离心泵内不稳定流动的试验及数值模型研究
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摘要
本文的研究工作是在国家自然科学基金项目“低比转数离心泵驼峰现象的不稳定流动机理研究”(No.51079062)资助下展开。
随着社会进步和科学技术的发展,离心泵的运行稳定性和可靠性越来越受到重视,而泵内部的非定常流动情况是决定运行稳定性的关键因素之一。为了更好地理解和研究离心泵的内部流动情况,本文从其内部不稳定流动的角度出发,采用试验和数值模拟相结合的方法,探索其叶轮内不稳定流动的发生和发展规律。同时针对离心叶轮流道内摩擦损失大、逆压梯度高和叶片曲率大等特点,在SST k-ω湍流模型的基础上提出了一种基于旋转和曲率修正的非线性湍流模型。基于OpenFOAM软件建立了一套适用于离心叶轮流道特点的数值模型。本文的主要工作和创造性成果有：
1.总结了离心泵PIV测试技术、压力脉动测试技术、振动测试技术的国内外研究现状；归纳了线性涡粘性模型的研究现状及不足,阐述了显式代数雷诺应力方程模型结合二方程湍流模型求解是工程上计算旋转和曲率流场的一种趋势。
2.首次采用PIV技术探索了一离心叶轮流道内不稳定流动涡的发生、发展规律,定量分析了不稳定流动对性能曲线的影响规律,揭示了不稳定流动对叶轮流道内绝对速度的影响规律,研究结果表明：(1)不稳定流在0.6QBEP工况开始产生,直到0.4QBEP工况得到发展,最后在0.1QBEP时几乎扩展到整个叶轮流道；叶轮旋转的过程中,靠近蜗壳隔舌处的叶轮流道内的流动最不稳定,也是最先出现分离涡的流道；随着流量的降低,附着于叶片工作面的分离涡逐渐增多、汇聚,不断发展的漩涡向流道出口移动的同时,也偏向于流道中心。(2)平均出口绝对速度圆周分量Vu2/U2随着流量的增加先升高后降低,在0.1QBEP到0.6QBEP之间出现驼峰现象；从0.6QBEP到1.0QBEP,平均出口绝对速度圆周分量和扬程均随着流量增加稳定下降；不稳定流动是导致离心泵性能曲线出现驼峰或平坦现象的主要原因。(3)绝对速度圆周分量vu随着流道半径的增加,呈先升高后降低的趋势；在不同工况下,vu的整体变化规律基本相似,其大小与流量成反比。绝对速度径向分量vm随着流道半径的增加,基本呈先下降后上升的趋势；在不同工况下,vm的整体大小与流量成正比。
3.采用HSJ2010水力机械综合测试仪和高频动态压力传感器对离心泵叶轮出口圆周方向的压力脉动特性进行了试验研究。获得了流道内不稳定流动和叶轮出口压力脉动之间的关系。研究结果表明：(1)“射流-尾迹”结构诱导的叶频脉动和叶轮流道内流动的不对称性诱导的轴频脉动是压力脉动的主要成分；(2)“射流-尾迹”结构引起的周期性压力脉动幅值随着叶轮与蜗壳壁面(正对叶轮出口的蜗壳壁面)间距的增加而逐渐衰弱,叶轮出流对压力脉动的影响逐渐减弱；(3)在叶轮出口处的压力脉动特征频域中存在一个100Hz～145Hz的宽带频率,大约介于4倍轴频到叶频之间,该宽频幅值随着不稳定涡尺度的增强逐渐变大。
4.采用INV3020C数据采集系统、DASP-V10软件以及ICP型振动加速度传感器对离心泵不稳定流动下的振动特征进行了试验研究。总结了离心泵叶轮流道内的不稳定流动现象对振动的影响规律,发现了振动信号与压力脉动信号在频域特征具有一定的相关性,彼此的主要激励频率均分布在轴频和叶频；对于振动信号而言,其在100Hz～145Hz之间(大约介于4倍轴频到叶频之间)同样存在一个由不稳定涡引起的宽频振动。
5.针对离心叶轮流道强旋转、大曲率的特点,在开源软件OpenFOAM平台上,首先用代数雷诺应力方程模型求解雷诺应力和涡粘性系数,然后用SST k-ω模型中考虑旋转和曲率改进的k方程和w方程进行封闭求解,最后用扩展内禀旋转张量对模型中的平均旋转张量进行修正,从而实现对SST k-ω湍流模型的旋转和曲率改进,并首次开发了一套适用于计算旋转和曲率流场的非线性湍流模型(EASMRC)程序。用旋转直通道和90°弯管进行了计算检验。结果表明,改进后的非线性湍流模型与原模型相比,计算结果更接近试验值。
6.首次将改进模型分别应用于OpenFOAM的MRFSimpleFoam和pimpleDyMFoam求解器中,并对研究模型进行了稳态和瞬态计算。将EASMRC计算结果与OpenFOAM的SST k-ω计算结果、CFX的SST k-ω计算结果、外特性测试结果、PIV测试结果、压力脉动测试结果进行了对比,结果表明：从外特性上看,EASMRC模型总体上与试验值更接近；从内流场上看,EASMRC在预测分离涡的发生、发展方面更接近PIV测量结果；从压力脉动特性上看,EASMRC计算的压力脉动幅值、时域结果以及频域结果与测量结果最接近。
The research is supported by National Natural Science Foundation of China (Grant No.51079062) project.
