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A finite element simulation for propagation in non-uniform ducts with compressible mean flow with a random source description is developed.
The propagation of sound is considered in an axisymmetric mean flow, with uniform axial velocity and non-uniform swirl, with angular velocity proportional to the radius.
This cannot be due to the interaction of the axisymmetric mean flow with the axisymmetric applied field (by well-known symmetry arguments, see Cowling (1934)), so it is argued that it must be due to a turbulent electromotive force (EMF) which breaks the symmetry of the system.
The model combustor was designed to provide a fairly comprehensive set of tested effects: sonic vs subsonic inlets; oxidizer tube lengths that were either quarter-wave, half-wave, or off-resonant acoustic equivalents to the combustion chamber; a significant injector mean flow with Ma∼0.4; and a varied combustion chamber length.
In previous work [A.J. Cooper & N. Peake, Journal of Fluid Mechanics 445 (2001) 207 234.] radially sheared axial mean flow with nonzero swirl in a slowly varying duct was considered, but in this paper we set the swirl to zero, thereby allowing simplification of the calculations of both the mean and unsteady flows.
For this very complex geometry, results demonstrate the capacity of the LES to predict the mean flow, with and without combustion, as well as its main unstable modes: it is shown, for example, that the PVC mode is very strong for the cold flow but disappears with combustion.
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The observed change of the mean flow pattern with incidence agrees with earlier studies and is consistent with previously reported behavior of the normal force component.
In the context, is the amplitude of a surface wave packet, while is the velocity potential of the mean flow interacting with the surface wave [6].
We further quantify the mean flow amplitude with the hydrodynamic Reynolds number Re for the hydrodynamic simulations and the magnetic Reynolds number Rm for the dynamo simulations.
In the context of water waves, u is the amplitude of a surface wave packet while v is the velocity potential of the mean flow interacting with the surface waves [23].
Nevertheless, ϕj was also found to have an effect on the mean flow field, with slightly higher magnitudes of reversed flow velocity and an increase in mean recirculation zone length observed as the fuel content of the jet is increased.
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