Rotor Model Research Articles

A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model

A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model

The Effects of Rotation and Solidity on the Aerodynamic Behavior of Low-Pressure Axial Flow Fans

Abstract Implicit axial flow fan models are commonly used for the numerical analysis of industrial heat exchanger systems. However, these fan models perform poorly within the often complex off-design flow environments characteristic of these systems, as their low-order formulations lose applicability under highly 3D flow conditions. At off-design flow conditions, rotation and blade solidity effects cause physical fan blade behavior to deviate from the anticipated 2D behavior characterized by the implicit models. Physical fan blade behavior at off-design flow conditions, however, remains uncertain and the specific effects of rotation and solidity are not yet widely understood. This study investigates off-design fan blade behavior by presenting explicit 3D computations of two low-pressure axial flow fans. The effects of rotation and blade solidity are then identified through a side-by-side comparison of the computed 3D fan blade data against isolated 2D airfoil data. The rotating fan blade lift characteristics are shown to be distinct from the comparative 2D airfoil trends. At low-flow (off-design) operating conditions, rotation establishes large radial flow movements, and the high blade solidities cause standing vortices to develop within the rotating blade passages. The radial outflow energizes the blades' boundary layers, and the vortices inhibit the flow from separating from the blades' surfaces. Consequently, blade stall is avoided and high lift coefficient values are realized. The presented fan blade lift characteristics are unique relative to literature on other turbomachines of lower blade solidity, highlighting the importance of considering solidity effects in implicit rotor model developments.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60.

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

Searching nontrivial magnetic equilibria using the deflated Newton method

Nonlinear systems that model physical experiments often have many equilibrium configurations, and the number of these static solutions grows with the number of degrees of freedom and the presence of symmetries. It is impossible to know a priori how many equilibria exist and which ones are stable or relevant, therefore from the modeler’s perspective, an exhaustive search and symmetry classification in the space of solutions are necessary. With this purpose in mind, the method of deflation (introduced by Farrell as a modification of the classic Newton iterative method) offers a systematic way of finding every possible solution of a set of equations. In this contribution we apply deflated Newton and deflated continuation methods to a model of macroscopic magnetic rotors, and find hundreds of new equilibria that can be classified according to their symmetry. We assess the benefits and limitations of the method for finding branches of solutions in the presence of a symmetry group, and explore the high-dimensional basins of attraction of the method in selected 2-dimensional sections, illustrating the effect of deflation on the convergence.

Pairing effect on critical spin in chiral rotation

The critical spin Ic (or critical frequency ħωc) represents the minimum spin (or rotational frequency) required for stable chiral solutions in nuclear systems. The effect of pairing on the critical spin has been examined for the particle-hole configuration π(1h11/2)⊗ν(1h11/2)−1 with a triaxial deformation parameter of γ=30∘ using the particle rotor model, which treats the total angular momentum as a good quantum number. Increasing pairing interaction keeps the critical spin Ic constant, but decreases the critical rotational frequency ħωc. This is due to that the enhanced pairing interaction causes valence nucleons angular momenta to align preferentially along the medium axis, resulting in a larger effective collective moment of inertia and facilitating the emergence of chiral rotation at a lower frequency. However, even with an increase in pairing gap from 0.0 to 2.0MeV, the resulting increase in medium axis alignment is less than 1ħ, which is insufficient to change the value of the critical spin Ic. This study suggests that the critical spin remains robust against the influence of pairing interaction.