With the development of society, science and technology, the stability and reliability of centrifugal pump operation is gradually important. While, the unsteady flow inside the pump is an essential factor that determines the stability of pump operation. In order to get a better understanding and researching about the internal flow in the pump, this paper takes the unstable flow pattern inside the impeller as the subject. The research method combining experiments and CFD has been applied to investigate the onset and development law of unstable flow within the impeller. Meanwhile, a new nonlinear turbulence model is generated based on SST k-co turbulence model, that aiming at simulating more precisely on the centrifugal pump because of its higher friction loss inside passage, higher adverse pressure gradient and bigger curvature of blade. Furthermore, a set of numerical method is set up for fitting the characteristics of centrifugal impeller passages based on OpenFOAM. The main research contents and creative achievements as below:
1. The present situations on measurements in centrifugal pump, such as PIV measurement technique, pressure fluctuation experiment technique and vibration measurement technique, were summarized. The present research status and defects on linear eddy viscosity model were concluded. The development trends for combining explicit algebraic stress equation model with turbulence model of quadratic equation to solve the flow with rotation and curvature were illustrated.
2. Onset and development rule of unstable vortex within the impeller were discovered using PIV technique. The effect law of unstable flow both on hydraulic performance curve and on absolute velocity distribution in impeller passages were quantitated and revealed separately. The main conclusions were following:(1) The flow was separated at0.6QBEP, developed at0.4QBEP, and spread almost the whole impeller passage at0.1QBEP In addition, flow in the passage near the tongue was the most unstable, and the vortex was also occurred in this passage firstly by comparing with rest of passages. With the flow rate decreasing, the vortex on the pressure side was increased and converged to a large-size vortex, in the end, the large-size vortex spread to the outlet of passage, and moved to the centre area of the passage.(2) The average circumferential component of absolute velocity vu2/u2at the impeller exit went up firstly, then down, and there was a hump on the above velocity distribution curve between0.1QBEP and0.6QBEP. Moreover, both vu2/u2and head fell steadily with the flow rate increased from0.6QBEP and1.0QBEP. Furthermore, the unstable flow was the main factor to cause the hump or flat area on the H-Q curve.(3) With the radius of the impeller passages increasing, the circumferential component of absolute velocity vu rose firstly, and then reduced. In addition, the changing law of vu was very similar under different working conditions, that was, it varied inversely as the flow rate. In contrast, the radial component of absolute velocity vm firstly decreased, and then increased with the radius of the impeller passages increasing. Meanwhile, the magnitude of vm was proportional to the flow rate.
3. The experimental investigation was performed on pressure fluctuation of impeller exit in circumferential direction by utilizing the HSJ2010tester and high-frequency dynamic pressure transducers. The relationship between pressure pulsation and unstable flow in the impeller passages was summarized. The following3results were obtained:(1) The blade passing frequency and the shaft frequency were the domain frequencies, here, the blade passing frequency was induced by "jet-wake" structure and the shaft frequency was induced by the asymmetric flow in the impeller passages.(2) The periodic pressure pulsation amplitude, which caused by "jet-wake" structure, was gradually decreasing along with the gap between impeller exit and volute wall(the wall which directly against the impeller exit) increasing. In other words, the pressure pulsation amplitude, which was influenced by impeller outlet flow, was weakened along with the gap between impeller and volute wall was increasing.(3) There was a100Hz-145Hz broad-band frequency among the overall frequency domain of pressure pulsation near the impeller exit, and the broad-band frequencies were between about4times the shaft frequency and the blade passing frequency. In addition, the amplitude of above broad-band frequency was increasing with the scale of the unstable vortex enlarging.
