scholarly journals Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer

2017 ◽  
Vol 815 ◽  
pp. 223-242 ◽  
Author(s):  
P. Bechlars ◽  
R. D. Sandberg
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Gradient ◽  
Evolution Equations ◽  
Turbulence Models ◽  
Turbulent Structures ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
The Mean ◽  
The Individual

In order to improve the physical understanding of the development of turbulent structures, the compressible evolution equations for the first three invariants $P$, $Q$ and $R$ of the velocity gradient tensor have been derived. The mean evolution of characteristic turbulent structure types in the $QR$-space were studied and compared at different wall-normal locations of a compressible turbulent boundary layer. The evolution of these structure types is fundamental to the physics that needs to be captured by turbulence models. Significant variations of the mean evolution are found across the boundary layer. The key features of the changes of the mean trajectories in the invariant phase space are highlighted and the consequences of the changes are discussed. Further, the individual elements of the overall evolution are studied separately to identify the causes that lead to the evolution varying with the distance to the wall. Significant impact of the wall-normal location on the coupling between the pressure-Hessian tensor and the velocity gradient tensor was found. The highlighted features are crucial for the development of more universal future turbulence models.

Dual-plane PIV technique to determine the complete velocity gradient tensor in a turbulent boundary layer

2005 ◽  
Vol 39 (2) ◽  
pp. 222-231 ◽  
Author(s):  
Bharathram Ganapathisubramani ◽  
Ellen K. Longmire ◽  
Ivan Marusic ◽  
Stamatios Pothos
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Dual Plane ◽  
Piv Technique

Lagrangian evolution of the invariants of the velocity gradient tensor in a turbulent boundary layer

2012 ◽  
Vol 24 (10) ◽  
pp. 105104 ◽  
Author(s):  
C. Atkinson ◽  
S. Chumakov ◽  
I. Bermejo-Moreno ◽  
J. Soria
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor

Dynamics of a low Reynolds number turbulent boundary layer

2000 ◽  
Vol 404 ◽  
pp. 87-115 ◽  
Author(s):  
JUAN M. CHACIN ◽  
BRIAN J. CANTWELL
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Velocity Gradient ◽  
Rapid Change ◽  
Joint Probability ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor

The generation of Reynolds stress, turbulent kinetic energy and dissipation in the turbulent boundary layer simulation of Spalart (1988) is studied using the invariants of the velocity gradient tensor. This technique enables the study of the whole range of scales in the flow using a single unified approach. In addition, it also provides a rational basis for relating the flow structure in physical space to an appropriate statistical measure in the space of invariants. The general characteristics of the turbulent motion are analysed using a combination of computer-based visualization of flow variables together with joint probability distributions of the invariants. The quantities studied are of direct interest in the development of turbulence models. The cubic discriminant of the velocity gradient tensor provides a useful marker for distinguishing regions of active and passive turbulence. It is found that the strongest Reynolds-stress and turbulent-kinetic-energy generating events occur where the discriminant has a rapid change of sign. Finally, the time evolution of the invariants is studied by computing along particle paths in a Lagrangian frame of reference. It is found that the invariants tend to evolve toward two distinct asymptotes in the plane of invariants. Several simplified models for the evolution of the velocity gradient tensor are described. These models compare well with several of the important features observed in the Lagrangian computation. The picture of the turbulent boundary layer which emerges is consistent with the ideas of Townsend (1956) and with the physical picture of turbulent structure set forth by Theodorsen (1955).

scholarly journals Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at a friction Reynolds number of 932

2016 ◽  
Vol 803 ◽  
pp. 356-394 ◽  
Author(s):  
A. Lozano-Durán ◽  
M. Holzner ◽  
J. Jiménez
Keyword(s):  
Velocity Gradient ◽  
Turbulent Channel Flow ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Filter Width ◽  
Strain Components ◽  
Order Of Magnitude ◽  
Self Similar ◽  
The Mean ◽  
Orbital Periods

The invariants of the velocity gradient tensor,$R$and$Q$, and their enstrophy and strain components are studied in the logarithmic layer of an incompressible turbulent channel flow. The velocities are filtered in the three spatial directions and the results are analysed at different scales. We show that the$R$–$Q$plane does not capture the changes undergone by the flow as the filter width increases, and that the enstrophy/enstrophy-production and strain/strain-production planes represent better choices. We also show that the conditional mean trajectories may differ significantly from the instantaneous behaviour of the flow since they are the result of an averaging process where the mean is 3–5 times smaller than the corresponding standard deviation. The orbital periods in the$R$–$Q$plane are shown to be independent of the intensity of the events, and of the same order of magnitude as those in the enstrophy/enstrophy-production and strain/strain-production planes. Our final goal is to test whether the dynamics of the flow is self-similar in the inertial range, and the answer turns out to be that it is not. The mean shear is found to be responsible for the absence of self-similarity and progressively controls the dynamics of the eddies observed as the filter width increases. However, a self-similar behaviour emerges when the calculations are repeated for the fluctuating velocity gradient tensor. Finally, the turbulent cascade in terms of vortex stretching is considered by computing the alignment of the vorticity at a given scale with the strain at a different one. These results generally support a non-negligible role of the phenomenological energy-cascade model formulated in terms of vortex stretching.

