LINEAR AND NONLINEAR DYNAMICS OF CANTILEVERED CYLINDERS IN AXIAL FLOW. PART 1: PHYSICAL DYNAMICS

This paper is the first in a three-part study of the dynamics of cantilevered cylinders in axial flow. After an extensive literature review, the physical dynamics of the system is examined; specifically (a) the experimental behaviour of elastomer cylinders in water flow, and (b) the energy transfer mechanisms, discussed from a work–energy perspective without solving the equations of motion. In general, the system loses stability by divergence and, as the flow velocity is increased, it is subject to second- and third-mode flutter, provided that the free end is well-streamlined; if, however, the free end is blunt, these instabilities do not occur. Oscillations are generally three-dimensional (orbital). The experimental observations are in good qualitative agreement with those expected from the energy transfer analysis, and in reasonably good quantitative agreement with solutions of the linearized equation of motion (obtained from Part 3 of this study). For some shapes of the free-end, resonances are observed with a fairly constant Strouhal number.     

On possible mechanisms of generation of a support by fishes at explosive accelerations

Methods of creating large specific supports during the explosive motion of a model profile, which are related with the generation of both self-similar flow with a closed dead zone of maximum possible volume and a circulatory flow, are considered. Possible mechanisms of using by birds and marine animals of the vortex energy of both the surrounding medium and a system of Π-shaped vortex bunches for facilitating their motion are discussed.     

Transient flow of magnetized Maxwell nanofluid: Buongiorno model perspective of Cattaneo-Christov theory

The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties. The Maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy. The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws, respectively. Additionally, the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the Maxwell fluid. The governing partial differential equations (PDEs) for the flow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation. Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations (ODEs). The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution. The results for the time relaxation parameter in the flow, thermal energy, and mass transport equations are discussed graphically. It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid. Further, larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid. Moreover, the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field. The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.     

Tensegrity deployment using infinitesimal mechanisms

Kinematic properties of tensegrity structures reveal that an ideal way of motion is by using their infinitesimal mechanisms. For example in motions along infinitesimal mechanisms there is no energy loss due to linearly kinetic tendon damping. Consequently, a deployment strategy which exploits these mechanisms and uses the structure’s nonlinear equations of motion is developed. Desired paths that are tangent to the directions determined by infinitesimal mechanisms are constructed and robust nonlinear feedback control is used for accurate tracking of these paths. Examples demonstrate the feasibility of this approach and further analysis reveals connections between the power and energy dissipated via damping, infinitesimal mechanisms, speed of the motion, and deployment time.     

Effect of Longitudinal Forced Motion on the Stability of Convection in a Plane Vertical Layer with Internal Heat Sources

The effect of longitudinal forced fluid motion on the mechanisms of instability of a convection flow developing in a plane vertical layer in the presence of internal heat sources is considered. It is found that forced motion which intensifies the central stream of the convection flow can lead to moderate stabilization of the hydrodynamic and thermal crisis mechanisms. In the presence of counterstream forced motion the flow stability increases sharply.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 14–17.Original Russian Text Copyright © 2005 by Lobov.     

A preliminary study of 3D difference scheme with energy dynamic equilibrium

In this paper, a difference scheme with energy dynamic equilibrium (DS-EDE) is presented, which can be used for the simulation of long-term atmosphere and sea motion. Based on three dimensional nonlinear evolution equations for atmosphere and sea motion, a three dimensional compact upwind scheme (CUWS) is constructed, as the basis of the DS-EDE. The DS-EDE satisfies the following condition of energy dynamic equilibrium (EDE): the total work of external forces on the region boundary is equal to the sum of the total effective variation of the kinetic energy and the energy dissipation in the average flow motion and the effective variation of the potential energy per unit time within the region of interest. It really reflects the basic mechanism of the action of external forces and dissipation in atmosphere and sea movement. Therefore, the DS-EDE developed in this paper is a suitable model for simulating long-term atmosphere and sea movement with forcing and dissipation.     

