Turbulent Plane Couette Flow and Scalar Transport at Low Reynolds Number

2003 ◽  
Vol 125 (6) ◽  
pp. 988-998 ◽  
Author(s):  
Chun-Ho Liu
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Root Mean Square ◽  
Correlation Coefficients ◽  
Streamwise Velocity ◽  
Conductive Heat ◽  
Mean Square ◽  
Plane Couette Flow ◽  
Maximum Root ◽  
Channel Center

The turbulence structure and passive scalar (heat) transport in plane Couette flow at Reynolds number equal to 3000 (based on the relative speed and distance between the walls) are studied using direct numerical simulation (DNS). The numerical model is a three-dimensional trilinear Galerkin finite element code. It is found that the structures of the mean velocity and temperature in plane Couette flow are similar to those in forced channel flow, but the empirical coefficients are different. The total (turbulent and viscous) shear stress and total (turbulent and conductive) heat flux are constant throughout the channel. The locations of maximum root-mean-square streamwise velocity and temperature fluctuations are close to the walls, while the location of maximum root-mean-square spanwise and vertical velocity fluctuations are at the channel center. The correlation coefficients between velocities and temperature are fairly constant in the center core of the channel. In particular, the streamwise velocity is highly correlated with temperature (correlation coefficient ≈−0.9). At the channel center, the turbulence production is unable to counterbalance the dissipation, in which the diffusion terms (both turbulent and viscous) bring turbulent kinetic energy from the near-wall regions toward the channel center. The snapshots of the DNS database help explain the nature of the correlation coefficients. The elongated wall streaks for both streamwise velocity and temperature in the viscous sublayer are well simulated. Moreover, the current DNS shows organized large-scale eddies (secondary rotations) perpendicular to the direction of mean flow at the channel center.

Direct numerical simulation of turbulence in injection-driven three-dimensional cylindrical flows

2011 ◽  
Vol 670 ◽  
pp. 176-203 ◽  
Author(s):  
JU ZHANG ◽  
THOMAS L. JACKSON
Keyword(s):  
Reynolds Number ◽  
Root Mean Square ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Wall Friction ◽  
Mean Square ◽  
The Mean ◽  
Wall Shear ◽  
Strong Injection ◽  
Near Wall

Incompressible turbulent flow in a periodic circular pipe with strong injection is studied as a simplified model for the core flow in a solid-propellant rocket motor and other injection-driven internal flows. The model is based on a multi-scale asymptotic approach. The intended application of the current study is erosive burning of solid propellants. Relevant analysis for easily accessible parameters for this application, such as the magnitudes, main frequencies and wavelengths associated with the near-wall shear, and the assessment of near-wall turbulence viscosity is focused on. It is found that, unlike flows with weak or no injection, the near-wall shear is dominated by the root mean square of the streamwise velocity which is a function of the Reynolds number, while the mean streamwise velocity is only weakly dependent on the Reynolds number. As a result, a new wall-friction velocity $\(u_\tau{\,=\,}\sqrt{\tau_w/\rho}\)$, based on the shear stress derived from the sum of the mean and the root mean square, i.e. $\(\tau_{w,inj} {\,=\,} \mu |{\partial (\bar{u}+u_{rms})}/{\partial r}|_w\)$, is proposed for the scaling of turbulent viscosity for turbulent flows with strong injection. We also show that the mean streamwise velocity profile has an inflection point near the injecting surface.

A resonance mechanism in plane Couette flow

1980 ◽  
Vol 98 (1) ◽  
pp. 149-159 ◽  
Author(s):  
L. HÅKan Gustavsson ◽  
Lennart S. Hultgren
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Velocity Component ◽  
Three Dimensional ◽  
Phase Speed ◽  
Maximum Amplitude ◽  
Streamwise Velocity ◽  
Plane Couette Flow ◽  
Mean Velocity ◽  
Streamwise Velocity Component

