Lock Range Research Articles

Numerical investigation of local scour around a 2-degree of freedom vibrating subsea pipeline in steady flow under sagging condition

Numerical simulations are conducted to investigate the local scour below a sagging subsea pipeline vibrating in two degrees of freedom (2-DOF), covering a sagging ratio from −0.3 to 0 and a wide range of reduced velocities from 0.5 to 15. A negative sagging ratio means that the static balance position of the bottom surface of the pipeline is below the sand surface. The combined effects of the sagging and 2-DOF vibration of the pipeline on the scour are investigated. The maximum scour depth of the 2-DOF vibrating pipeline in the lock-in range of the vibration increases by 10% compared to the 1-DOF; however, the reduced velocity where the maximum scour depth occurs changes from 5 to 6. The variations of the vibration amplitude with the reduced velocity for all the sagging ratios follow a similar trend. For embedment ratios of −0.4 to −0.3, initial condition of scour simulation affects the equilibrium scour depth and vibration amplitudes. Simulations with a flat sand surface as initial condition prevent full scour development because the pipeline reaches its static balance position due to weak flow through the pipeline-to-bed gap. However, if the simulation starts with a sufficiently large initial scour depth, scour can reach its equilibrium.

Multi-directional and multi-modal vortex-induced vibrations for wind energy harvesting

A conventional vortex-induced vibration (VIV)-based energy harvester is typically restricted to capturing wind energy from a very limited range of wind directions, making it inefficient in varying wind conditions. This Letter proposes a tri-section beam configuration for VIV-based piezoelectric energy harvester to enable harnessing wind energy from varying incident angle with different vibration modes being triggered. The finite element analysis investigates the tri-section beam harvester's mode shapes and natural frequencies. A wind tunnel experiment is conducted for a comparative study of the energy output performance of the harvesters with straight and tri-section beams. The findings show that the proposed harvester with the tri-section beam can efficiently capture wind energy from a much wider range of incident angles, as opposed to the specific limited directions of its counterpart with the straight beam. The proposed harvester can also widen the lock-in speed range with a higher bending mode being triggered and achieve the optimal output power of 1.388 mW when the proposed harvester works in the second mode at a higher natural frequency, superior to that of its counterpart (0.386 mW) that can only work in the first mode. The proposed configuration sheds light on developing multi-directional and multi-modal VIV-based energy harvesters adapted to wind conditions in natural environments.

Rotary Topological Defects in an Oscillator Lattice Loop and Their Injection Locked Properties

ABSTRACTThe lattice loop formed by adjacent coupling of tunnel diode LC oscillators has been shown to generate topological defects due to broken mirror symmetry, which rotate in the opposite direction to the rotating pulse. Leveraging the injection locking of the rotational dynamics of these topological defects can lead to a subharmonic injection locking scheme with a large division ratio. This paper aims to enhance the design by elucidating the relationship between loop size, the number of topological defects, and the division ratio. Furthermore, we perform bifurcation analysis of the injection locking system, demonstrating that when the external signal strength reaches a certain threshold, defect pinning by the external signal occurs, leading to an extension of the lock range. The dynamics of topological defects are well suited to the so‐called progressive multiphase injection locking. In this paper, we clarify the degree of lock range extension achieved by introducing this technique.

Reduction of vortex-induced vibrations of a cantilevered hydrofoil with passive piezoelectric shunt

This work first investigates the ability of a low order fluid-structure model to fit the vortex-induced vibrations (VIV) observed on a truncated hydrofoil in a hydrodynamic tunnel. A particular VIV area is scrutinized, for which a hydrodynamic excitation mechanism due to a Karman-type vortex wake organization successively locks the first torsional and second bending mode of the cantilevered hydrofoil. Coupling two structure oscillators with a Van der Pol wake oscillator satisfactorily reproduces the amplitude response and the lock-in frequency. In order to build a low order model allowing to optimize control strategy, a fourth degree of freedom corresponding to the electric circuit of a resonant piezoelectric shunt has been added. Composed of an inductance and a resistance connected to a piezoelectric patch, the passive shunt was tuned to minimize the vibration amplitude in the frequency lock-in range. Model predictions are finally compared with experimental results.

