Velocity Mode Research Articles

Global sensitivity analysis of stochastic re-entry trajectory using explainable surrogate models

The assessment of casualty risks associated with re-entry necessitates a comprehensive analysis of trajectories and the examination of pertinent safety-related quantities such as the ground impact area and ground reaching velocity. In practical scenarios, the presence of uncertainty in input conditions introduces variability in safety-related quantities. Consequently, employing stochastic re-entry trajectory analysis becomes crucial in overcoming the limitations of conventional deterministic analyses. Conducting sensitivity assessments during the break-up phase is imperative to gain more insights into how to manage the variability of safety-related measures. Therefore, this paper conducted a surrogate-based global sensitivity analysis and employed explainability machine learning techniques to unveil the complexities of the relationship between input uncertainty conditions and three key measures: ground-reaching velocity, falling range, and falling time, with the object of interest being the Apollo-type capsule. A three-step polynomial chaos expansion-based strategy was devised to efficiently approximate the discontinuous relationships. The results show that the relationship is characterized by severe discontinuity that separates two modes: low- and high-ground reaching velocity caused by the presence of two distinct trim points, with precautionary measures that should be taken to prevent the occurrence of the latter. From this set of procedures, three key input conditions that significantly affect the safety-related measures were identified, namely, the altitude, pitch rate, and path angle of the capsule during the breakup. Subsequently, explainability techniques were utilized to give suggestions on how to control the input variability and avoid the high ground reaching velocity mode, aiming to achieve more dependable predictions for the three safety parameters mentioned earlier.

Multi-type synchronization for coupled van der Pol oscillator systems with multiple coupling modes.

In this paper, we investigate synchronous solutions of coupled van der Pol oscillator systems with multiple coupling modes using the theory of rotating periodic solutions. Multiple coupling modes refer to two or three types of coupling modes in van der Pol oscillator networks, namely, position, velocity, and acceleration. Rotating periodic solutions can represent various types of synchronous solutions corresponding to different phase differences of coupled oscillators. When matrices representing the topology of different coupling modes have symmetry, the overall symmetry of the oscillator system depends on the intersection of the symmetries of the different topologies, determining the type of synchronous solutions for the coupled oscillator network. When matrices representing the topology of different coupling modes lack symmetry, if the adjacency matrices representing different coupling modes can be simplified into structurally identical quotient graphs (where weights can be proportional) through the same external equitable partition, the symmetry of the quotient graph determines the synchronization type of the original system. All these results are consistent with multi-layer networks where connections between different layers are one-to-one.

Rail Structural Health Monitoring using ultrasonic guided waves: system design and deployment

Railways are a central industrial infrastructure enabling people and goods transportation all across the globe and their use is due to increase in the forthcoming years to reduce the overall carbon footprint of our modern societies. Hence the need to ensure their reliable use, as traffic interruptions or accidents can have dire social, economic and environmental impacts. In particular, rail breaks can produce such incidents and need to be monitored and prevented if possible. Ultrasonic guided waves are a promising physical phenomenon to monitor rails as they can enable the monitoring of long portions with a limited number of sensors. This talk will present a SHM system relying on such waves for rail monitoring which has been deployed for industrial tests on a subway line. The electronics, the sensors and their coupling to the rail were optimized to ensure the measurement of guided waves after a long-range propagation throughout the life of the system. Indeed, specific couplings are needed to enable long-time coupling, and so ultrasound sensitivity of the system, while the rails are bearing high loads or dilating due to temperature changes. An experimental campaign was carried out to evaluate the sensitivity of the system to rail breaks, and to demonstrate its detection under representative, uncontrolled environmental conditions. Particular considerations linked to pulse-echo inspections, inducing a sensitivity to cut-off frequencies and zero-group velocity modes, will be presented.

