Three-dimensionality of elliptical cylinder wakes at low angles of incidence

2017 ◽  
Vol 825 ◽  
pp. 245-283 ◽  
Author(s):  
Anirudh Rao ◽  
Justin S. Leontini ◽  
Mark C. Thompson ◽  
Kerry Hourigan
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Incident Angle ◽  
Three Dimensional ◽  
Cylinder Wake ◽  
Periodic Mode ◽  
Dimensional Flow ◽  
Aspect Ratios ◽  
Two Dimensional Flow ◽  
Transition Scenario

The wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio ($\unicode[STIX]{x1D6E4}=\text{major:minor axis ratio}$) cylinders using stability analysis and direct simulations. In particular, two- and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis. The transition scenario for near-unity aspect ratio cylinders resembles that for a circular cylinder wake as Reynolds number is increased to $Re\lesssim 400$; first, with the transition from steady two-dimensional flow to unsteady two-dimensional flow, followed by the onset of three-dimensional flow via a long-wavelength instability (mode A), then, a short-wavelength instability (mode B) and, finally, an intermediary wavelength instability which is quasi-periodic in nature (mode QP). The effect of the incident angle on this transition scenario for the low-aspect-ratio cylinders is minimal. As the aspect ratio is increased towards 2, two synchronous modes, modes $\widehat{\text{A}}$ and $\widehat{\text{B}}$, become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode $\widehat{\text{A}}$ persists for all incident angles investigated here, mode $\widehat{\text{B}}$ is found only to be unstable for incident angles up to $10^{\circ }$. Surprisingly, for $1.8\lesssim \unicode[STIX]{x1D6E4}\lesssim 2.9$, the mode A instability observed at zero incident angle emerges as a quasi-periodic mode as the incident angle is increased even slightly. At higher incident angles, this quasi-periodic mode once again transforms to a real mode on increasing the Reynolds number. The parameter space maps for the various aspect ratios are presented in the Reynolds number–incident angle plane, and the three-dimensional modes are discussed in terms of similarities to and differences from existing modes. A key aim of the work is to map the different modes and various transition sequences as a simple body geometry is systematically changed and as the flow symmetry is systematically broken; thus, insight is provided on the overall path towards fully turbulent flow.

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 Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

Performance Simulations of Tesla Microfluidic Valves

2007 ◽  
Author(s):  
S. Zhang ◽  
S. H. Winoto ◽  
H. T. Low
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Rate ◽  
Three Dimensional ◽  
Model Performance ◽  
Hydraulic Diameter ◽  
Cross Sectional ◽  
Pressure Flow ◽  
Aspect Ratios ◽  
Tesla Valve

A three-dimensional (3-D) parametric model of Tesla-type valves is proposed. A geometrical relationship is derived for optimization study, and based on the model, performance investigations in terms of diodicity and pressure-flow rate characteristics of the valve are numerically carried out with same hydraulic diameter and different aspect ratios (of the model cross-sectional dimensions) ranging from 0.5 to 4. The 3-D computational simulations show that, for the same hydraulic diameter, the unity aspect ratio gives higher diodicity at Reynolds number less than 500 and higher will be achieved with bigger aspect ratio when the Reynolds number is above 500. Investigations of pressure-flow rate characteristics of the Tesla valve show that Tesla valve with high aspect ratio gives more flow control ability.

The effect of aspect ratio on the wake structure of finite wall-mounted square cylinders

2019 ◽  
Vol 875 ◽  
pp. 929-960 ◽  
Author(s):  
Yendrew Yauwenas ◽  
Ric Porteous ◽  
Danielle J. Moreau ◽  
Con J. Doolan
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Amplitude Modulation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Cylinder Wake ◽  
Near Wake ◽  
Wake Structure ◽  
Velocity Amplitude ◽  
Aspect Ratios

This paper presents a combined experimental and large-eddy simulation study to characterise the effect of aspect ratio on the near-wake structure of a square finite wall-mounted cylinder (FWMC). The cylinder aspect ratios (span $L$ to width $W$) investigated in the experiments were $1.4\leqslant L/W\leqslant 21.4$ and the oncoming boundary-layer thicknesses were $1.3W$ and $0.9W$ at a Reynolds number based on cylinder width of $1.4\times 10^{4}$ and $1.1\times 10^{4}$, respectively. In complementary simulations, the cylinder aspect ratios investigated were 1.4, 4.3, 10 and 18.6. The cylinder wake structure was visualised in three-dimensional space using a vortex core detection method and decomposed to its oscillation modes using the spectral proper orthogonal decomposition (SPOD) technique. A parametric diagram is proposed to predict whether the time-averaged wake structure is a dipole or a quadrupole pattern, based on oncoming boundary-layer height and aspect ratio. Cellular shedding occurs when the aspect ratio is high with up to three shedding cells occurring across the span for aspect ratios $L/W>18$. Each of these cells sheds at a distinct frequency, as evidenced by the spectral content of the surface pressure measured on the side face and the near-wake velocity. Amplitude modulation is also observed in the vortex shedding, which explains the amplitude modulation of the acoustic pressure emitted by square FWMCs. SPOD is shown to be a viable method to identify the occurrence of cellular shedding in the wake.

