Symmetric Rotor Research Articles

Active micromachines: Microfluidics powered by mesoscale turbulence

Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterized by mesoscale turbulence, which is the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organizes into a spin state where neighboring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elastic effects. Our virtual prototype demonstrates a new research direction for the design of micromachines powered by the nematohydrodynamic properties of active turbulence.

Studies of some high solidity symmetrical and unsymmetrical blade H-Darrieus rotors with respect to starting characteristics, dynamic performances and flow physics in low wind streams

Vertical axis wind turbines can be successfully installed in low wind speed conditions but its detailed starting characteristics in terms of starting torque, starting time and dynamic performances have not been investigated thoroughly which is important for increasing the energy yield of such turbines. Amongst their designs, H-Darrieus rotor, in spite of having good power coefficient, possesses poor self-starting features as symmetrical blade profiles are used most of the times. Instead of using symmetrical blades if unsymmetrical or cambered blades are used with high solidity, then starting performance of H-Darrieus rotor along with its power coefficients can be improved. Though this performance improvement measures are correlated with improvement in the starting characteristics, a detailed work in this direction would be useful and for this reason the present work has been carried out. Three types of blade designs have been considered; two unsymmetrical blades namely S815 and EN0005 and one conventional symmetrical NACA 0018 blade, and experiments are conducted using a centrifugal blower test rig for three-bladed H-Darrieus rotors using these three considered blades at low wind streams (4 m/s, 6 m/s and 8 m/s). Considering reality, the effects of flow non-uniformity and turbulence intensity on the rotor performance at optimum condition as well as flow physics have also been studied. It has been found that unsymmetrical S815 blade rotor has higher dynamic torque and higher power coefficient than unsymmetrical EN0005 and symmetrical NACA 0018 blade H-Darrieus rotors.

Closed-Form Vibration Response of a Special Class of Spinning, Cyclic Symmetric Rotor-Bearing-Housing Systems

Vibration of a spinning, cyclic symmetric rotor supported by flexible bearings and housing is governed by a set of ordinary differential equations with periodic coefficients. As a result, analytical solutions of such systems are generally not available. This paper is to prove that closed-form solutions are available for such systems if the following two conditions are met. First, the rotor has a rigid hub and the rest of the rotor is flexible. Second, elastic mode shapes of the rotor's flexible part only present axial displacement. Under these two conditions, the periodic coefficients will only appear between repeated modes of the spinning rotor and vibration modes of the stationary housing. This unique structure enables a coordinate transformation to convert the governing ordinary differential equations with periodic coefficients into a set of ordinary differential equations with constant coefficients, whose closed-form solution is readily available. Moreover, the coordinate transformation can be derived explicitly. Finally, we demonstrate the closed-form solution through a benchmark numerical model that consists of a spinning rotor, a stationary housing, and two elastic bearings. In particular, the rotor is a circular disk with four evenly spaced radial slots and a central rigid hub. The housing is a square plate with a central rigid shaft and is fixed at four corners. The two elastic bearings connect the rotor and the housing between the hub and shaft. Numerical results confirm that the original equation of motion with periodic coefficients and the closed-form solutions predict the same vibration response.

Analytical fluid film force calculation in the case of short bearing with a fully developed turbulent flow

The main purpose of this paper is to define a methodology to determine the analytical approximate closed-form expression of non-steady fluid film force and of the oil film coefficients for the liquid-lubricated journal bearings in the case of a fully developed turbulent flow regime. The considered model is a symmetrical rigid rotor supported on two lubricated journal bearings; this paper considers the cases of the short bearing approximation, introducing the turbulence correction flow factors in the classical Reynolds equation. The proposed methodology gives the opportunity to solve in approximate way the equation governing the distribution of pressure in the bearing oil gap and then to obtain the closed-form expressions for the non-steady fluid forces. This approach shows the benefit of minimising the calculation time required for the non-linear dynamic analysis of rotors on turbulent journal bearings without any significant loss of accuracy giving a better readability of the parameter involved on the system behaviour.

Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

This paper is to study ground-based response of a spinning, cyclic symmetric rotor assembled to a flexible housing via multiple bearings. In particular, interaction of the spinning rotor and the flexible housing is manifested theoretically, numerically, and experimentally. In the theoretical analysis, we show that the interaction primarily appears in coupled rotor–bearing–housing modes whose response is dominated by the housing. Specifically, let a housing-dominant mode have natural frequency ω(H) and the spin speed of the rotor to be ω3. In rotor-based coordinates, response of the spinning rotor for the housing-dominant mode will possess frequency splits ω(H)±ω3. In ground-based coordinates, response of the spinning rotor will possess alternative frequency splits ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3, where k is an integer determined by the cyclic symmetry of the rotor and the housing-dominant mode of interest. In the numerical analysis, we study a benchmark model consisting of a spinning slotted disk mounted on a stationary square plate via two ball bearings. The numerical model successfully confirms the frequency splits both in the rotor-based and ground-based coordinates. In the experimental analysis, we conduct vibration testing on a rotor–bearing–housing system that mimics the numerical benchmark model. Test results reveal two housing-dominant modes. As the rotor spins at various speed, measured waterfall plots confirm that the housing-dominant modes split according to ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3 as predicted.

