An experimental identification model of rotordynamic coefficients of seals using unbalanced synchronous excitation method

This study presents an improved impedance method based on unbalanced synchronous excitation to identify the rotordynamic coefficients of labyrinth seals. The rotordynamic coefficient test is implemented near the cylinder resonance frequency to enlarge the influence of seal force. The force generated by the rotor unbalance is used to provide synchronous frequency excitation for the rotordynamic coefficient test. Four unique equations are set up under two sets of different rotor unbalance conditions to obtain four unknown complex rotordynamic coefficients. The factors that influence the rotordynamic coefficients of seals, namely, unbalance mass, inlet/outlet pressure ratio, and rotating speed, are considered. The dynamic coefficients are minimally affected by different rotor unbalances. The direct items are nearly equal with same signs, whereas the cross-coupled items are nearly equal with opposite signs. All coefficients increase with increasing inlet/outlet pressure ratio and rotating speed. The direct stiffness coefficients increase more quickly than the cross-coupled items. In addition, the effect stiffness and effect damping coefficients are analyzed; results indicate that both coefficients increase with increasing rotating speed.     

迷宫气封三维非定常流场及转子动特性数值仿真

通过计算流体力学方法,采用近似的解析变换网格,以及混合有限分析格式,对迷宫气封流场进行三维非定常数值求解,进而求得密封气流对转子的气流激振力,获得转子的动特性系数。将计算结果与试验结果以及双控制体计算结果相比较,结果令人满意,说明了该计算程序是正确可靠的。该方法精度较高,适用范围广,可以应用于各种复杂的涡动情况及各种齿型,对气封转子的深入研究有重要意义。计算结果还显示了主刚度、主阻尼对气流进口周向速度不敏感,而交叉刚度对气流进口周向速度非常敏感。由于交叉刚度对转子的稳定性影响相当大,这一点是值得注意和利用的。     

反旋流对密封静力与动力特性影响的理论与试验研究

设计加工无/有反旋流共4种密封结构,从理论与实验两个方面研究反旋流对密封静力与动力特性的影响规律。建立反旋流密封静力特性CFD模型,理论分析反旋流对密封间隙流体切向速度、周向压力分布以及泄漏特性的影响;设计搭建反旋流密封动力特性试验台,试验测试无/有反旋流密封的泄漏特性,应用不平衡同频激励法试验研究反旋流对密封动力特性的影响。研究结果表明:反旋流可减小密封间隙流体的切向速度,进而降低密封间隙流体的周向压力差,且密封间隙流体周向压差随切向速度的减小而降低,这是反旋流抑制密封气流激振力的主要原因;密封的泄漏量随进出口压比的增加而增大,两者近似呈线性关系;与无反旋流密封相比,反旋流密封增加了密封的泄漏量,且随着进出口压比的增加,两者泄漏量差异增大;密封的动力特性系数的随密封进出口压比与转速的增加而增大。在相同工况下,主刚度大于交叉刚度约一个数量级,主阻尼与交叉阻尼数量级相同,且主阻尼大于交叉阻尼;反旋流可有效降低密封的等效刚度,增加密封的等效阻尼,提高密封的稳定性。     

离心压缩机蜂窝阻尼密封动力特性及转子稳定性*

新一代蜂窝阻尼密封在提升透平机械转子稳定性方面有优越的表现,其动力特性是评价转子稳定性的重要参数。应用非定常动网格技术和多频涡动模型,研究蜂窝密封动特性系数随转子涡动频率的变化规律,并与迷宫密封进行对比。结果表明：蜂窝密封动特性受转子涡动频率影响较大,直接刚度系数和交叉阻尼系数随涡动频率增大而增大,交叉刚度和直接阻尼系数随涡动频率增大而减小;迷宫密封动特性系数随涡动频率变化特征不明显;在低频率区蜂窝密封的有效阻尼远高于迷宫密封。在实际压缩机转子上的应用结果表明,蜂窝密封能显著提升转子稳定性。     

