模型比例尺将有效期原型机械。由于不可压缩的差价合约不要认为声的泻药现象，计算的换位压力脉动从计算模型原型条件可不物理为一些部分涡轮。音响效果在液模型比例尺测试也不转座的原型大小机械。相反，可压缩的差价合约模拟在模型比例尺同适应声速(规模音响效果)可一个良好解。Fig. 1 Acoustic wavelength depending on frequency for different speeds of sound图1听觉的的波长根据频率为不同声速Hydraulic compres

16、sibility effects can be properly taken into account by compressible CFD based on Navier-Stokes equations for weakly compressible fluids, incorporating the equation of state for = + ( p . p ) / a , (1)Water where the subscript 0 denotes a reference quantity, the density, and p the pressure. The speed

17、 of sound a0 is assumed to be constant. Therefore, the influence of compressibility effects can be investigated using different speeds of sound such as 900 m/s, 1100 m/s, and 1300 m/s which reveal phenomena of interest in hydraulic machinery. 液可压缩性影响可以要妥善考虑到由可压缩的差价合约以那微史托克方程为依据为弱可压缩流体，合并状态方程为水，下标0表示

18、一个参考量，密度，秕谷压力。声音的速度a0被假设常数。因此，可压缩性的影响影响可以被调查使用不同声速例如900米/s，1100米/s，1300米/s揭示对液压机械有兴趣的现象。 The current paper demonstrates the ability of compressible CFD to predict acoustic effects in hydraulic machinery and to provide a better understanding of the influence of water compressibility on pressure fluct

19、uations induced by RSI. At first, pipe flow with a harmonic velocity excitation is simulated using different grid densities and time step sizes. The computed results are compared with those predicted by a validated code for hydraulic networks (SIMSEN). Subsequently, the calibrated numerical method i

20、s applied to a simplified 2.5-dimensional pump-turbine configuration in model scale with an adapted speed of sound. Normalized pressurefluctuations are compared to numerical and experimental results of a prototype. Finally, a fully 3-dimensional configuration of a pump in model scale is investigated

21、. 近期论文演示能力的可压缩的差价合约预测音响效果在液压机械，提供更好地了解水的压缩系数的影响在压力波动促使由相对强弱指数。首先，管道流动同一个和音速度激发被模拟使用不一样的格密度，时间步大小。计算结果被比较那些预测由一个验证但只有基因编码性状液的网络(simsen)。后来，校准数值方法被适用于一个简化2。5-dimensional水泵水轮机组态在模型比例尺同一个适应声速。归一压力波动被比喻为数值，一个原型的实验结果。终于，一个充分3维一个的组态泵模型比例尺被调查。2. Evaluation of Compressible CFD for Hydraulic ApplicationsAs il

22、lustrated in Fig. 2, a pipe flow configuration with a length of L = 10 m and a diameter of D = 0.1 m is regarded. It is practically relevant and simple. Using the validated software tool SIMSEN 7, pipe flow dynamics is investigated for harmonic velocity fluctuations at the inlet. A grid width of z =

23、 0.02 m and a time step size of t = 5.10-5 s apply for computing the reference solution which is used to evaluate results of compressible CFD simulations.Fig. 2 Pipe flow configurationFor compressible CFD simulations with ANSYS-CFX, completely block structured hexahedral meshes with a uniform grid i

24、n axial direction apply. Two different discretizations are used, a high resolution (z = 0.02 m and t = 5.10-5 s) matching with the SIMSEN discretization and a coarser resolution (z = 0.05 m and t = 2.5.10-4 s) comparable to the discretization of runner channels in the simplified pump-turbine configu

