Laminar flow in a square duct of strong curvature

1977 ◽  
Vol 83 (3) ◽  
pp. 509-527 ◽  
Author(s):  
J. A. C. Humphrey ◽  
A. M. K. Taylor ◽  
J. H. Whitelaw
Keyword(s):  
Stokes Equations ◽  
Laser Doppler Anemometry ◽  
Longitudinal Velocity ◽  
Flow Analysis ◽  
Maximum Velocity ◽  
Outer Wall ◽  
Navier Stokes ◽  
Upstream Region ◽  
Dean Number ◽  
Navier Stokes Equations

Calculated values of the three velocity components and measured values of the longitudinal component are reported for the flow of water in a 90° bend of 40 x 40mm cross-section; the bend had a mean radius of 92mm and was located downstream of a 1[sdot ]8m and upstream of a 1[sdot ]2m straight section. The experiments were carried out at a Reynolds number, based on the hydraulic diameter and bulk velocity, of 790 (corresponding to a Dean number of 368). Flow visualization was used to identify qualitatively the characteristics of the flow and laser-Doppler anemometry to quantify the velocity field. The results confirm and quantify that the location of maximum velocity moves from the centre of the duct towards the outer wall and, in the 90° plane, is located around 85% of the duct width from the inner wall. Secondary velocities up to 65% of the bulk longitudinal velocity were calculated and small regions of recirculation, close to the outer corners of the duct and in the upstream region, were also observed.The calculated results were obtained by solving the Navier–Stokes equations in cylindrical co-ordinates. They are shown to exhibit the same trends as the experiments and to be in reasonable quantitative agreement even though the number of node points used to discretize the flow for the finite-difference solution of the differential equations was limited by available computer time and storage. The region of recirculation observed experimentally is confirmed by the calculations. The magnitude of the various terms in the equations is examined to determine the extent to which the details of the flow can be represented by reduced forms of the Navier–Stokes equations. The implications of the use of so-called ‘partially parabolic’ equations and of potential- and rotational-flow analysis of an ideal fluid are quantified.

Bifurcation in steady laminar flow through curved tubes

1982 ◽  
Vol 119 ◽  
pp. 475-490 ◽  
Author(s):  
K. Nandakumar ◽  
Jacob H. Masliyah
Keyword(s):  
Stokes Equations ◽  
Outer Wall ◽  
Dual Solutions ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Vortex Solution ◽  
Duct Geometry ◽  
Flow Through ◽  
Curved Ducts

The occurrence of dual solutions in curved ducts is investigated through a numerical solution of the Navier-Stokes equations in a bipolar-toroidal co-ordinate system. With the shape of duct being the region formed by the natural co-ordinate surfaces, it was possible to alter the duct geometry gradually and preserve the prevailing form of the velocity field, in a manner suggested by Benjamin (1978).In addition to the Dean number Dn = Re/Rc½, a geometrical parameter that defines the shape of the duct was also varied systematically to study the bifurcation of a two-vortex solution into a two- and four-vortex solution. Dual solutions have been found for all geometrical shapes investigated here. Of particular interest are the shapes of a full circle and a semicircle with a curved outer wall.

On laminar flow in curved semicircular ducts

1980 ◽  
Vol 99 (3) ◽  
pp. 469-479 ◽  
Author(s):  
Jacob H. Masliyah
Keyword(s):  
Secondary Flow ◽  
Stokes Equations ◽  
Outer Wall ◽  
Initial Guess ◽  
The Other ◽  
Navier Stokes ◽  
Dean Number ◽  
Solution Flow ◽  
Navier Stokes Equations ◽  
Semicircular Ducts

Calculations of the flow field under laminar conditions in a helical semicircular duct have been made by numerically solving the Navier–Stokes equations. With the flat wall of the duct being the outer wall, the solution of the momentum equations for Dean numbers below 105 gave, for the secondary flow, twin counter-rotating vortices of Taylor–Goertler type. However, above a Dean number of Dn = 105, two solutions were possible. One solution was similar to that obtained for Dn < 105. The other solution revealed four vortices for the secondary flow. For Dn > 105, convergence to either flow pattern depended on the initial guess used in the numerical solution. Flow visualization confirmed the possibility of the presence of both types of secondary flow patterns.

scholarly journals Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Lyapunov Analysis ◽  
Velocity Difference ◽  
Navier Stokes Equations ◽  
Previous Hypothesis ◽  
Kolmogorov Theory

The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity differenceΔuris derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics ofΔurand adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.