4. The experimental investigation was performed on vibration of centrifugal pump with unstable flow phenomena by utilizing the INV3020C data acquisition system, DASP-V10software and ICP acceleration sensors. Effects of unstable flow phenomena in impeller passages on vibration were summarized. Moreover, the correlation between vibration signals and pressure fluctuation signals among frequency domain was found. Here, their shaft frequency and blade passing frequency are the domain frequencies. For the vibration signals, there also existed a100Hz-145Hz broadband vibration, that was between about4times the shaft frequency and the blade passing frequency, caused by unstable vortex.
5. A new computational program with nonlinear turbulence model which considering the effects of rotation and curvature, that was EASMRC, was developed firstly based on an open source code named OpenFOAM. The idea of the nonlinear turbulence model was given as follows:Firstly, the Reynolds stress and the eddy viscosity were calculated by explicit algebraic stress equation model. Then, the improved k equation and co equation in SST k-co turbulence model which considered the effects of rotation and curvature were used for governing equations closure. Finally, the mean spin tensor in the above equations was improved by the extended intrinsic mean spin tensor. Therefore, a new nonlinear turbulence model combining explicit algebraic stress equation model and SST k-co turbulence model was improved. Both a rotating turbulent duct flow and a90°curved duct flow is simulated for validation. The result showed that the calculation result of improved nonlinear turbulence model was closer to experimental results.
6. The improved turbulence model (EASMRC) was added into MRFSimpleFoam and pimpleDyMFoam solver based on OpenFOAM respectively for the first time. Both steady simulation and transient simulation were performed on the pump internal flow. Then, the calculation results by EASMRC model was compared with the results by SST k-co turbulence model in OpenFOAM, the results by SST k-co turbulence model in CFX, the result by hydraulic performance test, the result by PIV measurement and the result by pressure pulsation measurement respectively. The results were followed:in terms of the pump hydraulic performance, the calculation accuracy of EASMRC was much better than original model both in OpenFOAM and CFX; in terms of the internal flow, EASMRC revealed that the evolution process of vortex in the impeller passages, which was more consistent with the PIV test; in terms of the pressure pulsation, EASMRC was much closer to test results from pressure pulsation charateristics, such as pressure fluctuation amplitude, pressure pulsation results on time domain, and on frequecy domain respectively,
随着社会进步和科学技术的发展,离心泵的运行稳定性和可靠性越来越受到重视,而泵内部的非定常流动情况是决定运行稳定性的关键因素之一。为了更好地理解和研究离心泵的内部流动情况,本文从其内部不稳定流动的角度出发,采用试验和数值模拟相结合的方法,探索其叶轮内不稳定流动的发生和发展规律。同时针对离心叶轮流道内摩擦损失大、逆压梯度高和叶片曲率大等特点,在SST k-ω湍流模型的基础上提出了一种基于旋转和曲率修正的非线性湍流模型。基于OpenFOAM软件建立了一套适用于离心叶轮流道特点的数值模型。本文的主要工作和创造性成果有：
1.总结了离心泵PIV测试技术、压力脉动测试技术、振动测试技术的国内外研究现状；归纳了线性涡粘性模型的研究现状及不足,阐述了显式代数雷诺应力方程模型结合二方程湍流模型求解是工程上计算旋转和曲率流场的一种趋势。
