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.

Effects of Inclination Angle of Ribs on the Flow Behavior in Rectangular Ducts

2004 ◽  
Vol 126 (4) ◽  
pp. 692-699 ◽  
Author(s):  
Xiufang Gao ◽  
Bengt Sunde´n
Keyword(s):  
Velocity Component ◽  
Flow Direction ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Streamwise Velocity ◽  
Flow Structures ◽  
Local Flow ◽  
Flow Motion ◽  
Streamwise Velocity Component

The flow behavior in rib-roughened ducts is influenced by the inclination of ribs and the effect is investigated in the present study by Particle Image Velocimetry (PIV). The local flow structures between two adjacent ribs were measured. The Reynolds number was fixed at 5800. The flow field description was based on the PIV results in planes both parallel and perpendicular to the ribbed walls at various locations. The rib angle to the main flow direction was varied as 30 deg, 45 deg, 60 deg and 90 deg. The ribs induce three dimensional flow fields. The flow separation and reattachment between adjacent ribs are clearly observed. In addition, the inclined ribs are found to alter the spanwise distribution of the streamwise velocity component. The streamwise velocity component has its highest values at the upstream end of the ribs, and decreases continuously to its lowest values at the downstream end. Strong secondary flow motion occurs over the entire duct cross section for the inclined ribs. The flow structures between two consecutive ribs show that the fluid flows along the ribs from one end of the ribs to the other end, and then turns back at the transverse center. Downwash and upwash flows are observed at the upstream end and downstream end of the ribs, respectively.

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.

scholarly journals Similarity of the streamwise velocity component in very-rough-wall channel flow

2010 ◽  
Vol 668 ◽  
pp. 174-201 ◽  
Author(s):  
DAVID M. BIRCH ◽  
JONATHAN F. MORRISON
Keyword(s):  
Channel Flow ◽  
Fourth Order ◽  
Velocity Component ◽  
Streamwise Velocity ◽  
Rough Wall ◽  
Self Similarity ◽  
Mean Velocity ◽  
Mesh Surface ◽  
Streamwise Velocity Component ◽  
The Mean

The streamwise velocity component is studied in fully developed turbulent channel flow for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a highly non-Gaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (±) the standard deviation) are, respectively, about 76(±42) and 145(±150) wall units. The flow is shown to be two-dimensional and fully developed up to the fourth-order moment of velocity. The mean velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0.04≤y/h≤0.06, but the profile over the mesh surface does not, even though the mean velocity deficit and higher moments (up to the fourth order) all exhibit outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. The wake strength is shown to increase slightly over the grit surface but decrease over the mesh surface. The latter result is contrary to recent measurements in rough-wall boundary layers. Single- and two-point velocity correlations reveal the presence of large-scale streamwise structures with circulation in the plane orthogonal to the mean velocity. Spanwise correlation length scales are significantly larger than corresponding ones for both internal and external smooth-wall flows.

scholarly journals Self-sustaining dual critical layer states in plane Poiseuille–Couette flow at large Reynolds number

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180881 ◽  
Author(s):  
Rishi Kumar ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Three Dimensional ◽  
Phase Speed ◽  
Wave Structure ◽  
Travelling Wave ◽  
Basic Flow ◽  
Large Reynolds Number ◽  
Amplitude Dependence ◽  
Critical Layers

The nonlinear stability of plane Poiseuille–Couette flow subjected to three-dimensional disturbances is studied asymptotically at large Reynolds number R . By analysing the nature of the instability for increasing disturbance size Δ, the scaling Δ =  O ( R −1/3 ) is identified at which a strongly nonlinear neutral wave structure emerges, involving the interaction of two inviscid critical layers. The striking feature of this structure is that the travelling wave disturbances have both streamwise and spanwise wavelengths comparable to the channel width, with an associated phase speed of O (1). An alternative method to the classical balancing of phase shifts is proposed, involving vorticity jumps, that uses a global property of the flow-field and enables the amplitude-dependence of the neutral modes to be determined in terms of the wavenumbers and the properties of the basic flow. Numerical computation of the Rayleigh equation which governs the flow outside of the critical layers shows that neutral solutions exist for non-dimensional wall sliding speeds in the range 0 ≤  V  < 2. It transpires that the critical layers merge and the asymptotic structure referred to above breaks down both in the large-amplitude limit and the limit V → 2 when the maximum of the basic flow becomes located at the upper wall.

Turbulence statistics in Couette flow at high Reynolds number

2014 ◽  
Vol 758 ◽  
pp. 327-343 ◽  
Author(s):  
Sergio Pirozzoli ◽  
Matteo Bernardini ◽  
Paolo Orlandi
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
High Reynolds Number ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Shear ◽  
Wall Region ◽  
Mean Velocity ◽  
Turbulent Shear Stress ◽  
High Reynolds

AbstractWe investigate the behaviour of the canonical turbulent Couette flow at computationally high Reynolds number through a series of large-scale direct numerical simulations. We achieve a Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau } = h/\delta _v \approx 1000$, where $h$ is the channel half-height and $\delta _v$ is the viscous length scale at which some phenomena representative of the asymptotic Reynolds-number regime manifest themselves. While a logarithmic mean velocity profile is found to provide a reasonable fit of the data, including the skin friction, closer scrutiny shows that deviations from the log law are systematic, and probably increasing at higher Reynolds numbers. The Reynolds stress distribution shows the formation of a secondary outer peak in the streamwise velocity variance, which is associated with significant excess of turbulent production as compared to the local dissipation. This excess is related to the formation of large-scale streaks and rollers, which are responsible for a substantial fraction of the turbulent shear stress in the channel core, and for significant increase of the turbulence intermittency in the near-wall region.

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).

Investigation of Turbulent Mixing in a Macro-Scale Multi-Inlet Vortex Nanoprecipitation Reactor by Stereoscopic-PIV

2014 ◽  
Author(s):  
Zhenping Liu ◽  
James C. Hill ◽  
Rodney O. Fox ◽  
Michael G. Olsen
Keyword(s):  
Reynolds Number ◽  
Turbulent Mixing ◽  
Three Dimensional ◽  
Stereoscopic Particle Image Velocimetry ◽  
Vortex Center ◽  
Mean Velocity ◽  
Vortex Model ◽  
Functional Nanoparticles ◽  
Turbulent Characteristics ◽  
Macro Scale

Flash Nanoprecipitation (FNP) is a technique to produce monodisperse functional nanoparticles through rapidly mixing a saturated solution and a non-solvent. Multi-inlet vortex reactors (MIVR) have been effectively applied to FNP due to their ability to provide both rapid mixing and the flexibility of inlet flow conditions. Until recently, only micro-scale MIVRs have been demonstrated to be effective in FNP. A scaled-up MIVR could potentially generate large quantities of functional nanoparticles, giving FNP wider applicability in the industry. In the present research, turbulent mixing inside a scaled-up, macro-scale MIVR was measured by stereoscopic particle image velocimetry (SPIV). Reynolds number of this reactor is defined based on the bulk inlet velocity, ranging from 3290 to 8225. It is the first time that the three-dimensional velocity field of a MIVR was experimentally measured. The influence of Reynolds number on mean velocity becomes more linear as Reynolds number increases. An analytical vortex model was proposed to well describe the mean velocity profile. The turbulent characteristics such as turbulent kinematic energy and Reynolds stress are also presented. The wandering motion of vortex center was found to have a significant contribution to the turbulent kinetic energy of flow near the center area.

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