Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano / The nonlinear regime of spanwise modulated wavetrains in a plane Poiseuille flow
AUTOR(ES)
Homero Ghioti da Silva
DATA DE PUBLICAÇÃO
2008
RESUMO
The current thesis had three objectives. The first objective was to develop a code of direct numerical simulation (DNS) to simulation of waves of instability in a plane Poiseuille flow. The other main objective was to analyze it through the method of manufactured solutions (MMS). Finally, a third objective was to study the nonlinear regime of spanwise modulated wavetrains in a plane Poiseuille flow. Using high-order finite differences and pseudo-spectral methods, the DNS code solved the incompressible three-dimensional Navier-Stokes equations in a vorticity-velocity formulation. The MMS is a verification method more complete than the others more often used, for example, comparison with linear stability theory. The code used different high-order finite differences in different regions of the domain. The MMS has been little used for this type of code. It was concluded that these codes generally do not operate in the so-called errar asymptotic range. In the working range, the observed arder changes in the computational domain in a manner consistent with the numerical methods employed. This allows, among other things, optimization of the numerical scheme. After testing, numerical simulations of the wavetrains were performed. The analysis of the results was made based on the primary and secondary instability theories and weakly non-linear theory. A modulated wavetrain was studied in a region of the stability diagram where several studies for monochromatic waves were performed. The results suggested that in this region the non-linear regime of transition of the modulation wavetrain is governed by the K-type instability. With the reduction of the magnitude of the initial disturbance, a more complex scenario, which may involve other mechanisms, was observed. Cases near the first branch of the instability diagram were also studied. In this region, the linear theory predicts tri-dimensional waves are the most unstable, a fact that could lead to the so-called oblique transition. The results indicated that the modulated wavetrain divided into two regions, which tend move further from each other. Despite being associated with the linear instability, this behavior was not anticipated in the literature. In this scenario, for isolated modulated wavetrains, the non-linear system could not be clearly correlated with any of the classic scenarios of transition. In this context, oblique transition may perhaps to situations involving the interaction between modulated wavetrains.
ASSUNTO(S)
escoamentos de poiseuille plano method of manufactured solutions transição natural verificação de código método das soluções manufaturadas spanwise modulated wavetrains plane poiseuille flow trens de ondas modulados code verification natural transition
