Stability characteristics of wavy walled channel flows

Selvarajan, S; Tulapurkara, E. G.; Ram, V. Vasanta

doi:10.1063/1.869946

Cited by 31 publications

(24 citation statements)

References 17 publications

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“…(2). This is the same decomposition approach as described by [18] and [19]. The linear analysis by [15] also shows that these linearized equations do demonstrate secondary instabilities induced by the traveling wave.…”

Section: B Moving-frame Decompositionmentioning

confidence: 87%

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Controller Synthesis for Periodic, Linear-Distributed Parameter Systems: A Channel Flow Application

Kang

Speyer

Kim

2015

AIAA Guidance, Navigation, and Control Conference

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A framework is presented in which temporally periodic, linear, distributed parameter systems can be converted to a time-invariant system. This conversion is key for the control of the secondary instabilities in three-dimensional channel flow induced by an upstream traveling wave of zero-net mass flux of wall transpiration. Linearized dynamical equations derived from Floquet analysis have shown that the instabilities are a direct result of the primary disturbance of the traveling wave but do not provide an analytical framework upon which to design a feedback controller. The necessary observation, although simple but subtle, is that the dynamics of the steady-state flow induced by a traveling wave must be linearized and decomposed in a frame of reference moving with the traveling wave. The resulting linear time-invariant equations are appropriate for system theoretic feedback control synthesis, i.e., H 2 and H ∞ methods. Although the linearization method produces a time-invariant linear system in the moving frame, the controller is periodic from a fixed reference frame. This approach for constructing a time-invariant system with periodic inputs is applicable to any system in which the dynamics are described as a combination of a static base and a periodic primary disturbance.

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Section: B Moving-frame Decompositionmentioning

confidence: 87%

“…Equations (A10), (A8), and (A9) match exactly that of [19]. These equations can be further manipulated to approximate the OrrSommerfeld and Squire equations by the following:…”

Section: Appendix A: Traveling Wave Induced Flow Equationsmentioning

confidence: 95%

Controller Synthesis for Periodic, Linear-Distributed Parameter Systems: A Channel Flow Application

Kang

Speyer

Kim

2015

AIAA Guidance, Navigation, and Control Conference

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“…It is important to point out that issues such as onset of instabilities need to be examined since it is well established that non-Newtonian effects precipitate the onset of instabilities (experimental study of Kolodner [60]) and that wall corrugation promotes flow instabilities [61,62] and these will be investigated in the future.…”

Section: Discussionmentioning

confidence: 99%

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Mukhopadhyay

Usha

Tulapurkara

2008

Numerical Methods in Fluids

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SUMMARYThe particle migration effects and fluid-particle interactions occurring in the flow of highly concentrated fluid-particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse-flux model. Semi-implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration.

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“…Various studies on the ow of Newtonian and non-Newtonian uids through channels and tubes whose walls are subjected to a wave-like forced excitation (experimental, theoretical as well as computational) have been carried out and these investigations have explored a variety of relevant information [1][2][3][4][5][6][7][8][9]. The peristaltic motion of a mixture of uid and solid particles has also been theoretically examined, e.g.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of particulate suspension flow through wavy-walled channels

Usha

Senthilkumar

Tulapurkara

2006

Int. J. Numer. Meth. Fluids

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SUMMARYThe particulate suspension ow in a channel whose walls describe a travelling wave motion is examined numerically. A perturbation method is employed and the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the ÿrst-order perturbation quantities are numerically determined by solving the governing system of ordinary di erential equations by shooting technique. The present approach does not impose any restriction on the Reynolds number of the ow and the wave number and frequency of the wavy-walled channel, although it is limited by the linear analysis. The wall shear stress and the positions of ow separation and reattachment points are computed and the in uence of the volume fraction density of the particles is examined. The variations of velocity and pressure of the particulate suspension ow with frequency of excitation are also presented.

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Stability characteristics of wavy walled channel flows

Cited by 31 publications

References 17 publications

Controller Synthesis for Periodic, Linear-Distributed Parameter Systems: A Channel Flow Application

Controller Synthesis for Periodic, Linear-Distributed Parameter Systems: A Channel Flow Application

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Numerical study of particulate suspension flow through wavy-walled channels

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