Experimental investigation on vortex-induced vibration characteristics of the dual parallel suspenders

This study investigates vortex-induced vibrations (VIVs) on dual parallel suspenders using wind tunnel experiments and employs a two-degree-of-freedom setup for each circular cylinder to closely simulate actual structural conditions. The VIV responses of dual cylinders exhibit notable deviations and complexity due to aerodynamic interaction. Results indicate a significant shift in the VIV lock-in range towards higher values for dual cylinders, compared to single ones. Both upstream and downstream cylinders demonstrate lower maximum VIV amplitudes than the single-cylinder. The cylinders exhibit effects of negative aerodynamic damping within the VIV process, with the aerodynamic damping becoming more pronounced as amplitude increases. Additionally, the time-dependent phase relationship between the cylinders contributes to these variations in response. Further analysis of surface wind pressure distribution reveals that aerodynamic interference in dual-cylinder systems leads to intricate pressure patterns and modal behaviors.

A V-band injection locking tripler with 26.8% locking range and 7.3-dBm output power in 65 nm CMOS

With a 65-nm CMOS process, a V-band wideband injection locking (IL) frequency tripler is proposed by cascading a multiplier and a driver amplifier stage. Concerning high output power and efficiency performance over a wideband locking range (LR), two transformer-based IL topologies are analyzed in the multiplier and driver stages, in which the cross-coupled pair is connected at the input and output ports of the transformer, respectively. Moreover, the active device is carefully designed in terms of the operating point of the harmonic generator and device sizing in the driver amplifier stage. With measurements, the proposed tripler achieves a maximum measured output power of 7.3 dBm with 22.4% output-to-DC power efficiency and 26.8% LR from 50.4 to 66 GHz. Including the output driver amplifier, the IL tripler consumes 24 mW DC power. The measured fundamental and 2nd-harmonic rejection ratios (HRR) are both better than 30 dBc, while the measured phase noise (PN) degradation is in close agreement with the theoretical value.

A 1–6.5 Gbps dual-loop CDR design with Coarse-fine Tuning VCO and modified DQFD

A dual-loop CDR (Clock and Data Recovery) is presented to recover digital data from 1 to 6.5 Gbps. The presented frequency acquisition technique is based on full rate clock architecture. By utilizing modified Digital Quadri-correlator Frequency Detector (DQFD) and Frequency Increment/Decrement Control circuit, the lock-in range is improved. Furthermore, the issue of state loss during wide frequency range detection is successfully mitigated. The inclusion of two control wires in the Coarse-fine Tuning VCO enables the utilization of separate loop filters in the dual loops, resulting in a more effective reduction of noise and jitter. Utilizing a 40-nm CMOS process, the presented CDR design has been implemented. The post-layout simulation results at 6.5 Gbps shows a P2P and root-mean-square jitter values are 17.1 ps and 5.79 ps, respectively, for the retimed data.

High-fidelity simulations of airfoil vortex-induced vibrations: from 2D to blade-like aspect ratios

Large edgewise vibrations due to vortex shedding can be suffered by a wind turbine blade when the rotor is stopped or idling and there is massively separated flow. High-fidelity simulations of these vortex-induced vibrations (VIV) with a full-blade model are very computationally expensive, and so currently reported results of this type are limited to short time series or reduced parameter spaces, far from being sufficient to predict the lock-in range and other characteristics of a full-scale blade response to VIV under real conditions. This computational cost has led researchers to, alternatively, study VIV using simplified approaches, like simulations of 2D and short-span airfoil sections. To help bridge the gap between expensive full-blade and short-span airfoil section simulations, in this work the VIV response of an airfoil section is obtained for three different aspect ratios —from 2D to a blade-like aspect ratio—, using CFD simulations coupled with a one-degree-of-freedom structural oscillator model. The results obtained show that inside the lock-in range the airfoil’s initial VIV response is very similar for all aspect ratios studied, despite notable differences in the Strouhal number obtained. In contrast, outside lock-in the aerodynamic forces vary substantially from one case to another.

