Measurement of Rotordynamic Coefficients for a Hydrostatic Radial Bearing

1991 ◽  
Vol 113 (3) ◽  
pp. 518-525 ◽  
Author(s):  
B. T. Murphy ◽  
M. N. Wagner
Keyword(s):  
Reynolds Number ◽  
Hydrostatic Pressure ◽  
Rotational Speed ◽  
Sole Source ◽  
Working Fluid ◽  
Test Apparatus ◽  
Matrix Solution ◽  
Rotordynamic Coefficients ◽  
Direct Stiffness ◽  
Stiffness And Damping

Measurement of rotordynamic coefficients is presented for a pair of hydrostatic radial bearings, including direct and cross-coupled stiffness and damping. Two different hydrostatic configurations were tested: (1) an externally fed bearing 74.7 mm (2.95 in.) in diameter with a nominal direct stiffness of approximately 210 MN/m (1.2 million lb/in.) and (2) an internally fed bearing 54.6 mm (2.15 in.) in diameter with a nominal direct stiffness of approximately 88 MN/m (0.5 million lb/in.). Each bearing had 6 equally spaced hydrostatic pressure pockets, stationary for the externally fed bearing and rotating for the internally fed bearing. Also, both bearings had extended exit regions to provide additional damping. The top rotational speed was 22,700 rpm and the maximum axial Reynolds number was 50,000 using a freon derivative, Freon-113, as the working fluid. The test apparatus was a “synchronous rig” as an intentionally eccentric journal was used as the sole source of excitation. Data reduction was done by performing a matrix solution to separate damping from stiffness. Results show the internally fed bearing to be 20 percent less stiff than predicted, and to have a significant amount of damping which agrees well with predictions. The internally fed bearing was found to be approximately 60 percent less stiff than predicted, and to be roughly neutral in terms of damping, as predicted.

High-Pressure Pocket Damper Seals: Leakage Rates and Cavity Pressures

2006 ◽  
Vol 129 (4) ◽  
pp. 826-834 ◽  
Author(s):  
Ahmed M. Gamal ◽  
Bugra H. Ertas ◽  
John M. Vance
Keyword(s):  
High Pressures ◽  
Prediction Models ◽  
Working Fluid ◽  
Dual Purpose ◽  
Rotordynamic Coefficients ◽  
Numerical Predictions ◽  
Theoretical Predictions ◽  
Mass Flow Rates ◽  
Direct Stiffness ◽  
Stiffness And Damping

The turbomachinery component of interest in this paper, the pocket damper seal, has the dual purpose of limiting leakage and providing an additional source of damping at the seal location. The rotordynamic coefficients of these seals (primarily the direct stiffness and damping) are highly dependent on the leakage rates through the seals and the pressures in the seals’ cavities. This paper presents both numerical predictions and experimentally obtained results for the leakage and the cavity pressures of pocket damper seals operating at high pressures. The seals were tested with air, at pressures up to 1000psi(6.92MPa), as the working fluid. Earlier flow-prediction models were modified and used to obtain theoretical reference values for both mass flow rates and pressures. Leakage and static pressure measurements on straight-through and diverging-clearance configurations of eight-bladed and twelve-bladed seals were used for code validation and for calculation of seal discharge coefficients. Higher than expected leakage rates were measured in the case of the twelve-bladed seal, while the leakage rates for the eight-bladed seals were predicted with reasonable accuracy. Differences in the axial pitch lengths of the cavities and the blade profiles of the seals are used to explain the discrepancy in the case of the twelve-bladed seal. The analysis code used also predicted the static cavity pressures reasonably well. Tests conducted on a six-bladed pocket damper seal to further investigate the effect of blade profile supported the results of the eight-bladed and twelve-bladed seal tests and matched theoretical predictions with satisfactory accuracy.

High-Pressure Pocket Damper Seals: Leakage Rates and Cavity Pressures

2006 ◽  
Author(s):  
Ahmed M. Gamal ◽  
Bugra H. Ertas ◽  
John M. Vance
Keyword(s):  
High Pressures ◽  
Prediction Models ◽  
Working Fluid ◽  
Dual Purpose ◽  
Rotordynamic Coefficients ◽  
Numerical Predictions ◽  
Theoretical Predictions ◽  
Mass Flow Rates ◽  
Direct Stiffness ◽  
Stiffness And Damping

