On the instabilities of a potential vortex with a free surface

In this paper, we address the linear stability analysis of a confined potential vortex with a free surface. This particular flow has been recently used by Tophøj et al. (Phys. Rev. Lett., vol. 110(19), 2013, article 194502) as a model for the swirling flow of fluid in an open cylindrical container, driven by rotating the bottom plate (the rotating bottom experiment) to explain the so-called rotating polygons instability (Vatistas J. Fluid Mech., vol. 217, 1990, pp. 241–248; Jansson et al., Phys. Rev. Lett., vol. 96, 2006, article 174502) in terms of surface wave interactions leading to resonance. Global linear stability results are complemented by a Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) analysis in the shallow-water limit as well as new experimental observations. It is found that global stability results predict additional resonances that cannot be captured by the simple wave coupling model presented in Tophøj et al. (2013). Both the main resonances (thought to be at the root of the rotating polygons) and these secondary resonances are interpreted in terms of over-reflection phenomena by the WKBJ analysis. Finally, we provide experimental evidence for a secondary resonance supporting the numerical and theoretical analysis presented. These different methods and observations allow to support the unstable wave coupling mechanism as the physical process at the origin of the polygonal patterns observed in free-surface rotating flows.

Download Full-text

A Comprehensive Model to Predict Simplex Atomizer Performance

Volume 3: Coal, Biomass and Alternative Fuels; Combustion and Fuels; Oil and Gas Applications; Cycle Innovations ◽

10.1115/98-gt-441 ◽

1998 ◽

Cited By ~ 2

Author(s):

Y. Liao ◽

A. T. Sakman ◽

S. M. Jeng ◽

M. A. Jog ◽

M. Benjamin

Keyword(s):

Stability Analysis ◽

Film Thickness ◽

Linear Stability ◽

Linear Stability Analysis ◽

Liquid Fuel ◽

Density Ratio ◽

Liquid Sheet ◽

Unstable Wave ◽

Liquid Sheets ◽

Breakup Model

The performance of liquid fuel atomizer has direct effects on combustion efficiency, pollutant emission and stability. Pressure swirl atomizer, or simplex atomizer, is widely used in liquid fuel combustion devices in aircraft and power generation industry. A computational, experimental, and theoretical study is conducted to predict its performance. The Arbitrary-Lagrangian-Eulerian method with finite volume scheme is employed in the CFD model. Internal flow characteristics of the simplex atomizer as well as its performance parameters such as discharge coefficient, spray angle and film thickness are predicted. A temporal linear stability analysis is performed for cylindrical liquid sheets under 3-D disturbance. The model incorporates swirling velocity component, finite film thickness and radius which are essential features of conical liquid sheets emanating from simplex atomizers. It is observed that the relative velocity between liquid and gas phase, density ratio and surface curvature enhance the interfacial aerodynamic instability. As Weber number and density ratio increase, both the wave growth rate and the unstable wave number range increase. Combination of axial and swirling velocity components is more effective than single axial component for disintegration of liquid sheet. A breakup model for conical liquid sheet is proposed. Combining the breakup model with linear stability analysis, mean drop sizes are predicted. The theoretical results are compared with measurement data and agreement is very good.

Download Full-text

Comparison of linear stability results with flight transition data

AIAA Journal ◽

10.2514/3.12349 ◽

1995 ◽

Vol 33 (1) ◽

pp. 161-163 ◽

Cited By ~ 5

Author(s):

J. A. Masad ◽

M. R. Malik

Keyword(s):

Linear Stability ◽

Stability Results

Download Full-text

Characteristics of Swirl Angle in Pump Intake Flow Near the Minimum Inlet Submergence

Volume 3B: Fluid Applications and Systems ◽

10.1115/ajkfluids2019-5053 ◽

2019 ◽

Author(s):

Tajul Ariffin Norizan ◽

Zambri Harun ◽

Wan Hanna Melini Wan Mohtar ◽

Shahrir Abdullah

Keyword(s):

