Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and downstream of an obstacle

2000 ◽  
Vol 424 ◽  
pp. 127-167 ◽  
Author(s):  
J.-Y. VINÇONT ◽  
S. SIMOËNS ◽  
M. AYRAULT ◽  
J. M. WALLACE
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Similarity Solution ◽  
Line Source ◽  
Concentration Field ◽  
Mean Square ◽  
Two Dimensional ◽  
Scalar Concentration ◽  
The Mean ◽  
Made In

Simultaneous measurements of the velocity and scalar concentration fields have been made in the plume emitting from a two-dimensional line source at the wall. The source is one obstacle height, h, downstream of a two-dimensional square obstacle located on the wall of a turbulent boundary layer. These measurements were made in two fluid media: water and air. In both media particle image velocimetry (PIV) was used for the velocity field measurements. For the scalar concentration measurements laser-induced uorescence (LIF) was used for the water flow and Mie scattering diffusion (MSD) for the air flow. Profiles of the mean and root-mean-square streamwise and wall-normal velocity components, Reynolds shear stress and mean and root-mean-square scalar concentration were determined at x = 4h and 6h downstream of the obstacle in the recirculation region and above it in the mixing region. At these streamwise stations the scalar fluxes, uc and vc, were also determined from the simultaneous velocity and scalar concentration field data. Both of these fluxes change sign from negative to positive with increasing distance from the wall in the recirculating region at 4h.A conditional analysis of the data was carried out by sorting them into the eight categories (octants) given by the sign combinations of the three variables: ±u, ±v and ±c. The octants with combinations of these three variables that correspond to types of scalar concentration flux motions that can be approximated by mean gradient scalar transport models are the octants that make the dominant contributions to uc and vc. However, in the recirculating zone, counter-gradient transport type motions also make significant contributions. Based on this conditional analysis, second-order mean gradient models of the scalar and the momentum uxes were constructed; they compare well to the measured values at 4h and 6h, particularly for the streamwise scalar flux, uc.Additional measurements of the velocity and concentration fields were made further downstream of the reattachment location in the wake region of the air flow. The mean velocity deficit profile determined from these measurements at x = 20h compares quite well to a similarity solution profile obtained by Counihan, Hunt & Jackson (1974). Their analysis was extended in the present investigation to the concentration field. The similarity solution obtained for the mean concentration compares well to profiles measured at x = 12h, 15h, and 20h, up to about three obstacle heights above the wall.

The response of a turbulent boundary layer to lateral divergence

1979 ◽  
Vol 94 (2) ◽  
pp. 243-268 ◽  
Author(s):  
A. J. Smits ◽  
J. A. Eaton ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Structural Parameters ◽  
Axial Flow ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Transition Section ◽  
Two Dimensional Flow ◽  
Made In

Measurements have been made in the flow over an axisymmetric cylinder-flare body, in which the boundary layer developed in axial flow over a circular cylinder before diverging over a conical flare. The lateral divergence, and the concave curvature in the transition section between the cylinder and the flare, both tend to destabilize the turbulence. Well downstream of the transition section, the changes in turbulence structure are still significant and can be attributed to lateral divergence alone. The results confirm that lateral divergence alters the structural parameters in much the same way as longitudinal curvature, and can be allowed for by similar empirical formulae. The interaction between curvature and divergence effects in the transition section leads to qualitative differences between the behaviour of the present flow, in which the turbulence intensity is increased everywhere, and the results of Smits, Young & Bradshaw (1979) for a two-dimensional flow with the same curvature but no divergence, in which an unexpected collapse of the turbulence occurred downstream of the curved region.

Wakes behind two-dimensional surface obstacles in turbulent boundary layers

1974 ◽  
Vol 64 (3) ◽  
pp. 529-564 ◽  
Author(s):  
J. Counihan ◽  
J. C. R. Hunt ◽  
P. S. Jackson
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Turbulent Boundary Layer ◽  
The Body ◽  
Wake Flow ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Velocity Deficit ◽  
Wind Tunnel Measurements ◽  
The Mean