Experimental study of ultrasonic wave propagation in a long waveguide sensor for fluid-level sensing

This work reports an ultrasonic long waveguide sensor for measuring the fluid level utilizing longitudinal L(0,1), torsional T(0,1), and flexural F(1,1) wave modes. These wave modes were transmitted and received simultaneously using stainless-steel wire. A long waveguide (12 m) covers a broader region of interest and is suitable in the process industry's hostile environment applications, "fluid levels and temperature measurements." In this work, we used fluids "diesel, water, and glycerin" for measuring fluid levels based on the sensor's reflection factors from time domain and frequency domain signals. We examined the impact of wave modes' attenuation effects for long waveguide sensor design while changing the waveguide lengths. Initially, we obtained the L(0,1) and T(0,1) modes reflections from the 12.6 m waveguide length when one end of the long waveguide was fixed with a shear transducer at 45° orientation. Subsequently, we want to study and identify all wave modes'' (especially F mode) travel distances. Hence, we would like to investigate the guided wave propagation characteristics (attenuation, ultrasonic velocity, and frequency of all wave modes) in the long waveguide while cutting systematically at intervals of 1 meter, starting from its original length of the waveguide 12.6 meters by analyzing the A-scan signals of various lengths of a single waveguide. This simple and cost-effective technique can monitor the high fluid depths and temperature in power plants, oil, and petrochemical industries while designing a long waveguide sensor with appropriate ultrasonic parameters.

Preliminary characterization of anelastic effects in the flexure mechanism for a new Kibble balance at NIST

A new Kibble balance is being built at the National Institute of Standards and Technology (NIST). For the first time in one of the highly accurate versions of this type of balance, a single passive flexure mechanism is used for both modes of operation: the weighing mode and the velocity mode. The mechanism is at the core of the new balance design as it represents a paradigm shift for NIST away from using knife edge-based balance mechanisms, which exhibit hysteresis in the measurement procedure of the weighing mode. Mechanical hysteresis may be a limiting factor in the performance of highly accurate Kibble balances approaching single digit nanonewton repeatability on a nominal 100g mass, as targeted in this work. Flexure-based mechanisms are known to have very good static hysteresis when used as a null detector. However, for larger and especially longer lasting deformations, flexures are known to exhibit anelastic drift. We seek to characterize, and ideally compensate for, this anelastic behavior after deflections during the velocity mode to enable a 10−8 accurate Kibble balance-measurement on a nominal 100g mass artifact with a single flexure-based balance mechanism. A measurement of the anelastic after-effect after static excitation hints that the apparatus produced a result for anelastic relaxation comparable to previously published work. Furthermore, a series of oscillatory displacements similar to those occurring in a velocity mode of a Kibble balance measurement are imposed upon the flexure mechanism and show a significant anelastic relaxation torque resulting in multiple micronewton of force relaxation. The amplitude of this force relaxation could be reduced by counterbending the flexures before performing a force measurement.

On a Spectral Method for β-particle Bound Excitation Collisions in Kilonovae

The interaction of β-particles with the weakly ionized plasma background is an important mechanism for powering the kilonova (KN) transient signal from neutron star mergers. For this purpose, we present an implementation of the approximate fast-particle collision kernel, described by Inokuti following the seminal formulation of Bethe, in a spectral solver of the Vlasov–Maxwell–Boltzmann equation. In particular, we expand the fast-particle plane-wave atomic excitation kernel into coefficients of the Hermite basis, and derive the relevant discrete spectral system. In this fast-particle limit, the approach permits the direct use of atomic data, including optical oscillator strengths, normally applied to photon–matter interaction. The resulting spectral matrix is implemented in the MASS-APP spectral solver framework, in a way that avoids full matrix storage per spatial zone. We numerically verify aspects of the matrix construction, and present a proof-of-principle 3D simulation of a 2D axisymmetric KN ejecta snapshot. Our preliminary numerical results indicate that a reasonable choice of Hermite basis parameters for β-particles in the KN is a bulk velocity parameter u = 0, a thermal velocity parameter α = 0.5c, and a 9 × 9 × 9 mode velocity basis set (Hermite orders of 0–8 in each dimension). For interior-ejecta sample zones, we estimate that the ratio of thermalization from large-angle (≳2.°5) bound excitation scattering to total thermalization is ∼0.002–0.003.

Early-Stage Ice Detection Utilizing High-Order Ultrasonic Guided Waves.

