Moderate-aspect-ratio elliptical cylinders in simple shear with inertia

2001 ◽  
Vol 442 ◽  
pp. 241-266 ◽  
Author(s):  
C. M. ZETTNER ◽  
M. YODA
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Simple Shear ◽  
Critical Reynolds Number ◽  
Rotation Period ◽  
Elliptical Cylinder ◽  
Aspect Ratios ◽  
Periodic Behaviour ◽  
Elliptical Cylinders ◽  
Stationary Behaviour

The effects of fluid inertia, geometry and flow confinement upon the dynamics of neutrally buoyant elliptical and non-elliptical cylinders over a wide range of aspect ratios in simple shear are studied experimentally for moderate shear-based Reynolds numbers Re. Unlike circular cylinders, elliptical cylinders of moderate aspect ratio cease to rotate, coming to rest at a nearly horizontal equilibrium orientation above a critical Reynolds number Recr (‘stationary behaviour’). Simple dynamics arguments are proposed to explain the effects of aspect ratio and flow confinement upon critical Reynolds number and particle dynamics. Experiments confirm results from previous numerical simulations that the normalized rotation period for Re < Recr (‘periodic behaviour’) is proportional to (Recr − Re)−0.5 for small Recr − Re. For periodic behaviour, maximum and minimum angular cylinder speeds both decrease, and period increases, as Recr − Re decreases. For stationary behaviour, the cylinder rotates until it achieves a nearly horizontal equilibrium orientation, which increases as the Reynolds number approaches the critical value. The experimental results are in good agreement with previous lattice-Boltzmann simulations for a 0.5 aspect ratio cylinder.Variation in angular speed over a rotation period decreases as aspect ratio increases, while Recr increases as flow confinement and aspect ratio increase. A non-elliptical cylinder of 0.33 aspect ratio also ceases to rotate above a certain Reynolds number. Although Recr is different from the corresponding elliptical case, the scaling of the normalized rotation period for this body as Recr → Re is identical to that for the elliptical cylinder, suggesting that this scaling is independent of particle shape (i.e. ‘universal’, as conjectured in previous numerical studies). The results also demonstrate that a variety of centrosymmetric bodies with aspect ratios below unity transition from periodic to stationary behaviour.

scholarly journals Numerical Computations of Vortex Formation Length in Flow Past an Elliptical Cylinder

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 157
Author(s):  
Matthew Karlson ◽  
Bogdan G. Nita ◽  
Ashwin Vaidya
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Vortex Formation ◽  
Project Based Learning ◽  
Unsteady Regime ◽  
Karman Vortex ◽  
Elliptical Cylinders ◽  
Asymmetric Configuration

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the bifurcation of the Karman vortex from steady symmetric to the unsteady, asymmetric configuration. Additionally, relationships between the vortex length and aspect ratio are also explored. The work presented here is an example of a module that can be used in a project based learning course on computational fluid dynamics.

Heat Transfer for High Aspect Ratio Rectangular Channels in a Stationary Serpentine Passage With Turbulated and Smooth Surfaces

2013 ◽  
Author(s):  
Matthew A. Smith ◽  
Randall M. Mathison ◽  
Michael G. Dunn
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Internal Cooling ◽  
Number Range ◽  
Aspect Ratios ◽  
Parallel Configuration

Heat transfer distributions are presented for a stationary three passage serpentine internal cooling channel for a range of engine representative Reynolds numbers. The spacing between the sidewalls of the serpentine passage is fixed and the aspect ratio (AR) is adjusted to 1:1, 1:2, and 1:6 by changing the distance between the top and bottom walls. Data are presented for aspect ratios of 1:1 and 1:6 for smooth passage walls and for aspect ratios of 1:1, 1:2, and 1:6 for passages with two surfaces turbulated. For the turbulated cases, turbulators skewed 45° to the flow are installed on the top and bottom walls. The square turbulators are arranged in an offset parallel configuration with a fixed rib pitch-to-height ratio (P/e) of 10 and a rib height-to-hydraulic diameter ratio (e/Dh) range of 0.100 to 0.058 for AR 1:1 to 1:6, respectively. The experiments span a Reynolds number range of 4,000 to 130,000 based on the passage hydraulic diameter. While this experiment utilizes a basic layout similar to previous research, it is the first to run an aspect ratio as large as 1:6, and it also pushes the Reynolds number to higher values than were previously available for the 1:2 aspect ratio. The results demonstrate that while the normalized Nusselt number for the AR 1:2 configuration changes linearly with Reynolds number up to 130,000, there is a significant change in flow behavior between Re = 25,000 and Re = 50,000 for the aspect ratio 1:6 case. This suggests that while it may be possible to interpolate between points for different flow conditions, each geometric configuration must be investigated independently. The results show the highest heat transfer and the greatest heat transfer enhancement are obtained with the AR 1:6 configuration due to greater secondary flow development for both the smooth and turbulated cases. This enhancement was particularly notable for the AR 1:6 case for Reynolds numbers at or above 50,000.