The temporal evolution of small three-dimensional disturbances on viscous flows between parallel walls is studied. The initial-value problem is formally solved by using Fourier–Laplace transform techniques. The streamwise velocity component is obtained as the solution of a forced problem. As a consequence of the three-dimensionality, a resonant response is possible, leading to algebraic growth for small times. It occurs when the eigenvalues of the Orr–Sommerfeld equation coincide with the eigenvalues of the homogeneous operator for the streamwise velocity component. The resonance has been investigated numerically for plane Couette flow. The phase speed of the resonant waves equals the average mean velocity. The wavenumber combination that leads to the largest amplitude corresponds to structures highly elongated in the streamwise direction. The maximum amplitude, and the time to reach this maximum, scale with the Reynolds number. The aspect ratio of the most rapidly growing wave increases with the Reynolds number, with its spanwise wavelength approaching a constant value of about 3 channel heights.

scholarly journals Numerical investigation of wall pressure fluctuations downstream of concentric and eccentric blunt stenosis models

2019 ◽  
Vol 234 (1) ◽  
pp. 48-60
Author(s):  
Kamil Ozden ◽  
Cuneyt Sert ◽  
Yigit Yazicioglu
Keyword(s):  
Reynolds Number ◽  
Root Mean Square ◽  
Acoustic Radiation ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Mean Square ◽  
Spectrum Level ◽  
Wall Pressure Fluctuations ◽  
Maximum Root ◽  
Calculated Amplitude

Pressure fluctuations that cause acoustic radiation from vessel models with concentric and eccentric blunt stenoses are investigated. Large eddy simulations of non-pulsatile flow condition are performed using OpenFOAM. Calculated amplitude and spatial-spectral distribution of acoustic pressures at the post-stenotic region are compared with previous experimental and theoretical results. It is found that increasing the Reynolds number does not change the location of the maximum root mean square wall pressure, but causes a general increase in the spectrum level, although the change in the shape of the spectrum is not significant. On the contrary, compared to the concentric model at the same Reynolds number, eccentricity leads to an increase both at the distance of the location of the maximum root mean square wall pressure from the stenosis exit and the spectrum level. This effect becomes more distinct when radial eccentricity of the stenosis increases. Both the flow rate and the eccentricity of the stenosis shape are evaluated to be clinically important parameters in diagnosing stenosis.

Intersession reliability of GPS-based and accelerometer-based physical variables in small-sided games with and without the offside rule

2021 ◽  
pp. 175433712098764
Author(s):  
Igor Junio de Oliveira Custódio ◽  
Gibson Moreira Praça ◽  
Leandro Vinhas de Paula ◽  
Sarah da Glória Teles Bredt ◽  
Fabio Yuzo Nakamura ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Global Positioning System ◽  
Intraclass Correlation ◽  
Correlation Coefficients ◽  
Mean Square ◽  
Physical Demands ◽  
Intraclass Correlation Coefficients ◽  
Total Distance ◽  
Global Positioning ◽  
High Level

This study aimed to analyze the intersession reliability of global positioning system (GPS-based) distances and accelerometer-based (acceleration) variables in small-sided soccer games (SSG) with and without the offside rule, as well as compare variables between the tasks. Twenty-four high-level U-17 soccer athletes played 3 versus 3 (plus goalkeepers) SSG in two formats (with and without the offside rule). SSG were performed on eight consecutive weeks (4 weeks for each group), twice a week. The physical demands were recorded using a GPS with an embedded triaxial accelerometer. GPS-based variables (total distance, average speed, and distances covered at different speeds) and accelerometer-based variables (Player Load™, root mean square of the acceleration recorded in each movement axis, and the root mean square of resultant acceleration) were calculated. Results showed that the inclusion of the offside rule reduced the total distance covered (large effect) and the distances covered at moderate speed zones (7–12.9 km/h – moderate effect; 13–17.9 km/h – large effect). In both SSG formats, GPS-based variables presented good to excellent reliability (intraclass correlation coefficients – ICC > 0.62) and accelerometer-based variables presented excellent reliability (ICC values > 0.89). Based on the results of this study, the offside rule decreases the physical demand of 3 versus 3 SSG and the physical demands required in these SSG present high intersession reliability.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

