Steady Flow in the Transition Length of a Straight Tube

1942 ◽  
Vol 9 (2) ◽  
pp. A55-A58 ◽  
Author(s):  
Henry L. Langhaar
Keyword(s):  
Velocity Field ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Straight Tube ◽  
Pressure Function ◽  
Navier Stokes Equations ◽  
Dimensionless Constant ◽  
The Family ◽  
Transition Length

Abstract By means of a linearizing approximation, the Navier-Stokes equations are solved for the case of steady flow in the transition length of a straight tube. The family of velocity profiles is defined by Bessel functions, and the parameter of this family is tabulated against the axial co-ordinate in a dimensionless form. Hence, the length of transition is obtained. The curves give a comparison of the author’s calculations of the velocity field with those of other investigators, and with the experimental data of Nikuradse. The pressure function is derived from the computed velocity field by means of the energy equation, and the pressure drop in the transition length is defined by a dimensionless constant m, which is computed to be 2.28. A discussion of this constant is given in the conclusions.

On the limitation of imposed velocity field strategy for Coulomb-driven electroconvection flow simulations

2013 ◽  
Vol 727 ◽  
Author(s):  
Philippe Traoré ◽  
Jian Wu
Keyword(s):  
Velocity Field ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Mobility Parameter ◽  
The Rich ◽  
Strong Injection ◽  
Unipolar Injection

AbstractThis study refers to the article of Chicón, Castellanos & Martion (J. Fluid Mech., vol. 344, 1997, pp. 43–66), who presented a numerical study of electroconvection in a layer of dielectric liquid induced by unipolar injection. An important characteristic of the numerical strategy proposed by Chicón et al. lies in the fact that the Navier–Stokes equations are never solved to obtain the velocity field, which is subsequently needed in the charge density transport equation. Instead, the velocity field is explicitly provided by an expression obtained with some assumptions about the flow structure and related to the electric field (the imposed velocity field approach; IVF). The validity of the above simplification is examined through a direct comparison of the solutions obtained by solving the Navier–Stokes equations (the Navier–Stokes computation approach; NSC). It is clearly demonstrated that, even in the strong injection regime ($C= 10$), the results look very similar for a given range of the mobility parameter $M$; however, in the weak injection regime ($C= 0. 1$), significant discrepancies are observed. The rich flow structures obtained with the NSC approach invalidate the use of the IVF approach in the weak injection regime.

Simulation of Flow Around Circular Cylinder Using a Collocation Spectral Method

2005 ◽  
Author(s):  
Johnny J. M. Rizales ◽  
Paulo T. T. Esperanc¸a ◽  
Andre´ Belfort Bueno
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Spectral Method ◽  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Navier Stokes Equations ◽  
Collocation Spectral Method

The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for low Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.

Simulating Liquid Dynamics by a Particle-Based Method

2013 ◽  
Vol 380-384 ◽  
pp. 1121-1124
Author(s):  
Ling Zou
Keyword(s):  
Velocity Field ◽  
Computer Games ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Natural Phenomena ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Virtual Construction ◽  
Natural Phenomena Simulation ◽  
Liquid Dynamics

There is much research focusing on natural phenomena simulation in virtual reality and computer graphics. Liquid is chosen as our research object, because it is one of the most common natural phenomena. A particle-based modeling method for dynamic liquid simulation is presented in this paper. In our approach, accurate solutions for the Navier-Stokes equations are first accomplished in an Euler-based grid at each time step. This returns a velocity field calculated based on the pressure solved from a converted Poisson equation. Finally, particle movements are advected through this velocity field in order to simulate the dynamics of fluid volume. Experiment shows that visual effect which can satisfy users requirement is achieved by this method. This application has promising potentials in the areas of movie making, computer games, virtual construction and virtual simulation in medicine, etc.

