Rotordynamic Stability Effects of Shrouded Centrifugal Impellers With Combined Whirl and Precession

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Eunseok Kim ◽  
Alan Palazzolo
Keyword(s):  
Tilt Angle ◽  
Centrifugal Impeller ◽  
Sixth International Symposium ◽  
Coupled Motion ◽  
Rotordynamic Coefficients ◽  
Dynamic Eccentricity ◽  
The Stability ◽  
The Moment ◽  
Rotordynamic Forces ◽  
Rotordynamic Coefficient

Whirling (translational) and precession (tilt) motion of the shrouded centrifugal impeller are possible vibration sources that can cause rotordynamic instability problems. Whirling motion of shrouded impellers and seals has been investigated by test and theory in the literature. However, there has been little study of the effects of coupled motion of whirling and precession of a centrifugal impeller on rotordynamic forces and moments using computational fluid dynamics (CFD). In the present study, the CFD approach for calculating the moment coefficients of the precessing impeller is developed and verified by comparison with the measured data for a precessing centrifugal compressor by Yoshida et al. (1996, “Measurement of the Flow in the Backshroud/Casing Clearance of a Precessing Centrifugal Impeller,” Sixth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Hawaii, Vol. 2, pp. 151–160). A full set (4 × 4) of rotordynamic coefficient matrices is calculated, using two separate models of (a) a precessing impeller with a tilt angle and (b) a whirling impeller with dynamic eccentricity to investigate the stability of the impeller. Rotordynamic stability is evaluated by using the whirl frequency ratio of the coupled motion, obtained from the full rotordynamic coefficient matrices, to show that the precession motion has a significant impact on rotordynamic stability. A similar conclusion is reached based on the whirling plus precession response of a finite element (FE) structural rotordynamic model including the 4 × 4 rotordynamic coefficient matrices. A stability analysis using the rotordynamic coefficients indicates that the precession motion with the positive tilt angle increases the tendency toward destabilization of the rotor.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

A Theoretical Analysis of Floating Bush Journal Bearing With Axial Oil Film Rupture Being Considered

2002 ◽  
Vol 124 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Kiyoshi Hatakenaka ◽  
Masato Tanaka ◽  
Kenji Suzuki
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Speed Ratio ◽  
Shaft Speed ◽  
Film Rupture ◽  
State Behavior ◽  
Oil Film ◽  
Rotordynamic Coefficients ◽  
The Stability ◽  
Very High

A new modified Reynolds equation is derived with centrifugal force acting on the hydrodynamic oil film being considered. This equation, together with a cavitation model, is used to obtain the steady-state equilibrium and calculate the rotordynamic coefficients of lightly loaded floating bush journal bearings operating at very high shaft speeds. The bush-to-shaft speed ratio and the linear cross-coupling spring coefficients of the inner oil film is found to decrease with the increase in shaft speed as the axial oil film rupture develops in the inner oil film. The present model can give reasonable explanation to the steady-state behavior and the stability behavior of the bearing observed in actual machines.

Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

2017 ◽  
Vol 21 (3) ◽  
pp. 782-807 ◽  
Author(s):  
Yanli Wang ◽  
Shudao Zhang
Keyword(s):  
Splitting Method ◽  
Linear Convergence ◽  
Mass Conservation ◽  
System A ◽  
Spectral Convergence ◽  
The Stability ◽  
The Moment ◽  
Stability And Accuracy ◽  
Fokker Planck Equations ◽  
Fokker Planck

AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

The Meniscus Instability of a Thin Liquid Film

1988 ◽  
Vol 55 (4) ◽  
pp. 975-980 ◽  
Author(s):  
H. Koguchi ◽  
M. Okada ◽  
K. Tamura
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Liquid Film ◽  
Tilt Angle ◽  
Stability Criterion ◽  
Thin Liquid Film ◽  
Normal Direction ◽  
Wave Number ◽  
The Stability ◽  
Maximum Amplification

This paper reports on the instability for the meniscus of a thin film of a very viscous liquid between two tilted plates, which are separated at a constant speed with a tilt angle in the normal direction of the plates. The disturbances on the meniscus moving with movement of the plates are examined experimentally and theoretically. The disturbances are started when the velocity of movement of the plates exceeds a critical one. The wavelength of the disturbances is measured by using a VTR. The instability of the meniscus is studied theoretically using the linearized perturbation method. A simple and complete analytical solution yields both a stability criterion and the wave number for a linear thickness geometry. These results compared with experiments for the instability show the validity of the stability criterion and the best agreement is obtained with the wave number of maximum amplification.