The turbomachinery component of interest in this paper, the pocket damper seal, has the dual purpose of limiting leakage and providing an additional source of damping at the seal location. The rotordynamic coefficients of these seals (primarily the direct stiffness and damping) are highly dependent on the leakage rates through the seals and the pressures in the seals’ cavities. This paper presents both numerical predictions and experimentally obtained results for the leakage and the cavity pressures of pocket damper seals operating at high pressures. The seals were tested with air, at pressures up to 1000 Psi (6.92 MPa), as the working fluid. Earlier flow-prediction models were modified and used to obtain theoretical reference values for both mass flow-rates and pressures. Leakage and static pressure measurements on straight-through and diverging-clearance configurations of eight-bladed and twelve-bladed seals were used for code validation and for calculation of seal discharge coefficients. Higher than expected leakage rates were measured in the case of the twelve-bladed seal, while the leakage rates for the eight-bladed seals were predicted with reasonable accuracy. Differences in the axial pitch lengths of the cavities and the blade profiles of the seals are used to explain the discrepancy in the case of the twelve-bladed seal. The analysis code used also predicted the static cavity pressures reasonably well. Tests conducted on a six-bladed pocket damper seal to further investigate the effect of blade profile supported the results of the eight-bladed and twelve-bladed seal tests and matched theoretical predictions with satisfactory accuracy.

Rotordynamic Coefficients for Compressible Flow in Tapered Annular Seals

1985 ◽  
Vol 107 (3) ◽  
pp. 318-325 ◽  
Author(s):  
C. C. Nelson
Keyword(s):  
Compressible Flow ◽  
Flow Model ◽  
Space Shuttle ◽  
Governing Equations ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Stiffness And Damping ◽  
Main Engine

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs’ turbulent bulk-flow model. Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients. Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure. The effects of preswirl and seal taper are shown for three different length-to-diameter ratios. Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness.

The Effect of Design Parameters on the Performance of Flagellar Propeller at Low Reynolds Number

2011 ◽  
Author(s):  
Hyejin Jeon ◽  
Yoon-Cheol Kim ◽  
Eun Goh ◽  
Dongwook Yim ◽  
Songwan Jin ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Rotational Speed ◽  
Low Reynolds Number ◽  
Stereoscopic Particle Image Velocimetry ◽  
Macroscopic Model ◽  
Maximum Efficiency ◽  
Design Parameters ◽  
Working Fluid ◽  
Inertia Force ◽  
Low Reynolds

To drive a small object which swims in low Reynolds number situation, we need a new type of propeller which is optimized for low Reynolds number usage since the flow at low Reynolds numbers is dominated by viscous force instead of inertia force. Propeller in a shape of bacterial flagellum can be a strong candidate for propeller of small swimming object. In this paper, we visualized velocity field induced by flagellar shaped propeller using stereoscopic particle image velocimetry. We also have experimentally evaluated the effect of pitch and rotational speeds on the performance of flagellar shaped propeller inspired by flagellum of E.coli using macroscopic model. Silicone oil whose viscosity is 100 times larger than water is used as working fluid to make low Reynolds number situation using macroscopic model. Thrust, torque and velocity were measured as a function of pitch and rotational speed, and efficiency was calculated using measured results. We found that the maximum efficiency of flagellar propeller reaches where the pitch angle is about 40°. However, the effect of rotational speed on the efficiency is relatively smaller than that of pitch. And the flow pattern behind the rotating propeller was altered by pitch of the propeller.

scholarly journals Comparison of Hirs’ Equation With Moody’s Equation for Determining Rotordynamic Coefficients of Annular Pressure Seals

1987 ◽  
Vol 109 (1) ◽  
pp. 144-148 ◽  
Author(s):  
C. C. Nelson ◽  
D. T. Nguyen
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Incompressible Flow ◽  
Flow Model ◽  
Bulk Flow ◽  
Rotordynamic Coefficients ◽  
Relative Roughness ◽  
Direct Stiffness ◽  
Pressure Seal

The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs’ equation, assumes the friction factor is a function of Reynolds number only. The second, Moody’s equation, approximates Moody’s diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs’ constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals (e/2H0 = 0.05) Moody’s equation predicts 44 percent greater direct stiffness, 35 percent greater cross-coupled stiffness, 19 percent smaller cross-coupled damping, 59 percent smaller cross-coupled inertia, and nominally the same direct damping and direct inertia.

