scholarly journals Transient instability in long, tilted water columns with fast-settling, particle-laden layers

2021 ◽  
Vol 929 ◽  
Author(s):  
Yu-Jen Chang ◽  
Ruey-Lin Chern ◽  
Yi-Ju Chou
Keyword(s):  
Flow Instability ◽  
Base Flow ◽  
Energy Gain ◽  
Shear Instability ◽  
Flow Energy ◽  
Peak Energy ◽  
Water Columns ◽  
Settling Speed ◽  
The Stability ◽  
Fast Settling

We study the stability of unsteady particle-laden flows in long, tilted water columns in batch settling mode, where the quasi-steady assumption of base flow no longer holds for the fast settling of particles. For this purpose, we introduce a settling time scale in the momentum and transport equations to solve the unsteady base flow, and utilise non-modal analysis to examine the stability of the disturbance flow field. The base flow increases in magnitude as the settling speed decreases and attains its maximum value when the settling speed becomes infinitesimal. The time evolution of the disturbance flow energy experiences an algebraic growth caused by the lift-up mechanism of the wall-normal disturbance, followed by an exponential growth owing to the shear instability of the base flow. The streamwise and spanwise wavenumbers corresponding to the peak energy gain are identified for both stages. In particular, the flow instability is enhanced as the Prandtl number increases, which is attributed to the sharpening of the particle-laden interface. On the other hand, the flow instability is suppressed by the increase in settling speed, because less disturbance energy can be extracted from the base flow. There exists an optimal tilted angle for efficient sedimentation, where the particle-laden flow is relatively stable and is accompanied by a smaller energy gain of the disturbance.

scholarly journals Stability of an isolated pancake vortex in continuously stratified-rotating fluids

2016 ◽  
Vol 801 ◽  
pp. 508-553 ◽  
Author(s):  
Eunok Yim ◽  
Paul Billant ◽  
Claire Ménesguen
Keyword(s):  
Angular Velocity ◽  
Baroclinic Instability ◽  
Base Flow ◽  
Shear Instability ◽  
Vertical Shear ◽  
Rossby Number ◽  
Centrifugal Instability ◽  
Pancake Vortex ◽  
To Come ◽  
The Stability

This paper investigates the stability of an axisymmetric pancake vortex with Gaussian angular velocity in radial and vertical directions in a continuously stratified-rotating fluid. The different instabilities are determined as a function of the Rossby number $Ro$, Froude number $F_{h}$, Reynolds number $Re$ and aspect ratio ${\it\alpha}$. Centrifugal instability is not significantly different from the case of a columnar vortex due to its short-wavelength nature: it is dominant when the absolute Rossby number $|Ro|$ is large and is stabilized for small and moderate $|Ro|$ when the generalized Rayleigh discriminant is positive everywhere. The Gent–McWilliams instability, also known as internal instability, is then dominant for the azimuthal wavenumber $m=1$ when the Burger number $Bu={\it\alpha}^{2}Ro^{2}/(4F_{h}^{2})$ is larger than unity. When $Bu\lesssim 0.7Ro+0.1$, the Gent–McWilliams instability changes into a mixed baroclinic–Gent–McWilliams instability. Shear instability for $m=2$ exists when $F_{h}/{\it\alpha}$ is below a threshold depending on $Ro$. This condition is shown to come from confinement effects along the vertical. Shear instability transforms into a mixed baroclinic–shear instability for small $Bu$. The main energy source for both baroclinic–shear and baroclinic–Gent–McWilliams instabilities is the potential energy of the base flow instead of the kinetic energy for shear and Gent–McWilliams instabilities. The growth rates of these four instabilities depend mostly on $F_{h}/{\it\alpha}$ and $Ro$. Baroclinic instability develops when $F_{h}/{\it\alpha}|1+1/Ro|\gtrsim 1.46$ in qualitative agreement with the analytical predictions for a bounded vortex with angular velocity slowly varying along the vertical.

Stability of Viscoelastic Channel Flow

2007 ◽  
Author(s):  
Nariman Ashrafi
Keyword(s):  
Reynolds Number ◽  
Viscosity Ratio ◽  
Weissenberg Number ◽  
Base Flow ◽  
Galerkin Projection ◽  
Large Reynolds Number ◽  
One Dimensional ◽  
Stress Effects ◽  
The Stability ◽  
The One