Ice detection poses significant challenges in sectors such as renewable energy and aviation due to its adverse effects on aircraft performance and wind energy production. Ice buildup alters the surface characteristics of aircraft wings or wind turbine blades, inducing airflow separation and diminishing the aerodynamic properties of these structures. While various approaches have been proposed to address icing effects, including chemical solutions, pneumatic systems, and heating systems, these solutions are often costly and limited in scope. To enhance the cost-effectiveness of ice protection systems, reliable information about current icing conditions, particularly in the early stages, is crucial. Ultrasonic guided waves offer a promising solution for ice detection, enabling integration into critical structures and providing coverage over larger areas. However, existing techniques primarily focus on detecting thick ice layers, leaving a gap in early-stage detection. This paper proposes an approach based on high-order symmetric modes to detect thin ice formation with thicknesses up to a few hundred microns. The method involves measuring the group velocity of the S1 mode at different temperatures and correlating velocity changes with ice layer formation. Experimental verification of the proposed approach was conducted using a novel group velocity dispersion curve reconstruction method, allowing for the tracking of propagating modes in the structure. Copper samples without and with special superhydrophobic multiscale coatings designed to prevent ice formation were employed for the experiments. The results demonstrated successful detection of ice formation and enabled differentiation between the coated and uncoated cases. Therefore, the proposed approach can be effectively used for early-stage monitoring of ice growth and evaluating the performance of anti-icing coatings, offering promising advancements in ice detection and prevention for critical applications.

Electric Vehicle Battery Disassembly Using Interfacing Toolbox for Robotic Arms

This paper showcases the integration of the Interfacing Toolbox for Robotic Arms (ITRA) with our newly developed hybrid Visual Servoing (VS) methods to automate the disassembly of electric vehicle batteries, thereby advancing sustainability and fostering a circular economy. ITRA enhances collaboration between industrial robotic arms, server computers, sensors, and actuators, meeting the intricate demands of robotic disassembly, including the essential real-time tracking of components and robotic arms. We demonstrate the effectiveness of our hybrid VS approach, combined with ITRA, in the context of Electric Vehicle (EV) battery disassembly across two robotic testbeds. The first employs a KUKA KR10 robot for precision tasks, while the second utilizes a KUKA KR500 for operations needing higher payload capacity. Conducted in T1 (Manual Reduced Velocity) mode, our experiments underscore a swift communication protocol that links low-level and high-level control systems, thus enabling rapid object detection and tracking. This allows for the efficient completion of disassembly tasks, such as removing the EV battery’s top case in 27 s and disassembling a stack of modules in 32 s. The demonstrated success of our framework highlights its extensive applicability in robotic manufacturing sectors that demand precision and adaptability, including medical robotics, extreme environments, aerospace, and construction.

Boosted Incremental Nonlinear Dynamic Inversion for Flexible Airplane Gust Load Alleviation

Active gust load alleviation is an important technology for reducing loads on future commercial airplanes so that the structure can be designed to be lighter in order to save fuel. For the intense reduction of gust loads, a highly reactive control system of sensors, control algorithms, and actuators is required, which is not yet available. In this paper, a control algorithm based on incremental nonlinear dynamic inversion is extended so that actuators respond faster. The control algorithm is applied to a future medium-range aircraft with distributed trailing-edge flaps. It is assumed that the vertical acceleration of the center of gravity and the displacement, velocity, and acceleration of the first wing bending mode are available as feedback variables. To allow comparability with other actuator and sensor setups, the authors abstract the actuator dynamics and sensor filter as control system time delay. The feedback gains are adjusted automatically to the control system time delay. In simulation, the authors investigate the influence of the control system time delay on the peak gust loads. They show that gust loads can indeed be intensely reduced with sufficiently small control system time delay in simulation.

Study on monitoring broken rails of heavy haul railway based on ultrasonic guided wave

