Transient growth in developing plane and Hagen Poiseuille flow

2005 ◽  
Vol 461 (2057) ◽  
pp. 1311-1333 ◽  
Author(s):  
Peter W Duck
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Alternative Mechanism ◽  
Fully Developed Flow ◽  
Circular Pipes ◽  
Flow Disturbances ◽  
High Reynolds ◽  
The Stability

The stability of developing entry flow in both two-dimensional channels and circular pipes is investigated for large Reynolds numbers. The basic flow is generated by uniform flow entering a channel/pipe, which then provokes the growth of boundary layers on the walls, until (far downstream) fully developed flow is attained; the length for this development is well known to be (Reynolds number)×the channel/pipe width/diameter. This enables the use of high-Reynolds-number theory, leading to boundary-layer-type equations which govern the flow; as such, there is no need to impose heuristic parallel-flow approximations. The resulting base flow is shown to be susceptible to significant, three-dimensional, transient (initially algebraic) growth in the streamwise direction, and, consequently, large amplifications to flow disturbances are possible (followed by ultimate decay far downstream). It is suggested that this initial amplification of disturbances is a possible and alternative mechanism for flow transition.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

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.

Ice ripple formation at large Reynolds numbers

2012 ◽  
Vol 694 ◽  
pp. 225-251 ◽  
Author(s):  
Carlo Camporeale ◽  
Luca Ridolfi
Keyword(s):  
Free Surface ◽  
Complete Solution ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Thermal Boundary Conditions ◽  
Ripple Formation ◽  
High Reynolds ◽  
Lower Temperature ◽  
The Stability ◽  
Stefan Condition

AbstractA free-surface-induced morphological instability is studied in the laminar regime at large Reynolds numbers ($\mathit{Re}= 1\text{{\ndash}} 1{0}^{3} $) and on sub-horizontal walls ($\vartheta \lt 3{0}^{\ensuremath{\circ} } $). We analytically and numerically develop the stability analysis of an inclined melting–freezing interface bounding a free-surface laminar flow. The complete solution of both the linearized flow field and the heat conservation equations allows the exact derivation of the upper and lower temperature gradients at the interface, as required by the Stefan condition, from which the dispersion relationship is obtained. The eigenstructure is obtained and discussed. Free-surface dynamics appears to be crucial for the triggering of upstream propagating ice ripples, which grow at the liquid–solid interface. The kinematic and the dynamic conditions play a key role in controlling the formation of the free-surface fluctuations; these latter induce a streamline distortion with an increment of the wall-normal velocities and a destabilizing phase shift in the net heat transfer to the interface. Three-dimensional effects appear to be crucial at high Reynolds numbers. The role of inertia forces, vorticity, and thermal boundary conditions are also discussed.

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.

Particle capture by a circular cylinder in the vortex-shedding regime

2013 ◽  
Vol 733 ◽  
pp. 171-188 ◽  
Author(s):  
Alexis Espinosa-Gayosso ◽  
Marco Ghisalberti ◽  
Gregory N. Ivey ◽  
Nicole L. Jones
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Aquatic Vegetation ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Capture Efficiency ◽  
Particle Capture ◽  
Number Range ◽  
Rapid Changes ◽  
High Reynolds

AbstractParticle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism for a range of environmental processes including suspension feeding by corals and ‘filtering’ by aquatic vegetation. In this paper, we use two- and three-dimensional direct numerical simulations to quantify the capture efficiency ($\eta $) of low-inertia particles by a circular cylindrical collector at intermediate Reynolds numbers in the vortex-shedding regime (i.e. for $47\lt \mathit{Re}\leq 1000$, where $\mathit{Re}$ is the collector Reynolds number). We demonstrate that vortex shedding induces oscillations near the leading face of the collector which greatly affect the quantity and distribution of captured particles. Unlike in steady, low-$\mathit{Re}$ flow, particles directly upstream of the collector are not the most likely to be captured. Our results demonstrate the dependence of the time-averaged capture efficiency on $\mathit{Re}$ and particle size, improving the predictive capability for the capture of particles by aquatic collectors. The transition to theoretical high-Reynolds-number behaviour (i.e. $\eta \sim {\mathit{Re}}^{1/ 2} $) is complex due to comparatively rapid changes in wake conditions in this Reynolds number range.

Efficient Computation of Three-Dimensional Flow in Helically Corrugated Hoses Including Swirl

2009 ◽  
Author(s):  
Bas J. van der Linden ◽  
Emmanuel Ory ◽  
Jacques Dam ◽  
Arris S. Tijsseling ◽  
Maxim Pisarenco
Keyword(s):  
Friction Factor ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Efficient Computation ◽  
Time Saving ◽  
Fully Developed Flow ◽  
High Reynolds ◽  
Positive Effect ◽  
Moody Diagram

In this article we propose an efficient method to compute the friction factor of helically corrugated hoses carrying flow at high Reynolds numbers. A comparison between computations of several turbulence models is made with experimental results for corrugation sizes that fall outside the range of validity of the Moody diagram. To do this efficiently we implement quasi-periodicity. Using the appropriate boundary conditions and matching body force, we only need to simulate a single period of the corrugation to find the friction factor for fully developed flow. A second technique is introduced by the construction of an appropriately twisted wedge, which allows us to furthermore reduce the problem by a further dimension while accounting for the Beltrami symmetry that is present in the full three-dimensional problem. We make a detailed analysis of the accuracy and time-saving that this novelty introduces. We show that the swirl inside the flow, which is introduced by the helical boundary, has a positive effect on the friction factor. Furthermore, we give a prediction for which corrugation angles the assumption of axisymmetry is no longer valid. It then has to make place for Beltrami-symmetry if accurate results are required.

