Exact solutions of starting flows for second grade fluid in a porous medium

This paper concentrates on the unsteady flows of a magnetohydrodynamic (MHD) second grade fluid filling a porous medium. The flow modeling involves modified Darcy's law. Three problems are considered. They are (i) starting flow due to an oscillating edge, (ii) starting flow in a duct of rectangular cross-section oscillating parallel to its length, and (iii) starting flow due to an oscillating pressure gradient. Analytical expressions of velocity field and corresponding tangential stresses are developed. These expressions are found to be significantly affected by the applied magnetic field, permeability of the porous medium and the material parameter of the fluid. Moreover, the influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn. Finally, a comparison is also made with the existing results in the literature.     

On two-dimensional laminar flows of a particulate suspension in the presence of gravity field

Three simple two-dimensional streaming motions of a mixture of solid particles with a continuous carrier fluid, or gas, in the presence of the gravity field are considered. These include flow of a mixture over an infinite stationary rigid plane perpendicular to the direction of the gravity field, flow near an oscillating rigid plane and flow in a mixture induced by a suddenly accelerated plane. The nature of the boundary conditions at the interface between a layer of sediment settling on the rigid boundary and the mixture above it suggests an introduction of the independent variables that enable simple analytical expressions for the solutions of the first two flows and a numerical solution by means of a Laplace transform in the last case.     

DNS of secondary flows over oscillating low-pressure turbine using spectral/hp element method

This paper investigates the secondary vortex flows over an oscillating low-pressure turbine blade using a direct numerical simulation (DNS) method. The unsteady flow governing equations over the oscillating blade are discretized and solved using a spectral/hp element method. The method employs high-degree piecewise polynomial basis functions which results in a very high-order finite element approach. The results show that the blade oscillation can significantly influence the transitional flow structure and the wake profile. It was observed that the separation point over vibrating T106A blades was delayed 4.71% compared to the stationary one at Re = 51,800. Moreover, in the oscillating case, the separated shear layers roll up, break down and shed from the trailing edge. However, the blade vibration imposes additional flow disturbances on the suction surface of the blade before leaving from the trailing edge. Momentum thickness calculations revealed that after flow separation point, the momentum thickness grows rapidly which is due to the inverse flow gradients which generate vortex flows in this area. It was concluded that the additional vortex generations due to the blade vibrations cause higher momentum thickness increment compared to the conventional stationary LPT blade.     

Planar dynamics of inclined curved flexible riser carrying slug liquid–gas flows

Flexible risers transporting hydrocarbon liquid–gas flows may be subject to internal dynamic fluctuations of multiphase densities, velocities and pressure changes. Previous studies have mostly focused on single-phase flows in oscillating pipes or multiphase flows in static pipes whereas understanding of multiphase flow effects on oscillating pipes with variable curvatures is still lacking. The present study aims to numerically investigate fundamental planar dynamics of a long flexible catenary riser carrying slug liquid–gas flows and to analyse the mechanical effects of slug flow characteristics including the slug unit length, translational velocity and fluctuation frequencies leading to resonances. A two-dimensional continuum model, describing the coupled horizontal and vertical motions of an inclined flexible/extensible curved riser subject to the space–time varying fluid weights, flow centrifugal momenta and Coriolis effects, is presented. Steady slug flows are considered and modelled by accounting for the mass–momentum balances of liquid–gas phases within an idealized slug unit cell comprising the slug liquid (containing small gas bubbles) and elongated gas bubble (interfacing with the liquid film) parts. A nonlinear hydrodynamic film profile is described, depending on the pipe diameter, inclination, liquid–gas phase properties, superficial velocities and empirical correlations. These enable the approximation of phase fractions, local velocities and pressure variations which are employed as the time-varying, distributed parameters leading to the slug flow-induced vibration (SIV) of catenary riser. Several key SIV features are numerically investigated, highlighting the slug flow-induced transient drifts due to the travelling masses, amplified mean displacements due to the combined slug weights and flow momenta, extensibility or tension changes due to a reconfiguration of pipe equilibrium, oscillation amplitudes and resonant frequencies. Single- and multi-modal patterns of riser dynamic profiles are determined, enabling the evaluation of associated bending/axial stresses. Parametric studies reveal the individual effect of the slug unit length and the translational velocity on SIV response regardless of the slug characteristic frequency being a function of these two parameters. This key observation is practically useful for the identification of critical maximum response.     

