Oscillatory flow in curved pipes. Part 1. The developing-flow case

1980 ◽  
Vol 98 (2) ◽  
pp. 383-395 ◽  
Author(s):  
T. Mullin ◽  
C. A. Greated
Keyword(s):  
Steady Flow ◽  
Frequency Parameter ◽  
Curved Pipe ◽  
Laser Anemometry ◽  
Curved Pipes ◽  
A Value ◽  
Flow Development ◽  
Developing Flow ◽  
Pressure Cycle ◽  
Curved Section

The results of an experimental investigation of the entry, into a curved pipe, of the fully developed oscillatory laminar flow in a straight section are presented. Laser anemometry has been used to measure velocity profiles in the plane of the bend at various stations around a 180°-curved section. The flow development is found to depend upon both the frequency parameter of the flow and the amplitude of oscillation.Results are presented for two values of the frequency parameter α. The first is for small α where the flow can be considered quasi-steady and the flow development is found to proceed as in previous steady-flow studies. The other case, more extensively studied, is where α has a value such that both viscous and inertial effects play important roles in establishing the basic flow at different parts of the pressure cycle. The flow development process around the curve is found to be complicated, but a general trend is found and the results are explained in terms of those already established for steady-flow development in a curved pipe.

Entry and exit flows in curved pipes

2017 ◽  
Vol 815 ◽  
pp. 570-591 ◽  
Author(s):  
Jesse T. Ault ◽  
Bhargav Rallabandi ◽  
Orest Shardt ◽  
Kevin K. Chen ◽  
Howard A. Stone
Keyword(s):  
Reynolds Number ◽  
Boundary Conditions ◽  
Transitional Flow ◽  
Governing Equations ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Developing Flow ◽  
Spatial Oscillations ◽  
Secondary Velocity ◽  
Pressure Perturbations

Solutions are presented for both laminar developing flow in a curved pipe with a parabolic inlet velocity and laminar transitional flow downstream of a curved pipe into a straight outlet. Scalings and linearized analyses about appropriate base states are used to show that both cases obey the same governing equations and boundary conditions. In particular, the governing equations in the two cases are linearized about fully developed Poiseuille flow in cylindrical coordinates and about Dean’s velocity profile for curved pipe flow in toroidal coordinates respectively. Subsequently, we identify appropriate scalings of the axial coordinate and disturbance velocities that eliminate dependence on the Reynolds number $Re$ and dimensionless pipe curvature $\unicode[STIX]{x1D6FC}$ from the governing equations and boundary conditions in the limit of small $\unicode[STIX]{x1D6FC}$ and large $Re$. Direct numerical simulations confirm the scaling arguments and theoretical solutions for a range of $Re$ and $\unicode[STIX]{x1D6FC}$. Maximum values of the axial velocity, secondary velocity and pressure perturbations are determined along the curved pipe section. Results collapse when the scalings are applied, and the theoretical solutions are shown to be valid up to Dean numbers of $D=Re^{2}\unicode[STIX]{x1D6FC}=O(100)$. The developing flows are shown numerically and analytically to contain spatial oscillations. The numerically determined decay of the velocity perturbations is also used to determine entrance/development lengths for both flows, which are shown to scale linearly with the Reynolds number, but with a prefactor ${\sim}60\,\%$ larger than the textbook case of developing flow in a straight pipe.

Heat Convection in a Horizontal Curved Pipe

1984 ◽  
Vol 106 (1) ◽  
pp. 71-77 ◽  
Author(s):  
L. S. Yao
Keyword(s):  
Centrifugal Force ◽  
Small Region ◽  
Relative Importance ◽  
Dean Number ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Developing Flow ◽  
Physical Importance ◽  
Hydrodynamically Developing Flow ◽  
Pipe Inlet

Thermally and hydrodynamically developing flow in heated horizontal curved pipes is analyzed. The perturbation solution is quantitatively valid only in a small region near the pipe inlet. The solution, however, provides information about the physical importance of centrifugal force and buoyancy on the developing flow. It also reveals the length and the velocity scales for the downstream regions where the secondary flow can not be treated as a small perturbation. The relative importance of centrifugal force and buoyancy is determined by the ratio of the Dean number and the Grashof number.

