A Numerical Investigation of Developing Flow in Concentric and Eccentric Curved Square Annuli

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
M. R. H. Nobari ◽  
D. Rajaei
Keyword(s):  
Aspect Ratio ◽  
Friction Factor ◽  
Second Order ◽  
Projection Algorithm ◽  
Staggered Grid ◽  
Square Root ◽  
Governing Equations ◽  
Dean Number ◽  
Square Duct ◽  
Continuity Equations

In this article developing incompressible viscous fluid flow in concentric and eccentric curved square annuli are numerically studied. A second order finite difference method based on the projection algorithm is implemented to solve the governing equations, including the full Navier–Stokes and continuity equations in a cylindrical coordinate system. To discretize the governing equations in the square annulus, a uniform staggered grid is used to enforce an exact second order numerical scheme. The effects of the governing nondimensional parameters involving the aspect ratio, curvature, Reynolds number, Dean number, and eccentricity on the flow field, both in developing and fully developed regions of the curved annular square duct, are studied in detail. The numerical results obtained indicate that the friction factor in the eccentric curved square annulus increases with the square root of the Dean number (κ1/2) and the aspect ratio and decreases with the eccentricity. Furthermore, when the square root of the Dean number becomes larger than about 17.3, the friction factor increases linearly with the square root of the Dean number in the range of the current study.

Numerical Procedure for the Laminar Developed Flow in a Helical Square Duct

2005 ◽  
Vol 127 (1) ◽  
pp. 136-148 ◽  
Author(s):  
V. D. Sakalis ◽  
P. M. Hatzikonstantinou ◽  
P. K. Papadopoulos
Keyword(s):  
Laminar Flow ◽  
Friction Factor ◽  
Cross Section ◽  
Numerical Procedure ◽  
Governing Equations ◽  
Axial Pressure ◽  
Dean Number ◽  
Square Duct ◽  
Orthogonal Coordinate System ◽  
Axial Pressure Gradient

The incompressible fully developed laminar flow in a helically duct of square cross section is studied expressing the governing equations in terms of an orthogonal coordinate system. Numerical results are obtained with the described continuity, vorticity, and pressure (CVP) numerical method using a colocation grid for all variables. Since there are not approximations, the interaction effects of curvature, torsion and axial pressure gradient on the velocity components and the friction factor are presented. The results show that the torsion deforms substantially the symmetry of the two centrifugal vortices of the secondary flow, which for large values of torsion combined with small curvature tend to one vortex covering the whole cross section. The friction factor decreases for torsion in the range 0 to 0.1 and increases as the torsion increases further, a behavior which is more profound as the Dean number increases. Our results are stable for the calculated Dean numbers.

Heat Transfer and Pressure Drop Correlation for Helicoidal Pipes of Rectangular Cross Section

2009 ◽  
Author(s):  
Christopher Katinas ◽  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Friction Factor ◽  
Cross Section ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Dean Number ◽  
Curvature Effects ◽  
The Impact

In this study, flow and heat transfer for laminar flow in curved channels of rectangular cross section is examined. The focus of the numerical solutions is on rectangular cross sections with an aspect ratio less than one, since little information is available for heat transfer in curved rectangular pipes whose width is greater than height. The study examines the impact of the aspect ratio and Dean number on both friction factor and Nusselt number. The results show that although both friction factor and Nusselt number increase as a result of curvature effects, the heat transfer enhancements significantly outweigh the friction factor penalty. Numerical solutions in this study consider the more realistic case of hydrodynamically developed and thermally developing flow.

Numerical Analysis of Fully Developed Flow in Curved Square Ducts With Internal Fins

2004 ◽  
Vol 126 (5) ◽  
pp. 752-757 ◽  
Author(s):  
P. K. Papadopoulos ◽  
P. M. Hatzikonstantinou
Keyword(s):  
Friction Factor ◽  
Functional Relation ◽  
Transverse Plane ◽  
Complex Flow ◽  
Dean Number ◽  
Simple Method ◽  
Fully Developed Flow ◽  
Square Duct ◽  
Internal Fins ◽  
Square Ducts

The laminar incompressible flow in a curved square duct with two or four internal longitudinal fins is studied numerically with the SIMPLE method. The results show an increase of the friction factor depending on the fin height and the Dean number. The visualization of the flow reveals the existence of complex flow patterns in the transverse plane of the channel, where up to ten vortices are found to form. The effect of the curvature on the friction factor is examined and a functional relation for the latter is developed in terms of the Dean number and the fin height.