scholarly journals Modeling of the emulsion stability using fractal dimensions

2008 ◽  
Vol 14 (3) ◽  
pp. 153-158 ◽  
Author(s):  
Snezana Pasalic ◽  
Predrag Jovanic
Keyword(s):  
Emulsion Stability ◽  
Fractal Dimensions ◽  
Ccd Camera ◽  
Stability Evaluation ◽  
Stable States ◽  
Water Emulsion ◽  
Box Counting Method ◽  
The Stability ◽  
The Moment ◽  
Life Circle

There are many developed strategies in the emulsion stability evaluation, for purpose of determining the life circle of emulsions. Most of them are based on the reological properties of the emulsions. There are very few which relay on the direct emulsion observations. In this paper we present the developed method for the emulsion stability evaluation by the direct observation of optical properties. As the stability quantification measure we propose the fractal dimension approach. The method is based on the measure of the emulsion transmittance properties, which are directly dependent on the emulsion stability at the moment of measurement. As the test emulsion the oil in the water emulsion was used. The system is classified as the stable emulsion and our intention was to find the moment when the emulsion starts to break. The emulsion transmittance properties were measured using an acquisition system, consisting of a CCD camera and a fast PC configuration equipped with the capturing software. The fractal dimensions were determined by the so called box counting method. The experimental emulsions were measured continuously within the period of 1200 h, from the moment of the emulsion creation. The changes of fractal dimensions were observed which indicates that the emulsion changed its state and therefore the stability during the time. Three regions of the emulsion life circle were divided according to the fractal dimensions measurement, which can be connected with the stable, unstable, and meta-stable states of the emulsion life circle. In the end, the model of the emulsion behavior was developed for the purpose of quantifying the changes in the experimental emulsion.

scholarly journals Annular Honeycomb Seals: Test Results for Leakage and Rotordynamic Coefficients; Comparisons to Labyrinth and Smooth Configurations

1989 ◽  
Vol 111 (2) ◽  
pp. 293-300 ◽  
Author(s):  
D. Childs ◽  
D. Elrod ◽  
K. Hale
Keyword(s):  
Labyrinth Seal ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Shaft Rotation ◽  
Honeycomb Seal ◽  
Cell Dimensions ◽  
Honeycomb Seals ◽  
Rotordynamic Coefficient

Test results are presented for leakage and rotordynamic coefficients for seven honeycomb seals. All seals have the same radius, length, and clearance; however, the cell depths and diameters are varied. Rotordynamic data, which are presented, consist of the direct and cross-coupled stiffness coefficients and the direct damping coefficients. The rotordynamic-coefficient data show a considerable sensitivity to changes in cell dimensions; however, no clear trends are identifiable. Comparisons of test data for the honeycomb seals with labyrinth and smooth annular seals shows the honeycomb seal had the best sealing (minimum leakage) performance, followed in order by the labyrinth and smooth seals. For prerotated fluids entering the seal, in the direction of shaft rotation, the honeycomb seal has the best rotordynamic stability followed in order by the labyrinth and smooth. For no prerotation, or fluid prerotation against shaft rotation, the labyrinth seal has the best rotordynamic stability followed in order by the smooth and honeycomb seals.

Diurnal variability of frontal dynamics, instability, and turbulence in a submesoscale upwelling filament

2021 ◽  
Author(s):  
Jen-Ping Peng ◽  
Lars Umlauf ◽  
Julia Dräger-Dietel ◽  
Ryan P. North
Keyword(s):  
Solar Radiation ◽  
Early Morning ◽  
Shear Instability ◽  
Surface Boundary ◽  
Surface Boundary Layer ◽  
Diurnal Variability ◽  
Frontal Dynamics ◽  
The Stability ◽  
The Moment ◽  
The Impact

AbstractRecent high-resolution numerical simulations have shown that the diurnal variability in the atmospheric forcing strongly affects the dynamics, stability, and turbulence of submesoscale structures in the surface boundary layer (SBL). Field observations supporting the real-ocean relevance of these studies are, however, largely lacking at the moment. Here, the impact of large diurnal variations in the surface heat flux on a dense submesoscale upwelling filament in the Benguela upwelling system is investigated, based on a combination of densely-spaced turbulence microstructure observations and surface drifter data. Our data show that during nighttime and early-morning conditions, when solar radiation is still weak, frontal turbulence is generated by a mix of symmetric and shear instability. In this situation, turbulent diapycnal mixing is approximately balanced by frontal restratification associated with the cross-front secondary circulation. During daytime, when solar radiation is close to its peak value, the SBL quickly restratifies, the conditions for frontal instability are no longer fulfilled, and SBL turbulence collapses except for a thin wind-driven layer near the surface. The drifter data suggest that inertial oscillations periodically modulate the stability characteristics and energetics of the submesoscale fronts bounding the filament.

