A sensitivity study of vortex breakdown onset to upstream boundary conditions

2010 ◽  
Vol 645 ◽  
pp. 81-119 ◽  
Author(s):  
BENJAMIN LECLAIRE ◽  
DENIS SIPP
Keyword(s):  
Boundary Conditions ◽  
Vortex Breakdown ◽  
Axisymmetric Flow ◽  
Sensitivity Study ◽  
Numerical Continuation ◽  
Smooth Transition ◽  
Inviscid Fluid ◽  
Weakly Nonlinear ◽  
Wide Range ◽  
New Type

This paper theoretically investigates the influence of the upstream boundary conditions on the bifurcation structure leading to vortex breakdown. The axisymmetric flow of an inviscid fluid in a pipe of constant cross-section and finite axial length is considered. Solutions bifurcating from the columnar solution at criticality are analysed via a weakly nonlinear expansion and computed in the fully nonlinear regime using numerical continuation, until a centreline recirculation is found at the pipe outlet. Bifurcation diagrams are determined for a parametric family of inflows describing a wide range of axial and azimuthal profiles, the third inlet condition being chosen either as a fixed azimuthal vorticity or as a vanishing radial velocity. Including the traditional picture given by Wang & Rusak (J. Fluid Mech., vol. 340, 1997a, p. 177), six different diagrams are found to be possible. In particular, a scenario of smooth transition to breakdown may exist as the swirl is increased, with no loss of stability and no hysteresis, breakdown appearing for swirl levels larger than the critical swirl in a pipe. This transition involves a new type of flow akin to a pre-breakdown flow. Our results, furthermore, suggest that rigidly rotating Poiseuille flow could correspond to the limit for which breakdown is impossible because it is predicted at infinitely large swirl numbers. We finally find that flows with a large rotational core are particularly sensitive to an accurate modelling of the upstream boundary conditions, weakly confined vortices being much more robust.

Instability of strongly nonlinear waves in vortex flows

1994 ◽  
Vol 269 ◽  
pp. 247-264 ◽  
Author(s):  
A. Kribus ◽  
S. Leibovich
Keyword(s):  
Linear Stability ◽  
Nonlinear Waves ◽  
Vortex Breakdown ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Vortex Flows ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Perturbation Problem ◽  
Bending Modes

Weakly nonlinear descriptions of axisymmetric cnoidal and solitary waves in vortices recently have been shown to have strongly nonlinear counterparts. The linear stability of these strongly nonlinear waves to three-dimensional perturbations is studied, motivated by the problem of vortex breakdown in open flows. The basic axisymmetric flow varies both radially and axially, and the linear stability problem is therefore nonseparable. To regularize the generalization of a critical layer, viscosity is introduced in the perturbation problem. In the absence of the waves, the vortex flows are linearly stable. As the amplitude of a wave constituting the basic flow increases owing to variation in the level of swirl, stability is first lost to non-axisymmetric ‘bending’ modes. This instability occurs when the wave amplitude exceeds a critical value, provided that the Reynolds number is larger enough. The critical wave amplitudes for instability typically are large, but not large enough to create regions of closed streamlines. Examination of the most-amplified eigenvectors shows that the perturbations tend to be concentrated downstream of the maximum streamline displacement in the wave, in a position consistent with the observed three-dimensional perturbations in the interior of a bubble type of vortex breakdown.

Effects of Flow and Geometry Boundary Conditions on Fluid Motion in a Motored IC Model Engine

1982 ◽  
Vol 196 (1) ◽  
pp. 1-10 ◽  
Author(s):  
C Arcoumanis ◽  
A F Bicen ◽  
N S Vlachos ◽  
J H Whitelaw
Keyword(s):  
Boundary Conditions ◽  
Cylinder Head ◽  
Laser Doppler Anemometry ◽  
Fluid Motion ◽  
Axisymmetric Flow ◽  
Ic Engine ◽  
Piston Cylinder ◽  
Wide Range ◽  
Inlet Geometry ◽  
Flow Configurations

