Rope Dynamics Research Articles

Computational Study of Pump Turbine Performance Operating at Off-Design Condition-Part I: Vortex Rope Dynamic Effects

As global power demand increases, hydropower plants often must operate beyond their optimal efficiency to meet grid requirements, leading to unstable, high-swirling flows under various load conditions that can significantly shorten the lifespan of turbine components. This paper presents an in-depth computational study on the performance and dynamics of a pump-turbine operating under 80% partial load, focusing on the formation and impact of vortex ropes. Large Eddy Simulation (LES) was utilized to model the turbulent flow, revealing complex patterns and significant pressure fluctuations. A pronounced straight vortex rope was identified in the draft tube, maintaining its trajectory and core size consistently, profoundly affecting flow characteristics. Pressure fluctuations were observed at various cross-sectional planes, with peaks and troughs primarily near the runner, indicating areas prone to instability. The standard deviation of pressure fluctuations ranged from 4.51 to 5.26 along the draft tube wall and 4.27 to 4.97 along the axial center, highlighting significant unsteady flow. Moreover, the frequency corresponding to the highest amplitude in pressure coefficient spectrographs remained consistent at approximately 9.93 to 9.95, emphasizing the persistent influence of vortex rope dynamics. These dynamics affected power generation, which was approximately 29.1 kW, with fluctuations accounting for about 3% of the total generated power, underscoring the critical impact of vortex rope formation on the performance and operational stability of pump-turbines under off-design conditions. This study provides essential insights vital for enhancing the design and operational strategies of these turbines, ensuring more efficient and reliable energy production in the face of increasing power demands.

Advances in elevator dynamics

The dynamics of an elevator system and therefore the ride quality in the car is governed by the masses, rope elasticities and a variety of excitations involved. In case of tall buildings, the rope mass significantly participates to the vertical dynamics and effects of longitudinal waves result in complex system interactions. The mechanical model presented allows to accurately simulate the vertical dynamics of an elevator system, including effects of wave propagation with reflection, standing waves and resonances depending on the parameters involved. Considering the drive control and its parameters as well, testing efforts can be heavily reduced, as ride quality and suitable control parameters can be determined in advance. To further improve ride quality, possible modifications of damping, decoupling and tuned mass dampers can be added to the model and real system if needed. Simulation results are presented and compared with measurements and provide additional insight into the rope dynamics, which are not accessible by measurements.

Dynamics and emission properties of flux ropes from two-temperature GRMHD simulations with multiple magnetic loops

Context. Flux ropes erupting in the vicinity of a black hole are thought to be a potential model for the flares observed in Sagittarius A*. Aims. In this study, we examine the radiative properties of flux ropes that emerged in the vicinity of a black hole. Methods. We performed three-dimensional two-temperature general relativistic magnetohydrodynamic (GRMHD) simulations of magnetized accretion flows with alternating multiple magnetic loops and general relativistic radiation transfer (GRRT) calculations. In the GRMHD simulations, we implemented two different sizes of initial magnetic loops. Results. In the small loop case, magnetic dissipation leads to a weaker excitement of magneto-rotational instability inside the torus, which generates a lower accretion rate compared to the large loop case. However, the small loop case generates more flux ropes due to frequent reconnection by magnetic loops with different polarities. By calculating the thermal synchrotron emission, we found that the variability of light curves and the emitting region are tightly related. At 230 GHz and higher, the emission from the flux ropes is relatively stronger compared to the background, which is responsible for the filamentary structure in the images. At lower frequencies (e.g., 43 GHz), emission comes from more extended regions, which have a less filamentary structure in the image. Conclusions. Our study shows that self-consistent electron temperature models are essential for the calculation of thermal synchrotron radiation and the morphology of the GRRT images. Flux ropes contribute considerable emission at frequencies ≳230 GHz.

Structural design and control strategy of a cable-driven robot under high-altitude facade conditions with large span and multiple constraints

