Wall-bounded shear flows (WBSF) can be regarded as turbulent, organized coherent structures and occur in many different circumstances. The self-similarity o f statistical characteristics o f turbulence at different heights in the log layer o f WBSF might reflect coherent structures which are also self-similar. McNaughton suggested that these coherent structures are in the form o f “Theodorsen ejection amplifier” (TEA) patterns. The TEA model o f the structure o f turbulence may be responsible for the formation o f the three-dimensional inverse cascade process in log layers over smooth walls. The inverse cascade can serve as an efficient mechanism o f 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 o f the thesis is to investigate numerically an upscale cascade process that has been hypothesized as a basic element o f WBSF, and to examine an inverse cascade o f 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 o f an ideal, ffictionless logarithmic flow while an equal volume o f 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 o f 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 o f 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 o f 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 o f 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 o f the initial LES experiment reproduced the formation o f 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 o f an upscale cascade o f ‘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 o f 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 o f the simulation domain, the low resolution runs did not indicate the formation o f 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 o f the low resolution domain, development o f the primary hairpin vortex was not affected by the inflow boundary. However, because o f 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 o f the small injection. All the high resolution runs that were done using a large slot and a high injection velocity showed the formation o f a primary ‘ejection amplifier’ cycle. The high resolution runs that were done using different injection periods also showed the formation o f primary ‘ejection amplifier’ cycles. However, none of the simulations developed fully into an inverse cascade o f 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 o f 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.