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Title: Modelling unsteady wall pressures beneath turbulent boundary layers
Author: Ahn, B.-K.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2005
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The objective is to estimate the surface pressure distributions and corresponding spectra induced by fully developed hairpin vortices inclined at an angle of 45 degree to the wall in turbulent boundary layers. On the assumption that fully developed hairpin vortices are governed by inviscid dynamics, we obtain an exact formulation for the stagnation pressure, in terms of a Green function integral along the vortex lines. We then evaluate the surface static pressure by subtracting the dynamic pressure from the results of this formulation applied to our vortex geometry. On the basis of the attached eddy model, which implies that the form of the wave number spectrum can be deduced from the properties of a single eddy, we develop the expressions needed for the surface pressure spectra in terms of eddy number-density. This approach draws on flow visualization evidence, which indicates that the number of eddies observed in both streamwise and spanwise directions of the flow is inversely proportional to their size. The overall wavenumber spectrum consists of contributions from eddies of all sizes, weighted by the number-density. From a parameter study we investigate the influence of varying the largest and smallest eddy scales for different eddy aspect ratios. We then validate our model against existing descriptions and measurements of turbulent boundary layer pressures. We examine the predicted wave number spectra and compare them with those of existing empirical models, available direct numerical simulation and also with the results of flight-test measurements. The present model clearly predicts a theoretically-expected characteristic of the wavenumber spectrum (the -1 slope), whereas this is absent from the empirical models. This discrepancy apart, good quantitative agreement is achieved, particularly for the spanwise (cross-flow) spectrum. The agreement is best for the novel formulation for off-axis correlations proposed by Smol'yakov and Tkachenko (1991), rather than the traditional form (e.g. Corcos). The comparison with flight-test data is made via predicted and measured spatial correlations, and again shows good agreement. The present hairpin vortex model shows that it is capable of predicting the properties of the wall pressure field, and is therefore a promising candidate for use in exploring features less readily obtainable by other methods, e.g. off-axis correlations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available