Real-time monitoring of broken rails in heavy haul railways is crucial for ensuring the safe operation of railway lines. U78CrV steel is a common material used for heavy haul line rails in China. In this study, the semi-analytical finite element (SAFE) method is employed to calculate the dispersion curves and modal shapes of ultrasonic guided waves in U78CrV heavy steel rails. Guided wave modes that are suitable for detecting rail cracks across the entire cross-section are selected based on the total energy of each mode and the vibration energy in the rail head, web, and foot. The excitation method for the chosen mode is determined by analyzing the energy distribution of the mode shape on the rail surface. The ultrasonic guided wave (UGW) signal in the rail is analyzed using ANSYS three-dimensional finite element simulation. The group velocity of the primary mode in the guided wave signal is obtained through continuous wavelet transform to confirm the existence of the selected mode. It is validated that the selected mode can be excited by examining the similarity between the vibration shapes of a specific rail section and all modal vibration shapes obtained through SAFE. Through simulation and field verification, the guided wave mode selected and excited in this study demonstrates good sensitivity to cracks at the rail head, web, and foot, and it can propagate over distances exceeding 1 km in the rail. By detecting the reflected signal of the selected mode or the degree of attenuation of the transmitted wave, long-distance monitoring of broken rails in heavy-haul railway tracks can be achieved.

Thermoacoustic velocity and pressure oscillations in one-dimensional combustors with spatially varying heat sources and thermal distributions

In this work, an asymptotically based framework using a naturally occurring perturbation parameter is further developed in the context of a one-dimensional tube with an open–open end point configuration without and with a spatially variable heat source. This approach is shown to produce accurate predictions of not only pressure waveforms, as previously demonstrated, but also of velocity mode shapes and frequencies for arbitrary temperature distributions that mimic a wide variety of flow heating arrangements. These include those associated with a Rijke tube as well as other thermoacoustic sound-generation devices. The underlying formulation consists of two linearly coupled partial differential equations that can be solved simultaneously while using a Green's function to capture the thermoacoustically induced velocity. The strategy leading to accurate predictions of the thermoacoustic velocity is described and then applied to several representative cases. Results pertaining to the acoustic velocity and pressure are systematically discussed and compared to other models in the literature. Overall, we find the axially dependent thermal gain to have the most significant impact on the mode shape structure, frequencies, and nodal locations. For example, higher thermal gains lead to elevated wave propagation speeds in the downstream segment of the tube. As such, they cause the velocity nodes to gradually shift upstream with successive increases in the thermal gain. Moreover, due in part to a non-homogeneous pressure–temperature pumping term that appears exclusively in the acoustic velocity formulation, the main difference between the acoustic pressure and velocity oscillation frequencies can be directly attributed to specific derivatives of the spatially varying thermal profiles.

Embedded shear layers in turbulent boundary layers of a NACA0012 airfoil at high angles of attack

An investigation of turbulent boundary layers (TBLs) is presented for a NACA0012 airfoil at angles of attack 9 and 12 deg. Wall-resolved large eddy simulations (LES) are conducted for a freestream Mach number M=0.2 and chord-based Reynolds number Re=4×105, where the boundary layers are tripped near the airfoil leading edge on the suction side. For the angles of attack analyzed, mild, moderate and strong adverse pressure gradients (APGs) develop over the airfoil. Despite the strong APGs, the mean flow remains attached along the entire airfoil suction side. Similarly to other APG-TBLs investigated in the literature, a secondary peak appears in the Reynolds stress and turbulence production profiles. This secondary peak arises in the outer layer and, for strong APGs, it may overcome the first peak typically observed in the inner layer. The analysis of the turbulence production shows that other components of the production tensor become important in the outer layer besides the shear term. For moderate and strong APGs, the mean velocity profiles depict three inflexion points, the third being unstable under inviscid stability criteria. In this context, an embedded shear layer develops along the outer region of the TBL leading to the formation of two-dimensional rollers typical of a Kelvin–Helmholtz instability which are captured by a spectral proper orthogonal decomposition (SPOD) analysis. The most energetic SPOD spatial modes of the tangential velocity show that streaks form along the airfoil suction side and, as the APG becomes stronger, they grow along the spanwise and wall-normal directions, having a spatial support along the entire boundary layer.

