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.

On the causal behaviour of flow over an elastic wall

1999 ◽  
Vol 396 ◽  
pp. 319-344 ◽  
Author(s):  
R. J. LINGWOOD ◽  
N. PEAKE
Keyword(s):  
Shear Layer ◽  
Finite Time ◽  
Radiation Condition ◽  
Flow Speed ◽  
Uniform Flow ◽  
Dispersion Function ◽  
Mean Flow ◽  
Wide Range ◽  
Line Force ◽  
Layer Flow

In this paper we consider the causal response of the inviscid shear-layer flow over an elastic surface to excitation by a time-harmonic line force. In the case of uniform flow, Brazier-Smith & Scott (1984) and Crighton & Oswell (1991) have analysed the long-time limit of the response. They find that the system is absolutely unstable for sufficiently high flow speeds, and that at lower speeds there exist certain anomalous neutral modes with group velocity directed towards the driver (in contradiction of the usual radiation condition of out-going disturbances). Our aim in this paper is to repeat their analysis for more realistic shear profiles, and in particular to determine whether or not the uniform-flow results can be regained in the limit in which the shear-layer thickness on a length scale based on the fluid loading, denoted ε, becomes small. For a simple broken-line linear shear profile we find that the results are qualitatively similar to those for uniform flow. However, for the more realistic Blasius profile very significant differences arise, essentially due to the presence of the critical layer. In particular, we find that as ε → 0 the minimum flow speed required for absolute instability is pushed to considerably higher values than was found for uniform flow, leading us to conclude that the uniform-flow problem is an unattainable singular limit of our more general problem. In contrast, we find that the uniform-flow anomalous modes (written as exp (ikx − iωt), say) do persist for non-zero shear over a wide range of ε, although now becoming non-neutral. Unlike the case of uniform flow, however, the k-loci of these modes can now change direction more than once as the imaginary part of ω is increased, and we describe the connection between this behaviour and local properties of the dispersion function. Finally, in order to investigate whether or not these anomalous modes might be realizable at a finite time after the driver is switched on, we evaluate the double Fourier inversion integrals for the unsteady flow numerically. We find that the anomalous mode is indeed present at finite time, once initial transients have propagated away, not only for impulsive start-up but also when the forcing amplitude is allowed to grow slowly from a small value at some initial instant. This behaviour has significant implications for the application of standard radiation conditions in wave problems with mean flow.

Can the Dean number Alone Characterize Flow Similarity in Differently Bent Tubes?

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Krzysztof Cieślicki ◽  
Adam Piechna
Keyword(s):  
Flow Resistance ◽  
Classical Problem ◽  
Nonlinear Flow ◽  
Nonlinear Dependence ◽  
Dean Number ◽  
Curvature Ratio ◽  
Coiled Tube ◽  
Newtonian Flows ◽  
Curved Channels ◽  
Wide Range

Although flows of fluids in curved channels belong to a classical problem of fluid dynamics, most publications are restricted to investigations of flows in tube coils, or in single bends. This paper presents experimental and numerical (CFD) results concerning Newtonian flows in a set of multiple S-type bends of various orientations. Investigations were conducted for a wide range of Re values (0–3500) and for a significant curvature ratio lying between 0.05 and 0.29, which corresponds to De value falling within the range 0.02–1200. A coiled tube was also examined and treated as the reference geometry. It was shown, that despite a completely different velocity pattern, the nonlinear dependence of normalized flow resistance of wavy tubes and coiled tube of the same curvature ratio overlap within a significant range of De. A novel, close phenomenological formula to estimate the nonlinear flow resistance of tortuous tube in a wide range of De was proposed and compared with those in the literature. The conditions were also determined in which the De might be the only dimensionless group that characterizes such flows.

scholarly journals ADHI: the African Database of Hydrometric Indices (1950–2018)