scholarly journals Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

2015 ◽  
Vol 766 ◽  
pp. 202-225 ◽  
Author(s):  
Rui Ni ◽  
Stefan Kramel ◽  
Nicholas T. Ouellette ◽  
Greg A. Voth
Keyword(s):  
Strain Rate ◽  
Velocity Gradient ◽  
Strong Dependence ◽  
Joint Probability ◽  
Weighted Average ◽  
Seeding Density ◽  
Full Description ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
The Mean

AbstractWe present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate from experimental results agree well with numerical findings. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (jPDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery’s equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the jPDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

Effects of pressure gradient on the evolution of velocity-gradient tensor invariant dynamics on a controlled-diffusion aerofoil at

2019 ◽  
Vol 868 ◽  
pp. 584-610 ◽  
Author(s):  
H. Wu ◽  
S. Moreau ◽  
R. D. Sandberg
Keyword(s):  
Pressure Gradient ◽  
Velocity Gradient ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Controlled Diffusion ◽  
Mean Pressure ◽  
The Mean ◽  
The Impact

A weakly compressible flow direct numerical simulation of a controlled-diffusion aerofoil at $8^{\circ }$ geometrical angle of attack, a chord-based Reynolds number of $Re_{c}=150\,000$ and a Mach number of $M=0.25$ based on the free-stream velocity relevant to many industrial applications was conducted to improve the understanding of the impact of the pressure gradient on the development of turbulent structures. The evolution equations for the two invariants $Q$ and $R$ of the velocity-gradient tensor have been studied at various locations along the aerofoil chord on its suction side. The shape of the mean evolution of the velocity-gradient tensor invariants were found to vary strongly when the flow encounters favourable, zero and adverse pressure gradients and as well for different wall-normal locations. The coupling between the pressure-Hessian tensor and the velocity-gradient tensor was found to be the major factor that causes these changes and is greatly influenced by the mean pressure-gradient condition and the wall-normal distance. Striking differences exist from the mean trajectories of this coupling at least in the log layer and outer layer subject to different mean pressure gradients. The nonlinearity and viscous diffusion effects keep their respective invariant characters regardless of the pressure-gradient effects and wall-normal locations. The wall and the mean adverse pressure gradient were both found to suppress the vortical stretching features of the flow. These features are of great importance for the development of future turbulence models on wall-bounded flows, especially on surfaces with significant curvature such as cambered aerofoils and blades for which significant mean pressure gradients exist.

PIV Investigation of Flow Behind Surface Mounted Detached Square Cylinder

2006 ◽  
Author(s):  
P. K. Panigrahi
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Velocity Gradient ◽  
Flow Structures ◽  
Wall Region ◽  
Gap Size ◽  
Vorticity Field ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Near Wall

The flow field behind surface mounted detached square ribs over an approaching flat plate turbulent boundary layer has been studied. The Reynolds number based on the rib height has been set equal to 11075. The ratio of gap size from the flat plate surface to the square rib size has been varied between 0.2 and 1.0. The ratio of the approaching boundary layer thickness to the rib height is equal to 0.2. The PIV (2-component and stereo) technique in both stream wise and cross-stream measurement planes have been implemented. The PIV data has been acquired at two different resolutions. The high resolution measurements have been used to show the flow field at immediate downstream of the detached ribs. The oil flow visualization study has been carried out to relate the surface flow patterns to that of the flow structures. The mean and rms velocity field, average stream wise and span wise vorticity field, turbulent energy production and stream traces have been reported. The invariant of the velocity gradient tensor has been calculated to distinguish between the rotational and shear contribution of the vorticity field. The recirculation bubbles with foci like structure behind the detached ribs are displaced upward and its size drops with an increase in the gap size. The flow below the detached rib is film like flow for lower gap size leading to significant near wall modification of the flow structures. For higher gap size, the viscous effect predominates in the near wall region. The stream traces in the cross stream plane show additional node-saddle patterns in the near wall region indicating greater near wall flow structures and hence better mixing. The turbulence intensity, vorticity and velocity gradient tensor invariant results confirm the efficacy of the detached rib with smaller gap to cylinder size as an effective passive flow control tool for near wall mixing enhancement.

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