scholarly journals Onset of vortex shedding around a short cylinder

2021 ◽  
Vol 933 ◽  
Author(s):  
Yongliang Yang ◽  
Zhe Feng ◽  
Mengqi Zhang
Keyword(s):  
Linear Stability ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Flow Patterns ◽  
Bluff Bodies ◽  
Mean Flow ◽  
Formula One ◽  
Stability Analyses ◽  
Cylinder Length ◽  
Aspect Ratios

This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq {\small \text{AR}} \leq 2$ , cylinder length over diameter) and Reynolds numbers ( $Re\leq 1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as ${\small \text{AR}}$ changes. The appearance of a steady wake pattern when ${\small \text{AR}} \leq 1.75$ has not been discussed earlier in the literature for this flow. Linear stability analyses based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$ , one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short- ${\small \text{AR}}$ bluff bodies in order that our discussions bear more general meanings.

Unravelling the large-scale circulation modes in turbulent Rayleigh–Bénard convection

2021 ◽  
Author(s):  
Susanne Horn ◽  
Peter J. Schmid ◽  
Jonathan M. Aurnou
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mean Flow ◽  
Large Scale Circulation ◽  
Convective Systems ◽  
Aspect Ratios ◽  
Mode Decomposition ◽  
Coherent Flow Structure

Abstract The large-scale circulation (LSC) is the most fundamental turbulent coherent flow structure in Rayleigh-B\'enard convection. Further, LSCs provide the foundation upon which superstructures, the largest observable features in convective systems, are formed. In confined cylindrical geometries with diameter-to-height aspect ratios of Γ ≅ 1, LSC dynamics are known to be governed by a quasi-two-dimensional, coupled horizontal sloshing and torsional (ST) oscillatory mode. In contrast, in Γ ≥ √2 cylinders, a three-dimensional jump rope vortex (JRV) motion dominates the LSC dynamics. Here, we use dynamic mode decomposition (DMD) on direct numerical simulation data of liquid metal to show that both types of modes co-exist in Γ = 1 and Γ = 2 cylinders but with opposite dynamical importance. Furthermore, with this analysis, we demonstrate that ST oscillations originate from a tilted elliptical mean flow superposed with a symmetric higher order mode, which is connected to the four rolls in the plane perpendicular to the LSC in Γ = 1 tanks.

Separating and Reattaching Flow Structure in a Suddenly Expanding Rectangular Duct

1995 ◽  
Vol 117 (1) ◽  
pp. 17-23 ◽  
Author(s):  
G. Papadopoulos ◽  
M. V. O¨tu¨gen
Keyword(s):  
Aspect Ratio ◽  
Flow Structure ◽  
Three Dimensional ◽  
Side Wall ◽  
Stream Velocity ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Wall Effects ◽  
Velocity Measurements ◽  
Aspect Ratios

The incompressible turbulent flow over a backward-facing step in a rectangular duct was investigated experimentally. The side wall effects on the core flow were determined by varying the aspect ratio (defined as the step span-to-height ratio) from 1 to 28. The Reynolds number, based on the step height and the oncoming free-stream velocity, was 26,500. Detailed velocity measurements were made, including the turbulent stresses, in a region which extended past the flow reattachment zone. Wall static pressure was also measured on both the step and flat walls. In addition, surface visualizations were obtained on all four walls surrounding the separated flow to supplement near-wall velocity measurements. The results show that the aspect ratio has an influence on both the velocity and wall pressure even for relatively large aspect ratios. For example, in the redevelopment region downstream of reattachment, the recovery pressure decreases with smaller aspect ratios. The three-dimensional side wall effects tend to slow down the relaxation downstream of reattachment for smaller aspect ratios as evidenced by the evolution of the velocity field. For the two smallest aspect ratios investigated, higher centerplane streamwise and transverse velocities were obtained which indicate a three-dimensional mean flow structure along the full span of the duct.

Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

1996 ◽  
Vol 326 ◽  
pp. 399-415 ◽  
Author(s):  
M. Wanschura ◽  
H. C. Kuhlmann ◽  
H. J. Rath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Onset Of Convection ◽  
Buoyant Convection ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

scholarly journals Three-dimensional instabilities in compressible flow over open cavities

2008 ◽  
Vol 599 ◽  
pp. 309-339 ◽  
Author(s):  
GUILLAUME A. BRÈS ◽  
TIM COLONIUS
Keyword(s):  
Compressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Vortical Flow ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Mean Flow ◽  
Aspect Ratios ◽  
Open Cavities

Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

Passive pitching of splitters in the trailing edge of elliptic cylinders

2017 ◽  
Vol 826 ◽  
pp. 363-375 ◽  
Author(s):  
Y. Jin ◽  
L. P. Chamorro
Keyword(s):  
Vortex Shedding ◽  
Semimajor Axis ◽  
Wake Flow ◽  
Recirculation Region ◽  
Mean Flow ◽  
Trailing Edge ◽  
Flow Measurements ◽  
High Background ◽  
Aspect Ratios ◽  
The Mean

The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ($AoA$) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios ($AR$) of the cylinder and freestream turbulence levels. High-resolution telemetry and hotwire anemometry were used to characterize and gain insight on the dynamics of splitters and wake flow. Results show that the motions of the splitters contain various dominating modes, e.g. $f_{p}$ and $f_{v}$, which are induced by the mean flow and wake dynamics. High background turbulence dampens the coherence of the regular vortex shedding leading to negligible $f_{v}$. For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode exists close to the leading and trailing edges of the splitter. In general, the splitters oscillate around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium is also possible with a strong recirculation region. This is the case with cylinders of low $AR$ and high $AoA$, where higher lift and drag occurs. Flow measurements at various transverse locations within the wake of the cylinder–splitter system indicate that the signature of the low-frequency splitter pitching is shifted in the wake in the cases with non-zero $AoA$ of the cylinder. Although the splitter pitching exhibits two dominant vortex shedding modes in various configurations, only the higher frequency is transmitted to the wake.

scholarly journals Parabolized stability analysis of jets from serrated nozzles

2016 ◽  
Vol 789 ◽  
pp. 36-63 ◽  
Author(s):  
Aniruddha Sinha ◽  
Kristján Gudmundsson ◽  
Hao Xia ◽  
Tim Colonius
Keyword(s):  
Linear Stability ◽  
Near Field ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Hydrodynamic Pressure ◽  
Linear Instability ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Instability Wave ◽  
Mean Flow

We study the viscous spatial linear stability characteristics of the time-averaged flow in turbulent subsonic jets issuing from serrated (chevroned) nozzles, and compare them to analogous round jet results. Linear parabolized stability equations (PSE) are used in the calculations to account for the non-parallel base flow. By exploiting the symmetries of the mean flow due to the regular arrangement of serrations, we obtain a series of coupled two-dimensional PSE problems from the original three-dimensional problem. This reduces the solution cost and manifests the symmetries of the stability modes. In the parallel-flow linear stability theory (LST) calculations that are performed near the nozzle to initiate the PSE, we find that the serrated nozzle reduces the growth rates of the most unstable eigenmodes of the jet, but their phase speeds are approximately similar. We obtain encouraging validation of our linear PSE instability wave results vis-à-vis near-field hydrodynamic pressure data acquired on a phased microphone array in experiments, after filtering the latter with proper orthogonal decomposition (POD) to extract the energetically dominant coherent part. Additionally, a large-eddy simulation database of the same serrated jet is investigated, and its POD-filtered pressure field is found to compare favourably with the corresponding PSE solution within the jet plume. We conclude that the coherent hydrodynamic pressure fluctuations of jets from both round and serrated nozzles are reasonably consistent with the linear instability modes of the turbulent mean flow.

Large-scale vortex structures in turbulent wakes behind bluff bodies. Part 1. Vortex formation processes

1987 ◽  
Vol 174 ◽  
pp. 233-270 ◽  
Author(s):  
A. E. Perry ◽  
T. R. Steiner
Keyword(s):  
Large Scale ◽  
Vector Fields ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Point Theory ◽  
Shear Stresses ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Mean Flow ◽  
Turbulent Wakes

An investigation of turbulent wakes was conducted and phase-averaged velocity vector fields are presented, as well as phase-averaged and global Reynolds normal and shear stresses. The topology of the phase-averaged velocity fields is discussed in terms of critical point theory. Here in Part 1, the vortex formation process in the cavity region of several nominally two-dimensional bluff bodies is investigated and described using phase-averaged streamlines where the measurements were made in a nominal plane of symmetry. It was found that the flows encountered were always three-dimensional and that the mean-flow patterns in the cavity region were quite different from those expected using classical two-dimensional assumptions.