25、ration in prototype scale. At the inlet plane, the flow is assumed to be fully turbulent using the mean velocity profile 2.可压缩的的评价差价合约为液的应用像说明在图2，一个管道流动组态同一个长度的半导体技术天地=10米，一个直径的公主日记=0。1米被关于。它几乎有关，简单。使用验证软件工具simsen，管流体动力学被调查为和音的速度波动在进口。一个的网格宽度尖椒土豆=0。02米，一个时间的步长吨=5。10-5s申请计算参考解决方案被过去常常评价可压缩的的结果差价合约模拟。

26、 图2 管道流动组态为可压缩的差价合约模拟同优化设计手册都会利用氟类材料，好块结构的六面体的网孔同一个均匀网格在轴向申请。二个不同离散被使用，一个高分辨率(z = 0.02 m and t = 5.10-5 s)配合simsen离散化，一个也显得更粗了决议(z = 0.05 m and t = 2.5.10-4 s)比得上离散化的亚军渠道在简化水泵水轮机组态在原型规模。在进口机，流量被假设充分动荡不安的用平均值流速剖面。where r0= 0.05 m is the radius of the pipe and w0= 30 m/s the mean velocity at center po

27、sition. The harmonicallyfluctuating part of the inlet velocity w = 0.1.w .0.5. (1. cos(2. f . t) (3)is added to the mean velocity profile w given in Eq. (2). In Eq. (3), f = 60 Hz is the excitation frequency and t the physical time. For the evaluation of results, monitor points are placed on the cen

28、terline of the pipe.The speed of sound is assumed to be 1000 m/s, and the density of water is defined by Eq. (1). The high resolution advection scheme of CFX, the second order backward Euler method for time integration, and the k- turbulence model with scalable wall functions are used. For inlet and

29、 outlet boundary conditions, the option “reflective” is selected in the acoustic reflectivity. The RMS residual target is set to 5.10-6 for velocity components and pressure to ensure converged solutions. For unsteady simulations, the steady state solution is taken as initial condition, and time-depe

30、ndent velocity distributions are specified at the inlet plane. The computed physical time is 0.2 s corresponding to 10 wave propagation periods in the pipe.Figure 3 shows time histories of pressure at z = 0 m (solid lines) and z = 4 m (dashed lines) on the centerline of the pipe predicted by CFX and

31、 SIMSEN. Although CFX results are based on 3-dimensional unsteady Reynolds-Averaged Navier-Stokes equations (URANS) and SIMSEN solutions on one-dimensional hydroacoustic analyses, they agree fairly well. Pressure differences between the SIMSEN solution and both CFX discretizations are quite small. T

32、herefore, CFX simulations of compressible water flow are proven to give realistic results and may be used to predict dynamic pressure pulsations in complex hydraulic machinery. 在r0=0。05米是半径的管，w0=30米/s平均速度在中心位置。和声地波动部分进口速度被增加平均值流速剖面瓦特让步相等。(2)。在相等。(3)，f为返回整型值的函数=60赫兹激励频率，吨物理时间。为结果的评价，监测点被放置在中心线的管。声音的速

33、度被假设1000米/s，水的密度被确定由相等。(1)。高分辨率平流都会利用氟类材料的方案，二阶落后欧拉方法给时间积分，k-湍流模型同延展的墙功能被使用。对进出口管径边界条件，期权“沉思的”被选择声反射率。均方根剩余的目标开始大吃5。10-6为速度元件和压力确保汇集解。为非定常模拟，稳态解被采取像初始条件，时间依赖性速度分配被提起在进口机。计算物理时间0。2s相应的10波的传播期间在管。图3显示时间毒理学史压力在z=0米(固体的线)，和z=4米(虚线)在中心线的管预测由都会利用氟类材料，simsen。尽管都会利用氟类材料结果被基于3维非定常雷诺兹平均纳维斯托克斯方程(乌兰)，simsen解在一维

34、水声分析，他们同意相当好。压力差异在之间simsen解，两都会利用氟类材料离散相当小。因此，cfx可压缩的的模拟水流被证明给实际结果,而且可能习惯于预测动态压力脉动在复杂的水力机械装置中。Fig. 3 Time histories of pressure predicted by CFX with different discretizations and by SIMSEN图3 时间毒理学史压力预测通过都会利用氟类材料同不同离散，通过simsen3. Compressible Simulation of RSI in a Simplified Pump-Turbine Configurati

