Dynamic Mode Decomposition of High Reynolds Number Supersonic Jet Flows

In this paper, we present a general description of the flow structures inside a two-dimensional Food and Drug Administration (FDA) nozzle. To this aim, we have performed numerical simulations using the numerical code Nek5000. The topology patters of the solution obtained, identify four different flow regimes when the flow is steady, where the symmetry of the flow breaks down. An additional case has been studied at higher Reynolds number, when the flow is unsteady, finding a vortex street distributed along the expansion pipe of the geometry. Linear stability analysis identifies the evolution of two steady and two unsteady modes. The results obtained have been connected with the changes in the topology of the flow. Finally, higher-order dynamic mode decomposition has been applied to identify the main flow structures in the unsteady flow inside the FDA nozzle. The highest-amplitude dynamic mode decomposition (DMD) modes identified by the method model the vortex street in the expansion of the geometry.

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Three-dimensional instability of a flow past a sphere: Mach evolution of the regular and Hopf bifurcations

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.664 ◽

2018 ◽

Vol 855 ◽

pp. 1088-1115 ◽

Cited By ~ 4

Author(s):

A. Sansica ◽

J.-Ch. Robinet ◽

F. Alizard ◽

E. Goncalves

Keyword(s):

Reynolds Number ◽

Gaussian White Noise ◽

Three Dimensional ◽

Base Flow ◽

Dynamic Mode Decomposition ◽

Dynamic Mode ◽

Weakly Nonlinear ◽

Mode Decomposition ◽

Mach Numbers ◽

Noise Amplifier

A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.

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Experiments on the instability waves in a supersonic jet and their acoustic radiation

Journal of Fluid Mechanics ◽

10.1017/s0022112075001322 ◽

1975 ◽

Vol 69 (1) ◽

pp. 73-95 ◽

Cited By ~ 139

Author(s):

Dennis K. Mclaughlin ◽

Gerald L. Morrison ◽

Timothy R. Troutt

Keyword(s):

Reynolds Number ◽

High Reynolds Number ◽

Large Scale ◽

Acoustic Radiation ◽

Low Reynolds Number ◽

Supersonic Jet ◽

Hot Wire ◽

Theoretical Predictions ◽

Low Reynolds ◽

High Reynolds

An experimental investigation of the instability and the acoustic radiation of the low Reynolds number axisymmetric supersonic jet has been performed. Hot-wire measurements in the flow field and microphone measurements in the acoustic field were obtained from different size jets at Mach numbers of about 2. The Reynolds number ranged from 8000 to 107000, which contrasts with a Reynolds number of 1·3 × 106for similar jets exhausting into atmospheric pressure.Hot-wire measurements indicate that the instability process in the perfectly expanded jet consists of numerous discrete frequency modes around a Strouhal number of 0·18. The waves grow almost exponentially and propagate downstream at a supersonic velocity with respect to the surrounding air. Measurements of the wavelength and wave speed of theSt= 0·18 oscillation agree closely with Tam's theoretical predictions.Microphone measurements have shown that the wavelength, wave orientation and frequency of the acoustic radiation generated by the dominant instability agree with the Mach wave concept. The sound pressure levels measured in the low Reynolds number jet extrapolate to values approaching the noise levels measured by other experimenters in high Reynolds number jets. These measurements provide more evidence that the dominant noise generation mechanism in high Reynolds number jets is the large-scale instability.

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