摘要
三峡电站采用混流式机组,其转轮叶片按“X”形设计,即所谓的负倾角叶片,这种形式的叶片对水头和负荷变化的适应范围广,而且水轮机具有较高的平均效率,也能很好的防止叶片进水边的脱流和空化,对高水头、小开度工况有利。然而,影响混流式机组稳定运行的因素非常复杂,某些因素目前还没有获得足够的认识。此外,三峡机组是巨型机组,水体的固有频率相对较低,容易激发产生水体共振。2003年8月6日,三峡左岸6号ALSTOM机组在过速试验的关机过程中,当活动导叶开度约为4%、转速约为73rpm时,机组出现了强烈的异常振动现象。经分析,振动的频率是1.359Hz,其中涡壳内部水压脉动最大峰峰值达500kPa,超过了试验时总水头(约68m)的一半。其他结构部件的振动虽然也有比较高的频率存在,但都受到了1.359Hz的影响。还有一个值得注意的现象是,活动导叶开口之前的水体水压脉动剧烈,而活动导叶开口之后的水体没有发现明显的水压脉动。
针对三峡机组的异常振动现象,供货商ALSTOM公司采用Gibson法估计出关机过程中流量的时间历程,并认为是负流量导致了异常振动;哈尔滨大电机研究所通过模型试验,得到了模型的全特性曲线,他们认为引起振动的原因,是水轮机从反水泵工况快速进入零流量,从而发生水锤现象所致。
三峡机组在机小开度下的异常振动现象,对机组安全构成了极大的威胁,也是迄今为止尚未报道过的现象。目前的水轮机稳定性理论尚无法作出解释。虽然供应商给出了一个解释,但是这个解释的根据并不充分,也不能为业界一致认可。
本文对三峡机组小开度异常振动现象进行了深入的研究,力图揭示发生这个现象的原因。鉴于目前的模型试验技术还不能模拟真机的动态特性,同时现场条件也不允许对真机的内部流动进行测量,本文在理论分析的基础上,主要采用动态数值模拟的方法研究水轮机内部水压脉动产生的机理。获得了如下成果:
首先,在研究方法方面,本文从网格生成、湍流模式、差分格式、时间步长控制以及输出控制等方面探索并发展了一套行之有效的水力机械动态数值解析策略。其中湍流模式采用DES,差分选用TVD型的MARS格式,并以经典的圆柱绕流问题进行了验证。本文作者还编写了C++程序,将耗时长、占用磁盘空间大的过程分解为若干子过程,并使得这些子过程能够自动的、稳健的执行。
其次,作为上述解析策略的算例并扩展水力机械漩涡流稳定性理论的内容,同时考虑到异常振动发生在小流量工况下,因此,本文结合小流量下轴流泵和离心泵内的不稳定漩涡流动,讨论了混流式水轮机在小流量下的流动特征。得到的结论是:
①轴流泵在一定流量下存在旋转失速现象。当旋转失速发生时,速度、压力脉动的主频低于叶轮转动的频率,幅值远大于设计流量下速度、压力脉动的幅值。
②离心泵在一定流量下存在失速现象,但并不意味着失速团一定会反向传播。本文中,8叶片数的离心泵内出现了失速现象,失速团仅仅在相对稳定的位置上绕叶片周期性脱落,没有反向传播;但当叶片数改为7,流量、网格拓扑结构等不变的情况下,失速团发生了缓慢的反向传播。文中结合旋转失速理论,认为在8叶片时,离心泵内4个失速团的发展程度是一致的,位置也是对称的,因而缺乏“旋转”起来的动力;而7叶片时,虽然还是4个失速团,但它们的发展程度不一致,空间位置也不对称,因而具有“旋转”起来的动力。
另外,文中还研究了7叶片时失速团的传播规律,发现失速团是跳跃式的传播,即从当前叶片传播到第三个叶片,而不是相邻的叶片。
③小流量下的水轮机叶片背面发生流动分离,在所研究的模型下,每个叶片间的流动分离程度几乎是一样的,分离团既没有失速,更没有旋转。结合轴流泵和离心泵的结论以及旋转失速的机理,本文认为水力机械内部发生旋转失速的条件之一是存在不稳定的和不对称的流动分离团。但水轮机是收缩流道,流道内是顺压梯度,分离团通常是稳定的,因此,水轮机中很难发生旋转失速现象。
第三,通过对三峡机组异常振动现象细节以及模型全特性曲线的深入分析,本文指出供货商提出的负流量说和水锤说不能成立,提出了“水体共振”的观点。
最后,通过对三峡机组异常振动工况动态特性的模拟,证实了在所研究的工况下,水轮机内部确实存在着1.359Hz的频率,并与实测结果保持一致。通过动态计算,还得到以下结果:
①活动导叶表面靠近其开口的下端存在局部高压,活动导叶开口处沿其高度方向的流动是不均匀的。活动导叶开口的下端存在回流,大部分流量从开口的上半部分流出到转轮。
这种流动特征表明,转轮上半部分和下半部分的工作状态是不一致的,转轮上半部分是水轮机的制动工况,而下半部分则是反水泵工况。
②活动导叶开口附近的区域存在明显的1.359Hz的速度和压力脉动,与异常振动的频率吻合的非常好。经分析,这种压力脉动发源于活动导叶开口附近的区域。为了严格证明振动的原因就是水体共振,需要证明两点:
其一,存在着一个频率与1.359Hz相等的激振力;
其二,振动体的固有频率为1.359Hz。
上述1.359Hz的脉动存在证明了第一点,但同时从逻辑上说明第二点也应该是成立的,最有力的证据是异常振动频率就是1.359Hz。此外,根据动态计算的设置和上述结论,也否定了负流量和水锤的说法。
③对活动导叶开口附近的单元进行统计分析,发现不论是速度脉动还是压力脉动,主频为1.359Hz的单元,在活动导叶中部它们的幅值取得最大值。因此,转轮上半部分和下半部分所发生的两种工作状态是不稳定的,这种不稳定导致了活动导叶开口附近的频率为1.359Hz的脉动发生。
从1.359Hz的脉动发生的位置和机制来看,都是以往的文献所不曾论述的,因此本文的结论扩展了混流式机组稳定性理论的内容。
