banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Biglobal linear stability analysis of the flow induced by wall injection
Rent this article for


Image of FIG. 1.
FIG. 1.

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).

Image of FIG. 2.
FIG. 2.

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 .

Image of FIG. 3.
FIG. 3.

Some streamlines corresponding to the Taylor-Culick basic flow (3).

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

Schematic view of the LP9 setup for the firing 15. The sizes are in mm.

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

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.

Image of FIG. 8.
FIG. 8.

Comparison between the measured frequencies in VALDO corresponding to five different positions of the hot wire and the dimensionalized theoretical modes.

Image of FIG. 9.
FIG. 9.

Velocity field and rms velocity filled contours of the eigenfunction associated to the mode computed for and .

Image of FIG. 10.
FIG. 10.

Radial cut of and for the two theories . The experimental values are plotted as symbols.

Image of FIG. 11.
FIG. 11.

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 .

Image of FIG. 12.
FIG. 12.

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.

Image of FIG. 13.
FIG. 13.

View of an hysteresis while superimposing the VALDO frequencies evolution for both cases up and down.

Image of FIG. 14.
FIG. 14.

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.


Generic image for table
Table I.

Comparison between stability modes computed with the viscous and the inviscid self-similar mean flow.

Generic image for table
Table II.

Typical operating conditions using VALDO, air is at ambient conditions so that the kinematic viscosity is about . The radius of the pipe is .

Generic image for table
Table III.

Range of values of , , and for the two considered setups.

Generic image for table
Table IV.

Comparison between the first five eigenvalues given by the ODE-based approach and by the biglobal approach for linearly growing modes.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Biglobal linear stability analysis of the flow induced by wall injection