By making simple assumptions, an analytical theory is deduced for the mean velocity behind a two-dimensional obstacle (of heighth) placed on a rigid plane over which flows a turbulent boundary layer (of thickness δ). It is assumed thath[Gt ] δ, and that the wake can be divided into three regions. The velocity deficit −uis greatest in the two regions in which the change in shear stress is important, a wall region (W) close to the wall and a mixing region (M) spreading from the top of the obstacle. Above these is the external region (E) in which the velocity field is an inviscid perturbation on the incident boundary-layer velocity, which is taken to have a power-law profileU(y) =U∞(y−y1)n/δn, wheren[Gt ] 1. In (M), assuming that an eddy viscosity (=KhU(h)) can be defined for the perturbed flow in terms of the incident boundary-layer flow and that the velocity is self-preserving, it is found thatu(x,y) has the form$\frac{u}{U(h)} = \frac{ C }{Kh^2U^2(h)} \frac{f(n)}{x/h},\;\;\;\; {\rm where}\;\;\;\; \eta = (y/h)/[Kx/h]^{1/(n+2)}$, and the constant which defines the strength of the wake is$C = \int^\infty_0 y^U(y)(u-u_E)dy$, whereu=uE(x, y) asy→ 0 in region (E).In region (W),u(y) is proportional to Iny.By considering a large control surface enclosing the obstacle it is shown that the constant of the wake flow is not simply related to the drag of the obstacle, but is equal to the sum of the couple on the obstacle and an integral of the pressure field on the surface near the body.New wind-tunnel measurements of mean and turbulent velocities and Reynolds stresses in the wake behind a two-dimensional rectangular block on a roughened surface are presented. The turbulent boundary layer is artificially developed by well-established methods (Counihan 1969) in such a way that δ = 8h. These measurements are compared with the theory, with other wind-tunnel measurements and also with full-scale measurements of the wind behind windbreaks.It is found that the theory describes the distribution of mean velocity reasonably well, in particular the (x/h)−1decay law is well confirmed. The theory gives the correct self-preserving form for the distribution of Reynolds stress and the maximum increase of the mean-square turbulent velocity is found to decay downstream approximately as$ (\frac{x}{h})^{- \frac{3}{2}} $in accordance with the theory. The theory also suggests that the velocity deficit is affected by the roughness of the terrain (as measured by the roughness lengthy0) in proportion to In (h/y0), and there seems to be some experimental support for this hypothesis.

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

2011 ◽  
Vol 46 (6) ◽  
pp. 917-934 ◽  
Author(s):  
V. Ya. Borovoi ◽  
I. V. Egorov ◽  
A. Yu. Noev ◽  
A. S. Skuratov ◽  
I. V. Struminskaya
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Incident Shock ◽  
Two Dimensional ◽  
Entropy Layer ◽  
Dimensional Interaction

A theory of turbulence in stratified fluids

1970 ◽  
Vol 42 (2) ◽  
pp. 349-365 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Density Profile ◽  
Richardson Number ◽  
Mixed Volume ◽  
Volume Of Fluid ◽  
Velocity Shear ◽  
Mean Velocity ◽  
Large Wave ◽  
The Mean

An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with heightzabove a turbulent boundary layer and the mean density decreases asz3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.Thecurvatureof the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

Prediction of compressible turbulent boundary layer via a symmetry-based length model

2018 ◽  
Vol 857 ◽  
pp. 449-468 ◽  
Author(s):  
Zhen-Su She ◽  
Hong-Yue Zou ◽  
Meng-Juan Xiao ◽  
Xi Chen ◽  
Fazle Hussain
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Structure ◽  
Analytic Form ◽  
Algebraic Model ◽  
Length Function ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Reynolds Analogy ◽  
The Mean

A recently developed symmetry-based theory is extended to derive an algebraic model for compressible turbulent boundary layers (CTBL) – predicting mean profiles of velocity, temperature and density – valid from incompressible to hypersonic flow regimes, thus achieving a Mach number ($Ma$) invariant description. The theory leads to a multi-layer analytic form of a stress length function which yields a closure of the mean momentum equation. A generalized Reynolds analogy is then employed to predict the turbulent heat transfer. The mean profiles and the friction coefficient are compared with direct numerical simulations of CTBL for a range of$Ma$from 0 (e.g. incompressible) to 6.0 (e.g. hypersonic), with an accuracy notably superior to popular current models such as Baldwin–Lomax and Spalart–Allmaras models. Further analysis shows that the modification is due to an improved eddy viscosity function compared to competing models. The results confirm the validity of our$Ma$-invariant stress length function and suggest the path for developing turbulent boundary layer models which incorporate the multi-layer structure.

scholarly journals Nonclassical Symmetry Analysis of Boundary Layer Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Rehana Naz ◽  
Mohammad Danish Khan ◽  
Imran Naeem
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Similarity Solution ◽  
Symmetry Analysis ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Nonclassical Symmetry ◽  
Nonclassical Symmetries

The nonclassical symmetries of boundary layer equations for two-dimensional and radial flows are considered. A number of exact solutions for problems under consideration were found in the literature, and here we find new similarity solution by implementing the SADE package for finding nonclassical symmetries.

Turbulent Wall-Pressure Fluctuations: A New Model for Off-Axis Cross-Spectral Density

1997 ◽  
Vol 119 (2) ◽  
pp. 277-280 ◽  
Author(s):  
B. A. Singer
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Spectral Density ◽  
Flow Direction ◽  
Wall Pressure ◽  
Mean Flow ◽  
New Approach ◽  
Cross Spectral Density ◽  
The Mean ◽  
The Cross

Models for the distribution of the wall-pressure under a turbulent boundary layer often estimate the coherence of the cross-spectral density in terms of a product of two coherence functions. One such function describes the coherence as a function of separation distance in the mean-flow direction, the other function describes the coherence in the cross-stream direction. Analysis of data from a large-eddy simulation of a turbulent boundary layer reveals that this approximation dramatically underpredicts the coherence for separation directions that are neither aligned with nor perpendicular to the mean-flow direction. These models fail even when the coherence functions in the directions parallel and perpendicular to the mean flow are known exactly. A new approach for combining the parallel and perpendicular coherence functions is presented. The new approach results in vastly improved approximations for the coherence.

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.

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