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 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 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.

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.

scholarly journals Residual conductance of correlated one-dimensional nanosystems: A numerical approach

2004 ◽  
Vol 39 (1) ◽  
pp. 107-120 ◽  
Author(s):  
R. A. Molina ◽  
P. Schmitteckert ◽  
D. Weinmann ◽  
R. A. Jalabert ◽  
G.-L. Ingold ◽  
...  
Keyword(s):  
Numerical Approach ◽  
One Dimensional ◽  
Residual Conductance

Numerical Comparison of Leakage Flow and Rotordynamic Characteristics for Two Types of Labyrinth Seals With Baffles

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Yuanqiao Zhang ◽  
Jun Li ◽  
Zhigang Li ◽  
Xin Yan
Keyword(s):  
Rotational Speed ◽  
Flow Resistance ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Numerical Comparison ◽  
Vibration Frequencies ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Brush Seal ◽  
Swirl Intensity

Abstract Cavity separation baffles can decrease the circumferential swirl intensity of labyrinth seals and increase the seals' rotordynamic characteristics. Compared with conventional baffles, the bristle packs of brush seal baffles can contact the rotor directly, thereby further reducing the swirl intensity of the seal cavity. This paper, using the numerical model combining a multifrequency elliptical whirling orbit model, a porous medium model, and transient Reynolds-averaged Navier–Stokes (RANS) solutions, compares the leakage flow and rotordynamic characteristics of a labyrinth seal with brush-seal baffles (LSBSB) and a labyrinth seal with conventional baffles (LSCB). Ideal air flows into the seal at an inlet preswirl velocity of 0 m/s (or 60 m/s or 100 m/s), total pressure of 690 kPa, and temperature of 14 °C. The outlet static pressure is 100 kPa and the rotational speed is 7500 r/min (surface speed of 66.8 m/s) or 15,000 r/min (surface speed of 133.5 m/s). Numerical results show that the LSBSB possesses the slightly less leakage flow rate than the LSCB due to the flow resistance of the bristle pack to the fluid. Compared with the LSCB, the LSBSB shows a higher positive effective stiffness (Keff) at all considered vibration frequencies and a higher effective damping (Ceff) for most vibration frequencies. What is more, the crossover frequency (fc0) of the LSBSB is significantly lower than that of the LSCB, which means that the LSBSB has a wider frequency range offering positive effective damping. The increasing inlet preswirl velocity and rotational speed only slightly affect the Keff for both seals. The Ceff of two seals decreases as the inlet preswirl velocity rises, especially for the LSCB. The Ceff of the LSCB slightly decreases because of the increasing rotational speed. In contrast, the Ceff of the LSBSB is not sensitive to the changes in rotational speed. In a word, the LSBSB possesses superior rotordynamic performance to the LSCB. Note that this work also investigates the leakage flow and rotordynamic characteristics a labyrinth seal with inclined baffles (LSIB) under the condition of u0 = 60 m/s and n = 15,000 r/min. The inclined baffles of the LSIB are same as the backing plates of LSBSB baffles. The LSIB has rotordynamic coefficients almost equal to the LSCB. Hence, the reason why the LSBSB possesses better rotordynamic performance than that of the LSCB is the flow resistance of bristle packs of brush seal baffles, not the inclination direction variation of baffles.

scholarly journals A Multispectral Bayesian Classification Method for Increased Acoustic Discrimination of Seabed Sediments Using Multi-Frequency Multibeam Backscatter Data

Geosciences ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 455 ◽  
Author(s):  
Timo Gaida ◽  
Tengku Tengku Ali ◽  
Mirjam Snellen ◽  
Alireza Amiri-Simkooei ◽  
Thaiënne van Dijk ◽  
...  
Keyword(s):  
Ground Truth ◽  
Single Frequency ◽  
Qualitative Comparison ◽  
Ground Truth Data ◽  
Geological Interpretation ◽  
Additional Information ◽  
Triple Frequency ◽  
Acoustic Discrimination ◽  
Multiple Frequencies ◽  
Seabed Sediments

Multi-frequency backscatter data collected from multibeam echosounders (MBESs) is increasingly becoming available. The ability to collect data at multiple frequencies at the same time is expected to allow for better discrimination between seabed sediments. We propose an extension of the Bayesian method for seabed classification to multi-frequency backscatter. By combining the information retrieved at single frequencies we produce a multispectral acoustic classification map, which allows us to distinguish more seabed environments. In this study we use three triple-frequency (100, 200, and 400 kHz) backscatter datasets acquired with an R2Sonic 2026 in the Bedford Basin, Canada in 2016 and 2017 and in the Patricia Bay, Canada in 2016. The results are threefold: (1) combining 100 and 400 kHz, in general, reveals the most additional information about the seabed; (2) the use of multiple frequencies allows for a better acoustic discrimination of seabed sediments than single-frequency data; and (3) the optimal frequency selection for acoustic sediment classification depends on the local seabed. However, a quantification of the benefit using multiple frequencies cannot clearly be determined based on the existing ground-truth data. Still, a qualitative comparison and a geological interpretation indicate an improved discrimination between different seabed environments using multi-frequency backscatter.

scholarly journals A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 453 ◽  
Author(s):  
Mukhtar ◽  
Sohaib ◽  
Ahmad
Keyword(s):  
Numerical Approximation ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Moment Generating Function ◽  
Numerical Approach ◽  
Test Problems ◽  
Batch Crystallization ◽  
One Dimensional ◽  
Engineering Sciences ◽  
The Moment

In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

Electron Transmission Through Modified Schottky Barriers

2001 ◽  
Vol 685 ◽  
Author(s):  
Kevin L. Jensen
Keyword(s):  
Schottky Barrier ◽  
Conduction Band ◽  
Current Density ◽  
Transport Mechanism ◽  
Airy Function ◽  
Numerical Approach ◽  
Schottky Barriers ◽  
Present Treatment ◽  
One Dimensional ◽  
Electron Transmission

AbstractThe effects of a Coulomb-like potential in the Schottky barrier existing between a material-diamond interface is analyzed. The inclusion is intended to mimic the effects of an ionized trap within the barrier, and therefore to account for charge injection into the conduction band of diamond via a Poole-Frenkel transport mechanism. The present treatment is to provide a qualitative account of the increase in current density near the inclusion, which can be substantial. The model is first reduced to an analytically tractable one-dimensional tunneling problem addressable by an Airy Function approach in order to investigate the nature of the effect. A more comprehensive numerical approach is then applied. Finally, statistical arguments are used to estimate emission site densities using the results of the aforementioned analysis.

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