Direct simulations of turbulent flow in a pipe rotating about its axis

1997 ◽  
Vol 343 ◽  
pp. 43-72 ◽  
Author(s):  
P. ORLANDI ◽  
M. FATICA
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Radial Direction ◽  
Uniform Grid ◽  
Grid Refinement ◽  
Streamwise Vorticity ◽  
Vorticity Field ◽  
Vortical Structures ◽  
The Mean ◽  
Grid Points

Flow in a circular pipe rotating about its axis, at low Reynolds number, is investigated. The simulation is performed by a finite difference scheme, second-order accurate in space and in time. A non-uniform grid in the radial direction yields accurate solutions with a reasonable number of grid points. The numerical method has been tested for the non-rotating pipe in the limit ν→0 to prove the energy conservation properties. In the viscous case a grid refinement check has been performed and some conclusions about drag reduction have been reached. The mean and turbulent quantities have been compared with the numerical and experimental non-rotating pipe data of Eggels et al. (1994a, b). When the pipe rotates, a degree of drag reduction is achieved in the numerical simulations just as in the experiments. Through the visualization of the vorticity field the drag reduction has been related to the modification of the vortical structures near the wall. A comparison between the vorticity in the non-rotating and in the high rotation case has shown a spiral motion leading to the transport of streamwise vorticity far from the wall.

scholarly journals Reynolds number dependence of mean flow structure in square duct turbulence

2010 ◽  
Vol 644 ◽  
pp. 107-122 ◽  
Author(s):  
ALFREDO PINELLI ◽  
MARKUS UHLMANN ◽  
ATSUSHI SEKIMOTO ◽  
GENTA KAWAHARA
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Buffer Layer ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
The Other ◽  
Streamwise Vorticity ◽  
Square Duct ◽  
Layer Structures ◽  
The Mean

We have performed direct numerical simulations of turbulent flows in a square duct considering a range of Reynolds numbers spanning from a marginal state up to fully developed turbulent states at low Reynolds numbers. The main motivation stems from the relatively poor knowledge about the basic physical mechanisms that are responsible for one of the most outstanding features of this class of turbulent flows: Prandtl's secondary motion of the second kind. In particular, the focus is upon the role of flow structures in its generation and characterization when increasing the Reynolds number. We present a two-fold scenario. On the one hand, buffer layer structures determine the distribution of mean streamwise vorticity. On the other hand, the shape and the quantitative character of the mean secondary flow, defined through the mean cross-stream function, are influenced by motions taking place at larger scales. It is shown that high velocity streaks are preferentially located in the corner region (e.g. less than 50 wall units apart from a sidewall), flanked by low velocity ones. These locations are determined by the positioning of quasi-streamwise vortices with a preferential sign of rotation in agreement with the above described velocity streaks' positions. This preferential arrangement of the classical buffer layer structures determines the pattern of the mean streamwise vorticity that approaches the corners with increasing Reynolds number. On the other hand, the centre of the mean secondary flow, defined as the position of the extrema of the mean cross-stream function (computed using the mean streamwise vorticity), remains at a constant location departing from the mean streamwise vorticity field for larger Reynolds numbers, i.e. it scales in outer units. This paper also presents a detailed validation of the numerical technique including a comparison of the numerical results with data obtained from a companion experiment.

Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow

2007 ◽  
Vol 584 ◽  
pp. 281-299 ◽  
Author(s):  
KYOUNGYOUN KIM ◽  
CHANG-F. LI ◽  
R. SURESHKUMAR ◽  
S. BALACHANDAR ◽  
RONALD J. ADRIAN
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Buffer Layer ◽  
Outer Region ◽  
Wall Turbulence ◽  
Channel Height ◽  
Large Contribution ◽  
Streamwise Vortices ◽  
Vortical Structures ◽  
Near Wall

The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.

scholarly journals Treat All Integrals as Volume Integrals: A Unified, Parallel, Grid-Based Method for Evaluation of Volume, Surface, and Path Integrals on Implicitly Defined Domains

2018 ◽  
Vol 18 (2) ◽  
Author(s):  
Mete Yurtoglu ◽  
Molly Carton ◽  
Duane Storti
Keyword(s):  
Convergence Rates ◽  
Path Integrals ◽  
Computing Time ◽  
Region Of Interest ◽  
Uniform Grid ◽  
Grid Refinement ◽  
Specific Domain ◽  
Stencil Computation ◽  
Grid Points ◽  
Grid Based

