Second-order Flow Research Articles

Propulsion of axisymmetric swimmers in viscoelastic liquids by means of torsional oscillations

Unconventional methods are needed in order to propel swimming objects in viscoelastic liquids. The paper deals with a locomotion principle based on a cyclic action which utilizes the elasticity of the fluid. The theoretical model considers any incompressible simple fluid of arbitrarily long memory and any axisymmetric swimmer of arbitrary profile which performs torsional oscillations of small amplitude. Perceiving the flow as unsteady perturbation of the rest state, an asymptotic analysis is developed, particularly with regard to the time-averaged speed of the swimmer in second-order approximation. In doing so, also inertia effects are considered in addition to the memory and the normal stress effects. A generalized reciprocal theorem including fluid elasticity proves to be extremely useful. It enables calculating the driving force on the swimmer without solving the second-order flow problem. General results are illustrated by means of a spherical swimmer. The analytical findings clearly show the influence of different process parameters including certain frequency dependent constitutive parameters on the driving force, on the swimming speed and on the secondary flow field.

Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel

Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel

Load Flow Analysis Using Second-Order Load Flow Methods and its Variations

The load flow or power flow computer program is the basic tool for investigating the steady-state conditions of power system. This paper introduces improved algorithms based on the basic Second-order Load Flow method for a wide range of electrical bus system sizes. It is attractive for accurate or approximate off- and on-line calculations for routine and contingency purposes. Tests of 4 different variations based on the basic Second-order Load Flow method are run on 6 different standard bus systems and the results are discussed in this paper.

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and Al2O3, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions are derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Final source eccentricity measured by HBT interferometry with the event shape selection

Azimuthal angle dependence of the pion source radii has been measured applying the event shape engineering technique at the PHENIX experiment. When events with higher magnitude of second-order flow vector are selected, the oscillation of the source radii is enhanced as well as v2 which leads to the enhancement of the measured final source eccentricity. The event twist effect in the spatial source distribution in the final state has been also explored with AMPT model. Results indicate a possible twisted source due to the initial longitudinal fluctuations.

Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number

This study investigates the numerical solution of a viscoelastic flow for an Oldroyd-B model, due to the rotation of a sphere about its diameter. Analysis of the elastic-viscous problem had been reported by Thomas and Walters (Q J Mech Appl Math 17:39–53, 1964), Walters and Savins (J Rheol 9:407–416, 1965) and Giesekus (Rheol Acta 9:30–38, 1970). In this respect, three different flow patterns (types 1–3) predicted by Thomas and Walters (Q J Mech Appl Math 17:39–53, 1964) have been successfully reproduced when using an Oldroyd-B fluid to represent a Boger fluid. Initially, solutions for the Oldroyd-B model were calibrated in the second-order regime against the analytical solution. Then, the work is extended to cover three different flows regimes (second-order regime, transitional and general flow) and two settings of polymeric solvent-fraction. Analysis based on the bounding sphere-radius, associated with type 2 flow, and through different flow regimes revealed that the distinctive symmetrical shape formed in the second-order regime was not preserved, but an elliptical shape was acquired. Moreover, for general and transitional flow regimes, a new and third vortex was identified in the polar region of the sphere. The adjustment of this feature between two different fluid compositions, with solutions for high-solvent and high-polymeric versions (low-high polymeric contributions), was contrasted. The second normal stress difference (N 2) on the field was increased as the m parameter developed across the different flow regimes. Different torque values for several m values were compared against the theory, demonstrating the expected linear behaviour. The numerical algorithm involved a hybrid sub-cell finite-element/finite volume discretisation (fe/fv), which solved the system of momentum-continuity-stress equations. It is based on a semi-implicit time-stepping Taylor-Galerkin/pressure-correction parent-cell finite element method for momentum continuity, whilst invoking a sub-cell cell-vertex fluctuation distribution finite volume scheme for the stress. The hyperbolic aspects of the constitutive equation were addressed discretely through finite volume upwind Fluctuation Distribution techniques and inhomogeneity calls upon Median Dual Cell approximation.

MAGNETOHYDRODYNAMIC VISCOUS FLOW OVER A SHRINKING SHEET IN A SECOND-ORDER SLIP FLOW MODEL

In this paper, we investigate a magnetohydrodynamic viscous flow over a permeable shrinking surface by means of a second-order slip flow model. We have obtained a closed form of exact solution for the Navier−Stokes equations by using the similarity variable technique. The effects of slip, suction, and magnetic parameters have been investigated in detail. The results show that there are two solution branches, namely, a lower solution branch and an upper solution branch. The behavior of velocity and shear stress profiles at different values of slip, suction, and magnetic parameters has been discussed through graphs.

