Unsteady Separation and Navier-Stokes Solutions at High Reynolds Numbers

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We compute the numerical solutionsfor Navier-Stokes and Prandtl’s equations in thecase of a uniform bidimensional flow past animpulsively started disk. The numerical approx-imation is based on a spectral methods imple-mented in a Grid environment. We investigate therelationship between the phenomena of unsteadyseparation of the flow and the exponential decayof the Fourier spectrum of the solutions. Weshow that Prandtl’s solution develops a separationsingularity in a finite time. Navier-Stokes solutionsare computed over a range of Reynolds numbersfrom 3000 to 50000. We show that the appearanceof large gradients of the pressure in the stream-wise direction, reveals that the viscous-inviscidinteraction between the boundary layer flow andthe outer flow starts before the singularity timefor Prandtl’s equation. We observe a relationshipbetween the formation of large gradients of pres-sure and the various stage of unsteady separationwith the loss of exponential decay of the spectrumof the solutions.
Lingua originaleEnglish
Numero di pagine8
Stato di pubblicazionePublished - 2010

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