Unsteady state fluid structure of two-sided nonfacing lid-driven cavity induced by a semicircle at different radii sizes and velocity ratios

2019 ◽  
Vol 30 (08) ◽  
pp. 1950060 ◽  
Author(s):  
Basma Souayeh ◽  
Fayçal Hammami ◽  
Najib Hdhiri ◽  
Huda Alfannakh
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Velocity Ratio ◽  
Time History ◽  
Standard Case ◽  
Driven Cavity ◽  
Opposite Case ◽  
Critical Reynolds Numbers ◽  
Volume Method ◽  
Radius Size

This paper aims in analyzing the effect of velocity ratio [Formula: see text] and Radius size of an inner semicircle inserted at the bottom wall of two-sided nonfacing lid-driven cavity on the bifurcation occurrence phenomena. The study has been performed by using finite volume method (FVM) and multigrid acceleration for certain pertinent parameters; Reynolds number, velocity ratios ([Formula: see text]) by step of 0.25 and Radius size of the inner semicircle ([Formula: see text]) by step of 0.05. An analysis of the flow evolution shows that, when increasing Re beyond a certain critical value, the flow becomes unstable then bifurcates for various velocity ratios and radius size of the semicircle. Therefore, critical Reynolds numbers are determined for each case. It is worth to mention that the transition to unsteadiness follows the classical scheme of a Hopf bifurcation. Results show also that in the standard case of a single lid-driven cavity ([Formula: see text]), the highest critical Reynolds number corresponds to the lowest radius of the semicircle and the same for ([Formula: see text]). Conversely, from ([Formula: see text]) where the left moving lid take effect, the opposite phenomenon occurs. In harmony with this, it has been found that elongating the cylinder radius accelerates the appearance of the unsteady regime and delays it in the opposite case. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. The numerical results are correlated in a sophisticated correlation of the critical Reynolds number with other parameters.

Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity

2020 ◽  
Vol 14 (3) ◽  
pp. 7269-7281
Author(s):  
El Amin Azzouz ◽  
Samir Houat
Keyword(s):  
Velocity Ratio ◽  
Two Dimensional ◽  
Lower Side ◽  
Square Cavity ◽  
Driven Cavity ◽  
Parallel Motion ◽  
Bottom Cavity ◽  
Secondary Vortices ◽  
Volume Method ◽  
Fluid Characteristics

The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers

1983 ◽  
Vol 133 ◽  
pp. 265-285 ◽  
Author(s):  
Günter Schewe
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Dynamic Range ◽  
Reynolds Numbers ◽  
Band Spectrum ◽  
Transitional Region ◽  
Force Measurements ◽  
Unsteady Forces ◽  
Number Range ◽  
Critical Reynolds Numbers

Force measurements were conducted in a pressurized wind tunnel from subcritical up to transcritical Reynolds numbers 2.3 × 104[les ]Re[les ] 7.1 × 106without changing the experimental arrangement. The steady and unsteady forces were measured by means of a piezobalance, which features a high natural frequency, low interferences and a large dynamic range. In the critical Reynolds-number range, two discontinuous transitions were observed, which can be interpreted as bifurcations at two critical Reynolds numbers. In both cases, these transitions are accompanied by critical fluctuations, symmetry breaking (the occurrence of a steady lift) and hysteresis. In addition, both transitions were coupled with a drop of theCDvalue and a jump of the Strouhal number. Similar phenomena were observed in the upper transitional region between the super- and the transcritical Reynolds-number ranges. The transcritical range begins at aboutRe≈ 5 × 106, where a narrow-band spectrum is formed withSr(Re= 7.1 × 106) = 0.29.