Mechanical resistance behind fiber-reinforced polymer pile: Role of clay minerals

Due to the geotechnical design requirements of the fiber-reinforced polymer (FRP) pile embedded in clay, interface friction evolution between the FRP pile and clay plays a crucial role in determining the pile shaft resistance. It is observed from the experimental evaluation that the earth pressure and shear rate affect the pile-soil interface behavior. In this study, a cross-linked epoxy resin is created to contact a siloxane surface of kaolinite in the molecular dynamic simulation. The interfacial accommodation between kaolinite and epoxy resin is studied. In order to investigate the effect of normal stress and sliding velocity on nanoscale friction characteristics, the steered molecular dynamics is utilized to simulate the sliding of the kaolinite model on the surface of the epoxy resin. Simulation results show that the calculated peak interface shear coefficient decreases nonlinearly as the normal stress increases, which follows a logarithmic relationship consistent with the FRP-soil interface shear test. On the other hand, it is observed that two distinct velocity regions, slow pulling mode (5–200 m/s) and fast pulling modes (300–800 m/s), are well fitted by extended Bell theory. The stick–slip motion is only found in slow sliding velocity mode. This increasing tendency of the energy barrier with the normal stresses indicates that higher pulling forces are required for the FRP to slide along the soil at higher normal stress. The present work provides a fundamental understanding of the friction mechanisms between kaolinite and epoxy resin.

Determination of Young’s Modulus of PET Sheets from Lamb Wave Velocity Measurement

BackgroundThe elastic modulus of polyethylene terephthalate (PET) sheets is typically measured through destructive tests that require specific sample preparation and time-consuming testing procedures.ObjectiveTo improve the efficiency of measuring the elastic modulus of PET sheets, research on a non-destructive measurement approach using guided Lamb waves was conducted.MethodsIn this approach, the group velocity of the zero-order symmetric Lamb wave mode (S0 mode) at a single frequency is first measured from PET sheets. The semi-analytical finite element method (SAFEM) is used as the forward model to calculate the corresponding numerical group velocity. Particle swarm optimisation (PSO) is used to update the elastic modulus in the SAFEM model until the numerical group velocity from the model matches the experimental results.ResultsThe results show that measuring the group velocity data at a single frequency is sufficient for elastic modulus measurement while the material thickness can be assumed as a constant, which improves the efficiency of the measurement. The identified modulus differs from the tensile modulus of the material due to the frequency dependence of the elastic modulus. However, this discrepancy could be eliminated by using a linear regression model.ConclusionsThe method mentioned above can achieve non-destructive and efficient measurement of the elastic modulus of PET sheets, which can potentially be applied for in-line quality inspection in PET bottle production processes.

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory. In semi-infinite space, a nondispersive Rayleigh wave mode exists, and the eigendisplacement decays exponentially with depth. In a layered model with increasing layer velocity, the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer. If the phase velocity is the same as the P- or S-wave velocity of the layer, which is called the critical mode or critical phase velocity of surface waves, the general solution of the wave equation is not a homogeneous (expressed by trigonometric functions) or inhomogeneous (expressed by exponential functions) plane wave, but one whose amplitude changes linearly with depth (expressed by a linear function). Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode, owing to the singularity at the critical phase velocity. In this study, based on the classical framework of generalized reflection and transmission coefficients, the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity. Therefore, the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem. The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models. In contrast to the normal mode, the eigendisplacement associated with the critical phase velocity exhibits different characteristics. If the phase velocity is equal to the S-wave velocity in the bottom half-space, the eigendisplacement remains constant with increasing depth.

Shedding Light on the Ejection History of Molecular Outflows: Multiple Velocity Modes and Precession

Variable accretion has been well studied in the evolved stages of low-mass star formation. However, the accretion history in the initial phases of star formation is still a seldom studied topic. The outflows and jets emerging from protostellar objects could shed some light on their accretion history. We consider the recently studied case of W43-MM1, a protocluster containing 46 outflows driven by 27 protostellar cores. The outflow kinematics of the individual cores and associated knots in W43-MM1 indicate episodic protostellar ejection. We take the observed parameters of an individual core system (core #8) and perform 3D hydrodynamic simulations of such a system, including episodic changes in the velocity of the outflow. The simulations consist of a collimated jet emerging from a core, taking into account one- and two-velocity modes in the variation of the ejection velocity of the jet. In addition, we investigated the effect of including the precession of the jet in the one- and two-velocity-mode models. From the simulations, we constructed position–velocity diagrams and compared them with the observations. We find that including a second mode in the ejection velocity, as well as the precession, are required to explain the positions of the outflow knots and other position–velocity features observed in core #8 in W43-MM1.