Numerical Prediction of Contaminant Removal from Cavity in Horizontal Channel by Constrained Interpolated Profile Method

2014 ◽  
Vol 695 ◽  
pp. 384-388
Author(s):  
Nor Azwadi Che Sidik ◽  
A.S. Ahmad Sofianuddin ◽  
K.Y. Ahmat Rajab
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Removal Rate ◽  
Contaminant Removal ◽  
Square Cavity ◽  
Profile Method ◽  
Aspect Ratios ◽  
Contaminants Removal ◽  
Parabolic Flow ◽  
High Removal Rate

In this paper, Constrained Interpolated Profile Method (CIP) was used to simulate contaminants removal from square cavity in channel flow. Predictions were conducted for the range of aspect ratios from 0.25 to 4.0. The inlet parabolic flow with various Reynolds number from 50 to 1000 was used for the whole presentation with the same properties of contaminants and fluid. The obtained results indicated that the percentage of removal increased at high aspect ratio of cavity and higher Reynolds number of flow but it shows more significant changes as increasing aspect ratio rather than increasing Reynolds number. High removal rate was found at the beginning of the removal process.

Power Augmentation of a HAWT by Mie-type Tip Vanes, considering Wind Tunnel Flow Visualisation, Blade-Aspect Ratios and Reynolds Number

2003 ◽  
Vol 27 (3) ◽  
pp. 183-194 ◽  
Author(s):  
Yukimaru Shimizu ◽  
Edmond Ismaili ◽  
Yasunari Kamada ◽  
Takao Maeda
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Aspect Ratio ◽  
Reynolds Numbers ◽  
Flow Visualisation ◽  
Velocity Measurements ◽  
Horizontal Axis Wind Turbine ◽  
Aspect Ratios ◽  
Detailed Surface ◽  
Blade Tips

Wind tunnel results are reported concerning the effects of blade aspect ratio and Reynolds number on the performance of a horizontal axis wind turbine (HAWT) with Mie-type1 tip attachments. The flow behaviour around the blade tips and the Mie-type tip vanes is presented. Detailed surface oil film visualization and velocity measurements around the blade tips, with and without Mie vanes, were obtained with the two-dimensional, Laser-Doppler Velocimetry method. Experiments were performed with rotors having blades with different aspect ratio and operating at different Reynolds numbers. The properties of the vortices generated by the Mie vanes and the blade tips were carefully studied. It was found that increased power augmentation by Mie vanes is achieved with blades having smaller aspect ratio and smaller Reynolds number.

Three-Dimensional Thermocapillary Convection in Open Cylindrical Annuli

2000 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Time Dependent ◽  
Infinite Layer ◽  
Aspect Ratios ◽  
Temperature Oscillations ◽  
Good Agreement

Abstract Three-dimensional, time-dependent thermocapillary convection in open cylindrical containers is investigated numerically. Results for aspect ratios (Ar) of 1, 2.5, 8, and 16 and a Prandtl number of 6.84 are obtained to compare the results of numerical simulations with ongoing experiments. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re). Transition to oscillatory states occurs at critical values of Re which depend on Ar. With Ar = 1.0 and 2.5, we observe, respectively, 5 and 9 azimuthal wavetrains travelling clockwise at the free surface near the critical Re. With Ar = 8.0 and 16.0, there are substantially more, but pulsating waves near the critical Re. In the case of Ar = 16.0, which approaches the conditions in an infinite layer, our results are in good agreement with linear theory. While the critical Reynolds number decreases with increasing aspect ratio in the case of azimuthal rotating waves, it increases with increasing aspect ratio in the case of azimuthal pulsating waves. The critical frequency of temperature oscillations is found to decrease linearly with increasing Ar. We have also computed supercritical time-dependent states and find that while the frequency increases with increasing Re near the critical region, the frequency of supercritical convection decreases with Re.

