scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

scholarly journals Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

2017 ◽  
Author(s):  
Thomas L. Kaiser ◽  
Thierry Poinsot ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Large Eddy Simulations ◽  
Mode Shapes ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Large Eddy ◽  
Good Agreement

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core. Mean flow fields of large eddy simulations, validated by experimental particle image velocimetry measurements are used as input for both local and global linear stability analysis. It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local linear stability analysis are compared to a dynamic mode decomposition based on large eddy simulation snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the precessing vortex core.

scholarly journals Linear Stability of a Steady Convective Flow between Permeable Cylinders

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 342
Author(s):  
Maksims Zigunovs ◽  
Andrei Kolyshkin ◽  
Ilmars Iltins
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Chemical Reaction ◽  
Linear Stability Analysis ◽  
Convective Flow ◽  
Base Flow ◽  
Marginal Stability ◽  
Heat Sources ◽  
Rate Of Increase

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls of the annulus is analyzed. The problem is relevant to biomass thermal conversion. The base flow solution is obtained by solving nonlinear boundary value problem. Linear stability analysis is performed, using collocation method. The calculations show that radial inward or outward flow has a stabilizing effect on the flow, while the increase in the Frank–Kamenetskii parameter (proportional to the intensity of the chemical reaction) destabilizes the flow. The increase in the Reynolds number based on the radial velocity leads to the appearance of the second minimum on the marginal stability curves. The rate of increase in the critical Grashof number with respect to the Reynolds number is different for inward and outward radial flows.

scholarly journals The Growth and Saturation of Submesoscale Instabilities in the Presence of a Barotropic Jet

2018 ◽  
Vol 48 (11) ◽  
pp. 2779-2797 ◽  
Author(s):  
Megan A. Stamper ◽  
John R. Taylor ◽  
Baylor Fox-Kemper
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Initial Conditions ◽  
Boussinesq Equations ◽  
Small Region ◽  
Computational Domain ◽  
Mean Flow ◽  
The Mean

AbstractMotivated by recent observations of submesoscales in the Southern Ocean, we use nonlinear numerical simulations and a linear stability analysis to examine the influence of a barotropic jet on submesoscale instabilities at an isolated front. Simulations of the nonhydrostatic Boussinesq equations with a strong barotropic jet (approximately matching the observed conditions) show that submesoscale disturbances and strong vertical velocities are confined to a small region near the initial frontal location. In contrast, without a barotropic jet, submesoscale eddies propagate to the edges of the computational domain and smear the mean frontal structure. Several intermediate jet strengths are also considered. A linear stability analysis reveals that the barotropic jet has a modest influence on the growth rate of linear disturbances to the initial conditions, with at most a ~20% reduction in the growth rate of the most unstable mode. On the other hand, a basic state formed by averaging the flow at the end of the simulation with a strong barotropic jet is linearly stable, suggesting that nonlinear processes modify the mean flow and stabilize the front.

Stability of flow in a wavy channel

2002 ◽  
Vol 457 ◽  
pp. 191-212 ◽  
Author(s):  
A. CABAL ◽  
J. SZUMBARSKI ◽  
J. M. FLORYAN
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stability Criteria ◽  
Streamwise Vortices ◽  
Critical Stability ◽  
Wavy Channel

Linear stability analysis of flow in a channel bounded by wavy walls is considered. It is shown that wall waviness gives rise to an instability that manifests itself through generation of streamwise vortices. The available results suggest that the critical stability criteria based on the Reynolds number based on the amplitude of the waviness can be formulated.

scholarly journals Theoretical Investigation of the Atlantic Multidecadal Oscillation

2015 ◽  
Vol 45 (9) ◽  
pp. 2189-2208 ◽  
Author(s):  
Florian Sévellec ◽  
Thierry Huck
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Atlantic Multidecadal Oscillation ◽  
Meridional Overturning Circulation ◽  
Internal Mode ◽  
Mean Flow ◽  
Coupled Models ◽  
Basin Scale ◽  
Level Model

