The Flexibility of Curved Pipes in Creep

1977 ◽  
Vol 99 (3) ◽  
pp. 444-453 ◽  
Author(s):  
J. T. Boyle ◽  
J. Spence
Keyword(s):  
Bending Moment ◽  
Continuous System ◽  
Straight Pipe ◽  
Initial Value ◽  
Approximate Methods ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Runge Kutta Method ◽  
Finite Set ◽  
Fifth Order

The redistribution of stress in a linear, thin shell model of a curved pipe creeping under the action of a constant applied in-plane bending moment is represented by an equation of evolution in time. Using finite differences, this continuous system is reduced to a finite set of initial value problems which are numerically integrated using a fifth order Runge-Kutta method. The flexibility of the curved pipe is compared to that of a similar elastic, and a similarly creeping, straight pipe. Results are compared with two simple approximate methods and with a previous-steady state analysis.

Analogy between laminar flows in curved pipes and orthogonally rotating pipes

1994 ◽  
Vol 268 ◽  
pp. 133-145 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Laminar Flows ◽  
Computational Studies ◽  
Flow Properties ◽  
Straight Pipe ◽  
Pipe Axis ◽  
Transfer Rates ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Data Similarity ◽  
Friction Factors

The secondary flow of a viscous fluid, caused by the Coriolis force, through a straight pipe rotating about an axis perpendicular to the pipe axis is analogous to that of a fluid, caused by the centrifugal force, through a stationary curved pipe. The quantitative analogy between these two fully developed laminar flows will be demonstrated through similarity arguments, computational studies and the use of experimental data. Similarity considerations result in two analogous governing parameters for each flow, which include a new one for the rotating flow. When one of these analogous pairs of parameters of the two flows is large, it will be demonstrated that there are strong similarities between the two flows regarding friction factors, heat transfer rates, flow patterns and flow properties for the same values of the other pair of parameters.

Experimental Investigations of Droplet Deposition and Coalescense in Curved Pipes

2012 ◽  
Author(s):  
Hung Nguyen ◽  
Shoubo Wang ◽  
Ram S. Mohan ◽  
Ovadia Shoham ◽  
Gene Kouba
Keyword(s):  
Kinetic Energy ◽  
Radius Of Curvature ◽  
Droplet Deposition ◽  
Straight Pipe ◽  
Pipe Bend ◽  
Horizontal Pipe ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Pipe Section ◽  
Pipe Fittings

Even though there have been several studies conducted by the industry on the use of different inlet devices for gas-liquid separation there have been limited laboratory and field evaluations on the use of external piping configurations as flow conditioning devices upstream of a separator inlet. The results of a systematic study of droplet deposition and coalescence in curved pipe and pipe fittings are reported in this paper. A facility has been designed consisting of two main test sections: a fixed horizontal straight pipe section and an interchangeable 180° return pipe section (or curved pipe section) of the same length. Both inlet and outlet to the 180° return are horizontal, but the plane of the 180° return pipe section can pivot about the axis of the inlet horizontal pipe to an angle as much as 10° downwards allowing downward flow in the return section. Various pipe fittings of different radius of curvature can be installed for comparison in the 180° return. Fittings evaluated in this study included: 180° pipe bend, 2 standard radius elbows (with radius of curvature of 1.5D), 2 long radius elbows (with radius of curvature of 6D), 2 target tee bend, and 2 cushion tee bend. Experiments have been carried out using water and air and varying gas velocities and liquid loadings. In order to compare the performance of geometries, Droplet Deposition Fractions (DDF) were measured in the horizontal straight pipe section and in the 180° return pipe section as a measure of coalescence efficiency. The results demonstrate that higher DDF occurs for curved fittings as compared to the straight pipe section. Two standard (short) radius elbows bend have approximately 10% DDF higher, whereas two long radius elbows along with 180° pipe bend perform better (by 15–20% DDF) than straight pipe. Additionally, no significant differences between DDF’s in three different inclination angles of a curved pipe were observed. It was found that the cushion tees and target tees can coalesce droplets at lower gas velocities but break up droplets at higher gas velocities. It can be concluded that 180° pipe bend or two 6D long radii elbows can serve as a droplet coalescer, a pair of cushion tees or target tee can also work as coalescer at low kinetic energy but as atomizers at high kinetic energy.

