Wilfried Coenen

Absolute instability of light jets emerging from circular injector tubes

We present a numerical study of the spatiotemporal, inviscid linear instability of light jets emerging from round tubes for values of the Reynolds number, Rej=ρjQ∕(πaμj)⪢1, where Q is the volumetric flow rate, ρj and μj are, respectively, the jet density and viscosity, and a is the injection tube radius. The analysis focuses on the influence of the injector length lt on the stability characteristics of the resulting jet, whose base velocity profile at the exit is computed in terms of the dimensionless tube length Lt=lt∕(Reja) by integrating the boundary-layer equations along the injector. Both axisymmetric (m=0) and helical (∣m∣=1) modes of instability are investigated for different values of the jet-to-ambient density ratio S=ρj∕ρ∞<1. For short tubes Lt⪡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 ax...

Global instability of low-density jets

The global stability of laminar axisymmetric low-density jets is investigated in the low Mach number approximation. The linear modal dynamics is found to be characterised by two features: a stable arc branch of eigenmodes and an isolated eigenmode. Both features are studied in detail, revealing that, whereas the former is highly sensitive to numerical domain size and its existence can be linked to spurious feedback from the outflow boundary, the latter is the physical eigenmode that is responsible for the appearance of self-sustained oscillations in low-density jets observed in experiments at low Mach numbers. In contrast to previous local spatio-temporal stability analyses, the present global analysis permits, for the first time, the determination of the critical conditions for the onset of global instability, as well the frequency of the associated oscillations, without additional hypotheses, yielding predictions in fair agreement with previous experimental observations. It is shown that under the conditions of those experiments, viscosity variation with composition, as well as buoyancy, only have a small effect on the onset of instability.

Diffusion-flame flickering as a hydrodynamic global mode

The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

Steady streaming around a cylinder pair

The steady streaming motion that appears around a pair of circular cylinders placed in a small-amplitude oscillatory flow is considered. Attention is focused on the case where the Stokes layer thickness at the surface of the cylinders is much smaller than the cylinder radius, and the streaming Reynolds number is of order unity or larger. In that case, the steady streaming velocity that persists at the edge of the Stokes layer can be imposed as a boundary condition to numerically solve the outer streaming motion that it drives in the bulk of the fluid. It is investigated how the gap width between the cylinders and the streaming Reynolds number affect the flow topology. The results are compared against experimental observations.

Oscillatory flow about a cylinder pair with unequal radii

We consider the oscillating flow about a pair of circular cylinders of unequal diameter. In addition to the relative size of the cylinders, the distance between them can be varied, as can the angle that the undisturbed oscillatory flow makes with the line joining the cylinder centres. For small-amplitude vibrations a time-independent, or steady streaming, motion develops that persists beyond the Stokes layer that forms at the solid boundary. This persistent streaming is considered for large values of a suitably defined streaming Reynolds number.