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TY - THES AU - Boschung, Jonas Peter Maria TI - Structure function analysis of turbulent flows PB - RWTH Aachen University VL - Dissertation CY - Aachen M1 - RWTH-2017-07234 SN - 978-3-8440-5449-1 T2 - Berichte aus der Strömungstechnik SP - 1 Online-Ressource (xxi, 245 Seiten) : Illustrationen, Diagramme PY - 2017 N1 - Auch veröffentlicht auf dem Publikationsserver der RWTH Aachen University N1 - Dissertation, RWTH Aachen University, 2017 AB - The present work focuses on structure functions in homogeneous isotropic turbulence. Structure functions are statistics (more precisely, higher-order moments) of the velocity difference evaluated at two points in space, separated by some distance r. While most of the work found in the literature is based on phenomenology and thus requires additional assumptions besides homogeneity and continuity, the present thesis aims at examining structure functions based on the Navier-Stokes equations, the governing equations of motion for incompressible fluids. For that reason, firstly the system of structure function equations is discussed and analysed, with emphasis on their dissipative and pressure source terms. It is found that the dissipative source terms and equations derived thereof contain the higher moments of the (pseudo-)dissipation. Next, the viscous range is examined more closely. It is found that there are exact solutions for even-order longitudinal structure functions, which are determined by the higher moments of the dissipation 〈ε<sup>N/2</sup> 〉 and the viscosity ν. These findings are then used to define exact order-dependent dissipative cut-off scales η<sub>C,N</sub> and u<sub>C,N</sub>, which reduce to the well-known Kolmogorov scales η and u<sub>η</sub> for the second order N=2. Considering the inertial range, one may use the previous dissipative range results to match both regimes and relate inertial range scaling exponents of longitudinal structure functions to the Reynolds number scaling of the moments of the dissipation when assuming Kolmogorov's refined similarity hypothesis (RSH). Furthermore, the inertial range scaling exponent of the trace of the fifth-order structure functions is examined with regard to the system of equations. It is found that the fifth order is mostly determined by the dissipation source term, which contains the second moment of the (pseudo)-dissipation. In the inertial range, terms acting on the large scales and viscous terms are usually neglected. However at finite Reynolds numbers, these terms contribute to the structure function equation balances. For that reason, their influence is examined for the second-order equations for decaying turbulence. It is found that both the unsteady and the viscous terms contribute significantly to the second-order balances at moderate Reynolds numbers and their influence decreases only slowly. Finally, streamline segment statistics are briefly considered, because the higher conditional moments are conceptually similar to the longitudinal structure functions. LB - PUB:(DE-HGF)3 ; PUB:(DE-HGF)11 DO - DOI:10.18154/RWTH-2017-07234 UR - https://publications.rwth-aachen.de/record/697733 ER -