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.

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.

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 Improved calculations of electron–ion bremsstrahlung Gaunt factors for astrophysical applications

2019 ◽  
Vol 492 (1) ◽  
pp. 177-194 ◽  
Author(s):  
Jens Chluba ◽  
Andrea Ravenni ◽  
Boris Bolliet
Keyword(s):  
Classical Problem ◽  
Microwave Background ◽  
Astrophysical Plasmas ◽  
Physical Conditions ◽  
Analytical Approximations ◽  
Wide Range ◽  
Relativistic Regime ◽  
Low Charge ◽  
Transfer Problems ◽  
Electron And Photon

ABSTRACT Electron–ion bremsstrahlung (free–free) emission and absorption occur in many astrophysical plasmas for a wide range of physical conditions. This classical problem has been studied multiple times, and many analytical and numerical approximations exist. However, accurate calculations of the transition from the non-relativistic to the relativistic regime remain sparse. Here we provide a comprehensive study of the free–free Gaunt factors for ions with a low charge (Z ≤ 10). We compute the Gaunt factor using the expressions for the differential cross-section given by Elwert and Haug (EH) and compare to various limiting cases. We develop a new software package, BRpack, for direct numerical applications. This package uses a combination of pre-computed tables and analytical approximations to efficiently cover a wide range of electron and photon energies, providing a representation of the EH Gaunt factor to better than $0.03{{\ \rm per\ cent}}$ precision for Z ≤ 2. Our results are compared to those of previous studies highlighting the improvements achieved here. BRpack should be useful in computations of spectral distortions of the cosmic microwave background, radiative transfer problems during reionization or inside galaxy clusters, and the modelling of galactic free–free foregrounds. The developed computational methods can furthermore be extended to higher energies and ion charge.

scholarly journals Predicate logic as a modeling language: modeling and solving some machine learning and data mining problems withIDP3

2014 ◽  
Vol 15 (6) ◽  
pp. 783-817 ◽  
Author(s):  
MAURICE BRUYNOOGHE ◽  
HENDRIK BLOCKEEL ◽  
BART BOGAERTS ◽  
BROES DE CAT ◽  
STEF DE POOTER ◽  
...  
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Phylogenetic Trees ◽  
Predicate Logic ◽  
Classical Problem ◽  
Modeling Language ◽  
Finite Model ◽  
Partial Functions ◽  
Inductive Definitions ◽  
Wide Range

AbstractThis paper provides a gentle introduction to problem-solving with the IDP3 system. The core of IDP3 is a finite model generator that supports first-order logic enriched with types, inductive definitions, aggregates and partial functions. It offers its users a modeling language that is a slight extension of predicate logic and allows them to solve a wide range of search problems. Apart from a small introductory example, applications are selected from problems that arose within machine learning and data mining research. These research areas have recently shown a strong interest in declarative modeling and constraint-solving as opposed to algorithmic approaches. The paper illustrates that the IDP3 system can be a valuable tool for researchers with such an interest. The first problem is in the domain of stemmatology, a domain of philology concerned with the relationship between surviving variant versions of text. The second problem is about a somewhat related problem within biology where phylogenetic trees are used to represent the evolution of species. The third and final problem concerns the classical problem of learning a minimal automaton consistent with a given set of strings. For this last problem, we show that the performance of our solution comes very close to that of the state-of-the art solution. For each of these applications, we analyze the problem, illustrate the development of a logic-based model and explore how alternatives can affect the performance.

Time-Dependent Laminar Flow in Curved Channels

1970 ◽  
Vol 37 (3) ◽  
pp. 838-843 ◽  
Author(s):  
R. J. Nunge
Keyword(s):  
Laminar Flow ◽  
Pressure Gradient ◽  
Constant Pressure ◽  
Time Dependent ◽  
Pressure Gradients ◽  
Straight Channel ◽  
Curvature Ratio ◽  
Curved Channels ◽  
Developing Flow ◽  
Time Required

The velocity distribution for time-dependent laminar flow in curved channels is derived. The analysis applies to flows with pressure gradients which are arbitrary functions of time. Numerical results are obtained for developing flow due to a constant pressure gradient. Developing flow in a straight channel is also discussed and it is found that the curvature ratio has only a small effect on the time required to reach the fully developed state.