DYNAMIC BEHAVIOR OF A STEADY FLOW IN AN ANNULAR TUBE WITH POROUS WALLS AT DIFFERENT TEMPERATURES

2009 ◽  
Vol 19 (09) ◽  
pp. 2939-2951 ◽  
Author(s):  
JACQUES HONA ◽  
ELISABETH NGO NYOBE ◽  
ELKANA PEMHA
Keyword(s):  
Steady Flow ◽  
Shooting Method ◽  
Energy Equation ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Navier Stokes ◽  
Specific Mass ◽  
Navier Stokes Equations ◽  
Different Temperatures ◽  
Annular Tube

In this paper, the axisymmetric flow of a viscous fluid through a porous annular tube with walls kept at different temperatures is studied theoretically. The physical properties of the fluid remain constant, notably its specific mass, its dynamic viscosity and its thermal diffusivity. The nondimensional parameters which the solutions of the problem depend on are defined. A numerical integration using the shooting method is applied for solving the Navier–Stokes equations and the energy equation. Bifurcation diagrams are presented and enable to highlight significant properties of the flow. Some thermal behaviors corresponding to specific values of the parameters are performed. Asymmetric solutions of the steady flow are described and some results about velocity components are also analyzed.

scholarly journals Instantaneous sentinel for the identification of the pollution term in Navier-Stokes system

2021 ◽  
Author(s):  
Teldja Laib ◽  
Imad Rezzoug ◽  
Taki-Eddine Oussaeif
Keyword(s):  
Distributed Systems ◽  
Velocity Field ◽  
Control Theory ◽  
Stokes System ◽  
Stokes Equations ◽  
The State ◽  
Navier Stokes ◽  
Initial Condition ◽  
Navier Stokes Equations ◽  
Control Functions

The aim of this paper is about presenting some results of the Sentinel Theory in Connection with Control Theory of Distributed Systems. There is of course a large variety of models where the results to follow could be applied. What we have particularly in mind is the classical set of Navier-Stokes equations. We shall denote here by the velocity field and the pressure, which is a quite unusual notation in the "Turbulence" circle. The reason is simply that in all what is following that we think of as the state of our system, this state depends on control functions, these control functions are being either "artificial" or "natural". Also in this work we are(trying) working to get instantaneous information at fixed instant "T" on pollution term in Navier-Stokes system in which the initial condition is incomplete. The best method which can solve this problem is the sentinel one; it allows the estimation of the pollution term at which we look for information independently of the missing term that we do not want to identify. So, we prove the existence of such instantaneous sentinel by solving a problem of controllability with a constraint on the control.

MHD FLOWS DUE TO NON-COAXIAL ROTATIONS OF POROUS DISK AND A VISCOUS FLUID AT INFINITY: GRAPHICAL SOLUTIONS USING MATLAB

2020 ◽  
Vol 9 (11) ◽  
pp. 9287-9301
Author(s):  
R. Lakshmi ◽  
Santhakumari
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Daily Life ◽  
Vital Role ◽  
Navier Stokes ◽  
Porous Disk ◽  
Navier Stokes Equations ◽  
Complex Phenomena

Fluids play a vital role in many aspects of our daily life. We drink water, breath air, fluids run through our bodies and it controls the weather. The study of motion of fluids is a complex phenomena. The equations which govern the flows of Newtonian fluids are Navier-Stokes equations. In this paper, the flows which are due to non – coaxial rotations of porous disk and a fluid at infinity are considered. Analytical solution for the velocity field using Laplace transform is derived. MATLAB coding is written to get the graphical solutions. The results are compared with the existing results. MATLAB software provides accurate results depending on the solution we obtained.

scholarly journals Steady streaming in a channel with permeable walls

2013 ◽  
Vol 25 (1) ◽  
pp. 65-82
Author(s):  
KONSTANTIN ILIN
Keyword(s):  
Asymptotic Expansion ◽  
Viscous Fluid ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Stokes Layer ◽  
Permeable Walls ◽  
Time Injection

We study steady streaming in a channel between two parallel permeable walls induced by oscillating (in time) injection/suction of a viscous fluid at the walls. We obtain an asymptotic expansion of the solution of the Navier–Stokes equations in the limit when the amplitude of normal displacements of fluid particles near the walls is much smaller than both the width of the channel and the thickness of the Stokes layer. It is shown that the steady part of the flow in this problem is much stronger than the steady flow produced by vibrations of impermeable boundaries. Another interesting feature of this problem is that the direction of the steady flow is opposite to what one would expect if the flow was produced by vibrations of impermeable walls.

Sign in / Sign up

Export Citation Format

Share Document