Linear stability of slip pipe flow

Chen, Kaiwen; Song, Baofang

doi:10.1017/jfm.2020.997

Cited by 8 publications

(2 citation statements)

References 35 publications

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“…However, it should be noted that the slip velocity considered here is caused not by rarefaction effects but by hydrophobic surfaces (Vinogradova 1999; Min & Kim 2005; Seo & Mani 2016; Pralits et al. 2017; Xiong & Tao 2020; Chen & Song 2021), polymers (Spille et al. 2000) and porous media (Gersting & John 1974; Straughan & Harfash 2013).…”

Section: Introductionmentioning

confidence: 99%

“…Confined flows, such as in channels and pipes, are common in MEMS. The influences of the slip velocity (length) on the flow stability have been widely studied based on NS linear stability equations (NS-LSEs) with slip boundary conditions (Gersting & John 1974; Vinogradova 1999; Spille, Rauh & BüHring 2000; Chu 2001, 2003, 2004; Lauga & Cossu 2005; Min & Kim 2005; He & Wang 2008; Průša 2009; Straughan & Harfash 2013; Seo & Mani 2016; Pralits, Alinovi & Bottaro 2017; Chai & Song 2019; Xiong & Tao 2020; Chen & Song 2021). However, it should be noted that the slip velocity considered here is caused not by rarefaction effects but by hydrophobic surfaces (Vinogradova 1999; Min & Kim 2005; Seo & Mani 2016; Pralits et al.…”

Section: Introductionmentioning

confidence: 99%

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A novel linear stability analysis method for plane Couette flow considering rarefaction effects

Zou

Zhong

et al. 2023

J. Fluid Mech.

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Following the stability analysis method in classic fluid dynamics, a linear stability equation (LSE) suitable for rarefied flows is derived based on the Bhatnagar–Gross–Krook (BGK) equation. The global method and singular value decomposition method are used for modal and non-modal analysis, respectively. This approach is validated by results obtained from Navier–Stokes (NS) equations. The modal analysis shows that LSEs based on NS equations (NS-LSEs) begin to fail when the Knudsen number ( $Kn$ ) increases past $\sim$ 0.01, regardless of whether a slip model is used. When $Kn\geq 0.01$ , the growth rate of the least stable mode is generally underestimated by the NS-LSEs. Under a fixed wavenumber, the pattern (travelling or standing wave) of the least stable mode changes with $Kn$ ; when the mode presents the same pattern, the growth rate decreases almost linearly with increasing $Kn$ ; otherwise, rarefaction effects may not stabilize the flow. The characteristic lengths of the different modes are different, and the single-scale classic stability analysis method cannot predict multiple modes accurately, even when combined with a slip model and even for continuum flow. However, non-modal analysis shows that this error does not affect the transient growth because modes with small growth rates offer little contribution to the transient growth. In rarefied flow, as long as the Mach number ( $Ma$ ) is large enough, transient growth will occur in some wavenumber ranges. The rarefaction effect plays a stabilizing role in transient growth. The NS-LSEs-based method always overestimates the maximum transient growth.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

Zou

Zhong

et al. 2023

J. Fluid Mech.

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The equivalence between BE-LSE and NS-LSEs under continuum assumption

Ma,

Lv,

2024

Communications in Nonlinear Science and Numerical Simulation

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Numerical study of supersonic boundary-layer modal stability for a slightly rarefied gas using Navier—Stokes approach

Chen

2021

Physics of Fluids

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In this paper, a systematic study on the supersonic boundary-layer modal stability for a slightly rarefied gas is conducted by considering velocity slip and temperature jump effects in the Navier–Stokes (NS) equations. The effects of slip boundary on the first- and second-mode instability at different conditions are presented in detail. The laminar flow is obtained by solving the NS equations along with no-slip and slip boundary conditions, which shows that the slip boundary causes the boundary layer becoming thinner and the supersonic region near the wall becoming narrower. The perturbation slip boundary conditions at the wall and their influence on the stability are carefully discussed. The tangential momentum accommodation coefficient and the thermal accommodation coefficient are set equal or unequal for a broad range to study the combined or leading effects of velocity slip and temperature jump, respectively. It is found that velocity slip significantly stabilizes the second-mode disturbances while largely destabilizes the first-mode perturbations. On the contrary, the temperature jump apparently enhances the second-mode instability, while it has little influence on the first mode. When velocity slip and temperature jump are both present, the first mode is more destabilized, while a competitive effect acts on the second mode. Additional results show that the neutral stability curves for the second and third modes as well as the synchronization between fast and slow modes are delayed further downstream due to velocity slip. These findings are shown consistently regardless of the wall cooling for both supersonic and hypersonic flows.

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Linear stability of slip pipe flow

Abstract: Abstract

Cited by 8 publications

References 35 publications

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

The equivalence between BE-LSE and NS-LSEs under continuum assumption

Numerical study of supersonic boundary-layer modal stability for a slightly rarefied gas using Navier—Stokes approach

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