Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow

Saikia, Bijaylakshmi; Ramachandran, Ashwin; Sinha, Krishnendu; Govindarajan, Rama

doi:10.1063/1.4974863

Cited by 6 publications

(3 citation statements)

References 33 publications

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“…As previously pointed out, dense gases are characterized by a peculiar behaviour of the transport properties and a strong variation of the Prandtl number. These effects have been analysed by Govindarajan & Sahu (2014) and Saika et al (2017), who showed that the stability is strongly affected by the stratification of the transport properties, which can be quantified by a single non-dimensional parameter, the Prandtl number. Other works of particular interest for the present study are the recent linear stability analyses including non-ideal fluid effects for plane Poiseuille flows (Ren, Fu & Pecnik 2019a) and compressible boundary layers (Ren, Marxen & Pecnik 2019b).…”

Section: Introductionmentioning

confidence: 99%

Dense-gas effects on compressible boundary-layer stability

et al. 2020

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Section: Introductionmentioning

confidence: 99%

Dense-gas effects on compressible boundary-layer stability

et al. 2020

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“…The study on wall heating and viscosity-stratification has also been extended to transient growth, secondary instability as well as instabilites in other types of flows (Chikkadi et al 2005;Sameen & Govindarajan 2007;Sameen et al 2011;Sahu 2011;. For compressible plane Couette flow, Malik et al (2008) showed that the flow is more stable with viscosity stratification, while recently, a further study on this flow is given by Saikia et al (2017), in which the effects of individual/combined viscosity-thermal conductivity stratification are elucidated. The influence of viscosity gradients on the edge state is recently studied by Rinaldi et al (2018), showing that in minimal channel flows, the kinetic energy level and the driving force of self-sustained cycle of the edge state depends on viscosity distribution.…”

Section: Introductionmentioning

confidence: 99%

Linear instability of Poiseuille flows with highly non-ideal fluids

Ren

Pečnik

2018

J. Fluid Mech.

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The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour-liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide (CO 2 ) at pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number (Re = ρ * w u * r h * /µ * w ), the product of Prandtl (Pr = µ * w C * pw /κ * w ) and Eckert number (Ec = u * 2 r /C * pw T * w ), and the wall temperature that in addition to pressure determines the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered, subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical, and supercritical temperature regime. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is more unstable in the subcritical regime, inviscid unstable in the transcritical regime, while significantly more stable in the supercritical regime. Following the corresponding states principle, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states.

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“…The authors mostly focused on acoustic instabilities appearing at supersonic Mach numbers, as also later studied by Malik, Dey & Alam (2008) and Saikia et al. (2017). In addition to the acoustic modes, Hu & Zhong (1998) recovered the existence of a viscous mode similar to that found in the aforementioned incompressible, viscosity-stratified studies.…”

Section: Introductionmentioning

confidence: 99%

Instability in strongly stratified plane Couette flow with application to supercritical fluids

Bugeat,

Boldini,

Hasan

et al. 2024

J. Fluid Mech.

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This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long-wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831–864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g. miscible fluids) is finally discussed.

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Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow

Cited by 6 publications

References 33 publications

Dense-gas effects on compressible boundary-layer stability

Dense-gas effects on compressible boundary-layer stability

Linear instability of Poiseuille flows with highly non-ideal fluids

Instability in strongly stratified plane Couette flow with application to supercritical fluids

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