Electric conductivity in non-Hermitian holography

We study the phase structure and charge transport at finite temperature and chemical potential in the non-Hermitian \mathcal{PT}𝒫𝒯-symmetric holographic model of [SciPost Phys. 9, 032 (2020)]. The non-Hermitian \mathcal{PT}𝒫𝒯-symmetric deformation is realized by promoting the parameter of a global U(1) symmetry to a complex number. Depending on the strength of the deformation, we find three phases: stable \mathcal{PT}𝒫𝒯-symmetric phase, unstable \mathcal{PT}𝒫𝒯-symmetric phase, and an unstable \mathcal{PT}𝒫𝒯-symmetry broken phase. In the three phases, the square of the condensate and also the spectral weight of the AC conductivity at zero frequency are, respectively, positive, negative, and complex. We check that the Ferrell-Glover-Tinkham sum rule for the AC conductivity holds in all the three phases. We also investigate a complexified U(1) rotor model with \mathcal{PT}𝒫𝒯-symmetric deformation, derive its phase structure and condensation pattern, and find a zero frequency spectral weight analogous to the holographic model.

Three-Dimensional Aeromechanical Analysis of Lift Offset Coaxial Rotors: A Helios Test Case

Three-dimensional (3-D) solid finite element analysis (FEA) is used to model and study coaxial helicopter rotors. The 3-D FEA is coupled with a lifting line aerodynamic model with free wake to capture rotor-rotor interactions. Two open-access models are developed: one is the Metaltail (a hingeless coaxial rotorcraft), and the other is the coaxial rotor built from articulated UH-60A-like rotors. The former is the main focus of this work and is developed as an example case for the U.S. Army/DoD rotorcraft simulation software CREATETM–AV Helios, while the latter is merely for a regression test. The analysis is performed on a low-speed transition flight for which qualitative data are available for the Sikorsky S-97 Raider aircraft for comparison. Predictions of performance, airloads, vibratory loads, and 3-D stresses are discussed. In the absence of available geometry or property data of the S-97, this study is primarily meant to serve as a capability demonstration of 3-D rotor structural dynamic modeling for such rotors.

Multi-domain analytical rotor model with buried permanent magnets in V-arrangement for high-speed applications

Multi-domain analytical rotor model with buried permanent magnets in V-arrangement for high-speed applications

Molecular rotators anchored on a rod-like anionic coordination polymer adhered by charge-assisted hydrogen bonds.

On the basis of variable-temperature single-crystal X-ray diffraction, variable-temperature/frequency dielectric analysis, variable-temperature solid-state nuclear magnetic resonance spectroscopy, and molecular dynamics simulations, here we present a new model of crystalline supramolecular rotor (i-PrNHMe2)[CdBr3], where a conformationally flexible near-spherical (i-PrNHMe2)+ cation functions as a rotator and a rod-like anionic coordination polymer {[CdBr3]-}∞ acts as the stator, and the adhesion of them is realized by charge-assisted hydrogen bonds.

Research on the additional drag of turboshaft engine inlet under complex aerodynamic interference

In response to the complex aerodynamic interference in the inlet flow field of a turboshaft engine and the difficulty in calculating additional drag, a study was conducted based on numerical algorithms to calculate additional drag. Through the numerical calculation of the internal and external interference flow field model of the helicopter rotor and body, the inlet, the integral component of the exit section parameter, and the inner channel drag are extracted, and the calculation model of additional drag based on the momentum balance of the inlet channel and the control body of the pre-inlet tube is established. The calculation and analysis are carried out according to different operating conditions such as flight speed and inlet flow change. The results show that the calculation model of additional drag based on the three-dimensional numerical value of the interference flow field, considering the aerodynamic interference of incoming flow conditions, rotor, and body on the flow field, can realize the additional drag analysis under complex conditions. The downwash flow generated by the rotor affects the inlet front streamlines and additional drag, and the additional drag of the left and right inlets will also be different.

Exploring tunneling ESEEM beyond methyl groups in nitroxides at low temperatures.