The flow due to an oscillating piston in a cylindrical tube: a comparison between experiment and a simple entrance flow theory

1971 ◽  
Vol 50 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. H. Gerrard ◽  
M. D. Hughes
Keyword(s):  
Steady Flow ◽  
Circular Tube ◽  
Characteristic Length ◽  
Cylindrical Tube ◽  
Axial Distance ◽  
Flow Development ◽  
Developing Flow ◽  
Oscillating Boundary ◽  
Entry Velocity ◽  
Steady Laminar

The velocity on the axis of a circular tube was measured over a range of distances from a piston reciprocating in simple harmonic motion. These velocities become independent of axial distance sufficiently far from the piston. The method of calculating the developing flow is based on a comparison with steady laminar flow which, in the entry region of a circular tube, approaches the fully developed state exponentially with distance x from the entry. The steady flow is a function of xν/R2u0 where ν is the kinematic viscosity, R is the tube radius and u0 is the entry velocity. It is shown that within the limits of experimental error, an oscillating flow follows the steady flow development if u0 is the instantaneous entry velocity and if the characteristic length is changed from R to the oscillating boundary-layer thickness in the established flow.

scholarly journals Numerical Investigation on Fluid Flow in a 90-Degree Curved Pipe with Large Curvature Ratio

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yan Wang ◽  
Quanlin Dong ◽  
Pengfei Wang
Keyword(s):  
Fluid Flow ◽  
Internal Flow ◽  
Fluid Flows ◽  
Detached Eddy Simulation ◽  
Number Range ◽  
Curvature Ratio ◽  
Large Curvature ◽  
Curved Pipe ◽  
Eddy Simulation ◽  
Curved Pipes

In order to understand the mechanism of fluid flows in curved pipes, a large number of theoretical and experimental researches have been performed. As a critical parameter of curved pipe, the curvature ratioδhas received much attention, but most of the values ofδare very small (δ<0.1) or relatively small (δ≤0.5). As a preliminary study and simulation this research studied the fluid flow in a 90-degree curved pipe of large curvature ratio. The Detached Eddy Simulation (DES) turbulence model was employed to investigate the fluid flows at the Reynolds number range from 5000 to 20000. After validation of the numerical strategy, the pressure and velocity distribution, pressure drop, fluid flow, and secondary flow along the curved pipe were illustrated. The results show that the fluid flow in a curved pipe with large curvature ratio seems to be unlike that in a curved pipe with small curvature ratio. Large curvature ratio makes the internal flow more complicated; thus, the flow patterns, the separation region, and the oscillatory flow are different.

Calculations of unsteady viscous flow past a circular cylinder

1958 ◽  
Vol 4 (1) ◽  
pp. 81-86 ◽  
Author(s):  
R. B. Payne
Keyword(s):  
Circular Cylinder ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Steady Flow ◽  
Reynolds Numbers ◽  
A Value ◽  
Unsteady Viscous Flow ◽  
Starting Flow ◽  
Forward Integration

A numerical solution has been obtained for the starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100. The method used is the step-by-step forward integration in time of Helmholtz's vorticity equation. The advantage of working with the vorticity is that calculations can be confined to the region of non-zero vorticity near the cylinder.The general features of the flow, including the formation of the eddies attached to the rear of the cylinder, have been determined, and the drag has been calculated. At R = 40 the drag on the cylinder decreases with time to a value very near that for the steady flow.

Benefits and Deep Water Install Ability Challenges of Residual Curvature Method for Lateral Buckling Mitigation

2017 ◽  
Author(s):  
Erwan Karjadi ◽  
Phil Cooper ◽  
Henk Smienk ◽  
Ferry Kortekaas
Keyword(s):  
High Pressure ◽  
Deep Water ◽  
Local Buckling ◽  
Bending Moment ◽  
Lateral Buckling ◽  
Curved Pipe ◽  
Fea Model ◽  
Water Pipelines ◽  
Residual Curvature ◽  
Curved Section