Purpose This paper explores the challenges of using cable-driven parallel robots on high-altitude, large-span facades, where redundancy in multicable systems and the elastic deformation of the cables are significant issues. This study aims to improve the accuracy and stability of the work platform through enhanced control strategies. These strategies address the redundancy in multicable systems and reduce the risks associated with cable deformation and mechanical failures during large-span movements. Design/methodology/approach The paper proposes a dynamic model for a four-rope parallel robot designed explicitly for large-span applications. The study introduces a position–force control strategy incorporating kinematic inverse solutions and a rope dynamics model to account for rope elasticity and its effects. This approach increases the number of system equations to match the unknowns, effectively solving the redundancy problem inherent in multicable systems. In addition, the tension changes of ropes and the stability of the working platform are examined under different motion distances (X = 50 m and X = 100 m) and varying Young’s modulus values (K = 5000 MPa and K = 8000 MPa). Findings This study’s large-span rope force–position control strategy successfully resolves the typical nonlinear characteristics and external disturbances in multicable parallel systems. By continuously monitoring and adjusting cable tension and end positions, this strategy ensures precise control over each cable’s tension, optimizes the distribution of cable tensions and maintains the system’s stability and response speed. The analysis in this paper indicates that this control strategy significantly improves the motion accuracy of robots operating on large-span high-altitude facades. Practical implications Industry adoption: The design and control strategies developed for the four-cable-driven parallel robot can be adopted by companies specializing in facade maintenance, construction or inspection. This could lead to safer, more efficient and cost-effective operations, especially in challenging environments like high-rise buildings. Innovation in robotic solutions: The research can inspire innovation within the field of robotics, particularly in developing robots for specific applications such as large surface maintenance. It showcases how adaptive control and stability can be achieved in complex operational scenarios. Safety improvements: By demonstrating a more stable and precise control mechanism for navigating large facades, the study could contribute to significant safety improvements, reducing the risk of accidents associated with manual facade maintenance and inspection tasks. Originality/value This paper combines the force/position hybrid control method with actual robotic applications, offering a novel solution to the complex issue of controlling cable-driven parallel robots in challenging environments. Thus, it contributes to the field. The proposed method significantly enhances the precision and stability of such systems and provides robust technical support for high-precision tasks in complex mechanical settings.

Multiple Flux Rope Dynamics: MMS Observations and Reconstruction Results

A series of six ion-scale magnetic flux ropes (FR1–6) and a thin current sheet, encountered by Magnetospheric Multiscale spacecraft in the magnetosheath side of the dayside magnetopause boundary layer, are studied for multiple flux rope dynamics in terms of energy conversion and two-dimensional geometry structure. The thin current sheet is identified in between FR1 and FR2. The energy exchange between electromagnetic fields and plasmas is dynamic in FR1–5 and also surrounding the flux ropes, while a low-energy conversion rate is seen in FR6. Different energy conversions exist in the flux ropes: energy dynamo is predominant in FR1 and FR5, while energy dissipation is dominated in FR2–4. Both the energy dynamo and dissipation primarily result from j ∥ E ∥. Strong dissipation, surrounded by an energy dynamo, happens at the thin current sheet and is accompanied by ion agyrotropic behavior. From the reconstructed magnetic field maps, the estimated aspect ratios of the six flux ropes are 0.78, 0.16, 0.66, 0.11, 0.40, and 0.46 in order, and the thickness of the thin current sheet is ∼63 km (∼1.8 ion inertial length). Evidently, the magnetic field map shows that FR4 is a coalescing flux rope where a pronounced dissipation is present. The overall finding agrees with the previous simulation studies of multiple island coalescence.

Magnetic Field Extrapolation in Active Region Well Comparable to Observations in Multiple Layers

Magnetic field extrapolation is a fundamental tool to reconstruct the three-dimensional magnetic field above the solar photosphere. However, the prevalently used force-free field model might not be applicable in the lower atmosphere with non-negligible plasma β, where the crucial process of flux rope formation and evolution could happen. In this work, we perform extrapolation in active region 12158, based on a recently developed magnetohydrostatic (MHS) method that takes plasma forces into account. By comparing the results with those from the force-free field extrapolation methods, we find that the overall properties, which are characterized by the magnetic free energy and helicity, are roughly the same. The major differences lie in the magnetic configuration and the twist number of the magnetic flux rope (MFR). Unlike previous works either obtained sheared arcades or one coherent flux rope, the MHS method derives two sets of MFR, which are highly twisted and slightly coupled. Specifically, the result in the present work is more comparable to the high-resolution observations from the chromosphere, through the transition region to the corona, such as the filament fibrils, pre-eruptive braiding characteristics, and the eruptive double-J-shaped hot channel. Overall, our work shows that the newly developed MHS method is more promising to reproduce the magnetic fine structures that can well match the observations at multiple layers, and future data-driven simulation based on such extrapolation will benefit in understanding the critical and precise dynamics of flux rope before eruption.