A velocity evaluation method for in-pipe metallic flow through inversion of magnetic field perturbation measured surrounding the pipe

It is important to measure the global and/or local velocity of an in-pipe metallic flow to control its running state in applications such as a Tokamak fusion reactor. The magnetic field outside the pipe wall will be perturbed by the motion induced eddy current when the liquid metal flows across an applied static magnetic field. This phenomenon gives a possibility to evaluate the in-pipe velocity from the measured magnetic field perturbation signals. In this paper, a non-intrusive velocity evaluation method is proposed accordingly for measuring the velocity of liquid metal through measurement and inversion of the magnetic field surrounding the pipe. An efficient forward simulation method to calculate the magnetic field near a metallic flow in a static environmental magnetic field is developed at first. An inversion scheme based on the singular value decomposition and the L-curve method is then proposed to reconstruct the velocity distribution at a pipe cross-section with the linear equations correlating the flow velocity and the magnetic field regulated using the Tikhonov method. The reconstruction results of pipe flows of different velocity modes verified the feasibility and efficiency of the proposed velocity measurement method for in-pipe metallic flows.

Enhancing magnetically driven microswimmer velocity via low Reynolds number hydrodynamic interactions

The motion of comoving magnetic microswimmers is modeled by considering the inter-hydrodynamic interactions (HI) under low Reynolds number conditions. The microswimmer is a two-link design consisting of a magnetic head attached to a slender tail via a torsional spring, and it is driven by an external planar oscillatory magnetic field. The inter-HI considered are the head-head and tail-tail interactions. The propulsion velocity for the comoving mode is calculated and compared with that of an isolated mode. The comparative results show that the comoving mode velocity can be either similar or greater than the isolated mode, depending on the actuation frequency. The parametric dependency results show that the velocity generated in comoving mode depends on the average separation distance and length-to-width ratio of the tail. For proof of concept, a low-cost fabrication protocol is implemented to design a millimeter-sized magnetic flagellated swimmer. The experimental result shows that the comoving swimming mode generates larger velocity in comparison to isolated swimming.

Low-order planar pressure reconstruction of stalled airfoils using particle image velocimetry data

We present planar time-resolved particle image velocimetry (PIV) measurements of flow in the streamwise surface-normal plane of a NACA 0012 airfoil at chord-based Reynolds number Rec=7×104. The angles of attack α=13∘ and 15∘ correspond to transient stall and deep stall flow regimes, respectively. A Poisson solver is utilized to reconstruct the instantaneous planar pressure fields from the PIV with satisfactory comparison in the mean pressure compared with dynamically matched Reynolds-averaged Navier-Stokes (RANS) simulations. Using the proper orthogonal decomposition (POD), a systematic reduced-order reconstruction of the velocity fields and subsequent pressure fields is used to quantify the required number of velocity modes to achieve a desired accuracy in the instantaneous pressure. Further, a Galerkin projection of the Poisson equation onto the POD subspace is used as a framework to identify the relative contribution of each velocity mode on the resulting pressure field via quadratic stochastic estimation (QSE). In both cases, the zeroth mode (corresponding to the mean) is of leading-order importance. In addition, a tendency of the zeroth mode to interact with vortex-shedding modes is identified. Published by the American Physical Society 2024

A conical spiral piezoelectric energy harvester with parallel beams for all-directional flow energy harvesting

Piezoelectric energy harvesting technology using flow-induced vibration is a type of interference-resistant and miniaturizable power generation technology, which is promising on powering the wireless micro electromechanical system in flow filed. However, the flow direction of the natural flow field is changeable while most existing flow-induced piezoelectric energy harvesters (PEHs) are limited by their working direction. In this paper, we propose a conical spiral piezoelectric energy harvester with parallel beams (CSPEH-PB) that can collect energy under flow excitation in all directions. Based on the multi-dimensional vibration analysis of conical spiral structure, we investigate the resonance mode and effective flow velocity range of the CSPEH-PB through numerical analysis. In comparative experiments with a bimorph flat PEH, we verify the effective flow velocity range and voltage of the CSPEH-PB and polyvinylidene fluoride (PVDF) films attached. The results demonstrate that the CSPEH-PB generates an effective voltage greater than 0.53 V through the PVDF films under any direction of the water flow, and has a wider resonance bandwidth than PEH with straight beam. This study provides a practical solution for adapting PEHs to changeable flow direction.