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# Geometrical Structure of Small Scales and Wall-bounded Turbulence

## Abstract

Turbulence is observed in most technical and natural environments involving fluid motion. However, the theory behind is still not fully understood. Due to the irregular, complex character of turbulence, it is treated statistically since a deterministic approach is usually not possible. Spatial structures in turbulence, known as eddies, are essential to describe the turbulent flow. In this thesis, a new method proposed by Wang & Peters (2006) is employed to decompose turbulent scalar fields completely and uniquely into small spatial sub-units. The approach is called Dissipation Element method. Gradient trajectories in the scalar field are traced in ascending and descending directions where they inevitably reach a minimum and a maximum point, respectively. All trajectories leading to the same pair of extremal points define a dissipation element (DE). In the present work, DE analysis is extended to the canonical wall-bounded turbulent channel flow. Special focus will be given to the effect of the wall boundaries with respect to the size of the DEs and their distribution along the wall-normal direction of the channel. To obtain data for analysis, Direct Numerical Simulations (DNS) have been conducted at different Reynolds numbers as presented in chapter 2 following a brief introduction in §1. Turbulent channel flow statistics are discussed in §3 which are later addressed to interpret results from DE analysis. In chapter 4, three-dimensional turbulent structures, called vortices, are presented which are obtained with classical methods. Classical turbulent length scales in Poiseuille flow are analyzed in §5 before the DE method is applied in chapter 6. Mean length of DEs and its variation with the distance from the wall will be addressed extensively. The influence of the Reynolds number and the choice of the scalar variable is discussed. Marginal, joint and conditional probability densities (pdf) of the Euclidean distance and scalar difference between extremal points are investigated. Employing Lie symmetry analysis, invariant solutions of the pdf are obtained. Further, a log-normal model for the pdf is derived. In addition to the classical Poiseuille flow, three different channel flows are investigated by means of the DE method, namely channel flows with wall-normal and streamwise rotations and wall transpiration. Finally, streamline segments are examined in chapter 7 with respect to the length and the velocity difference between their ending points. As in the case of DEs, marginal and conditional pdfs, as well as the influence of the wall distance and Reynolds number are discussed.

Item Type: Ph.D. Thesis
Erschienen: 2012
Creators: Aldudak, Fettah
Title: Geometrical Structure of Small Scales and Wall-bounded Turbulence
Language: English
Abstract:

Turbulence is observed in most technical and natural environments involving fluid motion. However, the theory behind is still not fully understood. Due to the irregular, complex character of turbulence, it is treated statistically since a deterministic approach is usually not possible. Spatial structures in turbulence, known as eddies, are essential to describe the turbulent flow. In this thesis, a new method proposed by Wang & Peters (2006) is employed to decompose turbulent scalar fields completely and uniquely into small spatial sub-units. The approach is called Dissipation Element method. Gradient trajectories in the scalar field are traced in ascending and descending directions where they inevitably reach a minimum and a maximum point, respectively. All trajectories leading to the same pair of extremal points define a dissipation element (DE). In the present work, DE analysis is extended to the canonical wall-bounded turbulent channel flow. Special focus will be given to the effect of the wall boundaries with respect to the size of the DEs and their distribution along the wall-normal direction of the channel. To obtain data for analysis, Direct Numerical Simulations (DNS) have been conducted at different Reynolds numbers as presented in chapter 2 following a brief introduction in §1. Turbulent channel flow statistics are discussed in §3 which are later addressed to interpret results from DE analysis. In chapter 4, three-dimensional turbulent structures, called vortices, are presented which are obtained with classical methods. Classical turbulent length scales in Poiseuille flow are analyzed in §5 before the DE method is applied in chapter 6. Mean length of DEs and its variation with the distance from the wall will be addressed extensively. The influence of the Reynolds number and the choice of the scalar variable is discussed. Marginal, joint and conditional probability densities (pdf) of the Euclidean distance and scalar difference between extremal points are investigated. Employing Lie symmetry analysis, invariant solutions of the pdf are obtained. Further, a log-normal model for the pdf is derived. In addition to the classical Poiseuille flow, three different channel flows are investigated by means of the DE method, namely channel flows with wall-normal and streamwise rotations and wall transpiration. Finally, streamline segments are examined in chapter 7 with respect to the length and the velocity difference between their ending points. As in the case of DEs, marginal and conditional pdfs, as well as the influence of the wall distance and Reynolds number are discussed.

Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 10 Jul 2012 10:22
Official URL: urn:nbn:de:tuda-tuprints-30353 Send an inquiry Show editorial Details