Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed.     

Influence of steam leakage through vane,gland, and shaft seals on rotordynamics of high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine

A comparative analysis of the influence of steam leakage through vane, gland, and shaft seals on the rotordynamics of the high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine was performed using numerical calculations. The rotordynamic coefficients associated with steam leakage through the three labyrinth seals were calculated using the control-volume method and perturbation analysis. A stability analysis of the rotor system subject to the steam forcing induced by the leakage flow was performed using the finite element method. An analysis of the influence of the labyrinth seal forcing on the rotordynamics was carried out by varying the geometrical parameters pertaining to the tooth number, seal clearance, and inner diameter of the labyrinth seals, along with the thermal parameters with respect to pressures and temperatures. The results demonstrated that the steam forcing with an increase in the length of the blade for the vane seal significantly influences the rotordynamic coefficients. Furthermore, the contribution of steam forcing to the instability of the rotor is decreased and increased with increases in the seal clearance and tooth number, respectively. The comparison of the rotordynamic coefficients associated with steam leakage through the vane seal, gland seal, and shaft seal convincingly disclosed that, although the steam forcing attenuates the stability of the rotor system, the steam turbine is still operating under safe conditions.     

Influence of leakage flow through labyrinth seals on rotordynamics: numerical calculations and experimental measurements

An extensive investigation of the influence of the leakage flow through a labyrinth seal at supply pressure of 12 bar on the rotordynamics was performed by using numerical calculations and experimental measurements. Toward this end, an experimental rotor setup was established in Shanghai Jiao Tong University. Two labyrinth seals were chosen for comparison, e.g., an interlocking seal and a stepped one. The numerical calculations based on the bulk-flow theory and the perturbation analysis were accomplished. Simultaneous acquisitions of the fluctuating static pressure at the stator wall and the displacement of the whirling rotor were made. The influence of the aerodynamic forcing on the rotor was analyzed in terms of the axial distribution of the mean static pressure, the circumferential distribution of the fluctuating pressure, the fist critical speed and the destabilization rotating speed of the rotor. The experimental results demonstrated that the sinusoidal distribution of the fluctuating static pressure on the stator wall was closely related to the whirling motion of the rotor. The first critical speed of the rotor was reduced by the aerodynamic forcing, resulting in intensified destabilization of the rotor system. Furthermore, the numerical analyses were in good agreement to the experimental measurements.     

超临界二氧化碳高低齿梳齿密封动力稳定性研究

建立超临界二氧化碳(supercritical carbon dioxide,SCO₂)高低齿梳齿密封三维数值计算模型,应用基于微元理论的密封动特性识别方法,研究凸台宽度及密封间隙对超临界二氧化碳梳齿密封动静特性的影响,并与传统梳齿密封进行对比. 研究表明:高低齿梳齿密封的交叉复合刚度系数对有效阻尼系数影响较小,主阻尼对其占主要影响. 在低涡动频率下(<160 Hz),传统梳齿密封动力稳定性较好;而涡动频率高于160 Hz时,高低齿梳齿密封的有效阻尼系数约为传统梳齿密封的105%~113%;且存在1个最佳凸台宽度使密封系统稳定性最好(本文最佳值为5.13 mm);随着密封间隙的减小,有效阻尼系数的大小与频率依赖性分别增大、增强. 高低齿梳齿密封泄漏量较传统梳齿密封降低约45.5%;凸台宽度5.13 mm、密封间隙0.4 mm时较原始模型(b=4 mm、c₂=0.5 mm)泄漏量分别降低约5%和19%,高低齿梳齿密封泄漏量随密封间隙的减小而降低.      

具有封严蓖齿转子系统的动力稳定性分析

封严蓖齿的气弹力对转子系统的稳定性起重要作用，本文建立了具有封严蓖齿的转子系统动力稳定性的分析方法，该方法利用传递矩阵法建立系统的主导方程，将封严蓖齿的气弹力以等效刚度及等效阻尼系数的方式引入转子系统的主导方程，用数值积分法解主导方程，求得系统的动力特性，根据扰动解判断系统的稳定性。本文所建立的分析软件，也可计算转子系统的不平衡响应、临界转速、突加不平衡响应等。文中对一模型转子进行了算例分析。     

