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.

scholarly journals Conjugate Solutions of Navier-Stokes Equation with Deformed Pore Structure

2014 ◽  
Vol 8 ◽  
pp. 30-48
Author(s):  
V.I. Popkov ◽  
V.I. Astafiev ◽  
V.P. Shakshin ◽  
S.V. Zatsepina
Keyword(s):  
Stokes Equation ◽  
Deformation Theory ◽  
Cluster Structure ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Porous Space ◽  
Navier Stokes Equation ◽  
Linear Solution ◽  
Regional Problems ◽  
Final Speed

Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space - to a well and from a well - to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered. Basing upon the analytical solution of Navier-Stokes equation and model of A.N. Kolmogorov we have obtained the energy model of turbulence pulsing controlled chaos, conjugated with risk stability of average well inflow and cluster structure of Earth defluidization.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document