We present a unified method for numerical evaluation of volume, surface, and path integrals of smooth, bounded functions on implicitly defined bounded domains. The method avoids both the stochastic nature (and slow convergence) of Monte Carlo methods and problem-specific domain decompositions required by most traditional numerical integration techniques. Our approach operates on a uniform grid over an axis-aligned box containing the region of interest, so we refer to it as a grid-based method. All grid-based integrals are computed as a sum of contributions from a stencil computation on the grid points. Each class of integrals (path, surface, or volume) involves a different stencil formulation, but grid-based integrals of a given class can be evaluated by applying the same stencil on the same set of grid points; only the data on the grid points changes. When functions are defined over the continuous domain so that grid refinement is possible, grid-based integration is supported by a convergence proof based on wavelet analysis. Given the foundation of function values on a uniform grid, grid-based integration methods apply directly to data produced by volumetric imaging (including computed tomography and magnetic resonance), direct numerical simulation of fluid flow, or any other method that produces data corresponding to values of a function sampled on a regular grid. Every step of a grid-based integral computation (including evaluating a function on a grid, application of stencils on a grid, and reduction of the contributions from the grid points to a single sum) is well suited for parallelization. We present results from a parallelized CUDA implementation of grid-based integrals that faithfully reproduces the output of a serial implementation but with significant reductions in computing time. We also present example grid-based integral results to quantify convergence rates associated with grid refinement and dependence of the convergence rate on the specific choice of difference stencil (corresponding to a particular genus of Daubechies wavelet).

Homogeneity of turbulence generated by static-grid structures

2010 ◽  
Vol 654 ◽  
pp. 473-500 ◽  
Author(s):  
Ö. ERTUNÇ ◽  
N. ÖZYILMAZ ◽  
H. LIENHART ◽  
F. DURST ◽  
K. BERONOV
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Uniform Grid ◽  
Reynolds Stresses ◽  
Hot Wire ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean

Homogeneity of turbulence generated by static grids is investigated with the help of hot-wire measurements in a wind-tunnel and direct numerical simulations based on the Lattice Bolztmann method. It is shown experimentally that Reynolds stresses and their anisotropy do not become homogeneous downstream of the grid, independent of the mesh Reynolds number for a grid porosity of 64%, which is higher than the lowest porosities suggested in the literature to realize homogeneous turbulence downstream of the grid. In order to validate the experimental observations and elucidate possible reasons for the inhomogeneity, direct numerical simulations have been performed over a wide range of grid porosity at a constant mesh Reynolds number. It is found from the simulations that the turbulence wake behind the symmetric grids is only homogeneous in its mean velocity but is inhomogeneous when turbulence quantities are considered, whereas the mean velocity field becomes inhomogeneous in the wake of a slightly non-uniform grid. The simulations are further analysed by evaluating the terms in the transport equation of the kinetic energy of turbulence to provide an explanation for the persistence of the inhomogeneity of Reynolds stresses far downstream of the grid. It is shown that the early homogenization of the mean velocity field hinders the homogenization of the turbulence field.

Vortical structures in the turbulent boundary layer: a possible route to a universal representation

2008 ◽  
Vol 602 ◽  
pp. 327-382 ◽  
Author(s):  
MICHEL STANISLAS ◽  
LAURENT PERRET ◽  
JEAN-MARC FOUCAUT
Keyword(s):  
Reynolds Number ◽  
Stereoscopic Particle Image Velocimetry ◽  
Length Scale ◽  
Wall Region ◽  
Mean Flow ◽  
Number Range ◽  
Vortical Structures ◽  
Kolmogorov Length Scale ◽  
The Mean ◽  
Near Wall

A study of streamwise oriented vortical structures embedded in turbulent boundary layers is performed by investigating an experimental database acquired by stereoscopic particle image velocimetry (SPIV) in a plane normal both to the mean flow and the wall. The characteristics of the experimental data allow us to focus on the spatial organization within the logarithmic region for Reynolds numbers Reθ up to 15000. On the basis of the now accepted hairpin model, relationships and interaction between streamwise vortices are first investigated via computation of two-point spatial correlations and the use of linear stochastic estimation (LSE). These analyses confirm that the shape of the most probable coherent structures corresponds to an asymmetric one-legged hairpin vortex. Moreover, two regions of different dynamics can be distinguished: the near-wall region below y+=150, densely populated with strongly interacting vortices; and the region above y+=150 where interactions between eddies happen less frequently. Characteristics of the detected eddies, such as probability density functions of their radius and intensity, are then studied. It appears that Reynolds number as well as wall-normal independences of these quantities are achieved when scaling with the local Kolmogorov scales. The most probable size of the detected vortices is found to be about 10 times the Kolmogorov length scale. These results lead us to revisit the equation for the mean square vorticity fluctuations, and to propose a new balance of this equation in the near-wall region. This analysis and the above results allow us to propose a new description of the near-wall region, leading to a new scaling which seems to have a good universality in the Reynolds-number range investigated. The possibility of reaching a universal scaling at high enough Reynolds number, based on the external velocity and the Kolmogorov length scale is suggested.