Reversible and Irreversible Tracer Dispersion in an Oscillating Flow Inside a Model Rough Fracture

We study the mixing dynamics of a dyed and a clear miscible fluid by an oscillating flow inside an Hele-Shaw cell with randomly distributed circular obstacles. A transparent setup allows us to analyze the distribution of the two fluids and the reversible and irreversible mixing components. At the lower Péclet numbers Pe (based on the averaged absolute fluid velocity), geometrical dispersion due to the disordered flow field between the obstacles is dominant: the corresponding dispersivity is constant with Pe and, at constant Pe, increases with the amplitude of the oscillations and is negligible at small ones. Compared to echo dispersion with only one injection–suction cycle, oscillating flows are shown to provide additional information when the number of oscillations and, as a result, the distance of transverse mixing are varied. Geometrical dispersion is dominant up to a limiting Pe increasing with the amplitude. At higher \({\textit{Pe}}'{\textit{s}}\), the results are similar to those of Taylor dispersion in cells with smooth walls.     

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

Experimental investigation of the fluid–structure interaction in an elastic 180° curved vessel at laminar oscillating flow

Fluid–structure interaction phenomena are extremely important when laminar flows through elastic vessels such as in biomedical flow problems are considered. In general, such elastic vessels are curved which is why an elastic 180° bend at a curvature ratio \(\delta = D/D_{\rm C} = 0.\bar{2}\) defines the reference geometry in this study. It is the purpose of this study to compare the results with the steady flow through a 180° rigid pipe bend and to quantify the impact of the fluid–structure interaction on the overall flow pattern and the vessel deformation at oscillating fully developed entrance flow. The findings comprise velocity, pressure, and structure deformation measurements. The vessel dilatation amplitude was varied between 3.75 % and 7 % of the vessel diameter at Dean De and Womersley number Wo ranges of \(327\,\le\,De\,\le\,350\) and \(7\,\le\,Wo\,\le\,8.\) The flow is investigated by time-resolved stereoscopic particle-image velocimetry in five radial cross sections located in the elastic 180° bend and in the inlet pipes. The unsteady static vessel pressure is measured synchronously at these cross sections. The comparison of the steady with the unsteady flow field shows a strong change in the axial and secondary velocity distributions at periods of transition between the centrifugal forces and the unsteady inertia forces dominated regimes. These changes are characterized by asymmetric fluctuations of the centers of the counter-rotating vortex pair. The investigation of the impact of the structure deformation amplitude on these fluctuations reveals a significant attenuation at high deformation amplitudes. The spatial motion of the elastic vessel due to the forces applied by the flow exhibits amplitudes up to 15 % of the vessel diameter. Considering the fluid–structure interaction, an amplification of the volume flux amplitude by a factor of 2.1 at the vessel outlet and phase lags up to 30° occur. The static pressure distribution is characterized by a pronounced asymmetry between forward and backward flow with a 40 % higher peak magnitude at backward flow and phase lags of 35°. The results evidence that a strong distortion of the velocity distribution in the bend, which is caused by the oscillating nature of the flow, is reduced as a result of the fluid–structure interaction.     

Natural convection induced in a fluid by the hot inner walls of a “submerged” channel

The jet flows induced around a submerged channel due to the hot inner channel walls and the flow inside the channel are calculated. The formation of high-and low-density regions at the inlet and outlet of the channel is detected. The dependence of the flow rate on the channel orientation relative to the gravity force is analyzed. The onset of coherent flow structures results in the development of unsteady oscillating flows. Natural convection in the fluid is studied using the JoinCAD/FEM program package. The regularized Oberbeck-Boussinesq equations are solved using a finite-element method with the same order of the approximating functions.     

The effect of magnetic fields on low frequency oscillating natural convection with pressure gradient

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐｒｅｓｅｎｔｐａｐｅｒ,ａｃｏｍｐｕｔａｔｉｏｎａｌｓｔｕｄｙｏｆｔｈｅｅｆｆｅｃｔｏｆｍａｇｎｅｔｉｃｆｉｅｌｄｏｎｌｏｗｆｒｅｑｕｅｎｃｙｏｓｃｉｌｌａｔｉｎｇｎａｔｕｒａｌｃｏｎｖｅｃｔｉｏｎｗｉｔｈｐｒｅｓｓｕｒｅｇｒａｄｉｅｎｔｉｓｃａｒｒｉｅｄｏｕｔ.Ｔｈｅｒｅｈａｓｂｅｅｎａｒｅｃｅｎｔｉｎｔｅｒｅｓｔｉｎｅｘｐｌｏｒｉｎｇｔｈｅｍａｇｎｅｔｉｃｄａｍｐｉｎｇｅｆｆｅｃｔｓｔｏｓｕｐｅｒｉｍｐｏｓｅｏｖｅｒｍｉｃｒｏｇｒａｖｉｔｙｆｏｒａｆｕｒｔｈ…     

