Time evolution of the frequency of the fluctuation associated to the largest amplitude in symbols. The dashed line represents the frequency evolution of the fundamental cavity mode. The evolution of the latter is due to small variations of the mean quantities. Experiments have been carried out at ONERA with a small scale motor called LP9 (see Ref. 28).
Cylindrical coordinate system . Flow is injected through the cylindrical wall located at with the injection velocity . The pipe is bounded by a solid wall located at .
Some streamlines corresponding to the Taylor-Culick basic flow (3).
Schematic view of the VALDO setup. Air is injected in the three (two, three, or four) elements; a grid aims to spread out the injected air. Finally air is injected in the cavity through a poral.
Schematic view of the LP9 setup for the firing 15. The sizes are in mm.
Contours of for the mode , and for three calculations: , 6, and 8. corresponds to the (colored) thick lines, to the dashed lines, and to the thin lines. In order to see the different details, the aspect ratio is not respected.
Eigenvalue spectrum for , and three different targets. All the eigenvalues obtained with a given target are represented by the same symbol. There is a perfect overlapping between the three computations.
Comparison between the measured frequencies in VALDO corresponding to five different positions of the hot wire and the dimensionalized theoretical modes.
Velocity field and rms velocity filled contours of the eigenfunction associated to the mode computed for and .
Radial cut of and for the two theories . The experimental values are plotted as symbols.
Comparison of the longitudinal evolution of the rms velocity between the VALDO measurements, the 1D theory, and the 2D approach (, which corresponds to the 2D mode , that is, ). The filled symbols represent the points of Fig. 8 for .
VALDO frequencies evolution with respect to . The lines correspond to the evolution of the 2D theoretical modes. Case up on the left, case down on the right.
View of an hysteresis while superimposing the VALDO frequencies evolution for both cases up and down.
LP9-15 frequencies evolution with respect to . The lines correspond to the evolution of the 2D theoretical modes. The first longitudinal acoustic mode is represented as a dashed line.
Comparison between stability modes computed with the viscous and the inviscid self-similar mean flow.
Typical operating conditions using VALDO, air is at ambient conditions so that the kinematic viscosity is about . The radius of the pipe is .
Range of values of , , and for the two considered setups.
Comparison between the first five eigenvalues given by the ODE-based approach and by the biglobal approach for linearly growing modes.
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