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.

Effects of an axisymmetric contraction on a turbulent pipe flow

2011 ◽  
Vol 687 ◽  
pp. 376-403 ◽  
Author(s):  
Seong Jae Jang ◽  
Hyung Jin Sung ◽  
Per-Åge Krogstad
Keyword(s):  
Pipe Flow ◽  
Core Region ◽  
Turbulent Pipe Flow ◽  
Wall Region ◽  
Mean Flow ◽  
The Core ◽  
Thin Region ◽  
Local Mean ◽  
The Mean ◽  
Near Wall

AbstractThe flow in an axisymmetric contraction fitted to a fully developed pipe flow is experimentally and numerically studied. The reduction in turbulence intensity in the core region of the flow is discussed on the basis of the budgets for the various turbulent stresses as they develop downstream. The contraction generates a corresponding increase in energy in the near-wall region, where the sources for energy production are quite different and of opposite sign compared to the core region, where these effects are caused primarily by vortex stretching. The vortices in the pipe become aligned with the flow as the stretching develops through the contraction. Vortices which originally have a spanwise component in the pipe are stretched into pairs of counter-rotating vortices which become disconnected and aligned with the mean flow. The structures originating in the pipe which are inclined at an angle with respect to the wall are rotated towards the local mean streamlines. In the very near-wall region and the central part of the contraction the flow tends towards two-component turbulence, but these structures are different. The streamwise and azimuthal stresses are dominant in the near-wall region, while the lateral components dominate in the central part of the flow. The two regions are separated by a rather thin region where the flow is almost isotropic.

Direct numerical simulations of Rayleigh–Bénard convection in water with non-Oberbeck–Boussinesq effects

2019 ◽  
Vol 881 ◽  
pp. 1073-1096 ◽  
Author(s):  
Andreas D. Demou ◽  
Dimokratis G. E. Grigoriadis
Keyword(s):  
Numerical Simulations ◽  
Two Dimensions ◽  
Direct Numerical Simulations ◽  
Wall Region ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

Sidewall finite-conductivity effects in confined turbulent thermal convection

2002 ◽  
Vol 473 ◽  
pp. 201-210 ◽  
Author(s):  
ROBERTO VERZICCO
Keyword(s):  
Boundary Conditions ◽  
Thermal Convection ◽  
Lateral Wall ◽  
Finite Conductivity ◽  
Mean Flow ◽  
Number Range ◽  
Additional Heat ◽  
Low Aspect Ratio ◽  
Temperature Boundary ◽  
The Mean

The effects of a sidewall with finite thermal conductivity on confined turbulent thermal convection has been investigated using direct numerical simulation. The study is motivated by the observation that the heat flowing through the lateral wall is not always negligible in the low-aspect-ratio cells of several recent experiments. The extra heat flux modifies the temperature boundary conditions of the flow and therefore the convective heat transfer. It has been found that, for usual sidewall thicknesses, the heat travelling from the hot to the cold plates directly through the sidewall is negligible owing to the additional heat exchanged at the lateral fluid/wall interface. In contrast, the modified temperature boundary conditions alter the mean flow yielding significant Nusselt number corrections which, in the low Rayleigh number range, can change the exponent of the Nu vs. Ra power law by 10%.

High-Fidelity Simulations of a High-Pressure Turbine Stage: Effects of Reynolds Number and Inlet Turbulence

2021 ◽  
Author(s):  
Yaomin Zhao ◽  
Richard D. Sandberg
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Suction Side ◽  
Rotor Blades ◽  
High Fidelity ◽  
Mean Flow ◽  
High Pressure Turbine ◽  
Flow Shear ◽  
Phase Lock ◽  
The Mean

Abstract We present the first wall-resolved high-fidelity simulations of high-pressure turbine (HPT) stages at engine-relevant conditions. A series of cases have been performed to investigate the effects of varying Reynolds numbers and inlet turbulence on the aerothermal behavior of the stage. While all of the cases have similar mean pressure distribution, the cases with higher Reynolds number show larger amplitude wall shear stress and enhanced heat fluxes around the vane and rotor blades. Moreover, higher-amplitude turbulence fluctuations at the inlet enhance heat transfer on the pressure-side and induce early transition on the suction-side of the vane, although the rotor blade boundary layers are not significantly affected. In addition to the time-averaged results, phase-lock averaged statistics are also collected to characterize the evolution of the stator wakes in the rotor passages. It is shown that the stretching and deformation of the stator wakes is dominated by the mean flow shear, and their interactions with the rotor blades can significantly intensify the heat transfer on the suction side. For the first time, the recently proposed entropy analysis has been applied to phase-lock averaged flow fields, which enables a quantitative characterization of the different mechanisms responsible for the unsteady losses of the stages. The results indicate that the losses related to the evolution of the stator wakes is mainly caused by the turbulence production, i.e. the direct interaction between the wake fluctuations and the mean flow shear through the rotor passages.