垂直参数激励表面波研究进展

受外激励的充液刚性容器中流体的波动问题有实际的工程应用背景.竖直方向的受周期性外激励的充液容器的自由表面波问题--Faraday波问题是流体力学三大不稳定性难题之一(另外两个不稳定性问题是Rayleigh-B\'enard对流和Taylor-Couette流).本文综述了在理想流体中和弱粘性流体中Faraday波的研究成果;介绍了作者在底部垂直激励的圆柱形容器中流体表面波图谱的实验研究和理论分析的结果.最后提出有待进一步研究的问题.图13,参74      

Turbulent Duct Flow Controlled with Spanwise Wall Oscillations

The spanwise oscillation of channel walls is known to substantially reduce the skin-friction drag in turbulent channel flows. In order to understand the limitations of this flow control approach when applied in ducts, direct numerical simulations of controlled turbulent duct flows with an aspect ratio of A R = 3 are performed. In contrast to channel flows, the spanwise extension of the duct is limited. Therefore, the spanwise wall oscillation either directly interacts with the duct side walls or its spatial extent is limited to a certain region of the duct. The present results show that this spanwise limitation of the oscillating region strongly diminishes the drag reduction potential of the control technique. We propose a simple model that allows estimating the achievable drag reduction rates in duct flows as a function of the width of the duct and the spanwise extent of the controlled region.     

浅谈动脉流体动力学分析

就我们所熟知,绝大部分正常动脉流,其血液的流动特性是属于层流范围,但随着弯曲和分 支部分会产生血液流之二次回流区,进而形成所谓近似非稳态流及紊流. 因此动脉流体的特 性会随动脉外形及条件的改变而改变. 在某些情形下,异常动脉的血液动力特性会造成动脉 的病变. 因此,近年来动脉血液流体的特性的研究,常着重于异常动脉的血液动力特性所形 成剪应力和病变部位动脉粥状硬化关系的探讨. 动脉血液流动经常包含分离流或二次回流运动,而这是流体力学的分析或数值模拟最困难的 部分. 有关分离流或二次回流的研究包括正常血管流和异常血管流,藉由二次回流的模拟与 测量可以观察血管病变的形成与演变,其中最受注目探讨题目是窄化血管如粥状斑块相关的 血液流动分析. 将回顾二维和三维、稳态、非稳态之动脉血流与窄化血管相关的几何外形作模拟研究和 实验. 并提供对血液动力学的研究方向,以作为未来医疗诊断与发展相关器材之参考.     

LDA measurements of steady streaming flows of Newtonian and viscoelastic fluids

LDA experiments have been conducted in a two-dimensional steady streaming flow field in order to determine the secondary velocity profiles. We describe here an LDA system developed to resolve small secondary-flow velocities and to detect flow reversals due to viscoelasticity. Results compare well with theoretical predictions. A detailed analysis of the errors and uncertainties involved in the measurements confirms the reliability and reproducibility of the measurements. Although the method has been applied here to a specific flow field, the technique should be applicable to a number of secondary flows, such as those which can occur in curved pipes and in oscillating pipe flows.The authors have benefited from discussions with Professor Bruce Chehroudi, from the Department of Mechanical Engineering, University of Illinois at Chicago. This work was supported by the Office of Naval Research through Contract Number N00015-85-K-0201.     

Trochoidal Solutions to the Incompressible Two-Dimensional Euler Equations

Within the Lagrangian framework we present an approach yielding some explicit solutions to the incompressible two-dimensional Euler equations, generalizing the celebrated Gerstner flow. The solutions so obtained, for which explicit formulas of each particle trajectory are provided, represent either flows in domains with a rigid boundary or free-surface flows for a fluid of infinite depth. For some of these solutions the trajectories are epitrochoids or hypotrochoids. Possibilities for obtaining further flows of this type are indicated.     

Pressure drop and friction factor of steady and oscillating flows in open-cell porous media

Open-cell metal foams are often used in heat exchangers and absorption equipment because they exhibit large specific surface area and present tortuous coolant flow paths. However, published research works on the characteristics of fluid flow in metal foams are relatively scarce, especially for the flow oscillation condition. The present experimental investigation attempts to uncover the behavior of steady and oscillating flows through metal foams with a tetrakaidecahedron structure. In the experiments, steady flow was supplied by an auto-balance compressor and flow oscillation was provided by an oscillating flow generator. The pressure drop and velocity were measured by the differential pressure transducer and hot-wire sensor, respectively. The friction factor of steady flow in metal foam channel was analyzed through the permeability and inertia coefficient of the porous medium. The results show that flow resistance in the metal foams increases with increasing form coefficient and decreasing permeability. The empirical equation obtained by the present study indicates that the maximum friction factor of oscillating flow through the tested aluminum foams with specific structure is governed by the hydraulic ligament diameter-based kinetic Reynolds number and the dimensionless flow amplitude.     

