Simulation of a valveless pump with an elastic tube

A valveless pump consisting of a pumping chamber with an elastic tube was simulated using an immersed boundary (IB) method. The interaction between the motion of the elastic tube and the pumping chamber generated a net flow toward the outlet throughout a full cycle of the pump. The net flow rate of the valveless pump was examined by varying the stretching coefficient (ϕ), bending coefficient (γ), the aspect ratio (l/d) of the elastic tube, and the frequency (f) of the pumping chamber. As the stretching and bending coefficients of the elastic tube increased, the net flow through the valveless pump decreased. Elastic tubes with aspect ratios in the range of 2 ⩽ l/d ⩽ 3 generated a higher flow rate than that generated for tubes with aspect rations of l/d = 1 or 4. As the frequency of the pumping chamber increased, the net flow rate of the pump for l/d = 2 increased. However, the net flow rate for l/d = 3 was nonlinearly related to the pumping frequency due to the complexity of the wave motions. Snapshots of the fluid velocity vectors and the wave motions of the elastic tube were examined over one cycle of the pump to gain a better understanding of the mechanism underlying the valveless pump. The relationship between the average gap in the elastic tube and the average flow rate of the pump was analyzed. A smaller gap in the elastic tube during the expansion mode and a wider gap in the elastic tube during the contraction mode played a dominant role in generating a high average flow rate in the pump, regardless of the stretching coefficient (ϕ), the aspect ratio (l/d) of the elastic tube, or the pumping frequency of the pumping chamber (f).     

Hydrodynamics of vertical falling films in a large-scale pilot unit – a combined experimental and numerical study

The hydrodynamics of vertical falling films in a large-scale pilot unit are investigated experimentally and numerically. We study a broad range of operating conditions with Kapitza and Reynolds numbers ranging from Ka = 191–3394 and Re 24–251, respectively. We compare film thickness measurements, conducted by a laser triangulation scanner, with those obtained by directly solving the full Navier–Stokes equations in two dimensions and using the volume of fluid (VOF) numerical framework. We examine the evolution of the liquid film at multiple locations over a vertical distance of 4.5 m. In both our experiments and simulations we identify a natural wave frequency of the system of approximately 10 Hz. We investigate the formulation of the inlet boundary condition and its effects on wave formation. We show how potentially erroneous conclusions can be made if the simulated domain is shorter than 1000 film thicknesses, by mistaking the forced inlet frequency for the natural wave frequency. We recommend an inlet disturbance consisting of a multitude of frequencies to achieve the natural wave frequency over relatively short streamwise distances.     

Propagation and localization of two-dimensional in-plane elastic waves in randomly disordered layered piezoelectric phononic crystals

Two-dimensional in-plane wave propagation and localization in the disordered layered piezoelectric phononic crystals with material 6 mm are investigated taking the electromechanical coupling into account. The electric field is approximated as quasi-static. The analytical solutions of elastic waves are obtained. The 6 × 6 transfer matrix between two consecutive unit cells is obtained by means of the mechanical and electrical continuity conditions. The expressions of the localization factor and localization length in the disordered periodic structures are presented by regarding the variables of the mechanical and electrical fields as the elements of the state vector. The numerical results of the localization factors and localization lengths are presented for two kinds of disordered piezoelectric phononic crystals, i.e. ZnO–PZT–5H and PVDF–PZT–5H piezocomposites. It is seen from the results that the incident angle of elastic waves and the thickness of the piezoelectric ceramics have significant effects on the wave localization characteristics. For different piezoelectric phononic crystals, the effects of the incident angle are very different. Moreover, with the increase of the disorder degree, the localization phenomenon is strengthened.     

