Non-normal effect of the velocity gradient tensor and the relevant subgrid-scale model in compressible turbulent boundary layer

2021 ◽  
Vol 33 (2) ◽  
pp. 025103
Author(s):  
Jia-Long Yu ◽  
Zhiye Zhao ◽  
Xi-Yun Lu
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Gradient ◽  
Scale Model ◽  
Subgrid Scale ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Subgrid Scale Model

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).

High-Pass Filtered Eddy-Viscosity Models for Large-Eddy Simulations of Compressible Wall-Bounded Flows

2004 ◽  
Author(s):  
Steffen Stolz
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Eddy Viscosity ◽  
Large Eddy Simulations ◽  
Scale Model ◽  
Subgrid Scale ◽  
Smagorinsky Model ◽  
Viscosity Models ◽  
Large Eddy ◽  
High Pass

Eddy-viscosity models such as the Smagorinsky model [1] are the most often employed subgrid-scale (SGS) models for large-eddy simulations (LES). However, for a correct prediction of the viscous sublayer of wall-bounded turbulent flows van-Driest wall damping functions or a dynamic determination of the constant [2] have to be employed. Alternatively, high-pass filtered (HPF) quantities can be used instead of the full velocity field for the computation of the subgrid-scale model terms. This approach has been independently proposed by Vreman [3] and Stolz et al. [4]. In this contribution we consider LES of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of approximately 4500, using the HPF Smagorinsky model. The model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique proposed by [5] where the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at inflow.

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