Correlation of helicopter rotor aeroelastic response with HART-II wind tunnel test data

Purpose - This paper aims to validate a comprehensive aeroelastic analysis for a helicopter rotor with the higher harmonic control aeroacoustic rotor test (HART-II) wind tunnel test data. Design/methodology/approach - Aeroelastic analysis of helicopter rotor with elastic blades based on finite element method in space and time and capable of considering higher harmonic control inputs is carried out. Moderate deflection and coriolis nonlinearities are included in the analysis. The rotor aerodynamics are represented using free wake and unsteady aerodynamic models. Findings - Good correlation between analysis and HART-II wind tunnel test data is obtained for blade natural frequencies across a range of rotating speeds. The basic physics of the blade mode shapes are also well captured. In particular, the fundamental flap, lag and torsion modes compare very well. The blade response compares well with HART-II result and other high-fidelity aeroelastic code predictions for flap and torsion mode. For the lead-lag response, the present analysis prediction is somewhat better than other aeroelastic analyses. Research limitations/implications - Predicted blade response trend with higher harmonic pitch control agreed well with the wind tunnel test data, but usually contained a constant offset in the mean values of lead-lag and elastic torsion response. Improvements in the modeling of the aerodynamic environment around the rotor can help reduce this gap between the experimental and numerical results. Practical implications - Correlation of predicted aeroelastic response with wind tunnel test data is a vital step towards validating any helicopter aeroelastic analysis. Such efforts lend confidence in using the numerical analysis to understand the actual physical behavior of the helicopter system. Also, validated numerical analyses can take the place of time-consuming and expensive wind tunnel tests during the initial stage of the design process. Originality/value - While the basic physics appears to be well captured by the aeroelastic analysis, there is need for improvement in the aerodynamic modeling which appears to be the source of the gap between numerical predictions and HART-II wind tunnel experiments.

Dipolar cross-correlation effects in the nuclear overhauser experiments of weakly and strongly coupled spins

The effect of dipolar cross correlation in 1H---1H nuclear Overhauser effect experiments is investigated by detailed calculation in an ABX spin system. It is found that in weakly coupled spin systems, the cross-correlation effects are limited to single-quantum transition probabilities and decrease in magnitude as ωτc increases. Strong coupling, however, mixes the states and the cross correlations affect the zero-quantum and double-quantum transition probabilities as well. The effect of cross correlation in steady-state and transient NOE experiments is studied as a function of strong coupling and ωτc. The results for steady-state NOE experiments are calculated analytically and those for transient NOE experiments are calculated numerically. The NOE values for the A and B spins have been calculated by assuming nonselective perturbation of all the transitions of the X spin. A significant effect of cross correlation is found in transient NOE experiments of weakly as well as strongly coupled spins when the multiplets are resolved. Cross correlation manifests itself largely as a multiplet effect in the transient NOE of weakly coupled spins for nonselective perturbation of all X transitions. This effect disappears for a measuring pulse of 90° or when the multiplets are not resolved. For steady-state experiments, the effect of cross correlation is analytically zero for weakly coupled spins and small for strongly coupled spins.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. I. Theory

Based on a method proposed by Reddy and Daum, the equations governing the steady inviscid nonreacting gasdynamic laser (GDL) flow in a supersonic nozzle are reduced to a universal form so that the solutions depend on a single parameter which combines all the other parameters of the problem. Solutions are obtained for a sample case of available data and compared with existing results to validate the present approach. Also, similar solutions for a sample case are presented.

Inertial effects in solvation dynamics

The dynamics of solvation of newly created charged species in dense dipolar liquids can proceed at a high speed with time constants often in the subpicosecond domain. The motion of the solvent molecules can be in the inertial limit at such short times. In this paper we present a microscopic study of the effects of inertial motion of solvent molecules on the solvation dynamics of a newly created ion in a model dipolar liquid. Interesting dynamical behavior emerges when the relative contribution of the translational modes in the wave-vector-dependent longitudinal relaxation time is significant. Especially, the theory predicts that the time correlation function of the solvation energy can become oscillatory in some limiting situations. In general, the dynamics becomes faster in the presence of the inertial contribution. We discuss the experimental situations where the inertial effects can be noticeable.