A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders

The behavior of vortices induced by a pair of side-by-side square cylinders in an oscillating flow is investigated using an in-house numerical model. The study is carried out for various Keulegan–Carpenter numbers, Reynolds numbers, and cylinder gap spacings. For an oscillating flow past a pair of side-by-side cylinders, the gap ratio plays a vital role in the flow pattern. A jet-like structure is observed when fluid flows through the gap. Moreover, the gap promotes the earlier appearance of asymmetric vortex shedding. In-line force and lift force coefficients of two square cylinders are analyzed using spectral analysis. An autocorrelation function is used to determine the relation between flow patterns around two cylinders. These results demonstrate the transition of the flow field from the periodic state to the chaotic state.     

The effect of the slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions

Stokes and Couette flows produced by an oscillatory motion of a wall are analyzed under conditions where the no-slip assumption between the wall and the fluid is no longer valid. The motion of the wall is assumed to have a generic sinusoidal behavior. The exact solutions include both steady periodic and transient velocity profiles. It is found that slip conditions between the wall and the fluid produces lower amplitudes of oscillations in the flow near the oscillating wall than when no-slip assumption is utilized. Further, the relative velocity between the fluid layer at the wall and the speed of the wall is found to overshoot at a specific oscillating slip parameter or vibrational Reynolds number at certain times. In addition, it is found that wall slip reduces the transient velocity for Stokes flow while minimum transient effects for Couette flow is achieved only for large and small values of the wall slip coefficient and the gap thickness, respectively. The time needed to reach to steady periodic Stokes flow due to sine oscillations is greater than that for cosine oscillations with both wall slip and no-slip conditions.     

Flow measurement on an oscillating pipe flow near the entrance using the UVP method

 The authors have carried out a study to investigate and clarify the characteristics of purely oscillating pipe flows over the developing region. The main objective of this study is to establish the method of time-dependent velocity profiles obtained by the ultrasonic velocity profile (UVP) measurement method. First, the relationship between the test fluids and the microparticles, as reflectors of ultrasonic pulses, was investigated. In addition, the relationship between the sound speeds of the test fluids and the wall materials was studied. Second, the UVP was used to obtain the instantaneous velocity profiles in oscillating pipe flows, and the developing characteristics of the flows were analyzed. Finally, the “entrance length” (by analogy with a unidirectional pipe flow) required for oscillating pipe flows was analyzed by examining the amplitude of the harmonic spectral components of the oscillating frequency. A fast Fourier transform (FFT) is proposed as the applicable method to estimate the “entrance length”. From the Fourier transform of the velocity on the centerline, nonlinear oscillation of fluid occurs in the “entrance length” of the oscillating flows, and the viscous dissipation of the higher-order velocity harmoncis determines the entrance region. The “entrance length” can be obtained from the dissipation length of the third-order harmonic. These results prove that the UVP method is highly applicable to carry out the flow measurement in the “entrance length” of oscillating pipe flow. Received: 20 March 2000 / Accepted: 10 August 2001     

On the immersed boundary‐lattice Boltzmann simulations of incompressible flows with freely moving objects

For simulating freely moving problems, conventional immersed boundary‐lattice Boltzmann methods encounter two major difficulties of an extremely large flow domain and the incompressible limit. To remove these two difficulties, this work proposes an immersed boundary‐lattice Boltzmann flux solver (IB‐LBFS) in the arbitrary Lagragian–Eulerian (ALE) coordinates and establishes a dynamic similarity theory. In the ALE‐based IB‐LBFS, the flow filed is obtained by using the LBFS on a moving Cartesian mesh, and the no‐slip boundary condition is implemented by using the boundary condition‐enforced immersed boundary method. The velocity of the Cartesian mesh is set the same as the translational velocity of the freely moving object so that there is no relative motion between the plate center and the mesh. This enables the ALE‐based IB‐LBFS to study flows with a freely moving object in a large open flow domain. By normalizing the governing equations for the flow domain and the motion of rigid body, six non‐dimensional parameters are derived and maintained to be the same in both physical systems and the lattice Boltzmann framework. This similarity algorithm enables the lattice Boltzmann equation‐based solver to study a general freely moving problem within the incompressible limit. The proposed solver and dynamic similarity theory have been successfully validated by simulating the flow around an in‐line oscillating cylinder, single particle sedimentation, and flows with a freely falling plate. The obtained results agree well with both numerical and experimental data. Copyright © 2016 John Wiley & Sons, Ltd.