The linear stability of high-frequency oscillatory flow in a channel

Blennerhassett, P. J.; Bassom, Andrew P.

doi:10.1017/s0022112006009141

Cited by 53 publications

(71 citation statements)

References 23 publications

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“…The maximum relative error is below 1%. In addition, figure 31 shows a comparison of our normal velocity eigenfunction and the results by Blennerhassett & Bassom (2006) for the even mode at Re = 700. Excellent agreement is observed.…”

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

“…Therefore, a Floquet expansion in time is required in order to accurately determine the stability of the time-periodic base flow. For example, Blennerhassett & Bassom (2006) studied the instability of an oscillatory Stokes layer with a Floquet expansion in time, and Luo & Wu (2010) compared the results to their direct numerical simulations of the same base flow at different Reynolds numbers. At subcritical Reynolds numbers, some phases of the base flow were instantaneously unstable, but others were stable.…”

Section: Secondary Instabilitymentioning

confidence: 99%

“…Time-periodic base flow: the oscillating plates problem The validation of the Floquet expansion in time was performed by comparing with the results of Blennerhassett & Bassom (2006), who studied the linear stability of the time-periodic flow between two oscillating plates. In their work, the streamwise flow was driven by viscosity only, and therefore there is no pressure gradient.…”

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

“…In their work, the streamwise flow was driven by viscosity only, and therefore there is no pressure gradient. The analytic form for the time-dependent base flow provided by Blennerhassett & Bassom (2006) was implemented in our Floquet solution algorithm. Stability calculations were performed at a plate separation of 32 units, where the wall-normal coordinate is scaled by √ 2ν/ω, and ω is the frequency of wall oscillation.…”

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

“…The decay rates of the least stable modes are compared to the results of Blennerhassett & Bassom (2006) , current results; × , Blennerhassett & Bassom (2006). in table 1.…”

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

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Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011

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The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the TollmienSchlichting (T-S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

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Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

Section: Secondary Instabilitymentioning

confidence: 99%

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

“…The decay rates of the least stable modes are compared to the results of Blennerhassett & Bassom (2006) , current results; × , Blennerhassett & Bassom (2006). in table 1.…”

Section: Appendix B Validation Of the Linear Stability Algorithmmentioning

confidence: 99%

See 3 more Smart Citations

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011

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Transition from periodic to chaotic AC electroosmotic flows near electric double layer

Zhao

et al. 2021

AIChE Journal

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Electroosmotic flows (EOFs) on insulated interfacial surface commonly exists as interfacial flows. Previously theoretical studies indicate that EOFs of Newtonian fluids on the insulated interfacial surface are steady in microchannels with symmetric zeta potentials (Suresh and Homsy, Physics of Fluids, 2004, 16, 2,349). Restricted by flow diagnostic methods in microfluidics, few velocity measurements of instantaneous EOFs have been reported, and the existence of unsteady EOFs on the insulated surface remains unclear. In this investigation, the velocity fluctuations of EOFs generated under AC electric field (named as ACFEOF) overlapped on a steady pressuredriven flow are measured by laser induced fluorescence photobleaching anemometer, at the diffuse electric double layer (EDL) on the bottom wall far from electrodes. Chaotic velocity fluctuations according to unsteady ACFEOF has been, for the first time, observed. Stokes number (St) and electrical Reynolds number (Re E) related to oscillation and electro-inertial effect are suggested to control chaotic ACFEOF.

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The impact of steady streaming and conditional turbulence on gas transport during high-frequency ventilation

Jacob

Tingay

Leontini

2021

Theor. Comput. Fluid Dyn.

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High-frequency ventilation is a type of mechanical ventilation therapy applied on patients with damaged or delicate lungs. However, the transport of oxygen down, and carbon dioxide up, the airway is governed by subtle transport processes which hitherto have been difficult to quantify. We investigate one of these mechanisms in detail, nonlinear mean streaming, and the impact of the onset of turbulence on this streaming, via direct numerical simulations of a model 1:2 bifurcating pipe. This geometry is investigated as a minimal unit of the fractal structure of the airway. We first quantify the amount of gas recirculated via mean streaming by measuring the recirculating flux in both the upper and lower branches of the bifurcation. For conditions modeling the trachea-to-bronchi bifurcation of an infant, we find the recirculating flux is of the order of 3–5% of the peak flux . We also show that for conditions modeling the upper generations, the mean recirculation regions extend a significant distance away from the bifurcation, certainly far enough to recirculate gas between generations. We show that this mean streaming flow is driven by the formation of longitudinal vortices in the flow leaving the bifurcation. Second, we show that conditional turbulence arises in the upper generations of the airway. This turbulence appears only in the flow leaving the bifurcation, and at a point in the cycle centered around the maximum instantaneous flow rate. We hypothesize that its appearance is due to an instability of the longitudinal-vortices structure.

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The linear stability of high-frequency oscillatory flow in a channel

Cited by 53 publications

References 23 publications

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

Transition from periodic to chaotic AC electroosmotic flows near electric double layer

The impact of steady streaming and conditional turbulence on gas transport during high-frequency ventilation

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