A sufficient condition for smoothness of solutions of Navier-Stokes equations

1968 ◽  
Vol 6 (4) ◽  
pp. 354-358 ◽  
Author(s):  
S. Kaniel
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Sufficient Condition ◽  
Navier Stokes Equations ◽  
Smoothness Of Solutions

VACUUM STATE FOR SPHERICALLY SYMMETRIC SOLUTIONS OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS

2006 ◽  
Vol 03 (03) ◽  
pp. 403-442 ◽  
Author(s):  
ZHOUPING XIN ◽  
HONGJUN YUAN
Keyword(s):  
Weak Solutions ◽  
Stokes System ◽  
Stokes Equations ◽  
Vacuum State ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Navier Stokes Equations ◽  
Vacuum States ◽  
Spherically Symmetric Solutions

We study the properties of vacuum states in weak solutions to the compressible Navier–Stokes system with spherical symmetry. It is shown that vacuum states cannot develop later on in time in a region far away from the center of symmetry, provided there is no vacuum state initially and two initially non-interacting vacuum regions never meet each other in the future. Furthermore, a sufficient condition on the regularity of the velocity excluding the formation of vacuum states is given.

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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