2.首次采用PIV技术探索了一离心叶轮流道内不稳定流动涡的发生、发展规律,定量分析了不稳定流动对性能曲线的影响规律,揭示了不稳定流动对叶轮流道内绝对速度的影响规律,研究结果表明：(1)不稳定流在0.6QBEP工况开始产生,直到0.4QBEP工况得到发展,最后在0.1QBEP时几乎扩展到整个叶轮流道；叶轮旋转的过程中,靠近蜗壳隔舌处的叶轮流道内的流动最不稳定,也是最先出现分离涡的流道；随着流量的降低,附着于叶片工作面的分离涡逐渐增多、汇聚,不断发展的漩涡向流道出口移动的同时,也偏向于流道中心。(2)平均出口绝对速度圆周分量Vu2/U2随着流量的增加先升高后降低,在0.1QBEP到0.6QBEP之间出现驼峰现象；从0.6QBEP到1.0QBEP,平均出口绝对速度圆周分量和扬程均随着流量增加稳定下降；不稳定流动是导致离心泵性能曲线出现驼峰或平坦现象的主要原因。(3)绝对速度圆周分量vu随着流道半径的增加,呈先升高后降低的趋势；在不同工况下,vu的整体变化规律基本相似,其大小与流量成反比。绝对速度径向分量vm随着流道半径的增加,基本呈先下降后上升的趋势；在不同工况下,vm的整体大小与流量成正比。
3.采用HSJ2010水力机械综合测试仪和高频动态压力传感器对离心泵叶轮出口圆周方向的压力脉动特性进行了试验研究。获得了流道内不稳定流动和叶轮出口压力脉动之间的关系。研究结果表明：(1)“射流-尾迹”结构诱导的叶频脉动和叶轮流道内流动的不对称性诱导的轴频脉动是压力脉动的主要成分；(2)“射流-尾迹”结构引起的周期性压力脉动幅值随着叶轮与蜗壳壁面(正对叶轮出口的蜗壳壁面)间距的增加而逐渐衰弱,叶轮出流对压力脉动的影响逐渐减弱；(3)在叶轮出口处的压力脉动特征频域中存在一个100Hz～145Hz的宽带频率,大约介于4倍轴频到叶频之间,该宽频幅值随着不稳定涡尺度的增强逐渐变大。
4.采用INV3020C数据采集系统、DASP-V10软件以及ICP型振动加速度传感器对离心泵不稳定流动下的振动特征进行了试验研究。总结了离心泵叶轮流道内的不稳定流动现象对振动的影响规律,发现了振动信号与压力脉动信号在频域特征具有一定的相关性,彼此的主要激励频率均分布在轴频和叶频；对于振动信号而言,其在100Hz～145Hz之间(大约介于4倍轴频到叶频之间)同样存在一个由不稳定涡引起的宽频振动。
5.针对离心叶轮流道强旋转、大曲率的特点,在开源软件OpenFOAM平台上,首先用代数雷诺应力方程模型求解雷诺应力和涡粘性系数,然后用SST k-ω模型中考虑旋转和曲率改进的k方程和w方程进行封闭求解,最后用扩展内禀旋转张量对模型中的平均旋转张量进行修正,从而实现对SST k-ω湍流模型的旋转和曲率改进,并首次开发了一套适用于计算旋转和曲率流场的非线性湍流模型(EASMRC)程序。用旋转直通道和90°弯管进行了计算检验。结果表明,改进后的非线性湍流模型与原模型相比,计算结果更接近试验值。
6.首次将改进模型分别应用于OpenFOAM的MRFSimpleFoam和pimpleDyMFoam求解器中,并对研究模型进行了稳态和瞬态计算。将EASMRC计算结果与OpenFOAM的SST k-ω计算结果、CFX的SST k-ω计算结果、外特性测试结果、PIV测试结果、压力脉动测试结果进行了对比,结果表明：从外特性上看,EASMRC模型总体上与试验值更接近；从内流场上看,EASMRC在预测分离涡的发生、发展方面更接近PIV测量结果；从压力脉动特性上看,EASMRC计算的压力脉动幅值、时域结果以及频域结果与测量结果最接近。
The research is supported by National Natural Science Foundation of China (Grant No.51079062) project.
With the development of society, science and technology, the stability and reliability of centrifugal pump operation is gradually important. While, the unsteady flow inside the pump is an essential factor that determines the stability of pump operation. In order to get a better understanding and researching about the internal flow in the pump, this paper takes the unstable flow pattern inside the impeller as the subject. The research method combining experiments and CFD has been applied to investigate the onset and development law of unstable flow within the impeller. Meanwhile, a new nonlinear turbulence model is generated based on SST k-co turbulence model, that aiming at simulating more precisely on the centrifugal pump because of its higher friction loss inside passage, higher adverse pressure gradient and bigger curvature of blade. Furthermore, a set of numerical method is set up for fitting the characteristics of centrifugal impeller passages based on OpenFOAM. The main research contents and creative achievements as below:
1. The present situations on measurements in centrifugal pump, such as PIV measurement technique, pressure fluctuation experiment technique and vibration measurement technique, were summarized. The present research status and defects on linear eddy viscosity model were concluded. The development trends for combining explicit algebraic stress equation model with turbulence model of quadratic equation to solve the flow with rotation and curvature were illustrated.
