10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017
Role of Initial Conditions in the Evolution of an Axisymmetric Turbulent Jet
Due to Geometrical Effects on the Near-field Coherence
M. Breda1∗ and O. R. H. Buxton1
1: Department of Aeronautics, Imperial College London, London, SW7 2AZ, United Kingdom.
∗ Correspondent author: [email protected]
Abstract
Various authors have been investigating the role of coherent free structures in affecting the evolution of a free shear flow.
Since the work of Townsend (1976), it has been generally accepted that a shear flow would become asymptotically independent
of its initial conditions. This statement was backed by the work of Antonia & Zhao (2001). George (1989), however, argued that
the self-similar state would be linked to the coherent structures. The work of Antonia & Pearson (2000) pointed in this direction,
since different mean energy dissipation rates were found for different axisymmetric wake generators. In order to explore this
topic further, a round, square and fractal orifice (fig. 1) are tested for an axisymmetric turbulent jet. Hot-wire anemometry and two
dimensional- two component (2D-2C) planar particle image velocimetry (PIV) are performed to study the jet both temporally and
spatially. It is found that the fractal geometry breaks-up the jet’s coherent structures, leading to a modification of the entrainment
rate and to an extension of the turbulent kinetic energy production region, suggesting the break-up of the Kelvin-Helmholtz
vortices may slow down the jet’s evolution downstream. This is found to be the case, since the radial terms of the time averaged
momentum equation (Chao & Sandborn, 1966) and of the entrainment rate shows comparable trends once rescaled in terms of
the eddy turnover time. The forcing through a noncircular geometry is found to mainly affect the streamwise evolution of the jet’s
mean momentum. Moreover, analysing the evolution towards the self-similar state, it is found that the microscales of the flow
take much longer than mean centreline velocity and Reynolds stresses to reach the self-similar state. Moreover, non-equilibrium
dissipation (as thoroughly described by Vassilicos (2015)) is found for all jets concurrent to locally self-similar Reynolds stresses.
Comparable findings have been observed for axisymmetric wakes and grid generated flows, suggesting it is a common property
for many turbulent shear flows.
(a) Round
(b) Square
(c) Fractal
Figure 1: Jet exits
REFERENCES
Antonia, R. A. & Pearson, B. 2000 Effect of initial conditions on the mean energy dissipation rate and the scaling exponent.
Physical Review E 62 (6), 8086–8090.
Antonia, R. A. & Zhao, Q. 2001 Effect of initial conditions on a circular jet. Experiments in Fluids 31 (3), 319–323.
Chao, J. L. & Sandborn, V. A. 1966 Evaluation of the momentum equation for a turbulent wall jet. Journal of Fluid Mechanics
26, 819–828.
George, William K. 1989 The Self-preservation of turbulent flows and its relation to initial conditions and coherent structures.
Tech. Rep.. University at Buffalo, Buffalo, New York, USA.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. New York: Cambridge University Press.
Vassilicos, John Christos 2015 Dissipation in Turbulent Flows. Annual Review of Fluid Mechanics 47, 95–114.