Scaling laws for pipe-flow turbulence

1975 ◽  
Vol 67 (2) ◽  
pp. 257-271 ◽  
Author(s):  
A. E. Perry ◽  
C. J. Abell
Keyword(s):  
Pipe Flow ◽  
Scaling Laws ◽  
Dynamic Calibration ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Number Range ◽  
Static Calibration ◽  
Calibration Methods ◽  
The Mean ◽  
Flow Turbulence

Using hot-wire-anemometer dynamic-calibration methods, fully developed pipe-flow turbulence measurements have been taken in the Reynolds-number range 80 × 103 to 260 × 103. Comparisons are made with the results of previous workers, obtained using static-calibration methods. From the dynamic-calibration results, a consistent and systematic correlation for the distribution of turbulence quantities becomes evident, the resulting correlation scheme being similar to that which has previously been established for the mean flow. The correlations reported have been partly conjectured in the past by many workers but convincing experimental evidence has always been masked by the scatter in the results, no doubt caused by the difficulties associated with static-calibration methods, particularly the earlier ones. As for the mean flow, the turbulence intensity measurements appear to collapse to an inner and outer law with a region of overlap, from which deductions can be made using dimensional arguments. The long-suspected similarity of the turbulence structure and its consistency with the established mean-flow similarity appears to be confirmed by the measurements reported here.

scholarly journals Exact coherent states of attached eddies in channel flow

2019 ◽  
Vol 862 ◽  
pp. 1029-1059 ◽  
Author(s):  
Qiang Yang ◽  
Ashley P. Willis ◽  
Yongyun Hwang
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Coherent Structures ◽  
Time Scale ◽  
Coherent States ◽  
Plane Channel ◽  
Reynolds Numbers ◽  
Wall Region ◽  
Self Similar ◽  
Near Wall

A new set of exact coherent states in the form of a travelling wave is reported in plane channel flow. They are continued over a range in $Re$ from approximately $2600$ up to $30\,000$, an order of magnitude higher than those discovered in the transitional regime. This particular type of exact coherent states is found to be gradually more localised in the near-wall region on increasing the Reynolds number. As larger spanwise sizes $L_{z}^{+}$ are considered, these exact coherent states appear via a saddle-node bifurcation with a spanwise size of $L_{z}^{+}\simeq 50$ and their phase speed is found to be $c^{+}\simeq 11$ at all the Reynolds numbers considered. Computation of the eigenspectra shows that the time scale of the exact coherent states is given by $h/U_{cl}$ in channel flow at all Reynolds numbers, and it becomes equivalent to the viscous inner time scale for the exact coherent states in the limit of $Re\rightarrow \infty$. The exact coherent states at several different spanwise sizes are further continued to a higher Reynolds number, $Re=55\,000$, using the eddy-viscosity approach (Hwang & Cossu, Phys. Rev. Lett., vol. 105, 2010, 044505). It is found that the continued exact coherent states at different sizes are self-similar at the given Reynolds number. These observations suggest that, on increasing Reynolds number, new sets of self-sustaining coherent structures are born in the near-wall region. Near this onset, these structures scale in inner units, forming the near-wall self-sustaining structures. With further increase of Reynolds number, the structures that emerged at lower Reynolds numbers subsequently evolve into the self-sustaining structures in the logarithmic region at different length scales, forming a hierarchy of self-similar coherent structures as hypothesised by Townsend (i.e. attached eddy hypothesis). Finally, the energetics of turbulent flow is discussed for a consistent extension of these dynamical systems notions to high Reynolds numbers.

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.

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.

Experimental Investigation of Perforated Plate Turbulent Flow Past a Solid Sphere

2004 ◽  
Author(s):  
Himanshu Tyagi ◽  
Rui Liu ◽  
David S.-K. Ting ◽  
Clifton R. Johnston
Keyword(s):  
Perforated Plate ◽  
Solid Sphere ◽  
Length Scale ◽  
Freestream Turbulence ◽  
Comprehensive Investigation ◽  
Mean Velocity ◽  
Kolmogorov Length Scale ◽  
Turbulence Effect ◽  
Plastic Sphere ◽  
The Mean

As the first stage of a comprehensive investigation of turbulence effect on the aerodynamics of sphere, the effect of freestream turbulence on the wake generated behind a sphere is investigated in this study. A 10 cm (4 in) diameter plastic sphere was placed in a wind tunnel of cross section 75 cm by 75 cm. The freestream turbulence was generated by fixing a perforated plate to the entrance of the test section. The wake was characterized using a normal constant-temperature hotwire at 30D, 40D and 50D (11.25d, 15d & 18.75d respectively) downstream of the sphere (where D = 3.75 cm is the diameter of the perforated plate hole, and d is the diameter of the sphere). The Reynolds number of the flow, based on the mean velocity and the diameter of the sphere, was 6.6 × 104. Based on the instantaneous velocity measurement, Kolmogorov length scale, integral length scale and relative turbulence intensity in the wake were deduced.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

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