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 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

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

1996 ◽  
Vol 326 ◽  
pp. 151-179 ◽  
Author(s):  
Junhui Liu ◽  
Ugo Piomelli ◽  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Shear Stresses ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Production Term

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

The Interaction of Rolling Vortices With a Turbulent Boundary Layer

1995 ◽  
Vol 117 (4) ◽  
pp. 564-570
Author(s):  
M. J. Donnelly ◽  
O. K. Rediniotis ◽  
S. A. Ragab ◽  
D. P. Telionis
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Life Span ◽  
Turbulent Kinetic Energy ◽  
Laser Doppler Velocimetry ◽  
Doppler Velocimetry ◽  
Turbulence Level ◽  
Periodic Field ◽  
Entire Boundary

Laser-Doppler velocimetry is employed to measure the periodic field created by releasing spanwise vortices in a turbulent boundary layer. Phase-averaged vorticity and turbulence level contours are estimated and presented. It is found that vortices with diameter of the order of the boundary layer quickly diffuse and disappear while their turbulent kinetic energy spreads uniformly across the entire boundary layer. Larger vortices have a considerably longer life span and in turn feed more vorticity into the boundary layer.

scholarly journals Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

2018 ◽  
Vol 474 (2212) ◽  
pp. 20170706 ◽  
Author(s):  
Daniel Wacks ◽  
Ilias Konstantinou ◽  
Nilanjan Chakraborty
Keyword(s):  
Velocity Gradient ◽  
Joint Probability ◽  
Lewis Number ◽  
Gradient Tensor ◽  
Local Flow ◽  
Reaction Progress ◽  
Velocity Gradient Tensor ◽  
Progress Variable ◽  
Joint Probability Density ◽  
Turbulent Premixed

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

scholarly journals Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow

2017 ◽  
Vol 817 ◽  
pp. 1-20 ◽  
Author(s):  
O. R. H. Buxton ◽  
M. Breda ◽  
X. Chen
Keyword(s):  
Turbulent Flows ◽  
Velocity Gradient ◽  
Joint Probability ◽  
Shear Layers ◽  
Velocity Fields ◽  
Gradient Tensor ◽  
Drop Shape ◽  
Velocity Gradient Tensor ◽  
Flow Physics ◽  
Joint Probability Density

Tomographic particle image velocimetry experiments were performed in the near field of the turbulent flow past a square cylinder. A classical Reynolds decomposition was performed on the resulting velocity fields into a time invariant mean flow and a fluctuating velocity field. This fluctuating velocity field was then further decomposed into coherent and residual/stochastic fluctuations. The statistical distributions of the second and third invariants of the velocity-gradient tensor were then computed at various streamwise locations, along the centreline of the flow and within the shear layers. These invariants were calculated from both the Reynolds-decomposed fluctuating velocity fields and the coherent and stochastic fluctuating velocity fields. The range of spatial locations probed incorporates regions of contrasting flow physics, including a mean recirculation region and separated shear layers, both upstream and downstream of the location of peak turbulence intensity along the centreline. These different flow physics are also reflected in the velocity gradients themselves with different topologies, as characterised by the statistical distributions of the constituent enstrophy and strain-rate invariants, for the three different fluctuating velocity fields. Despite these differing flow physics the ubiquitous self-similar ‘tear drop’-shaped joint probability density function between the second and third invariants of the velocity-gradient tensor is observed along the centreline and shear layer when calculated from both the Reynolds decomposed and the stochastic velocity fluctuations. These ‘tear drop’-shaped joint probability density functions are not, however, observed when calculated from the coherent velocity fluctuations. This ‘tear drop’ shape is classically associated with the statistical distribution of the velocity-gradient tensor invariants in fully developed turbulent flows in which there is no coherent dynamics present, and hence spectral peaks at low wavenumbers. The results presented in this manuscript, however, show that such ‘tear drops’ also exist in spatially developing inhomogeneous turbulent flows. This suggests that the ‘tear drop’ shape may not just be a universal feature of fully developed turbulence but of turbulent flows in general.

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