Acoustic testing of the vortex structure produced by an air flow about an array of cylinders

Results of experiments on the scattering of a plane ultrasonic wave from a vortex wake formed in an air flow behind a lattice of vertical cylinders are presented. The lattice is periodic in the direction perpendicular to the oncoming flow. The experiments are performed in a wind tunnel for two values of the Reynolds number, namely, Re = 75 and 500, and for lattices with different numbers of cylinders and with different lattice periods g = (2.5–15)d (where d is the diameter of the cylinders). The measured parameters of the scattered waves are used to estimate the degree of transverse correlation between the vortex wakes formed behind the cylinders for flows with different Reynolds numbers. The results obtained from an analysis of the characteristics of the scattered sound are compared with the results of direct hot-wire anemometer measurements and with the data obtained by other researchers.     

Natural vibration of unsymmetric cross-ply laminates

This study considers the linear vibration characteristics of square [0_n/90_n]_T laminates relative to their room-temperature static equilibrium configurations. A Rayleigh-Ritz approach combined with Hamilton's principle is used to provide approximate solutions to this vibration problem. The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations. Hamilton's principle then results in the so-called zero- and first-order equations. The zero-order equations lead to the classic static equilibrium results of past investigations, presented here in nondimensional form with analytical solutions at the bifurcation point. The first-order equations, combined with zero-order results, lead to the vibration characteristics for each zero-order static configuration. Interest centers on the lowest natural frequency and the associated mode shape for laminates clamped at their midpoints, with special attention as to how these vibration characteristics depend on the laminate side-length-to-thickness ratio. With an imaginary-valued frequency, the static saddle configuration for side-length-to-thickness ratios larger than the critical value is correctly assessed as unstable. A finite element model is also used to study the vibration characteristics and to compare with the findings for the developed analysis. The qualitative comparisons between the developed analysis and the finite element model are generally good, and the quantitative comparisons are also satisfactory.     

VORTEX-INDUCED VIBRATIONS OF TWO SIDE-BY-SIDE EULER-BERNOULLI BEAMS

Vortex-induced vibration of two side-by-side elastic beams in a cross flow is numerically studied. The two beams are identical and fixed at both ends. In the numerical approach, the Euler-Bernoulli beam theory is used to model the beam vibration, and the laminar Navier-Stokes equations are solved to give the flow field. The flow equations are resolved using a finite element method and the flow-induced forces are calculated at every time step in order to correctly reflect the fluid-beam interaction. The beam response is calculated using the modal analysis method. Free vibrations of the two beams with three pitch ratios, T/D=1·13, 1·7 and 3·0, where T is the gap between the centers of the two beams and D is the beam diameter, are simulated at Re=800. Results obtained are compared with experimental measurements and other numerical results obtained assuming a two-degree-of-freedom (2-d.o.f.) model. The agreement is good in general. Correlation analysis is carried out, showing that the phase relation is different for differentT /D. The short-time Fourier transform (STFT) method is used to carry out the spectral analysis, along with the conventional auto-regressive moving averaging (ARMA) method for comparison. The STFT analysis shows that the time evolution of fluid force and beam vibration for T/D=1·13 and 3·0 are stationary. For theseT /D ratios, the STFT results are consistent with the ARMA results, but give a clearer picture of the higher order harmonics. For T/D=1·7, the time evolution is non-stationary. The STFT analysis shows that there are three types of frequency spectrum for the fluid force, with one, two, and three dominant frequencies respectively. The spectra intermittently change in a random way during the evolution. The ARMA results, though consistent with previous experiments, can only reveal a particular feature of the three different types of spectrum. This suggests that the STFT method is more appropriate to analyze the spectra of non-stationary time series in the study of flow-induced vibrations.     

Analysis of the flow-induced vibrations of viscoelastically supported rectangular plates

The purpose of this study was to develop a theoretical model for the flow-induced vibration of viscoelastically supported rectangular plates. In particular, the influence of the dynamic mechanical properties of the elements supporting the plate was investigated. The case of a homogeneous rectangular plate supported along all four edges by a complex viscoelastic element was treated. The Rayleigh-Ritz method was used applying beam functions as the trial functions. This approach ensured a fast convergence rate, which is advantageous for vibration analysis of high order modes. The flow-induced vibration of the plate was calculated using the Corcos model for the surface pressure loading. The results suggest that there is an optimal support stiffness that minimizes the flow-induced vibration response of the plate.     