A data-driven approach for modifying the rope dynamics model of the flexible hoisting system

In the flexible hoisting system, past research focused on the physical modeling without considering complex external environmental variables such as guided rails excitation and shaft effect, leading to a significant deviation between the physical model and the actual model. However, the physical modeling is difficult to model the actual dynamics of the rope strictly under the actual working conditions. This paper takes a high-speed elevator hoisting system as an example. A modified model combining the physical model and the data-driven model is proposed to mitigate the deviation between the physical model and the actual model. In the experiments, the vibration signals of the rope were extracted from images collected by a camera. A beat-like phenomenon of the vibration signals is discovered in the vibration signals of the rope during the acceleration stage. The experiment results demonstrate that the modified model can more accurately model the dynamics of the rope under the actual working conditions and reduce the absolute error of 75.9% compared with the physical model. The proposed model also provides a reference for the modification of the complex dynamic models.

Kinetic-scale Flux Ropes: Observations and Applications of Kinetic Equilibrium Models

Abstract Magnetic flux ropes with helical field lines and a strong core field are ubiquitous structures in space plasmas. Recently, kinetic-scale flux ropes have been identified by high-resolution observations from the Magnetospheric Multiscale (MMS) spacecraft in the magnetosheath, which have drawn a lot of attention because of their nonideal behavior and internal structures. Detailed investigation of flux rope structure and dynamics requires the development of realistic kinetic models. In this paper, we generalize an equilibrium model to reconstruct a kinetic-scale flux rope previously reported via MMS observations. The key features in the magnetic field and electron pitch-angle distribution measurements of all four satellites are simultaneously reproduced in this reconstruction. Besides validating the model, our results also indicate that the anisotropic features previously attributed to asymmetric magnetic topologies in the magnetosheath can be alternatively explained by the spacecraft motion in the flux rope rest frame.

The SLED project and the dynamics of coronal flux ropes

Investigations of the dynamics of the hot coronal plasma are crucial for understanding various space weather phenomena and making in-depth analyzes of the global heating of the solar corona. We present here numerical simulations of observations of siphon flows along loops (simple semi-circular flux ropes) to demonstrate the capabilities of the Solar Line Emission Dopplerometer (SLED), a new instrument under construction for imaging spectroscopy. It is based on the Multi-channel Subtractive Double Pass (MSDP) technique, which combines the advantages of filters and slit spectrographs. SLED will observe coronal structures in the forbidden lines of FeX 6374 Å and FeXIV 5303 Å, and will measure Doppler shifts up to 150 km s−1 at high precision (50 m s−1) and cadence (1 Hz). It is optimized for studies of the dynamics of fast evolving events such as flares or Coronal Mass Ejections (CMEs), as well as for the detection of high-frequency waves. Observations will be performed with the coronagraph at Lomnický Štít Observatory (LSO), and will also occur during total solar eclipses as SLED is a portable instrument.

Variational Formulations of Flexible Ropes Dynamics Problems

Variational statements of the problems of the dynamics of flexible ropes with significant displacements, the shape of which is determined by constraints and load, are obtained. The position of the flexible rope axis is described by a vector of Cartesian coordinates. The stress state of the rope is characterized by the force in the rope. At present, the methods of calculating the ropes systems are based on a differential formulation. Variational formulations of such problems are proposed.

Examining the Magnetic Geometry of Magnetic Flux Ropes from the View of Single-point Analysis

Abstract Magnetic flux ropes, characterized as magnetic field lines that wrap and rotate around a central axis, are observed ubiquitously in the space-plasma environment. Accurately examining the physical parameters (e.g., axis orientation, helical handedness, current density, curvature radius, and size) of flux ropes is essential for studying their evolution and associated dynamics. The geometric parameters of flux ropes can be resolved by a cluster of at least four spacecraft with the separation scale much smaller than the flux ropes. However, most spacecraft missions are of single-point measurements, especially for the missions on other planets (e.g., Mars, Venus, Mercury), thus, the method for investigating the flux ropes based on single-point measurements becomes particularly important. A single-point method that infers the axis orientation of flux ropes was recently developed by Rong et al. Here, we apply this method to study two flux ropes observed by the Magnetospheric Multiscale Mission (MMS), one close to the force-free field and the other close to the non-force-free field, by comparing them with the multipoint analysis of MMS. Our study demonstrates that, apart from axis orientation, the method of Rong et al. can reasonably infer the current density, curvature radius of magnetic field, and the transverse size of flux ropes. We discussed the main error sources of calculated parameters, and suggest that it is worthwhile to widely apply the method by Rong et al. to single-point spacecraft missions for the purpose of examining the geometry and dynamics of flux ropes.