Simulation of Dense Solid-Liquid Two-Phase Flow in a Pump Impeller

2004 ◽  
Author(s):  
Shuhong Liu ◽  
Xuelin Tang ◽  
Yulin Wu ◽  
Michihiro Nishi
Keyword(s):  
Strain Rate ◽  
Dynamic Model ◽  
Rotation Rate ◽  
Second Order ◽  
Staggered Grid ◽  
Strain Rate Tensor ◽  
Governing Equations ◽  
Two Phase ◽  
Pump Impeller ◽  
Solid Liquid

In the present study, simulation with the second-order dynamic model for sub-grid stress is used to solve the governing equations of dense solid-liquid two-phase (DSLTP) flow numerically, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the current second-order dynamic model with double dynamic coefficients, the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor. This model considers the symmetry of the sub-grid-scale stresses, dimensional consistency with the Cauchy-Helmholtz theorem, the Smagorinsky model and the invariants of the strain-rate tensor and the rotation-rate tensor in large eddy simulation (LES). In the numerical calculation, the SIMPLEC algorithm and a staggered grid system were applied for the solution of the discretized particle-liquid turbulent flow equations, and Body-fitted Coordinates were used to simulate the flow over the complex geometry field. In this paper, the second-order dynamic model for turbulent dense solid-liquid two-phase flows was applied to a centrifugal pump impeller.

A Numerical Study of Laminar 90-Degree Bend Duct Flow With Different Discretization Schemes

1991 ◽  
Vol 113 (4) ◽  
pp. 563-568 ◽  
Author(s):  
R. W. Yeo ◽  
P. E. Wood ◽  
A. N. Hrymak
Keyword(s):  
Numerical Study ◽  
Higher Order ◽  
Staggered Grid ◽  
Grid Refinement ◽  
Duct Flow ◽  
Governing Equations ◽  
Square Duct ◽  
Flow Problems ◽  
Discretization Schemes ◽  
Curvilinear Coordinate

Three different discretization schemes were used to study the flow in a 90-degree bend square duct. The numerical method consists of a general curvilinear coordinate formulation of the governing equations and a non-staggered grid for the variables. A stable method of implementing the higher-order schemes is proposed. The second-order upwinding and QUICK schemes give results which compare more favourably with the experimental data than the first-order upwinding method. In 3-D flow problems, the grid-refinement is severely limited by the amount of computer storage and the use of higher-order upwinding schemes provides a better alternative in obtaining accurate flow predictions.

Experimental Investigation of Flow Characteristics in a Square Duct With Delta-Wing Vortex Generators

2013 ◽  
Author(s):  
Vadiraj V. Katti ◽  
Anandkumar S. Malipatil ◽  
Mahesh R. Ingalagi
Keyword(s):  
Aspect Ratio ◽  
Friction Factor ◽  
Delta Wing ◽  
Flow Characteristics ◽  
Vortex Generator ◽  
Hydraulic Diameter ◽  
Vortex Generators ◽  
Geometrical Parameters ◽  
Square Duct ◽  
Factor Ratios

The influence of delta wing vortex generators on the wall of square duct and the pressure loss penalty has been experimentally investigated in this study. The combined effects of geometrical parameters of delta wing vortex generators on friction factor ratios are reported for the Reynolds number based on the duct hydraulic diameter in the range of 8000–24000. The geometrical parameters of vortex generators systematically varied in this study are the pitch to vortex generator height ratio (p/e), vortex generator height to duct hydraulic diameter ratio (e/Dh), aspect ratio of vortex generator (ar). Results are reported for 0.1 ≤ e/Dh ≤ 0.5, 1.6 ≤ p/e ≤ 16, 1.6 ≤ ar ≤ 14.9, in duct having aspect ratio AR = 1. The experimental results of the present study for friction factor in smooth square duct agree well with values estimated from correlations proposed by Blasius.

