Influence of freestream and forced disturbances on the shear layers of a square prism

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Lander, Daniel Chapman
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Electronic thesis
Civil engineering
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Flow around the square prism, an archetypal bluff body, has applications in all areas of fluid mechanics: vibration, mixing, combustion and noise production to name a few. It also has distinct importance to wind loading on architectural and industrial structures such as tall buildings, bridges, and towers. The von-Kármán (VK) vortex street is a major reason for its significance: a flow phenomenon which has received intense scrutiny from scientific and engineering communities for more than 100 years! However, the characteristics of the shear layers separating from the sharp edges, essential to the vortex shedding, have received comparatively little attention. This is surprising considering the Kelvin-Helmholtz (KH) instability of shear layers produce the first signatures of turbulence in the wake. Furthermore, the shear layers are conduits for the passage of vorticity between the boundary layer and the turbulent wake. Many details of their structure and role in the shedding process remain unexplored. This dissertation aims to address this deficiency.
A freestream disturbance condition with intensity √̅u²⟌U∞ = 0.065$ and longitudinal integral length scale, $Lx/u=0.33$ was considered for the case of ReD=50,000. Disturbances were introduced by means of small circular cylinder placed upstream of the stagnation streamline. The disturbance moved the time-averaged position of the shear layer towards the body but did not substantially alter the growth rate of its width. The "normal" transition-to-turbulence pathway, via laminar vortex formation and subsequent pairing of vortices in the initial stages of the shear layer was shown to be highly sensitive to external disturbances. The disturbance interrupted the typical transition pathway and was associated with a Bypass-transition mechanism, which subsequently increased the likelihood of intermittent shear layer reattachment on the downstream surface of the body. Triple decomposition was used to study the random and coherent components of the VK structures in the wake. Data indicated a narrowing and lengthening of the wake, which was accompanied by a rise in base pressure and a reduction in time-averaged drag. The unsteady coherent vorticity field revealed a streamwise elongation of the VK vortex structures, which complemented the time-averaged wake lengthening. It appears that the influence of freestream disturbances, in particular, by their stochastic nature, is to suppress the formation of the coherent structures in the shear layer.
Forced disturbances imposed on the shear layers at the leading edges of the square prism were considered at ReD=16,700 for excitation frequencies $f_e = fₖₕ, fᵥₖ and 0. The response of the shear layer to forcing at steady and fᵥₖ frequencies had little impact on the time-averaged position or growth. For fₑ = fₖₕ, the growth of the momentum thickness was dramatically increased while the time-averaged position moved toward the body. The evolution of the integrated turbulent kinetic energy as a function of the streamwise coordinate, $x$, indicated an advanced state of transition was induced by increasing the amplification rate of the KH instability. This caused the KH instability to saturate with a reduced strength, compared to the baseline. It was noted that this mechanism was categorically opposite that of freestream disturbances, on account of the enhancement of the coherent structures in the initial shear layer, rather than their suppression. Phase-locked data for the case of forcing at fₑ = fₖₕenabled the KH vortex formation and transition processes to be observed. The growth of the shear layer momentum thickness exhibited a phase dependent, nonlinear oscillation associated with the passage of a KH vortex through the shear layer. The time-averaged momentum thickness growth---which exhibited a power-law relation---was therefore found to be proportional to the spacing between vortices, which decreased with increasing x. This feature is not shared by the plane mixing layer and therefore was suggested to be related to the curved trajectory of the shear layer. Finally, the interaction between the shear layer and wake was interpreted by considering the wake formation and diffusion lengths. The changes to the shear layer wake interaction were similar to those observed under the influence of freestream disturbances.
Specifically, this project considered the influence of three variables on the characteristics of the transition-to-turbulence in the square prism shear layers. These are: (1) Reynolds number; (2) freestream disturbances and (3) forced disturbances. In each case, the dynamics of the shear layer--wake interaction were considered. Particle image velocimetry and constant temperature anemometry measurements were used to document the shear layer during inception and evolution as it passes into the wake.
With increasing Reynolds number, ReD=Ū∞D/v in the range 16,700--148,000, the transition-to-turbulence in the initially laminar shear layer moves toward separation. A coordinate system local to the time-averaged shear layer axis was used such that the tangent and normal velocities, turbulent stresses and gradient quantities could be obtained for the curved shear layer. Characteristic frequencies, lengths and transition points of the KH instability were documented and shown to exhibit features distinct from the plane mixing layer. The evolution of the integrated turbulent kinetic energy was documented and a linear region of growth was associated with the amplification of the KH instability. A scaling relationship of the Kelvin-Helmholtz to von-Kármán frequencies was established for the square prism shear layer. fₖₕ/fᵥₖ was shown to be a power-law function of ReD, with differing characteristics to the much more studied circular cylinder. Increasing ReD up to ~70,000 bolsters the Reynolds stresses in the shear layers as they enter the wake, shortening the wake formation length, LF. The shear layer diffusion length, LD was quantified and the Gerrard-Product, LF X LD, was introduced to account for constant StD in the presence of the reduced LF as function of ReD.
May 2017
School of Engineering
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Rensselaer Polytechnic Institute, Troy, NY
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