Test Results for Leakage and Rotordynamic Coefficients of Floating Ring Seals in a High-Pressure,High-Speed Turbopump

Test results are presented for short floating ring seals (D = 53.0 mm, L/D = 0.15) using a smooth surface and a round-hole pattern defined as a damper floating ring seal (h/C_r = 3, γ = 0.34: the ratio of hole area to surface area) for supplied pressures of 3.0, 5.0, and 7.0 MPa, respectively, with the shaft operating speed up to 24,800 rpm. The measured data includes leakage, attitude angle, eccentricity ratio, and rotordynamic coefficients such as stiffness, damping, and inertia. When the floating ring seals are locked up, the eccentricity ratio of the smooth surface floating ring seal is lower than that of the damper floating ring seal. The attitude angle increases linearly with the operating speeds. The damping coefficients of the damper floating ring seal are higher than those of the floating ring seal. Whirl frequency ratios of the floating ring seal are lower than the damper floating ring seal with high eccentricity ratio at low operating speed range. The design parameters determined from these test results will be used for high-pressure and high-speed turbopump seals in a liquid rocket engine system.     

Annular seal rotordynamic stability enhancement with circumferential spiral flow control using helical deflectors

Rotordynamic instability problem caused by seal force widely exists in turbo-machines. The fluid-induced force in the seal is determined by the pressure distribution associated with the flow field structure, particularly with the circumferential flow characteristics. In the previous study, the authors found that the helix-comb seal can effectively change the circumferential flow field. The specially designed helical deflectors can reverse the circumferential flow direction of the fluid inside the seal. A considerable static stability enhancement is obtained. However, the transient rotordynamic characteristics of the helix-comb seal are not reported. In the present study, the transient rotordynamic characteristics of the helix-comb seal are investigated further. The rotordynamic coefficients, effective damping, and aerodynamic work of the helix-comb seal are calculated and compared with those of the labyrinth seal. Results reveal that compared with the labyrinth seal, the helix-comb seal considerably improves rotordynamic stability, particularly at a high preswirl ratio. The desirable rotordynamic stability can be obtained with flow field control.

     

周向波度气体密封的动态特性

基于摄动法求解周向波度气体密封的动态Reynolds方程,得到动态气膜压力分布。计算周向波度气体密封的气膜动态刚度和阻尼系数,分析扰动频率及密封端面几何参数,如波数、波幅和坝宽比对气膜动态特性系数的影响规律。结果表明:当扰动频率小于转轴角速度时,其对气膜动态特性系数影响不大,反之有较大影响;波数对气膜动态特性系数影响不大,随着波幅的增加主刚度系数和阻尼系数都随之减小,耦合刚度系数则几乎不受影响,随着坝宽比的增加刚度系数基本保持不变,阻尼系数均增加。     

A rotordynamic analysis of circumferentially-grooved pump seals based on a three-control-volume theory

In this paper the leakage prediction and rotordynamic analysis of an annular seal with a smooth rotor and circumferentially grooved stator are performed based on a three-control-volume theory. The present analysis is validated by comparing with the experimental data of Iwatsubo and Sheng and theoretical results suggested by Marquette and Childs. For the leakage prediction the present analysis shows a good agreement with Marquette and Childs’ result and a qualitation agreement with Iwatsubo and Shengs’ experimental data. Direct and cross-coupled stiffness coefficients show closer agreement with the experimental values than those of Marquette and Childs. However, direct damping coefficient shows greater discrepancy from the experimental value than Marquette and Childs’.     

