Global stability for the fractional Navier-Stokes equations in the Fourier-Herz space

2018 ◽  
Vol 41 (10) ◽  
pp. 3696-3717
Author(s):  
Jing Chen ◽  
Changming Song
Keyword(s):  
Global Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Herz Space ◽  
Navier Stokes Equations

scholarly journals Global stability of large solutions to the 3D Navier-Stokes equations

1994 ◽  
Vol 159 (2) ◽  
pp. 329-341 ◽  
Author(s):  
G. Ponce ◽  
R. Racke ◽  
T. C. Sideris ◽  
E. S. Titi
Keyword(s):  
Global Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Solutions

Global stability of axisymmetric flow focusing

2017 ◽  
Vol 832 ◽  
pp. 329-344 ◽  
Author(s):  
F. Cruz-Mazo ◽  
M. A. Herrada ◽  
A. M. Gañán-Calvo ◽  
J. M. Montanero
Keyword(s):  
Boundary Conditions ◽  
Global Stability ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Navier Stokes ◽  
Transition Curve ◽  
Flow Focusing ◽  
Stable States ◽  
Navier Stokes Equations ◽  
Wide Range

In this paper, we analyse numerically the stability of the steady jetting regime of gaseous flow focusing. The base flows are calculated by solving the full Navier–Stokes equations and boundary conditions for a wide range of liquid viscosities and gas speeds. The axisymmetric modes characterizing the asymptotic stability of those flows are obtained from the linearized Navier–Stokes equations and boundary conditions. We determine the flow rates leading to marginally stable states, and compare them with the experimental values at the jetting-to-dripping transition. The theoretical predictions satisfactorily agree with the experimental results for large gas speeds. However, they do not capture the trend of the jetting-to-dripping transition curve for small gas velocities, and considerably underestimate the minimum flow rate in this case. To explain this discrepancy, the Navier–Stokes equations are integrated over time after introducing a small perturbation in the tapering liquid meniscus. There is a transient growth of the perturbation before the asymptotic exponential regime is reached, which leads to dripping. Our work shows that flow focusing stability can be explained in terms of the combination of asymptotic global stability and the system short-term response for large and small gas velocities, respectively.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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