RT Dissertation/Thesis
T1 Absolute instability in the near field of low-density jets
A1 Coenen, Wilfried
AB Variable density jets are known to support self-sustained oscillationswhen the jet-to-ambient density ratio is sufficiently small. Thischange in dynamical response to small perturbations is associatedwith a transition from convective to absolute instability of the underlyingunperturbed base flow. The focus of this dissertation lies in theuse of linear stability theory to describe the convective to absoluteinstability transition of buoyancy-free low-density jets emergingfrom a circular injector tube at moderately high Reynolds numbersand low Mach numbers. Particular interest is given to the in- fluenceof the length of the injector tube on the stability characteristicsof the resulting jet flow, whose base velocity profile at the jetexit is computed in terms of the nondimen- sional tube length L$_{t}$by integrating the boundary layer equations along the injector. Webegin with the investigation of inviscid axisymmetric and helicalmodes of in- stability in a heated jet for different values of thejet-to-ambient density ratio. For short tubes L$_{t}$ $\ll$ 1 thebase velocity profile at the tube exit is uniform except in a thinsur- rounding boundary layer. Correspondingly, the stability analysisreproduces previous results of uniform velocity jets, according towhich the jet becomes absolutely unstable to axisymmetric modes fora critical density ratio S$_{c}$ $\simeq$ 0.66, and to helical modesfor S$_{c}$ $\simeq$ 0.35. For tubes of increasing length the analysisreveals that both modes exhibit absolutely unstable regions for allvalues of L$_{t}$ and small enough values of the density ratio. Inthe case of the helical mode, we find that S$_{c}$ increases monotonicallywith L$_{t}$ , reaching its maximum value S $\simeq$ 0.5 as theexit velocity approaches the Poiseuille pro- file for L$_{t}$ $\gg$1. Concerning the axisymmetric mode, its associated value of S$_{c}$achieves a maximum value S$_{c}$ $\simeq$ 0.9 for $_{t}$ $\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-Poiseuillejet profiles are however extremely small for m = 0, in agreement withthe fact that axisymmetric dis- turbances of a jet with parabolicprofile are neutrally stable. As a result, for S < 0.5 the absolutegrowth rate of the helical mode becomes larger than that of the axisymmetricmode for sufficiently large values of L$_{t}$ , suggesting that thehelical mode may prevail in the instability development of very lightjets issuing from long injectors. A second part of this dissertationis devoted to the viscous linear instability of parallel gas flowswith 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 (J. Fluid Mech.vol. 10, 1961, p. 571), by contemplating the possibility of arbitraryjumps in density and transport properties between two uniform streamsseparated by a vortex sheet. The eigenfunctions, obtained analyticallyin the regions of uniform flow, are matched through an appropriateset of jump conditions at the discontinuity of the basic flow, whichare derived by repeated integration of the linearized conservationequations in their primitive variable form. The development leadsto an algebraic dispersion relation that is validated through comparisonswith stability calculations performed with continuous profiles andis applied, in particular, to study the effects of molecular transporton the spatiotemporal stability of parallel nonisothermal gaseousjets and wakes with very thin shear layers. Finally we go back tothe stability analysis of low-density jets emerging from circularnozzles or tubes, this time considering viscous perturbations so thatthe Reynolds number enters the stability problem. We consider separatelythe two particular cases of a hot gas jet discharging into a colderambient of the same gas, as well as the isothermal discharge of ajet of gas with molecular weight smaller than that of the ambientgas. In both cases, we consider the detailed downstream evolutionof the local stability properties in the near field of the jet withthe aim at establishing the convective or absolute nature of the instability.We discuss the relationship of our results with those obtained inprevious works with use made of parametric velocity and density profiles,and compare both approaches with the actual global transition observedin experiments performed with hot and light jets.
YR 2010
FD 2010-04
LK https://hdl.handle.net/10016/9193
UL https://hdl.handle.net/10016/9193
LA eng
DS e-Archivo
RD 19 may. 2024