An investigation of turbulent plane Couette flow at low Reynolds numbers

1995 ◽  
Vol 286 ◽  
pp. 291-325 ◽  
Author(s):  
Knut H. Bech ◽  
Nils Tillmark ◽  
P. Henrik Alfredsson ◽  
Helge I. Andersson
Keyword(s):  
Couette Flow ◽  
Reynolds Stress ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Turbulence Structure ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Near Wall

The turbulent structure in plane Couette flow at low Reynolds numbers is studied using data obtained both from numerical simulation and physical experiments. It is shown that the near-wall turbulence structure is quite similar to what has earlier been found in plane Poiseuille flow; however, there are also some large differences especially regarding Reynolds stress production. The commonly held view that the maximum in Reynolds stress close to the wall in Poiseuille and boundary layer flows is due to the turbulence-generating events must be modified as plane Couette flow does not exhibit such a maximum, although the near-wall coherent structures are quite similar. For two-dimensional mean flow, turbulence production occurs only for the streamwise fluctuations, and the present study shows the importance of the pressure—strain redistribution in connection with the near-wall coherent events.

Secondary flow in weakly rotating turbulent plane Couette flow

1996 ◽  
Vol 317 ◽  
pp. 195-214 ◽  
Author(s):  
Knut H. Bech ◽  
Helge I. Andersson
Keyword(s):  
Kinetic Energy ◽  
Secondary Flow ◽  
Couette Flow ◽  
Three Dimensional ◽  
Wall Turbulence ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Comparable Amount ◽  
Flow Vorticity ◽  
Turbulent Plane

As in the laminar case, the turbulent plane Couette flow is unstable (stable) with respect to roll cell instabilities when the weak background angular velocity Ωk is antiparallel (parallel) to the spanwise mean flow vorticity (-dU/dy)k. The critical value of the rotation number Ro, based on 2Ω and dU/dy of the corresponding laminar flow, was estimated as 0.0002 at a low Reynolds number with fully developed turbulence. Direct numerical simulations were performed for Ro = ±0.01 and compared with earlier results for non-rotating Couette flow. At the low rotation rates considered, both senses of rotation damped the turbulence and the number of near-wall turbulence-generating events was reduced. The destabilized flow was more energetic, but less three-dimensional, than the non-rotating flow. In the destabilized case, the two-dimensional roll cells extracted a comparable amount of kinetic energy from the mean flow as did the turbulence, thereby decreasing the turbulent kinetic energy. The turbulence anisotropy was practically unaffected by weak spanwise rotation, while the secondary flow was highly anisotropic due to its inability to contract and expand in the streamwise direction.

Scaling Turbulent Wall Layers

1990 ◽  
Vol 112 (4) ◽  
pp. 425-432 ◽  
Author(s):  
Ronald L. Panton
Keyword(s):  
Reynolds Number ◽  
Reynolds Stress ◽  
Reynolds Numbers ◽  
Additive Constant ◽  
Low Reynolds Numbers ◽  
Matching Process ◽  
Low Reynolds ◽  
Turbulent Wall ◽  
Layer Concept ◽  
Overlap Region

The two-layer concept is a framework for interpreting events and constructing mathematical models of turbulent wall layers. In this paper an asymptotic theory is constructed employing the idea that the interaction between the layers is the most important aspect. It is shown that the matching process for the layers can be used to define a characteristic scale, u*, and to produce an equation that relates u* to the known parameters; U∞, v, h, e, and dp/dx. At infinite Reynolds number the scale u* is equal to uτ, the friction velocity, but they are distinct at moderate Reynolds numbers. The theory produces very simple results. For instance, the overlap velocity laws are logarithmic with an invariant von Ka´rma´n constant; at low Reynolds numbers the additive constant changes while the slope remains the same. The effect of low Reynolds numbers on the Reynolds stress in the overlap layer is also analyzed. A composite expansion explains the strong Reynolds number effect on the stress profiles. This occurs because the mixing of outer and inner layer phenomena take place at different locations as the size of the overlap region changes. The location of the maximum Reynolds stress is given by y+max = (Re/k)1/2. The overlap region was not found to be a region of constant stress, as put forth in many heuristic arguments.