Measurements of ensemble-averaged axial velocities and the r.m.s. of the corresponding fluctuations, obtained by laser-Doppler anemometry, are reported for axisymmetric flow in a non-compressing piston-cylinder assembly motored at 200 rev/min simulating an IC engine. The inlet geometry comprised an open valve, located centrally and flush with the cylinder head, with seat angles of 30° and 60° and incorporating 30° swirl vanes. Results are presented for bore-to-stroke ratios of 0.83 and 1.25 and swept-to-clearance volume ratios of 2,3 and 9. The results indicate strong similarities between the flow structures for different stroke and clearance; a system of vortices is formed with a large vortex occupying most of the flow space and with smaller vortices in the corners between the wall, piston and cylinder head. The influence of valve seat angle is more pronounced and results, for the 30° angle, in adherence of the incoming jet to the cylinder head with increase of the overall turbulence levels and creation of stronger and longer living vortices. Previous results obtained in related compressing and non-compressing flow configurations are reviewed and, together with the present results, enable the influence of a wide range of possible geometric and flow boundary conditions to be quantified.

Large-amplitude wavetrains and solitary waves in vortices

1990 ◽  
Vol 216 ◽  
pp. 459-504 ◽  
Author(s):  
S. Leibovich ◽  
A. Kribus
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Vortex Breakdown ◽  
Continuation Method ◽  
Soliton Solutions ◽  
Numerical Continuation ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Velocity Changes ◽  
Produce Flow

Large-amplitude axisymmetric waves on columnar vortices, thought to be related to flow structures observed in vortex breakdown, are found as static bifurcations of the Bragg–Hawthorne equation. Solutions of this equation satisfy the steady, axisymmetric, Euler equations. Non-trivial solution branches bifurcate as the swirl ratio (the ratio of azimuthal to axial velocity) changes, and are followed into strongly nonlinear regimes using a numerical continuation method. Four types of solutions are found: multiple columnar solutions, corresponding to Benjamin's ‘conjugate flows’, with subcritical–supercritical pairing of wave characteristics; solitary waves, extending previously known weakly nonlinear solutions to amplitudes large enough to produce flow reversals similar to the breakdown transition; periodic wavetrains; and solitary waves superimposed on the conjugate flow that emerge from the periodic wavetrain as the wavelength or amplitude becomes sufficiently large. Weakly nonlinear soliton solutions are found to be accurate even when the perturbations they cause are fairly strong.

Global stability of axisymmetric flow focusing

2017 ◽  
Vol 832 ◽  
pp. 329-344 ◽  
Author(s):  
F. Cruz-Mazo ◽  
M. A. Herrada ◽  
A. M. Gañán-Calvo ◽  
J. M. Montanero
Keyword(s):  
Boundary Conditions ◽  
Global Stability ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Navier Stokes ◽  
Transition Curve ◽  
Flow Focusing ◽  
Stable States ◽  
Navier Stokes Equations ◽  
Wide Range

In this paper, we analyse numerically the stability of the steady jetting regime of gaseous flow focusing. The base flows are calculated by solving the full Navier–Stokes equations and boundary conditions for a wide range of liquid viscosities and gas speeds. The axisymmetric modes characterizing the asymptotic stability of those flows are obtained from the linearized Navier–Stokes equations and boundary conditions. We determine the flow rates leading to marginally stable states, and compare them with the experimental values at the jetting-to-dripping transition. The theoretical predictions satisfactorily agree with the experimental results for large gas speeds. However, they do not capture the trend of the jetting-to-dripping transition curve for small gas velocities, and considerably underestimate the minimum flow rate in this case. To explain this discrepancy, the Navier–Stokes equations are integrated over time after introducing a small perturbation in the tapering liquid meniscus. There is a transient growth of the perturbation before the asymptotic exponential regime is reached, which leads to dripping. Our work shows that flow focusing stability can be explained in terms of the combination of asymptotic global stability and the system short-term response for large and small gas velocities, respectively.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

scholarly journals Electrically turning periodic structures in cholesteric layer with conical–planar boundary conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Oxana Prishchepa ◽  
Mikhail Krakhalev ◽  
Vladimir Rudyak ◽  
Vitaly Sutormin ◽  
Victor Zyryanov
Keyword(s):  
Boundary Conditions ◽  
Periodic Structures ◽  
Cholesteric Liquid Crystal ◽  
Growth Direction ◽  
Smooth Transition ◽  
Defect Structures ◽  
Optical Cell ◽  
Elastic Continuum ◽  
The One ◽  
Experimental Findings