Power extraction using flow-induced vibration of a circular cylinder placed near another fixed cylinder

We conducted an experiment in a towing tank to investigate the performance of an energy extraction system using the flow-induced vibration of a circular cylinder. This experiment tested three different cases involving the following arrangements of cylinder(s) of identical diameter: the upstream fixed–downstream movable arrangement (case F); the upstream movable–downstream fixed arrangement (case R); and a movable isolated cylinder (case I). In cases F and R, the separation distance (ratio of the distance between the centers of the two cylinders to their diameters) is fixed at 1.30. Measurement results show that while cases F and I generate vortex-induced vibration (VIV) resonance responses, case R yields wake-induced vibration (WIV) at reduced velocity over 9.0, which is significantly larger than that of the VIV response, leading to the induction of higher electronic power in a generator. Accordingly, primary energy conversion efficiency is higher in the case involving WIV.     

Instability of parametric dynamic systems with non-uniform damping

A unified way of looking at parametric and combination resonances in systems with periodic coefficients and different amounts of damping in the various modes of vibration is presented. The stability boundaries of the coupled Mathieu equations are determined by the harmonic balance method, Fourier series with periods 2T and T being assumed. The basic characteristics of the solution are discussed and the method is applied to multiple-degree-of-freedom dynamic systems. The destabilizing effect on the combination resonances is obtained by the present method.     

管外流诱导管束振动强化传热试验研究

本文提出了利用管外流体诱导振动实现强化传热的新方法.采用了一种新的传热元件-弹性管束,它对管外流体流动具有良好的振动响应特性.提出了正置三角柱脉动流发生装置,该装置可诱导起弹性管束一定频率的周期性振动,并对强化传热具有显著的促进作用.在恒热流条件下,对管外水流诱导振动强化对流换热规律进行了试验研究,得到了管外对流换热的准则方程式.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral and vertical whole-body vibration

It is currently assumed that the same frequency weightings, derived from studies of vibration discomfort, can be used to evaluate the severity of vibration at all vibration magnitudes from the threshold of vibration perception to the vibration magnitudes associated with risks to health. This experimental study determined equivalent comfort contours for the whole-body vibration of seated subjects over the frequency range 2-315 Hz in each of the three orthogonal axes (fore-and-aft, lateral and vertical). The contours were determined at vibration magnitudes from the threshold of perception to levels associated with severe discomfort and risks to health.At frequencies greater than 10 Hz, thresholds for the perception of vertical vibration were lower than thresholds for fore-and-aft and lateral vibration. At frequencies less than 4 Hz, thresholds for vertical vibration were higher than thresholds for fore-and-aft and lateral vibration. The rate of growth of sensation with increasing vibration magnitude was highly dependent on the frequency and axis of vibration. Consequently, the shapes of the equivalent comfort contours depended on vibration magnitude. At medium and high vibration magnitudes, the equivalent comfort contours were reasonably consistent with the frequency weightings for vibration discomfort in current standards (i.e. W_b and W_d). At low vibration magnitudes, the contours indicate that relative to lower frequencies the standards underestimate sensitivity at frequencies greater than about 30 Hz. The results imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of whole-body vibration.     

Dynamics of arrays of cylinders with internal and external axial flow

Various aspects of the dynamics and stability of clusters of tubular cylinders containing internally flowing fluid and surrounded by a bounded external axial flow are examined. The general character of free motions is established by obtaining the eigenfrequencies of the system and studying their evolution with increasing flow, internal or external. Stability diagrams have been obtained for the critical flow velocities, beyond which the system would lose stability by buckling (divergence), under the combined effect of internal and external flow. Free vibration, following an initial disturbance of one of the cylinders, is studied, in order further to examine the effect of hydrodynamic coupling. It is found that beating phenomena may arise, implying energy transfer between cylinders and the possibility of transient amplitudes much larger than the initial disturbances. Also, the vibration of the system (in still fluid) when one cylinder is constrained to oscillate in a prescribed manner is examined, establishing that transmission of vibration from cylinder to cylinder can be very rapid; indeed, such constrained motion of one cylinder at certain frequencies may induce large amplified motions of others.     

The use of seat effective amplitude transmissibility (SEAT) values to predict dynamic seat comfort

The Seat Effective Amplitude Transmissibility (SEAT) value is the ratio of the vibration experienced on top of the seat and the vibration that one would be exposed to when sitting directly on the vibrating floor. SEAT values have been widely used to determine the vibration isolation efficiency of a seat. In this article the subjective evaluations of six persons were compared to the SEAT values estimated from experimentally obtained transmissibility curves for 16 different automobile seats ranging from sedans to SUVs and pickups. A vertical rough road stimulus was used as input for both the subjective testing and the SEAT calculations. The SEAT values were estimated using the power spectral density of the vertical vibration input at the seat track and the measured transmissibility data to compute the response in the vertical direction at the seat top. The averaged, estimated SEAT values were compared to averaged measured values and significant correlation (R²=0.94) was obtained. The subjective ratings were obtained on the Ford Vehicle Vibration Simulator using a paired comparison methodology that eliminated static comfort bias during the evaluation. The results indicated that there is good correlation (R²=0.94) between the subjective ratings and the SEAT values when the subjective ratings and transmissibilities are averaged over the six subjects.     