2. Onset and development rule of unstable vortex within the impeller were discovered using PIV technique. The effect law of unstable flow both on hydraulic performance curve and on absolute velocity distribution in impeller passages were quantitated and revealed separately. The main conclusions were following:(1) The flow was separated at0.6QBEP, developed at0.4QBEP, and spread almost the whole impeller passage at0.1QBEP In addition, flow in the passage near the tongue was the most unstable, and the vortex was also occurred in this passage firstly by comparing with rest of passages. With the flow rate decreasing, the vortex on the pressure side was increased and converged to a large-size vortex, in the end, the large-size vortex spread to the outlet of passage, and moved to the centre area of the passage.(2) The average circumferential component of absolute velocity vu2/u2at the impeller exit went up firstly, then down, and there was a hump on the above velocity distribution curve between0.1QBEP and0.6QBEP. Moreover, both vu2/u2and head fell steadily with the flow rate increased from0.6QBEP and1.0QBEP. Furthermore, the unstable flow was the main factor to cause the hump or flat area on the H-Q curve.(3) With the radius of the impeller passages increasing, the circumferential component of absolute velocity vu rose firstly, and then reduced. In addition, the changing law of vu was very similar under different working conditions, that was, it varied inversely as the flow rate. In contrast, the radial component of absolute velocity vm firstly decreased, and then increased with the radius of the impeller passages increasing. Meanwhile, the magnitude of vm was proportional to the flow rate.
3. The experimental investigation was performed on pressure fluctuation of impeller exit in circumferential direction by utilizing the HSJ2010tester and high-frequency dynamic pressure transducers. The relationship between pressure pulsation and unstable flow in the impeller passages was summarized. The following3results were obtained:(1) The blade passing frequency and the shaft frequency were the domain frequencies, here, the blade passing frequency was induced by "jet-wake" structure and the shaft frequency was induced by the asymmetric flow in the impeller passages.(2) The periodic pressure pulsation amplitude, which caused by "jet-wake" structure, was gradually decreasing along with the gap between impeller exit and volute wall(the wall which directly against the impeller exit) increasing. In other words, the pressure pulsation amplitude, which was influenced by impeller outlet flow, was weakened along with the gap between impeller and volute wall was increasing.(3) There was a100Hz-145Hz broad-band frequency among the overall frequency domain of pressure pulsation near the impeller exit, and the broad-band frequencies were between about4times the shaft frequency and the blade passing frequency. In addition, the amplitude of above broad-band frequency was increasing with the scale of the unstable vortex enlarging.
4. The experimental investigation was performed on vibration of centrifugal pump with unstable flow phenomena by utilizing the INV3020C data acquisition system, DASP-V10software and ICP acceleration sensors. Effects of unstable flow phenomena in impeller passages on vibration were summarized. Moreover, the correlation between vibration signals and pressure fluctuation signals among frequency domain was found. Here, their shaft frequency and blade passing frequency are the domain frequencies. For the vibration signals, there also existed a100Hz-145Hz broadband vibration, that was between about4times the shaft frequency and the blade passing frequency, caused by unstable vortex.
5. A new computational program with nonlinear turbulence model which considering the effects of rotation and curvature, that was EASMRC, was developed firstly based on an open source code named OpenFOAM. The idea of the nonlinear turbulence model was given as follows:Firstly, the Reynolds stress and the eddy viscosity were calculated by explicit algebraic stress equation model. Then, the improved k equation and co equation in SST k-co turbulence model which considered the effects of rotation and curvature were used for governing equations closure. Finally, the mean spin tensor in the above equations was improved by the extended intrinsic mean spin tensor. Therefore, a new nonlinear turbulence model combining explicit algebraic stress equation model and SST k-co turbulence model was improved. Both a rotating turbulent duct flow and a90°curved duct flow is simulated for validation. The result showed that the calculation result of improved nonlinear turbulence model was closer to experimental results.
6. The improved turbulence model (EASMRC) was added into MRFSimpleFoam and pimpleDyMFoam solver based on OpenFOAM respectively for the first time. Both steady simulation and transient simulation were performed on the pump internal flow. Then, the calculation results by EASMRC model was compared with the results by SST k-co turbulence model in OpenFOAM, the results by SST k-co turbulence model in CFX, the result by hydraulic performance test, the result by PIV measurement and the result by pressure pulsation measurement respectively. The results were followed:in terms of the pump hydraulic performance, the calculation accuracy of EASMRC was much better than original model both in OpenFOAM and CFX; in terms of the internal flow, EASMRC revealed that the evolution process of vortex in the impeller passages, which was more consistent with the PIV test; in terms of the pressure pulsation, EASMRC was much closer to test results from pressure pulsation charateristics, such as pressure fluctuation amplitude, pressure pulsation results on time domain, and on frequecy domain respectively,
引文
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