scholarly journals Numerical Analysis of Nanofluids in Differentially Heated Enclosure Undergoing Orthogonal Rotation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
H. Saleh ◽  
I. Hashim
Keyword(s):  
Heat Transfer ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Staggered Grid ◽  
Governing Equations ◽  
Nanoparticles Concentration ◽  
Quantity Of Heat ◽  
Velocity Pressure

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction,0.0 ≤ ϕ ≤ 0.05, and the rotational speeds,3.5≤ Ω ≤ 17.5 rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1%ϕof the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds.

scholarly journals Bursting Oscillations and Sliding Motion in Permanent Magnet Synchronous Motor Systems with Friction Factor

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Rui Qu ◽  
Shaolong Li
Keyword(s):  
Permanent Magnet ◽  
Friction Factor ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Governing Equations ◽  
Bursting Oscillations ◽  
Sliding Motion ◽  
Friction Function ◽  
Filippov Type ◽  
Theoretical Results

The main purpose of this paper is to investigate the qualitative effects of external excitation and friction factor on the response of permanent magnet synchronous motor (PMSM) system. Three different modes of bursting oscillations are found. In particular, the introduction of friction function changes the governing equations from a smooth type to a nonsmooth (Filippov) type in which the special sliding motion is observed. The mechanism, attractor structure, vector field structure, and analytic bifurcation conditions of bursting oscillation and sliding motion are discussed in detail. The validity of theoretical results obtained is verified by numerical simulations and analysis.

scholarly journals Flow through a helical pipe with rectangular cross-section

1970 ◽  
Vol 4 (2) ◽  
pp. 99-110
Author(s):  
Md Mahmud Alam ◽  
Delowara Begum ◽  
K Yamamoto
Keyword(s):  
Aspect Ratio ◽  
Iterative Method ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Main Tool ◽  
Numerical Approach ◽  
Dean Number ◽  
Helical Pipe ◽  
Flow Through ◽  
Marine Engineering

The effects of torsion, aspect ratio and curvature on the flow in a helical pipe of rectangular cross- section are studied by introducing a non-orthogonal helical coordinate system. Spectral method is applied as main tool for numerical approach where Chebyshev polynomial is used. The numerical calculations are obtained by the iterative method. The calculations are carried out for 0≤ δ ≤0.02, 1≤ λ ≤ 2.85, 1≤ γ ≤2.4, at Dn = 50 & 100 respectively, where d is the non-dimensional curvature, l the torsion parameter, g the aspect ratio and  Dn the pressure driven parameter (Dean number).DOI: http://dx.doi.org/10.3329/jname.v4i2.991 Journal of Naval Architecture and Marine Engineering Vol.4(2) 2007 p.99-110

Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

Volume 1 ◽  
2004 ◽  
Author(s):  
Mandar V. Joshi ◽  
U. N. Gaitonde ◽  
Sushanta K. Mitra
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Heat Generation ◽  
Central Region ◽  
Analytical Study ◽  
Vertical Direction ◽  
Maximum Temperature ◽  
Small Aspect Ratio ◽  
Governing Equations ◽  
Volumetric Heat Generation

A semi-analytical method for natural convection in a two dimensional rectangular enclosure, with uniform volumetric heat generation, having insulated horizontal boundaries, and isothermal vertical boundaries, has been studied here. In this method, the governing equations for natural convection, have been solved under the assumption that for a cavity with small aspect ratio, the flow in the central region of the cavity is only in the vertical direction. It is found that for the cavities with small aspect ratio, the temperature in central region of the cavity is nearly constant along the horizontal direction. However, there is a uniform temperature gradient in the vertical direction, which can be related to the maximum temperature in conduction. The velocity profiles and temperature profiles obtained in the present work, are compared with the numerical simulations by Fluent and a fair agreement is found between these results.

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