The Stability of Water Flow Over Heated and Cooled Flat Plates

1968 ◽  
Vol 90 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Ahmed R. Wazzan ◽  
T. Okamura ◽  
A. M. O. Smith
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Temperature ◽  
Heated Wall ◽  
Flat Plates ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Sommerfeld Equation

The theory of two-dimensional instability of laminar flow of water over solid surfaces is extended to include the effects of heat transfer. The equation that governs the stability of these flows to Tollmien-Schlichting disturbances is the Orr-Sommerfeld equation “modified” to include the effect of viscosity variation with temperature. Numerical solutions to this equation at high Reynolds numbers are obtained using a new method of integration. The method makes use of the Gram-Schmidt orthogonalization technique to obtain linearly independent solutions upon numerically integrating the “modified Orr-Sommerfeld” equation using single precision arithmetic. The method leads to satisfactory answers for Reynolds numbers as high as Rδ* = 100,000. The analysis is applied to the case of flow over both heated and cooled flat plates. The results indicate that heating and cooling of the wall have a large influence on the stability of boundary-layer flow in water. At a free-stream temperature of 60 deg F and wall temperatures of 60, 90, 120, 135, 150, 200, and 300deg F, the critical Reynolds numbers Rδ* are 520, 7200, 15200, 15600, 14800, 10250, and 4600, respectively. At a free-stream temperature of 200F and wall temperature of 60 deg F (cooled case), the critical Reynolds number is 151. Therefore, it is evident that a heated wall has a stabilizing effect, whereas a cooled wall has a destabilizing effect. These stability calculations show that heating increases the critical Reynolds number to a maximum value (Rδ* max = 15,700 at a temperature of TW = 130 deg F) but that further heating decreases the critical Reynolds number. In order to determine the influence of the viscosity derivatives upon the results, the critical Reynolds number for the heated case of T∞ = 40 and TW = 130 deg F was determined using (a) the Orr-Sommerfeld equation and (b) the present governing equation. The resulting critical Reynolds numbers are Rδ* = 140,000 and 16,200, respectively. Therefore, it is concluded that the terms pertaining to the first and second derivatives of the viscosity have a considerable destabilizing influence.

scholarly journals Asymmetrical Flow Driving in Two-Sided Lid-Driven Square Cavity with Antiparallel Wall Motion

2020 ◽  
Vol 330 ◽  
pp. 01009
Author(s):  
El Amin Azzouz ◽  
Samir Houat
Keyword(s):  
Wall Motion ◽  
Velocity Ratio ◽  
Two Dimensional ◽  
Square Cavity ◽  
Driven Cavity ◽  
Dimensional Flow ◽  
Fluid Properties ◽  
Two Dimensional Flow ◽  
Vertical Walls ◽  
Volume Method

The two-dimensional flow in a two-sided lid-driven cavity is often handled numerically for the same imposed wall velocities (symmetrical driving) either for parallel or antiparallel wall motion. However, in this study, we present a finite volume method (FVM) based on the second scheme of accuracy to numerically explore the steady two-dimensional flow in a two-sided lid-driven square cavity for antiparallel wall motion with different imposed wall velocities (asymmetrical driving). The top and the bottom walls of the cavity slide in opposite directions simultaneously at different velocities related to various imposed velocity ratios, λ = -2, -6, and -10, while the two remaining vertical walls are stationary. The results show that varying the velocity ratio and consequently the Reynolds ratios have a significant effect on the flow structures and fluid properties inside the cavity.

Stability of obliquely driven cavity flow

2021 ◽  
Vol 928 ◽  
Author(s):  
Pierre-Emmanuel des Boscs ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Couette Flow ◽  
Critical Reynolds Number ◽  
Cavity Flow ◽  
Basic Flow ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
Driven Cavity Flow ◽  
Yaw Angle