Francis turbines are used in Three Gorges hydraulic-generator unit and the X-type blades are utilized. There are many advantages to utilize this kind of blade, such as good flexibilities of wide range varying of head and load, high average efficiency, good performance for preventing flow separations and cavitations at leading edges under high head or small opening conditions. However, there are many factors to affect the stabilities of Francis turbine operation; some of them have not been recognized sufficiently. In addition, the Three Gorges units are huge and accordingly, the natural frequency of water is low and water resonance vibration is easily happen. On 6 Aug 2003, a strong abnormal vibration happened during the over-speed test on the unit 6 of the Three Gorges left bank hydropower station. When vibration occurs, the opening of the guide is about 4% and the rotational speed is about 73rpm. The frequency of vibration is 1.359Hz and its max peak to peak value reaches 500kPa in the spiral, which is larger than the half of the total test head (about 68m). Although there is high frequency in the vibration of structure, it is affected by the 1.359Hz. Besides, the vibration of water before the guide open is very strong; however, the vibration after the guide open is small.
Considering this kind of vibration, ALSTOM Co. evaluated the time history of flow utilizing Gibson method; and they believed that the vibration reason is the negative flow. A model test was carried out by Harbin Institute of Large Electrical Machinery in China and the full performance curves of model were obtained. According to the model test, the water hammer is believed to be the reason leading to abnormal vibration.
The abnormal vibration under extremely small opening condition, which is a very serious threat for unit to operate safely, is never reported until now and can not be explained using the actual stability theory of hydro turbine. Vendors have given out the explanations as above, but it is not tenable and can not be accepted widely. In-depth studies for the vibration have been done in this paper. Considering the fact that the model test can not reflect dynamic characteristic of prototype and it is unallowed to measure the interior flow of prototype, the dynamic numerical method is utilized to research the vibration mechanism based on the theoretical analysis. The results are as follow.