阻旋栅对梳齿密封动静特性影响研究

阻旋栅可改变密封进口流体周向流动与进口预旋,是提高系统稳定性的主要方法之一. 本文作者应用计算流体力学方法研究了阻旋栅几何参数对梳齿密封动静特性的影响,计算分析了阻旋栅在不同长度、间隙、周向个数及不同进口预旋比下密封流场分布与动力特性系数,并与无阻旋栅梳齿密封进行对比. 研究表明:阻旋栅能够有效抑制密封进口周向流动、降低密封腔室周向压力;随着阻旋栅周向个数与阻旋栅间隙的减小,其抑制效果增强,阻旋栅长度的增加对周向速度影响则越来越小;提高预旋比将使密封内流体周向速度增加. 与传统梳齿密封相比,具有阻旋栅的梳齿密封直接阻尼增加,交叉刚度降低,进而有效阻尼提高. 阻旋栅间隙s=0.20 mm、长度l=3.25 mm、数量n=90时密封有效阻尼较大,系统稳定性最好.      

偏心迷宫密封动静特性研究

建立了不同偏心状态下迷宫密封三维数值分析模型,应用基于微元理论的密封动力特性系数识别方法计算密封静态和动态特性. 结果表明:转子偏心会降低密封抑制流体泄漏的效果;密封腔内周向压力高点随偏心率增大逐渐偏离最小间隙处. 低偏心率(≤ 0.5)下,静态直接刚度K与静态交叉刚度k变化较小,高偏心率(> 0.5)下K和k的绝对值减小. 随着偏心率的增大,密封小间隙侧流动黏性效应增强是产生负静态直接刚度的主要原因. 密封偏心涡动时,低偏心率(< 0.6)下刚度和阻尼系数变化较小,随偏心率和涡动频率的升高直接刚度逐渐变为负值;随偏心率的增大,交叉刚度在正交两个方向上大小不再相等,有效阻尼降低,高偏心率(≥ 0.6)下有效阻尼受偏心率影响更显著.      

Experimental and numerical analysis of nonlinear dynamics of rotor–bearing–seal system

Nonlinear dynamics and stability of the rotor–bearing–seal system are investigated both theoretically and experimentally. An experimental rotor–bearing–seal device is designed and corresponding tests are carried out. The experimental rotor system is simplified as the Jeffcott rotor. The nonlinear oil–film forces are obtained under the short bearing theory and Muszynska nonlinear seal force model is used. Numerical method is utilized to solve the nonlinear governing equations. Bifurcation diagrams, waterfall plots, Poincaré maps, spectrum plots and rotor orbits are drawn to analyze various nonlinear phenomena and system unstable processes. Theoretical results from numerical analysis are in good agreement with results from experiments. Conclusions are drawn and prove that this study will contribute to the further understanding of nonlinear dynamics and stability of the rotor system with the fluid-induced forces from oil–film bearings and the seals.     

迷宫密封湍流增阻的数值研究

迷宫密封是依靠节流间隙中的节流过程和迷宫空腔内的动能耗散过程来实现密封的,这两个流体流动过程从本质上规定了迷宫密封的密封性能。通过密封内部流动本质的研究,合理利用湍流流动的规律和特点,能够发挥密封内部湍流的增阻作用,提高密封性能。本文数值计算了一种锯齿型径向迷宫密封的内部流动,得到了密封内部的流动形态,揭示了密封内部流动与密封性能的关系。结果表示,密封存在一个最佳的齿插入长度。在最佳齿插入长度时,尽管节流间隙较大,但由于节流间隙内流动收缩和偏转,间隙的有效通流面积却很小,泄漏介质可以在间隙中获得较大的速度,在迷宫空腔内形成正确的耗散涡流,密封具有最佳的密封效果。所以,充分发挥湍流增阻的作用,可以突破节流间隙的微小尺寸限制,实现较大间隙下的良好密封。这不仅会给迷官密封的制造、安装及运行等带来很大的方便,而且可以为发展新的迷宫密封技术奠定理论基础。     

迷宫-蜂窝混合型密封静态稳定性与泄漏特性研究

建立迷宫-蜂窝混合型密封三维数值分析模型,研究密封在阻塞/非阻塞流动状态及不同偏心率下静态稳定性与泄漏特性,并与传统迷宫密封进行对比分析. 结果表明:两种不同结构型式的密封泄漏量均随偏心率的增大而增加,但迷宫-蜂窝混合型密封相较于传统迷宫密封有更好的封严性能. 在阻塞与非阻塞状态下,两种密封均表现为负的静态刚度系数,系统易产生静态失稳现象. 与传统迷宫密封相比,迷宫-蜂窝混合型密封静态刚度系数绝对值较小,稳定性较高.      