Mathematical Insights Into Linear Mode Localization in Nearly Cyclic Symmetric Rotors With Mistune

In this paper, we develop a mathematical analysis to gain insights of mode localization often encountered in nearly cyclic symmetric rotors that contain slight mistune. First, we conduct a Fourier analysis in the spatial domain to show that mode localization can appear only when a group of tuned rotor modes form a complete set in the circumferential direction. In light of perturbation theories, these tuned rotor modes must also have very similar natural frequencies, so that they can be linearly combined to form localized modes when the mistune is present. Second, the natural frequency of these tuned rotor modes can further be represented in terms of a mean frequency and a deviatoric component. A Rayleigh–Ritz formulation then shows that mode localization occurs only when the deviatoric component and the rotor mistune are about the same order. As a result, we develop an effective visual method—through use of the deviatoric component and the rotor mistune—to precisely identify those modes needed to form localized modes. Finally, we show that curve veering is not a necessary condition for mode localization to occur in the context of free vibration. Not all curve veering leads to mode localization, and not all modes in curve veering contribute to mode localization. Numerical examples on a disk–blade system with mistune confirm all the findings above.

The σ‐Hole Interaction Between Sulfur Hexafluoride and Ammonia Characterised by Broadband Rotational Spectroscopy

A weakly-bound complex of SF6 and NH3 is generated within an expanding gas jet and characterised by broadband rotational spectroscopy. The spectra of isotopologues (32) SF6 ⋅⋅⋅(14) NH3 , (32) SF6 ⋅⋅⋅(14) ND3 , (32) SF6 ⋅⋅⋅(15) NH3 and (34) SF6 ⋅⋅⋅(15) NH3 are observed and assigned to determine the spectroscopic parameters. These parameters are consistent with the complex having a C3v symmetric rotor geometry, in which the nitrogen atom of NH3 coordinates to SF6 such that the C3v axis of the NH3 sub-unit is aligned with a local C3 axis on the SF6 sub-unit. The geometry of the complex is rationalized in terms of a σ-hole interaction. The observed spectra and ab initio calculations also reveal evidence of internal dynamics involving internal rotation of one monomer sub-unit with respect to the other about the symmetry axis of the complex.

Conditions for stable rotation of a rotor with a float self-balancer

The angular velocities at which a flexible symmetric rotor with a float self-balancer loses dynamic stability are determined analytically and numerically depending on the external and internal viscous friction coefficients. The gyroscopic and refined inertial and potential forces of the system are considered. Conclusions about the efficiency of the use of such a device on high-speed rotors are made.

Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

The modal interaction which leads to Hamiltonian Hopf bifurcation is studied for a nonlinear rotating bladed-disk system. The model, which is discussed in the paper, is a Jeffcott rotor carrying a number of planar blades which bend in the plane of the motion. The rigid rotating disk is supported on nonlinear bearings. It is supposed that this dynamical system is a Hamiltonian system which is perturbed by small dissipative and nonlinear forces. Krein’s theorem is employed for obtaining a stability criterion. The nonlinear eigenvalue equations on the stability boundary are turned into ordinary differential equations (ODEs) by differentiating them over the rotating speed. By solving these ODEs, the eigenmodes and the eigenvalues on the stability boundary are obtained. The bifurcation analysis is performed by applying multiple scales method around the boundary. The rotor nonlinear behavior and damping effects are studied for different conditions on the rotating speed and nonlinearity type by the bifurcation equation. It is shown that the damping distribution between the blades and bearings may shift the unstable mode. Depending on the nonlinearity type, subcritical and supercritical Hopf bifurcation are possible.

Special Issue of Applied Mechanics Reviews in Collaboration With the Journal of Vibration and Acoustics

Special Issue of Applied Mechanics Reviews in Collaboration With the Journal of Vibration and Acoustics