Structure of a streamwise-oriented vortex incident upon a wing

2017 ◽  
Vol 816 ◽  
pp. 306-330 ◽  
Author(s):  
C. McKenna ◽  
M. Bross ◽  
D. Rockwell
Keyword(s):  
Root Mean Square ◽  
Cross Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
Mean Square ◽  
Swirl Ratio ◽  
Streamwise Vorticity ◽  
Image Velocimetry ◽  
Unsteady Loading ◽  
Drag Ratio

Impingement of a streamwise-oriented vortex upon a fin, tail, blade or wing represents a fundamental class of flow–structure interaction that extends across a range of applications. It can give rise to unsteady loading known as buffeting and to changes of the lift to drag ratio. These consequences are sensitive to parameters of the incident vortex as well as the location of vortex impingement on the downstream aerodynamic surface, generically designated as a wing. Particle image velocimetry is employed to determine patterns of velocity and vorticity on successive cross-flow planes along the vortex, which lead to volume representations and thereby characterization of the streamwise evolution of the vortex structure as it approaches the downstream wing. This evolution of the incident vortex is affected by the upstream influence of the downstream wing, and is highly dependent on the spanwise location of vortex impingement. Even at spanwise locations of impingement well outboard of the wing tip, a substantial influence on the structure of the incident vortex at locations significantly upstream of the leading edge of the wing was observed. For spanwise locations close to or intersecting the vortex core, the effects of upstream influence of the wing on the vortex are to: decrease the swirl ratio; increase the streamwise velocity deficit; decrease the streamwise vorticity; increase the azimuthal vorticity; increase the upwash; decrease the downwash; and increase the root-mean-square fluctuations of both streamwise velocity and vorticity. The interrelationship between these effects is addressed, including the rapid attenuation of axial vorticity in presence of an enhanced defect of axial velocity in the central region of the vortex. When the incident vortex is aligned with, or inboard of, the tip of the wing, the swirl ratio decreases to values associated with instability of the vortex, thereby giving rise to enhanced values of azimuthal vorticity relative to the streamwise (axial) vorticity, as well as relatively large root-mean-square values of streamwise velocity and vorticity.

scholarly journals The linear instability of the stratified plane Couette flow

2018 ◽  
Vol 853 ◽  
pp. 205-234 ◽  
Author(s):  
Giulio Facchini ◽  
Benjamin Favier ◽  
Patrice Le Gal ◽  
Meng Wang ◽  
Michael Le Bars
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Vertical Direction ◽  
Stability Diagram ◽  
Linear Instability ◽  
Plane Couette Flow ◽  
Horizontal Shear ◽  
The Stability

We present the stability analysis of a plane Couette flow which is stably stratified in the vertical direction orthogonal to the horizontal shear. Interest in such a flow comes from geophysical and astrophysical applications where background shear and vertical stable stratification commonly coexist. We perform the linear stability analysis of the flow in a domain which is periodic in the streamwise and vertical directions and confined in the cross-stream direction. The stability diagram is constructed as a function of the Reynolds number $Re$ and the Froude number $Fr$, which compares the importance of shear and stratification. We find that the flow becomes unstable when shear and stratification are of the same order (i.e. $Fr\sim 1$) and above a moderate value of the Reynolds number $Re\gtrsim 700$. The instability results from a wave resonance mechanism already known in the context of channel flows – for instance, unstratified plane Couette flow in the shallow-water approximation. The result is confirmed by fully nonlinear direct numerical simulations and, to the best of our knowledge, constitutes the first evidence of linear instability in a vertically stratified plane Couette flow. We also report the study of a laboratory flow generated by a transparent belt entrained by two vertical cylinders and immersed in a tank filled with salty water, linearly stratified in density. We observe the emergence of a robust spatio-temporal pattern close to the threshold values of $Fr$ and $Re$ indicated by linear analysis, and explore the accessible part of the stability diagram. With the support of numerical simulations we conclude that the observed pattern is a signature of the same instability predicted by the linear theory, although slightly modified due to streamwise confinement.

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