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.

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.

Effects of Cross-Section Ovalization of Subsea Thin-Walled Bends Under In-Plane Bending

2010 ◽  
Author(s):  
Ranil Banneyake ◽  
Ayman Eltaher ◽  
Paul Jukes
Keyword(s):  
Cross Section ◽  
Computational Cost ◽  
Straight Pipe ◽  
Limit States ◽  
Element Analysis ◽  
High Tendency ◽  
Thin Walled ◽  
Plane Bending ◽  
The Cross ◽  
The Impact

Ovalization of the cross-section of bends under in-plane bending (a.k.a. Brazier effect) is a known phenomenon caused by the longitudinal stress acting on the cross-section as the pipe bends. Besides its tendency to induce stresses in the bend above what is predicted using simple beam theory, excessive cross-section ovalization is particularly critical to subsea pipes, as it can lead to collapse of the pipe under external pressure. Also, being in a plastic regime may cause the bend material to ratchet and undergo excessive strains under cyclic operational loads, especially under high-pressure high-temperature (HPHT) conditions. Ovalization normally results in local increase of stresses and could lead to failure of the bend before the bend globally reaches its limiting capacity. The offshore industry standards and design codes address the impact of initial ovality in straight pipes, but their applicability to bends is not clear. Therefore, this paper presents an investigation into the increased tendency of thin-walled bends to ovalize, and the effect of bend cross-section ovalization on their stiffness and yielding and collapse limit states, with emphasis on offshore applications. Due to the lack of analytical solutions for the bend response taking into account cross-section ovalization, finite element analysis (FEA) is used in this study. Predictions of the bend models are compared with those of straight pipe models and predictions of models of the bend made of beam elements (with pipe section) are compared with those of models made of brick /shell elements. The increased tendency of thin-walled bends to ovalize compared to straight pipes is investigated (e.g. 100 times in the linear range), and the impact and significance of ovalization in bends are assessed (e.g., stress increase of the order of 35% has been observed in some example situations). Also discussed in the paper is the selection of proper element specifications in order to accurately capture the ovalization response while keeping the computational cost manageable. Recommendations as to how to account for ovalization effects are presented. This paper helps to gain a better understanding of the response of subsea thin-walled bends under in-plane bending and their comparatively high tendency to ovalize compared to straight pipe, and emphasizes the significance of local effects such as cross-section ovalization, the overlooking of which may result in a significant underestimation of involved stresses and strains.

Streamwise and Spanwise Flow Structures Over Backward Facing Step in Low Reynolds Number

2006 ◽  
Author(s):  
Shunsuke Yamada ◽  
Tatsuya Matsumoto ◽  
Takashi Nagumo ◽  
Shinji Honami
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Low Reynolds Number ◽  
Spanwise Direction ◽  
Streamwise Direction ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
The Cross ◽  
Low Reynolds

A study on the low Reynolds number flow such as the flow in or around the micro device is strongly required along with the development of the micro manufacturing technology. The low Reynolds number flow over a backward facing step is selected as one of the representative examples of the vortex dominant flows in the present study, because the mixing promotion is expected by an oscillatory motion of the vortex in the separating and reattaching shear layer over the step. It is important to clarify the flow fields in small channel or around the small device by flow visualization, since minimum disturbance in the measurement is achieved due to non-intrusive method. The objective of the present study is to clarify the flow behavior in the cross section in the spanwise, transverse and streamwise direction by the flow visualization using a high speed video camera. The Reynolds number based on the step height and the bulk velocity is set at 380 to 960. The visualization results in the cross section in the spanwise direction show that the separating shear layer from the step edge introduces a series of the primary vortices which have a rotation axis around the spanwise direction, and the main stream has a regularly whipping, wavy motion caused by the vortices moving toward the downstream direction along the upper and lower walls. The observation in the cross section in the transverse direction indicates that a scale of the vortex length in the streamwise direction is almost constant, but the primary vortex shows a periodic change in the spanwise direction, as the Reynolds number increases.

Instability of a Curved Pipe Flow With a Sudden Expansion

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Michael Shusser ◽  
Artyom Ramus ◽  
Oleg Gendelman
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Oscillatory Flow ◽  
Outer Wall ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Straight Pipe ◽  
Periodic Oscillations ◽  
Curved Pipe ◽  
Flow Variables

Numerical calculations of laminar flow of an incompressible fluid through an axisymmetric sudden expansion followed by a curved pipe recently done by the authors discovered an early instability of this flow for a certain expansion ratio, as it becomes unsteady with periodic oscillations of the flow variables at a Reynolds number when both curved pipe flow and flow in a straight pipe with an axisymmetric sudden expansion remain stable. This study describes in detail the created oscillatory flow and suggests that the early instability of the ratio 3 flow could be caused by the higher velocity gradient near the outer wall of the bend.