WIDESPREAD ROTATIONALLY HOT HYDRONIUM ION IN THE GALACTIC INTERSTELLAR MEDIUM

We present new observations of the (6,6) and (9,9) inversion transitions of the hydronium ion toward Sagittarius B2(N) and W31C. Sensitive observations toward Sagittarius B2(N) show that the high, ~ 500 K, rotational temperatures characterizing the population of the highly-excited metastable H3O+ rotational levels are present over a wide range of velocities corresponding to the Sagittarius B2 envelope, as well as the foreground gas clouds between the Sun and the source. Observations of the same lines toward W31C, a line of sight that does not intersect the Central Molecular Zone, but instead traces quiescent gas in the Galactic disk, also imply a high rotational temperature of ~ 380 K, well in excess of the kinetic temperature of the diffuse Galactic interstellar medium. While it is plausible that some fraction of the molecular gas may be heated to such high temperatures in the active environment of the Galactic center, characterized by high X-ray and cosmic ray fluxes, shocks and high degree of turbulence, this is unlikely in the largely quiescent environment of the Galactic disk clouds. We suggest instead that the highly-excited states of the hydronium ion are populated mainly by exoergic chemical formation processes and temperature describing the rotational level population does not represent the physical temperature of the medium. The same arguments may be applicable to other symmetric top rotors, such as ammonia. This offers a simple explanation to the long-standing puzzle of the presence of a pervasive, hot molecular gas component in the central region of the Milky Way. Moreover, our observations suggest that this is a universal process, not limited to the active environments associated with galactic nuclei.

J0540302 低重心風車とバタフライ風車の特性比較([J054-03]再生可能エネルギー(3))

Two types of vertical axis wind turbines (VAWTs) characterized by armless structure, i.e., low-center-of-gravity wind turbine (LCGWT) and butterfly wind turbine (BWT), had been compared in terms of the torque and power coefficients in the cases of symmetrical-blade rotor and cambered-blade rotor. The common rotor diameter is 0.4 m, and the rotor height of LCGWT is 0.25m and that of BWT is 0.3 m. The results are following: in both types, under the high tip speed ratio (TSR) conditions (λ > 0.75), cambered blade rotor was superior to symmetrical blade rotor. Under the low TSR conditions (λ ≤ 0.5 ), cambered-blade rotor showed higher performance than symmetrical-blade rotor in the LCGWT type, on the other hand, symmetrical-blade rotor showed better performance than cambered-blade rotor in the BWT type. According to the comparison between the cambered-blade LCGWT and BWT, BWT was superior to LCGWT under the condition of low TSR (λ ≤ 0.75), and LCGWT was superior to BWT under the condition of high TSR (λ ≥ 1.25). The maximum power coefficient (Cp = 0.113) was obtained in the case of cambered-blade BWT at wind speed of 6 m/s.

New exact solution of Euler’s equations (rigid body dynamics) in the case of rotation over the fixed point

A new exact solution of Euler’s equations (rigid body dynamics) is presented here. All the components of angular velocity of rigid body for such a solution differ from both the cases of symmetric rigid rotor (which has two equal moments of inertia: Lagrange’s or Kovalevskaya’s case), and from the Euler’s case when all the applied torques are zero, or from other well-known particular cases. The key features are the next: the center of mass of rigid body is assumed to be located at meridional plane along the main principal axis of inertia of rigid body, besides, the principal moments of inertia are assumed to satisfy to a simple algebraic equality. Also, there is a restriction at choosing of initial conditions. Such a solution is also proved to satisfy to Euler–Poinsot equations, including invariants of motion and additional Euler’s invariant (square of the vector of angular momentum is a constant). So, such a solution is a generalization of Euler’s case.

Algorithms for computer detection of symmetry elements in molecular systems

Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry.

Structure of transactinide nuclei with relativistic energy density functionals

A microscopic theoretical framework based on relativistic energy density functionals (REDFs) is applied to studies of shape evolution, excitation spectra, and decay properties of transactinide nuclei. Axially symmetric and triaxial relativistic Hartree-Bogoliubov (RHB) calculations, based on the functional DD-PC1 and with a separable pairing interaction, are performed for the even-even isotopic chains between Fm and Fl. The occurrence of a deformed shell gap at neutron number $N=162$ and its role on the stability of nuclei in the region around $Z=108$ is investigated. A quadrupole collective Hamiltonian, with parameters determined by self-consistent constrained triaxial RHB calculations, is used to examine low-energy spectra of No, Rf, Sg, Hs, and Ds with neutron number in the interval $158\ensuremath{\le}N\ensuremath{\le}170$. In particular, we analyze the isotopic dependence of several observables that characterize the transitions between axially symmetric rotors, $\ensuremath{\gamma}$-soft rotors, and spherical vibrators. An interesting example of a possible occurrence of shape-phase transitions and critical-point phenomena in this mass region is explored.

