scholarly journals On the stability of global solutions to the three-dimensional Navier-Stokes equations

2018 ◽  
Vol 5 ◽  
pp. 843-911
Author(s):  
Hajer Bahouri ◽  
Jean-Yves Chemin ◽  
Isabelle Gallagher
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Global Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability

Some stability results on global solutions to the Navier–Stokes equations

Analysis ◽  
2015 ◽  
Vol 35 (3) ◽  
Author(s):  
Isabelle Gallagher
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Global Solutions ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions ◽  
Whole Space ◽  
The Stability ◽  
Stability Results

AbstractIn these notes we present some results concerning the existence of global smooth solutions to the three-dimensional Navier–Stokes equations set in the whole space. We are particularly interested in the stability of the set of initial data giving rise to a global smooth solution.

Linear Stability Analysis of LPT Rotor Packets: Part II — Three-Dimensional Results and Mistuning Effects

2004 ◽  
Author(s):  
Roque Corral ◽  
Juan Manuel Gallardo ◽  
Carlos Vasco
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Stability Limit ◽  
Mode Shapes ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Frequency ◽  
Stability Maps ◽  
The Stability ◽  
The One

Part II of this paper compares the aerodynamic damping of a modern Low Pressure Turbine (LPT) interlock bladed-disc to the one obtained when the blades are welded in pairs through the lateral face of the shroud. The damping is computed using the linearized Reynolds averaged Navier-Stokes equations on a moving grid. It is concluded that the increase in stability of the welded-pair with respect the cantilever configuration due to the modification of the mode-shapes, is smaller than the one due to the overall raise of the reduced frequencies of a bladed-disc with an interlock design. The modification of the flutter boundaries due to mistuning effects is taken into account using the reduced order model known as the Fundamental Mistuning Model (FMM). It is shown that the modification on the stability limit of a interlock bladed-disc is negligible, while for a welded-pair configuration an increase of 0.15% on the critical damping may be expected. Two realistic welded-pair bladed-discs are analysed in this work. It is shown that both are aerodynamically unstable, which is in agreement with the experimental observations. Critical reduced frequency stability maps accounting for mistuning effects are derived for both, freestanding and welded in pairs airfoils. The airfoils are assumed to be identical and mechanically uncoupled. The stabilizing effect of mistuning is also retained in these maps.

Numerical and Experimental Studies of Oscillatory Airflows Induced by Rotation of a Grass-Cutting Blade

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
F. Abbasian ◽  
J. Cao ◽  
S. D. Yu
Keyword(s):  
Background Noise ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Tetrahedral Mesh ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Unstructured Tetrahedral Mesh ◽  
The Stability ◽  
Mesh Convergence

Three-dimensional oscillatory airflows induced by a rotating grass-cutting blade in a cylindrical chamber are studied experimentally and numerically in this paper. Experimental pressure results are obtained using a sound pressure transducer and a data acquisition system. The measured pressure data contain background noise and high-frequency sound signals due to the blade vibrations. The background noise is separately measured; its effect on the signal is determined from a spectral subtraction algorithm. A time-accurate finite volume numerical solution to the three-dimensional incompressible unsteady Navier–Stokes equations is also sought using the sliding frame technique and the unstructured tetrahedral mesh. Convergence studies are conducted using various combinations of mesh sizes and time increments to ensure the stability of the numerical scheme. The experimental and numerical pressure results are in good agreement.

A HYBRID FINITE-ANALYTIC ALGORITHM FOR SOLVING THREE-DIMENSIONAL ADVECTION-DIFFUSION EQUATIONS

2004 ◽  
Vol 01 (03) ◽  
pp. 407-430 ◽  
Author(s):  
H. M. HU ◽  
K.-H. WANG
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability

The hybrid finite-analytic (HFA) method for discretization of a three-dimensional advection-diffusion equation is developed using the superposition of the HFA solutions of locally linearized one-dimensional advection-diffusion equations. An example calculation of a system of three-dimensional nonlinear equations is conducted to test the convergence and accuracy of the 7-point numerical scheme. Good agreements between calculated and analytical solutions are obtained. An algorithm based on the HFA method with multigrid technique and Gauss-Seidel iteration is also developed to solve the three-dimensional Navier-Stokes equations in a staggered grid system. The stability and efficiency of the method are demonstrated by performing calculations of the fluid flow in a three-dimensional cubic cavity with a moving top wall. The proposed procedure is observed to exhibit good rates of smoothing and almost grid-independent convergence rates in comparison with a single-grid iteration method. The results are in excellent agreement with other published computational results.

Sensitivity Analysis With Respect to Flutter-Free Design of Compressor Blades

2010 ◽  
Author(s):  
Markus May
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Compressor Blades ◽  
Similarity Parameter ◽  
Navier Stokes Equations ◽  
Stability Behaviour ◽  
The Stability ◽  
German Aerospace

In this paper, the rotor geometries of two consecutive design loops are compared numerically with respect to aeroelastic stability. Therefore, the TRACE code of the German Aerospace Center DLR is used to compute the flutter predictions: based on a three-dimensional steady solution, the time-linearized Navier-Stokes equations are solved in order to assess the aerodynamic damping so that the critical inter-blade phase angles can be determined. Apart from the global stability behaviour the computation of local excitation per surface area is presented, facilitating the identification of stabilizing and destabilizing effects due to blade motion and flow field disturbances. Aiming for flutter-free design of compressor blades, an exemplary sensitivity analysis on the first mode is performed. Within the scope of this study, reduced frequency and mass ratio are varied and the influence of these parameters on the stability behaviour is deduced. For a tuned system, the nondimensional flutter equations are derived introducing the flutter index as aeroelastic similarity parameter. Differing tendencies of the aerodynamic work entry and the corresponding logarithmic decrement concerning flutter susceptibility are discussed in detail.

scholarly journals Axisymmetric flows in the exterior of a cylinder

2019 ◽  
Vol 150 (4) ◽  
pp. 1671-1698 ◽  
Author(s):  
K. Abe ◽  
G. Seregin
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Initial Boundary Value

AbstractWe study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $\Pi =\{x=(x_{h}, x_3)\ \vert \vert x_{h} \vert \gt 1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^{3}\cap L^{2}(\Pi )$ satisfying the decay condition of the swirl component $ru^{\theta }_{0}\in L^{\infty }(\Pi )$.

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