Secondary vortex, laminar separation bubble and vortex shedding in flow past a low aspect ratio circular cylinder

Large eddy simulation of flow past a circular cylinder of low aspect ratio ( $AR=1$ and $3$ ), spanning subcritical, critical and supercritical regimes, is carried out for $2\times 10^3 \le Re \le 4\times 10^5$ . The end walls restrict three-dimensionality of the flow. The critical $Re$ for the onset of the critical regime is significantly lower for small aspect ratio cylinders. The evolution of secondary vortex (SV), laminar separation bubble (LSB) and the related transition of boundary layer with $Re$ is investigated. The plateau in the surface pressure due to LSB is modified by the presence of SV. Proper orthogonal decomposition of surface pressure reveals that although the vortex shedding mode is most dominant throughout the $Re$ regime studied, significant energy of the flow lies in a symmetric mode that corresponds to expansion–contraction of the vortex formation region and is responsible for bursts of weak vortex shedding. A triple decomposition of the time signals comprising of contributions from shear layer vortices, von Kármán vortex shedding and low frequency modulation due to the symmetric mode of flow is proposed. A moving average, with appropriate size of window, is utilized to estimate the component due to vortex shedding. It is used to assess the variation, with $Re$ , of strength of vortex shedding as well as its coherence along the span. Weakening of vortex shedding in the high subcritical and critical regime is followed by its rejuvenation in the supercritical regime. Its spanwise correlation is high in the subcritical regime, decreases in the critical regime and improves again in the supercritical regime.

The transverse electric plasmonic modes in a negative refractive index black phosphorene waveguide structure

We consider the transverse electric (TE) plasmonic modes supported by black phosphorene (BP) in a parallel waveguide structure with left-handed material (LHM) instead of the conventional right-handed dielectric material. The existence condition of the TE BP surface plasmon polariton (SPP) is $\mathrm{Im}\sigma>0$. When an electric field is polarized along one of the two orthogonal crystal axes, the anisotropic symmetric and anti-symmetric plasmonic modes depend on the incident optical energy, the chemical potential, and the distance between two BP sheets can be observed. The symmetric mode has a more extensive effective refractive index, which possesses stronger field confinement. With a decreasing distance $d$ between two BP sheets, the coupling strength between the two separate BPSPP waves increases. When $d$ is small enough, the anti-symmetric mode root does not exist. LHMs can be used to realize a TE BPSPP mode to enhance the localization of the BPSPP, which is a practical method in optoelectronic devices based on black phosphorene.

Flexoelectric effect on thickness-shear vibration of a rectangular piezoelectric crystal plate

Thickness-shear (TSh) vibration of a rectangular piezoelectric crystal plate is studied with the consideration of flexoelectric effect in this paper. The developed theoretical model is based on the assumed displacement function which includes the anti-symmetric mode through thickness and symmetric mode in length. The constitutive equation with flexoelectricity, governing equations and boundary conditions are derived from the Gibbs energy density function and variational principle. For the effect of flexoelectricity, we only consider the shear strain gradient in the thickness direction so as to simply the mathematical model. Thus, two flexoelectric coefficients are used in the present model. The electric potential functions are also obtained for different electric boundary conditions. The present results clearly show that the flexoelectric effect has significant effect on vibration frequencies of thickness-shear modes of thin piezoelectric crystal plate. It is also found that the flexoelectric coefficients and length to thickness ratio have influence on the thickness-shear modes. The results tell that flexoelectricity cannot be neglected for design of small size piezoelectric resonators.

Extreme-Point Symmetric Mode Decomposition to Define the Turbulence Characteristics of a Flume Flow

Turbulence is a key feature of solid-liquid two-phase flows, and the pulsating velocity is the basis for calculating turbulence characteristics. In general, the method of mathematical expectation is used to calculate pulsating velocity. However, this method does not reflect the fluctuating state of the instantaneous velocity. Therefore, the method of extreme-point symmetric mode decomposition (ESMD) is adopted to calculate pulsating velocity and turbulence characteristics. The ESMD involves two stages, namely, modal decomposition and time-frequency analysis. The optimal adaptive global mean (AGM), which is the result of modal decomposition, can accurately reflect the fluctuation state of the instantaneous velocity, and the theory of the pulsating velocity defined on this basis is reasonable. Moreover, the flow pattern and turbulence behaviour of a two-phase flow can be predicted using the calculated turbulence characteristics. The method is used to analyse the pulsating velocity of the flume, and its rationality in theoretically predicting the turbulence behaviour of flume flows is demonstrated.

