Multiple Frequencies Elliptical Whirling Orbit Model and Transient RANS Solution Approach to Rotordynamic Coefficients of Annual Gas Seals Prediction

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Xin Yan
Keyword(s):  
Numerical Method ◽  
Dynamic Monitoring ◽  
Leakage Flow ◽  
Deformation Method ◽  
Frequency Dependent ◽  
Solution Approach ◽  
Rotordynamic Coefficients ◽  
Multiple Frequencies ◽  
Gas Seals ◽  
Orbit Model

A numerical method using the multiple frequencies elliptical whirling orbit model and transient Reynolds-averaged Navier–Stokes (RANS) solution was proposed for prediction of the frequency dependent rotordynamic coefficients of annular gas seals. The excitation signal was the multiple frequencies waveform that acts as the whirling motion of the rotor center. The transient RANS solution combined with mesh deformation method was utilized to solve the leakage flow field in the annular gas seal and obtain the transient response forces on the rotor surface. Frequency dependent rotordynamic coefficients were determined by transforming the dynamic monitoring data of response forces and rotor motions to the frequency domain using the fast fourier transform. The frequency dependent rotordynamic coefficients of three types of annular gas seals, including a labyrinth seal, a fully partitioned pocket damper seal and a hole-pattern seal, were computed using the presented numerical method at thirteen or fourteen frequencies of 20–300 Hz. The obtained rotordynamic coefficients of three types of annular gas seals were all well agreement with the experimental data. The accuracy and availability of the proposed numerical method was demonstrated. The static pressure distributions and leakage flow rate of three types of annular gas seals were also illustrated.

Investigations on the Rotordynamic Coefficients of Pocket Damper Seals Using the Multifrequency, One-Dimensional, Whirling Orbit Model and RANS Solutions

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jun Li ◽  
Zhigang Li ◽  
Zhenping Feng
Keyword(s):  
Numerical Approach ◽  
Single Frequency ◽  
Response Force ◽  
Vibration Frequencies ◽  
Deformation Method ◽  
One Dimensional ◽  
Rotordynamic Coefficients ◽  
Motion Signal ◽  
Multiple Frequencies ◽  
Orbit Model

The numerical approach using the multifrequency one-dimensional whirling orbit model and Reynolds-averaged Navier-Stokes (RANS) solution was proposed for prediction of rotordynamic coefficients of pocket damper seal (PDS). By conducting the multiple frequencies one-dimensional whirling orbit for rotor center as the excitation signal, the unsteady RANS solutions combined with mesh deformation method were utilized to calculate the transient response forces on the PDS rotor surface. Unlike the single frequency whirling orbit models which require a separate computation for each frequency, the multifrequency whirling orbit model yields results for multiple frequencies and therefore requires only one computation for different frequencies. The rotor motion signal and response force signal were transformed to the frequency domain using the fast fourier transform, then the eight rotordynamic coefficients of the PDS were determined at fourteen different vibration frequencies 20–300 Hz. The numerical results of rotordynamic coefficients of the PDS were in good agreement with experimental data. The accuracy and availability of the proposed method was demonstrated. The effects of vibration frequencies and pressure ratios on the rotordynamic coefficients of PDS were also investigated using the presented numerical method. The multifrequency one-dimensional whirling orbit model is a promising method for prediction of the rotordynamic coefficients of the PDS.

Investigations on the Rotordynamic Coefficients of Pocket Damper Seals Using the Multi-Frequency, One-Dimensional, Whirling Orbit Model and RANS Solutions

2012 ◽  
Author(s):  
Jun Li ◽  
Zhigang Li ◽  
Zhenping Feng
Keyword(s):  
Numerical Approach ◽  
Single Frequency ◽  
Response Force ◽  
Vibration Frequencies ◽  
Deformation Method ◽  
One Dimensional ◽  
Rotordynamic Coefficients ◽  
Motion Signal ◽  
Multiple Frequencies ◽  
Orbit Model

The numerical approach using the multi-frequency one-dimensional whirling orbit model and Reynolds-Averaged Navier-Stokes (RANS) solution was proposed for prediction of rotordynamic coefficients of pocket damper seal (PDS). By conducting the multiple frequencies one-dimensional whirling orbit for rotor center as the excitation signal, the unsteady RANS solutions combined with mesh deformation method were utilized to calculate the transient response forces on the PDS rotor surface. Unlike the single frequency whirling orbit models which require a separate computation for each frequency, the multi-frequency whirling orbit model yields results for multiple frequencies and therefore requires only one computation for different frequencies. The rotor motion signal and response force signal were transformed to the frequency domain using the Fast Fourier Transform (FFT), then the eight rotordynamic coefficients of the PDS were determined at fourteen different vibration frequencies 20–300Hz. The numerical results of rotordynamic coefficients of the PDS were in good agreement with experimental data. The accuracy and availability of the proposed method was demonstrated. The effects of vibration frequencies and pressure ratios on the rotordynamic coefficients of PDS were also investigated using the presented numerical method. The multi-frequency one-dimensional whirling orbit model is a promising method for prediction of the rotordynamic coefficients of the PDS.