scholarly journals Turbulent plane Couette flow at moderately high Reynolds number

2014 ◽  
Vol 751 ◽  
Author(s):  
V. Avsarkisov ◽  
S. Hoyas ◽  
M. Oberlack ◽  
J. P. García-Galache
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Wall Layer ◽  
Wall Region ◽  
Plane Couette Flow ◽  
Turbulent Plane ◽  
High Reynolds ◽  
Near Wall

AbstractA new set of numerical simulations of turbulent plane Couette flow in a large box of dimension ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}20\pi h,\, 2h,\, 6\pi h$) at Reynolds number $(\mathit{Re}_{\tau }) =125$, 180, 250 and 550 is described and compared with simulations at lower Reynolds numbers, Poiseuille flows and experiments. The simulations present a logarithmic near-wall layer and are used to verify and revise previously known results. It is confirmed that the fluctuation intensities in the streamwise and spanwise directions do not scale well in wall units. The scaling failure occurs both near to and away from the wall. On the contrary, the wall-normal intensity scales in inner units in the near-wall region and in outer units in the core region. The spectral ridge found by Hoyas & Jiménez (Phys. Fluids, vol. 18, 2003, 011702) for the turbulent Poiseuille flow can also be seen in the present flow. Away from the wall, very large-scale motions are found spanning through all the length of the channel. The statistics of these simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

Mixing Characteristics in a Conical Taylor-Couette Flow System at Low Reynolds Numbers

2004 ◽  
Vol 37 (4) ◽  
pp. 546-550 ◽  
Author(s):  
Naoto Ohmura ◽  
Mohamed Nabil Noui-Mehidi ◽  
Kenji Sasaki ◽  
Kazuhiro Kitajima ◽  
Kunio Kataoka
Keyword(s):  
Couette Flow ◽  
Flow System ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Mixing Characteristics ◽  
Taylor Couette ◽  
Low Reynolds ◽  
Taylor Couette Flow

scholarly journals Relaminarization of wall turbulence by high-pressure ramps at low Reynolds numbers

2016 ◽  
Vol 20 (suppl. 1) ◽  
pp. 93-102 ◽  
Author(s):  
Kwonyul Song ◽  
Jovan Jovanovic ◽  
Ahmed Al-Salaymeh ◽  
Cornelia Rauh ◽  
Antonio Delgado
Keyword(s):  
High Pressure ◽  
Pipe Flow ◽  
Silicone Oil ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Working Fluid ◽  
Hot Wire ◽  
Low Reynolds Numbers ◽  
Reverse Transition ◽  
Low Reynolds

Reverse transition from the turbulent towards the laminar flow regime was investigated experimentally by progressively increasing the pressure up to 400 MPa in a fully developed pipe flow operated with silicone oil as the working fluid. Using hot-wire anemometry, it is shown indirectly that at low Reynolds numbers a rapid increase in pressure modifies the turbulence dynamics owing to the processes which induce the effects caused by fluid compressibility in the region very close to the wall. The experimental results confirm that under such circumstances, the traditional mechanism responsible for self-maintenance of turbulence in wall-bounded flows is altered in such a way as to lead towards a state in which turbulence cannot persist any longer.

Thermal convection in a horizontal plane Couette flow

1971 ◽  
Vol 49 (1) ◽  
pp. 193-205 ◽  
Author(s):  
Robert P. Davies-Jones
Keyword(s):  
Rayleigh Number ◽  
Kinetic Energy ◽  
Couette Flow ◽  
Rectangular Channel ◽  
Critical Rayleigh Number ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Low Reynolds Numbers ◽  
Critical Wavelength ◽  
The Mean