螺旋槽气体轴承动态特性及失稳分析

针对高速动静压气体轴承气膜的复杂非线性动力学行为,以球面螺旋槽动静压气体轴承为研究对象,建立润滑分析数学模型;采用有限差分法与导数积分法进行求解,得到动态扰动压力分布及动态特性系数,并研究切向供气条件下螺旋槽参数、径向偏心率、供气压力、转速对气膜刚度阻尼系数的影响规律;建立线性稳定性计算模型,预测气膜涡动失稳转速,分析运行参数对失稳转速的影响。结果表明:气膜阻尼是一种抑制涡动的因素,气膜的稳定性取决于气膜刚度与阻尼的协同作用;气膜刚度阻尼随着槽宽比、槽深比、螺旋角的增大,整体上呈先增大后减小的趋势;刚度随转速的升高而增大,阻尼则随转速的升高而减小;径向偏心率和供气压力越大,气膜刚度和阻尼越大;在一定范围内,提高供气压力、增大径向偏心率能够提高系统失稳转速;合理地选取轴承结构参数和运行参数,能够优化轴承动态特性,保证气体轴承较高的运行稳定性。     

Influence of rub groove on rotordynamics associated with leakage air flow through a labyrinth seal

An extensive investigation of influence of rub grooves on dynamics and stability of the rotor, which is subjected to aerodynamic forcing associated with the leakage flow through 44 straight-through seals, was performed by using numerical calculations based on the single control-volume method and the perturbation analysis. Three cases of different groove configurations were chosen for the comparative study, e.g., the seal without rub groove (case1), the seal with upstream shifting of the seal tooth in respect to the rub groove (case2) and the seal with location of the seal tooth in the middle station of the rub groove (case3). The orifice contract coefficient adopted in reduction of rotordynamic coefficients was provided by using Computational Fluid Dynamics (CFD). Influence of rub grooves on the leakage flow was obtained in terms of the close-up view of the flow pattern near the seal tooth, leakage flow rate, distributions of the mean pressure and circumferential velocity in cavities. In comparison to case 1, the leakage flow in case 3 is considerably intensified, while which in case 2 is slightly increased. Dynamics and instability of the rotor in all cases was discussed in terms of the rotordynamic coefficients and the logarithmic decrement, respectively. The results disclosed that the aerodynamic forcing in case 2 intensified the destabilization of the rotor system.     

Numerical simulation of rotordynamic coefficients for eccentric annular-type-plain-pump seal using CFD analysis

Annular seals are primarily used to control the leakage in turbomachinery, such as pumps. Consequently, annular seals substantially affect the stability of turbomachinery. Designing the annular seals of high performance pumps require the accurate prediction of the seal’s leakage flow rate and rotordynamic coefficients. The bulk-flow model is the traditional means for leakage flow rate analysis and predictions. Bulk-flow analysis is based on the Hirs’ lubrication equation, which simplifies the Navier-Stokes equation. However, the analysis of the bulk-flow model requires a great amount of time to develop an analysis code. Furthermore, the code possesses many constraints for analyzing seals with complicated shapes. 3D CFD simulations provide faster and less expensive estimates of the flow field for a wide variety of operating parameters and flow conditions. In this study, the flow field and the rotordynamic coefficients of a plain-eccentricannular seal were simulated with circular whirl orbits using 3D CFD code. A relative coordinate system was defined to calculate the 3D velocity profile and the dynamic pressure distribution of the seal clearance for each rotor whirling speed. The rotordynamic coefficients were determined by reaction forces of seal fluid, which were calculated by integrating the dynamic pressures to the whole area of seal. The results from our analyses were compared to existing theoretical calculations as well as compared to results acquired from experiments. The present 3D CFD results of leakage and rotordynamic coefficients of K and C showed better improvement in prediction.     

新型涡流槽密封泄漏特性与动力特性研究

提出一种密封入口周向均匀设置有涡流槽的新型密封结构,建立了传统迷宫密封与新型涡流槽密封泄漏特性及动力特性求解模型,在实验验证数值计算方法准确性的基础上,通过比较分析了传统迷宫密封与新型涡流槽密封在不同进出口压比、预旋比工况下的泄漏特性与动力特性,研究了新型涡流槽结构对密封泄漏特性及动力特性的影响机理。研究结果表明：随着涡流槽数量的增加,涡流槽密封的泄漏量逐渐降低;在同一压比下,不同涡流槽数新型密封的泄漏量之间差值随着压比的增大而增大。当压比为6时,64涡流槽的新型密封较传统迷宫密封,泄漏量下降了3.37%;在高预旋比的工况下,不同涡流槽数量密封的切向气流力均与转子涡动方向相反,起到抑制转子涡动的作用,且随着涡流槽数量的增加,切向气流力也随着增大;随着转子涡动频率的增大,三种不同涡流槽数量密封的交叉刚度先减小到负值然后增大到正值。涡流槽密封的有效阻尼均高于传统迷宫密封,新型涡流槽密封可以提高转子系统的稳定性。     