Apparent mass of seated man—First determination with a soft seat and dynamic seat pressure distributions

Data of the impedance and/or the apparent mass of the sitting human body during the exposure to whole-body vibration in z-direction using rigid seats were standardized in the ISO 5982. These data are available as target functions for model developments. Models developed on this data basis should also apply to driver seats with a soft seat and backrest cushion, although the qualitative different contact conditions were neglected. Due to insufficient technical prerequisites, the determination of forces at the interface between subject and soft seat was impossible until very recently. Results of studies during static conditions showed clear differences in the pressure distributions between the rigid and the soft contact areas. In this experimental study pressure distributions on a seat cushion were measured during whole-body vibration in z-direction (random signal in the frequency range between 0.3 and 20 Hz, vibration magnitudes 0.25, 0.8, and 1.6 m s⁻² unweighted root mean square measured at the seat base) with a sampling rate of 32 m s. The apparent masses were calculated by the forces derived from the pressure distributions and accelerations measured at one point of the seat cushion near the buttocks. The moduli of the apparent masses derived for the soft seat were clearly lower than those determined for a rigid seat. These apparent masses showed a similar dependence on the vibration magnitude as the apparent mass functions derived in the usual way for rigid seats. Factors that could explain differences between the apparent mass functions derived for the soft and rigid seat were discussed and evaluated. The data of this study indicate the possibility and necessity to consider the contact conditions at the interface when deriving target functions for the model development. Recommendations for technical improvements and further experimental studies with driver seats were derived.     

Comparison of the apparent masses and cross-axis apparent masses of seated humans exposed to single- and dual-axis whole-body vibration

Humans are exposed to whole-body vibration in many types of environment. In almost all cases, the vibration to which the human is exposed comprises multi-axis vibration, such that vibration occurs in all directions simultaneously. Despite the complex nature of vibration to which humans are exposed in the workplace, almost all laboratory studies investigating the biomechanical response of the person have been completed using single-axis simulators. This paper presents a study whereby 15 male subjects were exposed to single-axis whole-body vibration in the x-, y- and z-directions and dual-axis vibration in the xy-, xz-, and yz-directions using a 6 degree-of-freedom vibration simulator. All vibration magnitudes were 0.4 ms⁻² rms in each axis. Acceleration and force was measured in the x-, y-, and z-direction during all trials. Subjects sat in two postures (‘back-on’ and ‘back-off’) on a flat rigid seat. Apparent masses measured using single-axis and dual-axis vibration stimuli showed comparable results; similarly, cross-axis apparent masses (i.e. the ratio of the force in one direction to the acceleration in another direction) were almost identical for the single- and dual-axis vibration stimuli. All results were in agreement with data previously published using single-axis vibration. In most cases, the peaks in the apparent mass and the cross-axis apparent mass occurred at a slightly lower frequency for the dual-axis vibration than for the single-axis vibration. It is hypothesised that this change is due to a nonlinear effect, analogous to that which occurs with increasing vibration magnitude for single-axis vibration.     

Numerical Study on the Coagulation and Breakage of Nanoparticles in the Two-Phase Flow around Cylinders

The Reynolds averaged N-S equation and dynamic equation for nanoparticles are numerically solved in the two-phase flow around cylinders, and the distributions of the concentration M₀ and geometric mean diameter d_g of particles are given. Some of the results are validated by comparing with previous results. The effects of particle coagulation and breakage and the initial particle concentration m₀₀ and size d₀ on the particle distribution are analyzed. The results show that for the flow around a single cylinder, M₀ is reduced along the flow direction. Placing a cylinder in a uniform flow will promote particle breakage. For the flow around multiple cylinders, the values of M₀ behind the cylinders oscillate along the spanwise direction, and the wake region in the flow direction is shorter than that for the flow around a single cylinder. For the initial monodisperse particles, the values of d_g increase along the flow direction and the effect of particle coagulation is larger than that of particle breakage. The values of d_g fluctuate along the spanwise direction; the closer to the cylinders, the more frequent the fluctuations of d_g values. For the initial polydisperse particles with d₀ = 98 nm and geometric standard deviation σ = 1.65, the variations of d_g values along the flow and spanwise directions show the same trend as for the initial monodisperse particles, although the differences are that the values of d_g are almost the same for the cases with and without considering particle breakage, while the distribution of d_g along the spanwise direction is flatter in the case with initial polydisperse particles.     

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of “edge functions” that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1−c/a), and the notch angle is defined as (360°−α). For a very small notch angle (1° or less), the notch may be regarded as a “sharp radial crack.” Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°−α), depths (1−c/a), and thickness ratios (a/h for plates and h/a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r(θ), several of which are described for future investigations and close extensions of this work.     

