Non-similar solution of the forced convection of laminar gaseous slip flow over a flat plate with viscous dissipation: linear stability analysis for local similar solution

Meccanica ◽  
2015 ◽  
Vol 51 (1) ◽  
pp. 99-115 ◽  
Author(s):  
Elhoucine Essaghir ◽  
Youssef Haddout ◽  
Abdelaziz Oubarra ◽  
Jawad Lahjomri
Keyword(s):  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Linear Stability Analysis ◽  
Slip Flow ◽  
Similar Solution ◽  
Gaseous Slip Flow

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

A Linear Stability Analysis of Cavitation in a Finite Blade Count Impeller

2000 ◽  
Vol 122 (4) ◽  
pp. 798-805 ◽  
Author(s):  
Hironori Horiguchi ◽  
Satoshi Watanabe ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Stability Analysis ◽  
Flat Plate ◽  
Steady Flow ◽  
Linear Stability ◽  
Phase Difference ◽  
Linear Stability Analysis ◽  
Previous Analysis ◽  
Flow Analysis ◽  
Cavity Volume ◽  
Inlet Duct

The linear stability analysis of cavitation in flat plate cascades corresponding to 2, 3, 4, and 5-bladed impeller was carried out to clarify the effect of the blade count on cavitation instabilities. Each blade is treated independently so that all possible modes in those impellers can be found. In steady flow analysis the alternate blade cavitation was found only for impellers with even number of blades. For 2 or 4-bladed impeller, it was confirmed that there exists no additional destabilizing mode to those found in the previous analysis in which the inter-blade phase difference of disturbance was assumed. It was shown that the modes with total cavity volume fluctuation depend on the inlet duct length while the modes without total cavity volume fluctuation are independent on the system. [S0098-2202(00)01304-3]

Washing wedges: capillary instability in a gradient of confinement

2016 ◽  
Vol 790 ◽  
pp. 619-633 ◽  
Author(s):  
Ludovic Keiser ◽  
Rémy Herbaut ◽  
José Bico ◽  
Etienne Reyssat
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Linear Stability Analysis ◽  
Theoretical Description ◽  
Oil Droplets ◽  
Bulk Viscous ◽  
Open Question ◽  
Wetting Liquid

We present experimental results on the extraction of oil trapped in the confined region of a wedge. Upon addition of a more wetting liquid, we observe that oil fingers develop into this extracting liquid. The fingers eventually pinch off and form droplets that are driven away from the apex of the wedge by surface tension along the gradient of confinement. During an experiment, we observe that the size of the expelled oil droplets decreases as the unstable front recedes towards the wedge. We show how this size can be predicted from a linear stability analysis reminiscent of the classical Saffman–Taylor instability. However, the standard balance of capillary and bulk viscous dissipation does not account for the dynamics found in our experiments, leaving as an open question the detailed theoretical description of the instability.

scholarly journals Nonlinear stability analysis of Darcy’s flow with viscous heating

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160036 ◽  
Author(s):  
Michele Celli ◽  
Leonardo S. de B. Alves ◽  
Antonio Barletta
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Nonlinear Stability ◽  
Linear Stability Analysis ◽  
Integral Transform ◽  
Internal Heat ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Rate Analysis

The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.

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