2021 ◽  
Vol 13 (4) ◽  
pp. 1547-1560
Author(s):  
Yves Tramblay ◽  
Nathalie Rouché ◽  
Jean-Emmanuel Paturel ◽  
Gil Mahé ◽  
Jean-François Boyer ◽  
...  
Keyword(s):  
River Discharge ◽  
Flow Characteristics ◽  
African Continent ◽  
Mean Flow ◽  
Discharge Data ◽  
Climatic Regions ◽  
Wide Range ◽  
Daily Discharge ◽  
The One ◽  
Different Sources

Abstract. The African continent is probably the one with the lowest density of hydrometric stations currently measuring river discharge despite the fact that the number of operating stations was quite important until the 1970s. This new African Database of Hydrometric Indices (ADHI) provides a wide range of hydrometric indices and hydrological signatures computed from different sources of data after a quality control. It includes 1466 stations with at least 10 years of daily discharge data over the period 1950–2018. The average record length is 33 years, and 131 stations have complete records over 50 years. With this new dataset spanning most climatic regions of the African continent, several hydrometric indices have been computed, representing mean flow characteristics and extremes (low flows and floods), and are accessible to the scientific community. The database will be updated on a regular basis to include more hydrometric stations and longer time series of river discharge. The ADHI is available for download at: https://doi.org/10.23708/LXGXQ9 (Tramblay and Rouché, 2020).

Laminar flow in rotating curved pipes

1996 ◽  
Vol 329 ◽  
pp. 373-388 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Experimental Data ◽  
Laminar Flow ◽  
Friction Factor ◽  
Flow Structure ◽  
Flow Characteristics ◽  
Laminar Flows ◽  
Dean Number ◽  
Governing Parameter ◽  
Curved Pipes ◽  
Wide Range

When a curved pipe rotates about the centre of curvature, the fluid flowing in it is subjected to both Coriolis and centrifugal forces. Based on the analogy between laminar flows in stationary curved pipes and in orthogonally rotating pipes, the flow characteristics of fully developed laminar flow in rotating curved pipes are made clear and definite by similarity arguments, computational studies and using experimental data. Similarity arguments clarify that the flow characteristics in loosely coiled rotating pipes are governed by three parameters: the Dean number KLC, a body force ratio F and the Rossby number Ro. As the effect of Ro is negligible when Ro is large, computational results are presented for this case first, and then the effect of Ro is studied. Flow structure and friction factor are studied in detail. Variations of flow structure show secondary flow reversal at F ≈ −1, where the two body forces are of the same order but in opposite directions. It is also shown how the Taylor–Proudman effect dominates the flow structure when Ro is small. Computed curves of the friction factor for constant Dean number have their minimum at F ≈ −1. A composite parameter KL is introduced as a convenient governing parameter and used to correlate the characteristics. By applying KL to the analogy formula previously derived for two limiting flows, a semi-empirical formula for the friction factor is presented, which shows good agreement with the experimental data for a wide range of the parameters.

An experimental study of pressure drop in helical pipes

1994 ◽  
Vol 444 (1921) ◽  
pp. 307-316 ◽  
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Cross Section ◽  
Circular Cross Section ◽  
Square Root ◽  
Dean Number ◽  
Curvature Ratio ◽  
Pressure Drops ◽  
Newtonian Flows ◽  
Fanning Friction Factor

Pressure drops of fully-developed incompressible laminar newtonian flows in helical pipes of constant circular cross-section having a finite pitch are experimentally investigated. For the case of loosely coiled pipes of 0 < η/λ < 41.22, f Re ( f is the Fanning friction factor and Re is the Reynolds number) is found to be proportional to the square root of the flow Dean number, Dn = Re λ ½ . Here λ and η are the normalized curvature ratio and torsion which incorporate both the coil radius and its pitch. In all cases studied, the experimental results for f Re are in excellent agreement with the theoretical prediction of Liu & Masliyah.