scholarly journals Ice and ocean tilt measurements in the beaufort sea

1976 ◽  
Vol 17 (75) ◽  
pp. 61-71 ◽  
Author(s):  
J.R. Weber ◽  
M. Erdelyi
Keyword(s):  
Sea Ice ◽  
Tilt Angle ◽  
Ice Sheet ◽  
Ocean Surface ◽  
Beaufort Sea ◽  
Velocity Change ◽  
Drag Coefficients ◽  
The Moment ◽  
Hydrostatic Level ◽  
Drift Direction

Abstract During the AIDJEX pilot study 1972 in the Beaufort Sea, the tilt changes of the fluid ocean surface and of the sea ice were measured with a hydrostatic level. Preliminary results indicate a tilt range of ± 5 μrad for the water surface and of ± 30 (μrad for the sea ice. The tilt change of the sea ice Δ δ appears to be directly proportional to the component of the velocity change of the ice drift parallel to the hydrostatic level ΔUd , according to the relationship Δ δ = 180ΔUd μrad m-1 s. It is conclugerd that the ice tilt is wind induced, and that the ice sheet tilts downward in the drift direction as a result of the moment exerted on it by wind and water drag. It is postulated that this tilt causes the ice to break at right angles to the drift direction. The tilt is a function of the length of an ice floe (or of the unbroken distance between two cracks), of the average ice thickness, of the average drag coefficients, and of wind and current velocities. Calculation of the ice tilt using a simple mogerl of a floating, rigid ice slab gives values which are very much smaller than the observed tilts. If the discrepancy between theory and observation can be resolved, or if an empirical formula between wind velocity and tilt angle can be gerduced freom continuous tilt observations which will be carried out during the AIDJEX main experiment, it will be possible, for a given wind, to estimate the maximum length of an unbroken ice sheet freom its estimated thickness, drag coefficients, and tensile strength. It should also be possible to calculate the average drag coefficients of a freee-floating ice pan, or of an ice island, freom tilt, wind, and current measurements. The curious relationship between tilt angle and atmospheric pressure gradient that Browne and Crary observed on the ice island T-3 in 1952 is explained as being the wind-induced tilt of the ice island rather than that of the fluid ocean surface.

ON THE WORKLOAD PROCESS IN A FLUID QUEUE WITH A RESPONSIVE BURSTY INPUT AND SELECTIVE DISCARDING

2003 ◽  
Vol 17 (4) ◽  
pp. 527-543
Author(s):  
Parijat Dube ◽  
Eitan Altman
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Feedback System ◽  
Moment Generating Function ◽  
General Distribution ◽  
Finite Buffer ◽  
Fluid Queue ◽  
The Stability ◽  
The Moment ◽  
Stationary Workload

We analyze a feedback system consisting of a finite buffer fluid queue and a responsive source. The source alternates between silence periods and active periods. At random epochs of times, the source becomes ready to send a burst of fluid. The length of the bursts (length of the active periods) are independent and identically distributed with some general distribution. The queue employs a threshold discarding policy in the sense that only those bursts at whose commencement epoch (the instant at which the source is ready to send) the workload (i.e., the amount of fluid in the buffer) is less than some preset threshold are accepted. If the burst is rejected then the source backs off from sending. We work within the framework of Poisson counter-driven stochastic differential equations and obtain the moment generating function and hence the probability density function of the stationary workload process. We then comment on the stability of this fluid queue. Our explicit characterizations will further provide useful insights and “engineering” guidelines for better network designing.

Effect of Intermediate Support on Instabilities of a Cantilever With Terminal Dynamic Moment

2019 ◽  
Author(s):  
Mahmoud Abdullatif ◽  
Ranjan Mukherjee
Keyword(s):  
Negative Slope ◽  
Positive Slope ◽  
Critical Stability ◽  
Flutter Instability ◽  
Intermediate Support ◽  
Instability Modes ◽  
Stability Point ◽  
The Stability ◽  
The Moment ◽  
Dynamic Moment

Abstract The stability characteristics of a cantilever beam, with and without an intermediate support, subjected to a dynamic terminal moment, is investigated. The moment is assumed to be proportional to the slope of a point along the length of the beam. The proportionally constant, which can be positive or negative, is varied to find the critical stability point. In the absence of intermediate support, stability is lost through divergence when the dynamic moment is proportional to the positive slope, and through flutter when the dynamic moment is proportional to the negative slope. In contrast, the nature of instability switches between divergence and flutter, and between different flutter instability modes while undergoing flutter, in the presence of an intermediate support.

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