Topology of vortex breakdown bubbles in a cylinder with a rotating bottom and a free surface

2001 ◽  
Vol 428 ◽  
pp. 133-148 ◽  
Author(s):  
MORTEN BRØNS ◽  
LARS K. VOIGT ◽  
JENS N. SØRENSEN
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Hopf Bifurcation ◽  
Numerical Methods ◽  
Aspect Ratio ◽  
Vortex Breakdown ◽  
Stability Limit ◽  
Similarities And Differences ◽  
The Stability ◽  
Two Parameters

The flow patterns in the steady, viscous flow in a cylinder with a rotating bottom and a free surface are investigated by a combination of topological and numerical methods. Assuming the flow is axisymmetric, we derive a list of possible bifurcations of streamline structures on varying two parameters, the Reynolds number and the aspect ratio of the cylinder. Using this theory we systematically perform numerical simulations to obtain the bifurcation diagram. The stability limit for steady flow is found and established as a Hopf bifurcation. We compare with the experiments by Spohn, Mory & Hopfinger (1993) and find both similarities and differences.

A Parametric Absorber for Friction-Induced Vibrations

2003 ◽  
Author(s):  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Harmonic Function ◽  
Stability Limit ◽  
Conventional System ◽  
Mass System ◽  
Main Mass ◽  
System A ◽  
Excited System ◽  
Excitation Force ◽  
The Stability

This contribution deals with the suppression of friction-induced vibrations of a mechanical system. A two-mass system is considered, with the main mass excited by a friction-generated self-excitation force and a smaller second mass attached to the main mass. The parameter of the connecting stiffness between the main mass and the absorber mass is a harmonic function of time and represents a parametric excitation. The purpose of the second mass is to act as a “parametric absorber” and to cancel vibrations. Critical values for the damping parameters of the conventional system are calculated, where the system operates on the stability limit. Analytical and numerical methods are employed to determine the stability of the parameter-excited system. A study for selected parameters shows within which limits friction-induced vibrations can be suppressed effectively by a parametric absorber.

Breakdown of Tip Leakage Vortices in Compressors at Flow Conditions Close to Stall

1997 ◽  
Author(s):  
Stefan Schlechtriem ◽  
Michael Lötzerich
Keyword(s):  
Vortex Breakdown ◽  
Stability Limit ◽  
Flow Conditions ◽  
Mixed Flow ◽  
Stall Inception ◽  
Tip Leakage ◽  
Transonic Compressor ◽  
Flow Compressor ◽  
The Stability ◽  
Operating Points

The breakdown of tip leakage vortices at operating points close to the stability limit of transonic compressor rotors has been detected. The aerodynamic phenomenon is considered to have a major impact on stall inception. Computations have been carried out and a detailed visualization of the phenomenon is given. In addition the connection of vortex breakdown to rotating instabilities and stall is discussed. Furthermore the tip flow field of the axial rotor is compared to the results for a centrifugal and a mixed flow compressor operating at similar tip speeds.

Study of the Tip Leakage Flow in a Compressor Cascade With Incidence Exceeding the Stability Limit

2019 ◽  
Author(s):  
Markus W. Leitner ◽  
Stephan Staudacher ◽  
Martin G. Rose
Keyword(s):  
Water Table ◽  
Vortex Breakdown ◽  
Stability Limit ◽  
Leakage Flow ◽  
Angle Of Incidence ◽  
Compressor Cascade ◽  
Tip Leakage Flow ◽  
Unstable Flow ◽  
Tip Leakage ◽  
The Stability

Abstract In axial compressors, tip leakage flow is disadvantageous to efficiency and mass flow stability. We analyzed the tip leakage flow in a compressor cascade on a water table at various angles of incidence. When the angle of incidence is systematically increased, the flow rate is decreased and, finally, the stability limit is exceeded. To study the flow structures and vortex behavior, we installed Particle Tracking Velocimetry (PTV) on the water table. 3D-trajectories of the stable and unstable flow reveal significant effects. Increasing incidence generates a significant change in the nature of the flow. The tip leakage flow fluctuates and features unstable flow phenomena. A large blockage of the flow passage occurs, probably due vortex breakdown. Such a serious disturbance of the incoming flow may induce stall.