scholarly journals Linear biglobal analysis of Rayleigh–Bénard instabilities in binary fluids with and without throughflow

2012 ◽  
Vol 713 ◽  
pp. 216-242 ◽  
Author(s):  
Jun Hu ◽  
Daniel Henry ◽  
Xie-Yuan Yin ◽  
Hamda BenHadid
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Critical Rayleigh Number ◽  
Two Dimensional ◽  
Binary Fluids ◽  
Transverse Modes ◽  
Aspect Ratios ◽  
Rayleigh Benard ◽  
Mode A

AbstractThree-dimensional Rayleigh–Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor $\psi = \ensuremath{-} 0. 01$, giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as ${S}_{l} $ modes (those which keep the left–right symmetry) or ${R}_{x} $ modes (those which keep the symmetry of rotation of $\lrm{\pi} $ about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers $k$ have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number ${\mathit{Ra}}_{c} $. With the increase of the duct aspect ratio $A$, the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value ${\mathit{Ra}}_{c} = 1743. 894$ obtained in a two-dimensional situation, one of the mode (a ${S}_{l} $ mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities ($k\approx 0$) corresponding to either ${S}_{l} $ or ${R}_{x} $ modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio $A$ is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios $A$, the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as $A= 7$, different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.

An Experimental Study of Convective Heat Transfer in Radially Rotating Rectangular Ducts

1991 ◽  
Vol 113 (3) ◽  
pp. 604-611 ◽  
Author(s):  
C. Y. Soong ◽  
S. T. Lin ◽  
G. J. Hwang
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Rotational Speed ◽  
Main Flow ◽  
Buoyancy Flow ◽  
Aspect Ratios

The paper presents an experimental study of convective heat transfer in radially rotating isothermal rectangular ducts with various height and width aspect ratios. The convective heat transfer is affected by secondary flows resulting from Coriolis force and the buoyancy flow, which is in turn due to the centrifugal force in the duct. The growth and strength of the secondary flow depend on the rotational Reynolds number; the effect of the buoyancy flow is characterized by the rotational Rayleigh number. The aspect ratio of the duct may affect the secondary flow and the buoyancy flow, and therefore is also a critical parameter in the heat transfer mechanism. In the present work the effects of the main flow, the rotational speed, and the aspect ratio γ on heat transfer are subjects of major interest. Ducts of aspect ratios γ=5, 2, 1, 0.5, and 0.2 at rotational speed up to 3000 rpm are studied. The main flow Reynolds number ranges from 700 to 20,000 to cover the laminar, transitional, and turbulent flow regimes in the duct flow. Test data and discussion are presented.

On the linear instability of elliptic pipe flow

1996 ◽  
Vol 316 ◽  
pp. 307-324 ◽  
Author(s):  
R. R. Kerswell ◽  
A. Davey
Keyword(s):  
Aspect Ratio ◽  
Pipe Flow ◽  
Critical Reynolds Number ◽  
Linear Instability ◽  
Asymptotic Result ◽  
Ratio Analysis ◽  
Plane Poiseuille Flow ◽  
Small Aspect Ratio ◽  
Aspect Ratios ◽  
Ratio Asymptotics

The linear stability of elliptic pipe flow is considered for finite aspect ratios thereby bridging the gap between the small-aspect-ratio analysis of Davey & Salwen (1994) and the large-aspect-ratio asymptotics of Hocking (1977). The flow is found to become linearly unstable above an aspect ratio of about 10.4 to the spanwise-modulated analogue of the Orr-Sommerfeld mode to which plane Poiseuille flow first loses stability. This disturbance is found to possess a series of intense vortices along its critical layer at lateral stations far removed from the central minor axis. The critical Reynolds number appears to fall from infinity as the aspect ratio increases above 10.4, ultimately approaching Hocking's (1977) asymptotic result at much larger aspect ratios.

scholarly journals Effect of the number of vortices on the torque scaling in Taylor–Couette flow

2014 ◽  
Vol 748 ◽  
pp. 756-767 ◽  
Author(s):  
B. Martínez-Arias ◽  
J. Peixinho ◽  
O. Crumeyrolle ◽  
I. Mutabazi
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Couette Flow ◽  
Scaling Laws ◽  
Taylor Vortex ◽  
Large Radius ◽  
Aspect Ratios ◽  
Taylor Vortex Flow ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractTorque measurements in Taylor–Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque–speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

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