低频弹性波超材料的若干进展

超材料是一类新兴的具有超常物理性质的人造周期/拟周期材料, 能够改变电磁波、声波以及弹性波等在介质中的传播特性. 因在航天、国防以及民用科学等方面的巨大应用潜力, 超材料自被提出后便受到极大的关注并引发研究热潮. 弹性波超材料是超材料的一种, 能够基于弹性波与超材料结构的相互耦合作用实现对弹性波的操控. 带隙是评估弹性波超材料实现弹性波操控的重要工具, 其性质与超材料的材料参数、晶格常数以及局域振子的固有频率相关. 受制于超材料的承载能力、外观尺寸以及局域振子结构等因素, 利用传统超材料开启低频(约100 Hz)弹性波带隙依然存在较大困难. 文章首先简要介绍超材料开启弹性波带隙的基本原理, 然后从低频弹性波超材料基本结构与低频带隙实现方法、低频带隙优化与调控策略、低频带隙潜在应用等三个方面详细总结低频弹性波超材料的研究工作. 其中, 低频带隙超材料的基本结构主要包括布拉格散射型超材料、传统局域共振型超材料以及准零刚度局域共振超材料. 文章通过总结低频弹性波超材料的研究进展, 分析了目前研究中的不足并对未来低频弹性波的研究方向进行了展望.      

In-plane free vibration of a single-crystal silicon ring

In this paper the natural frequencies and the associated mode shapes of in-plane free vibration of a single-crystal silicon ring are analyzed. It is found that the Si(1 1 1) ring is two-dimensionally isotropic in the (1 1 1) plane for elastic constants but three-dimensionally anisotropic, while the Si(1 0 0) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with coefficients being periodic in polar variable. Expressing the radial and tangential displacements in sinusoidal form with non-predetermined amplitudes, and through the integration with respect to the circumferential variable, the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form. The exact expressions for frequencies and mode shapes are obtained. It is found that for Si(1 0 0) rings the frequencies of a pair of modes, which are equal for an isotropic ring, split due to the anisotropic effect only for the second in-plane vibration mode. The phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups. When the single-crystal silicon is replaced by the polycrystalline silicon, which is isotropic in elastic constants, the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting.     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

A Gradient-Based Optimization Method for the Design of Layered Phononic Band-Gap Materials

Phononic materials with specific band-gap characteristics at desired frequency ranges are in great demand for vibration and noise isolation, elastic wave filters, and acoustic devices.The attenuation coefficient curve depicts both the frequency range of band gap and the attenuation of elastic wave, where the frequency ranges corresponding to the none-zero attenuation coefficients are band gaps. Therefore, the band-gap characteristics can be achieved through maximizing the attenuation coefficient at the corresponding frequency or within the corresponding frequency range. Because the attenuation coefficient curve is not smooth in the frequency domain,the gradient-based optimization methods cannot be directly used in the design optimization of phononic band-gap materials to achieve the maximum attenuation within the desired frequency range. To overcome this difficulty, the objective of maximizing the attenuation coefficient is transformed into maximizing its Cosine, and in this way, the objective function is smoothed and becomes differentiable. Based on this objective function, a novel gradient-based optimization approach is proposed to open the band gap at a prescribed frequency range and to further maximize the attenuation efficiency of the elastic wave at a specific frequency or within a prescribed frequency range. Numerical results demonstrate the effectiveness of the proposed gradient-based optimization method for enhancing the wave attenuation properties.     

Evaluation of X-ray sources for quantitative two- and three-dimensional imaging of liquid mass distribution in atomizing sprays