交错式扇贝阻尼密封动力特性研究

建立交错式扇贝阻尼密封三维数值分析模型,基于动网格及多频椭圆涡动模型研究密封动力特性沿轴向分布规律,计算分析错开角度(α=0°、11.25°、22.5°、33.75°)与密封腔深度(h=2.8、3.3、3.8和4.3 mm)对密封动力特性的影响. 结果表明:上游腔室(C1~C4)具有较大的正直接刚度和有效阻尼,对抑制转子涡动、提升系统稳定性的贡献相对较大. 相对并列式(α=0°)结构,交错式扇贝阻尼密封流体周向速度较小、湍流耗散增加,系统稳定性提升,同时密封泄漏量降低. 错开角度为33.75°时的有效阻尼约为0°时的111%~121%;错开角度为22.5°时的泄漏量相较于0°时约降低了2.11%. 有效阻尼随密封腔深度减小而增大,密封腔深度为2.8 mm时的有效阻尼约为4.3 mm时的146%~211%;密封泄漏量随密封腔深度增大而降低,密封腔深度为4.3 mm时的泄漏量相较于2.8 mm时降低了约3.73%.      

涡轮泵转子-迷宫密封系统的非线性稳定性和分岔

研究迷宫密封对某一工程涡轮泵转子系统动力特性的影响,迷宫密封力采用Muszynska非线性力模型,应用有限元法建立转子系统的动力学方程,采取系统动力学方程中包含的高阶线性自由度和低阶的非线性自由度进行分块处理的方法,有效地缩短了求解时间。根据Floquet理论,判别系统的临界失稳转速,并由Floquet乘子来确定系统失稳后分岔方式。采用分块-Newmark法数值模拟了转子二涡轮盘的轴心轨迹。最后分析了涡轮泵转子二涡轮盘的质量偏心同相位和存在90度相位差时对转子系统运动特性的影响。     

Research on the dynamic characteristics of crack damage of a seal-rotor system

Nonlinear Dynamics - In rotor systems, the labyrinth seal system is the core component to suppress fluid leakage between the rotor and the stator. In this paper, based on the finite element method,...     

型孔形状和方向对孔型阻尼密封泄漏特性影响

研究了型孔形状和方向性对孔型阻尼密封泄漏特性的影响. 建立了孔型阻尼密封流场特性CFD数值模型,对比分析了不同转速和密封间隙下圆孔阻尼密封、蜂窝密封、迷宫密封和光滑面密封的泄漏特性,研究不同转速下型孔形状、超椭圆系数和倾斜角对广义孔型阻尼密封泄漏特性的影响规律,探讨了方向性型孔阻尼密封阻流控漏机制. 结果表明:紧密排列的孔型阻尼密封相较于迷宫密封和光滑面密封具有显著优异的密封性能;倾斜角为30°、超椭圆系数为2且边数为2的类椭圆型孔阻尼密封在静止时具有最小的泄漏率,且可通过减小周向或轴向排列间距进一步减小泄漏;一定倾斜角条件下,超椭圆系数较大的类椭圆型孔出口尖端附近能形成明显的低速阻流区,从而达到阻流控漏的效果.      

迷宫密封转子系统非线性动力稳定性的研究

研究迷宫密封对转子系统动力稳定性的影响，迷宫密封的气动力采用Muszynska非线性力模型，计算了单盘Jeffcott转子非线性动力学特性。对Jacobi矩阵的分析表明，在密封力的影响下，转子达到一定转速后开始失稳，发生Hopf分岔，进入周期涡动状态，涡动幅度随转速的提高而增大，提高到一定程度，密封和转子发生碰摩，采用Runge-Kutta法数值模拟了转子的轴心轨迹。最后分析了迷宫密封的物理和结构参数对系统运动特性的影响。     

Nonlinear dynamic behaviors of a rotor-labyrinth seal system

The nonlinear model of rotor-labyrinth seal system is established using Muszynska’s nonlinear seal forces. We deal with dynamic behaviors of the unbalanced rotor-seal system with sliding bearing based on the adopted model and Newmark integration method. The influence of the labyrinth seal one the nonlinear characteristics of the rotor system is analyzed by the bifurcation diagrams and Poincare’ maps. Various phenomena in the rotor-seal system, such as periodic motion, double-periodic motion, quasi-periodic motion and Hopf bifurcation are investigated and the stability is judged by Floquet theory and bifurcation theorem. The influence of parameters on the critical instability speed of the rotor-seal system is also included.     

