scholarly journals Stable solution zone for fluid flow through curved pipe with circular cross-section

2011 ◽  
Vol 7 (1) ◽  
pp. 19-26 ◽  
Author(s):  
M. A. Masud ◽  
Md. Rabiul Islam ◽  
Md. Rasel Sheikh ◽  
Mahmud Md. Alam
Keyword(s):  
Cross Section ◽  
Numerical Study ◽  
Circular Cross Section ◽  
Stable Solution ◽  
Main Tool ◽  
Collocation Methods ◽  
Dean Number ◽  
Curved Pipe ◽  
Wide Range ◽  
Flow Through

Numerical study is performed to examine numerically the stable solution for the incompressible viscous steady flow through a curved pipe with circular cross-section. Also the combined effects of high Dean Number Dn and curvature δ on the flow are investigated. Spectral method is applied as a main tool for the numerical technique; where, Fourier series, Chebyshev polynomials, Collocation methods, and Iteration method are used as secondary tools. The flow patterns have been shown graphically for large Dean Numbers and a wide range of curvature, 0.01≤δ≤0.9.Two vortex solutions have been found for secondary flow. Axial velocity has been found to increase with the increase of Dean number and decrease with the increase of curvature. For high Dean number and low curvature almost all the fluid particles leave the inner half of the cross-section. The stable solution zone increases with the increase of curvature up to a certain limit, then decrease.DOI: 10.3329/jname.v7i1.3630

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

On the fully developed flow in a curved pipe at large Dean number

1991 ◽  
Vol 434 (1891) ◽  
pp. 473-478 ◽  
Keyword(s):  
Cross Section ◽  
Asymptotic Form ◽  
Pipe Wall ◽  
Complete Solution ◽  
Circular Cross Section ◽  
Dean Number ◽  
Fully Developed Flow ◽  
Core Flow ◽  
Curved Pipe ◽  
Viscous Boundary

In this paper we consider the asymptotic form, for large Dean number, of the solution which describes the fully developed laminar flow in a curved pipe of circular cross section. Although we have not been able to provide a complete solution we present strong evidence in favour of an asymptotic structure which is based upon an in viscid core flow enclosed by viscous boundary layers at the pipe wall.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

Extended Stokes series: laminar flow through a loosely coiled pipe

1978 ◽  
Vol 86 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Milton Van Dyke
Keyword(s):  
Laminar Flow ◽  
Flow Speed ◽  
Square Root ◽  
Mean Flow ◽  
Dean Number ◽  
Curvature Ratio ◽  
Wide Range ◽  
Square Root Singularity ◽  
Flow Through ◽  
The One

Dean's series for steady fully developed laminar flow through a toroidal pipe of small curvature ratio has been extended by computer to 24 terms. Analysis suggests that convergence is limited by a square-root singularity on the negative axis of the square of the Dean number. An Euler transformation and extraction of the leading and secondary singularities at infinity render the series accurate for all Dean numbers. For curvature ratios no greater than$\frac{1}{250} $, experimental measurements of the laminar friction factor agree with the theory over a wide range of Dean numbers. In particular, they confirm our conclusion that the friction in a loosely coiled pipe grows asymptotically as the one-quarter power of the Dean number based on mean flow speed. This contradicts a number of incomplete boundary-layer analyses in the literature, which predict a square-root variation.

Hot-Wire Measurements of Turbulence Correlations in a Triangular Duct

1962 ◽  
Vol 29 (4) ◽  
pp. 609-614 ◽  
Author(s):  
C. J. Cremers ◽  
E. R. G. Eckert
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Cross Section ◽  
Circular Tube ◽  
Turbulent Transport ◽  
Circular Cross Section ◽  
Hot Wire ◽  
Round Tube ◽  
Flow Through ◽  
Hot Wires

Previous studies by flow visualization have indicated that the flow through a duct of triangular cross section is in its characteristics quite different from flow through a duct with circular cross section. They revealed among others that purely laminar flow exists in the corners of the duct even though the bulk of the fluid moves in turbulent motion. Heat-transfer measurements in such a duct appear to indicate that the turbulent transport in the direction of the height of the duct is considerably smaller than expected from circular tube measurements. The present paper reports the measurements of turbulent correlations for turbulent flow through such a duct. These measurements have been made with hot wires of very small dimensions. They again reveal the existence of a laminar corner region. In the bulk of the fluid, the differences of the correlations to those in a round tube turned out to be smaller than originally suspected.

Numerical Method for Studying Bearing Gap Pressure Wave Development and Subsequent Performance Mapping of Externally Pressurized Gas Journal Bearings

2019 ◽  
Author(s):  
Tom M. Lawrence ◽  
Marvin D. Kemple
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Mass Flow ◽  
Pressure Wave ◽  
Design Space ◽  
Numerical Study ◽  
Pressure Waves ◽  
Wide Range ◽  
Wave Development ◽  
Static Instability

Abstract In previous work, numerical methods were developed to determine the pressure waves (pressure distribution) in the bearing gap of round externally pressurized gas bearings (EPB’s) that were pressurized through porous liners (PL bearings) or through liners with rows of feedholes (FH bearings). When integrated and differentiated these pressure portraits yield the net hydrodynamic force (FH) between the shaft and the bushing and the mass flow rates through the bearing gap. These results successfully replicated force-deflection curves and mass flow rate data for experimentally tested prototype FH and PL bearings over a wide range of mass flow constriction and clearances. Subsequently the numerical study was expanded to a broader design space of clearance and mass flow compensation. Also, a bearing performance mapping method of mapping the normalized bearing load over the clearance-eccentric deflection plane was developed for different levels of mass compensation. These performance maps produced a very interesting result as they indicated certain areas in the design space of FH bearings where static instability (negative stiffness) would be encountered. This static instability was not observed in the experimental data but is noted in references as known to occur in practice. Because this numerical method is based on the development of pressure wave portraits, the FH pressure wave could then be “dissected” in the areas of the onset of static instability which gave much insight as to the possible causes of static instability. This initial work, then, was perhaps the first to predict where in design space static instability would occur and yield some insight via examination of the corresponding pressure waves as to the cause. The numeric techniques developed, however are in no way limited to non-rotating bearings but are extensible to rotating bearings. The method is also easily extensible to examination of any configuration of feedholes or orifices. Nor is it limited to parallel deflections but can yield results for unbalanced loads. The method is also not limited to round bearings but can be applied to any cross-section configuration of bearing gap cross section such as a 3 lobed bearing or a slotted 3 lobed bearing. Examination of the resulting pressure wave development patterns for different scenarios can be examined to garner insight as to the causes of differing performance that can be applied to alterations towards optimization. Thus sharing in detail the developed numerical method underlying these studies seems worthwhile.

Sign in / Sign up

Export Citation Format

Share Document