Singular limit problem for the Navier–Stokes equations in a curved thin domain

2020 ◽  
Author(s):  
Tatsu-Hiko Miura
Keyword(s):  
Stokes Equations ◽  
Limit Problem ◽  
Singular Limit ◽  
Navier Stokes ◽  
Thin Domain ◽  
Navier Stokes Equations

scholarly journals Gevrey stability of hydrostatic approximate for the Navier–Stokes equations in a thin domain

Nonlinearity ◽  
2021 ◽  
Vol 34 (10) ◽  
pp. 7185-7226
Author(s):  
Chao Wang ◽  
Yuxi Wang ◽  
Zhifei Zhang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Thin Domain ◽  
Navier Stokes Equations

scholarly journals A rigorous derivation of the stationary compressible Reynolds equation via the Navier–Stokes equations

2018 ◽  
Vol 28 (04) ◽  
pp. 697-732 ◽  
Author(s):  
I. S. Ciuperca ◽  
E. Feireisl ◽  
M. Jai ◽  
A. Petrov
Keyword(s):  
Reynolds Equation ◽  
Stokes System ◽  
Stokes Equations ◽  
A Priori ◽  
Limit Problem ◽  
Navier Stokes ◽  
Rigorous Derivation ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier–Stokes system on a thin domain. In particular, the existence of solutions to the Navier–Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the one-dimensional case.

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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