Free Surface ◽

Swirling Flow ◽

Pump Efficiency ◽

Angle Distribution ◽

Pump Impeller ◽

Load Imbalance ◽

Swirl Angle ◽

Free Surface Vortex ◽

Pump Inlet ◽

Intake Flow

Abstract Swirling flow in pump sump intake has been the subject of discussion for the past decades due to the detrimental effects brought about by its existence. Among the effects of swirling flow are reduced pump efficiency, cavitation, excessive vibration and load imbalance at the pump impeller which are caused by hydraulic problems associated to swirling flow such as swirls and vortices. One of the remedial measures for preventing such occasion is by keeping the pump inlet submerged above a defined value known as the minimum inlet submergence. It is the minimum submergence required to reduce the probability of the occurrence of free surface vortices. However, this requirement may not be fulfilled in some situations due to on site conditions or operational restrictions. In this paper, an experimental study was conducted to investigate the characteristics of swirl angle in the pump intake flow when the pump inlet is submerged near the value of minimum inlet submergence. The ratio of pump submergence to the minimum submergence was varied between 0.8 to 1.2 with constant inlet Froude Number which referred to as submergence ratio. The strength of the swirl in the intake flow was determined by measuring the swirl angle which was accomplished using a swirl meter attached in the suction pipe. Measurements using Acoustic Doppler Velocimeter (ADV) was performed to capture the velocity profile in the intake sump. The swirl angle distribution across the range of submergence ratios was dominated by a subsurface vortex formed at the sump floor. As soon as the submergence was reduced below the minimum submergence, a free surface vortex emerged near the pump inlet and brought a swirl retardation effect to the swirl meter rotation resulting in a bigger fluctuation of the swirl meter reading. An anti vortex device (AVD) called the floor splitter commonly used to reduce vorticity at pump inlet was installed and its effect on the reduction of swirls and vortices was evaluated.

Download Full-text

Impact of Swirling Flow Structure on Shear Layer Vorticity Fluctuation Mechanisms

Volume 4A: Combustion, Fuels and Emissions ◽

10.1115/gt2016-56460 ◽

2016 ◽

Cited By ~ 3

Author(s):

Benjamin Mathews ◽

Samuel Hansford ◽

Jacqueline O’Connor

Keyword(s):

Shear Layer ◽

Swirling Flow ◽

Coupling Mechanism ◽

Acoustic Oscillations ◽

Flow Topology ◽

Precessing Vortex Core ◽

Acoustic Fluctuations ◽

Vorticity Fluctuation ◽

Different Response ◽

The Impact

Vorticity fluctuations have been identified as an important coupling mechanism during velocity-coupled combustion instability in swirl-stabilized flames. Acoustic oscillations in the combustor can cause all components of vorticity to oscillate, particularly the cross-stream, or azimuthal, vorticity that is excited in shear layer roll-up, and streamwise, or axial, vorticity that is excited during swirl fluctuations. These fluctuations can be induced by longitudinal acoustic fluctuations that oscillate across the swirler and dump plane upstream of the flame. While these fluctuations have been identified in a number of configurations, the sensitivity of this mechanism to flow configuration and boundary conditions has not been studied parametrically. In this study, we investigate the impact of time-averaged swirl level, confinement, and forcing frequency and amplitude on vorticity fluctuation dynamics in the azimuthal direction of a non-reacting swirling jet. The goal of this work is to better understand the dependence of vorticity fluctuations on these parameters as well as the vorticity conversion processes that occur in the flow. We have shown that vorticity fluctuation levels vary with time-averaged swirl number, particularly in the presence of a self-excited precessing vortex core, which dampens most acoustically-driven motion. Additionally, variations in forcing frequency excite flow response in different portions of the flow, particularly for different swirl numbers. Finally, confinement drastically changes the flow topology and unforced dynamics, resulting in significantly different response to forcing and generation of vortical fluctuations.

Download Full-text

Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations

Journal of Fluid Mechanics ◽

10.1017/s0022112001006516 ◽

2002 ◽

Vol 451 ◽

pp. 261-282 ◽

Cited By ~ 36

Author(s):

F. GRAF ◽

E. MEIBURG ◽

C. HÄRTEL

Keyword(s):

