High-order moments of streamwise fluctuations in a turbulent channel flow with spanwise rotation

A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re=U_{b}h/\unicode[STIX]{x1D708}$ is varied from a low 3000 to a moderate 31 600 and the rotation number $Ro=2\unicode[STIX]{x1D6FA}h/U_{b}$ is varied from 0 to 2.7, where $U_{b}$ is the mean bulk velocity, $h$ the channel half-gap, $\unicode[STIX]{x1D708}$ the viscosity and $\unicode[STIX]{x1D6FA}$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ a characteristic linear part with a slope near to $2\unicode[STIX]{x1D6FA}$, and a corresponding linear part in the profiles of the production and dissipation rate of turbulent kinetic energy appears. With increasing $Ro$, a distinct unstable side with large spanwise and wall-normal Reynolds stresses and a stable side with much weaker turbulence develops in the channel. The flow starts to relaminarize on the stable side of the channel and persisting turbulent–laminar patterns appear at higher $Re$. If $Ro$ is further increased, the flow on the stable side becomes laminar-like while at yet higher $Ro$ the whole flow relaminarizes, although the calm periods might be disrupted by repeating bursts of turbulence, as explained by Brethouwer (Phys. Rev. Fluids, vol. 1, 2016, 054404). The influence of the Reynolds number is considerable, in particular on the stable side of the channel where velocity fluctuations are stronger and the flow relaminarizes less quickly at higher $Re$. Visualizations and statistics show that, at $Ro=0.15$ and 0.45, large-scale structures and large counter-rotating streamwise roll cells develop on the unstable side. These become less noticeable and eventually vanish when $Ro$ rises, especially at higher $Re$. At high $Ro$, the largest energetic structures are larger at lower $Re$.

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A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

Journal of Computational Physics ◽

10.1016/j.jcp.2017.07.039 ◽

2017 ◽

Vol 348 ◽

pp. 634-659 ◽

Cited By ~ 39

Author(s):

Benjamin Krank ◽

Niklas Fehn ◽

Wolfgang A. Wall ◽

Martin Kronbichler

Keyword(s):

Discontinuous Galerkin ◽

Channel Flow ◽

Incompressible Flow ◽

Turbulent Channel Flow ◽

High Order

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Turbulent Channel Flow With a Modified k-ω Turbulence Model for High-Order Finite Element Methods

Volume 2: Computational Fluid Dynamics ◽

10.1115/ajkfluids2019-5501 ◽

2019 ◽

Cited By ~ 1

Author(s):

Nojan Bagheri-Sadeghi ◽

Brian T. Helenbrook ◽

Kenneth D. Visser

Keyword(s):

Finite Element ◽

Channel Flow ◽

Turbulence Model ◽

Grid Point ◽

Turbulent Channel Flow ◽

Accurate Estimate ◽

Accurate Solution ◽

High Order ◽

Element Discretization ◽

Aspect Ratios

Abstract One-dimensional fully developed channel flow was solved using a modified k–ω turbulence model that was recently proposed for use with high-order finite element schemes. In order to study this new turbulence model’s behavior, determine its dependence on boundary conditions and model constants, and find efficient methods for obtaining solutions, the model was first examined using a linear finite element discretization in 1D. The results showed that an accurate estimate of the parameter εk which is used to define k in terms of the working variable k~ is essential to get an accurate solution. Also, the turbulence model depended sensitively on an accurate estimate of the distance of the first grid point from the wall, which can be difficult to estimate in unstructured grids. This is used for the boundary condition of specific dissipation rate on the wall. This model was then implemented in a high-order finite element code that uses an unstructured mesh of triangles to verify that the 1D results were predictive of the behavior of the full 2D discretization. High-order 2D results were obtained on triangular meshes with element aspect ratios up to 250000.

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