Abstracts - KTH Mechanics

2
Global stability of jets and sensitivity of the mode to inflow
perturbations.
F. Giannetti ∗ and P. Luchini ∗
Recent experiments on coaxial jets 1 have revealed, for particular values of the parameters,
the existence of a self-exciting mechanism between the vortical structures
created inside the nozzle and the jet evolution in the external region. The spectral
analysis of the experimental data indicates that when this occurs, the flow field in
the proximity of the nozzle exit is modulated by the instability of the external shear
layer and consequently is characterized by a single dominant frequency. Numerical
simulations on geometries resembling the experimental set up 2 confirm this behavior
and show an unexpected sensitivity of the flow field to the imposed inflow conditions.
Computations performed on simplified geometries, in fact, exhibit a remarkably different
evolution of the system according as the full geometry (nozzle + jet) is simulated
or only the region downstream of the exit is considered. This behavior brings evidence
of a strong feedback between different locations of the flow and suggests the presence
of an unstable global mode 3 .
In this paper we perform a linear stability analysis on a jet emerging from a
converging nozzle. The aim is to investigate the possible existence of an unstable
global mode and to study its main characteristics. The steady axially-symmetric
base flow is obtained trough the numerical solution of the incompressible Navier-
Stokes equations and an immersed-boundary technique is used to represents the nozzle
geometry. The first instability of the steady flow is studied by linearizing the governing
equations and using a normal mode expansion. The resulting numerical eigenvalue
problem is solved numerically and a parametric study is performed to evaluate the
critical Reynolds number. The properties of the adjoint eigenfunctions are analyzed
in order to study the receptivity of the system to initial conditions and to external
forcing. The sensitivity of the jet to the imposed inflow and outflow conditions and
the existence of localized feedbacks are determined through a stability analysis to
perturbations of the differential operator, a technique originally developed to study
the stability of the wake behind a circular cylinder 45 . The spatial characteristics of
the product of the direct and adjoint modes are analyzed to identify the regions where
the instability mechanism acts and to determine the locations where the feedback is
stronger. In order to verify the results, the stability analysis is repeated on several
restricted domains, allowing in this way a direct comparison of the influence of the
inflow and outflow conditions on the eigenvalues.
∗ DIMEC, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy.
1 Buresti G., Documenti del Dip. di Ing. Aerospaziale di Pisa, DDIA 2002-1 (2002).
2 Tessicini et al. , Proc. XV AIMeTA Congress of Theoret. and Appl. Mech., SP FL 20 (2001).
3 Huerre and Monkewitz, Annual Review of Fluid Mechanics,22,pp 473-537 (1990).
4 Giannetti and Luchini,V Euromech Fluid Mechanics Conference, Toulouse, August 24-28, 2003.
5 Giannetti and Luchini,Journal of Fluid Mechanics, (submitted) .