Fault Diagnosis of Axial Piston Pump Based on Extreme-Point Symmetric Mode Decomposition and Random Forests

Aiming at fault diagnosis of axial piston pumps, a new fusion method based on the extreme-point symmetric mode decomposition method (ESMD) and random forests (RFs) was proposed. Firstly, the vibration signal of the axial piston pump was decomposed by ESMD to get several intrinsic mode functions (IMFs) and an adaptive global mean curve (AGMC) on the local side. Secondly, the total energy was selected as the data of feature extraction by analyzing the whole oscillation intensity of the signal. Thirdly, the data were preprocessed and the labels were set, and then, they were adopted as the training and testing set of machine learning samples. Lastly, the RFs model was created based on machine learning service (MLS) to diagnose the faults of the axial piston pump on the cloud. Using the test and verifying the data set for comparative testing, the fault diagnosis precision rates of the model are above 90.6%, the recall rates are more than 90.9%, the F1 score is higher than 90.7%, and the accuracy rate of this model reached 97.14%. A benchmark data simulation of mechanical transmission systems and an experimental data investigation of an axial piston pump are performed to manifest the superiority of the present method by comparing with classification and regression trees (CART) and support vector machine (SVM).

Understanding the interaction of the fundamental Lamb-wave modes with material discontinuity: finite element analysis and experimental validation

The interaction of guided waves with a material discontinuity is not well understood. This study investigates the propagation behavior of the fundamental Lamb-wave modes, the symmetric mode ( S0) and the anti-symmetric mode ( A0), upon interaction with welded joints of dissimilar materials. A plate with an intact AA6061-T6/AZ31B dissimilar joint was employed, and the interaction of the propagating wave with the material interface was scrutinized numerically and validated experimentally. Plane-wave approximation was also adopted to investigate the behavior of the symmetric modes, and its performance was compared to the numerical and experimental results. The effect of the angle of incidence on the reflection, transmission, and mode conversion of the incident modes was analyzed. The study was conducted as the excited Lamb wave propagated from AA6061-T6 to AZ31B (forward), and when the propagation direction was reversed (backward). Different techniques were developed to identify the in-plane and out-of-plane modes from the three-dimensional measurements and to separate wave reflections and transmissions of the joint. The fundamental shear-horizontal guided-wave mode ( SH0 mode) has evolved upon the interaction of the obliquely-incident Lamb-wave S0 mode with the interface. While the reflection of the SH0 mode from the joint was found to be well-pronounced, its transmission to the other material is extremely weak. The analytical solution, using plane-wave approximation, was accurate for predicting the behavior of the in-plane modes ( S0 and S0– SH0 modes). Despite the peaks appearing at the critical angle, the absolute values of the reflection coefficients of the studied modes have shown similar trends between the forward and the backward propagation directions. The total reflection of the excited wave, from the material interface, was not observed in any condition. The transmission coefficients of the S0 and A0 modes are almost constant until reaching very steep incidence angles [Formula: see text]. The results were experimentally validated on an intact AA6061-T6/AZ31B friction-stir-welded joint using an excitation frequency of 200 kHz. Measurements along the transmission and reflection directions were conducted using a three-dimensional scanning laser vibrometer. Experimental results showed very good agreement with both the analytical and the numerical ones.

Time-reversal symmetric component of the flagellar beat enhances the translational and rotational velocities of isolated Chlamydomonas flagella

The beating of cilia and flagella is essential to perform many important biological functions, including generating fluid flows on the cell surface or propulsion of micro-organisms. In this work, we analyze the motion of isolated and demembranated flagella from green algae Chlamydomonas reinhardtii, which act as ATP-driven micro-swimmers. The waveform of the Chlamydomonas beating flagella has an asymmetric waveform that is known to involve the superposition of a static component, corresponding to a fixed, intrinsic curvature, and a dynamic wave component traveling in the base-to-tip direction at the fundamental beat frequency, plus higher harmonics. Here, we demonstrate that these modes are not sufficient to reproduce the observed flagella waveforms. We find that two extra modes play an essential role to describe the motion: first, a time-symmetric mode, which corresponds to a global oscillation of the axonemal curvature, and second, a secondary tip-to-base wave component at the fundamental frequency that propagates opposite to the dominant base-to-tip wave, albeit with a smaller amplitude. Although the time-symmetric mode cannot, by itself, contribute to propulsion (scallop theorem), it does enhance the translational and rotational velocities of the flagellum by approximately a factor of 2. This mode highlights a long-range coupled on/off activity of force-generating dynein motors and can provide further insight into the underling biology of the ciliary beat.

On symmetric wedge mode of an elastic solid

The existence of a symmetric mode in an elastic solid wedge for all admissible values of the Poisson ratio and arbitrary interior angles close to π has been proven.