scholarly journals On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations

2021 ◽  
Vol 359 (6) ◽  
pp. 639-644
Author(s):  
Hongjun Gao ◽  
Šárka Nečasová ◽  
Tong Tang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrostatic Approximation

REGULARIZATION BY MONOTONE PERTURBATIONS OF THE HYDROSTATIC APPROXIMATION OF NAVIER–STOKES EQUATIONS

2004 ◽  
Vol 14 (12) ◽  
pp. 1819-1848 ◽  
Author(s):  
FRANCISCO ORTEGÓN GALLEGO
Keyword(s):  
Existence Of Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Energy Identity ◽  
Nonlinear Perturbations ◽  
Smooth Functions ◽  
Regularization Technique ◽  
Navier Stokes Equations ◽  
Hydrostatic Approximation ◽  
Functional Setting

Due to the lack of regularity of the solutions to the hydrostatic approximation of Navier–Stokes equations, an energy identity cannot be deduced. By including certain nonlinear perturbations to the hydrostatic approximation equations, the solutions to the perturbed problem are smooth enough so that they satisfy the corresponding energy identity. The perturbations considered in this paper are of the monotone class. Three kinds of problems are then studied. To do that, we introduce a functional setting and show in every case that the set of smooth functions with compact support is dense in the space where we search for solutions. When the perturbations are small enough in a certain sense, the solutions of the perturbed problem are close to those of the original one. As a result, this gives a new proof of the existence of solutions to the hydrostatic approximation of Navier–Stokes equations. Finally, this regularization technique has been applied to the analysis of a one-equation hydrostatic turbulence model.

scholarly journals Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations

Nonlinearity ◽  
2020 ◽  
Vol 33 (12) ◽  
pp. 6502-6516
Author(s):  
Ken Furukawa ◽  
Yoshikazu Giga ◽  
Matthias Hieber ◽  
Amru Hussein ◽  
Takahito Kashiwabara ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Primitive Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrostatic Approximation

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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