Quantitative measurement of liquid mass distribution is demonstrated in an impinging-jet atomizing spray using a broadband, ∼80 keV X-ray tube source for 2-D radiography and 3-D computed tomography (CT). The accuracy, precision, and sensitivity of these data are evaluated using narrowband, ∼10 keV, synchrotron radiation from the Argonne National Laboratory Advanced Photon Source (APS) at the same flow conditions. It is found that the broadband X-ray tube source can be used for 2-D measurement of the equivalent path length (EPL) and 3-D CT imaging of liquid mass distribution with typical error of 5–10%. Data are compared for cases with and without the use of potassium iodide (KI), which at 15% concentration by mass increases the attenuation coefficient eightfold and enables 2-D and 3-D measurement of EPL with a signal-to-noise ratio (SNR) of 5:1 down to 15 μm. At this concentration, the effects of energy-dependent attenuation (i.e., spectral beam hardening) are negligible for EPL up to 5 mm. Hence, the use of broadband X-ray tube sources is feasible for many practical engineering sprays with a dynamic range in EPL of ∼330:1. The advantages and limitations of using broadband and narrowband X-ray sources are discussed, and recommendations for improving performance are presented.     

End reflections in a layered piezoelectric circular cylinder

End reflection phenomenon in a semi-infinitely long layered piezoelectric circular cylinder is constructed with modal data from a spectral decomposition of the differential operator governing its natural vibrations. These modal data consist of all propagating modes and edge vibrations and they constitute the basis for a wave function expansion of the reflection of waves arriving at the traction-free end of the cylinder. Without any other external stimulus, a passive reflection event occurs. This traction-free end condition is enforced at the Gaussian integration points over the end cross-section on the combination of incoming and reflected wave fields. Reflections due to monochromatic incoming axisymmetric (m = 0) and flexural (m = 1) waves are studied and two numerical examples are presented.For an incoming axisymmetric wave, there is a particular frequency that induces an end resonance, which is characterized by high (but finite) amplitudes of end displacements vis-a-vis those of neighboring (i.e., slightly different) frequencies. This phenomenon is illustrated in the two cylinder examples.It is possible to modify the passive reflection event by imposing some voltage distribution over the free end. For an oscillating end voltage that is out-of-phase with the incoming wave, it is possible to extract electrical energy from it, i.e., energy harvesting. Examples of such an oscillating voltage with a particular radial distribution are given, that illustrate the amount of extracted energy as a function of the frequency of the incident monochromatic wave.     

Lattice Boltzmann simulation of the convective heat transfer from a stream-wise oscillating circular cylinder

In this paper, we studied the convective heat transfer from a stream-wise oscillating circular cylinder. Two dimensional numerical simulations are conducted at Re = 100–200, A = 0.1–0.4 and F = f_o/f_s = 0.2–3.0 with the aid of the lattice Boltzmann method. In particular, detailed attentions are paid on the extensive numerical results elucidating the influence of oscillation frequency, oscillation amplitude and Reynolds number on the time-average and RMS value of the Nusselt number. Over the ranges of conditions considered herein, the heat transfer characteristics are observed to be influenced in an intricate manner by the value of the oscillation frequency (F), oscillation amplitude (A) and Reynolds number (Re). Firstly, the heat transfer is enhanced when the cylinder oscillates stream-wise with small amplitude and low frequency, while it will be reduced by large amplitude and high frequency. Secondly, the average Nusselt number (Nu (ave)) decreases against the increasing value of oscillation frequency, while the RMS value of the Nusselt number, Nu (RMS), displays an opposite trend. Third, we obtained a similar frequency effect on the heat transfer over the range of Reynolds numbers investigated in this paper. In addition, detailed analyses on phase portraits, energy spectrum are also made.     

Characterization of various structures in gas-solid fluidized beds by recurrence quantification analysis

Gas-solid fluidized beds are widely considered as nonlinear and chaotic dynamic systems. Pressure fluc- tuations were measured in a fluidized bed of 0.15 m in diameter and were analyzed using multiple approaches： discrete Fourier transform （DFT）, discrete wavelet transform （DWT）, and nonlinear recur- rence quantification analysis （RQA）. Three different methods proposed that the complex dynamics of a fluidized bed system can be presented as macro, meso and micro structures. It was found from DFT and DWT that a minimum in wide band energy with an increase in the velocity corresponds to the transition between macro structures and finer structures of the fluidization system. Corresponding transition veloc- ity occurs at gas velocities of 0.3, 0.5 and 0.6 m]s for sands with mean diameters of 150, 280 and 490/~m, respectively. DFT, DWT, and RQA could determine frequency range of0-3.125 Hz for macro, 3. ! 25-50 Hz for meso, and 50-200 Hz for micro structures. The RQA showed that the micro structures have the least periodicity and consequently their determinism and laminarity are the lowest. The results show that a combination of DFT, DWT, and RQA can be used as an effective approach to characterize multi-scale flow behavior in gas-solid fluidized beds.     