Direct numerical simulation of turbulent wake behind a surface-mounted square cylinder

In this research, direct numerical simulation has been performed to study the turbulent wake behind a wall-mounted square cylinder with aspect ratio 4 and Reynolds number 12000 (based on the free-stream velocity and obstacle side length) in a developing boundary layer. Owing to the relatively high Reynolds number and high aspect ratio of the cylinder tested, the wake is wide spread behind the cylinder and exhibits complex and energetic vortex motions. The lateral and tip vortex shedding patterns at different frequencies, coherent structures downstream of the obstacle, the production rate and distribution of turbulent kinetic energy, and the instantaneous pressure distribution in the wake region have been thoroughly investigated. In order to validate the numerical results, the first- and second-order flow statistics obtained from the simulations have been carefully compared against available wind-tunnel measurement data.

Second-Order Slip Flow and Heat Transfer in a Long Isoflux Microchannel

Second-Order Slip Flow and Heat Transfer in a Long Isoflux Microchannel

Second-Order Slip Flow and Heat Transfer in a Long Isoflux Microchannel

Second-Order Slip Flow and Heat Transfer in a Long Isoflux Microchannel

Acoustic streaming measurements in standing wave resonator using Particle Image Velocimetry

This paper experimentally investigates the measurement of acoustic streaming in a 7 m long-standing wave air-filled acoustic resonator. One can describe the acoustic streaming as a second-order steady flow, which is superimposed on the dominant acoustic velocity. It is induced by the nonlinearities of the acoustic propagation inside the resonator. The exploration of the acoustic velocity field by the synchronized PIV (stands for Particle Image Velocimetry) technique enabled to highlight and quantify these secondary flows. The PIV measurements of the acoustic velocity fields at different phases over the excitation signal period gave information on streaming profiles and the post processing applied allowed plotting the acoustic velocity over time. These results were compared to the outcome of a 2D numerical study performed with the commercial software Fluent, where good agreements were found. It indicates the ability of this method to accurately measure second order steady flow variations of the acoustic velocity field.

Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow

We study the asymptotic complete entrainment of Kuramoto oscillators with inertia on symmetric and connected network. We provide several sufficient conditions for the asymptotic complete entrainment in terms of initial phase-frequency configurations, strengths of inertia and coupling, and natural frequency distributions. For this purpose, we reinterpret the Kuramoto oscillators with inertia as a second-order gradient-like flow, and adopt analytical methods based on several Lyapunov functions to apply the convergence estimate studied by Haraux and Jendoubi [21]. Our approach does not require any spectral information of the graph associated with the given network structure.

Second-Order Shallow-Flow Theory and Dupuit Approximation for Phreatic Aquifers

AbstractOne-dimensional (1D) hydraulic models for phreatic aquifers are commonly based on Dupuit’s approximation for near-horizontal flows. In the past, improved 1D models were developed by inclusion of streamline curvature in the governing equations. However, the models developed for steady flow are quite different from those developed for unsteady curvilinear flow. In this paper, a single mathematical model is proposed for application to both steady and unsteady curvilinear phreatic flows. Unsteady flow equations for phreatic aquifers are presented by adopting the shallow flow approximation. The resulting model converges to that originating from perturbation methods, thereby providing a generalized result. Limitations of the second-order shallow flow theory and Dupuit’s approximation are investigated for steady flow through a dam and unsteady flow in the bank storage problems. The results obtained from the present model are compared with two-dimensional data, indicating that Dupuit’s theory is valid und...

A method to simplify perturbation analyses of periodical flows

Perturbation methods up to first order with respect to motion or wave amplitude are common in seakeeping predictions. For higher than first order, lengthy theoretical analyses are required. They result in complicated formulae requiring high programming effort, and often the well-established numerical methods for first-order quantities fail when applied to second-order flow quantities. Both the derivation of the required expressions and their programming are simplified by using mathematical entities called perturbators. The concept of perturbators is described, and their application is demonstrated, for a two-dimensional test problem: A cylinder with horizontal axis partly immersed into an ideal fluid. The cylinder performs sinusoidal heave, sway, and roll motions. Stationary and double-frequency second-order forces are determined. For a heaving semicircle, vertical forces are determined numerically and compared to published results.