Cycle-to-cycle variation analysis of in-cylinder flow in a gasoline engine with variable valve lift

In spark ignition engines, cycle-to-cycle variation (CCV) limits the expansion of the operating range because it induces the load variations and the occurrence of misfire and/or knock. Variable valve actuation (VVA) or variable valve lift (VVL) has been widely used in SI engines to improve the volumetric efficiency or to reduce the pumping losses. It is necessary to investigate the CCV of in-cylinder gas motion and mixing processes in SI engines with VVA/VVL system. This study is aimed to analyze the CCV of the tumble flow in a gasoline direct injection (GDI) engine when VVL is employed. Cycle-resolved digital particle image velocimetry (CRD-PIV) data were acquired for the in-cylinder flow field of a motored four-stroke multi-valve GDI optical engine. The CCV of in-cylinder gas motion with a series of valve profiles and different maximum valve lift (MVL) was analyzed, including cyclic variation characteristics of bulk flow (tumble centre and tumble ratio), large- and small-scale fluctuation, total kinetic energy, and circulation. The results show that the CCV of the in-cylinder flow is increased with reduced MVL. With lower MVLs, stable tumble flow cannot be formed in the cylinder, and the ensemble-averaged tumble ratio decreases to zero before the end of the compression stroke due to violent variation. In addition, the evolution of the circulation shows larger variation with lower MVLs that indicates the ??spin?? of the small-scale eddy in the flow field presents violent fluctuation from one cycle to another, especially at the end of the compression stroke. Moreover, the analyze of the kinetic energy indicates the total energy of the flow field with lower MVLs increases significantly comparing with higher MVL conditions due to the intake flow jet at the intake valve seat in the intake stroke. However, the CCV of the in-cylinder flow becomes more violent under lower MVL conditions, especially for the low-frequency fluctuation kinetic energy. Thus, present strong tumble flow can lower the CCV of the air motion. It is necessary to manage strong tumble or other bulk flow (such as swirl flow) in order to improve the stability of ignition and combustion for GDI engines with VVL, especially at the lower MVL conditions.     

Vortex motion in a rotating barotropic fluid layer

To study vortex motion and the mechanisms of geostrophic adjustment (i.e. the equilibrium between pressure gradient and Coriolis force, which leads to the weakening of inertio-gravity waves) in large scale geophysical flows, we simulate the dynamics of a shallow-water layer in uniform rotation, without any forcing other than the initial injection of energy and potential enstrophy. Such a flow generates inertio-gravity waves which interact with the rotational eddies. We found that both inertio-gravity waves and rotation reduce the non-linear interactions between vortices, namely the condensation of the vorticity field into isolated coherent vortices, corresponding to the inverse rotational energy cascade, and the associated production of vorticity filaments, due to the direct potential enstrophy cascade. Rotation also inhibits the direct inertio-gravitational energy cascade for scales larger than the Rossby deformation radius. Therefore, if inertio-gravity waves are initially excited at large enough scales, they will remain trapped there due to rotation and there will be no geostrophic adjustment. On the contrary, if inertio-gravity waves are only present at scales smaller than the Rossby deformation radius, which are insensitive to the effect of rotation, they will non-linearly interact and cascade towards the dissipative scales, leaving the flow in geostrophic equilibrium.     

Stereoscopic multi-planar PIV measurements of in-cylinder tumbling flow

The non-reacting flow field within the combustion chamber of a motored direct-injection spark-ignition engine with tumble intake port is measured. The three-dimensionality of the flow necessitates the measurement of all three velocity components via stereoscopic particle-image velocimetry in multiple planes. Phase-locked stereoscopic PIV is applied at 15 crank angles during the intake and compression strokes, showing the temporal evolution of the flow field. The flow fields are obtained within a set of 14 axial planes, covering nearly the complete cylinder volume. The stereoscopic PIV setup applied to engine in-cylinder flow and the arising problems and solutions are discussed in detail. The three-dimensional flow field is reconstructed and analyzed using vortex criteria. The tumble vortex is the dominant flow structure, and this vortex varies significantly regarding shape, strength, and position throughout the two strokes. The tumble vortex center moves clockwise through the combustion chamber. At first, the tumble has a c-shape which turns into an almost straight tube at the end of the compression. Small-scale structures are analyzed by the distribution of the turbulent kinetic energy. It is evident that the symmetry plane only represents the 3D flow field after 100 CAD. For earlier crank angles, both kinetic energy (KE) and turbulent kinetic energy (TKE) in the combustion chamber are well below the KE and TKE in the symmetry plane. This should be taken into account when the injection and breakup of the three-dimensional fuel jet are studied. The mean kinetic energy is conserved until late compression by the tumble motion. This conservation ensures through the excited air motion an enhancement of the initial air-fuel mixture which is of interest for direct-injection gasoline engines.     

Crack arrest in elastic sheets

The analysis of the motion of a crack of finite length extending in an infinite isotropic elastic sheet loaded in the extensional mode forms the basis for the treatment of the motion and the arrest of a brittle crack in a more general two-dimensional structure of finite size. The energy flow to the cracktip is expressed in terms of the value of the static J-integral times a dynamic function depending on the instantaneous crack-tip velocity. This energy flow is equal to the fracture energy which is supposed to be a specific function only of the crack-tip velocity for a given material. If the energy release (calculated as described) becomes less than the fracture energy in some segment along the prospective fracture path, then additional energy will be needed for the crack to be propagated. Such additional energy is available owing to the kinetic state of the structure. An upper limit to the amount of additional energy is determined. A conservative crack-arrest condition is given by the assumption that all this additional energy is consumed in a continued slow extension of the crack. Experimental results for edge-cracked sheets of polymethylmethacrylate conform well with the crack-arrest condition suggested.     