First-order hyperbolic form of velocity-stress equations for waves in elastic solids with hexagonal symmetry

This paper reports a theoretical framework to analyze wave propagation in elastic solids of hexagonal symmetry. The governing equations include the equations of motions and partial differentiation of elastic constitutive relations with respect to time. The result is a set of nine, first-order, fully-coupled, hyperbolic partial differential equations with velocities and stress components as the unknowns. The equation set is then cast into a vector form with three 9 × 9 coefficient (or Jacobian) matrices. Physics of wave propagation are fully described by the eigen structure of these matrices. In particular, the eigenvalues of the Jacobian matrices are the wave speeds and a part of the left eigenvectors represents the wave polarization. Without invoking the plane wave solution and the Christoffel equation, two- and three-dimensional slowness profiles can be calculated. As an example, slowness profiles of a cadmium sulfide crystal are presented.     

Spatially resolved wall temperature measurements during flow boiling in microchannels

Spatial and temporal variations of channel wall temperature during flow boiling microchannel flows using infrared thermography are presented and analyzed. In particular, the top channel wall temperature in a branching microchannel silicon heat sink is measured non-intrusively. Using this technique, time-averaged temperature measurements, with a spatial resolution of 10 μm, are presented over an 18 mm × 18 mm area of the heat sink. Also presented, within a specific sub-region of the heat sink, are intensity maps that are recorded at a rate of 120 frames per second. Time series data at selected point locations in this sub-region are analyzed for their frequency content, and dominant temperature fluctuations are extracted using proper orthogonal decomposition.Results at low-vapor-quality boiling condition indicate that temperatures can be determined from recorded radiation intensities with a temperature uncertainty varying from 0.9 °C at 25 °C to 1.0 °C at 125 °C. The time series data indicate periodic wall temperature fluctuations of approximately 2 °C that are attributed to the passage of vapor slugs. A dominant band of frequencies around 2–4 Hz is suggested by the frequency analysis. Proper orthogonal decomposition results indicate that first six orthogonal modes account for approximately 90% of the variance in temperature. The first mode reconstruction accounts for temporal variations in the dataset in the sub-region analyzed; however the magnitude of fluctuations and spatial variations in temperature are not accurately captured. A reconstruction using the first 25 modes is considered sufficient to capture both the temporal and spatial variations in the data.     

Pressure and friction dependent mechanical strength – cracks and plastic flow

The mechanical properties of a polymer composite plastic bonded explosive, EDC37, have been investigated as a function of hydrostatic confining pressure between 0.1 and 138 MPa. The results indicate different failure processes in two pressure ranges, a low pressure range between about 0.1 and 7 MPa and a higher pressure range between about 7 and 138 MPa. In the low pressure range slow crack processes are important in failure while in the higher pressure range plastic flow dominates. The pressure dependence of the compressive strength in the low pressure range is attributed to coulomb friction between surfaces of closed shear cracks and from the observed linear increase of the strength with pressure and the angle of the fracture plane a friction coefficient is obtained. Friction coefficients can also be obtained from the ratio of the compressive to tensile strength and directly from the above angle. The friction coefficients obtained from these separate observations are in agreement and this is taken as strong evidence for the importance of this friction in determining strength and mechanical failure. These results clearly establish experimentally the role of friction in determining strength with or without applied pressure. An empirical relationship between strength, pressure and strain rate is also obtained for this pressure range and the failure strength of EDC37 is more sensitive to pressure than strain rate.     

