scholarly journals Metric for attractor overlap

2019 ◽  
Vol 874 ◽  
pp. 720-755 ◽  
Author(s):  
Rishabh Ishar ◽  
Eurika Kaiser ◽  
Marek Morzyński ◽  
Daniel Fernex ◽  
Richard Semaan ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Particle Image Velocimetry Data ◽  
Open Loop ◽  
Operating Conditions ◽  
Wall Turbulence ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Starting Point

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e. ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshot-to-snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by a few representative centroids. We employ MAO for two quite different actuated flow configurations: a two-dimensional wake with vortices in a narrow frequency range and three-dimensional wall turbulence with a broadband spectrum. In the first application, seven control laws are applied to the fluidic pinball, i.e. the two-dimensional flow around three circular cylinders whose centres form an equilateral triangle pointing in the upstream direction. These seven operating conditions comprise unforced shedding, boat tailing, base bleed, high- and low-frequency forcing as well as two opposing Magnus effects. In the second example, MAO is applied to three-dimensional simulation data from an open-loop drag reduction study of a turbulent boundary layer. The actuation mechanisms of 38 spanwise travelling transversal surface waves are investigated. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.

The Three-Dimensional Turbulent Boundary Layer on an Infinite Yawed Wing

1971 ◽  
Vol 22 (4) ◽  
pp. 346-362 ◽  
Author(s):  
J. F. Nash ◽  
R. R. Tseng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Numerical Representation ◽  
Two Dimensional ◽  
Incompressible Turbulent Boundary Layer ◽  
Displacement Thickness ◽  
Attachment Line

SummaryThis paper presents the results of some calculations of the incompressible turbulent boundary layer on an infinite yawed wing. A discussion is made of the effects of increasing lift coefficient, and increasing Reynolds number, on the displacement thickness, and on the magnitude and direction of the skin friction. The effects of the state of the boundary layer (laminar or turbulent) along the attachment line are also considered.A study is made to determine whether the behaviour of the boundary layer can adequately be predicted by a two-dimensional calculation. It is concluded that there is no simple way to do this (as is provided, in the laminar case, by the principle of independence). However, with some modification, a two-dimensional calculation can be made to give an acceptable numerical representation of the chordwise components of the flow.

scholarly journals Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory

1975 ◽  
Vol 70 (1) ◽  
pp. 127-148 ◽  
Author(s):  
B. Van Den Berg ◽  
A. Elsenaar ◽  
J. P. F. Lindhout ◽  
P. Wesseling
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Swept Wing ◽  
Test Plate ◽  
Turbulent Shear Stress

First a three-dimensional turbulent boundary-layer experiment is described. This has been carried out with the specific aim of providing a test-case for calculation methods. Much attention has been paid to the design of the test set-up. An infinite swept-wing flow has been simulated with good accuracy. The initially two-dimensional boundary layer on the test plate was subjected to an adverse pressure gradient, which led to three-dimensional separation near the trailing edge of the plate. Next, a calculation method for three-dimensional turbulent boundary layers is discussed. This solves the boundary-layer equations numerically by finite differences. The turbulent shear stress is obtained from a generalized version of Bradshaw's two-dimensional turbulent shear stress equation. The results of the calculations are compared with those of the experiment. Agreement is good over a considerable distance; but large discrepancies are apparent near the separation line.

Flows over surface-mounted bluff bodies with different spanwise widths submerged in a deep turbulent boundary layer

2019 ◽  
Vol 877 ◽  
pp. 717-758 ◽  
Author(s):  
Xingjun Fang ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Separation Bubble ◽  
Body Height ◽  
Three Dimensional ◽  
The Body ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Wake Region ◽  
Separation Bubbles