Numerical investigation of vortex induced vibrations on cylinders

The paper addresses Vortex Induced Vibrations (VIV) caused by tower vortex shedding through LES simulations of a wind tunnel experiment. A high-fidelity (HiFi), Fluid Structure Interaction (FSI) framework for aeroelastic analysis of 3D flexible cylinders is established, based on the open-source Computational Fluid Dynamics (CFD) code OpenFOAM and the coupling library preCICE. In the present study, the FSI framework is employed with the aim to replicate a low Reynolds (Re=26000) forced vibrations wind tunnel experiment of a circular cross-section rigid cylinder. The paper compares predictions of the aerodynamic damping of the oscillating cylinder for different oscillation frequencies within the lock-in range and amplitudes against experimental results. While the model consistently predicts the lock-in range of frequencies and the trends in the variation of the aerodynamic damping with the oscillation amplitude, it falls short of accurately capturing the maximum value of the aerodynamic damping at the onset of lock-in.

Robust damping improvement against the vortex-induced vibration in flexible bridges using multiple tuned mass damper inerters

The tuned mass damper inerter (TMDI) is considered as one of countermeasures to mitigate the very-low-frequency vertical bending vortex-induced vibration (VIV) in flexible bridges. However, the control robustness of the TMDI against the system uncertainty is a serious concern due to the limited inerter span capacity. In this paper, the multiple tuned mass damper inerter (MTMDI) is used instead of identical TMDIs to provide a robust equivalent damping ratio against the uncertain VIV within the entire lock-in wind speed range. A design framework of the MTMDI considering the inerter span length is proposed based on a universal VIV model suitable for the fully closed, centrally slotted, and semi-closed box decks. In the framework, the fluctuation of VIV characteristics with the wind speed, the probability of occurrence of the VIV, and the uncertainties in VIV characteristics and deck dynamics are considered, simultaneously. Two objection functions are defined to focus on the maximizing the equivalent damper ratio and reducing the VIV mitigation failure, respectively. Finally, numerical analysis of a flexible bridge-MTMDI system subjected to the VIV is performed. The results show that the wind speed probability distribution plays a role of weighting coefficient in the MTMDI optimization. The choice of the objective function depends on the mass ratio of the MTMDI and the level of the system uncertainty. The well-optimized MTMDI achieved a more robust control result than the TMDI within the entire lock-in wind speed range.

Self-cascode and self-biased Dickson charge pump for fast locking wide lock range PLL with reduced phase noise

The charge pump is a fundamental component in phase-locked loop (PLL) circuits, essential for generating a control voltage that adjusts the frequency and phase of the voltage-controlled oscillator (VCO) to match the input reference signal. The self-cascode and self-biased Dickson charge pump architecture presented in this work addresses several key challenges encountered in conventional PLL designs. By integrating self-cascode techniques, the charge pump exhibits enhanced charging and discharging capabilities, enabling faster locking times essential for wide lock range PLLs. This comprehensive approach offers a compact and integrated solution that simultaneously enhances locking speed, widens the lock range, reduces phase noise, and simplifies design complexity, making it highly suitable for demanding applications in communication systems, radar, and wireless technologies. The novel CP is implemented in 90-nm CMOS technology with a 1.0-V supply voltage. It is integrated with a phase-locked loop (PLL) that has a lock time of 1.0 us, a negligible reference spur, and an average power consumption of 34.7 mW. The PLL is having a wide lock range of 0.98 GHz to 2.98 GHz with a center frequency of 1.54 GHz where the phase noise is calculated to be −100.9 dBc/Hz at 1 MHz offset frequency. This makes the PLL compatible with both GSM having 1.8 GHz and Wi-Fi having 2.8 GHz frequency bands. The proposed PLL is also capable of operating at a wide range of temperatures (−27 °C, 0 °C, 27 °C, 84 °C) and at various corners (NN, FS, SF, SS, FF) making it reliable in adverse circumstances.

