Nominally 2-Dimensional Flow About a Normal Flat Plate

Citation

Lisoski, Derek Lee Ashton (1993) Nominally 2-Dimensional Flow About a Normal Flat Plate. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/AZEG-2T16. https://resolver.caltech.edu/CaltechETD:etd-04042005-105646

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Towing tank and water channel experiments and a two-dimensional vortex element numerical model were used to study the forces experienced by a bluff flat plate set normal to a nominally two-dimensional flow. Intrinsic (small scale) and extrinsic (large scale) three-dimensional motions in the experimental flow were isolated and their separate and combined effects on forces and overall wake development were studied. Transient flow development starting from rest, as well as steady flow conditions, were investigated. A force balance was used to measure the unsteady lift and drag of vertically oriented models projecting through a free surface with various lower end conditions; simultaneous LIF flow visualizations imaged the structure of the vortices in the wake. Plate aspect ratio, lower end condition and angle of attack were varied to effect changes in large scale three-dimensional motions, while changes in Reynolds number and Richardson number (flow stratification) modified the small scale three dimensionality intrinsic to the flow. Towing tank experiments indicated that normal plates required sixty to one hundred chord lengths of travel to establish steady vortex shedding. An initial drag peak during acceleration was followed by a drag minimum of [...] reached while the wake was confined to a symmetric vortex bubble. Subsequent to the breakdown of this bubble, a region of symmetric flow with [...] and no vortex shedding was apparent for twenty to thirty chord lengths, followed by the final onset of vortex shedding which occurred exponentially. During this onset forces overshot their final steady-state values [...]. Flows with less large scale extrinsic three dimensionality (higher aspect ratio, "more two-dimensional" end conditions, and stratified flow) had longer development times and higher subsequent overshoot levels. Small geometric asymmetries (angle of attack variations) increased the minimum drag level seen after the acceleration and resulted in an earlier breakdown of the closed wake, followed by an immediate transition to steady shedding. The breakdown of the initial bubble in this case was more coherent spanwise and did not result in a long-lasting symmetric nonshedding flow. During "steady-state" shedding, modulation in the vortex shedding amplitude at a time scale of five to ten Strouhal periods resulted in a twenty percent fluctuation in mean drag level, with a corresponding increase in rms lift. This modulation accompanied a slow oscillation in the formation distance of the shed vorticity, the period of which was Reynolds number independent but decreased with increasing aspect ratio, reaching a minimum value of six Strouhal periods for aspect ratios greater than ten. Agreement between three-dimensional experimental and two-dimensional numerical-model results was good at early times, indicating the experiments were two-dimensional until the breakdown of the closed wake bubble following the initial acceleration. Prior to this breakdown the numerical model of a normal plate gave a drag coefficient [...], similar to that given by the Kirchhoff-Rayleigh free-streamline prediction but lower than experiments. Small asymmetries of the 2d model resulted in an increase in the minimum drag level to [...] . Subsequent to the closed wake breakdown, drag levels of [...] are 65% higher than steady-state experimental values. Although no region corresponding to the post-acceleration non-vortex-shedding seen experimentally was found in the basic numerical results, the addition of circulation decay to the numerical-model resulted in a region which appeared qualitatively similar. This circulation decay also decreased mean drag levels [...] and gave an exponential shedding onset with subsequent long period shedding modulation. Stabilizing spanwise stratification of the experimental flow had little effect for Richardson numbers [...] (based on chord). For [...] and [...] a longer lasting post-acceleration closed wake was followed by strong initial shedding and a large drag overshoot, with a subsequent decrease in shedding amplitude and increase in formation distance to the levels seen in the unstratified [...] case, which exhibited considerable Reynolds number dependence. For plates at [...] angle of attack the symmetric nonvortex shedding region was reduced in duration and subsequent "steady-state" drag levels were increased ten to fifteen percent [...] from the unstratified case.

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