We investigate the behaviour of infinitesimal perturbations introduced into an unstably stratified horizontal Couette flow. We assume that the fluid is Boussinesq and contained in an infinite conducting rectangular channel which is uniformly heated from below. The sidewalls are rigid and the Couette flow is generated by moving them with equal and opposite velocities along the channel. The top and bottom are assumed to be free so that we can separate variables.Without shear, the preferred modes of convection closely resemble transverse ‘finite rolls’ (Davies-Jones 1970). Shear increases the critical wavelength so that the preferred modes become longitudinally elongated cells, or even longitudinal rolls in some cases. The critical Rayleigh number increases quite rapidly at fist with Reynolds number, but at higher Reynolds numbers it levels off to a constant value (which cannot be greater than the shear-independent Rayleigh number at which longitudinal disturbances fist become unstable).We also find that the disturbances are tilted in the same direction as the shear, and that the marginally stable ones transfer kinetic energy from the mean flow to the perturbations. Except at low Reynolds numbers, the long wave perturbations gain more energy through the conversion of mean flow kinetic energy than through the release of potential energy, even though the instability is convective in origin.

Effects of Free Stream Turbulence on Low Reynolds Number Boundary Layers

1984 ◽  
Vol 106 (3) ◽  
pp. 298-306 ◽  
Author(s):  
I. P. Castro
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Length Scale ◽  
Mean Flow ◽  
Low Reynolds Numbers ◽  
Free Stream Turbulence ◽  
Reynolds Number Effects ◽  
Low Reynolds

This paper documents some of the effects of free stream turbulence on the mean flow properties of turbulent boundary layers in zero pressure gradients. Attention is concentrated on flows for which the momentum thickness Reynolds number is less than about 2000. Direct Reynolds number effects are therefore significant and it is shown that such effects reduce as the level of free stream turbulence rises. A modification to Hancock’s [1] empirical correlation relating the fractional increase in skin friction at constant Reynolds number to a free stream turbulence parameter containing a dependence on both intensity and length scale is proposed. While this modification has the necessary characteristic of being a function of the free stream turbulence parameters as well as the Reynolds number, it is argued that the relative importance of intensity and length scale changes at low Reynolds numbers; the data are not inconsistent with this idea. The experiments cover the range 500 ⪝ Reθ ⪝ 2500, u′/Ue ⪝ 0.07, 0.8 ⪝ Le/δ ⪝ 2.9, where u′/Ue is the free stream turbulence intensity and Le/δ is the ratio of the dissipation length scale of the free stream turbulence to the 99 percent thickness of the boundary layer.

Investigation on the effect of leading edge tubercles of sweptback wing at low reynolds number

2020 ◽  
Vol 21 (6) ◽  
pp. 621
Author(s):  
Veerapathiran Thangaraj Gopinathan ◽  
John Bruce Ralphin Rose ◽  
Mohanram Surya
Keyword(s):  
Leading Edge ◽  
Reynolds Numbers ◽  
Sweep Angle ◽  
Laminar Separation ◽  
Low Reynolds Numbers ◽  
Flow Energy ◽  
Airplane Wing ◽  
Low Reynolds ◽  
Naca 0015 ◽  
Wing Performance

Aerodynamic efficiency of an airplane wing can be improved either by increasing its lift generation tendency or by reducing the drag. Recently, Bio-inspired designs have been received greater attention for the geometric modifications of airplane wings. One of the bio-inspired designs contains sinusoidal Humpback Whale (HW) tubercles, i.e., protuberances exist at the wing leading edge (LE). The tubercles have excellent flow control characteristics at low Reynolds numbers. The present work describes about the effect of tubercles on swept back wing performance at various Angle of Attack (AoA). NACA 0015 and NACA 4415 airfoils are used for swept back wing design with sweep angle about 30°. The modified wings (HUMP 0015 A, HUMP 0015 B, HUMP 4415 A, HUMP 4415 B) are designed with two amplitude to wavelength ratios (η) of 0.1 & 0.24 for the performance analysis. It is a novel effort to analyze the tubercle vortices along the span that induce additional flow energy especially, behind the tubercles peak and trough region. Subsequently, Co-efficient of Lift (CL), Co-efficient of Drag (CD) and boundary layer pressure gradients also predicted for modified and baseline (smooth LE) models in the pre & post-stall regimes. It was observed that the tubercles increase the performance of swept back wings by the enhanced CL/CD ratio in the pre-stall AoA region. Interestingly, the flow separation region behind the centerline of tubercles and formation of Laminar Separation Bubbles (LSB) were asymmetric because of the sweep.

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