Numerical investigation of vortex-induced vibrations (VIV) of a rotating cylinder in in-line and cross-flow directions subjected to oscillatory flow

This study investigates vortex-induced vibration (VIV) generated by a rotating circular cylinder across various rotation rates (α = 0, 0.25, 0.50, 0.75, and 1) subjected to oscillatory flow through two-dimensional numerical simulations. Numerical simulations are performed for two Keulegan-Carpenter (KC) numbers, 5 and 10, at Reynolds number (Re) of 150. A wide range of Reduced Velocity (Vr) is considered, ranging from 1 to 20. The vibration amplitude in both inline and cross-flow directions is significantly affected by the rotation of the cylinder, as well as the KC number and Vr. Notably, the impact of rotation is more pronounced on cross-flow direction vibrations than on in-line direction vibrations. For a non-rotating cylinder (α = 0), the cross-flow direction vibration for both KC numbers nearly ceases after surpassing the critical value of reduced velocity: Vr = 6 for KC = 5 and Vr = 11 for KC = 10. In rotating cylinders (α ≠ 0), vibration amplitude becomes zero only at the critical reduced velocity, beyond which it increases and eventually stabilizes. It is also observed that rotation rates significantly influence VIV behavior, notably widening the lock-in range of Vr for rotating cylinders compared to non-rotating ones. The vortex shedding is significantly affected by the rotation and becomes asymmetric.

Optimal external forces of the lock-in phenomena for flow past an inclined plate in uniform flow.

We theoretically studied the optimal control, frequency lock-in, and phase lock-in phenomena due to the spatially localized periodic forcing in flow past an inclined plate. Although frequency lock-in is evident in many fluid phenomena, especially fluid-structure interactions, not many researchers have investigated it using a theoretical approach based on flow details. We obtained detailed information on the lock-in phenomena to external periodic forcing using phase reduction theory, a mathematical method for extracting the dynamics near the limit cycle. Furthermore, the optimal forces applied to the velocity field were determined under the condition of the minimum forcing energy and maximum lock-in range. The study of uniform periodic forces applied within spatially confined regions led to the conclusion that the effective lock-in position, which includes both the upstream and downstream areas of the plate, depends on the principal frequency of the force. The frequency lock-in range of these forces was analyzed and compared with theoretical predictions.

Angular vortex-induced vibrations of a cylinder

We consider the response of a flexibly-mounted cylinder placed in flow and free to oscillate on a curved path about a pivot point. The curved path could be concave (i.e., bent toward the incoming flow) or convex (i.e., bent away from the incoming flow). We consider different radii of curvature for both the concave and the convex paths and show that oscillations are observed for radii of curvature larger than one cylinder diameter. In general, we show that the oscillations are of larger amplitudes in the convex orientation, reaching angles of oscillations of up to 38° and normalized (with respect to the cylinder's diameter) amplitudes of oscillations in the transverse and inline directions of up to 1.1 and 0.35, respectively. The oscillations on the concave path are of smaller amplitudes, but last up to higher values of reduced velocities than those in the convex orientation. The shedding and oscillation frequencies increase with increasing reduced velocity for the concave orientation reaching values of around 1.8 times the system's natural frequency in water at the end of the lock-in range, while for the convex orientation, the frequencies stay close to the natural frequency and only jump from values slightly lower than the natural frequency to values slightly higher than the natural frequency when the oscillation amplitude drops from an upper branch to a lower branch in the VIV amplitude response. Two single vortices are observed in the wake when oscillation amplitudes are relatively low, and two pairs of vortices of different sizes are observed in the wake when amplitudes are relatively larger. When two pairs of vortices are observed, the cylinder carries two bound vortices with it during its transverse oscillations and sheds them in the form of a pair of vortices of different sizes at the end of each half cycle. In the cases with the largest amplitudes of oscillations, besides the vortices that are shed synchronized with the oscillation frequency, several smaller-size vortices are shed in the wake as the cylinder traverses its crossflow path. We relate the reason for observing larger amplitudes of oscillations on the convex path to the relative orientation of the fluctuating forces that are exerted on the cylinder due to the shedding of vortices in its wake with respect to its oscillation path.