Instability of optimal non-axisymmetric base-flow deviations in pipe Poiseuille flow

2007 ◽  
Vol 588 ◽  
pp. 189-215 ◽  
Author(s):  
GUY BEN-DOV ◽  
JACOB COHEN
Keyword(s):  
Reynolds Number ◽  
Minimum Energy ◽  
Axisymmetric Flow ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Transient Growth ◽  
Mathematical Technique ◽  
Pipe Radius ◽  
Exponential Instability ◽  
The Stability

The stability of pipe flow when mildly deviating from the developed Poiseuille profile by a non-axisymmetric azimuthally periodic distortion is examined. The motivation for this is to consider deviations, the origin of which may be attributed to small-amplitude disturbances having sinusoidal periodicity along the azimuthal coordinate, which are known to be the ones most amplified by the transient growth linear mechanism. A mathematical technique for finding the minimum energy density of azimuthally periodic deviations triggering exponential instability is presented. The results show that owing to bifurcations multiple solutions of optimal deviations exist. As the Reynolds number is increased additional bifurcations appear and create more distinct solutions. The different solutions correspond to different radial distributions of the deviations, and at Reynolds numbers of about 2000 they are distributed over less than a half of the pipe radius. It is found that the dependence of the optimal deviation velocity leading to instability on the Reynolds number Re is approximately 20/Re. A comparison to axisymmetric base-flow deviations shows that the minimum energy required for an azimuthally periodic deviation to trigger instability is almost twice that for the axisymmetric flow. However, azimuthally periodic deviations, which are shown to have a streaky pattern, may have a role in the self-sustaining process. They may be formed as a result of a transient growth amplification of initial streamwise rolls and can produce, via self-interactions between the resulting growing waves, patterns of streamwise rolls as well.

Computational Study of Taper Effect of a Hydrofoil at Different Reynolds Numbers on the Length of Cavity and Lift and Drag Coefficients

2009 ◽  
Author(s):  
Mohammad J. Izadi ◽  
Mahdi Mirtorabi
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Cavity Length ◽  
Computational Study ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
High Reynolds ◽  
Lift And Drag

In this paper a cavitating flow around a three dimensional tapered hydrofoil in an incompressible fluid is modeled and studied. The variables in this study are the taper ratio, angle of attack and the Reynolds number. The taper ratio changes from 0.2 to 1, the angles of attack varies from −2 to 12 degrees and all these are computed at two Reynolds numbers (Re = 5.791·107 and Re = 1.99·108). The flow is assumed to be unsteady and isothermal. Coefficients of drag and lift and also the cavity length are computed numerically. Comparing the numerical results of five investigated models (five tapered hydrofoils) and the work done by Kermeen experimentally, it can be seen that the tapered hydrofoil in some cases gave better results, reducing the cavity length and improving the lift coefficient. At the low Reynolds number, the length of the cavity is calculated to be small in comparison with the length gained at the high Reynolds number, and therefore the change of the taper and the angles of attack did change the amount of the lift coefficient as much. For high Reynolds number, as the angle of attack increased, the tapering effect became more important and the best lift coefficient and minimum cavity length is obtained at a taper ratio of 0.4 for an averaged angles of attack.

Airfoil Section Characteristics at a Low Reynolds Number

1997 ◽  
Vol 119 (1) ◽  
pp. 129-135 ◽  
Author(s):  
Shigeru Sunada ◽  
Akitoshi Sakaguchi ◽  
Keiji Kawachi
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Aerodynamic Performance ◽  
Flight Performance ◽  
High Reynolds ◽  
Shape Characteristics ◽  
Sharp Leading Edge

The aerodynamic characteristics of airfoils operating at Re = 4 × 103 were examined, varying the parameters related to the airfoil shape such as thickness, camber, and roughness. Airfoils with good aerodynamic performance at this Re have the following shape characteristics: (1) they are thinner than airfoils for higher Re numbers, (2) they have a sharp leading edge, and (3) they have a camber of about five percent with its maximum camber at about mid-chord. The characteristics of airfoils are strongly affected by leading edge vortices. The measured two-dimensional airfoil characteristics indicate that the planform, which greatly affects the flight performance of the three-dimensional wing at high Reynolds numbers, has little effect on the flight performance at this Reynolds number.

scholarly journals A Numerical and Experimental Study of the Aerodynamics and Stability of a Horizontal Parachute

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mazyar Dawoodian ◽  
Abdolrahman Dadvand ◽  
Amir Hassanzadeh
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Numerical Simulations ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Flow Conditions ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
The Stability ◽  
Good Agreement

The flow past a parachute with and without a vent hole at the top is studied both experimentally and numerically. The effects of Reynolds number and vent ratio on the flow behaviour as well as on the drag coefficient are examined. The experiments were carried out under free-flow conditions. In the numerical simulations, the flow was considered as unsteady and turbulent and was modelled using the standard - turbulence model. The experimental results reveal good agreement with the numerical ones. In both the experiments and numerical simulations, the Reynolds number was varied from 85539 to 357250 and the vent ratio was increased from zero to 20%. The results show that the drag coefficient decreases by increasing the Reynolds number for all the cases tested. In addition, it was found that at low and high Reynolds numbers, the parachutes, respectively, with 4% vent ratio and without vent are deemed more efficient. One important result of the present work is related to the effect of vent ratio on the stability of the parachute.

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