Tunneling of methyl rotors coupled to an electron spin causes magnetic field independent electron spin echo envelope modulation (ESEEM) at low temperatures. For nitroxides containing alkyl substituents, we observe this effect as a contribution at the beginning of the Hahn echo decay signal occurring on a faster time scale than the matrix-induced decoherence. The tunneling ESEEM contribution includes information on the local environment of the methyl rotors, which manifests as a distribution of rotation barriers P(V3) when measuring the paramagnetic species in a glassy matrix. Here, we investigate the differences in tunneling behaviour of geminal methyl and ethyl group rotors in nitroxides while exploring different levels of theory in our previously introduced methyl quantum rotor (MQR) model. Moreover, we extend the MQR model to analyze the tunneling ESEEM originating from two different rotor types coupled to the same electron spin. We find that ethyl groups in nitroxides give rise to stronger tunneling ESEEM contributions than methyl groups because the difference between hyperfine couplings of their methyl protons better matches the tunneling frequency. The methyl rotors of both ethyl and propyl groups exhibit distributions at lower rotation barriers compared to geminal methyl groups. This is in good agreement with density functional theory (DFT) calculations of their rotation barriers and showcases that conformational flexibility impacts the hindrance of rotation. Using Monte-Carlo based fitting in combination with an identifiability analysis of the MQR model parameter space, we extract rotation barrier distributions for the individual rotor types in mixed-rotor nitroxides as well as identify which rotors dominate the observed tunneling contribution in the Hahn echo decay signal.

Triaxial rotor in the O(6) limit of the interacting boson model

A mapping from the triaxial rotor Hamiltonian to that of the O(6) limit in the interacting boson model (IBM) is established, which is achieved by introducing the symmetry-conserving high-order interactional terms The validity of the proposed mapping scheme is further examined for the cases with γ = 0 and γ = π/6, respectively. It is shown that the rotor model results can be well reproduced in its O(6) image especially for the low-spin states. It thus provides an alternative way to understand the triaxiality in the finite-N systems and additional insight into the O(6) IBM theory.

Physics-Informed Neural Networks for the Condition Monitoring of Rotating Shafts.

Condition monitoring of rotating shafts is essential for ensuring the reliability and optimal performance of machinery in diverse industries. In this context, as industrial systems become increasingly complex, the need for efficient data processing techniques is paramount. Deep learning has emerged as a dominant approach due to its capacity to capture intricate data patterns and relationships. However, a prevalent challenge lies in the black-box nature of many deep learning algorithms, which often operate without adhering to the underlying physical characteristics intrinsic to the studied phenomena. To address this limitation and enhance the fusion of data-driven methodologies with the fundamental physics of the system under study, this paper leverages physics-informed neural networks (PINNs). Specifically, a simple but realistic numerical case study of an extended Jeffcott rotor model, encompassing damping effects and anisotropic supports for a more comprehensive modelling, is considered. PINNs are used for the estimation of five parameters that characterize the health state of the system. These parameters encompass the radial and angular position of the static unbalance due to the disk installed on the shaft, the stiffness along the principal axes of elasticity, and the non-rotating damping coefficient. The estimation is conducted solely by exploiting the displacement signals from the centre of the disk and, to showcase the efficacy and precision provided by this novel methodology, various scenarios involving different constant rotational speeds are examined. Additionally, the impact of noisy input data is also taken into account within the analysis and the performance is compared to that of traditional optimization algorithms used for parameters estimation.

Theoretical and experimental applications of a rotor balancing technique without using trial weights based on augmented Kalman filter

Unbalance is the most common fault of rotating machines and efforts devoted to developing balancing techniques are the goal of several researchers around the world. The most common balancing approach is the well-known influence coefficient method, which requires the use of trial weights to determine the relationship between unbalance forces and vibration responses of the rotor; consequently, it is time-consuming regarding industrial applications. The present contribution investigates the augmented Kalman filter (AKF) technique to balance a flexible rotor without using trial weights. There are few studies in this area and the majority of the previous research works are dedicated to theoretical studies using simple or reduced rotor models. This paper considers a finite element (FE) model of a realistic rotor system and investigates the effectiveness of the AKF as a balancing technique by considering several unbalance conditions. Therefore, the novelty of the present contribution is characterized by a complete numerical and experimental AKF based balancing procedure that is performed by using a realistic rotor system. As mentioned above, limited experimental contributions are found in the literature involving real-world applications. Additionally, a sensitivity analysis on the force covariance matrix is proposed to investigate the most favorable conditions to apply the AKF technique in the context of rotor balancing. The methodology proved to be effective to deal with a variety of rotor balancing applications.

