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Title: Investigation of the inverse cascade process in wall-bounded logarithmic flow as a solution of the Euler equation
Author: Chittabathini, Kumaraswamy
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2008
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Wall-bounded shear flows (WBSF) can be regarded as turbulent, organized coherent structures and occur in many different circumstances. The self-similarity of statistical characteristics of turbulence at different heights in the log layer of WBSF might reflect coherent structures which are also self-similar. McNaughton suggested that these coherent structures are in the form of 'Theodorsen ejection amplifier' (TEA) patterns. The TEA model of the structure of turbulence may be responsible for the formation of the three-dimensional inverse cascade process in log layers over smooth walls. The inverse cascade can serve as an efficient mechanism of energy transfer from small to large scales and enables us to understand the dynamics of large-scale coherent structures in the near-wall region. As far as the author is aware, no previous research has been conducted into the existence of a 3-D inverse cascade in WBSF. The objective of the thesis is to investigate numerically an upscale cascade process that has been hypothesized as a basic element of WBSF, and to examine an inverse cascade of this kind as a valid solution of the Euler equations. Initially, the numerical experiments were performed using the commercial Computational Fluid Dynamics (CFD) FLUENT 6.0 software, to reproduce the 'ejection amplifier' cycle (TEA structure) found by McNaughton and Bluendell (2002). In the numerical experiments, fluid was injected from the wall into the base of an ideal, ffictionless logarithmic flow while an equal volume of fluid was removed by suction along two flanking slots. This arrangement is known to create hairpin vortices in physical experiments. The FLUENT simulation results followed the subsequent formation of a hairpin eddy which induced a second, larger ejection from within its arc. The limited computing resources did not allow the FLUENT simulations to be followed far enough to examine possibility of any subsequent hairpins and ejections, so the feasibility of the TEA cascade was not firmly established. Research-oriented Large-Eddy Simulation (LES) code has been used to examine the inverse cascade process, and to overcome the computational limitations of the FLUENT solver. Several numerical experiments have been done using the LES code. The flow velocity data obtained from the simulations have been used to study the formation and growth of hairpin vortices and ejections, and their regeneration into 'ejection amplifier' structures. A comparison has been made between the CFD FLUENT predictions and initial LES run results so as to validate the LES solver. The results of the initial LES experiment reproduced the formation of the primary hairpin vortex (PHV), but did not reproduce the formation of primary a 'ejection amplifier' cycle. This is because the injection parameters and the spatial resolution were influencing primary hairpin development. The possibility of an upscale cascade of 'ejection amplifier' structure formation has been investigated by changing the injection/suction velocity, size and location in both low and high resolution domains. Fifteen LES simulation runs have been done, in which sets of variables and parameters have been systematically varied. The results obtained from all the LES runs showed that the injected disturbance developed into a primary hairpin vortex. When the slot was near the inflow boundary of the simulation domain, the low resolution runs did not indicate the formation of a primary 'ejection amplifier' cycle from the primary hairpin vortex development. These results suggest that the frequency of hairpin generation decreases with decreasing injection velocity. When the disturbance was injected at the center of the low resolution domain, development of the primary hairpin vortex was not affected by the inflow boundary. However, because of the large injection velocity and large slot the primary hairpin vortex also did not evolve into a primary 'ejection amplifier' cycle. The low resolution simulations done using a small slot with large injection velocity showed that the primary hairpin vortex developed into a primary 'ejection amplifier' cycle, but its development was discontinued because of the small injection. All the high resolution runs that were done using a large slot and a high injection velocity showed the formation of a primary 'ejection amplifier' cycle. The high resolution runs that were done using different injection periods also showed the formation of primary 'ejection amplifier' cycles. However, none of the simulations developed fully into an inverse cascade of ejection amplifier structures. In general, these results suggested that the TEA structure formation depends on the injection parameters (injection velocity, injection size, injection duration and injection location) and resolution. The injected disturbances are able to generate TEA structures, but have not been able to generate upscale cascades of TEA structures in log flow. This suggests that the present LES is not able to establish the 3-D inverse cascade process in wall-bounded log flow.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available