Measurements of Flow Rate and Force Coefficients in a Short-Length Annular Seal Supplied with a Liquid/Gas Mixture (Stationary Journal)

Deep sea compression systems must work under strenuous conditions with either gas in liquid or liquid in gas mixtures, mostly inhomogeneous. Off-design operation affects the mechanical system's overall efficiency and reliability, with penalties in leakage and rotordynamic performance of secondary flow components, namely, seals. This article introduces a test rig to characterize the leakage and dynamic force coefficients of a short-length annular seal (L/D = 0.36, clearance = 0.127 mm) operating under various flow regimes ranging from pure gas, to bubbly (liquid in gas), to foamy (gas in liquid), to pure liquid. The test rig includes of rotating journal and a softy supported cartridge that make a clearance annular seal that is supplied with a liquid/gas mixture. Flowmeters record the fluid's passage, and with manual control of the streams, the mixture has a known liquid (or gas) volume fraction at the seal inlet plane. Two orthogonally mounted electromagnetic shakers excite the cartridge with periodic (single-frequency) forces spanning a wide frequency range. Eddy current sensors and accelerometers record the seal cartridge motions and a frequency domain parameter identification method delivers the seal dynamic force coefficients.

For tests with a pressure supply/pressure discharge ratio = 3.0 and 3.5 and a nonrotating journal, the article reports the flow rate for an ISO VG10 oil in air mixture with liquid volume fraction (LVF) at the inlet plane increasing from pure gas to pure liquid. Wet seal stiffness and mass and damping force coefficients follow for a seal operating with a pressure supply/pressure discharge ratio = 2.0 and operating with air (only) and also with an oil-in-air mixture with inlet LVF = 2% and 4%. The experimental results, the first reported, reveal that a small amount of liquid increases the damping coefficients of the wet seal 10-fold (or more). Predictions from a computational bulk flow model also demonstrate that the seal damping coefficient varies greatly with small contents of liquid in the oil/gas mixture, although agreement with the experimental force coefficients is not compelling due to the likely inhomogeneity of the mixture flowing though the seal.     

高压离心泵滑动轴承稳定性分析

分析了高压离心泵轴承的动力学模型,通过径向滑动轴承的非定常运动雷诺方程计算出油膜的八个刚度系数和阻尼系数,并以此计算出转子的综合刚度和涡动比平方,得到油膜的失稳转速,最后以高压离心泵实际结构参数进行了轴承的稳定性分析,得出转子正常工作时是安全的结论.     

转子涡动工况下螺旋槽液膜密封性能研究

基于转子在临界转速下的涡动特性,分析转子涡动的轴心运动轨迹.由于动环圆心运动轨迹追随转子,故以动环圆心的圆形运动轨迹为研究点,建立动环偏心的液膜区域模型.采用有限差分法对广义雷诺方程进行离散,通过SOR迭代方法对离散方程进行求解,得到液膜密封端面压力分布,并探讨动环偏心距对液膜开启力、摩擦扭矩、泄漏量以及空化率等液膜密...     