Laminar secondary flows in curved rectangular ducts

1990 ◽  
Vol 217 ◽  
pp. 421-440 ◽  
Author(s):  
S. Thangam ◽  
N. Hur
Keyword(s):  
Aspect Ratio ◽  
Secondary Flow ◽  
Vortex Pair ◽  
Stability Diagram ◽  
Secondary Flows ◽  
Dean Number ◽  
Single Vortex ◽  
Curvature Ratio ◽  
Wide Range ◽  
Good Agreement

The occurrence of secondary flow in curved ducts due to the centrifugal forces can often significantly influence the flow rate. In the present work, the secondary flow of an incompressible viscous fluid in a curved duct is studied by using a finite-volume method. It is shown that as the Dean number is increased the secondary flow structure evolves into a double vortex pair for low-aspect-ratio ducts and roll cells for ducts of high aspect ratio. A stability diagram is obtained in the domain of curvature ratio and Reynolds number. It is found that for ducts of high curvature the onset of transition from single vortex pair to double vortex pair or roll cells depends on the Dean number and the curvature ratio, while for ducts of small curvature the onset can be characterized by the Dean number alone. A comparison with the available theoretical and experimental results indicates good agreement. A correlation for the friction factor as a function of the Dean number and aspect ratio is developed and is found to be in good agreement with the available experimental and computational results for a wide range of parameters.

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

Observations Regarding the Nature of Oil-Water Phase Inversion and Instability in Laminar Flow Through Circular Tubes Containing Static Mixers

2005 ◽  
Author(s):  
Arun Sood ◽  
Eric Cheluget ◽  
Umesh Karnik
Keyword(s):  
Laminar Flow ◽  
Phase Inversion ◽  
Flow Instabilities ◽  
Smooth Transition ◽  
Stable Phase ◽  
Dispersed Phase ◽  
Inversion Point ◽  
Static Mixers ◽  
Wide Range ◽  
Flow Through

Liquid-liquid emulsions will undergo a phase inversion, in which the dispersed phase becomes the continuous phase and vice versa, under certain conditions. A phase inversion is not a smooth transition and an emulsion close to the inversion point may oscillate back and forth between the oil-in-water (O/W) and water-in-oil (W/O) forms, creating flow instabilities that may be detrimental in certain industrial situations. The results of laboratory laminar flow experiments in which an aqueous and an organic liquid phase are emulsified as they flow through a circular tube containing a commercial high-shear static mixer are discussed. As the concentration of the dispersed phase and/or its flow rate is increased, flow instabilities are initiated in the test-section and are measured as fluctuations in pressure drop. The intensity of these fluctuations reaches a maximum as the liquid-liquid system approaches the phase inversion point. Once a stable phase inversion is achieved, the fluctuations subside. This phenomenon was observed over a wide range of viscosity ratios for the two liquid phases, but was absent for low viscosity ratios and low-shear static mixers.

Variation of the Recirculation Length of Newtonian and Non-Newtonian Power-Law Fluids in Laminar Flow Through a Suddenly Expanded Axisymmetric Geometry

2006 ◽  
Vol 129 (2) ◽  
pp. 245-250 ◽  
Author(s):  
Debabrata Nag ◽  
Amitava Datta
Keyword(s):  
Laminar Flow ◽  
Power Law ◽  
Numerical Study ◽  
Shear Thickening ◽  
Expansion Ratio ◽  
Rheological Parameters ◽  
Power Law Fluids ◽  
Wide Range ◽  
Flow Through ◽  
Recirculation Length

A numerical study has been carried out for the laminar flow of Newtonian and non-Newtonian power-law fluids through a suddenly expanded axisymmetric geometry. Mathematical correlations are proposed for the prediction of the length of the recirculating eddy in terms of Reynolds number, expansion ratio and rheological parameters. A wide range of expansion ratios (1.25⩽ER⩽8.0) has been covered for the Newtonian fluid and both the shear-thinning and shear-thickening flow characteristic fluids have been considered for the non-Newtonian fluids.

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