Linear spatial stability of pipe Poiseuille flow

Garg, Vijay K.; Rouleau, W. T.

doi:10.1017/s0022112072000564

Cited by 92 publications

(53 citation statements)

References 11 publications

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“…T his work explores the effect of wall roughness on the long known contradiction between the linear stability analysis result of infinitely stable flow in pipes with smooth boundaries and the experimental observation (1) that flows become unstable at a Reynolds number of Ϸ2,000 for ordinary pipes (2)(3)(4). A hint that wall roughness may be important can be gathered from experiments which show that for smoothed pipes, the onset of the instability can greatly exceed 2,000 (5).…”

mentioning

confidence: 99%

Instability in pipe flow

Cotrell

McFadden

Alder

2008

Proc. Natl. Acad. Sci. U.S.A.

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The long-puzzling, unphysical result that linear stability analyses lead to no transition in pipe flow, even at infinite Reynolds number, is ascribed to the use of stick boundary conditions, because they ignore the amplitude variations associated with the roughness of the wall. Once that length scale is introduced (here, crudely, through a corrugated pipe), linear stability analyses lead to stable vortex formation at low Reynolds number above a finite amplitude of the corrugation and unsteady flow at a higher Reynolds number, where indications are that the vortex dislodges. Remarkably, extrapolation to infinite Reynolds number of both of these transitions leads to a finite and nearly identical value of the amplitude, implying that below this amplitude, the vortex cannot form because the wall is too smooth and, hence, stick boundary results prevail.

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mentioning

confidence: 99%

Instability in pipe flow

Cotrell

McFadden

Alder

2008

Proc. Natl. Acad. Sci. U.S.A.

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“…There are one or two independent solutions for m = 0 (torsional and meridional modes respectively), and three solutions for m > 0. The asymptotics of these solutions at the specified regions can be found analytically (Garg & Rouleau 1971;Morris 1976). In what follows, we present the orthonormalization algorithm for finding eigenvalues for problem (2.26) and consider the case of nonaxisymmetric disturbances m = 1.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…The initial conditions q i (R) are specified according to the asymptotical solution to (2.26) for r 1, which involves Hankel functions of first and second orders depending on the governing parameters (Morris 1976). At the jet axis r = ε, ε 1 the linear combination of solutions q i (r), i = 1, 2, 3, should be matched with a linear combination of asymptotical independent solutions to (2.26) at r 1 (Garg & Rouleau 1971). If the Reynolds number Re is large, initially independent vectors q j , j = 1, 2, 3, tend to become linear-dependent in the process of integration, which reduces the accuracy of calculations significantly.…”

Section: Numerical Solutionmentioning

confidence: 99%

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Non-modal stability of round viscous jets

2013

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Hydrodynamic stability of round viscous fluid jets is considered within the framework of the non-modal approach. Both the jet fluid and surrounding gas are assumed to be incompressible and Newtonian; the effect of surface capillary pressure is taken into account. The linearized Navier-Stokes equations coupled with boundary conditions at the jet axis, interface and infinity are reduced to a system of four ordinary differential equations for the amplitudes of disturbances in the form of spatial normal modes. The eigenvalue problem is solved by using the orthonormalization method with Newton iterations and the system of least stable normal modes is found. Linear combinations of modes (optimal disturbances) leading to the maximum kinetic energy at a specified set of governing parameters are found. Parametric study of optimal disturbances is carried out for both an air jet and a liquid jet in air. For the velocity profiles under consideration, it is found that the non-modal instability mechanism is significant for non-axisymmetric disturbances. The maximum energy of the optimal disturbances to the jets at the Reynolds number of 1000 is found to be two orders of magnitude larger than that of the single mode. The largest growth is gained by the streamwise velocity component.

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“…To the best of our knowledge, the e ect of thixotropy on the stability of pipe ow has not been addressed in the past. The interest in the stability of pipe ow stems from the fact that this particular geometry is widely used for the transport of Newtonian and nonNewtonian uids [9][10][11][12][13][14][15]. In previous studies dealing with non-Newtonian uids, the e ect of shear-thinning and yield stress has already been investigated on the critical Reynolds number in pipe ow.…”

Section: Introductionmentioning

confidence: 99%

Stability of Thixotropic Fluids in Pipe Flow

2017

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Abstract. Linear stability of a thixotropic uid obeying the Moore model is investigated in pipe ow using a temporal stability analysis in which in nitesimally small perturbations, represented by normal modes, are superimposed on the base ow and their evolution in time is monitored in order to detect the onset of instability. An eigenvalue problem is obtained, which is solved numerically using the pseudo-spectral Chebyshev-based collocation method. The neutral instability curve is plotted as a function of the thixotropy number of the Moore model. Based on the results obtained in this work, it is concluded that the thixotropic behavior of the Moore uid has a destabilizing e ect on pipe ow.

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Linear spatial stability of pipe Poiseuille flow

Cited by 92 publications

References 11 publications

Instability in pipe flow

Instability in pipe flow

Non-modal stability of round viscous jets

Stability of Thixotropic Fluids in Pipe Flow

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