A Linear Stability Analysis of Incompressible Coaxial Jets Using an Accurate Boundary-Layer Approximation as Base Flow
Helio Ricardo de Aguiar Quintanilha Júnior1; Leonardo Santos de Brito Alves2; Oberdan Miguel Rodrigues de Souza3; Marcio Teixeira de Mendonça4
1 Universidade Federal Fluminense, Niteroi, RJ, 24210-240, Brazil.; 2 Universidade Federal Fluminense, Niteroi, RJ, 24210-240, Brazil; 3 Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, 22451-900, Brazil; 4 Comando Geral de Tecnologia Aeroespacial, Instituto de Aeronáutica e Espaço, São José dos Campos, SP
doi:10.20906/CPS/COB-2015-1811
Resumo
A linear stability analysis is employed to study convectively unstable incompressible coaxial jets with a momentum thickness that is much smaller than the jet diameter. In other words, curvature effects are neglected and the coaxial jet is modeled as multiple planar mixing-layers. The main goal is to investigate the formation of new modes of instability through the interaction between these mixing-layers. In order to do so, an accurate base flow must be employed. It is created in the present paper by combining individual mixing-layers using matched asymptotic expansions, which generates a solution with the same accuracy order of the standard boundary-layer approximation. Two cases are considered, where the inner nozzle wall separating both streams has negligible as well as non-negligible thicknesses. Furthermore, two different techniques are used to solve the linear stability problem. First, a matrix forming approach built with second-order finite- differences on non-uniform meshes generates low accuracy estimates for all eigenvalues. Second, these values are used as initial guesses for a shooting method to generate high accuracy solutions for the unstable eigenvalues. Preliminary results obtained so far indicate the appearance of more modes than inflection points for certain parameter choices for both cases considered.
Palavras-chave: Mixing Layer; Double Mixing Layer; Linear Stability Analysis; Coaxial Jets; Jet Inner Nozzle; Eigenvalue Problem