Investigations on the Rotordynamic Characteristics of a Hole-Pattern Seal Using Transient CFD and Periodic Circular Orbit Model

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xin Yan ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Circular Orbit ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Numerical Approach ◽  
Deformation Method ◽  
Rotordynamic Coefficients ◽  
Forward Orbit ◽  
Reaction Forces ◽  
Orbit Model

Numerical investigations on the rotordynamic characteristics of a typical hole-pattern seal using transient three-dimensional Reynolds-averaged Navier–Stokes (RANS) solution and the periodic circular orbit model were conducted in this work. The unsteady solutions combined with mesh deformation method were utilized to solve the three-dimensional RANS equations and obtain the transient reaction forces on a typical hole-pattern seal rotor at five different excitation frequencies. The relation between the periodic reaction forces and frequency dependent rotordynamic coefficients of the hole-pattern seal was obtained by considering the rotor with a periodic circular orbit (including forward orbit and backward orbit) of the seal center. The rotordynamic coefficients of the hole-pattern seal were then solved based on the obtained unsteady reaction forces and presented numerical method. Compared with the experimental data, the predicted rotordynamic coefficients of the hole-pattern seal are more agreeable with the experiment than that of the ISO-temperature (ISOT) bulk flow analysis and numerical approach with one-direction-shaking model. Furthermore, the unsteady leakage flow characteristics in the hole-pattern seal were also illustrated and discussed in detail.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals—Part I: Effects of Pressure Ratio, Rotational Speed, and Inlet Preswirl

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Rotational Speed ◽  
Pressure Ratio ◽  
Cross Coupling ◽  
Inlet Pressure ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Outlet Pressure ◽  
Swirl Velocity ◽  
Coupling Stiffness ◽  
Orbit Model

Effects of pressure ratio, rotational speed and inlet preswirl on the leakage and rotordynamic characteristics of a eight-bladed fully partitioned pocket damper seal (FPDS) were numerically investigated using proposed three-dimensional (3D) transient computational fluid dynamics (CFD) methods based on the multifrequency elliptical whirling orbit model. The accuracy and availability of the multifrequency elliptical whirling orbit model and the transient CFD numerical methods were demonstrated with the experimental data of frequency-dependent rotordynamic coefficients of the FPDS at two rotational speeds with high preswirl conditions. The frequency-dependent rotordynamic coefficients of the FPDS at three pressure ratios (three inlet pressures and three outlet pressures), three rotational speeds, three inlet preswirls were computed. The numerical results show that changes in outlet pressure have only weak effects on most rotordynamic coefficients. The direct damping and effective damping slightly increase in magnitude with decreasing outlet pressure at the frequency range of 20–200 Hz. The effect of inlet pressure is most prominent, and increasing inlet pressure for the FPDS results in a significant increase in the magnitudes of all rotordynamic coefficients. The magnitudes of the seal response force and effective damping are proportional to pressure drop through the seal. Increasing rotational speed and increasing inlet preswirl velocity both result in a significant decrease in the effective damping term due to the obvious increase in the magnitude of the destabilizing cross-coupling stiffness with increasing rotational speed or increasing preswirl velocity. The crossover frequency of effective damping significantly increases and the peak magnitude of effective damping decreases with increasing rotational speed or increasing preswirl velocity. The destabilizing cross-coupling stiffness is mainly caused by the circumferential swirl velocity generating from high rotational speed and inlet preswirl. Reducing swirl velocity (such as swirl brake) can greatly enhance the stabilizing capacity of the FPDS.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals: Part I — Effects of Pressure Ratio, Rotational Speed and Inlet Preswirl

2014 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Rotational Speed ◽  
Pressure Ratio ◽  
Cross Coupling ◽  
Inlet Pressure ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Outlet Pressure ◽  
Swirl Velocity ◽  
Coupling Stiffness ◽  
Orbit Model

Effects of pressure ratio, rotational speed and inlet preswirl on the leakage and rotordynamic characteristics of a eight-bladed fully-partitioned pocket damper seal (FPDS) were numerically investigated using proposed 3D transient CFD methods based on the multi-frequency elliptical whirling orbit model. The accuracy and availability of the multi-frequency elliptical whirling orbit model and the transient CFD numerical methods were demonstrated with the experimental data of frequency-dependent rotordynamic coefficients of the FPDS at two rotational speeds with high preswirl conditions. The frequency-dependent rotordynamic coefficients of the FPDS at three pressure ratios (three inlet pressures and three outlet pressures), three rotational speeds, three inlet preswirls were computed. The numerical results show that changes in outlet pressure have only weak effects on most rotordynamic coefficients. The direct damping and effective damping slightly increase in magnitude with decreasing outlet pressure at the frequency range of 20–200Hz. The effect of inlet pressure is most prominent, and increasing inlet pressure for the FPDS results in a significant increase in the magnitudes of all rotordynamic coefficients. The magnitudes of the seal response force and effective damping are proportional to pressure drop through the seal. Increasing rotational speed and increasing inlet preswirl velocity both result in a significant decrease in the effective damping term due to the obvious increase in the magnitude of the destabilizing cross-coupling stiffness with increasing rotational speed or increasing preswirl velocity. The crossover frequency of effective damping significantly increases and the peak magnitude of effective damping decreases with increasing rotational speed or increasing preswirl velocity. The destabilizing cross-coupling stiffness is mainly caused by the circumferential swirl velocity generating from high rotational speed and inlet preswirl. Reducing swirl velocity (such as swirl brake) can greatly enhance the stabilizing capacity of the FPDS.