Fold and fabric relationships in temporally and spatially evolving slump systems: A multi-cell flow model

Folds generated in ductile metamorphic terranes and within unlithified sediments affected by slumping are geometrically identical to one another, and distinguishing the origin of such folds in ancient lithified rocks is therefore challenging. Foliation is observed to lie broadly parallel to the axial planes of tectonic folds, whilst it is frequently regarded as absent in slump folds. The presence of foliation is therefore often considered as a reliable criterion for distinguishing tectonic folds from those created during slumping. To test this assertion, we have examined a series of well exposed slump folds within the late Pleistocene Lisan Formation of the Dead Sea Basin. These slumps contain a number of different foliation types, including an axial–planar grain-shape fabric and a crenulation cleavage formed via microfolding of bedding laminae. Folds also contain a spaced disjunctive foliation characterised by extensional displacements across shear fractures. This spaced foliation fans around recumbent fold hinges, with kinematics reversing across the axial plane indicating a flexural shear fold mechanism. Overall, the spaced foliation is penecontemporaneous with each individual slump where it occurs, although in detail it is pre, syn or post the local folds. The identification of foliations within undoubted slump folds indicates that the presence or absence of foliation is not in itself a robust criterion to distinguish tectonic from soft-sediment folds. Extensional shear fractures displaying a range of temporal relationships with slump folds suggests that traditional single-cell flow models, where extension is focussed at the head and contraction in the lower toe of the slump, are a gross simplification. We therefore propose a new multi-cell flow model involving coeval second-order flow cells that interact with neighbouring cells during translation of the slump.

A Practical Second-Order Based Method for Power Losses Estimation in Distribution Systems With Distributed Generation

Power losses estimation under time-varying distributed generation (DG) conditions usually demands several power flow simulations, which is a time-consuming task. To handle this issue, this paper proposes a method that uses the information of only one (base case) power flow to estimate the total power losses of distribution networks for any new DG condition. The method is based on the second-order power flow sensitivities, which are suitable to model the nonlinear nature of power losses. As a result, the method has the potential to speed up the solution of power losses reduction optimization problems, such as DG allocation problems, in which several DG configurations need to be considered. Moreover, a practical index is proposed to quantify the responsibility of each DG for the total power losses in a multi-DG scenario. The test results verified the validity of the proposed concept and method.

Effects of Hall Current on MHD Boundary Layer Second-Order Viscoelastic Fluid Flow Induced by a Continuous Surface with Heat Transfer

Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction/injection by taking viscous dissipation into account. Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as homotopy analysis method (HAM). Convergence of the solutions is ensured with the help of -curves. Graphical and tabular results for the effects of Hall current reveal that it has a significant influence on: complex velocity, complex temperature, magnitude of the shear stress at the surface, magnitude of the rate of heat transfer at the surface and on boundary layer thickness.

Second-Order Seakeeping Analyses using Perturbators

Perturbation methods up to first order are common in seakeeping predictions. For higher than first order, lengthy theoretical analyses are retired; they result in complicated formulae requiring high programming effort, and often the well-established numerical methods for first-order quantities fail when applied to second-order flow quantities. Both the derivation of the required expressions and their programming can be simplified substantially by using mathematical entities called perturbators. Here the concept of perturbators is described, and their application is demonstrated for a two-dimensional test problem: the force and moment up to second order acting on a fixed, partly immersed cylindrical body in a regular wave.

Simultaneously developing laminar flow in an isothermal micro-tube with slip flow models

In this study, a two-dimensional steady state simultaneously developing laminar flow inside a micro-tube is investigated numerically under slip flow conditions. The first and second-order slip flow models have been implemented for the case where the viscous dissipation and axial conduction are included and a constant wall temperature boundary condition is specified. The results are obtained for several combinations of the Knudsen number Kn, the coefficient β and the Brinkman number Br. The study reveals a significant impact of slip flow and temperature jump on the hydrodynamic and thermal fields. A comparison of the first and second-order slip flow shows a considerable variation of the hydrodynamic flow and a weak impact on the thermal field particularly when the flow is fully developed.

Advance in research of several types of streaming of pulse tube refrigerators

The pulse tube refrigerator (PTR) is a promising small-scale cryocooler. This paper first briefly introduces the history of the pulse tube refrigerator. It has pointed out that technology improvements and theoretical developments of the pulse tube refrigerator closely relate with the internal streaming effects. Then the discovering history and classification of the streaming or DC (direct current) flow effect are summarized. It proposes for the first time that the physical significance of the streaming contains the driving mechanisms and the transport mechanisms. It demonstrates that the driving mechanisms are the asymmetry of fluid flow and temperature while the transport mechanisms are a loop or vorticity, which transmits nonlinear dissipations. The important advancements have been made over the past two decades all over the world in research of streaming of the pulse tube refrigerator including Gedeon DC flow, Rayleigh streaming, the third type of DC flow and the regenerator circulation. With regard to Gedeon DC flow, theoretical and experimental analyses have been made and different suppression methods are summarized. In the aspect of Rayleigh streaming, it mainly focuses on the analytical solution of the second-order mass flow and the research of tapered pulse tubes. In particular, limited research on the third type of DC flow and regenerator circulation is presented. The experimental measurement techniques of streaming also are summarized. Finally, this paper briefly discusses the key scientific and technical issues of the current research, and foretells the future development trends of streaming research in PTR.