35、on3.1 Modeling and Numerical SetupThe computational domain of regarded pump-turbine with a specific speed of nq=50 consists of a spiral case, a tandem cascade with 20 stay vanes and wicket gates, a runner with 9 blades, and a draft tube, considering the influence of non-uniform inflow from the spira

36、l case. The regarded turbine mode operating point is 70% wicket gate opening close to optimum. Since this study is focused on the influence of compressibility effects on pressure pulsations, the original configuration is reduced to a simplified 2.5-dimensional model, see Fig. 4,minimizing the comput

37、ational effort. The third dimension is not of a constant thickness but reflects the varying cross-sectional area.3.可压缩的模拟的相对强弱指数在一个简化水泵水轮机组态3.1 造型，数值设置 关于的计算域水泵水轮机同一个脉实舣的比转速=50由一个组成蜗壳，一个串列叶栅同20呆货车和边门门，一个跑步者同9个刀片，一个尾水管，考虑影响的非均匀流入从蜗壳。注意涡轮模式工作点70%边门导叶开度离最佳近。自从本研究被关注可压缩性的影响影响压力脉动，原始配置被减少一个简化2。5量纲模型，请看图4

38、。最小化计算工作。真实感不是的一个不断厚度但反映变化横截面积。 The structured hexahedral mesh in prototype size with approximately 5.8 million elements used in previous works 1 is scaled to model dimensions. At the inlet plane, the mass flow rate with normal flow direction is specified, and at the outlet plane, an opening conditi

39、on is applied. All surfaces of turbine components which are in contact to the water passage are defined as no-slip walls, while the remaining surfaces which reduce the third dimension to a small distance are defined as free-slip walls, see boundary conditions in Fig. 4 (a). Between opposed free-slip

40、 walls, only two elements are located. 他结构六面体的网在原型大小同约5。8个百万元素使用在以前的工作1被攀登模型维。在进口机，质量流量同正常流动方向被提起，在出口机，一个开放条件被申请。所有涡轮的表面元件在联系水通道被确定由于没有的滑墙，而仍表面减少真实感一个小距离被确定由于自由的滑墙，请在图4（a）中观察边界条件。在反对之间自由的滑墙，只二元素被定位。 The time step size is selected such that one runner revolution is divided into 400 time steps corresp

41、onding to an angular change of 0.9 degree and being sufficient to resolve dynamic effects of interest. For all computations, 10 revolutions are carried out. The last revolution is used to plot time histories of pressure fluctuations, while the last 6 revolutions are used to perform Fourier transform

42、ations of time domain results. 时间步长被选择如此那个一亚军革命被分为400时间步相应的一个有角的0.9的改变学位，足以解决动态兴趣效能。尽管计算，10场革命被进行。最后革命被过去常常情节时间毒理学史压力波动，而最后6场革命被过去常常演出时域的傅立叶变换结果。 The high resolution advection scheme of CFX, the second order backward Euler method for time integration,and the k- turbulence model with scalable wall fu

43、nctions are used. The RMS residual target is set to 10-5 for velocity components and pressure to ensure converged solutions. Between rotating and stationary components,circumferential averaging is used for steady state calculations and a transient rotor-stator interface for unsteady simulations. The

44、 steady state solution is taken as initial condition for unsteady simulations. Since non-reflecting acoustic boundary conditions implemented in CFX do not work properly for high pressure fluctuations, a special technique is introduced by means of user subroutines to remedy reflections of acoustical