Stability and bifurcation of unbalance rotor/labyrinth seal system

The influence of labyrinth seal on the stability of unbalanced rotor system was presented . Under the periodic excitation of rotor unbalance , the whirling vibration of rotor is synchronous if the rotation speed is below stability threshold, whereas the vibration becomes severe and asynchronous which is defined as unstable if the rotation speed exceeds threshold . The. Muszynska model of seal force and shooting method were used to investigate synchronous solution of the dynamic equation of rotor system. Then , based on Floquet theory the stability of synchronous solution and unstable dynamic characteristic of system were analyzed.     

锯齿型径向迷宫密封的数值研究

数值研究了锯齿型径向迷宫密封的密封性能,对密封的内部流场进行了有限元模拟,展示了节流间隙中有效能流宽度及泄漏介质通流速度随齿插入长度变化的规律,得到了不同齿插入长度时的密封性能,发现密封性以并不是随着齿插八长度的增加而单调增加,而是存在一个最佳的齿插入长度。最佳齿插入长度时,尽管此时的节流间隙较宽,但由于间隙是流动的强烈偏转,使实际的有效通流面积减小,泄漏介质在节波间隙中因而可以获得较大的速度,所     

A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

Determination of the aerodynamic configuration of wake is the key to analysis and evaluation of the rotor aerodynamic characteristics of a horizontal-axis wind turbine.According to the aerodynamic configuration, the real magnitude and direction of the onflow velocity at the rotor blade can be determined, and subsequently, the aerodynamic force on the rotor can be determined. The commonly employed wake aerodynamic models are of the cylindrical form instead of the actual expanding one. This is because the influence of the radial component of the induced velocity on the wake configuration is neglected. Therefore, this model should be called a "linear model". Using this model means that the induced velocities at the rotor blades and aerodynamic loads on them would be inexact. An approximately accurate approach is proposed in this paper to determine the so-called "nonlinear" wake aerodynamic configuration by means of the potential theory,where the influence of all three coordinate components of the induced velocity on wake aerodynamic configuration is taken into account to obtain a kind of expanding wake that approximately looks like an actual one. First, the rotor aerodynamic model composed of axial(central), bound, and trailing vortexes is established with the help of the finite aspect wing theory. Then, the Biot-Savart formula for the potential flow theory is used to derive a set of integral equations to evaluate the three components of the induced velocity at any point within the wake. The numerical solution to the integral equations is found,and the loci of all elementary trailing vortex filaments behind the rotor are determined thereafter. Finally, to formulate an actual wind turbine rotor, using the nonlinear wake model, the induced velocity everywhere in the wake, especially that at the rotor blade,is obtained in the case of various tip speed ratios and compared with the wake boundary in a neutral atmospheric boundary layer. Hereby, some useful and referential conclusions are offered for the aerodynamic computation and design of the rotor of the horizontal-axis wind turbine.     

螺旋槽端面微间隙高速气流润滑密封特性

考虑入口气流压力损失和出口阻塞效应,建立了微间隙端面高速气体润滑密封分析数学模型,对螺旋槽端面微间隙高速气流润滑密封特性进行研究.重点分析了不同密封间隙、密封压力和转速等工况条件下,入口压力损失和出口阻塞效应对开启力、泄漏率及气膜刚度等密封特性参数的影响规律.结果表明:高速气体阻塞效应使出口压力高于环境压力,压力损失使入口气膜压力下降,导致泄漏率和气膜刚度明显下降,并使开启力增加.随着密封压力和密封间隙的增加,阻塞效应增强,导致泄漏率和气膜刚度显著降低.密封压力10 MPa时,泄漏率降低可达20%,气膜刚度的下降可达30%以上.