HOPF BIFURCATION OF TIME-DELAY LIENARD EQUATIONS

1999 ◽  
Vol 09 (05) ◽  
pp. 939-951 ◽  
Author(s):  
JIAN XU ◽  
QI-SHAO LU
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Null Solution ◽  
Liénard Equations ◽  
Linearized Stability ◽  
Normal Form Method ◽  
The Stability ◽  
Two Parameters ◽  
Nonlinear Delay

The linearized stability and Hopf bifurcation of the delay Lienard equations are studied. The linearized asymptotic stability for the null solution of the equations with two parameters is analyzed. The Hopf bifurcation and the stability of periodic solutions are investigated by constructing the center manifold and using the normal form method. Several examples for typical nonlinear delay Lienard equations are given to show the coincidence between the theoretical analysis and the numerical results.

Ultrasonic Doppler Velocimetry Measurement of Flow and Instabilities in a Rotating Lid-Driven Cylinder

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Zhao C. Kong ◽  
Duncan O. Eddy ◽  
Nathan K. Martin ◽  
Brent C. Houchens
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Velocity Profiles ◽  
Base Flow ◽  
Doppler Velocimetry ◽  
Two Parameters ◽  
Ultrasonic Doppler Velocimetry

The steady, axisymmetric base flow and instabilities in a rotating lid-driven cylinder are investigated experimentally via ultrasonic Doppler velocimetry and verified with computations. The flow is governed by two parameters: the Reynolds number (based on the angular velocity of the top lid, the cylinder radius, and kinematic viscosity) and the aspect ratio (cylinder height/radius). Base states and instabilities are explored using ultrasonic Doppler velocimetry in two mixtures of glycerol and water. Velocity profiles in the cylinder are constructed for aspect ratio 2.5 and Reynolds numbers between 1000 and 3000. The results are compared to computational spectral element simulations, as well as previously published findings. The base flow velocity profiles measured by ultrasonic Doppler velocimetry are in good agreement with the numerical results below the critical Reynolds number. The same is true for time-averaged results above the critical Reynolds number. Prediction of the first axisymmetric instability is demonstrated, although not always at the expected critical Reynolds number. Advantages and limitations of ultrasonic Doppler velocimetry are discussed.

Viscous centre modes in the stability of swirling poiseuille flow

1988 ◽  
Vol 324 (1580) ◽  
pp. 473-512 ◽  
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Vortex Breakdown ◽  
Neutral Curve ◽  
Inviscid Limit ◽  
Rotating Flow ◽  
Additional Parameter ◽  
Highly Oscillatory ◽  
The Stability

Centre modes in the neighbourhoods of both branches of the neutral curve are identified for viscous rotating flow in a pipe when the Reynolds number is sufficiently large. Limit equations satisfied by these modes are established, and solutions are computed as functions of the azimuthal wavenumber and one additional parameter, p,say, representing the distance from a neutral curve; these compare favourably with existing calculations of the full equations at large but finite values of The question of the attainment of an inviscid limit as f-> oo is addressed, and it is shown that the solution on the unstable side of the neutral curve is dominantly viscous. The resulting highly oscillatory viscous modes are examined and are shown to be present throughout the region bounded by the neutral curve. It is anticipated that the results may have application in the study of vortex breakdown.

Free-Surface Effects for Yawed Surface-Piercing Plates

1976 ◽  
Vol 20 (03) ◽  
pp. 125-136
Author(s):  
R. B. Chapman
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Angle Of Attack ◽  
Present Formulation ◽  
Surface Conditions ◽  
Side Force ◽  
Experimental Values ◽  
Two Parameters ◽  
Nonlinear Free Surface ◽  
Good Agreement

The problem of a yawed surface-piercing flat plate is solved by applying the slender-body approximation and solving the resulting equations by a finite-difference method. The solution is shown to depend on two parameters & the product of the length Froude number and the square root of the aspect ratio of the plate, and the ratio of the angle of attack to the aspect ratio. Numerical methods are developed with linear, second-order, and nonlinear free-surface conditions. Calculated side force and yawing moment coefficients show good agreement with experimental values near the limit of zero angle of attack. At finite angles of attack, the experimental data exhibit nonlinearities not contained in the present formulation.