Reorientational motion of acetone in solutions

Dipolar correlation functions of acetone in various solvents are obtained by Fourier transform of infrared spectra. The analysis of the shapes of correlation functions shows that the reorientational process is diffusional in the time scale longer than about 0.3 × 10^?12 sec. In nonpolar solvents the ratios of correlation times τ_A : τ_B : τ_C do not vary in different solvents, and the reorientation around b axis is more restricted than around the other axis. The length of correlation time is dependent on the density of solvent rather than the viscosity. These observations are unexpected if only the electrostatic interaction is considered. In polar solvents correlation times are longer than in nonpolar solvents and the tendency is especially remarkable in τ_B. An electrostatic interaction between polar molecules seems to be responsible for these observations. The solvent effect on the frequency shifts of carbonyl stretching vibration is consistent with the result of correlation times.     

基于浸入边界-多松弛时间格子玻尔兹曼通量求解法的流固耦合算法研究

针对流固耦合问题,发展了基于浸入边界-多松弛时间格子玻尔兹曼通量求解法(immersed boundary method multi-relaxation-time lattice Boltzmann flux solver,IB-MRT-LBFS)的弱耦合算法.依据多尺度Chapman-Enskog展开,建立不可压宏观方程状态变量和通量与格子玻尔兹曼方程中粒子密度分布函数之间的关系;采用强制浸入边界法处理流固界面使固壁表面满足无滑移边界条件,根据修正的速度求解动量方程力源项;结构运动方程采用四阶龙格-库塔法求解.格子模型与浸入边界法的引入使流固耦合计算可以在笛卡尔网格下进行,无需生成贴体网格及运用动网格技术,简化了计算过程.数值模拟了单圆柱横向涡激振动、单圆柱及串列双圆柱双自由度涡激振动问题.结果表明,IB-MRT-LBFS能够准确预测圆柱涡激振动的锁定区间、振动响应、受力情况以及捕捉尾流场结构形态,验证了该算法在求解流固耦合问题的有效性和可行性.     

Inter-cycle variation in whole-body vibration exposures of operators driving track-type loader machines

Whole-body vibration (WBV) measurements are an important aspect of performing risk assessments for those exposed to vibration. A large array of variables affect the outcome of a vibration measurement and its extrapolation to a daily dose measure: e.g. variability in driving style, road surface roughness, loading. The variability in vibration emission is an inherent property for most vibrating environments and there is a risk that a vibration measurement might not be representative of the long-term exposures. It is important to acknowledge the variation inherent to WBV exposure to help understand how this variation will affect health risk assessments. A field investigation was conducted in order to characterise the variation of WBV magnitudes between work cycles of track-type loaders. Six different track-type loaders were measured at four different work sites. The vibrations were measured at the operators seat in three translational axes (x-, y-, and z-axis) in accordance with ISO 2631-1 (1997). The findings indicate the worst axis of vibration for the track-type loaders was predominantly the fore-and-aft (x-axis), for most operations. The most severe emission values were measured for machine C at site 2 (1.12 ms⁻² rms) and machine D at site 2 (1.03 ms⁻² rms). These machines would exceed the action value of the Physical Agents (Vibration) Directive within 2 h of exposure. All of the machines measured would exceed the exposure action value of the Directive within an 8 h working period. The lateral (y-axis) produced the greatest amount of variability between work cycles (coefficient of variation up to 20%). It is concluded that the inherent variability between work cycles and tasks reinforces the requirement to perform a full task analysis prior to measuring WBV exposures to ensure that all tasks are measured and that adequate cycles are measured to obtain a reliable indication of the vibration emission.     

Experimental and numerical investigation of the unsteady flow field and tone generation in an isolated centrifugal fan impeller

In spite of a low circumferential Mach number the sound of isolated centrifugal fan impellers is sometimes dominated by distinctive tones at blade passing frequency (BPF) and integer multiples. This paper reports on an experimental and numerical investigation intended to unveil the tone generating mechanism. The sound spectra from three impellers operating at a large range of speed were measured and decomposed into Strouhal and Helmholtz number dependent functions. This led to the preliminary conclusion that the BPF related tones are exclusively flow-induced. Based on hot-wire and blade pressure fluctuation measurements and a subsequent correlation analysis, coherent flow structures different from those associated with the principal azimuthal flow pattern due to the blades were detected. Eventually a numerical three-dimensional unsteady flow simulation revealed an inlet vortex. It takes on a helical form, with the vortex core slowly varying its position with respect to the impeller center. As the blades cut through that quasi-stationary helical vortex they encounter blade force fluctuations, producing the BPF tones. Slow spin of the vortex core and slow variation of vortex strength were identified as the reasons for amplitude modulation of the BPF tone.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.