The nonlinear stability and bifurcation of the one-dimensional channel (Poiseuille) flow is examined for a Johnson-Segalman fluid. The velocity and stress are represented by orthonormal functions in the transverse direction to the flow. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. The stability picture is dramatically influenced by the viscosity ratio. The range of shear rate or Weissenberg number for which the base flow is unstable increases from zero as the fluid deviates from the Newtonian limit as decreases. Typically, two turning points are observed near the critical Weissenberg numbers. The transient response is heavily influenced by the level of inertia. It is found that the flow responds oscillatorily. When the Reynolds number is small, and monotonically at large Reynolds number when elastic effects are dominated by inertia.

scholarly journals Dispersion stability and rheological characteristics of water and ethylene glycol based zinc oxide nanofluids

2020 ◽  
pp. 187-187
Author(s):  
Adnan Qamar ◽  
Attique Arshad ◽  
Zahid Anwar ◽  
Rabia Shaukat ◽  
Muhammad Amjad ◽  
...  
Keyword(s):  
Experimental Data ◽  
Ethylene Glycol ◽  
Industrial Applications ◽  
Deionized Water ◽  
Rheological Characteristics ◽  
Particle Loading ◽  
Viscosity Models ◽  
Vis Spectroscopy ◽  
Settling Speed ◽  
The Stability

With advancement of nanoscience, ?nanofluids? are becoming quite popular among thermal engineers. High thermal conductivity, relatively less settling speed, and higher surface area of nanoparticles are a few key promoting properties. The last two decades have seen dramatic progress towards using nanoparticles in industrial applications. However, the stability and rheological characteristics of prepared nanofluids have serious effects on their transport characteristics, but unfortunately, this has not found proper attention from researchers. In this study, stability and rheological characteristics of ZnO nanoparticles within deionized water, ethylene glycol, and their blends have been extensively tested. Stability was observed using UV-vis spectroscopy, while the viscosity was measured with the help of a rheometer. The data was collected with 0.011-0.044 wt. % loading of nanoparticles, while experiments were conducted within 15-55oC temperature range. Better stability was recorded when nanofluids were prepared with pure ethylene glycol. Experiments showed that the viscosity increased with particle loading, whereas the effect of surfactants appeared to be insignificant. Research results were used to assess predictions of different viscosity models. Experimental data was overpredicted by Einstein, Brinkman, and Batchelor?s models.

The Stability-Limiting Flow Mechanisms in a Subsonic Axial-Flow Compressor and Its Passive Control With Casing Treatment

2008 ◽  
Author(s):  
Xingen Lu ◽  
Junqiang Zhu ◽  
Chaoqun Nie ◽  
Weiguang Huang
Keyword(s):  
Flow Instability ◽  
State Of The Art ◽  
Axial Flow ◽  
Flow Mechanism ◽  
Blade Passage ◽  
Casing Treatment ◽  
Compressor Rotor ◽  
Flow Compressor ◽  
The Stability ◽  
End Wall

The phenomenon of flow instability in the compression system such as fan and compressor has been a long-standing “bottle-neck” problem for gas turbines/aircraft engines. With a vision of providing a state-of-the-art understanding of the flow field in axial-flow compressor in the perspective of enhancing their stability using passive means. Two topics are covered in this paper. The first topic is the stability-limiting flow mechanism close to stall, which is the basic knowledge needed to manipulate end-wall flow behavior for the stability improvement. The physical process occurring when approaching stall and the role of complex tip flow mechanism on flow instability in current high subsonic axial compressor rotor has been assessed using single blade passage computations. The second topic is flow instability manipulation with casing treatment. In order to advance the understanding of the fundamental mechanisms of casing treatment and determine the change in the flow field by which casing treatment improve compressor stability, systematic studies of the coupled flow through a subsonic compressor rotor and various end-wall treatments were carried out using a state-of-the-art multi-block flow solver. The numerically obtained flow fields were interrogated to identify complicated flow phenomenon around and within the end-wall treatments and describe the interaction between the rotor tip flow and end-wall treatments. Detailed analyses of the flow visualization at the rotor tip have exposed the different tip flow topologies between the cases with treatment casing and with untreated smooth wall. It was found that the primary stall margin enhancement afforded by end-wall treatments is a result of the tip flow manipulation. Compared to the smooth wall case, the treated casing significantly dampen or absorb the blockage near the upstream part of the blade passage caused by the upstream movement of tip clearance flow and weakens the roll-up of the core vortex. These mechanisms prevent an early spillage of low momentum fluid into the adjacent blade passage and delay the onset of flow instability.