The linear stability of the incompressible flow in an infinitely extended cavity with rectangular cross-section is investigated numerically. The basic flow is driven by a lid which moves tangentially, but at yaw with respect to the edges of the cavity. As a result, the basic flow is a superposition of the classical recirculating two-dimensional lid-driven cavity flow orthogonal to a wall-bounded Couette flow. Critical Reynolds numbers computed by linear stability analysis are found to be significantly smaller than data previously reported in the literature. This finding is confirmed by independent nonlinear three-dimensional simulations. The critical Reynolds number as a function of the yaw angle is discussed for representative aspect ratios. Different instability modes are found. Independent of the yaw angle, the dominant instability mechanism is based on the local lift-up process, i.e. by the amplification of streamwise perturbations by advection of basic flow momentum perpendicular to the sheared basic flow. For small yaw angles, the instability is centrifugal, similar as for the classical lid-driven cavity. As the spanwise component of the lid velocity becomes dominant, the vortex structures of the critical mode become elongated in the direction of the bounded Couette flow with the lift-up process becoming even more important. In this case the instability is made possible by the residual recirculating part of the basic flow providing a feedback mechanism between the streamwise vortices and the streamwise velocity perturbations (streaks) they promote. In the limit when the basic flow approaches bounded Couette flow the critical Reynolds number increases very strongly.

Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow

2018 ◽  
Vol 28 (4) ◽  
pp. 943-962 ◽  
Author(s):  
Faicel Hammami ◽  
Nader Ben-Cheikh ◽  
Brahim Ben-Beya ◽  
Basma Souayeh
Keyword(s):  
Reynolds Number ◽  
Hopf Bifurcation ◽  
Phase Space ◽  
Time History ◽  
Content Type ◽  
Driven Cavity ◽  
State Flow ◽  
Aspect Ratios ◽  
Unsteady Regime ◽  
Periodic State

Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0). Design/methodology/approach The numerical method is based on the FVM and multigrid acceleration. Findings Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories. Originality/value The bifurcations between steady and unsteady states are investigated.

Stability of film flow over inclined topography based on a long-wave nonlinear model

2013 ◽  
Vol 729 ◽  
pp. 638-671 ◽  
Author(s):  
D. Tseluiko ◽  
M. G. Blyth ◽  
D. T. Papageorgiou
Keyword(s):  
Reynolds Number ◽  
Model Equation ◽  
Critical Reynolds Number ◽  
Wave Model ◽  
Absolute Instability ◽  
Spatial Period ◽  
Integer Multiple ◽  
Long Wave ◽  
Critical Reynolds Numbers ◽  
Theoretical Finding

AbstractThe stability of a viscous liquid film flowing under gravity down an inclined wall with periodic corrugations is investigated. A long-wave model equation valid at near-critical Reynolds numbers is used to study the film dynamics, and calculations are performed for either sinusoidal or rectangular wall corrugations assuming either a fixed flow rate in the film or a fixed volume of fluid within each wall period. Under the two different flow assumptions, steady solution branches are delineated including subharmonic branches, for which the period of the free surface is an integer multiple of the wall period, and the existence of quasi-periodic branches is demonstrated. Floquet–Bloch theory is used to determine the linear stability of steady, periodic solutions and the nature of any instability is analysed using the method of exponentially weighted spaces. Under certain conditions, and depending on the wall period, the flow may be convectively unstable for small wall amplitudes but undergo transition to absolute instability as the wall amplitude increases, a novel theoretical finding for this class of flows; in other cases, the flow may be convectively unstable for small wall amplitudes but stable for larger wall amplitudes. Solutions with the same spatial period as the wall become unstable at a critical Reynolds number, which is strongly dependent on the period size. For sufficiently small wall periods, the corrugations have a destabilizing effect by lowering the critical Reynolds number above which instability occurs. For slightly larger wall periods, small-amplitude corrugations are destabilizing but sufficiently large-amplitude corrugations are stabilizing. For even larger wall periods, the opposite behaviour is found. For sufficiently large wall periods, the corrugations are destabilizing irrespective of their amplitude. The predictions of the linear theory are corroborated by time-dependent simulations of the model equation, and the presence of absolute instability under certain conditions is confirmed. Boundary element simulations on an inverted substrate reveal that wall corrugations can have a stabilizing effect at zero Reynolds number.