Analysis of the Aeroacoustic Characteristics of a Rigid Coaxial Rotor in Forward Flight Based on the CFD/VVPM Hybrid Method

This study develops a hybrid solver with reversed overset assembly technology (ROAT), a viscous vortex particle method (VVPM), and a CFD program based on the URNS method, in order to study the aerodynamic and acoustic characteristics of coaxial rigid rotors. The aerodynamic load of the “AH-1G” helicopter rotor is first calculated based on the hybrid method and compared with available experimental data. The prediction of the linear noise of the OLS rotor is then performed and the obtained results are compared with available experimental data. These results allow the evaluation of the accuracy of the hybrid method for emulating rotor aerodynamics and acoustics. Afterwards, the hybrid and CFD methods are applied to obtain the aerodynamic and acoustic characteristics of the given coaxial rigid rotor model, while taking into account the trim of the collective pitch. The obtained results demonstrate that the hybrid method has high proficiency in capturing blade–vortex-interaction impulsive loads and high computational efficiency in predicting associated loading noise characteristics. Furthermore, the effect of the hybrid method on the noise characteristics of coaxial rigid rotors under a different advance ratio, blade tip speed, shaft angle, and other conditions, as well as the impact of the upper and lower rotors on the noise contribution of the coaxial rotor are analyzed. Finally, the impacts of the initial phase and the vertical spacing on the sound pressure level are studied.

Computer simulation of a rotor creep

The issue of determining the stress-strain state during creep in models of rotors of steam and gas turbines is considered. The formulation of the problem is based on the general approach of Solid Mechanics using incremental theory to describe creep strains. The Finite Element Method was used as a solution method in the implementation of professional engineering software. The influence of the centrifugal forces on the stress-strain state, which varies during 10,000 hours of creep of the rotor material, is analyzed. Two models of the rotor are considered: a simplified cylindrical and a drum-type rotor, which is described by the geometry of the body of revolution and which consists of several cylindrical parts. Due to the symmetry of the models, the calculation schemes are built on the basis of the use of a two-dimensional finite element of the body of revolution. Algorithms are applied for the preparation of input data can be recommended for use in the design practice of energy industry enterprises. The Norton law was used for creep calculations. The creep of the models in different temperature conditions with the use of various steels used in turbo-building as their material was analyzed. According to the results of the performed computer simulation of the creep of rotor models, the levels of deformation and the nature of the redistribution of stresses that occur under the same load by centrifugal forces in different temperature conditions caused by the operational processes in the turbine have been established. The stress and strain levels in the drum-type rotor were analyzed and the most loaded and deformed areas of it were determined. It is noted that according to the simulation data for the considered model of the drum-type rotor, the level of accumulated strains, is moderate and does not exceed 0.4%, which is suitable from the point of view of the analysis of operational properties.

Accelerating model evaluations in uncertainty propagation on tensor grids using computational graph transformations

