Search results for "Boundary Layer Theory"
showing 5 items of 5 documents
Unsteady Separation and Navier-Stokes Solutions at High Reynolds Numbers
2010
We compute the numerical solutions for Navier-Stokes and Prandtl’s equations in the case of a uniform bidimensional flow past an impulsively started disk. The numerical approx- imation is based on a spectral methods imple- mented in a Grid environment. We investigate the relationship between the phenomena of unsteady separation of the flow and the exponential decay of the Fourier spectrum of the solutions. We show that Prandtl’s solution develops a separation singularity in a finite time. Navier-Stokes solutions are computed over a range of Reynolds numbers from 3000 to 50000. We show that the appearance of large gradients of the pressure in the stream- wise direction, reveals that the visc…
Sound absorption prediction of linear damped acoustic resonators using a lightweight hybrid model
2019
International audience; A lightweight numerical method is developed to predict the sound absorption coefficient of resonators whose cross-section dimensions are significantly larger compared to the viscous and thermal boundary layer’s thicknesses. This method is based on the boundary layer theory and on the perturbations theory. According to the perturbations theory, in acoustical domains with large dimensions, the fluid viscosity and thermal conductivity only affect the boundary layers. The model proposed in this article combines the lossless Helmholtz wave equation derived from a perfect fluid hypothesis, with viscosity and thermal conductivity values of a real fluid to compute the sound …
Transition to turbulence and Singularity in Boundary Layer Theory
2007
We compute the solutions of Prandtl’s and Navier- Stokes equations for the two dimensional flow induced by an array of periodic rectilinear vortices interacting with a boundary in the halfplane. This initial datum develops, in a finite time, a separation singularity for Prandtl’s equation. We investigate the different stages of unsteady separation in Navier-Stokes solutions for various Reynolds numbers. We show the presence of a large- scale interaction between viscous boundary layer and inviscid outer flow in all Re regimes, while the presence of a small-scale interaction is visible only for moderate-high Re numbers. We also investigate the asymptotic validity of boundary layer theory in t…
Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions
2010
In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the ana…
Well-posedness of Prandtl equations with non-compatible data
2013
In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.