Dynamics of revolving wings for various aspect ratios

2014 ◽  
Vol 748 ◽  
pp. 932-956 ◽  
Author(s):  
D. J. Garmann ◽  
M. R. Visbal
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Pressure Gradient ◽  
Centrifugal Force ◽  
Vortex Breakdown ◽  
Delta Wing ◽  
Strong Dependence ◽  
Tip Vortex ◽  
Aspect Ratios ◽  
Gradient Forces

AbstractHigh-fidelity, direct numerical simulations (DNSs) are conducted to examine the vortex structure and aerodynamic loading of unidirectionally revolving wings in quiescent fluid. Wings with aspect ratios $({\mathit{AR}}) = 1$, 2 and 4 are considered at a fixed root-based Reynolds number of 1000. Each wing is shown to generate a coherent leading-edge vortex (LEV) that remains in close proximity to the surface and provides persistent suction throughout the motion. Towards the tip, the LEV lifts off as an arch-like structure and reorients itself along the chord through its connection with the tip vortex. The substantial and sustained aerodynamic loads achieved during the motion saturate with aspect ratio resulting from the chordwise growth of the LEV along the span eventually becoming geometrically constrained by the trailing edge. Further, for ${\mathit{AR}}=4$, substructures develop in the feeding sheet of the LEV, which appear to directly correlate with the local, span-based Reynolds number achieved during rotation. The lower-aspect-ratio wings do not have sufficient spans for these transitional elements to manifest. In contrast, vortex breakdown, which occurs around midspan for each aspect ratio, shows a strong dependence on the spanwise pressure gradient established between the root and tip of the wing and not local Reynolds number. This independent development of shear-layer substructures and vortex breakdown parallels very closely with what has been observed in delta wing flow. Next, the centrifugal, Coriolis and pressure gradient forces are also analysed at several spanwise locations across each wing, and the centrifugal and pressure gradient forces are shown to be responsible for the spanwise flow above the wing. The Coriolis force is directed away from the surface at the base of the LEV, indicating that it is not a contributor to LEV attachment, which is contrary to previous hypotheses. Finally, as a means of emphasizing the importance of the centrifugal force on LEV attachment, the ${\mathit{AR}}=2$ wing is simulated with the addition of a source term in the governing equations to oppose and eliminate the centrifugal force near the surface. The initial formation and development of the LEV is unhindered by the absence of this force; however, later in the motion, the outboard lift-off of the LEV moves inboard. Without the opposing outboard-directed centrifugal force to keep the separation past midspan, the entire vortex eventually separates and moves away from the surface.

Modulated rotating waves in an enclosed swirling flow

2002 ◽  
Vol 465 ◽  
pp. 33-58 ◽  
Author(s):  
H. M. BLACKBURN ◽  
J. M. LOPEZ
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Low Frequency ◽  
Rotating Waves ◽  
Axisymmetric Solution ◽  
Axisymmetric Mode ◽  
Very Low Frequency

The loss of axisymmetry in a swirling flow that is generated inside an enclosed cylindrical container by the steady rotation of one endwall is examined numerically. The two dimensionless parameters that govern these flows are the cylinder aspect ratio and a Reynolds number associated with the rotation of the endwall. This study deals with a fixed aspect ratio, height/radius = 2.5. At low Reynolds numbers the basic flow is steady and axisymmetric; as the Reynolds number increases the basic state develops a double recirculation zone on the axis, so-called vortex breakdown bubbles. On further increase in the Reynolds number the flow becomes unsteady through a supercritical Hopf bifurcation but remains axisymmetric. After the onset of unsteadiness, another two unsteady axisymmetric solution branches appear with further increase in Reynolds number, each with its own temporal characteristic: one is periodic and the other is quasi-periodic with a very low frequency modulation. Solutions on these additional branches are unstable to three-dimensional perturbations, leading to nonlinear modulated rotating wave states, but with the flow still dominated by the corresponding underlying axisymmetric mode. A study of the flow behaviour on and bifurcations between these solution branches is presented, both for axisymmetric and for fully three-dimensional flows. The presence of modulated rotating waves alters the structure of the bifurcation diagram and gives rise to its own dynamics, such as a truncated cascade of period doublings of very-low-frequency modulated states.

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