The slightly compressible Navier–Stokes equations revisited

A theorem by J. M. Ghidaglia and R. Temam shows the existence and finitness of attractors for 2-D Navier–Stokes equations for a sligthly compressible fluid. In this paper we extend their result to the equations of thermohydraulic for the same fluid.

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On the existence of slow manifolds for problems with different timescales

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1994.0016 ◽

1994 ◽

Vol 346 (1679) ◽

pp. 159-171 ◽

Cited By ~ 9

Keyword(s):

Compressible Flows ◽

Stokes Equations ◽

Slow Manifold ◽

Time Dependent ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Slightly Compressible ◽

Finite Dimensional ◽

Uniformly Smooth ◽

Dimensional Dynamical System

We consider time dependent systems of partial differential equations (PDE) whose solutions can vary on two different timescales. An example is given by the Navier-Stokes equations for slightly compressible flows. By proper initialization, the fast timescale can be suppressed to any given order; however, this does generally not imply the existence of a slow manifold. Since the PDE solutions are uniformly smooth in space, one can approximate the PDE system by a finite dimensional Galerkin system. Under suitable assumptions, this finite dimensional dynamical system will have a slow manifold.

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Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050200032x ◽

2002 ◽

Vol 132 (03) ◽

pp. 627

Keyword(s):

Asymptotic Behaviour ◽

Stokes Equations ◽

Half Line ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Asymptotic Behaviour Of Solutions

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

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.14.4.2020.05.0579 ◽

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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