AbstractA weakly damped mode of variability, corresponding to the oceanic signature of the Atlantic multidecadal oscillation (AMO) was found through the linear stability analysis of a realistic ocean general circulation model. A simple two-level model was proposed to rationalize both its period and damping rate. This model is extended here to three levels to investigate how the mode can draw energy from the mean flow, as found in various ocean and coupled models. A linear stability analysis in this three-level model shows that the positive growth rate of the oscillatory mode depends on the zonally averaged isopycnal slope. This mode corresponds to a westward propagation of density anomalies in the pycnocline, typical of large-scale baroclinic Rossby waves. The most unstable mode corresponds to the largest scale one (at least for low isopycnal slope). The mode can be described in four phases composing a full oscillation cycle: 1) basin-scale warming of the North Atlantic (AMO positive phase), 2) decrease in upper-ocean poleward transport [hence a reduction of the Atlantic meridional overturning circulation (AMOC)], 3) basin-scale cooling (negative AMO), and 4) AMOC intensification. A criterion is developed to test, in oceanic datasets or numerical models, whether this multidecadal oscillation is an unstable oceanic internal mode of variability or if it is stable and externally forced. Consistent with the classical theory of baroclinic instability, this criterion depends on the vertical structure of the mode. If the upper pycnocline signature is in advance of the deeper pycnocline signature with respect to the westward propagation, the mode is unstable and could be described as an oceanic internal mode of variability.

Stability and Transition Over a Low-Reynolds Number Airfoil

2016 ◽  
Author(s):  
Paul Ziadé ◽  
Pierre E. Sullivan
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Peak Frequency ◽  
Laminar Separation Bubble ◽  
Airfoil Surface ◽  
Laminar Separation

Large-eddy simulation and linear stability analysis were performed on a NACA 0025 airfoil at a chord Reynolds number of 105 and four angles of attack. The computations showed that the initial vortex roll-up quickly breaks down to three-dimensional turbulence. Flow separation was observed at all angles, whereas only the lowest angle of attack formed a laminar separation bubble due to flow transition occuring close to the airfoil surface. A Chebyshev collocation method was employed to solve the viscous and inviscid stability equations. Linear stability analysis demonstrated that high-frequency disturbances occur in the laminar separation bubble case, whereas lower frequencies are present for the fully separated angles of attack. The maximum disturbance growth rates were dampened with the addition of viscosity but negligible change in peak frequency was noted.

Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling

2015 ◽  
Author(s):  
Pedro Paredes ◽  
Vassilis Theofilis ◽  
Steffen Terhaar ◽  
Kilian Oberleithner ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Flow Field ◽  
Prediction Models ◽  
Global Analysis ◽  
Local Analysis ◽  
Reacting Flow ◽  
Dynamics Modeling ◽  
Mean Flow ◽  
Global Mode ◽  
Precessing Vortex Core

Coherent flow structures in shear flows are generated by instabilities intrinsic to the hydrodynamic field. In a combustion environment, these structures may interact with the flame and cause unsteady heat release rate fluctuations. Prediction and modeling of these structures is thereby highly wanted for thermo-acoustic prediction models. In this work we apply hydrodynamic linear stability analysis to the time-averaged flow field of swirl-stabilized combustors obtained from experiments. Recent fundamental investigations have shown that the linear eigenmodes of the mean flow accurately represent the growth and saturation of the coherent structures. In this work biglobal and local stability analysis is applied to the reacting flow in an industry-relevant combustion system. Both the local and the biglobal analysis accurately predicts the onset and structure of a self-excited global instability that is known in the combustion community as a precessing vortex core (PVC). However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis wrongly predicts an unstable global growth rate. The predicted spatial distribution of the amplitude functions using both analysis agree very well to the experimentally identified global mode. The presented tools are considered as very promising for the understanding of the PVC and physics based flow control.

A Linear Stability Analysis of Cavitation in a Finite Blade Count Impeller

2000 ◽  
Vol 122 (4) ◽  
pp. 798-805 ◽  
Author(s):  
Hironori Horiguchi ◽  
Satoshi Watanabe ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Stability Analysis ◽  
Flat Plate ◽  
Steady Flow ◽  
Linear Stability ◽  
Phase Difference ◽  
Linear Stability Analysis ◽  
Previous Analysis ◽  
Flow Analysis ◽  
Cavity Volume ◽  
Inlet Duct

The linear stability analysis of cavitation in flat plate cascades corresponding to 2, 3, 4, and 5-bladed impeller was carried out to clarify the effect of the blade count on cavitation instabilities. Each blade is treated independently so that all possible modes in those impellers can be found. In steady flow analysis the alternate blade cavitation was found only for impellers with even number of blades. For 2 or 4-bladed impeller, it was confirmed that there exists no additional destabilizing mode to those found in the previous analysis in which the inter-blade phase difference of disturbance was assumed. It was shown that the modes with total cavity volume fluctuation depend on the inlet duct length while the modes without total cavity volume fluctuation are independent on the system. [S0098-2202(00)01304-3]

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