Three-Dimensional Instability of Plane Channel Flows at Subcritical Reynolds Numbers

1982 ◽  
pp. 69-86 ◽  
Author(s):  
Steven A. Orszag ◽  
Anthony T. Patera
Keyword(s):  
Three Dimensional ◽  
Plane Channel ◽  
Reynolds Numbers ◽  
Channel Flows ◽  
Dimensional Instability

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

Experimental Study on the Stability of the Flow Behind an Accelerating Circular Cylinder

2007 ◽  
Author(s):  
A. Inasawa ◽  
K. Toda ◽  
M. Asai
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Cylinder Wake ◽  
Global Instability ◽  
The Stability ◽  
Dimensional Instability ◽  
Wake Oscillation

Disturbance growth in the wake of a circular cylinder moving at a constant acceleration is examined experimentally. The cylinder is installed on a carriage moving in the still air. The results show that the critical Reynolds number for the onset of the global instability leading to a self-sustained wake oscillation increases with the magnitude of acceleration, while the Strouhal number of the growing disturbance at the critical Reynolds number is not strongly dependent on the magnitude of acceleration. It is also found that with increasing the acceleration, the Ka´rma´n vortex street remains two-dimensional even at the Reynolds numbers around 200 where the three-dimensional instability occurs to lead to the vortex dislocation in the case of cylinder moving at constant velocity or in the case of cylinder wake in the steady oncoming flow.

Dynamics and stability of the wake behind tandem cylinders sliding along a wall

2013 ◽  
Vol 722 ◽  
pp. 291-316 ◽  
Author(s):  
A. Rao ◽  
M. C. Thompson ◽  
T. Leweke ◽  
K. Hourigan
Keyword(s):  
Three Dimensional ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Feedback Cycle ◽  
Tandem Cylinders ◽  
Two Dimensional Flow ◽  
Shedding Frequency ◽  
Dimensional Instability ◽  
Unsteady Regimes

AbstractThe dynamics and stability of the flow past two cylinders sliding along a wall in a tandem configuration is studied numerically for Reynolds numbers ($\mathit{Re}$) between 20 and 200, and streamwise separation distances between 0.1 and 10 cylinder diameters. For cylinders at close separations, the onset of unsteady two-dimensional flow is delayed to higher $\mathit{Re}$ compared with the case of a single sliding cylinder, while at larger separations, this transition occurs earlier. For Reynolds numbers above the threshold, shedding from both cylinders is periodic and locked. At intermediate separation distances, the wake frequency shifts to the subharmonic of the leading-cylinder shedding frequency, which appears to be due to a feedback cycle, whereby shed leading-cylinder vortices interact strongly with the downstream cylinder to influence subsequent leading-cylinder shedding two cycles later. In addition to the shedding frequency, the drag coefficients for the two cylinders are determined for both the steady and unsteady regimes. The three-dimensional stability of the flow is also investigated. It is found that, when increasing the Reynolds number at intermediate separations, an initial three-dimensional instability develops, which disappears at higher $\mathit{Re}$. The new two-dimensional steady flow again becomes unstable, but with a different three-dimensional instability mode. At very close spacings, when the two cylinders are effectively seen by the flow as a single body, and at very large spacings, when the cylinders form independent wakes, the flow characteristics are similar to those of a single cylinder sliding along a wall.

The Development Lengths of Laminar Pipe and Channel Flows

2005 ◽  
Vol 127 (6) ◽  
pp. 1154-1160 ◽  
Author(s):  
F. Durst ◽  
S. Ray ◽  
B. Ünsal ◽  
O. A. Bayoumi
Keyword(s):  
Research Work ◽  
Plane Channel ◽  
Reynolds Numbers ◽  
Short Review ◽  
Channel Flows ◽  
Axial Position ◽  
Development Length ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Plane Channel Flow

The authors’ research work into fully developed pulsating and oscillating laminar pipe and channel flows raised questions regarding the development length of the corresponding steady flow. For this development length, i.e., the distance from the entrance of the pipe to the axial position where the flow reaches the parabolic velocity profile of the Hagen-Poiseuille flow, a wide range of contradictory data exists. This is shown through a short review of the existing literature. Superimposed diffusion and convection, together with order of magnitude considerations, suggest that the normalized development length can be expressed as L∕D=C0+C1Re and for Re→0 one obtains C0=0.619, whereas for Re→∞ one obtains C1=0.0567. This relationship is given only once in the literature and it is presumed to be valid for all Reynolds numbers. Numerical studies show that it is only valid for Re→0 and Re→∞. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: L∕D=C0′+C1′; Re, where C0′=0.631 and C1′=0.044. Finally, correlations are given to express L∕D analytically for the entire Re range for both laminar pipe and channel flows.

scholarly journals Three-dimensional flow instability in a lid-driven isosceles triangular cavity

2011 ◽  
Vol 675 ◽  
pp. 369-396 ◽  
Author(s):  
L. M. GONZÁLEZ ◽  
M. AHMED ◽  
J. KÜHNEN ◽  
H. C. KUHLMANN ◽  
V. THEOFILIS
Keyword(s):  
Flow Instability ◽  
Three Dimensional ◽  
Steady Motion ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Driven Cavity ◽  
Neutral Curves ◽  
Critical Reynolds Numbers ◽  
Dimensional Instability ◽  
Steady Laminar

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

Characteristics of Coherent Structures in Channel Flows During Low Reynolds Number Mixed Convection

2014 ◽  
Author(s):  
Ahmed Elatar ◽  
Kamran Siddiqui
Keyword(s):  
Mixed Convection ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Velocity Fields ◽  
Channel Flows ◽  
Heated Wall ◽  
Low Reynolds Numbers ◽  
Square Channel ◽  
Low Reynolds

Characteristics of coherent structures generated in channel flows during low Reynolds numbers mixed convection have been investigated in a square channel. The Gr/Re2 ranged between 21 and 206 which indicates that natural convection was dominant over forced convection. Two-dimensional velocity fields were measured using particle image velocimetry (PIV) technique in different planes to obtain a three-dimensional perspective of the flow field in the channel. The coherent structures were detected from the turbulent velocity fields using an algorithm based on the velocity gradient tensor second invariant (Q). The location of each detected coherent structure was recorded and its turbulent kinetic energy was computed. It was found that the strength of coherent structures increased with an increase in the bottom wall temperature. The results also indicate that the coherent structures present in the region away from the bottom heated wall were more energetic compared to the coherent structures present within the thermal boundary layer.

THREE-DIMENSIONAL INSTABILITY OF VISCOUS LIQUID SHEETS

1996 ◽  
Vol 6 (6) ◽  
pp. 649-665 ◽  
Author(s):  
E. A. Ibrahim ◽  
E. T. Akpan
Keyword(s):  
Viscous Liquid ◽  
Three Dimensional ◽  
Liquid Sheets ◽  
Dimensional Instability

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

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