Propagation of Bleustein–Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid

The influence of a viscous liquid on acoustic waves propagating in elastic or piezoelectric materials is of particular significance for development of liquid sensors. Bleustein–Gulyaev wave is a shear-type surface acoustic wave and has the advantage of not radiating energy into the adjacent liquid. These features make the B–G wave sensitive to changes in both mechanical and electrical properties of the surrounding environment. The Bleustein–Gulyaev wave has been reported to be a good candidate for liquid sensing application. In this paper, we investigate the potential application of B–G wave in 6 mm crystals for liquid sensing. The explicit dispersion relations for both open circuit and metalized surface boundary conditions are given. A numerical example of PZT-5H piezoelectric ceramic in contact with viscous liquid is calculated and discussed. Numerical results of attenuation and phase velocity versus viscosity, density of the liquid and wave frequency are presented. The paper is intended to provide essential data for liquid senor design and development.     

Observation and analysis of near-surface atmospheric aerosol optical properties in urban Beijing

Year-round measurements of the mass concentration and optical properties of fine aerosols (PM_2.5) from June 2009 to May 2010 at an urban site in Beijing were analyzed. The annual mean values of the PM_2.5 mass concentration, absorption coefficient (Ab), scattering coefficient (Sc) and single scattering albedo (SSA) at 525 nm were 67 ± 66 μg/m³, 64 ± 62 Mm⁻¹, 360 ± 405 Mm⁻¹ and 0.82 ± 0.09, respectively. The bulk mass absorption efficiency and scattering efficiency of the PM_2.5 at 525 nm were 0.78 m²/g and 5.55 m²/g, respectively. The Ab and Sc showed a similar diurnal variation with a maximum at night and a minimum in the afternoon, whereas SSA displayed an opposite diurnal pattern. Significant increases in the Ab and Sc were observed in pollution episodes caused by the accumulation of pollutants from both local and regional sources under unfavorable weather conditions. Aerosol loadings in dust events increased by several times in the spring, which had limited effects on the Ab and Sc due to the low absorption and scattering efficiency of dust particles. The frequency of haze days was the highest in autumn because of the high aerosol absorption and scattering under unfavorable weather conditions. The daily PM_2.5 concentration should be controlled to a level lower than 64 μg/m³ to prevent the occurrence of haze days according to its exponentially decreased relationship with visibility.     

Instantaneous flow field above the free end of finite-height cylinders and prisms

The flow above the free ends of surface-mounted finite-height circular cylinders and square prisms was studied experimentally using particle image velocimetry (PIV). Cylinders and prisms with aspect ratios of AR = 9, 7, 5, and 3 were tested at a Reynolds number of Re = 4.2 × 10⁴. The bodies were mounted normal to a ground plane and were partially immersed in a turbulent zero-pressure-gradient boundary layer, where the boundary layer thickness relative to the body width was δ/D = 1.6. PIV measurements were made above the free ends of the bodies in a vertical plane aligned with the flow centreline. The present PIV results provide insight into the effects of aspect ratio and body shape on the instantaneous flow field. The recirculation zone under the separated shear layer is larger for the square prism of AR = 3 compared to the more slender prism of AR = 9. Also, for a square prism with low aspect ratio (AR = 3), the influence of the reverse flow over the free end surface becomes more significant compared to that for a higher aspect ratio (AR = 9). For the circular cylinder, a cross-stream vortex forms within the recirculation zone. As the aspect ratio of the cylinder decreases, the reattachment point of the separated flow on the free end surface moves closer to the trailing edge. For both the square prism and circular cylinder cases, the instantaneous velocity vector field and associated in-plane vorticity field revealed small-scale structures mostly generated by the separated shear layer.     