A 3D Unsteady Flow Analysis in a Doubly Constricted Tube

2000 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
T. Yamaguchi ◽  
H. Liu ◽  
R. Himeno
Keyword(s):  
Pressure Drop ◽  
Unsteady Flow ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
In Series ◽  
3D Unsteady Flow

Abstract Unsteady flow dynamics in a doubly constricted vessel is analyzed by using a time accurate Finite Volume solution of three dimensional incompressible Navier-Stokes equations. Computational experiments are carried out for various values of Reynolds number in order to assess the criticality of multiple mild constrictions in series and also to bring out the subtle 3D features like vortex formation. Studies reveal that pressure drop across a series of mild constrictions can get physiologically critical. Further this pressure drop is found to be sensitive to the spacing between the constrictions and also to the oscillatory nature of the inflow profile.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

scholarly journals INVESTIGATION OF HEAT DISTRIBUTION PROCESSES ON THE INNER SURFACE OF THE ENCLOSING STRUCTURE, TAKING INTO ACCOUNT THE MOVEMENT OF AIR IN THE BOUNDARY AREA BETWEEN THE DEVICE AND FENCING

2019 ◽  
Vol 16 (32) ◽  
pp. 345-361
Author(s):  
B. A. UNASPEKOV ◽  
Z. O. ZHUMADILOVA ◽  
S. S. AUELBEKOV ◽  
A. S. TAUBALDIEVA ◽  
G. B. ALDABERGENOVA
Keyword(s):  
Stokes Equations ◽  
Outer Wall ◽  
Conjugate Problem ◽  
Navier Stokes ◽  
Geometrical Parameters ◽  
Downward Flow ◽  
Navier Stokes Equations ◽  
Boundary Area ◽  
Air Mass ◽  
Hydrodynamic Motion

A study was made of the nature of the movement of air mass in the space between the device that warms the room and the confining outer wall of the room. The hydrodynamic motion of the air mass was simulated on the basis of the two-dimensional in space Navier-Stokes equations and the convective heat conduction equation to find out a detailed picture of the physical processes that occur. Also for some particular cases, analytical solutions were obtained for the conjugate problem, where the movement of air is caused by its thermal expansion and the action of gravity in areas with different densities (Archimedes' forces). The simulation of more complex types of air movement with the formation of vortex flows using numerical methods and the corresponding program codes written in C++. It was found that the movement of air mass in the space between the device and the fence strongly depends not only on the temperature of the device, the wall, and the outside air. It was revealed that hydrodynamics and heat transfer are significantly influenced by two geometrical parameters: the distance between the device and the wall, and the distance from the flooring to the bottom of the device. In particular, a thin layer of the downward flow of cold air along the fence and above the floor is possible. The condition for the occurrence of such a downward flow has been found, it is determined by the ratio of the temperature of the wall, the device, and the average temperature in the room.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

Cascade viscous flow analysis using the Navier-Stokes equations

1987 ◽  
Vol 3 (5) ◽  
pp. 406-414 ◽  
Author(s):  
Roger L. Davis ◽  
Ron-Ho Ni ◽  
James E. Carter
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equations

Aerodynamic and Aeroacoustic Analyses of a Regenerative Blower

2015 ◽  
Author(s):  
Man-Woong Heo ◽  
Tae-Wan Seo ◽  
Chung-Suk Lee ◽  
Kwang-Yong Kim
Keyword(s):  
Shear Stress ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Side Channel ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Unsteady Flow Analysis

This paper presents a parametric study to investigate the aerodynamic and aeroacoustic characteristics of a side channel regenerative blower. Flow analysis in the side channel blower was carried out by solving three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence closure. Aeroacoustic analysis was conducted by solving the variational formulation of Lighthill’s analogy on the basis of the aerodynamic sources extracted from the unsteady flow analysis. The height and width of the blade and the angle between inlet and outlet ports were selected as three geometric parameters, and their effects on the aerodynamic and aeroacoustic performances of the blower have been investigated. The results showed that the aerodynamic and aeroacoustic performances were enhanced by decreasing height and width of blade. It was found that angle between inlet and outlet ports significantly influences the aerodynamic and aeroacoustic performances of the blower due to the stripper leakage flow.

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

Sign in / Sign up

Export Citation Format

Share Document