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Modal and transient dynamics of jet flows
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10.1063/1.4801751
/content/aip/journal/pof2/25/4/10.1063/1.4801751
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801751
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) and (b) effect of on the leading eigenmodes for the advection–diffusion–reaction model (for = 25 and = 1). The least stable part of the eigenvalue spectrum is shown in (a), and the leading eigenmode for each value of (represented in (a) by circles) are displayed in (b). (c) spectrum (+ symbols) and iso-contours of the pseudo-spectrum for = 25, = 5, and = 1 (logarithmic scale). (d) Spatial growth rate of the leading global mode (measured as ψ′(10)/ψ(10)) as a function of parameters and . The solid contour represents the limit between growing and decaying modes, the dashed lines give the maximum value of the advection parameter for which computation is possible in a domain of a given length (indicated on the curve).

Image of FIG. 2.
FIG. 2.

Flow configuration for (a) incompressible and (b) compressible computations. The incompressible Navier–Stokes equations are solved on the 2D domain Ω using a finite element formulation, with an inflow boundary condition (BC) on Γ (thin solid line), a no slip BC on Γ (thick solid line), a stress-free BC on Γ (dashed line), and compatibility conditions on the axis Γ (dashed-dotted line). No sponge layers are used in this case. The compressible Navier–Stokes equations are discretized using high order Finite Differences (FD) on the rectangular domain represented in (b). The shaded regions correspond to sponge layers, and the presence of an infinitely thin adiabatic wall for = 1 and ⩽ 0 is taken into account by means of appropriate FD schemes.

Image of FIG. 3.
FIG. 3.

Axial velocity field of the two base flows. (a) laminar base flow, computed as a steady solution of the Navier–Stokes equations. (b) turbulent mean flow, adapted from an analytical model.

Image of FIG. 4.
FIG. 4.

Spatio-temporal evolution of the optimal initial condition for = 0 and = 10 for the turbulent jet mean profile in the incompressible case. The value of the axial velocity along the line = 0.9 is represented at various time steps, as indicated next to the curve.

Image of FIG. 5.
FIG. 5.

Gains associated with the optimal perturbations for (a) the laminar and (b) the model base flows. Thick solid line: = 0, dashed line: = 1, dashed-dotted line: = 2, dotted line: = 3, and thin solid line: = 4.

Image of FIG. 6.
FIG. 6.

(a) Optimal perturbations for the model subsonic jet at Ma = 0.75 for = 0 (solid line) and = 1 (dashed line). (b) and (c) Azimuthal vorticity field for the optimal initial condition for = 0 and = 12, and the corresponding perturbation at = 12. (d) and (e) Dilatation field for the optimal initial condition for = 0 and = 30, and the corresponding perturbation at = 30.

Image of FIG. 7.
FIG. 7.

Global modes computed for = 0 on the laminar base flow. (a) eigenfrequency spectrum. (b)–(e) axial velocity magnitude of four selected modes, in logarithmic scale, as indicated in (a).

Image of FIG. 8.
FIG. 8.

Axial velocity for global modes (c) and (d) of Figure 7 , in linear scale.

Image of FIG. 9.
FIG. 9.

Spectra computed for various domain lengths using stress-free (a) and convective outflow (b) boundary conditions at the outlet. Crosses: = 40 (black). Triangles: = 60 (blue). Plusses: = 80 (green). Circles: = 100 (red). The dashed lines correspond to the estimated decay rate (11) .

Image of FIG. 10.
FIG. 10.

Global spectra computed for = 0 for the model base flow. Crosses: = 40 (black). Triangles: = 60 (blue). Plusses: = 80 (green). The dashed lines correspond to the estimated decay rate of the spurious branch given by (11) .

Image of FIG. 11.
FIG. 11.

Axial velocity fields of selected global modes computed for = 0 for the model base flow with = 60 and stress-free outflow boundary conditions (logarithmic scale). (a) ω = 0.22 − 0.11i, (b) ω = 1.0 − 0.17i, (c) ω = 0.98 − 0.23i.

Image of FIG. 12.
FIG. 12.

Global modes computed for = 0 on the model subsonic jet at Ma = 0.75. (a) eigenvalue spectrum. (b) − (d) azimuthal vorticity of three selected modes, as indicated in (a).

Image of FIG. 13.
FIG. 13.

Optimal transient amplification of axisymmetric perturbations for the laminar incompressible jet. (Thick line) computation using the adjoint equations, as computed in Sec. IV . (Thin lines) optimal gains computed by projecting the dynamics onto the space spanned by the least stable eigenmodes.

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/content/aip/journal/pof2/25/4/10.1063/1.4801751
2013-04-16
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Modal and transient dynamics of jet flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801751
10.1063/1.4801751
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