Quasi-Periodic Structure of Vortical Flows Produced in the Wake of Finite Bluff Bodies Partially Immersed in a Boundary Layer

2010 ◽  
Author(s):  
Jason A. Bourgeois ◽  
Pooria Sattari ◽  
Robert J. Martinuzzi
Keyword(s):  
Cross Section ◽  
Wavelet Transforms ◽  
Dominant Role ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Vortex Sheet ◽  
Bluff Bodies ◽  
Continuous Wavelet Transforms ◽  
Aspect Ratios ◽  
Image Velocimetry

The quasi-periodic vortex shedding structure in the wake of finite surface-mounted square- and circular-cross-section cylinders is investigated for several aspect ratios. Complex continuous wavelet transforms (CWT’s) are used to obtain a phase function φ(t) from hot-wire measurements. Mean relative phases and phase averaged particle image velocimetry (PIV) measurements indicate an upstream bending of the initially vertical shed vortex structures for all obstacles investigated. This upstream bending mechanism reorients vorticity streamwise and is described in terms of Biot-Savart induction that occurs at the junction of the tip and side shear layers. This mechanism of vorticity concentration/reorientation is inherently three-dimensional and interacts with the nominally two-dimensional mechanism of alternate vortex sheet roll-up from the opposing obstacle side faces. This mechanism typically acts higher along the height for square-as opposed to circular-cross section cylinders and plays a more dominant role for smaller aspect ratios.

Influence of Reynolds Numbers on the Flow and Heat Transfer Around Row of Magnetic Obstacles

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Xidong Zhang ◽  
Guiping Zhu ◽  
Yin Zhang ◽  
Hongyan Wang ◽  
Hulin Huang
Keyword(s):  
Heat Transfer ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Vortical Structures ◽  
Magnetic Vortices ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Maximum Value

An incompressible electrically conducting viscous fluid flow influenced by a local external magnetic field may develop vortical structures and eventually instabilities similar to those observed in flows around bluff bodies (such as circular cylinder), denominated magnetic obstacle. The present investigation analyzes numerically the three-dimensional flow and heat transfer around row of magnetic obstacles. The vortex structures of magnetic obstacles, heat transfer behaviors in the wake of magnetic obstacles, and flow resistance are analyzed at different Reynolds numbers. It shows that the flow behind magnetic obstacles contains four different regimes: (1) one pair of magnetic vortices, (2) three pairs namely, magnetic, connecting, and attached vortices, (3) smaller vortex shedding from the in-between magnetic obstacles, i.e., quasi-static, and (4) regular vortex shedding from the row of magnetic obstacles. Furthermore, downstream cross-stream mixing induced by the unstable wakes can enhance wall-heat transfer, and the maximum value of percentage heat transfer increment (HI) is equal to about 35%. In this case, the thermal performance factor is more than one.

scholarly journals The wave-induced flow of internal gravity wavepackets with arbitrary aspect ratio

2017 ◽  
Vol 834 ◽  
pp. 385-408 ◽  
Author(s):  
T. S. van den Bremer ◽  
B. R. Sutherland
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Mean Flow ◽  
One Dimensional ◽  
Unidirectional Flow ◽  
Aspect Ratios ◽  
Non Local ◽  
Flow Through ◽  
Induced Flow ◽  
Wave Induced

We examine the wave-induced flow of small-amplitude, quasi-monochromatic, three-dimensional, Boussinesq internal gravity wavepackets in a uniformly stratified ambient. It has been known since Bretherton (J. Fluid Mech., vol. 36 (4), 1969, pp. 785–803) that one-, two- and three-dimensional wavepackets induce qualitatively different flows. Whereas the wave-induced mean flow for compact three-dimensional wavepackets consists of a purely horizontal localized circulation that translates with and around the wavepacket, known as the Bretherton flow, such a flow is prohibited for a two-dimensional wavepacket of infinite spanwise extent, which instead induces a non-local internal wave response that is long compared with the streamwise extent of the wavepacket. One-dimensional (horizontally periodic) wavepackets induce a horizontal, non-divergent unidirectional flow. Through perturbation theory for quasi-monochromatic wavepackets of arbitrary aspect ratio, we predict for which aspect ratios which type of induced mean flow dominates. We compose a regime diagram that delineates whether the induced flow is comparable to that of one-, two- or compact three-dimensional wavepackets. The predictions agree well with the results of fully nonlinear three-dimensional numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document