A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

2012 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire
Keyword(s):  
System Identification ◽  
Measurement Uncertainty ◽  
Excitation Frequency ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Adjoint Systems ◽  
Dynamic Coefficients ◽  
Backward Whirl ◽  
Identification Technique ◽  
Damped Systems

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

scholarly journals PEMAHAMAN METODE NUMERIK MENGGUNAKAN PEMPROGRMAN MATLAB (Studi Kasus : Metode Secant)

2017 ◽  
Vol 1 (1) ◽  
pp. 89
Author(s):  
Melda Panjaitan
Keyword(s):  
Approximate Solution ◽  
Problem Solving ◽  
Numerical Methods ◽  
Numerical Method ◽  
Mathematical Problem ◽  
Secant Method ◽  
Mathematical Problem Solving ◽  
Real Solution ◽  
True Solution ◽  
Solution Approach

Abstract - The numerical method is a powerful mathematical problem solving tool. With numerical methods, we get a solution that approaches or approaches a true solution so that a numerical solution is also called an approximate solution or solution approach, but almost the solution can be made as accurately as we want. The solution almost certainly isn't exactly the same as the real solution, so there is a difference between the two. This difference is called an error. the solution using numerical methods is always in the form of numbers. The secant method requires two initial estimates that must enclose the roots of the equation. Keywords - Numerical Method, Secant Method

An Extended Three-Control-Volume Theory for Circumferentially-Grooved Liquid Seals

1996 ◽  
Vol 118 (2) ◽  
pp. 276-285 ◽  
Author(s):  
O. R. Marquette ◽  
D. W. Childs
Keyword(s):  
Control Volume ◽  
Current Theory ◽  
Flow Section ◽  
Leakage Flow ◽  
Centrifugal Pumps ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Through Flow ◽  
Control Volumes ◽  
Theoretical Results

Circumferentially-grooved seals are used in centrifugal pumps to reduce leakage flow. They can also have a significant impact on pump rotordynamic characteristics. Florjancic (1990) developed an analysis for leakage and rotordynamic coefficients, using a partition of the seal into three control volumes. This paper presents a new theory, based on an extension of Florjancic’s work (1990) for circumferentially-grooved liquid seals. The current theory differs from Florjancic’s analysis in the retention of transfer momentum terms and the introduction of diverging flow in the through-flow section within a seal groove. Validation of the new analysis is achieved through a comparison with existing experimental data taken from Kilgore (1988), and Florjancic (1990). Theoretical results are reasonable and consistent; i.e., a modification in the seal parameters induces a correct evolution of the rotordynamic coefficients. Direct and cross-coupled stiffness coefficients are slightly underpredicted, whereas the direct damping coefficient is underpredicted within 40 percent. Leakage flow predictions are very good.

scholarly journals Dynamic analysis of liquid annular seals with herringbone grooves on the rotor based on the perturbation method

2018 ◽  
Vol 5 (6) ◽  
pp. 180101 ◽  
Author(s):  
Lulu Zhai ◽  
Zhang Zhenjie ◽  
Chi Zhonghuang ◽  
Guo Jia
Keyword(s):  
Dynamic Characteristics ◽  
Operating Conditions ◽  
Geometric Parameters ◽  
Leakage Flow ◽  
Flow Rates ◽  
Rotordynamic Coefficients ◽  
Sealing Performance ◽  
Spiral Angle ◽  
Herringbone Grooves ◽  
Annular Seals

Annular seals have significant effects on the hydraulic and rotordynamic performances of turbomachinery. In this paper, an analysis method for calculating the leakage flow rates and dynamic characteristics of liquid annular seals with herringbone grooves on the rotor is proposed and verified. Leakage flow rates and dynamic characteristics of the model seals under different operating conditions are theoretically analysed and compared with those of plain and spiral-grooved seals of the same size. In addition, the influence of geometric parameters such as spiral angle and the lengths of the constituent parts on the sealing and rotordynamic coefficients of seals with herringbone grooves are also discussed. The results show that seals with herringbone grooves have better sealing performance, while providing better support actions and damping characteristics than the other two seal types under the same operating conditions. The seal geometric parameters including spiral angle, the lengths of the constituent parts and the clearance value have a significant influence on the dynamic characteristics of seals with herringbone grooves.

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