45、waves at inlet and outlet boundaries and to improve the convergence behavior. 高分辨率平流都会利用氟类材料的方案，二阶落后欧拉方法给时间积分，k-湍流模型同延展的墙功能被使用。均方根剩余的目标设置在10-5为速度元件和压力确保汇集解。在轮流之间，固定的的元件，圆周的平均被用于稳态数，一个瞬态电流定子接口为非定常模拟。稳态解被采取由于初始条件为非定常模拟。稳态解被采取像初始条件为非定常模拟。自从非反射的声边界条件执行在都会利用氟类材料不工作妥善为高压力波动，一个特殊技术处理被介绍用用户子程序补救声学的反射波在进出口管径

46、边界，改善收敛行为。Monitor points RU1, RU2, and RU3 are defined on the centerline of a runner channel, while monitor point 14 is located in vaneless space in the stationary domain close to the rotor-stator interface, see Fig. 4 (b).In order to transpose acoustic effects predicted in model scale simulations t

47、o prototype conditions, the simplified pump-turbine configuration in model scale is simulated with an adapted sonic speed of 348 m/s which corresponds to a value of 1100 m/s in prototype scale. To compare dynamic effects in different scales,frequencies are divided by the rotational frequency of the

48、runner fr and pressure fluctuations are normalized according to where p denotes the time averaged pressure, R0 the external runner radius, and the angular frequency of the runner speed. 监测点ru1，ru2，ru3被确定在中心线的一个运动渠道，而监测点14被在某一点设置vaneless空间在固定域离近转子定子接口，看图4（b）。 为了转音响效果预测在模型比例尺模拟原型条件，简化水泵水轮机组态在模型比例尺被模拟同

49、一个适应348的声速米/s符合1100的值米/s在原型规模。比较活跃的影响在不一样的规模，频率被除以跑步者的转动频率神父，压力波动被归一据哪里所说秕谷表示时间平均压力，r0外部跑步者半径，跑步者的角频率速度。3.2 ResultsTime histories of pressure fluctuations measured in the prototype (experimental) are compared with numerical results at monitor point 14 in vaneless space in the stationary frame of ref

50、erence, see Fig. 5 (a). In the prototype, the dynamic pressure in vaneless space was measured with a flush mounted pressure sensor of the type PCB 121A31/AB. The black line represents the compressible simulation in model scale with adapted speed of sound, the red line the compressible simulation in

51、prototype scale, and the blue line the incompressible simulation in prototype scale. Both experimental and numerical results are clearly periodical and stable. The agreement between measurement and all simulations is quite good. However, the amplitude of the second no-slip wallfree-slip wall inlet o

52、utlet harmonic cannot be captured accurately by the incompressible simulation, but is well predicted by compressible simulations, see the small picture in Fig. 5 (a) with enlarged time histories of normalized pressure fluctuations.Pressure fluctuations of the different compressible simulations are v

53、ery similar. Deviations may be explained by different resolutions of boundary layer effects in prototype and model scale. 3.2结果 时间毒理学史压力波动测量在原型(实验)被比较数值结果在监测点14在vaneless空间在静止的参照系，参照图5（a）。在原型，动态压合vaneless空间被测量同一个直接的山类型的压力传感器印刷电路板121a31/水。黑线代表可压缩的模拟在模型比例尺同适应声速，红线可压缩的模拟在原型规模，蓝线不可压缩的模拟在原型规模。实验，数值结果明确地期刊

54、和马厩。协议在测量之间，所有模拟相当好。然而，振幅的第二没有的滑墙自由的滑墙壁的的进口插座谐波不能被捕获准确由不可压缩的模拟，观察图5a中的小图片，同放大时间毒理学史归一压力fluctuations。pressure的波动不同可压缩的模拟非常相似。差异可说明以不一样的决议的边界图层效果在原型，模型比例尺。差异可说明以不一样的决议的边界图层效果在原型，模型比例尺。Frequency spectra of pressure fluctuations from numerical results are given in Fig. 5 (b). The peaks correspond to the