Analysis of the Experimental and CFD-Based Theoretical Methods for Studying Rotordynamic Characteristics of Labyrinth Gas Seals

2010 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Martin Deckner
Keyword(s):  
Measurement Techniques ◽  
Experimental Results ◽  
Theoretical Methods ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Dynamic Methods ◽  
Inlet Swirl ◽  
Direct Stiffness ◽  
Gas Seals ◽  
Stiffness And Damping

This paper presents an analysis of the experimental and theoretical methods used to study rotordynamic characteristics of short staggered labyrinth gas seal. Two experimental identification procedures referred to as static and dynamic methods are presented. The static method allows determining direct and cross-coupled stiffness coefficients of the seal by integrating measured circumferential pressure distribution in cavities at various shaft eccentric positions. In the dynamic method, identification of stiffness and damping coefficients is based on the rotor excitation using a magnetic actuator and utilizes the effect of alternation of rotor vibrations due to aerodynamic forces acting in the seal. The experimental results obtained by the static and dynamic methods demonstrate an apparent discrepancy most of all in the direct stiffness coefficients. A CFD-based model of the seal is used to predict rotordynamic coefficients and to analyze the discrepancies between the static and dynamic measurements. The seal forces are calculated in two ways similar to the experimental procedures. The predictions are in good agreement with experimental results obtained by both measurement techniques. The effects of pressure differential, inlet swirl, shaft rotational speed, shaft eccentricity, and inflow cavity on seal stiffness and damping are presented. The discrepancies between different methods must be kept in mind while studying rotordynamic characteristics of seals.

scholarly journals An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2747
Author(s):  
José Gabriel Mendoza-Larios ◽  
Eduardo Barredo ◽  
Manuel Arias-Montiel ◽  
Luis Alberto Baltazar-Tadeo ◽  
Saulo Jesús Landa-Damas ◽  
...  
Keyword(s):  
Rotational Speed ◽  
Algebraic Approach ◽  
Rotational Inertia ◽  
Fe Model ◽  
Rotordynamic Coefficients ◽  
Rotor Bearing ◽  
Identification Technique ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Bearing System

In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of a rotor-bearing system with multiple degree-of-freedom (DOF). This model considers the effects of rotational inertia, gyroscopic moments, shear deformations, external damping and linear forces attributable to stiffness and damping parameters of the supports. The proposed identifier only requires the system’s vibration response as input data. The performance of the proposed identifier is evaluated and analyzed for both schemes, constant and variable rotational speed of the rotor-bearing system, and numerical results are obtained. In the presented results, it can be observed that the proposed identifier accurately determines the stiffness and damping parameters of the bearings in less than 0.06 s. Moreover, the identification procedure rapidly converges to the estimated values in both tested conditions, constant and variable rotational speed.

Altitude Effects on the Performance of Small Radial Turbomachinery: Part I — Compressor Impellers

2016 ◽  
Author(s):  
Dries Verstraete ◽  
Kjersti Lunnan
Keyword(s):  
Reynolds Number ◽  
Performance Analysis ◽  
Rotational Speed ◽  
Pressure Ratio ◽  
Unmanned Aircraft ◽  
Good Match ◽  
One Dimensional ◽  
Design Changes ◽  
Current Article ◽  
The Impact

Small unmanned aircraft are currently limited to flight ceilings below 20,000 ft due to the lack of an appropriate propulsion system. One of the most critical technological hurdles for an increased flight ceiling of small platforms is the impact of reduced Reynolds number conditions at altitude on the performance of small radial turbomachinery. The current article investigates the influence of Reynolds number on the efficiency and pressure ratio of two small centrifugal compressor impellers using a one-dimensional meanline performance analysis code. The results show that the efficiency and pressure ratio of the 60 mm baseline compressor at the design rotational speed drops with 6–9% from sea-level to 70,000 ft. The impact on the smaller 20 mm compressor is slightly more pronounced and amounts to 6–10%. Off-design changes at low rotational speeds are significantly higher and can amount to up to 15%. Whereas existing correlations show a good match for the efficiency drop at the design rotational speed, they fail to predict efficiency changes with rotational speed. A modified version is therefore proposed.

EXPERIMENTAL STUDY ON THERMAL TRANSPORT PHENOMENON OF NANOFLUIDS AS WORKING FLUID IN HEAT EXCHANGER

2014 ◽  
Vol 22 (01) ◽  
pp. 1450005 ◽  
Author(s):  
SHUICHI TORII
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Performance ◽  
Pure Water ◽  
Horizontal Tube ◽  
Constant Heat Flux ◽  
Working Fluid ◽  
Transfer Performance ◽  
Nanoparticles Concentration ◽  
Transfer Behavior

This paper aims to study the convective heat transfer behavior of aqueous suspensions of nanoparticles flowing through a horizontal tube heated under constant heat flux condition. Consideration is given to the effects of particle concentration and Reynolds number on heat transfer enhancement and the possibility of nanofluids as the working fluid in various heat exchangers. It is found that (i) significant enhancement of heat transfer performance due to suspension of nanoparticles in the circular tube flow is observed in comparison with pure water as the working fluid, (ii) enhancement is intensified with an increase in the Reynolds number and the nanoparticles concentration, and (iii) substantial amplification of heat transfer performance is not attributed purely to the enhancement of thermal conductivity due to suspension of nanoparticles.

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