Firstly, an effective method and strategy to research the flow in hydraulic machinery dynamically is put forward and developed from many aspects such as mesh, turbulent model, difference scheme, time step control and output control etc., of which DES (Detached-Eddy Simulation) is chosen as the turbulent model and MARS (Monotone Advection and Reconstruction Scheme) which is a TVD (Total Variation Diminishing) type is chosen as the difference scheme. These choices have been validated by the classical cylinder flow problem. In addition, the author of this thesis writes a C++ code to decompose the time-consuming and hard-disk-consuming solution process into some sub processes. These sub processes can be executed automatically and steadily.
Secondly, the flow characteristic of hydraulic machinery in small flow is discussed according to the basic principle in this thesis. The results are: (1) Rotating stall happens at some flows for an axial pump. When this occurs, the main frequency of velocity and pressure is below the frequency of rotation of the impeller. However, the amplitudes are far greater than those in design conditions. (2) Stall happens at some flows for a centrifugal pump; however, the stall cells do not always propagate back along the annular cascades. In this thesis, a stall happens in a centrifugal pump with 8 blades, but the stall cells are stable with the impeller speed and do not propagate back along the annular cascades. However, when the number of blades is changed to 7 and the flow, the topology of mesh remain unchanged, slow propagation happens. Combining the rotating stall theory, the author deems that the developments of the four stall cells are same and the positions of them are symmetry for the centrifugal pump with 8 blades, so there is a lack of power of rotation; for the pump with 7 blades, the number of stall cells is still four, but the developments are not same and the positions are not symmetry, so there is the power of rotation.
In addition, the propagation rule is researched for 7-blades pump. The propagation way is found to be jumping, that is, the stall cell propagates to the third blade but not the adjacent one.
(3) The flow separates from the suction surface of the blade at small flow for hydro-turbine. The developments of the separations are same for the researched model. Neither stalls nor rotating stalls happens. Combining the results of axial pump and centrifugal pump and the mechanism of rotating stall, the author infers that one of conditions leading to rotating stall for hydraulic machinery is that there are unstable separations exist. However, it is contracting channel for hydro-turbine and accelerating pressure gradient exists in the channel, the separations is stable in general and accordingly, it is difficult for rotating stall in hydro-turbine to occur.
Thirdly, through the analysis of the vibration detail messages and the full performance curves of model, the author deems that the viewpoints of the vendors are not acceptable and put forward the view point of water resonance.
Finally, the dynamic numerical simulations on the abnormal vibration condition of the Three Gorges units validate the existence of the excitation source. The frequency of the excitation source has a good agreement with the experiment data. The computational results can be summarized as:
(1) A local high pressure region exists on the front surface of the guide near the lower end of the exits of guides. The flow is non uniform along the direction of the guide height. A back flow exists near the lower end of the exits of guides. This makes most of the water flow out to runner from the top half of the exits of guides. The characteristic of flow shows that the runner’s state of the bottom half and the top half is non uniform, that is, the bottom half is reverse pump and the top half is brake operation of hydro turbine.
(2) An obvious velocity and pressure fluctuation of which frequency is 1.359Hz exists in and originates from the region near the exits of guides. There are two points should be proved for the explanation of water resonance: one is that there is an excitation source of which frequency is equal to 1.359Hz; the other is that the natural frequency of the vibrating body is 1.359Hz.
The existing of the frequency of 1.359Hz proves the first point, but then it indicates logically that the second one also is true. In addition, the vibration reason about negative flow and water hammer is deduced to be not correct according to the settings of dynamic numerical computation and above results.
(3) The statistical analysis for the fluid cells near the exits of guides shows that the amplitude values of which corresponding frequency is 1.359Hz reach maximum in the center section of the guides. Combining the results of (1), it can be deduced that the runner states of the top half and the bottom half are unstable which leads to the frequency of 1.359Hz.
From the view of the position and the mechanism about the frequency of 1.359Hz, it is never reported previously, so the results of this thesis development the contents of stability theory of Francis turbine.
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