Influence of the Reynolds Number on Spar Vortex Induced Motions (VIM): Multiple Scale Model Test Comparisons

2009 ◽  
Author(s):  
Dominique Roddier ◽  
Tim Finnigan ◽  
Stergios Liapis
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Multiple Scale ◽  
Scale Model ◽  
Taylor Model ◽  
Testing Procedures ◽  
Critical Reynolds Numbers ◽  
Number Of Publications ◽  
Six Degree Of Freedom ◽  
First Time

There have been a number of publications on spar Vortex-Induced-Motions (VIM) model testing procedures and results over the past few years. All tests allowing full 6 DOF response to date have been done under sub-critical Reynolds Number conditions. Prior to 2006 tests under super-Critical Reynolds Number conditions had only been done with a fully submerged 1 DOF rig. Early in 2006, a series of Spar VIM experiments was undertaken in three different facilities: Force Technology in Denmark, the David Taylor Model Basin in Bethesda Maryland and UC Berkeley in California. The motivation of this work was to investigate the effect of Reynolds Number and hull appurtenances on spar vortex induced motions (VIM) for a vertically moored 6DOF truss spar hull model with strakes. The three series of tests were done at both sub and super-critical Reynolds Numbers, with matching Froude Numbers. In order to assess the importance of appurtenances (chains, pipes and anodes) and current heading on strake effectiveness, tests were done with several sets of appurtenances, and at various headings and reduced velocities. These experiments were unique and groundbreaking in many ways: • For the first time the issue of scalability of Spar VIM experiments has been addressed and tested in a systematic way. • For the first time the effect of appurtenances (pipes, chains and anodes) was systematically tested. • The model tested at the David Taylor Model Basin (DTMB) had a diameter of 5.8′ and a weight of 15,600 lbs. It is the largest spar model ever tested. Furthermore the DTMB tests series is the only supercritical spar VIM performed with a six degree of freedom (6DOF) rig. This paper describes the three model tests campaigns, focusing on the efforts made to ensure three complete geo-similar programs, and on the significant findings of these tests, effectively that the influence of Re is to add some conservativeness in the results as the testing scale is smaller.

On the stability of flow in an elliptic pipe which is nearly circular

1978 ◽  
Vol 87 (2) ◽  
pp. 233-241 ◽  
Author(s):  
A. Davey
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Cross Section ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Major Axis ◽  
Reynolds Numbers ◽  
Minor Axis ◽  
Critical Reynolds Numbers ◽  
The Stability

The linear stability of Poiseuille flow in an elliptic pipe which is nearly circular is examined by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. We show that the temporal damping rates of non-axisymmetric infinitesimal disturbances which are concentrated near the wall of the pipe are decreased by the ellipticity. In particular we estimate that if the length of the minor axis of the cross-section of the pipe is less than about 96 ½% of that of the major axis then the flow will be unstable and a critical Reynolds number will exist. Also we calculate estimates of the ellipticities which will produce critical Reynolds numbers ranging from 1000 upwards.

Three-Dimensional Flow Problems in a Lid-Driven Cubical Cavity with a Circular Cylinder

2017 ◽  
Vol 18 (3-4) ◽  
pp. 187-196 ◽  
Author(s):  
Faycel Hammami ◽  
Basma Souayeh ◽  
Brahim Ben-Beya
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Transverse Velocity ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Number Range ◽  
Driven Cavity ◽  
Flow Problems ◽  
Volume Method ◽  
Cubical Cavity

AbstractThree-dimensional numerical simulations were conducted for lid-driven cavity phenomena around an inner circular cylinder positioned in the center of a cubic enclosure in the Reynolds number range of (100≤Re≤2000) at the Prandtl number of Pr=0.71. The numerical method is based on the finite volume method (FVM) and multigrid acceleration. In this study, the transition of the flow regime from steady state to the unsteady state and consequent three-dimensionality in the system induced by the increase of Reynolds number to (Re=1798) were investigated. By increasing further Reynolds number over the critical value, the flow in the cavity exhibits a complex behavior. Typical distributions of the transverse velocity contours and kinetic energy fields at (Re=2000) have been obtained.

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