55、 blade passing frequency fBPF = 9 fr (frequency of rotation times number of runner blades) and its higher harmonics. For the first harmonic (f/fr= 9), pressure amplitudes are nearly equal for all types of simulation. The most significant difference between compressible and incompressible simulations

56、 arises at the second harmonic of the blade passing frequency (f/fr= 18), where compressible simulations exhibit higher amplitudes than incompressible simulations. Comparing compressible simulations in model and prototype scale, pressure fluctuation amplitudes are almost equal for all harmonics.频率压力

57、波动的光谱从数值结果在图5（b)中给出。高峰符合叶片通过频率fbpf=9fr(自转的频率倍转轮叶片的数)，它的高次谐波。为一次谐波(f为返回整型值的函数f/fr=9)，压力振幅将近相同尽管类型模拟。大多数重大的差异在可压缩的之间，不可压缩的模拟出现在二次谐波的叶片通过频率(f为返回整型值的函数f/fr=18)，可压缩的模拟展览更高的振幅比不可压缩的模拟。比较可压缩的模拟在模型和原型规模，压力波动振幅几乎相等尽管谐波。Looking at time histories and corresponding frequency spectra of normalized pressure fluct

58、uations inside of a runner channel close to the turbine inlet (monitor point RU1), two dominant frequencies can be detected, see Fig.6. On the one hand the frequency of runner rotation fr and on the other hand the gate passing frequency fGPF = 20 fr (frequency of rotation times number of wicket gate

59、s). The amplitude at fr which is caused by the spiral case is comparable to the amplitude at fGPF and should be considered for fatigue life evaluations, too. At fGPF, pressure fluctuations of compressible simulations exceed those of the incompressible simulation clearly. In contrast, pressure fluctu

60、ations of compressible simulations in model scale with adapted speed of sound and in prototype scale are almost equal. 查阅历史，对应频率归一的光谱压力波动一个运动的内渠道离涡轮近进口(监测点ru1)，二个主导频率可以被检测，看图6.一方面，另一方面门经过频率fgpf=20fr(自转的频率时间边门的数门)。振幅在fr被造成蜗壳比得上振幅在fgpf，将也被视为为疲劳寿命评价。在fgpf，可压缩的的压力波动模拟超过那些的不可压缩的模拟明确地。相反，可压缩的的压力波动模拟在模型比例尺

61、同适应声速，在原型规模几乎相等。Fig. 6 Comparison of pressure fluctuations in time domain (a) and frequency domain (b) at monitor point RU125th IAHR Symposium on Hydraulic Machinery and Systems IOP PublishingIOP Conf. Series: Earth and Environmental Science 12 (2010) 012008 doi:10.1088/1755-1315/12/1/0120085RU1 RU2

62、 RU3For a better understanding of the influence of water compressibility on pressure fluctuations inside of runner channels, pressure amplitudes from the different simulations belonging to the gate passing frequency fGPF arecompared in Fig. 7 (a) at monitor points RU1, RU2, and RU3. In addition to t

63、he sonic speed of a0= 1100 m/s,compressible results in prototype scale are given also for a0= 900 m/s and a0= 1300 m/s. Comparing pressurefluctuation amplitudes of the model scale simulation with adapted sonic speed of a0= 348 m/s with corresponding prototype scale results for a0= 1100 m/s, good agr

64、eement is observed with slightly smaller amplitudes in model scale simulations.Considering that the distance between monitor points RU2 and RU3 is larger than the distance between RU1and RU2, pressure amplitudes of the incompressible simulation decrease linearly along centerlines of runnerchannels.

65、In contrast, pressure amplitudes of compressible simulations exhibit sinusoidal distributions. This behavior coincides with a simplified analytical approach of one-dimensional acoustics, shown in Fig. 7 (b), where L is the length of a runner channel and = a0/f the acoustic wavelength. The linear pressure characteristics(L / 1/4) is valid for incompressible fluids, and with increasing compressibility (decreasing s