Optimizing Bladeless Wind Turbines: Morphological Analysis and Lock-In Range Variations

This study presents a comprehensive exploration centred on the morphology and surface structure of bladeless wind turbines (BWTs) aimed at optimizing their wind energy harvesting capability. Unlike conventional wind technology where vortex-induced vibration (VIV) is seen as problematic due to aeroelastic resonance, this effect becomes advantageous in BWT energy harvesters, devoid of frictional contact or gears. The primary objective of this study is to develop an optimal BWT design for maximizing energy output. Specifically, this study delves into optimizing the energy performance of these VIV wind energy harvesters, investigating how the geometry (shape and roughness) influences their operating range, known as Lock-In range. The results demonstrate how variations in geometry (convergent, straight, or divergent) can shift the Lock-In range to different Reynolds numbers (Re), modelled by the equation: Re (max Lock-In) = 0.30 α + 4.06. Furthermore, this study highlights the minimal impact of roughness within the considered test conditions.

An evenly-spaced-phase all-digital DLL using dual-loop SAR control

This study introduces an all-digital delay-locked loop (ADDLL), which generates 20 evenly-spaced-phase clock signals. A successive-approximation register (SAR)-based dual-loop control is used to realize the locking process of the ADDLL. A modified SAR unit combined with a tri-state digital phase detector (TSDPD) is adopted to achieve a closed-loop operation of the ADDLL. A delay matrix, which can significantly reduce the jitter accumulation, is used to generate evenly spaced phases without using a long-cascaded delay line. Additional harmonic-lock detector circuits are added to the two control loops to avoid the harmonic lock issue. The ADDLL is designed and fabricated using a 0.18μm mixed-signal CMOS technology with an active area of 0.109 μm2. The lock range of the ADDLL is 30–230 MHz and the power consumption of the ADDLL is 8.9 mW at 100 MHz. The measured rms jitter is 23.3 ps at 100 MHz, and the results show a good linearity of the multiphase outputs at a 100 MHz input clock where the maximum DNL and INL are 0.08 and -0.22 LSB, respectively. The proposed ADDDLL is highly suitable for low-frequency, low-power, and high-time-resolution applications.

A wide locking range injection‐locked frequency divider with an auto‐adjusted injection bias

AbstractThis paper presents a Ku‐band divide‐by‐2 direct injection‐locked frequency divider (ILFD) with a wide locking range (LR) and high input sensitivity. The proposed ILFD incorporates an auto‐adjusted injection bias that uses a power detector (PD) to convert the power of the injected signal to a DC voltage. The bias voltage of the injection transistor is then auto‐adjusted in response to the output of the PD. The proposed ILFD employs a 2‐bit switched capacitor array to further enhance the entire LR. Implemented in a 65‐nm CMOS process, the experimental results show that the proposed ILFD achieves an LR of 62.3% (10.5–20 GHz) and 51.2% (11.2–18.9 GHz) at 0 and −10 dBm injection power, respectively. The proposed ILFD consumes 3.6 mW from a 0.6 V supply, and the core area is 0.067 mm2.

A Self-Adaptive Dual-ILRO Clock-Recovery Technique for Two-Tone Battery-Free Crystal-Free Neural-Recording SoC.