Numerical investigation of the turbulent energy budget in the wake of freely oscillating elastically mounted cylinder at low reduced velocities

We present a numerical study of the turbulent kinetic energy budget in the wake of cylinders undergoing Vortex-Induced Vibration (VIV). We show three-dimensional Large Eddy Simulations (LES) of an elastically mounted circular cylinder in the synchronization regime at Reynolds number of Re=8000. The Immersed Boundary Method (IBM) is used to account for the presence of the cylinder. The flow field in the wake is decomposed using the triple decomposition splitting the flow variables in mean, coherent and stochastic components. The energy transfer between these scales of motions are then studied and the results of the free oscillation are compared to those of a forced oscillation. The turbulent kinetic energy budget shows that the maximum amplitude of VIV is defined by the ability of the mean flow to feed energy to the coherent structures in the wake. At amplitudes above this maximum amplitude, the energy of the coherent structures needs to be fed additionally by small scale, stochastic energy in form of backscatter to sustain its motion. Furthermore, we demonstrate that the maximum amplitude of the VIV is defined by the integral length scale of the turbulence in the wake.     

Boundary layer flow of Maxwell fluid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field. The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial differential equations (PDEs) governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the flow becomes turbulent. Thus, the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the flow, heat, and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion. The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.     

An analysis model of pulsatile blood flow in arteries

IntroductionTheperiodicallypulsatilebloodflowinthearterycausesthecircumferentialandaxialmotionoftheelasticbloodvesselandinturntheoscillationofthevesselaffectsthatofthebloodflow .Womersley[1]resolvedsuccessfullythisfluid_solidcouplingproblembysolvingbothlinearNavier_Stokesequationsandthemotionequationsofthethin_walledelastictubeandgainedtheexpressionsofthebloodflowvelocitiesandthevasculardisplacements.Histheoryhasbeenthebasisforthequantitativeanalysisoftherelationshipofthearterialstructureandi…     

关于颗粒悬浮机理和悬浮动的讨论

从分析气体分子的悬浮和静水中Ｂｒｏｗｎ微粒的悬浮之机理出发，论述了重力场中粒子（分子、微粒等）的悬浮不一定需要其它外力，粒子本身的任何形式的无规则运动，达到一定强度后都能使粒子弥散悬浮．河流中的泥沙颗粒和气（水）力输送管道中的颗粒的悬浮也主要靠颗粒物的无规则运动．作用于颗粒的升力和其它力可改变颗粒悬浮沿高度的分布，但仅用这些力（若无任何无规则运动）无法解释颗粒的弥散悬浮状态．讨论了颗粒对流动阻力的双重作用：支持颗粒悬浮的湍流脉动因引入颗粒而削弱，这是颗粒的减阻作用；颗粒增阻的一个主要机制是，流体给予颗粒的水平动量在颗粒一壁面碰撞中不断地损失．用悬浮动概念解释颗粒引起的增阻是不正确的．     

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.     

Amplification and amplitude limitation of heave/pitch limit-cycle oscillations close to the transonic dip

Recent results from flutter experiments of the supercritical airfoil NLR 7301 at flow conditions close to the transonic dip are presented. The airfoil was mounted with two degrees-of-freedom in an adaptive solid-wall wind tunnel, and boundary-layer transition was tripped. Flutter boundaries exhibiting a transonic dip were determined and limit-cycle oscillations (LCOs) were measured. The local energy exchange between the fluid and the structure during LCOs is examined and leads to the following findings: at supercritical Mach numbers below that of the transonic-dip minimum the presence of a shock-wave and its dynamics destabilizes the aeroelastic system such that the decreasing branch of the transonic dip develops. At higher Mach numbers the shock-wave motion has a stabilizing effect such that the flutter boundary increases to higher flutter-speed indices with increasing Mach number. Amplified oscillations near this branch of the flutter boundary obtain energy from the flow mainly due to the dynamics of a trailing-edge flow separation. A slight nonlinear amplitude dependency of the shock motion and a possibly occurring boundary-layer separation cause the amplitude limitation of the observed LCOs. The impact of the findings on the numerical simulation of these phenomena is discussed.     