Influence of cross-correlation between dipolar and chemical shift anisotropy relaxation mechanisms upon the transverse relaxation rates of 15N in macromolecules

Heteronuclear multiple-quantum coherence relaxation rate are calculated for the individual transitions of the S spin in an AIS nuclear spin system assuming that the heteronucleus (S spin) has relaxation contributions from both intramolecular dipole-dipole and chemical shift anisotropy relaxation. The individual multiplet components of the heteronuclear zero- and double-quantum coherences are shown to have different transverse relaxation rates. The cross-correlation between the two relaxation mechanisms is shown to be the dominant cause of the calculated differential line broadening. Experimental data are presented using as an example a uniformly 15N labelled sample of human epidermal growth factor.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Theory of the effects of destruction of localization by inelastic scattering in the resistivity of pure thin potassium wires

Measurements of the electrical resistivity of thin potassium wires at temperatures near 1 K have revealed a minimum in the resistivity as a function of temperature. By proposing that the electrons in these wires have undergone localization, albeit with large localization length, and that inelastic-scattering events destroy the coherence of that state, we can explain both the magnitude and shape of the temperature-dependent resistivity data. Localization of electrons in these wires is to be expected because, due to the high purity of the potassium, the elastic mean free path is comparable to the diameters of the thinnest samples, making the Thouless length lT (or inelastic diffusion length) much larger than the diameter, so that the wire is effectively one dimensional. The inelastic events effectively break the wire into a series of localized segments, whose resistances can be added to obtain the total resistance of the wire. The ensemble-averaged resistance for all possible segmented wires, weighted with a Poisson distribution of inelastic-scattering lengths along the wire, yields a length dependence for the resistance that is proportional to [L3/lin(T)], provided that lin(T)?L, where L is the sample length and lin(T) is some effective temperature-dependent one-dimensional inelastic-scattering length. A more sophisticated approach using a Poisson distribution in inelastic-scattering times, which takes into account the diffusive motion of the electrons along the wire through the Thouless length, yields a length- and temperature-dependent resistivity proportional to (L/lT)4 under appropriate conditions. Inelastic-scattering lifetimes are inferred from the temperature-dependent bulk resistivities (i.e., those of thicker, effectively three-dimensional samples), assuming that a minimum amount of energy must be exchanged for a collision to be effective in destroying the phase coherence of the localized state. If the dominant inelastic mechanism is electron-electron scattering, then our result, given the appropriate choice of the channel number parameter, is consistent with the data. If electron-phason scattering were of comparable importance, then our results would remain consistent. However, the inelastic-scattering lifetime inferred from bulk resistivity data is too short. This is because the electron-phason mechanism dominates in the inelastic-scattering rate, although the two mechanisms may be of comparable importance for the bulk resistivity. Possible reasons why the electron-phason mechanism might be less effective in thin wires than in bulk are discussed.

Relationship between microscopic and macroscopic orientational relaxation times in polar liquids

Microscopic relations between single-particle orientational relaxation time (T, ) , dielectric relaxation time ( T ~ )a,n d many-body orientational relaxation time ( T ~o)f a dipolar liquid are derived. We show that both T~ and T~ are influenced significantly by many-body effects. In the present theory, these many-body effects enter through the anisotropic part of the two-particle direct correlation function of the polar liquid. We use mean-spherical approximation (MSA) for dipolar hard spheres for explicit numerical evaluation of the relaxation times. We find that, although the dipolar correlation function is biexponential, the frequency-dependent dielectric constant is of simple Debye form, with T~ equal to the transverse polarization relaxation time. The microscopic T~ falls in between Debye and Onsager-Glarum expressions at large values of the static dielectric constant.

Homonuclear NOE in spatially periodic spin systems

The nuclear Overhauser effect equations are solved analytically for a homonuclear group of spins whose sites are periodically arranged, including the special cases where the spins lie at the vertices of a regular polygon and on a one-dimensional lattice. t is shown that, for long correlation times, the equations governing magnetization transfer resemble a diffusion equation. Furthermore the deviation from exact diffusion is quantitatively related to the molecular tumbling correlation time. Equations are derived for the range of magnetization travel subsequent to the perturbation of a single spin in a lattice for both the case of strictly dipolar relaxation and the more general situation where additional T1 mechanisms may be active. The theory given places no restrictions on the delay (or mixing) times, and it includes all the spins in the system. Simulations are presented to confirm the theory.

A parity-violatingU4-gravitation theory

The general structure of a metric-torsion theory of gravitation allows a parity-violating contribution to the complete action which is linear in the curvature tensor and vanishes identically in the absence of torsion. The resulting action involves, apart from the constant ¯K E =8pgr/c4, a coupling (B) which governs the strength of the parity interaction mediated by torsion. In this model the Brans-Dicke scalar field generates the torsion field, even though it has zero spin. The interesting consequence of the theory is that its results for the solar-system differ very little from those obtained from Brans-Dicke (BD) theory. Therefore the theory is indistinguishable from BD theory in solar-system experiments.