scholarly journals Accurate Numerical Method for Singular Initial-Value Problems

2021 ◽  
Vol 08 (03) ◽  
pp. 01-11
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa ◽  
Gashu Gadisa Kiltu
Keyword(s):  
Numerical Method ◽  
Initial Value Problems ◽  
Approximate Solutions ◽  
Stability And Convergence ◽  
Order System ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.

scholarly journals Study of Numerical Solution of Fourth Order Ordinary Differential Equations by fifth order Runge-Kutta Method

2019 ◽  
pp. 230-238
Author(s):  
Najmuddin Ahamad ◽  
Shiv Charan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Initial Value Problems ◽  
Computational Cost ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper we present fifth order Runge-Kutta method (RK5) for solving initial value problems of fourth order ordinary differential equations. In this study RK5 method is quite efficient and practically well suited for solving boundary value problems. All mathematical calculation performed by MATLAB software for better accuracy and result. The result obtained, from numerical examples, shows that this method more efficient and accurate. These methods are preferable to some existing methods because of their simplicity, accuracy and less computational cost involved.

Experimental Investigations of Droplet Deposition and Coalescence in Curved Pipes

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Hung Nguyen ◽  
Shoubo Wang ◽  
Ram S. Mohan ◽  
Ovadia Shoham ◽  
Gene Kouba
Keyword(s):  
Kinetic Energy ◽  
Radius Of Curvature ◽  
Droplet Deposition ◽  
Straight Pipe ◽  
Pipe Bend ◽  
Horizontal Pipe ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Pipe Section ◽  
Pipe Fittings

Even though there have been several studies conducted by the industry on the use of different inlet devices for gas–liquid separation, there have been limited laboratory and field evaluations on the use of external piping configurations as flow conditioning devices upstream of a separator inlet. The results of a systematic study of droplet deposition and coalescence in curved pipe and pipe fittings are reported in this paper. A facility has been designed consisting of two main test sections: a fixed horizontal straight pipe section and an interchangeable 180 deg return pipe section (or curved pipe section) of the same length. Both inlet and outlet to the 180 deg return are horizontal, but the plane of the 180 deg return pipe section can pivot about the axis of the inlet horizontal pipe to an angle as much as 10 deg downwards allowing downward flow in the return section. Various pipe fittings of different radius of curvature can be installed for comparison in the 180 deg return. Fittings evaluated in this study included: 180 deg pipe bend, short elbow bend (with standard radius of curvature of 1.5D), long elbow bend (with custom radius of curvature of 6D), target tee bend, and cushion tee bend. Experiments have been carried out using water and air, and varying gas velocities and liquid loadings. In order to compare the performance of geometries, Droplet Deposition Fractions (DDF) were measured in the horizontal straight pipe section and in the 180 deg return pipe section as a measure of coalescence efficiency. The results demonstrate that higher DDF occurs for curved fittings as compared to the straight pipe section. The short elbow bend has approximately 10% DDF higher, whereas long elbow bend along with 180 deg pipe bend perform better (by 15–20% DDF) than straight pipe. It was found that the cushion tee and target tee bends can coalesce droplets at lower gas velocities but break up droplets at higher gas velocities. Additionally, no significant differences between DDF's in three different inclination angles of a curved pipe were observed. It can be concluded that 180 deg pipe bend or two 6D long radius elbow bend can serve as a droplet coalescer; a pair of cushion tees or target tees can also work as coalescers at low kinetic energy but as atomizers at high kinetic energy.

scholarly journals The criterion for turbulence in curved pipes

1929 ◽  
Vol 124 (794) ◽  
pp. 243-249 ◽  
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Small Hole ◽  
Stream Line ◽  
Straight Pipe ◽  
Curved Pipe ◽  
Curved Pipes ◽  
The Cross

Summary .—Experiments are described in which coloured fluid is introduced through a small hole in the side of a glass helix through which water is running. The conclusion reached by Mr. C. M. White, as a result of resistance measurements, that a higher speed of flow is necessary to maintain turbulence in a curved pipe than in a straight one, is verified directly. In a pipe bent into a helix the diameter of which was 18 times that of the cross-section, steady stream-line motion persisted up to a Reynolds number, 5830, i. e ., 2·8 times Reynolds' criterion for a straight pipe. This occurred in spite of the fact that the flow was highly turbulent on entering the helix.

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