Performance characteristics of a chilled water spirally coiled finned tube in cross flow for air conditioning applications

2012 ◽  
Vol 227 (2) ◽  
pp. 320-331 ◽  
Author(s):  
Abdalla Gomaa ◽  
Wael IA Aly ◽  
Ashraf Mimi Elsaid ◽  
Eldesuki I Eid
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Factor ◽  
Flow Direction ◽  
Cross Flow ◽  
Finned Tube ◽  
Performance Characteristics ◽  
Curvature Ratio ◽  
Coiled Tube ◽  
Chilled Water

In the present study, the thermo-fluid characteristics of a spirally coiled finned tube in cross flow were experimentally investigated. This investigation covered different design parameters such as curvature ratio, air velocity, flow direction, fin pitch and flow rate of chilled water on performance characteristics of the spirally coiled finned tube. The purpose was to evaluate this kind of the spirally finned-tube cooling coils with particular reference to bare coiled tube. Six test specimens were designed and manufactured with curvature ratios of 0.027, 0.03, 0.04, tube pitches of 18, 20, 30 mm and fin pitches of (33, 22, 11 mm). Experiments were carried out in a pilot wind tunnel with air Reynolds number ranging from 35,500 to 245,000. Two types of chilled water flow directions entering the spiral coil were tested at Reynolds number ranging from 5700 to 25,300, the first was inward flow direction and the other was to outward flow direction. The results revealed that the inward flow direction has significant enhancement effect on the Nusselt number compared with outward flow direction by 37.0% for tube pitch of 18 mm and curvature ratio of 0.027. The decrease of fin pitch enhances the Nusselt number by 21.92% on expense of friction factor by 10.9%. In the case of spirally coiled bare tube, the decreasing of the curvature ratio increases air side Nusselt number by 33.69% on expense of friction factor by 18.36%. General correlations of Nusselt number and air friction factor for bare and finned spirally coiled tube were correlated based on reported experimental data.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Xiaolei Song ◽  
Haijun Liu
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Classical Problem ◽  
Mode Shapes ◽  
Wide Range ◽  
Fundamental Understanding ◽  
Clamped Beams ◽  
Transverse Deflection ◽  
Symmetric And Antisymmetric Modes ◽  
Good Agreement

Abstract Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

Magnetic Ordering of Perovskite-Like La-, Nd-, and Gd-Doped Bismuth Ferrite

MRS Advances ◽  
2019 ◽  
Vol 4 (36) ◽  
pp. 1989-1999 ◽  
Author(s):  
Valery Sobol ◽  
Barys Korzun ◽  
Olga Mazurenko ◽  
Temirkhan Bizhigitov ◽  
Sabit Tomaev
Keyword(s):  
Magnetic Field ◽  
Exchange Interaction ◽  
Bismuth Ferrite ◽  
Magnetic Ordering ◽  
Solid State Reaction Method ◽  
Nonlinear Dependence ◽  
X Ray Diffraction ◽  
Wide Range ◽  
Pure Grade ◽  
The Magnetic Field

ABSTRACTBismuth ferrite (BiFeO3) and La-, Nd- and Gd-substituted bismuth ferrite of the Bi1-xLaxFeO3, Bi1-xNdxFeO3, and Bi1-xGdxFeO3 types with the atomic part of the substitution element x equal up to 0.20 were synthesized by the solid-state reaction method using powders of oxides Bi2O3, Fe2O3, and La2O3, or Nd2O3, or Gd2O3 of pure grade quality and investigated using X-ray diffraction analysis. The magnetization was measured in the magnetic field up to 6.5⋅106 A/m at 5 and 300 K. It was found that the total substitution up to 0.20 atomic part of Bi by La, Nd, and Gd leads to the paramagnetic behavior of the doped bismuth ferrite at low temperatures in a wide range of magnetic field. Strong nonlinear dependence of magnetization on the magnetic field was detected and a ferromagnetic-like dependence of magnetization was observed for small magnetic fields. This can be explained by the exchange interaction between doping magnetic ions, as well as by the exchange interaction of these ions with ions of iron. The enhancement of magnetic properties with the increase of the content of the substitution is monotone and is more pronounced for the Bi1-xGdxFeO3 ceramics.

Design Optimization of Solenoid Actuated Butterfly Valves Dynamically Coupled in Series

2015 ◽  
Author(s):  
Peiman Naseradinmousavi ◽  
C. Nataraj
Keyword(s):  
Intelligent Design ◽  
Nonlinear Modeling ◽  
Nonlinear Flow ◽  
Efficient Operation ◽  
Smart Systems ◽  
Critical Design ◽  
Highly Nonlinear ◽  
Wide Range ◽  
In Series ◽  
Gradient Based

In this effort, we present novel nonlinear modeling of two solenoid actuated butterfly valves operating in series and then develop an optimal configuration in the presence of highly coupled nonlinear dynamics. The valves are used in the so-called “Smart Systems” to be employed in a wide range of applications including bioengineering, medicine, and engineering fields. Typically, tens of the actuated valves are instantaneously operating to regulate the amount of flow and also to avoid probable catastrophic disasters which have been observed in the practice. We focus on minimizing the amount of energy used in the system as one of the most critical design criteria to yield an efficient operation. We optimize the actuation subsystems interacting with the highly nonlinear flow loads in order to minimize a lumped amount of energy consumed. The contribution of this work is to include coupled nonlinearities of electromechanical valve systems to optimize the actuation units. Stochastic, heuristic, and gradient based algorithms are utilized in seeking the optimal design of two sets. The results indicate that substantial amount of energy can be saved by an intelligent design that helps select parameters carefully but also uses flow torques to augment the closing efforts.

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