Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Applicability Range of Stoneys Formula and Modified Formulas for a Film/Substrate Bilayer

In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

Flow Characteristics and Its Friction Coefficient of Laminar Near-Wall Boundary Layer in Dusty Atmosphere

采用双向耦合的双流体模型,研究了大气悬浮沙尘的存在对大气边界层中层流底层流动特性及摩阻系数的影响,计算并讨论了不同沙尘含量下含尘大气相对于无尘大气摩阻系数的变化。结果表明：摩阻系数的变化取决于悬浮沙尘的初始运动状态和质量载荷率。

Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma=0.7

Direct numerical simulation (DNS) of a spatially evolving flat-plate boundary layer transition process at free stream Mach number 0.7 is performed. Tollmien-Schlichting (T-S) waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the transition process plays an important role in the laminar breakdown process.

Experimental Study on Vortex-Induced Vibrations of Submarine Pipeline Near Seabed Boundary in Ocean Currents

Unlike most previous studies on vortex- induced vibrations of a cylinder far from a boundary, this paper focuses On the influences of close proximity of a submarine pipeline to a rigid seabed boundary upon the dynamic responses of the pipeline in ocean currents. The effects of gap-to-diameter ratio and those of the stability parameter on the amplitude and frequency responses of a pipeline are investigated experimentally with a novel hydro-elastic facility. A comparison is made between the present experimental results Of the amplitude and frequency responses for the pipes with seabed boundary effects and those for wall-free cylinders given by Govardhan and Williamson (2000) and Anand ( 1985). The comparison shows that the close proximity of a pipeline to seabed has much influence on the vortex- induced vibrations of the pipeline. Both the width of the lock-in ranges in terms of V, and the dimensionless amplitude ratio A(max)/D become larger with the decrease of the gap-to-diameter ratio e/D. Moreover, the vibration of the pipeline becomes easier to occur and its amplitude response becomes more intensive with the decrease of the stability parameter, while the pipeline frequency responses are affected slightly by the stability parameter.

Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Direct Numerical Simulation of Supersonic Turbulent Boundary Layer Flow

Direct numerical simulations of a spatially evolving supersonic flat-plate turbulent boundary layer flow with free Mach number M = 2.25 and Reynolds number Re = 365000/in are performed. The transition process from laminar to turbulent flow is obtained by solving the three-dimensional compressible Navier-Stokes, equations, using high-order accurate difference schemes. The obtained statistical results agree well with the experimental and theoretical data. From the numerical results it can be seen that the transition process under the considered conditions is the process which skips the Tolimien-Schlichting instability and the second instability through the instability of high gradient shear layer and becomes of laminar flow breakdown. This means that the transition process is a bypass-type transition process. The spanwise asymmetry of the disturbance locally upstream imposed is important to induce the bypass-type transition. Furthermore, with increasing the time disturbance frequency the transition will delay. When the time disturbance frequency is large enough, the transition will disappear.

A Study on the Microstructure Characteristic of the Cold-Rolled Deformed Nanocrystalline Nickel

In this paper the microstructure characteristic of the cold-rolled deformed nanocrystalline Nickel metal has been studied by transmission electron microscopy (TEM). The results show that there were step structures near by grain boundary (GB), and the contrast of stress field in front of the step corresponds to the step in the shape. It indicates that the interaction between twins and dislocations is not a necessary condition to realizing the deformation. In the later stage of the deformation when the grain size became about 100 nm, the deformation occurs only depend upon the moving of the boundary of the stack faults (SFs) which result from the imperfection dislocations emitted from GBs. In the other word, the movement of the boundary dislocations of SFs results to growing-up of the size of the SFs, therefore realizes deformation. However, when the size of stack faults grows up, the local internal stress which is in front of the step gradually becomes higher. When this stress reach a critical value stopping the gliding of the partial dislocations, the SFs will stop growing up and leave a step structure behind.

Crack Tip Field and J-Integral with Strain Gradient Effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory Two typical crack Problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

Step Structure in Cold-Rolled Deformed Nanocrystalline Nickel

The microstructure characteristic of the cold-rolled deformed nanocrystalline nickel metal is studied by transmission electron microscopy. The results show that there are step structures nearby the grain boundary (GB), and the contrast of stress field in front of the step corresponds to the step in the shape. It is indicated that the interaction between twins and dislocations is not a necessary condition to realizing the deformation. In the later stage of the deformation when the grain size becomes about 100nm, the deformation can depend upon the moving of the boundary of the stack faults (SFs) which result from the partial dislocations emitted from GBs. However, when the size of SFs grows up, the local internal stress which is in front of the step gradually becomes higher. When this stress reaches a critical value which stops the gliding of the partial dislocations, the SFs will stop to grow up and leave a step structure behind.

DNS of Compressible Turbulent Boundary Layer Over a Blunt Wedge

Direct numerical simulation of spatially evolving compressible boundary layer over a blunt wedge is performed in this paper. The free-stream Mach number is 6 and the disturbance source produced by wall blowing and suction is located downstream of the sound-speed point. Statistics are studied and compared with the results in incompressible flat-plate boundary layer. The mean pressure gradient effects on the vortex structure are studied.

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Finite Boundary Effects in Problem of a Crack Perpendicular to and Terminating at a Bimaterial Interface

In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731-2755) are discussed also.

Two-Phase Flow In Fuel Cells In Short-Term Microgravity Condition

A visual observation of liquid-gas two-phase flow in anode channels of a direct methanol proton exchange membrane fuel cells in microgravity has been carried out in a drop tower. The anode flow bed consisted of 2 manifolds and 11 parallel straight channels. The length, width and depth of single channel with rectangular cross section was 48.0 mm, 2.5 mm and 2.0 mm, respectively. The experimental results indicated that the size of bubbles in microgravity condition is bigger than that in normal gravity. The longer the time, the bigger the bubbles. The velocity of bubbles rising is slower than that in normal gravity because buoyancy lift is very weak in microgravity. The flow pattern in anode channels could change from bubbly flow in normal gravity to slug flow in microgravity. The gas slugs blocked supply of reactants from channels to anode catalyst layer through gas diffusion layer. When the weakened mass transfer causes concentration polarization, the output performance of fuel cells declines.

Flow-Induced Vibrations Of A Cylinder With Two Degrees Of Freedom Near Rigid Plane Boundary

Based on similarity analyses, the flow-induced vibrations of a near-wall cylinder with 2 degrees of freedom are investigated experimentally by employing a hydroelastic apparatus in conjunction with a flume. The cylinder's vibration amplitude, vibration frequency and vortex shedding frequency were measured and analyzed. The effects of gap-to-diameter ratio (e,ID) upon the vibration responses are further investigated. The experimental results indicate that, when the reduced velocity (Vr) is small (e.g. Vr = 1.2 similar to 2.6), only streamwise vibration occurs, and its frequency is quite close to its natural frequency in still water. When increasing Vr (e.g. Vr > 3.4), both streamwise and transverse vibrations of the near-wall cylinder may occur. In the examined range of gap-to-diameter ratio (0.42 < e(0)/D < 2.68), 2 vibration stages (in terms of Vr) of streamwise vibrations usually exist: First Streamwise Vibration (FSV) and Second Streamwise Vibration (SSV). In the SSV stage, the vortex shedding frequency may either undergo a jump to that of the streamwise vibration, or stay consistent with that of the transverse vibration. The amplitudes of transverse vibration are usually much larger than those of streamwise vibration for the same value of e(0)/D. The maximum amplitudes of both streamwise and transverse vibration get larger with the increase of e(0)/D (0.42 < e(0)/D < 2.68).