One way to control lateral buckling in the operation phase for High Pressure High Temperature (HPHT) pipelines is by deliberately introducing residual curvature sections at intervals along the pipeline by adjusting the straightener settings of the pipelay tower, as described in a patent held by Statoil [1]. This method has been applied with reel-lay installation for a number of shallow water pipelines in Europe (Statoil’s Skuld project and Total’s Edradour project). The paper presents the benefits as well as the feasibility of the use of Residual Curvature Method (RCM) to control lateral buckling for deep water applications which involves high top tension in the overbend and high pressure and twist of the RC section in the sagbend. The study cases consider the application of the method for pipelines in 1850m water depth which are pushing the pipe top tension close to the limit of the capacity of the tensioners of Heerema Marine Contractor’s (HMC) Reel-lay vessel the Aegir. There are some challenges of the application of the residual curve method for deep water pipelines. Due to high top tension, some potential issues are investigated during lowering of the curved section from the straightener, passing the tensioners and through the J-lay tower into the water to the seabed. Detailed analyses have been performed to check the interaction of the residual curved pipe section against the tensioners (the effect of the squeeze load on the RC section) and to assess the maximum bending moment generated when the residual curved section is under high top tension below the tensioners against the Load Controlled Condition (LCC) for local buckling bending moment limit. Another consideration is the increase of hydrostatic pressure in deep water which could limit the allowable bending moment in the sagbend when lowering the curved sections to the seabed. Discussions are presented to the feasibility of the concept including the proposed ways of mitigation for the aforementioned potential issues. The paper will also show an improved prediction of pipe twist/roll by comparing a published analytical 2D plane solution against the 3D FEA model prediction. The improved prediction, which considers the out of plane bending component of the pipe catenary, results in an increase of pipe twist in the sagbend section. This reduces the bending moment in the residual curved section when entering the sagbend and increases the probability to roll the curved section over to the horizontal plane on the seabed.

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.

Flow Visualization Experiments on Secondary Flow Patterns in an Isothermally Heated Curved Pipe

1987 ◽  
Vol 109 (1) ◽  
pp. 55-61 ◽  
Author(s):  
K. C. Cheng ◽  
F. P. Yuen
Keyword(s):  
Flow Visualization ◽  
Secondary Flow ◽  
Theoretical Models ◽  
Flow Patterns ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Number Range ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Numerical Predictions

Secondary flow patterns at the exit of a 180 deg bend (tube inside diameter d = 1.99 cm, radius of curvature Rc = 10.85 cm) are presented to illustrate the combined effects of centrifugal and buoyancy forces in hydrodynamically and thermally developing entrance region of an isothermally heated curved pipe with both parabolic and turbulent entrance velocity profiles. Three cases of upward, horizontal, and downward-curved pipe flows are studied for constant wall temperatures Tw=55–91°C, Dean number range K=22–1209 and ReRa=1.00×106–8.86×107. The flow visualization was realized by the smoke injection method. The secondary flow patterns shown are useful for future comparison with numerical predictions and confirming theoretical models. The results can be used to assess qualitatively the limit of the applicability of the existing correlation equations for laminar forced convection in isothermally heated curved pipes without buoyancy effects.

Laser anemometer study of flow development in curved circular pipes

1978 ◽  
Vol 85 (3) ◽  
pp. 497-518 ◽  
Author(s):  
Y. Agrawal ◽  
L. Talbot ◽  
K. Gong
Keyword(s):  
Axial Velocity ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Upstream Region ◽  
Uniform Motion ◽  
Dean Number ◽  
Number Range ◽  
Curved Pipe ◽  
Laser Anemometry ◽  
Pipe Radius

An experimental investigation was carried out of the development of steady, laminar, incompressible flow of a Newtonian fluid in the entry region of a curved pipe for the entry condition of uniform motion. Two semicircular pipes of radius ratios 1/20 and 1/7 were investigated, covering a Dean number range from 138 to 679. The axial velocity and the component of secondary velocity parallel to the plane of curvature of the pipe were measured using laser anemometry. It was observed that, in the upstream region where the boundary layers are thin compared with the pipe radius, the axial velocity within the irrotational core first develops to form a vortex-like flow. In the downstream region, characterized by viscous layers of thickness comparable with the pipe radius, there appears to be three-dimensional separation at the inner wall. There is also an indication of an additional vortex structure embedded within the Dean-type secondary motion. The experimental axial velocity profiles are compared with those constructed from the theoretical analyses of Singh and Yao & Berger. The quantitative agreement between theory and experiment is found to be poor; however, some of the features observed in the experiment are in qualitative agreement with the theoretical solution of Yao & Berger.

Sign in / Sign up

Export Citation Format

Share Document