Successive stages and the role of natural vortex dislocations in three-dimensional wake transition

2001 ◽  
Vol 439 ◽  
pp. 1-41 ◽  
Author(s):  
M. BRAZA ◽  
D. FAGHANI ◽  
H. PERSILLON
Keyword(s):  
Reynolds Number ◽  
Stability Theory ◽  
Longitudinal Velocity ◽  
Three Dimensional ◽  
Time History ◽  
Optimum Shape ◽  
Cylinder Wake ◽  
Two Dimensional Flow ◽  
Karman Vortex ◽  
Definition Of

The time-history of the development of the three-dimensional transition features in a nominally two-dimensional flow configuration is established for Reynolds number 220 in a cylinder wake. The identification of the successive stages that evolve very fast during experiments is possible by means of direct numerical simulation. The physical processes related to the creation of streamwise and vertical vorticity components and their impact on the spanwise waviness of the main von Kármán vortex filaments are analysed by means of the Craik–Leibovich shearing instability mechanism and a comparative discussion is given with respect to the elliptic stability theory. This study proves the existence of a further stage in the three-dimensional transition, which substantially modifies the regular spanwise undulation. This is a systematic and repetitive development of natural vortex dislocations in the near wake. The definition of this kind of structure is provided, as well as its properties related to a drastic reduction of the fundamental frequency and to the selection of a lower path in the Strouhal–Reynolds number relation. The induced amplitude modulation of the flow properties along the span is also evaluated. Quantification of these properties is carried out by using wavelet analysis and autoregressive modelling of the time series. The reasons for the development of natural vortex dislocations are analysed and related to specific modulations of the spanwise structure of the longitudinal velocity upstream separation. From this part of the study an optimum shape for the spanwise distribution of this component can be specified, able to trigger the vortex dislocations in wake flows and therefore useful to apply in the context of stability theory analyses and in further DNS studies.

Wake behaviour and instability of flow through a partially blocked channel

2007 ◽  
Vol 582 ◽  
pp. 319-340 ◽  
Author(s):  
M. D. GRIFFITH ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN ◽  
W. P. ANDERSON
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
Recirculation Bubble ◽  
Dimensional Flow ◽  
Starting Point ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
The Stability

The two-dimensional flow through a constricted channel is studied. A semi-circular bump is located on one side of the channel and the extent of blockage is varied by adjusting the radius of the bump. The blockage is varied between 0.05 and 0.9 of the channel width and the upstream Reynolds number between 25 and 3000. The geometry presents a simplified blockage specified by a single parameter, serving as a starting point for investigations of other more complex blockage geometries. For blockage ratios in excess of 0.4, the variation of reattachment length with Reynolds number collapses to within approximately 15%, while at lower ratios the behaviour differs. For the constrained two-dimensional flow, various phenomena are identified, such as multiple mini-recirculations contained within the main recirculation bubble and vortex shedding at higher Reynolds numbers. The stability of the flow to three-dimensional perturbations is analysed, revealing a transition to a three-dimensional state at a critical Reynolds number which decreases with higher blockage ratios. Separation lengths and the onset and structure of three-dimensional instability observed from the geometry of blockage ratio 0.5 resemble results taken from backward-facing step investigations. The question of the underlying mechanism behind the instability being either centrifugal or elliptic in nature and operating within the initial recirculation zone is analytically tested.

scholarly journals Vorticity forces on an impulsively started finite plate

2012 ◽  
Vol 694 ◽  
pp. 464-492 ◽  
Author(s):  
Jian-Jhih Lee ◽  
Cheng-Ta Hsieh ◽  
Chien C. Chang ◽  
Chin-Chou Chu
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Longitudinal Component ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Force Analysis ◽  
Finite Plate ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
The Difference

AbstractIn this study, we consider various contributions to the forces on an impulsively started finite plate from the perspective of a diagnostic vorticity force theory. The wing plate has an aspect ratio (AR) between 1 and 3, and is placed at low and high angles of attack ($\ensuremath{\alpha} \leq $ and ${\gt }2{0}^{\ensuremath{\circ} } $), while the Reynolds number is either 100 or 300. The theory enables us to quantify the contributions to the forces exerted on the plate in terms of all of the fluid elements with non-zero vorticity, such as in the tip vortices (TiVs), leading- and trailing-edge vortices (LEV and TEV) as well on the plate surface. This line of force analysis has been pursued for two-dimensional flow in our previous studies. In contrast to the pressure force analysis (PFA), the vorticity force analysis (VFA) reveals new salient features in its applications to three-dimensional flow by examining sectional force contributions along the spanwise direction. In particular, at a large aspect ratio ($\mathit{AR}= 3$), the force distributions of PFA and VFA show close agreements with each other in the middle sections, while at a lower aspect ratio ($\mathit{AR}= 1$), the force distribution of PFA is substantially larger than that of VFA in most of the sections. The difference is compensated for by the contributions partly by the edge sections and mainly by the vortices in the outer regions. Further investigation is made fruitful by decomposing the vorticity into the spanwise (longitudinal) component (the only one in two-dimensional flow) and the other two orthogonal (transverse) components. The relative importance of the force contributions credited to the transverse components in the entire flow regions as well as in the two outer regions signifies the three-dimensional nature of the flow over a finite plate. The interplay between the LEV and the TiVs at various time stages is shown to play a key role in distinguishing the force contributions for the plate with a smaller aspect ratio and that with a larger aspect ratio. The present VFA provides a better perspective for flow control by relating the forces directly to the various sources of vorticity (or vortex structures) on or near the wing plate.

scholarly journals The Effect of the Reynolds Number on the Three-Dimensional Flow in a Straight Compressor Cascade

1988 ◽  
Author(s):  
Václav Cyrus
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Compressor Cascade ◽  
Simple Correlation ◽  
Three Dimensional Flow ◽  
Flow Angle ◽  
Low Reynolds Numbers ◽  
Dimensional Flow

A straight compressor cascade of aspect ratio 2 was tested in a low speed tunnel within Reynolds number Re1 = 45 000 – 150 000 and inlet flow angle α1 = 35° – 48°. The profile of the blade was NACA 65-12-10. The purpose of the paper was to obtain data on three–dimensional flow in a straight cascade at low Reynolds numbers. Some experimental results on secondary flow have been made into simple correlation relations.

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