Study on the method of reducing the pressure fluctuation of hydraulic turbine by optimizing the draft tube pressure distribution

Francis turbines within hydropower plants are required to operate under off-design conditions to meet the grid demand and ensure stability. In line with this, part-load conditions are generally accompanied with draft tube vortex rope appearance and associated pressure pulsations, which may cause structural vibrations and possible plant disruption for severe cases. Therefore, this study makes an attempt weaken the draft tube vortex rope and the associated pressure pulsations for a Francis turbine under part-load conditions (0.6Q opt. ), through the modification of runner hub extension (RHE) design. Four RHE designs were numerically tested, namely Type A, B, C, and D. Experimental tests were carried out to explore real time vortex rope dynamics, which were replicated by numerical simulation method. The RHE design was found to considerably influence the draft tube pressure field characteristics through its filling effect to low pressure zones. The draft tube pressure pulsation analysis showed that all RHE designs exhibited the same pulsation frequency equivalent to 28% of the runner rotational frequency, with different amplitudes. With Type C design, the draft tube vortex rope energy was considerably weakened, leading to lowest pressure pulsation amplitude. Note that this design is a cylindrical RHE with a thickened tail. • Experiments are conducted on Francis turbine part-load conditions. • The draft tube flow is simulated with DES model reproducing the vortex rope presence. • Pressure distribution characteristics were analyzed for different runner hub shapes. • Fast Fourier Transform-based pressure pulsations spectra were extracted for every shape.

Experimental Assessments on the Evaluation of Wire Rope Characteristics as Helical Symmetrical Multi-body Ensembles

The existing literature provides various computational models related to the dynamic behavior of strand wire ropes. It starts from the simple longitudinally oscillating beam, to the complex nonlinear multi-body configuration based on helical structural symmetry. The challenge is the prior availability of characteristic parameters for material behavior, structural configuration, and functional capability. Experimental investigation is the main source for evaluation of these characteristics. However, tests have specifically been performed according to each case, minimizing the generalization aspect. This is the main frame of this study. Hereby, the authors propose an ensemble of spectral investigations, applied to a reduced set of experimental tests regarding wire rope dynamics. The research goal consists of wire rope characterization in terms of the flexible and adaptive groups of parameters, related to the conservative and dissipative behaviors. An experimental setup is considered here according to the rope exploitation conditions in order to enable an extension of the method application from the experimental mode to the operational mode. Experiments are conducted based on classical vibration measurement procedures. The analysis is performed using a spectral method ensemble, including discrete Fourier transform, time-frequency joint analysis, and the Prony method. The result show that the proposed assessments can provide suitable information related to a large group of wire rope models.

Formation of Macroscale Flux Transfer Events at Mercury

Abstract Flux transfer events (FTEs) are magnetic flux ropes that are produced via magnetic reconnection at the planetary magnetopause where the solar wind directly interacts with the magnetosphere. Previous observations show that FTEs with a duration of several seconds, corresponding to a spatial scale of ∼0.5–1 R M, can occur at Mercury. However, the formation of these macroscale FTEs at a small dimensional magnetopause with a radius of ∼1.5 R M remains unclear. Here, we report the observations of active magnetic reconnection events at Mercury’s magnetopause by the MESSENGER spacecraft. The reconnection process is dominated by the formation of a series of multi-scale FTEs. Ion-scale flux ropes, typically with durations of ∼1 s or less, may be produced by the tearing instability in the thin current sheet near the subsolar position. Moreover, the commonly observed macroscale FTEs consist of three to tens of successive small-scale FTEs. We propose that macroscale FTEs at Mercury are generated by the interaction and merging of multiple ion-scale flux ropes, probably through two or more steps. This is distinct from the formation of typical FTEs, mainly between a pair of X-lines, at Earth’s magnetopause. Thus, the formation and evolution of FTEs may differ among planetary magnetospheres with a vast range of scale sizes. We further conclude that Mercury’s magnetopause is a natural plasma laboratory to study flux rope dynamics and evolution for the upcoming Bepi-Colombo mission.

A New Transmission Theory of “Global Dynamic Wrap Angle” for Friction Hoist Combining Suspended and Wrapped Wire Rope

A new transmission theory of “global dynamic wrap angle” for friction hoist is proposed. The theory is based on a mine hoist simulation model which combines the suspended rope with the wrapped rope. Rope dynamics in a suspended section are verified by the field experiment results. The theory holds that the mechanical state of wire rope is dynamic through the whole wrap angle, including deformation, contact and friction. When the rope enters the wrap angle, it provides positive friction and changes direction at a certain boundary point. The demarcation of the boundary depends on the rope load on both sides of the friction pulley. The theory is suitable for accurately analyzing the kinetics of high-speed and heavy-load friction hoisting.