Wireless implantable devices are widely used in medical treatment, which should meet clinical constraints such as longevity, miniaturization, and reliable communication. Wireless power transfer (WPT) can eliminate the battery to reduce system size and prolong device life, while it's challenging to generate a reliable clock without a crystal. In this work, we propose a self-adaptive dual-injection-locked-ring-oscillator (dual-ILRO) clock-recovery technique based on two-tone WPT and integrate it into a battery-free neural-recording SoC. The 2[Formula: see text]-order inter-modulation (IM2) component of the two WPT tones is extracted as a low-frequency reference for battery-free SoC, and the proposed self-adaptive dual-ILRO technique extends the lock range to ensure an anti-interference PVT-robust clock generation. The neural-recording SoC includes a low-noise signal acquisition unit, a power management unit, and a backscatter circuit to perform neural signal recording, wireless power harvesting, and neural data transmission. Benefiting from the 6.4 μW low power of the clock recovery circuit, the overall SoC power is cut down to 49.8 μW. In addition, the proposed clock-recovery technique enables both signal acquisition and uplink communication to perform as well as that synchronized by an ideal clock, i.e., an effective number of 9.6 bits and a bit error rate (BER) less than 4.8 × 10-7 in chip measurement. The SoC takes a die area of 2.05 mm 2, and an animal test is conducted in a Sprague-Dawley rat to validate the wireless neural-recording performance, compared to a crystal-synchronized commercial chip.

Spatio-temporal distribution of aerodynamic forces and their associated vortex drift patterns around a closed-box girder during torsional vortex-induced vibration

Torsional vortex-induced vibrations (VIVs) pose potential risks to prototype bridges with increasing spans and lower damping levels. However, the underlying mechanism remains unclear. Wind tunnel tests revealed that torsional VIVs occurred at an initial attack angle of + 3°. To unravel the VIV mechanism throughout the lock-in range, encompassing the ascent stage, amplitude extremum, and descent stage, the spatio-temporal distribution of aerodynamic forces around the bridge girder was analyzed. The results demonstrated the presence of traveling pressure waves with approximately 2.5 wavelengths and three uniformly distributed separated vortices over the upper side throughout the lock-in range. The primary source of these travelling pressure waves stemmed from the vortex drift patterns, with the aerodynamic wave travelling velocity equating the vortex drift velocity. The formation of separated vortices, known as the “double-vortex model”, occurred at the windward barrier on the upper side and windward maintenance rail on the lower side. These vortices directly imposed travelling pressure waves on the girder, thereby inducing torsional VIVs. Among them, the former vortices contributed more to the VIVs than the latter. Therefore, the formation of separated vortices and their related aerodynamic waves in the windward edge with the 2nd SVM/AWM modes predominantly governed the occurrence of torsional VIVs. Furthermore, both the ratio of the wave travelling time to the vibration period and the mean value of the wave travelling velocity ratio exhibited an inverse relationship with the VIV responses. However, the actions exerted by the vortex drift patterns were proportional to the VIV responses on both the upper and lower sides. Therefore, there existed evolutionary characteristics of aerodynamic waves and their related vortex drift patterns throughout the lock-in range, which was responsible for the “lock-in” phenomena.

Suppression of vortex-induced vibrations of a cylinder in inertial-elastic flow

We study Vortex-Induced Vibration (VIV) of a one-degree-of-freedom cylinder placed in inertial-elastic flows experimentally. We show that there is a critical Reynolds number for the onset of VIV in these flows and this critical Reynolds number increases when the elasticity in the fluid is increased. We also show that at a constant Reynolds number, adding elasticity to the fluid reduces the amplitude of oscillations and eventually suppresses VIV entirely. For the cases where VIV is observed, the onset of the lock-in range does not depend on the Reynolds number, as a result of the competing effects of shear-thinning and elasticity. The vortices that are observed in the wake are significantly different from those observed in Newtonian VIV: the vortices are S-shaped with relatively long tails that influence the formation of the vortices that are formed in the following cycle.