An improved sample-and-hold reconstruction procedure for estimation of power spectra from LDA data

Techniques for deriving the auto or power spectrum (PSD) of turbulence from laser Doppler anemometry (LDA) measurements are reviewed briefly. The low pass filter and step noise errors associated with the sample-and-hold process are considered and a discrete version of the low pass filter for the resampled signal is derived. This is then used to develop a procedure by which the PSD estimates obtained from sample and hold measurements can be corrected. The application of the procedures is examined using simulated data and the results show that the frequency range of the analysis can be extended beyond the Nyquist frequency based on the mean sample rate. The results are shown to be comparable to those obtained using the method of Nobach et al. (1998) but the new procedures are more straightforward to implement. The technique is then used to determine the PSD of real LDA data and the results are compared with those from a hot wire anemometer.     

Multivariate hydrodynamic analysis of boiling channel flow stability from inherent noise measurements

Perturbations in the inlet flow, temperature, channel power, pressure drop and exit void fraction were monitored on a test channel for a range of power levels up to flow stability threshold. Multivariate spectral analysis methods are used to determine the significant frequency response relationships between the measured variables, and the significant cross-spectral density estimates are compared with those obtained from a distributed frequency domain model whose subcooled boiling, two-phase slip and friction correlations are optimised using a special parameter estimation procedure. The optimised model gives the physical mechanisms (perturbed pressure drop components) which tend to drive the channel unstable. The spectral analysis and modelling techniques are generally applicable to performance and diagnostic studies in commercial heat transfer plant where traditional methods of superimposing test signals are impractical during normal operation.     

Structural Analysis of a Dragonfly Wing

Dragonfly wings are highly corrugated, which increases the stiffness and strength of the wing significantly, and results in a lightweight structure with good aerodynamic performance. How insect wings carry aerodynamic and inertial loads, and how the resonant frequency of the flapping wings is tuned for carrying these loads, is however not fully understood. To study this we made a three-dimensional scan of a dragonfly (Sympetrum vulgatum) fore- and hindwing with a micro-CT scanner. The scans contain the complete venation pattern including thickness variations throughout both wings. We subsequently approximated the forewing architecture with an efficient three-dimensional beam and shell model. We then determined the wing’s natural vibration modes and the wing deformation resulting from analytical estimates of 8 load cases containing aerodynamic and inertial loads (using the finite element solver Abaqus). Based on our computations we find that the inertial loads are 1.5 to 3 times higher than aerodynamic pressure loads. We further find that wing deformation is smaller during the downstroke than during the upstroke, due to structural asymmetry. The natural vibration mode analysis revealed that the structural natural frequency of a dragonfly wing in vacuum is 154 Hz, which is approximately 4.8 times higher than the natural flapping frequency of dragonflies in hovering flight (32.3 Hz). This insight in the structural properties of dragonfly wings could inspire the design of more effective wings for insect-sized flapping micro air vehicles: The passive shape of aeroelastically tailored wings inspired by dragonflies can in principle be designed more precisely compared to sail like wings —which can make the dragonfly-like wings more aerodynamically effective.     

Improved error and work estimates for high‐order elements

Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. Copyright © 2013 John Wiley & Sons, Ltd.     

Broadband asymmetric transmission and polarization conversion of a linearly polarized wave based on chiral metamaterial in terahertz region

A novel chiral metamaterial consisting of double L resonators on two sides of the dielectric substrate is proposed in this paper. The structure can realize broadband asymmetric transmission and polarization conversion of a linearly polarized wave in the terahertz band. The polarization conversion ratio of the linearly polarized wave is more than 80% across a wide frequency range from 2.65 THz to 5.58 THz. Furthermore, the structure realizes three bands polarization angle independent 90° polarization rotator. In addition, optical activity and chirality parameter changing with frequency are studied in detail. The physical mechanism of the polarization conversion is also analyzed by the electric field distributions.     

Effect of incomplete datasets on the calculation of continuous relaxation spectra from dynamic-mechanical data

In this article, the effect of an incomplete frequency range on relaxation spectra calculated with the new spline-based method (Stadler and Bailly, Rheol Acta 48(1):33–49, 2009) presented before is discussed. The range, in which the spectrum can be determined, is limited by the range of the input data, but not directly by the inverse frequency. The actual limits depend on the range of input data. Depending on the shape of the spectrum the relaxation spectrum can be determined from the input data in a range up to three decades larger than the input data. This can be explained by the influence of the modes outside the inverse frequency range. For this purpose, a new concept, the relevance factor analysis, was introduced, which allows for a determination of the limits of spectrum calculation. The characteristic relaxation times are discussed in comparison for to the calculation of J_e⁰J_e^{\rm 0} and η ₀ from the spectrum.     

Full Range Scattering Estimates and Their Application to Cloaking

We establish very precise estimates for the time harmonic scattering effects of an inhomogeneity. Our estimates are valid at all frequencies, and are independent of the contents of the inhomogeneity. The involved constants are independent of the frequency. We use these estimates to assess the effectivity of approximate electromagnetic cloaks constructed by so called “mapping techniques”.     

Scattering coefficient reconstruction in plates using focused acoustic beams

A method has been developed and proven using highly focused acoustic beams that allows for the rapid reconstruction of scattering coefficients of a thin anisotropic plate immersed in liquid. In a single bistatic coordinate scan, nearly the entire range of wave number within the spatial and temporal frequency bandwidth of the transducer can be reconstructed. This paper also reports the development of a multiple-source complex transducer point model that includes all extrinsic factors and permits prediction of the wave number-frequency (k–f) domain result obtained from a scan of focused transducers in a pitch-catch reflection or transmission arrangement. Extensive experiments have been performed to test the method and the model and to demonstrate transducer beam effects on the k–f domain results, leading to a very efficient method for mapping major portions of the guided wave dispersion spectrum in thin-plate media. As a demonstration of the technique, an estimate of material elastic properties in an isotropic and a transversely-isotropic plate is reported, making only minimal use of the highly redundant dispersion data. Acoustic velocities inferred from these experiments show a disparity of less than 3% from contact acoustic estimates of the same parameters in either plate.     