Dynamic Model of Magnetic Flux Ropes

Developing ideas of the paper Zaitsev and Stepanov (2018) with regards to activation of a current-carrying filament with an increase in electric current, in which the Ampere force is opposed by gravity and medium viscosity, we take into account the influence of an external magnetic field. It is shown that, depending on mutual directions of the external magnetic field and electric current in the flux rope, the additional Ampere force can lead to the deceleration or to additional eruption of the flux rope. A phase diagram describing the peculiarities of flux rope dynamics has been constructed. The maximum height and velocity of the flare loop are determined for the event on March 30, 2001.

POD analysis of a vortex rope with transient boundary conditions

The paper presents the results of a POD analysis of the flow in a swirl generator. The generator has two separate inlets – one straight axial inlet and one tangential inlet ended by a spiral case. This allows to set different operating points, which are in turn connected with different shapes of the vortex rope present in the flow field. In this case, the investigation is aimed at linearly varying flow rates at the boundaries, namely, the ratio of the tangential flow rate is increased from 40 % up to more than 80 % of the total flow rate, which is maintained constant. Substituting the POD modes into the energy equation provides additional insight into the energy fluxes between the modes and consequently into a major part of the turbulent flow energy cascade as the input data were gained from a CFD simulation using scale-resolving Stress-Blended Eddy Simulation model. The POD modes can be used to construct a simplified model of the vortex rope dynamics covering a wider operating range rather than just one point.

A study on load position control and vibration attenuation in crane operation using sub-actuator

The main purpose of any crane system is to move a load to a specified place. Accurate load positioning in the presence of unpredictable external factors is an important issue when operating a crane. Attenuation of load vibration during crane operation is immensely critical in order to satisfy rigorous requirements for safety and efficiency. When a crane is installed and operated on a vessel at sea, work conditions become even more difficult and thus require more stringent attention to load positioning and attenuation of load vibration. At sea, this process is complicated due to factors such as waves and wind, making accurate crane operation nearly impossible. For these reasons, active heave compensation systems have been developed to suppress the effects of disturbances raised from the harsh sea environment including vessel motions. This paper explores the suppression method of unexpected vertical vibration of load. Unlike past research on the topic, this research includes rope dynamics in the control system design for suppressing load vibration. In addition, this research considers uncertain disturbances—vessel motions not controlled by any active force that result in undesirable heave motion of a crane. Load motion is indirectly estimated using a load cell because we do not yet have any useful tool to measure it directly. In the considered crane system, two winches were used, one for moving the load and the other for suppressing residual vibration. To evaluate the proposed control strategy and system performance, several control techniques were applied: proportional–integral–derivative control, sliding mode control, and feedback linearization control methods.

Intense Electric Fields and Electron‐Scale Substructure Within Magnetotail Flux Ropes as Revealed by the Magnetospheric Multiscale Mission

AbstractThree flux ropes associated with near‐Earth magnetotail reconnection are analyzed using Magnetospheric Multiscale observations. The flux ropes are Earthward propagating with sizes from ∼3 to 11 ion inertial lengths. Significantly different axial orientations are observed, suggesting spatiotemporal variability in the reconnection and/or flux rope dynamics. An electron‐scale vortex, associated with one of the most intense electric fields (E) in the event, is observed within one of the flux ropes. This E is predominantly perpendicular to the magnetic field (B); the electron vortex is frozen‐in with E × B drifting electrons carrying perpendicular current and causing a small‐scale magnetic enhancement. The vortex is ∼16 electron gyroradii in size perpendicular to B and potentially elongated parallel to B. The need to decouple the frozen‐in vortical motion from the surrounding plasma implies a parallel E at the structure's ends. The formation of frozen‐in electron vortices within reconnection‐generated flux ropes may have implications for particle acceleration.

Longitudinal dynamic characteristics of steel wire rope in a friction hoisting system and its coupling effect with friction transmission

Abstract The longitudinal rope dynamics in a friction hoisting system and its coupling effect with friction transmission are investigated. The tension and longitudinal vibration characteristics of the rope are obtained through experiments. The dynamics of rope and friction transmission are obtained by a validated simulation model. The results show that the rope tension is divided into the dynamic tension regime and inertial tension regime due to the multi-frequency cross-linking. The longitudinal rope vibration is embodied as random perturbation. The reduction of the friction coefficient will increase the sliding between the rope and lining, and it will be beneficial to narrowing the dynamic tension regime. The increase in the longitudinal rope vibration will reduce the friction force between the rope and lining.