Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Stability of Navier–Stokes Equations

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Stokes System ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Well Posedness ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Three Space

In this chapter we intend to investigate the stability of the Leray solutions constructed in the previous chapter. It is useful to start by analyzing the linearized version of the Navier–Stokes equations, so the first section of the chapter is devoted to the proof of the well-posedness of the time-dependent Stokes system. The study will be applied in Section 3.2 to the two-dimensional Navier–Stokes equations, and the more delicate case of three space dimensions will be dealt with in Sections 3.3–3.5.

Fluid motion inside a spinning nutating cylinder

1985 ◽  
Vol 150 ◽  
pp. 121-138 ◽  
Author(s):  
Harold R. Vaughn ◽  
William L. Oberkampf ◽  
Walter P. Wolfe
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Internal Fluid

The incompressible three-dimensional Navier–Stokes equations are solved numerically for a fluid-filled cylindrical cannister that is spinning and nutating. The motion of the cannister is characteristic of that experienced by spin-stabilized artillery projectiles. Equations for the internal fluid motion are derived in a non-inertial aeroballistic coordinate system. Steady-state numerical solutions are obtained by an iterative finite-difference procedure. Flow fields and liquid induced moments have been calculated for viscosities in the range of 0.9 × 104−1 × 109 cSt. The nature of the three-dimensional fluid motion inside the cylinder is discussed, and the moments generated by the fluid are explained. The calculated moments generally agree with experimental measurements.

Fluid-Structure Interaction in Annular Flows With Several Modes of Vibration

2010 ◽  
Author(s):  
Abolghasem Mekanik ◽  
Naser Sayma
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Outer Cylinder ◽  
Time Integration ◽  
Time Discretization ◽  
Navier Stokes ◽  
Time Level ◽  
Navier Stokes Equations ◽  
Modes Of Vibration ◽  
The Stability

This paper describes two accurate Flow-Induced Vibration (FIV) methods used to analyze the induced vibrations caused by the laminar fluid flows in uniform annular geometries. In both methods, the uniform annuli which are composed of two concentric cylinders are considered. The outer cylinder is set on translational oscillation without or with a predetermined mode of vibration and with a known initial velocity. In the first method, the small amplitude motion of the outer cylinder is used to analyze the problem considered by using the direct coupling of the fluid and structure through the accurate simultaneous solution of the Navier-Stokes and structural equations. In the computational domain, the problem has been solved using an accurate time-integration method based on a finite-difference formulation and primitive variables. In this method, the real-time discretization of the Navier-Stokes equations for unsteady incompressible flows is based on a three-time-level implicit scheme. A pseudo-time integration with artificial compressibility is then introduced to advance the solution to a new real-time level. An implicit Euler scheme is used for the pseudo-time discretization, and the finite-difference spatial discretization is based on a stretched staggered grid. In the second method, the Reynolds-averaged Navier-Stokes equations are used to represent the unsteady flow in a nonlinear time-accurate fashion. In this case, the structural model is based on a linear modal model. The fluid mesh is moved at each time-step according to the structural motion, so that the changes in fluid-dynamic damping and flow unsteadiness can be accommodated. Based on the second approach, a code named SURF was generated to handle the solution from the steady state solution till the unsteady one which is in the form of vibratory motion of the outer cylinder. In this way the stability analyses can be performed for the structure by using several modes of vibration of the structure vis-a`-vis to the first method in which only translational motion of the outer cylinder is taken into account. The stability of the outer cylinder assessed by two methods in terms of the damped oscillation of the cylinder represents the decay in the amplitudes of vibration due to the fluid added damping. The results of this research can be used for the FIV and FSI analyses of the annular flows which could be found in many industries.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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