The local and global stability of confined planar wakes at intermediate Reynolds number

2011 ◽  
Vol 686 ◽  
pp. 218-238 ◽  
Author(s):  
M. P. Juniper ◽  
O. Tammisola ◽  
F. Lundell
Keyword(s):  
Recirculation Zone ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Flat Plates ◽  
Apparent Contradiction ◽  
Wake Flows ◽  
Flow Parameters ◽  
High Reynolds ◽  
Global And Local

AbstractAt high Reynolds numbers, wake flows become more globally unstable when they are confined within a duct or between two flat plates. At Reynolds numbers around 100, however, global analyses suggest that such flows become more stable when confined, while local analyses suggest that they become more unstable. The aim of this paper is to resolve this apparent contradiction by examining a set of obstacle-free wakes. In this theoretical and numerical study, we combine global and local stability analyses of planar wake flows at $\mathit{Re}= 100$ to determine the effect of confinement. We find that confinement acts in three ways: it modifies the length of the recirculation zone if one exists, it brings the boundary layers closer to the shear layers, and it can make the flow more locally absolutely unstable. Depending on the flow parameters, these effects work with or against each other to destabilize or stabilize the flow. In wake flows at $\mathit{Re}= 100$ with free-slip boundaries, flows are most globally unstable when the outer flows are 50 % wider than the half-width of the inner flow because the first and third effects work together. In wake flows at $\mathit{Re}= 100$ with no-slip boundaries, confinement has little overall effect when the flows are weakly confined because the first two effects work against the third. Confinement has a strong stabilizing effect, however, when the flows are strongly confined because all three effects work together. By combining local and global analyses, we have been able to isolate these three effects and resolve the apparent contradictions in previous work.

An Experimental and Numerical Study of Heat Transfer and Pressure Loss in a Rectangular Channel With V-Shaped Ribs

2006 ◽  
Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Pressure Loss ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Transfer Enhancement ◽  
High Reynolds Numbers ◽  
High Reynolds

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.

On the spatial instability of piecewise linear free shear layers

1987 ◽  
Vol 174 ◽  
pp. 553-563 ◽  
Author(s):  
T. F. Balsa
Keyword(s):  
Velocity Profile ◽  
Numerical Solutions ◽  
Piecewise Linear ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Spatial Instability ◽  
Free Shear Layers ◽  
Linear Shear ◽  
High Reynolds ◽  
Sommerfeld Equation

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. We do this by obtaining numerical solutions to the Orr–Sommerfeld equation at high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. We find that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qualitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. In a nutshell, we see nothing wrong with the inviscid spatial instability of piecewise linear shear flows.

Three Dimensional Numerical Modelling of Staggered Tube Bundle Turbulent Crossflow in Duct

2005 ◽  
Author(s):  
Ahad Ramezanpour ◽  
Hassan Shirvani ◽  
Ramin Rahmani ◽  
Iraj Mirzaee
Keyword(s):  
Nusselt Number ◽  
Numerical Study ◽  
Tube Bundle ◽  
Three Dimensional ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Wall Function ◽  
Flat Plates ◽  
Geometrical Characteristics ◽  
Commercial Code

A numerical study has been conducted to investigate the three dimensional (3D) staggered tube bundle turbulent cross flow confined between two parallel flat plates using RNG k-ε model and standard wall function utilizing commercial code FLUENT. The maximum Reynolds numbers of 1000, 5000, and 50000 and the distance between plates of H = 3, 5, 10, 15, and 20 mm have been considered. The arrangement of the staggered tube bundle is fix with geometrical characteristics of Sn/D = 1.5 and Sp/D = 1.2 which has been found optimum in previous two-dimensional studies. The constant temperature of 360K on tubes, constant inlet flow and plates’ temperature of 300K have been set as the boundary conditions. The global Nusselt number, friction factor for the dissimilar Reynolds numbers, distance between plates, local Nusselt number and different angles on first and third tubes have been evaluated.

scholarly journals Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method

1991 ◽  
Vol 233 ◽  
pp. 243-263 ◽  
Author(s):  
Chien-Cheng Chang ◽  
Ruey-Ling Chern
Keyword(s):  
Finite Difference ◽  
Circular Cylinder ◽  
Numerical Study ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Numerical Results ◽  
High Reynolds Numbers ◽  
Small Times ◽  
Axis Of Symmetry ◽  
High Reynolds

Impulsively started flow around a circular cylinder at various Reynolds numbers is studied by a deterministic hybrid vortex method. The key feature of the method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection. The vorticity is updated along the surface of the cylinder to satisfy the no-slip condition. The present method is basically different from previous applications of vortex methods, which are primarily in the context of random vortex algorithms. The Reynolds numbers of the flows under investigation range from 300 to 106. Numerical results are compared with analytical solutions at small times, and compared with finite-difference solutions and flow visualization results at relatively long times. Satisfactory agreement is found in the evolutions of the separation angles, wake lengths, surface pressure and drag coefficients, streamline patterns, and some velocities on the axis of symmetry behind the circular cylinder. The present hybrid vortex method is highly stable and suffers from little numerical diffusivity, yielding convincing numerical results for unsteady vortical flows at moderately high Reynolds numbers.

scholarly journals Vortex shedding from an impulsively started rotating and translating circular cylinder

1991 ◽  
Vol 233 ◽  
pp. 265-298 ◽  
Author(s):  
Chien-Cheng Chang ◽  
Ruey-Ling Chern
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Numerical Study ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Speed Ratio ◽  
Stagnation Points ◽  
Time Variations ◽  
Strong Competition ◽  
High Reynolds

A numerical study is made of the flow past an impulsively started rotating and translating circular cylinder using a hybrid vortex method. The Reynolds number (Re) ranges from 103 to 106 while the (counter-rotating) rotating-to-translating speed ratio (α) is increased from 0 to 2. It is found that three basic patterns of vortex shedding can be identified according to the behaviour of the stagnation points associated with the first upper and the first lower vortices. Depending on the parameters Re and α, the rotation may favour the shedding of the first upper vortex, or the first lower vortex (typically at high Reynolds numbers). In a transition region, strong competition for shedding exists between the first two vortices in the form of double transposition of stagnation (closure) points associated with the two vortices. Time variations of lift coefficients characterize different shedding patterns; the cylinder may first experience a substantial maximal downward lift when the first shedding vortex is from the upper wake, or a maximal upward lift otherwise.

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