Dynamics of vortical structures in a homogeneous shear flow

1994 ◽  
Vol 274 ◽  
pp. 43-68 ◽  
Author(s):  
Shigeo Kida ◽  
Mitsuru Tanaka
Keyword(s):  
Longitudinal Vortex ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Vorticity Field ◽  
Navier Stokes Equation ◽  
Vortical Structures ◽  
Homogeneous Shear ◽  
The Mean ◽  
Spanwise Vorticity ◽  
Vortex Tubes

The mechanism of generation, development and interaction of vortical structures, extracted as concentrated-vorticity regions, in homogeneous shear turbulence is investigated by the use of the results of a direct numerical simulation of the Navier-Stokes equation with 1283 grid points. Among others, a few of typical vortical structures are identified as important dynamical elements, namely longitudinal and lateral vortex tubes and vortex layers. They interact strongly with each other. Longitudinal vortex tubes are generated from a random fluctuating vorticity field through stretching of fluid elements caused by the mean linear shear. They are inclined toward the streamwise direction by rotational motion due to the mean shear. There is a small (about 10°) deviation in direction between the longitudinal vortex tubes and vorticity vectors therein, which makes the vorticity vectors turn toward the spanwise direction (against the mean vorticity) until the spanwise components of the fluctuating vorticity become comparable in magnitude with the mean vorticity. These longitudinal vortex tubes induce straining flows perpendicular to themselves which generate vortex layers with spanwise vorticity in planes spanned by the tubes and the spanwise axis. These vortex layers are unstable, and roll up into lateral vortex tubes with concentrated spanwise vorticity through the Kelvin-Helmholtz instability. All of these vortical structures, through strong mutual interactions, break down into a complicated smallscale random vorticity field. Throughout the simulated period an oblique stripe structure dominates the whole flow field: initially it is inclined at about 45° to the downstream and, as the flow develops, the inclination angle decreases but eventually stays at around 10°–20°.

High Reynolds Number Micro-Bubble and Polymer Drag Reduction Experiments

2008 ◽  
Author(s):  
Steven L. Ceccio ◽  
David R. Dowling ◽  
Marc Perlin ◽  
Michael Solomon
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
High Reynolds Number ◽  
Polymer Drag Reduction ◽  
Micro Bubble ◽  
High Reynolds

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

scholarly journals Noise Reduction Effect of Superhydrophobic Surfaces with Streamwise Strip of Channel Flow

2021 ◽  
Vol 11 (9) ◽  
pp. 3869
Author(s):  
Chen Niu ◽  
Yongwei Liu ◽  
Dejiang Shang ◽  
Chao Zhang
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Noise Reduction ◽  
Channel Flow ◽  
Superhydrophobic Surface ◽  
Sound Field ◽  
Flow Noise ◽  
Slip Boundary ◽  
Eddy Simulation ◽  
Reduction Effect

Superhydrophobic surface is a promising technology, but the effect of superhydrophobic surface on flow noise is still unclear. Therefore, we used alternating free-slip and no-slip boundary conditions to study the flow noise of superhydrophobic channel flows with streamwise strips. The numerical calculations of the flow and the sound field have been carried out by the methods of large eddy simulation (LES) and Lighthill analogy, respectively. Under a constant pressure gradient (CPG) condition, the average Reynolds number and the friction Reynolds number are approximately set to 4200 and 180, respectively. The influence on noise of different gas fractions (GF) and strip number in a spanwise period on channel flow have been studied. Our results show that the superhydrophobic surface has noise reduction effect in some cases. Under CPG conditions, the increase in GF increases the bulk velocity and weakens the noise reduction effect. Otherwise, the increase in strip number enhances the lateral energy exchange of the superhydrophobic surface, and results in more transverse vortices and attenuates the noise reduction effect. In our results, the best noise reduction effect is obtained as 10.7 dB under the scenario of the strip number is 4 and GF is 0.5. The best drag reduction effect is 32%, and the result is obtained under the scenario of GF is 0.8 and strip number is 1. In summary, the choice of GF and the number of strips is comprehensively considered to guarantee the performance of drag reduction and noise reduction in this work.

Sign in / Sign up

Export Citation Format

Share Document