scholarly journals Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields

2014 ◽  
Vol 756 ◽  
pp. 191-225 ◽  
Author(s):  
Michael Wilczek ◽  
Charles Meneveau
Keyword(s):  
Evolution Equation ◽  
Velocity Gradient ◽  
Small Scale ◽  
Viscous Effects ◽  
Local Pressure ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Starting Point ◽  
The Impact ◽  
Gaussian Closure

AbstractUnderstanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the velocity gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian velocity gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon.

scholarly journals On the small-scale structure of turbulence and its impact on the pressure field

2018 ◽  
Vol 861 ◽  
pp. 422-446 ◽  
Author(s):  
Dimitar G. Vlaykov ◽  
Michael Wilczek
Keyword(s):  
Velocity Gradient ◽  
Pressure Field ◽  
Reynolds Numbers ◽  
Scale Structure ◽  
Small Scale ◽  
Local Pressure ◽  
Small Scale Structure ◽  
Kolmogorov Scale ◽  
Non Local ◽  
The Impact

Understanding the small-scale structure of incompressible turbulence and its implications for the non-local pressure field is one of the fundamental challenges in fluid mechanics. Intense velocity gradient structures tend to cluster on a range of scales which affects the pressure through a Poisson equation. Here we present a quantitative investigation of the spatial distribution of these structures conditional on their intensity for Taylor-based Reynolds numbers in the range [160, 380]. We find that the correlation length of the second invariant of the velocity gradient is proportional to the Kolmogorov scale. It is also a good indicator for the spatial localization of intense enstrophy and strain-dominated regions, as well as the separation between them. We describe and quantify the differences in the two-point statistics of these regions and the impact they have on the non-locality of the pressure field as a function of the intensity of the regions. Specifically, across the examined range of Reynolds numbers, the pressure in strong rotation-dominated regions is governed by a dissipation-scale neighbourhood. In strong strain-dominated regions, on the other hand, it is determined primarily by a larger neighbourhood reaching inertial scales.

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.

Predicting viscous-range velocity gradient dynamics in large-eddy simulations of turbulence

2017 ◽  
Vol 837 ◽  
pp. 80-114 ◽  
Author(s):  
Perry L. Johnson ◽  
Charles Meneveau
Keyword(s):  
Velocity Gradient ◽  
Volume Fraction ◽  
Large Eddy Simulations ◽  
Coarse Grained ◽  
Small Scale ◽  
Turbulence Structure ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Large Eddy ◽  
Scale Turbulence

The detailed dynamics of small-scale turbulence are not directly accessible in large-eddy simulations (LES), posing a modelling challenge, because many micro-physical processes such as deformation of aggregates, drops, bubbles and polymers dynamics depend strongly on the velocity gradient tensor, which is dominated by the turbulence structure in the viscous range. In this paper, we introduce a method for coupling existing stochastic models for the Lagrangian evolution of the velocity gradient tensor with coarse-grained fluid simulations to recover small-scale physics without resorting to direct numerical simulations (DNS). The proposed approach is implemented in LES of turbulent channel flow and detailed comparisons with DNS are carried out. An application to modelling the fate of deformable, small (sub-Kolmogorov) droplets at negligible Stokes number and low volume fraction with one-way coupling is carried out and results are again compared to DNS results. Results illustrate the ability of the proposed model to predict the influence of small-scale turbulence on droplet micro-physics in the context of LES.

scholarly journals Structure and dynamics of small-scale turbulence in vaporizing two-phase flows

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Radouan Boukharfane ◽  
Aimad Er-raiy ◽  
Matteo Parsani ◽  
Nilanjan Chakraborty
Keyword(s):  
Strain Rate ◽  
Velocity Gradient ◽  
Liquid Interface ◽  
Small Scale ◽  
Two Phase Flows ◽  
Gradient Tensor ◽  
Two Phase ◽  
Velocity Gradient Tensor ◽  
Carrier Liquid ◽  
Wide Range

AbstractImproving our fundamental understanding of multiphase turbulent flows will be beneficial for analyses of a wide range of industrial and geophysical processes. Herein, we investigate the topology of the local flow in vaporizing forced homogeneous isotropic turbulent two-phase flows. The invariants of the velocity-gradient, rate-of-strain, rate-of-rotation tensors, and scalar gradient were computed and conditioned for different distances from the liquid–gas surface. A Schur decomposition of the velocity gradient tensor into a normal and non-normal parts was undertaken to supplement the classical double decomposition into rotation and strain tensors. Using direct numerical simulations results, we show that the joint probability density functions of the second and third invariants have classical shapes in all carrier-gas regions but gradually change as they approach the carrier-liquid interface. Near the carrier-liquid interface, the distributions of the invariants are remarkably similar to those found in the viscous sublayer of turbulent wall-bounded flows. Furthermore, the alignment of both vorticity and scalar gradient with the strain-rate field changes spatially such that its universal behaviour occurs far from the liquid–gas interface. We found also that the non-normal effects of the velocity gradient tensor play a crucial role in explaining the preferred alignment.

Invariants of velocity gradient tensor in supersonic turbulent pipe, nozzle, and diffuser flows

2018 ◽  
Vol 30 (1) ◽  
pp. 015104 ◽  
Author(s):  
Komal Kumari ◽  
Susila Mahapatra ◽  
Somnath Ghosh ◽  
Joseph Mathew
Keyword(s):  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor
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