Stability of the Base Flow to Axisymmetric and Plane-Polar Disturbances in an Electrically Driven Flow Between Infinitely-Long, Concentric Cylinders

2000 ◽  
Vol 123 (1) ◽  
pp. 31-42
Author(s):  
J. Liu ◽  
G. Talmage ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Axial Magnetic Field ◽  
Normal Modes ◽  
Azimuthal Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
The Stability

The method of normal modes is used to examine the stability of an azimuthal base flow to both axisymmetric and plane-polar disturbances for an electrically conducting fluid confined between stationary, concentric, infinitely-long cylinders. An electric potential difference exists between the two cylinder walls and drives a radial electric current. Without a magnetic field, this flow remains stationary. However, if an axial magnetic field is applied, then the interaction between the radial electric current and the magnetic field gives rise to an azimuthal electromagnetic body force which drives an azimuthal velocity. Infinitesimal axisymmetric disturbances lead to an instability in the base flow. Infinitesimal plane-polar disturbances do not appear to destabilize the base flow until shear-flow transition to turbulence.

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 The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness

1998 ◽  
Vol 44 (147) ◽  
pp. 285-292 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Large Scale ◽  
Flow Instability ◽  
Ice Thickness ◽  
Ice Flow ◽  
Perturbation Amplitude ◽  
Sediment Flow ◽  
Viscous Models ◽  
The Stability ◽  
Parameter Ranges ◽  
Ice Sheet Modelling

AbstractA perturbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This sheet-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-sheet modelling.

Validation of Hydrodynamic Stability of Supercritical Once-Through Boiler

2008 ◽  
Author(s):  
Bing Wei ◽  
Dong Zhou
Keyword(s):  
Flow Instability ◽  
Hydrodynamic Instability ◽  
Pressure Head ◽  
Operating Conditions ◽  
Hydrodynamic Characteristics ◽  
Boiler Operation ◽  
Calculation Results ◽  
Low Mass ◽  
The Stability ◽  
Heating Loads

Operating safety is one of the most important things to supercritical once-through boilers. To study the hydrodynamic characteristics of fluid in water walls of supercritical once-through boilers and to find out the instable factors will be of great significance to boiler operation. In this paper the mathematical models for hydrodynamic characteristics of fluid in water walls are established. With an example of 600MW boiler, by using the calculation program, the hydrodynamic characteristics curves without and with the throttles at the inlets of the water walls at different operating conditions are presented, the fluid flow instability and the reasons are analyzed. The calculation results show that the boiler operates stably and safely at 100% MCR (Maximum Continuous Rating) condition, the hydrodynamic instability exists at low heating loads of 30% MCR. The method of installing the throttles at the inlets of the water wall pipes will increase the parabola characteristics, help to improve the fluid instability to a certain stable extent, but due to the small curve slopes at low mass flowrates, still need to pay more attention to the low heating loads operation. The existence of gravity pressure head is good to the stability of the vertical upward flow.

Stability of the Prandtl model for katabatic slope flows

2019 ◽  
Vol 865 ◽  
Author(s):  
Cheng-Nian Xiao ◽  
Inanc Senocak
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Slope Angle ◽  
Transverse Mode ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Vortical Flow ◽  
Longitudinal Modes ◽  
Prandtl Model ◽  
The Stability

We investigate the stability of the Prandtl model for katabatic slope flows using both linear stability theory and direct numerical simulations. Starting from Prandtl’s analytical solution for uniformly cooled laminar slope flows, we use linear stability theory to identify the onset of instability and features of the most unstable modes. Our results show that the Prandtl model for parallel katabatic slope flows is prone to transverse and longitudinal modes of instability. The transverse mode of instability manifests itself as stationary vortical flow structures aligned in the along-slope direction, whereas the longitudinal mode of instability emerges as waves propagating in the base-flow direction. Beyond the stability limits, these two modes of instability coexist and form a complex flow structure crisscrossing the plane of flow. The emergence of a particular form of these instabilities depends strongly on three dimensionless parameters, which are the slope angle, the Prandtl number and a newly introduced stratification perturbation parameter, which is proportional to the relative importance of the disturbance to the background stratification due to the imposed surface buoyancy flux. We demonstrate that when this parameter is sufficiently large, then the stabilising effect of the background stratification can be overcome. For shallow slopes, the transverse mode of instability emerges despite meeting the Miles–Howard stability criterion of $Ri>0.25$. At steep slope angles, slope flow can remain linearly stable despite attaining Richardson numbers as low as $3\times 10^{-3}$.

scholarly journals The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness

1998 ◽  
Vol 44 (147) ◽  
pp. 285-292 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Large Scale ◽  
Flow Instability ◽  
Ice Thickness ◽  
Ice Flow ◽  
Perturbation Amplitude ◽  
Sediment Flow ◽  
Viscous Models ◽  
The Stability ◽  
Parameter Ranges ◽  
Ice Sheet Modelling

AbstractA perturbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This sheet-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-sheet modelling.

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