Error quantification of 3D homogeneous and isotropic turbulence measurements using 2D PIV

Particle image velocimetry (PIV) has become a popular non-intrusive tool for measuring various types of flows. However, when measuring three dimensional flows with 2D PIV, there is inherent measurement error due to out-of-plane motion. Errors in the measured velocity field propagate to turbulence statistics. Since this can distort the overall flow characteristics, it is important to understand the effect of this out-of-plane error. In this study, the effect of out-of-plane motion on turbulence statistics is quantified. Using forced isotropic turbulence direct numerical simulation (DNS) flow field data provided by the Johns Hopkins turbulence database (JHTDB), synthetic image tests are performed. Turbulence statistics such as turbulence kinetic energy, dissipation rate, Taylor microscale, Kolmogorov scale, and velocity correlations are calculated. Various test cases were simulated while controlling three main parameters which affect the out-of-plane motion: PIV interrogation window size, camera inter-frame time, and laser sheet thickness. The amount of out-of-plane motion was first quantified, and then the error variation according to these parameters was examined. This information can be useful when examining fully three dimensional flows such as homogeneous and isotropic turbulence via 2D PIV.     

Numerical simulation of the horizontal Bridgman growth. Part III: Calculation of the interface

We study the transient motion of the solidification front during the growth of semiconductor crystals in the horizontal Bridgman geometry. The calculation is based on a two-dimensional flow. We use finite elements which deform with the motion of the interface. The energy equation is coupled with the isothermal constraint of the interface in an implicit transient algorithm. Several examples show the oscillatory motion of the interface caused by the periodic flow of the melt, and they reveal the importance of the growth rate on the shape of the interface.     

Over-reflection and instabilities in shear flows of shallow water with bottom friction

In a two-dimensional shear flow of shallow water, the bottom friction relates uniquely the spanwise profile of the depth-averaged velocity to the bottom topography. If the basic flow varies weakly in the spanwise direction, the local analysis of stability at every spanwise position gives the region of the flow parameters for which the classic hydraulic instability due to the bottom friction cannot occur. In this region, the linear analyses of the waves scattering and instability due to the lateral shear can be performed effectively by means of the frictionless linearized equations if both the bottom slope and friction are equally small.The energy of the total perturbed flow can be split into three main parts that correspond to the basic flow, small amplitude wave motion and induced mean flow. The waves can be either amplified or damped near the critical layers, where their streamwise phase velocity equals the velocity of the basic flow. Two physical mechanisms of this amplification exist. The first one is similar to that suggested by Takehiro and Hayashi for a linear frictionless shallow water flow. The incident and transmitted waves carry energy of opposite signs, which results in an increase in the amplitude of the reflected wave compared to that of the incident one. This mechanism of over-reflection operates for any combination of the flow parameters. The other mechanism is similar to Landau damping in plasma flows; it is related to the energy exchange between the waves and fluid particles at the critical layers due to the velocity synchronism. It may lead to either additional amplification or damping of the waves for different flow conditions. In particular, its significance can be reduced by stronger bottom friction. If the basic flow has uniform potential vorticity, Landau damping is negligible, and over-reflection always occurs. If the feed-back is provided by another critical layer, the net over-reflection results in the formation of trapped modes.     

Investigation of the Effect of the In-Cylinder Tumble Motion on Cycle-to-Cycle Variations in a Direct Injection Spark Ignition (DISI) Engine Using Large Eddy Simulation (LES)

Cycle-to-cycle variations (CCVs) limit the extension of the operating range by inducing load variations and even misfire and/or knock for direct injection spark ignition (DISI) engines and hence need to be controlled. One of the effective and flexible ways to reduce CCV is to employ a charge motion control valve. This study is aimed to analyze the flow characteristics and CCV using large eddy simulation (LES) and fast Fourier transform (FFT) in a non-reacting, DISI engine equipped with a tumble flap (i.e., a specific type of charge motion control valve) inside the intake port. The in-cylinder flow characteristics are analyzed in detail, and the possible effects of multi-scale structures of the fluid field on the subsequent ignition and combustion processes are also discussed. Computational results indicate that closing the tumble flap helps enhance the intensity of the coherent structures and increase the total integral length scale (ILS) while decreasing the Kolmogorov scale and stabilizing the flow field by suppressing the CCV of tumble ratio and tumble center. Furthermore, based on a newly developed FFT triple decomposition, each instantaneous flow field is decomposed into three subfields, termed ensemble mean part and low- and high-spatial frequency parts, respectively. It is found that switching the tumble flap position greatly affects the first two subfields, but it has negligible effect on the last part. With the closed tumble flap, the energy portion of the mean part increases, the rate of energy decay reduces, and the CCV of the low- and high-spatial frequency parts decreases.