Experimental Data ◽

Growth Rate ◽

Linear Stability ◽

Stokes Equations ◽

Three Dimensional ◽

Two Dimensional ◽

Interface Thickness ◽

Gap Width ◽

Stability Results ◽

Hele Shaw Cell

We consider the situation of a heavier fluid placed above a lighter one in a vertically arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this configuration, experiments and nonlinear simulations recently reported by Fernandez et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on the order of five times the gap width. These findings are in disagreement with linear stability results based on the gap-averaged Hele-Shaw approach, which predict much smaller wavelengths. Similar observations have been made for immiscible flows as well (Maxworthy 1989).In order to resolve the above discrepancy, we perform a linear stability analysis based on the full three-dimensional Stokes equations. A generalized eigenvalue problem is formulated, whose numerical solution yields both the growth rate and the two-dimensional eigenfunctions in the cross-gap plane as functions of the spanwise wavenumber, an ‘interface’ thickness parameter, and Ra. For large Ra, the dispersion relations confirm that the optimally amplified wavelength is about five times the gap width, with the exact value depending on the interface thickness. The corresponding growth rate is in very good agreement with the experimental data as well. The eigenfunctions indicate that the predominant fluid motion occurs within the plane of the Hele-Shaw cell. However, for large Ra purely two-dimensional modes are also amplified, for which there is no motion in the spanwise direction. Scaling laws are provided for the dependence of the maximum growth rate, the corresponding wavenumber, and the cutoff wavenumber on Ra and the interface thickness. Furthermore, the present results are compared both with experimental data, as well as with linear stability results obtained from the Hele-Shaw equations and a modified Brinkman equation.

Download Full-text

Sediment-laden fresh water above salt water: linear stability analysis

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.474 ◽

2011 ◽

Vol 691 ◽

pp. 279-314 ◽

Cited By ~ 37

Author(s):

P. Burns ◽

E. Meiburg

Keyword(s):

Growth Rate ◽

Linear Stability ◽

Fresh Water ◽

Settling Velocity ◽

Interface Thickness ◽

Particle Settling ◽

Salinity Field ◽

Unstable Layer ◽

Stability Results ◽

Double Diffusive

AbstractWhen a layer of particle-laden fresh water is placed above clear, saline water, both Rayleigh–Taylor and double diffusive fingering instabilities may arise. For quasi-steady base profiles, we obtain linear stability results for such situations by means of a rational spectral approximation method with adaptively chosen grid points, which is able to resolve multiple steep gradients in the base state density profile. In the absence of salinity and for a step-like concentration profile, the dominant parameter is the ratio of the particle settling velocity to the viscous velocity scale. As long as this ratio is small, particle settling has a negligible influence on the instability growth. However, when the particles settle more rapidly than the instability grows, the growth rate decreases inversely proportional to the settling velocity. This damping effect is a result of the smearing of the vorticity field, which in turn is caused by the deposition of vorticity onto the fluid elements passing through the interface between clear and particle-laden fluid. In the presence of a stably stratified salinity field, this picture changes dramatically. An important new parameter is the ratio of the particle settling velocity to the diffusive spreading velocity of the salinity, or alternatively the ratio of the unstable layer thickness to the diffusive interface thickness of the salinity profile. As long as this quantity does not exceed unity, the instability of the system and the most amplified wavenumber are primarily determined by double diffusive effects. In contrast to situations without salinity, particle settling can have a destabilizing effect and significantly increase the growth rate. Scaling laws obtained from the linear stability results are seen to be largely consistent with earlier experimental observations and theoretical arguments put forward by other authors. For unstable layer thicknesses much larger than the salinity interface thickness, the particle and salinity interfaces become increasingly decoupled, and the dominant instability mode becomes Rayleigh–Taylor-like, centred at the lower boundary of the particle-laden flow region.

Download Full-text

Linear stability analysis for periodic travelling waves of the Boussinesq equation and the Klein–Gordon–Zakharov system

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210512000741 ◽

2014 ◽

Vol 144 (3) ◽

pp. 455-489 ◽

Cited By ~ 3

Author(s):

Sevdzhan Hakkaev ◽

Milena Stanislavova ◽

Atanas Stefanov

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Wide Class ◽

Boussinesq Equation ◽

Travelling Waves ◽

Periodic Waves ◽

Zakharov System ◽

Klein Gordon ◽

Spatially Periodic ◽

Stability Results

The question of the linear stability of spatially periodic waves for the Boussinesq equation (in the cases p = 2, 3) and the Klein–Gordon–Zakharov system is considered. For a wide class of solutions, we completely and explicitly characterize their linear stability (instability) when the perturbations are taken with the same period T. In particular, our results allow us to completely recover the linear stability results, in the limit T → ∞, for the whole-line case.

Download Full-text