Viscous laminar flow in a curved pipe of elliptical cross-section

1987 ◽  
Vol 184 ◽  
pp. 571-580 ◽  
Author(s):  
H. C. Topakoglu ◽  
M. A. Ebadian
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Finite Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Expansion Method ◽  
Elliptic Cross Section ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Elliptic Cross

In this paper, the analysis on secondary flow in curved elliptic pipes of Topakoglu & Ebadian (1985) has been extended up to a point where the rate-of-flow expression is obtained for any value of flatness ratio of the elliptic cross-section. The analysis is based on the double expansion method of Topakoglu (1967). Therefore, no approximation is involved in any step other than the natural limitation of the finite number of calculated terms of the expansions. The obtained results are systematically plotted against the curvature of centreline of the curved pipe for different values of Reynolds number.

Unsteady viscous flow in a curved pipe

1971 ◽  
Vol 45 (1) ◽  
pp. 13-31 ◽  
Author(s):  
W. H. Lyne
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Asymptotic Theory ◽  
Circular Cross Section ◽  
Radius Of Curvature ◽  
Curved Pipe ◽  
Unsteady Viscous Flow

The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency ω. The radius of the pipeais assumed small in relation to the radius of curvature of its axisR. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter β = (2ν/ωa2)½, where ν is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number$R_s = \overline{W}^2a/R \omega\nu$, where$\overline{W}$is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of β it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.

Resonance in Flow-Induced Cable Vibration: Analytical Prediction and Numerical Simulation

2005 ◽  
Author(s):  
M. K. Kwan ◽  
R. R. Hwang ◽  
C. T. Hsu
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Cross Section ◽  
Flow Direction ◽  
Cross Flow ◽  
Transverse Cross Section ◽  
Analytical Prediction ◽  
Water Flows ◽  
Flow Displacement ◽  
The Cross

Flow-induced resonance for a two-end hinged cable under uniform incoming flows is investigated using analytical prediction and numerical simulation. In this study, the fundamental mode is analyzed for simplicity. First, based on a series of physical judgments, the approximate cable trajectory is predicted — the whole cable vibrates as a standing wave, with its locus on the transverse cross-section having a convex “8”-like shape. To find the exact path, however, experiment or numerical simulation is necessary. Hence, a bronze cable at aspect ratio (length/diameter) of 100 under water flows at Reynolds number (based on cable diameter and incoming velocity) of 200 is computed. The result confirms our predictions. Moreover, it is found that the amplitude of the cross-flow displacement is much higher than that of the streamwise displacement, despite the higher streamwise fluid force. As a consequence, energy transfer from fluid to solid is maximized in the cross-flow direction.

Laminar flow in a curved pipe with varying curvature

1976 ◽  
Vol 73 (4) ◽  
pp. 735-752 ◽  
Author(s):  
S. Murata ◽  
Y. Miyake ◽  
T. Inaba
Keyword(s):  
Reynolds Number ◽  
Flow Direction ◽  
Circular Cross Section ◽  
Outer Side ◽  
Large Reynolds Number ◽  
Phase Lag ◽  
Mean Flow ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Centre Line

The steady laminar motion of fluid through pipes of circular cross-section, the curvature of whose centre-line varies locally, is analysed theoretically. The flow in three kinds of pipes whose centre-lines are specified by \[ \hat{y} = a(1+\kappa^2\hat{x}^2)^{\frac{1}{2}},\quad\hat{y} = a\tan h\kappa\hat{x}\quad{\rm and}\quad\hat{y} = a\sin\kappa\hat{x} \] are treated as the examples of once-, twice- and periodically-curved pipes, respectively. The analysis is valid for any other two-dimensionally curved pipes, when centre-line curvature is small. At very small Reynolds number, the position of maximum axial velocity shifts towards the inner side of the pipe section; at large Reynolds number, on the contrary, it tends to the outer side, owing to centrifugal force. Furthermore, in the latter case, adaptation of the flow follows the change of mean-flow direction, with a phase lag.

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 Влияние числа Рейнольдса на распределение пульсационной составляющей вихря скорости по сечению плоского канала

2019 ◽  
Vol 89 (3) ◽  
pp. 347
Author(s):  
Ю.Г. Чесноков
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Cross Section ◽  
Liquid Flow ◽  
Direct Numerical Simulations ◽  
Mean Square ◽  
Flat Channel ◽  
Analysis Of Results ◽  
The Cross ◽  
Vortex Velocity

AbstractBased on the analysis of results from different authors using direct numerical simulations of the liquid flow in a flat channel, the effect of Reynolds number on the distribution of mean-square values of projections of a pulsed component of vortex velocity through the cross-section of a flat channel has been studied.

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