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

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

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).

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.

Sign in / Sign up

Export Citation Format

Share Document