Experimental Study of the Flow Field Inside a Whirling Annular Seal

The flow field inside a whirling annular seal has been measured using a 3-D Laser Doppler Anemometer (LDA) system. The seal investigated has a clearance of 1.27 mm, a length of 37.3 mm and is mounted on a drive shaft with a 50 percent eccentricity ratio. This results in the rotor whirling at the same speed as the shaft rotation (whirl ratio = 1.0). The seal is operated at a Reynolds number of 12000 and a Taylor number of 6300 (3600 rpm). The 3-D LDA system is equipped with a rotary encoding system which is used to produce phase averaged measurements of the entire mean velocity vector field and Reynolds stress tensor field from 0.13 mm upstream to 0.13 mm downstream of the seal. The mean velocity field reveals a highly three-dimensional flow field with large radial velocities near the inlet of the seal as well as a recirculation zone on the rotor surface. The location of maximum mean axial velocity migrates from the pressure side of the rotor at the inlet to the stiction side at the exit. Turbulence production is a maximum near the seal inlet as indicated by the rapid increase of the turbulence kinetic energy (κ). However, turbulence production and dissipation attain equilibrium fairly quickly with K remaining relatively constant over the last half of the seal.     

Prediction of leakage and rotordynamic coefficients for the circumferential-groove-pump seal using CFD analysis

The circumferential-groove seal is commonly used in various turbopumps to reduce leakage. The main goal of this paper is to develop the method of three-dimensional CFD analysis for determining leakage and rotordynamic coefficients of the circumferential-groove-pump seal. A relative coordinate system was defined for steady-state simulation to calculate the velocity and pressure distributions of the seal clearance at each rotor whirl speed. Instead of setting the inlet and outlet pressures as the boundary conditions in the three-dimensional CFD analysis, as it is more commonly done, we used the inlet velocity and outlet pressure obtained from a preliminary two-dimensional CFD analysis. For prediction leakage, the presented analysis shows improvement from the bulk-flow model analysis. For the prediction of rotordynamic coefficients of K, k and C, the presented analysis provides results in closer agreement with the experimental values than those of the bulk-flow model analysis at several rotor speeds.     

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.     

Numerical prediction of rotordynamic coefficients for an annular-type plain-gas seal using 3D CFD analysis

Annular-type gas seals in many types of compressors and turbines are designed to reduce leakage and enhance the vibrational stability of the turbo machinery. Many researchers have attempted precise theoretical evaluation of the leakage and the rotordynamic coefficients from reaction forces of small seal gaps. The Bulk-flow model, which is based on Hirs’ lubrication equation, is a general method with advantages of simplicity and short computing time. However, due to the disadvantage of the long time required to develop analysis code, and constraints from complicated seal shapes, CFD analysis is currently preferred. In the present, the method for determining the rotordynamic coefficients of an annular plain-gas seal, which is the simplest shape of gas seals, is suggested by extending the analysis of an annular plain-pump seal. A relative coordinate system for steady-state simulation is defined to calculate the compressible flow field and dynamic pressure distribution of the seal gap. The present analysis is verified by comparison with results acquired from Bulk-flow analysis code and published experimental results. The 3D CFD rotordynamic coefficients results of direct stiffness(K) and cross coupled stiffness(k) show better improvements in prediction.     

Identification of Journal Bearing Force Coefficients under High Dynamic Loading Centered Static Operation

Lightly damped rotor bearing systems experience large amplitudes of vibration when traversing critical speeds. Bearing linearized force coefficients, strictly valid for minute motions about an equilibrium position, may not be reliable for design or troubleshooting in rotordynamics predictive analyses. Experiments assessing the dynamic forced response of a plain journal bearing undergoing large orbital motions due to single-frequency excitation forces were conducted in a test rig. The short test bearing of slenderness ratio L/D = 0.25 has a nominal radial clearance of 0.127 mm (5 mils). Tests were conducted at three rotor speeds (900, 1800, and 2700 rpm), three feed pressures (1, 3, and 6 psig), and three excitation frequencies (15, 30, and 45 Hz). Baseline bearing motions due to shaft runout are recorded and subtracted in the parameter identification procedure. The forces exerted on the bearing induce large orbital motions with peak amplitudes exceeding 50% of the nominal bearing clearance. Identified cross-coupled stiffness and direct damping coefficients fall within value bands predicted by the π and 2π models of the fluid film, even for the largest amplitudes of motion. The bearing whirl frequency ratio approaches the typical 50% value at the highest speed tested. Excitation frequency has a marked influence of the test direct dynamic stiffness coefficients with added mass coefficients at least twice as large as predicted values.