AbstractElectro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by $$180^\circ$$ 180 ∘ . The $$U^+$$ U + and $$U^-$$ U - -defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of $$0\le \, V \le 1.3$$ 0 ≤ V ≤ 1.3  V during the process. Resulting orientation and distance between the lines don’t change under voltage. However, at $$V>1.3$$ V > 1.3  V $$U^+$$ U + -defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell’s center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.

scholarly journals Subject-specific multiscale modeling of aortic valve biomechanics

2021 ◽  
Author(s):  
G. Rossini ◽  
A. Caimi ◽  
A. Redaelli ◽  
E. Votta
Keyword(s):  
Aortic Valve ◽  
Boundary Conditions ◽  
Narrow Range ◽  
Radial Strain ◽  
Length Scale ◽  
Length Scales ◽  
Anatomical Features ◽  
Wide Range ◽  
Subject Specific ◽  
Cell Strains

AbstractA Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range ($$0.36-0.87$$ 0.36 - 0.87 ) with a strong correlation with the organ length-scale radial strain ($$R^{2}= 0.95$$ R 2 = 0.95 ); conversely, circumferential cell strains spanned a very narrow range ($$0.75-0.88$$ 0.75 - 0.88 ) showing no correlation with the circumferential strain at the organ level ($$R^{2}= 0.02$$ R 2 = 0.02 ). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.

Dynamics and Performance of a Harmonically Excited Vertical Impact Damper

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Sanjiv Ramachandran ◽  
George Lesieutre
Keyword(s):  
Loss Factor ◽  
Vertical Direction ◽  
Theoretical Models ◽  
Coefficient Of Restitution ◽  
Numerical Continuation ◽  
Particle Impact ◽  
Impact Damper ◽  
High Loss ◽  
Wide Range ◽  
And Performance

Particle impact dampers (PIDs) have been shown to be effective in vibration damping. However, our understanding of such dampers is still limited, based on the theoretical models existing today. Predicting the performance of the PID is an important problem, which needs to be investigated more thoroughly. This research seeks to understand the dynamics of a PID as well as those parameters which govern its behavior. The system investigated is a particle impact damper with a ceiling, under the influence of gravity. The base is harmonically excited in the vertical direction. A two-dimensional discrete map is obtained, wherein the variables at one impact uniquely dictate the variables at the next impact. This map is solved using a numerical continuation procedure. Periodic impact motions and “irregular” motions are observed. The effects of various parameters such as the gap clearance, coefficient of restitution, and the base acceleration are analyzed. The dependence of the effective damping loss factor on these parameters is also studied. The loss factor results indicate peak damping for certain combinations of parameters. These combinations of parameters correspond to a region in parameter space where two-impacts-per-cycle motions are observed over a wide range of nondimensional base accelerations. The value of the nondimensional acceleration at which the onset of two-impacts-per-cycle solutions occurs depends on the nondimensional gap clearance and the coefficient of restitution. The range of nondimensional gap clearances over which two-impacts-per-cycle solutions are observed increases as the coefficient of restitution increases. In the regime of two-impacts-per-cycle solutions, the value of nondimensional base acceleration corresponding to onset of these solutions initially decreases and then increases with increasing nondimensional gap clearance. As the two-impacts-per-cycle solutions are associated with high loss factors that are relatively insensitive to changing conditions, they are of great interest to the designer.

Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
R. Gaudron ◽  
D. Yang ◽  
A. S. Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

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