Methods such as non-intrusive polynomial chaos (NIPC), and stochastic collocation are frequently used for uncertainty propagation problems. Particularly for low-dimensional problems, these methods often use a tensor-product grid for sampling the space of uncertain inputs. A limitation of this approach is that it encounters a significant challenge: the number of sample points grows exponentially with the increase of uncertain inputs. Current strategies to mitigate computational costs abandon the tensor structure of sampling points, with the aim of reducing their overall count. Contrastingly, our investigation reveals that preserving the tensor structure of sample points can offer distinct advantages in specific scenarios. Notably, by manipulating the computational graph of the targeted model, it is feasible to avoid redundant evaluations at the operation level to significantly reduce the model evaluation cost on tensor-grid inputs. This paper presents a pioneering method: Accelerated Model Evaluations on Tensor grids using Computational graph transformations (AMTC). The core premise of AMTC lies in the strategic modification of the computational graph of the target model to algorithmically remove the repeated evaluations on the operation level. We implemented the AMTC method within the compiler of a new modeling language called the Computational System Design Language (CSDL). We demonstrate the effectiveness of AMTC by using it with the full-grid NIPC method to solve four low-dimensional UQ problems involving an analytical piston model, a multidisciplinary unmanned aerial vehicle design model, a multi-point air taxi mission analysis model, and a single-disciplinary rotor model, respectively. For three of the four test problems, AMTC reduces the model evaluation cost by between 50% and 90%, making the full-grid NIPC the most efficacious method to use among the UQ methods implemented.

Design Methodology of Wind Turbine Rotor Models Based on Aerodynamic Thrust and Torque Equivalence

Limited by scaling effects, the physical model tests of FOWTs (floating offshore wind turbines) cannot simulate the aerodynamic loads on rotors correctly. To solve this problem, the real-time hybrid model tests in wind tunnels were developed and provided a feasible solution for the aerodynamic simulation. To perform the wind tunnel tests, the design of aerodynamic equivalent rotor models is most critical. In this study, an innovative methodology of aerodynamic equivalent design for the wind turbine rotors is developed based on GA (genetic algorithm). The NREL (National Renewable Energy Laboratory) 5 MW and DTU (Technical University of Denmark) 10 MW rotors are employed for the case studies to validate the proposed methodology. According to the results, the model-scale aerodynamic thrust performance can be accurately matched with the prototype in the entire region between cut-in and cut-out wind speeds, which allows the rotor model to provide correct thrust at different wind speeds. The variance of the aerodynamic torque with the wind speeds for the developed model is also in good agreement with the prototype, which could be beneficial for the design of the model-scale active pitch control strategy. Moreover, the applicability of the fitness functions of GA is discussed.

Understanding the fixed pitch RPM-controlled rotor modeling for the conceptual design of UAM vehicles

AbstractMost of the introduced eVTOL models in the UAM market utilize electrically driven rotors with fixed pitch blades, controlled by their rotational speed. This design approach brings new features and challenges that need to be considered during the conceptual design stage, taking new aspects into account, among them the rotor dynamic response. This paper presents an initial parameterization of the rpm-controlled rotors along with the electric motor, based on the conducted literature research. Several isolated rotor variants are modeled and analyzed in terms of performance, and the dynamic response of the rotor rotational speed. The relations between aerodynamics and inertia are discussed, and their effects on the rotor dynamic response are elaborated on.

Rotordynamics of a rotor radially and axially supported by active bump-type foil bearings and bump-type thrust foil bearings

The rotordynamics of a rotor supported by gas foil bearings (GFBs) has been studied, focusing mainly on the relation between radial loads and lateral vibration. Nevertheless, the various axial loads occurring during operation must be compensated by thrust GFBs. Their effect on lateral and axial vibrations of the rotor must be addressed. This research studied the effect of axial load on the rotordynamics of a rotor supported by active bump-type foil bearings (ABFBs). Two ABFBs and a pair of bump-type thrust foil bearings (BTFBs) supported a rigid rotor along the radial and axial directions, respectively. The 5 degree of freedom nonlinear dynamic model for the rigid rotor is shown in this paper and was validated through experimental measurements. The study considered the coupling of the time-variant nonlinear bearing forces of ABFBs and BTFBs. The rotordynamic behaviors of a rotor under various axial loads, rotor unbalances, and voltages are predicted. Moreover, the effects of various disk misalignments on the minimum gas film thickness of the BTFBs are discussed.