Tesis doctoral de Wilfried Coenen
Variable density jets are known to support self-sustained oscillations when the jet-to-ambient density ratio is sufficiently small. This change in dynamical response to small perturbations is associated with a transition from convective to absolute instability of the underlying unperturbed base flow. The focus of this dissertation lies in the use of linear stability theory to describe the convective to absolute instability transition of hot and light jets emerging from a circular injector tube at moderately high reynolds numbers and low mach numbers. Particular interest is given to the influence of the length of the injector tube on the stability characteristics of the resulting jet flow, whose base velocity profile at the jet exit is computed in terms of the nondimensional tube length $l_t$ by integrating the boundary layer equations along the injector. we begin with the investigation of inviscid axisymmetric and helical modes of instability in a heated jet for different values of the jet-to-ambient density ratio $s= ho_j/ ho_{infty}<1$. For short tubes $l_t ll 1$ the base velocity profile at the tube exit is uniform except in a thin surrounding boundary layer. Correspondingly, the stability analysis reproduces previous results of uniform velocity jets, according to which the jet becomes absolutely unstable to axisymmetric modes for a critical density ratio $s_c simeq 0.66$, and to helical modes for $s_csimeq 0.35$. For tubes of increasing length the analysis reveals that both modes exhibit absolutely unstable regions for all values of $l_t$ and small enough values of the density ratio. In the case of the helical mode, we find that $s_c$ increases monotonically with $l_t$, reaching its maximum value $s_c simeq 0.5$ as the exit velocity approaches the poiseuille profile for $l_t gg 1$. Concerning the axisymmetric mode, its associated value of $s_c$ achieves a maximum value $s_csimeq 0.9$ for $l_t simeq 0.04$ and then decreases to approach $s_c simeq 0.7$ for $l_t gg 1$. The absolute growth rates in this limiting case of near-poiseuille jet profiles are however extremely small for $m=0$, in agreement with the fact that axisymmetric disturbances of a jet with parabolic profile are neutrally stable. As a result, for $s < 0.5$ the absolute growth rate of the helical mode becomes larger than that of the axisymmetric mode for sufficiently large values of $l_t$, suggesting that the helical mode may prevail in the instability development of very light jets issuing from long injectors. a second part of this dissertation is devoted to the viscous linear instability of parallel gas flows with piecewise constant base profiles in the limit of low mach numbers, both for planar and axisymmetric geometries such as mixing layers, jets and wakes. Our results generalize those of drazin (emph{j. Fluid mech.} Vol. 10, 1961, p.~571), by contemplating the possibility of arbitrary jumps in density and transport properties between two uniform streams separated by a vortex sheet. The eigenfunctions, obtained analytically in the regions of uniform flow, are matched through an appropriate set of jump conditions at the discontinuity of the basic flow, which are derived by repeated integration of the linearised conservation equations in their primitive variable form. The development leads to an algebraic dispersion relation that is validated through comparisons with stability calculations performed with continuous profiles and is applied, in particular, to study the effects of molecular transport on the spatiotemporal stability of parallel nonisothermal gaseous jets and wakes with very thin shear layers. finally we go back to the more general case of light and hot jets emerging from circular injector tubes, this time considering viscous perturbations so that the reynolds number enters the stability problem. We treat the case of a heated jet, as well as the case where the jet-to-ambient density ratio is induced by a mixture of two ideal gases. In particular, the results are presented for a he-air jet.
Datos académicos de la tesis doctoral «Absolute instability in the near field of low-density jets«
- Título de la tesis: Absolute instability in the near field of low-density jets
- Autor: Wilfried Coenen
- Universidad: Carlos III de Madrid
- Fecha de lectura de la tesis: 21/05/2010
Dirección y tribunal
- Director de la tesis
- Alejandro Sevilla Santiago
- Tribunal
- Presidente del tribunal: norman Riley
- ramón Fernández feria (vocal)
- José Manuel Gordillo arias de saavedra (vocal)
- Jesús Carlos Martínez bazán (vocal)