Effect of side ratio on fluid flow and heat transfer from rectangular cylinders using the PANS method

A computational study of heat transfer from rectangular cylinders is carried out. Rectangular cylinders are distinguished based on the ratio of the length of streamwise face to the height of the cross-stream face (side ratio, R). The simulations were performed to understand the heat transfer in a flow field comprising separation, reattachment, vortex shedding and stagnation. The Partially-Averaged Navier–Stokes (PANS) modeling approach is used to solve the turbulent flow physics associated and the wall resolve approach is used for the near wall treatment because of the flow separation involved. The simulations were performed using a finite volume based opensource software, OpenFOAM, at Reynolds number (Re) = 22,000 for rectangular cylinder at constant temperature kept in an air stream. Two critical side ratios were obtained, R = 0.62 and 3.0. At R = 0.62, the maximum value of the drag coefficient (C_d) = 2.681 was observed which gradually reduced by 54% at R = 4.0. The base pressure coefficient and global Nusselt number also attained the maximum value at R = 0.62 and from R = 2.5 to 3.0 a sharp discontinuous increase by 140% in the Strouhal number was observed. At R = 0.62, it was observed that the separated flow reattaches at the trailing edge after rolling over the side face and therefore increases the overall Nusselt number. The phase averaging was also performed to analyze the unsteady behavior of heat transfer.     

Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro-contraction

We have studied the flow of thermodynamically ideal solutions of a high molecular weight (M_w = 6.9 MDa) atactic polystyrene in the θ solvent dioctyl phthalate (aPS in DOP) through a micro-fabricated 8:1 planar abrupt contraction geometry. The channel is much deeper than most micro-scale geometries, providing an aspect ratio of 16:1 and a good approximation to 2D flow in the narrow channel. The solutions span a range of concentration 0.03 wt.% < c < 0.6 wt.%, encompassing the dilute to semi-dilute regimes and providing a range of fluid viscosities and relaxation times such that we achieve a range of Weissenberg numbers (8.7 < Wi < 1562) and Reynolds numbers (0.07 < Re < 11.2), giving elasticity numbers between 31 < El < 295. We study the flow using a combination of micro-particle image velocimetry (μ-PIV) to characterize the flow field, pressure measurements to evaluate the non-Newtonian viscosity, and birefringence measurements to assess macromolecular strain. Flow field observations reveal three broad flow regimes characterized by Newtonian-like flow, unstable flow and vortex growth in the upstream salient corners. Transitions between the flow regimes scale with Wi, independent of El, indicating the dominance of elastic over inertial effects in all the fluids. Transitions in the flow field are also reflected by transitions in the relative viscosity (determined from the pressure drop) and the macromolecular strain (determined from birefringence measurements). The strain through the 8:1 contraction saturates at a value of ～4–5 at high Wi. The results of these experiments broaden the limited set of literature on flow through micro-fluidic planar contractions and should be of significant value for optimizing lab-on-a-chip design and for comparison with modeling studies with elasticity dominated fluids.     

Saturated nucleate boiling to binary and ternary mixtures on horizontal cylinder

In this investigation, a large number of experiments have been performed to determine saturated nucleate pool boiling heat transfer coefficients of MEA/water and DEA/water binary mixtures and that of water/MEA/DEA ternary mixtures. These heat transfer coefficients have been measured at atmospheric pressure and over a wide range of heat fluxes and solution concentrations. The heat flux has been varied in 14 different levels from 7 to about 230 kW/m² and amines concentration has been changed in 10 different levels from zero to 84 wt%. Results show that strong reduction of heat transfer coefficient occurs as a result of mass transfer interference in this phenomenon. Furthermore, in this study, all the correlations proposed during the last years for the prediction of nucleate boiling heat transfer coefficient of mixtures have been categorized in three groups. Some experimental results have been compared with the most accurate representatives of these three groups and the corresponding RMS errors have been calculated. Also, impacts of important existing parameters in these correlations like ideal heat transfer coefficient (h_id.) on the prediction have been discussed.