Flowfield around a Body with Elastic Walls

2008 ◽  
Vol 33-37 ◽  
pp. 1083-1088
Author(s):  
Norio Arai ◽  
Kota Fujimura ◽  
Yoko Takakura
Keyword(s):  
Stokes Equation ◽  
Bluff Body ◽  
Incompressible Flows ◽  
Small Deformation ◽  
Uniform Flow ◽  
The Body ◽  
Body Motion ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Elastic Walls

When a bluff body is located in a uniform flow, the flow is separated and vortices are formed. Consequently, the vortices cause “flow-induced vibrations”. Especially, if the Strouhal number and the frequency of the body oscillation coincide with the natural frequency, the lock-in regime will occur and we could find the large damages on it. Therefore, it is profitable, in engineering problems, to clarify this phenomenon and to suppress the vibration, in which the effect of elastic walls on the suppression is focused. Then, the aims of this article are to clarify the oscillatory characteristics of the elastic body and the flowfield around the body by numerical simulations, in which a square pillar with elastic walls is set in a uniform flow. Two dimensional incompressible flows are solved by the continuity equation, Navier-Stokes equation and the Poisson equation which are derived by taking divergence of Navier-Stokes equation. Results show that a small deformation of elastic walls has a large influence on the body motion. In particular, the effect is very distinct at the back.

scholarly journals On lower-dimensional models in lubrication, Part A: Common misinterpretations and incorrect usage of the Reynolds equation

2020 ◽  
pp. 135065012097379
Author(s):  
Andreas Almqvist ◽  
Evgeniya Burtseva ◽  
Kumbakonam Rajagopal ◽  
Peter Wall
Keyword(s):  
Stokes Equation ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Constant Viscosity ◽  
Incompressible Navier Stokes Equation ◽  
Lower Dimensional

Most of the problems in lubrication are studied within the context of Reynolds’ equation, which can be derived by writing the incompressible Navier-Stokes equation in a dimensionless form and neglecting terms which are small under the assumption that the lubricant film is very thin. Unfortunately, the Reynolds equation is often used even though the basic assumptions under which it is derived are not satisfied. One example is in the mathematical modelling of elastohydrodynamic lubrication (EHL). In the EHL regime, the pressure is so high that the viscosity changes by several orders of magnitude. This is taken into account by just replacing the constant viscosity in either the incompressible Navier-Stokes equation or the Reynolds equation by a viscosity-pressure relation. However, there are no available rigorous arguments which justify such an assumption. The main purpose of this two-part work is to investigate if such arguments exist or not. In Part A, we formulate a generalised form of the Navier-Stokes equation for piezo-viscous incompressible fluids. By dimensional analysis of this equation we, thereafter, show that it is not possible to obtain the Reynolds equation, where the constant viscosity is replaced with a viscosity-pressure relation, by just neglecting terms which are small under the assumption that the lubricant film is very thin. The reason is that the lone assumption that the fluid film is very thin is not enough to neglect the terms, in the generalised Navier-Stokes equation, which are related to the body forces and the inertia. However, we analysed the coefficients in front of these (remaining) terms and provided arguments for when they may be neglected. In Part B, we present an alternative method to derive a lower-dimensional model, which is based on asymptotic analysis of the generalised Navier-Stokes equation as the film thickness goes to zero.

A proposal concerning laminar wakes behind bluff bodies at large Reynolds number

1956 ◽  
Vol 1 (4) ◽  
pp. 388-398 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Bluff Body ◽  
The Body ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Bluff Bodies ◽  
Proper Solution ◽  
Navier Stokes Equation ◽  
Limit Solution

This note advocates a model of the steady flow about a bluff body at large Reynolds number which is different from the classical free-streamline model of Helmholtz and Kirchhoff. It is suggested that, although the free-streamline model may be a proper solution of the Navier-Stokes equation with μ = 0, it is unlikely to be the limit, as μ → 0, of the solution describing the steady flow due to the presence of a bluff body in an otherwise uniform stream. The limit solution proposed here is one which gives a closed wake.A closed wake contains a standing eddy, or eddies, whose general features can be inferred from the results of an earlier investigation of steady flow in a closed region at large Reynolds number. In all cases, the drag (coefficient) on the body tends to zero as the Reynolds number tends to infinity. The proccedure for finding the details of the closed wake behind two-dimensional and axisymmetrical bodies is described, although no particular case has yet been worked out.

scholarly journals Basics of Fluid Dynamics

2021 ◽  
Author(s):  
Nahom Alemseged Worku
Keyword(s):  
Stokes Equation ◽  
Incompressible Flows ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Conservation Of Energy ◽  
Conservation Of Momentum ◽  
Almost All ◽  
Transport Theorem

In this chapter, studies on basic properties of fluids are conducted. Mathematical and scientific backgrounds that helps sprint well into studies on fluid mechanics is provided. The Reynolds Transport theorem and its derivation is presented. The well-known Conservation laws, Conservation of Mass, Conservation of Momentum and Conservation of Energy, which are the foundation of almost all Engineering mechanics simulation are derived from Reynolds transport theorem and through intuition. The Navier–Stokes equation for incompressible flows are fully derived consequently. To help with the solution of the Navier–Stokes equation, the velocity and pressure terms Navier–Stokes equation are reduced into a vorticity stream function. Classification of basic types of Partial differential equations and their corresponding properties is discussed. Finally, classification of different types of flows and their corresponding characteristics in relation to their corresponding type of PDEs are discussed.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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