Application of spectral collocation techniques to the stability of swirling flows

Khorrami, Mehdi R.; Malik, Mujeeb R.; Ash, Robert L.

doi:10.1016/0021-9991(89)90071-5

Cited by 215 publications

(144 citation statements)

References 15 publications

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“…The reader is referred to Gottlieb, Hussaini & Orszag (1984) for a full discussion of the theory and to Khorrami, Malik & Ash (1989) or Schmid & Henningson (2001) for the main details. The idea is that the function φ is expanded in a series of Chebyshev polynomials T n as…”

Section: Methodsmentioning

confidence: 99%

Stability of circular PoiseuilleCouette flow to axisymmetric disturbances

Walton

2004

J. Fluid Mech.

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The stability of circular Poiseuille-Couette flow to axisymmetric disturbances is investigated theoretically. First, the governing circular Orr-Sommerfeld equation for linear perturbations is formulated and analysed asymptotically at large values of the Reynolds number. The existence of multiple regions of instability is predicted and their dependence upon radius ratio and inner cylinder velocity is determined explicitly. These findings are confirmed when the linear problem is solved numerically at finite Reynolds number and multiple neutral curves are found. The relevance of these results to the thread injection of medical implants is discussed, and it is shown how the linear modes are connected to nonlinear amplitude-dependent modes at high Reynolds number that exist for O(1) values of the inner cylinder velocity.

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Section: Methodsmentioning

confidence: 99%

Stability of circular PoiseuilleCouette flow to axisymmetric disturbances

Walton

2004

J. Fluid Mech.

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“…The local linear stability eigenvalue problem is efficiently solved by using a Chebyshev spectral collocation method (Khorrami, Malik & Ash 1989;Trefethen 2000). A detailed description of the numerical scheme is given by Oberleithner et al (2011).…”

Section: Numerical Implementationmentioning

confidence: 99%

On the impact of swirl on the growth of coherent structures

Oberleithner

Paschereit

Wygnanski³

2014

J. Fluid Mech.

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Spatial linear stability analysis is applied to the mean flow of a turbulent swirling jet at swirl intensities below the onset of vortex breakdown. The aim of this work is to predict the dominant coherent flow structure, their driving instabilities and how they are affected by swirl. At the nozzle exit, the swirling jet promotes shear instabilities and, less unstable, centrifugal instabilities. The latter stabilize shortly downstream of the nozzle, contributing very little to the formation of coherent structures. The shear mode remains unstable throughout generating coherent structures that scale with the axial shear-layer thickness. The most amplified mode in the nearfield is a co-winding double-helical mode rotating slowly in counter-direction to the swirl. This gives rise to the formation of slowly rotating and stationary large-scale coherent structures, which explains the asymmetries in the mean flows often encountered in swirling jet experiments. The co-winding single-helical mode at high rotation rate dominates the farfield of the swirling jet in replacement of the co-and counter-winding bending modes dominating the non-swirling jet. Moreover, swirl is found to significantly affect the streamwise phase velocity of the helical modes rendering this flow as highly dispersive and insensitive to intermodal interactions, which explains the absence of vortex pairing observed in previous investigations. The stability analysis is validated through hot-wire measurements of the flow excited at a single helical mode and of the flow perturbed by a time-and space-discrete pulse. The experimental results confirm the predicted mode selection and corresponding streamwise growth rates and phase velocities.

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“…The validity of the approach has been addressed by Khorrami and Malik. 21 The following boundary condition for the pressure is assumed to be respected at the wall:…”

Section: ͑10͒mentioning

confidence: 99%

“…The codes have been written following the example of Khorrami and Malik. 21 The accuracy of the cylindrical codes has been verified by benchmarking toward results published in the literature.…”

Section: B Validationmentioning

confidence: 99%

Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry

et al. 2008

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Recently, it has been observed that simple geometry characterized by a low level of symmetry present interesting peculiarities in the process of transition from laminar Poiseuille flow to turbulent flow. Examples of this type of geometry are eccentric channels and, more generally, parallel channels containing a narrow gap. In the present work, a global linear stability analysis for the flow in this class of geometry has been performed. The problem is discretized through spectral collocation and the eigenvalue problem has been solved with the Arnoldi-method based algorithms and the QZ algorithm. Since no numerical studies of this type have yet been performed to address the issue of transition in this geometry, the codes have been validated toward results obtained in simplified geometries ͑e.g., concentric annular channel and square channel͒. The eigenvalue spectra of the Poiseuille flow in eccentric channels and a U-shaped channel have then been computed and analyzed for a wide range of geometric parameters. After comparison with spectra typical of channel flow and pipe flow it is shown that an additional linear mechanism of instability is present, related to the spanwise variation of the laminar velocity profile.

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Application of spectral collocation techniques to the stability of swirling flows

Cited by 215 publications

References 15 publications

Stability of circular PoiseuilleCouette flow to axisymmetric disturbances

Stability of circular PoiseuilleCouette flow to axisymmetric disturbances

On the impact of swirl on the growth of coherent structures

Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry

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