The spatio-temporal dynamics of separation bubbles induced by surface-mounted bluff bodies with different spanwise widths and submerged in a thick turbulent boundary layer is experimentally investigated. The streamwise extent of the bluff bodies is fixed at 2.36 body heights and the spanwise aspect ratio ($AR$), defined as the ratio between the width and height, is increased from 1 to 20. The thickness of the upstream turbulent boundary layer is 4.8 body heights, and the dimensionless shear and turbulence intensity evaluated at the body height are 0.23 % and 15.8 %, respectively, while the Reynolds number based on the body height and upstream free-stream velocity is 12 300. For these upstream conditions and limited streamwise extent of the bluff bodies, two distinct and strongly interacting separation bubbles are formed over and behind the bluff bodies. A time-resolved particle image velocimetry is used to simultaneously measure the velocity field within these separation bubbles. Based on the dynamics of the mean separation bubbles over and behind the bluff bodies, the flow fields are categorized into three-dimensional, transitional and two-dimensional regimes. The results indicate that the low-frequency flapping motions of the separation bubble on top of the bluff body with $\mathit{AR}=1$ are primarily influenced by the vortex shedding motion, while those with larger aspect ratios are modulated by the large-scale streamwise elongated structures embedded in the oncoming turbulent boundary layer. For $\mathit{AR}=1$ and 20, the flapping motions in the wake region are strongly influenced by those on top of the bluff bodies but with a time delay that is dependent on the $AR$. Moreover, an expansion of the separation bubble on the top surface tends to lead to an expansion and contraction of separation bubbles in the wake of $\mathit{AR}=20$ and 1, respectively. As for the transitional case of $\mathit{AR}=8$, the separation bubbles over and behind the body are in phase over a wide range of time difference. The dynamics of the shear layer in the wake region of the transitional case is remarkably more complex than the limiting two-dimensional and three-dimensional configurations.

scholarly journals Turbulent structures in a statistically three-dimensional boundary layer

2018 ◽  
Vol 859 ◽  
pp. 543-565 ◽  
Author(s):  
Kevin Kevin ◽  
Jason Monty ◽  
Nicholas Hutchins
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Outer Region ◽  
Flow Region ◽  
Secondary Flows ◽  
Wall Turbulence ◽  
Turbulent Structures ◽  
Turbulence Structures

We investigate the behaviour of large-scale coherent structures in a spanwise-heterogeneous turbulent boundary layer, using particle image velocimetry on multiple orthogonal planes. The statistical three-dimensionality is imposed by a herringbone riblet surface, although the key results presented here will be common to many cases of wall turbulence with embedded secondary flows in the form of mean streamwise vortices. Instantaneous velocity fields in the logarithmic layer reveal elongated low-momentum streaks located over the upwash-flow region, where their spanwise spacing is forced by the $2\unicode[STIX]{x1D6FF}$ periodicity of the herringbone pattern. These streaks largely resemble the turbulence structures that occur naturally (and randomly located) in spanwise-homogeneous smooth-/rough-wall boundary layers, although here they are directly formed by the roughness pattern. In the far outer region, the large spanwise spacing permits the streaks to aggressively meander. The mean secondary flows are the time-averaged artefact of the unsteady and spanwise asymmetric large-scale roll modes that accompany these meandering streaks. Interestingly, this meandering, or instability, gives rise to a pronounced streamwise periodicity (i.e. an alternating coherent pattern) in the spatial statistics, at wavelengths of approximately 4.5$\unicode[STIX]{x1D6FF}$. Overall, the observed behaviours largely resemble the streak-instability model that has been proposed for the buffer region, only here at a much larger scale and at a forced spanwise spacing. This observation further confirms recent observations that such features may occur at an entire hierarchy of scales throughout the turbulent boundary layer.

Fluctuating Forces on a Rectangular Prism and a Circular Cylinder Placed Vertically in a Turbulent Boundary Layer

1984 ◽  
Vol 106 (2) ◽  
pp. 160-166 ◽  
Author(s):  
H. Sakamoto ◽  
S. Oiwake
Keyword(s):  
Boundary Layer ◽  
Experimental Study ◽  
Aspect Ratio ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Cross Section ◽  
Boundary Layer Thickness ◽  
Bluff Body ◽  
Three Dimensional ◽  
Circular Cylinders

An experimental study was conducted to investigate the fluctuating force generated by the shedding of vortices from a three-dimensional bluff body placed vertically in a turbulent boundary layer. A conventional strain-gauge balance was modified and used in the experiment. The balance used has a relatively high natural frequency and gives a linear relation between force and strain. Prisms with a square cross section and circular cylinders were selected as three-dimensional bodies varing in aspect ratio and height. The aspect ratio and the ratio of the height to the boundary layer thickness were varied in the measurement of the fluctuating force on a body.

Sign in / Sign up

Export Citation Format

Share Document