Torsion–Inversion Tunneling Patterns in the CH-Stretch Vibrationally Excited States of the G12 Family of Molecules Including Methylamine

Two torsion-inversion tunneling models (models I and II) are reported for the CH-stretch vibrationally excited states in the G12 family of molecules. The torsion and inversion tunneling parameters, h(2v) and h(3v), respectively, are combined with low-order coupling terms involving the CH-stretch vibrations. Model I is a group theoretical treatment starting from the symmetric rotor methyl CH-stretch vibrations; model II is an internal coordinate model including the local-local CH-stretch coupling. Each model yields predicted torsion-inversion tunneling patterns of the four symmetry species, A, B, E1, and E2, in the CH-stretch excited states. Although the predicted tunneling patterns for the symmetric CH-stretch excited state are the same as for the ground state, inverted tunneling patterns are predicted for the asymmetric CH-stretches. The qualitative tunneling patterns predicted are independent of the model type and of the particular coupling terms considered. In model I, the magnitudes of the tunneling splittings in the two asymmetric CH-stretch excited states are equal to half of that in the ground state, but in model II, they differ when the tunneling rate is fast. The model predictions are compared across the series of molecules methanol, methylamine, 2-methylmalonaldehyde, and 5-methyltropolone and to the available experimental data.

Parametric Resonances of a Spinning Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

This paper is meant to model free vibration of a coupled rotor-bearing-housing system. In particular, the rotor is cyclic symmetric and spins at constant speed while the housing is stationary and flexible. The rotor and housing are assembled via multiple, linear, elastic bearings. A set of equations of motion is derived using component mode synthesis, in which the rotor and the housing each are treated as a component. The equations of motion take the form of ordinary differential equations with periodic coefficients. Analyses of the equations of motion indicate that instabilities could appear at certain spin speed in the form of combination resonances of the sum type. To demonstrate the validity of the formulation, two numerical examples are studied. For the first example, the spinning rotor is an axisymmetric disk, and the housing is a square plate with a central shaft. The rotor and the housing are connected via two linear elastic bearings. For the second example, the rotor is cyclic symmetric in the form of a disk with four evenly spaced radial slots. The housing and bearings remain the same. In both examples, instability appears as a combination resonance of the sum type between a rotor mode and an elastic housing mode. The cyclic symmetric rotor, however, has more instability zones. Finally, effects of damping are studied. Damping of the housing widens the instability zones, whereas the damping of the rotor does the opposite.

Evaluation of Uncertainty of Ideal-Gas Entropy and Heat Capacity Calculations by Density Functional Theory (DFT) for Molecules Containing Symmetrical Internal Rotors

The uncertainty of thermophysical data is indispensable information when reporting both experimental and calculated values. In this paper, we present an evaluation of the uncertainty of the ideal-gas entropy and heat capacity calculations by density functional theory (DFT) for molecules containing symmetrical internal rotors. The rigid-rotor harmonic oscillator (RRHO) and one-dimensional hindered rotor (1-DHR) models are compared as well as the effect of the scale factors employed. The calculations of the standard ideal-gas entropy (Sg0) are performed for a selected set of 33 molecules for which reliable reference data were found in the literature. The RRHO model provides Sg0 with the absolute average percentage deviations (σr) about 2 % from the reference data. Scaling the frequencies does not lead to any improvement when using the RRHO model. A significant improvement is achieved when the 1-DHR model and scale factors for low and high frequencies are applied simultaneously (σr less than 0.3 %). The idea...

Infrared spectrum of the CS2 tetramer: Observation of a structure with D2d symmetry

Infrared spectra of carbon disulfide clusters are studied in the region of the CS2 ν3 fundamental band (≈1535cm−1), using a tuneable diode laser to probe a pulsed supersonic slit jet expansion. A symmetric rotor parallel band at 1551.438cm−1 is assigned to CS2 tetramer. The likely structure is a staggered and tilted barrel with D2d symmetry, similar to the previously observed oblate tetramer of nitrous oxide, and in reasonable agreement with that calculated from an empirical CS2 intermolecular potential function. This is the first high-resolution spectroscopic detection of CS2 tetramer, and the calculations suggest that there could be other low energy isomers of (CS2)4 which are not yet observed.

Vibration Control in a Helicopter with Semi-Active Hydraulic Lag Dampers

This paper describes the research on the use of semi-active hydraulic lag dampers for vibration control in helicopters. A semi-active vibration control of the hydraulic lag damper is investigated in the context of a midsized production helicopter in steady level flight. The semi-active operation of the damper is achieved via periodic flow restrictor modulation. The influence of the modulations and constraints on the nonrotating hub loads of a five-bladed main rotor is evaluated. The selected harmonic modulation frequencies are determined by the combination of the hydromechanical coupling in the damper and the mechanical filtering effect of the symmetric rotor. The modulation frequencies of 3, 5, and 7 per revolution are used to modify the 5-per-revolution lateral and longitudinal hub loads, whereas the frequencies of 4 and 6 per revolution are efficient at modifying the 5-per-revolution hub yaw moment. The harmonic modulations larger than seven per revolution are not used due to limited damper responses at these frequencies. The out-of-plane hub loads and moments cannot be significantly influenced by the rotor-damper configuration considered. A maximum load reduction of 72% on the lateral hub load component decreases to 58% when considering a limited damper response authority due to the relief valve activation.