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.

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.

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.

Flow in heated curved pipes

1978 ◽  
Vol 88 (2) ◽  
pp. 339-354 ◽  
Author(s):  
Lun-Shin Yao ◽  
Stanley A. Berger
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Temperature Distribution ◽  
Dean Number ◽  
Representative Case ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Axial Temperature ◽  
Buoyancy Forces ◽  
Rayleigh Numbers

The fully developed laminar flow in a heated curved pipe under the influence of both centrifugal and buoyancy forces is studied analytically. The pipe is assumed to be heated so as to maintain a constant axial temperature gradient. Both horizontal and vertical pipes are considered. Solutions for these two cases are obtained by regular perturbations in the Dean number and the product of the Reynolds and Rayleigh numbers; the solutions are therefore limited to small values of these parameters. Predictions of the axial and secondary flow velocities, streamlines, shear stress, temperature distribution and heat transfer are given for a representative case.

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.

Effects of Fe3O4/Water Nanofluid on the Efficiency of a Curved Pipe

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Milad Kelidari ◽  
Ali Jabari Moghadam
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Volume Concentration ◽  
Volume Fraction ◽  
Working Fluid ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Curved Pipe ◽  
Overall Efficiency

Different-radius of curvature pipes are experimentally investigated using distilled water and Fe3O4–water nanofluid with two different values of the nanoparticle volume fraction as the working fluids. The mass flow rate is approximately varied from 0.2 to 0.7 kg/min (in the range of laminar flow); the wall heat flux is nearly kept constant. The experimental results reveal that utilizing the nanofluid increases the convection heat transfer coefficient and Nusselt number in comparison to water; these outcomes are also observed when the radius of curvature is decreased and/or the mass flow rate is increased (equivalently, a rise in Dean number). The resultant pressure gradient is, however, intensified by an increase in the volume concentration of nanoparticles and/or by a rise in Dean number. For any particular working fluid, there is an optimum mass flow rate, which maximizes the system efficiency. The overall efficiency can be introduced to include hydrodynamic as well as thermal characteristics of nanofluids in various geometrical conditions. For each radius of curvature, the same overall efficiency may be achieved for two magnitudes of nanofluid volume concentration.

Classification of Pulsating Flow Patterns in Curved Pipes

1996 ◽  
Vol 118 (3) ◽  
pp. 311-317 ◽  
Author(s):  
Shigeru Tada ◽  
Shuzo Oshima ◽  
Ryuichiro Yamane
Keyword(s):  
Secondary Flow ◽  
Amplitude Ratio ◽  
Circular Cross Section ◽  
Volumetric Flow Rate ◽  
Flow Patterns ◽  
Womersley Number ◽  
Dean Number ◽  
Curved Pipes ◽  
Convection Dominated

The fully developed periodic laminar flow of incompressible Newtonian fluids through a pipe of circular cross section, which is coiled in a circle, was simulated numerically. The flow patterns are characterized by three parameters: the Womersley number Wo, the Dean number De, and the amplitude ratio β. The effect of these parameters on the flow was studied in the range 2.19 ≤ Wo ≤ 50.00, 15.07 ≤ De ≤ 265.49 and 0.50 ≤ β ≤ 2.00, with the curvature ratio δ fixed to be 0.05. The way the secondary flow evolved with increasing Womersley number and Dean number is explained. The secondary flow patterns are classified into three main groups: the viscosity-dominated type, the inertia-dominated type, and the convection-dominated type. It was found that when the amplitude ratio of the volumetric flow rate is equal to 1.0, four to six vortices of the secondary flow appear at high Dean numbers, and the Lyne-type flow patterns disappear at β ≥ 0.50.

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.

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