Reological behaviour of concentrated monodisperse suspensions as a function of preshear conditions and temperature: an experimental study

 The influence of preshearing on the rheological behaviour of model suspensions was investigated with a stress-controlled cone-and-plate rheometer. The used matrix fluids showed Newtonian behaviour over the whole range of applied shear stresses. Highly monodisperse spherical glass spheres with various particle diameters were used as fillers. By applying steady preshearing at a low preshear stress, where a diffusion of particles can be expected, it was found for all model suspensions investigated at volume fractions ranging from 0.20 to 0.35 that the time-temperature superposition in the steady shear and in the dynamic mode holds within the chosen temperature range. Furthermore, all presheared model suspensions displayed a high and a low frequency range which are either separated by a shoulder or by a plateau value of G′ at intermediate frequencies. It could clearly be demonstrated that the low frequency range strongly depends on the preshear conditions. Hence, the features observed in the low frequency range can be attributed to a structure formation of a particulate network. In the high frequency range a frequency-dependent behaviour was observed which obeys the classical behaviour of Newtonian fluids (G′∝ω², G′′∝ω). The resulting temperature shift factors from the dynamic and the steady shear mode are identical and independent of the volume fraction and the particle size of the filler. Received: 29 November 2000 Accepted: 12 July 2001     

Residual frequency autocorrelation as an indicator of non-linearity

A new temporal analysis approach using discrete frequency models has recently been introduced by the authors. These models relate the steady-state output of non-linear vibrating systems at each frequency to the excitation at that frequency and the output at other frequencies. The discrete frequency modeling approach is used here to derive an experimental frequency domain indicator function for non-linear vibrations. These indicator functions are autocorrelation functions of residuals from multiple input, multiple output frequency response function estimates. Unlike ordinary spectral coherence functions, which only indicate input–output linearity locally at a single frequency, the autocorrelation functions relate the error at each frequency to the errors at frequencies across the frequency band of interest. This feature enables residual autocorrelation functions to distinguish between system non-linearities and bias errors localized in frequency. Non-linearities in a simulated single-degree-of-freedom system, an analog computer system, and a complicated multiple-degree-of-freedom system are detected using the new indicator function.     

Error and work estimates for high‐order elements

Error and work estimates for high‐order elements are derived. The comparison of error and work estimates shows that for relative accuracy in the 1% range, which is typical of engineering interest, it may prove very difficult to improve on linear elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. Copyright © 2011 John Wiley & Sons, Ltd.     

Convective heat transfer characteristics of laminar pulsating pipe air flow

 Heat transfer characteristics to laminar pulsating pipe flow under different conditions of Reynolds number and pulsation frequency were experimentally investigated. The tube wall of uniform heat flux condition was considered. Reynolds number was varied from 780 to 1987 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by pulsation frequency while it is slightly affected by Reynolds number. The results showed enhancements in the relative mean Nusselt number. In the frequency range of 1–4 Hz, an enhancement up to 30% (at Reynolds number of 1366 and pulsation frequency of 1.4 Hz) was obtained. In the frequency range of 17–25 Hz, an enhancement up to 9% (at Reynolds number of 1366 and pulsation frequency of 17.5 Hz) was indicated. The rate of enhancement of the relative mean Nusselt number decreased as pulsation frequency increased or as Reynolds number increased. A reduction in relative mean Nusselt number occurred outside these ranges of pulsation frequencies. A reduction in relative mean Nusselt number up to 40% for pulsation frequency range of 4.1–17 Hz and a reduction up to 20% for pulsation frequency range of 25–29.5 Hz for Reynolds numbers range of 780–1987 were considered. This reduction is directly proportional to the pulsation frequency. Empirical dimensionless equations have been developed for the relative mean Nusselt number that related to Reynolds number (750 < Re < 2000) and the dimensionless frequency (3<Ω<18) with about 10% rms. Received on 16 May 2000 / Published online: 29 November 2001     

Stabilization of liquid-gas interface in the presence of interaction with acoustic fields in the gas

It is shown that in the framework of the assumptions in [8] it is possible not only to describe surface stabilization in the presence of supercritical negative loads but also to determine more accurately the frequency range on which such stabilization is possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 80–86, May–June, 1991.     

Heat transfer characteristics and Nusselt number correlation of turbulent pulsating pipe air flows

Heat transfer characteristics to turbulent pulsating pipe flows under a wide range of Reynolds number and pulsation frequency were experimentally investigated under uniform heat flux condition. Reynolds number was varied from 8462 to 48540 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by both pulsation frequency and Reynolds number. Enhancements in mean Nusselt number of up to 50% were obtained at medium pulsation frequency between 4.1 and 13.9 Hz for Reynolds number range of 8462 to 14581. An enhancement of up to 50% in mean Nusselt number was obtained at high pulsation frequency range between 13.9 and 29.5 Hz, specially as Reynolds number is close to 15000, while a reduction was observed at higher Reynolds number more than 21200. This reduction, at high Reynolds number, increased as pulsation frequency increased. Also, there was a reduction in mean Nusselt number of up to 20% that obtained at low pulsation frequency range between 1 and 4.1 Hz for Reynolds number range of 8462 to 48543. A significant reduction in mean Nusselt number of up to 40% was obtained at medium pulsation frequency between 4.1 and 13.9 Hz for Reynolds number range of 21208 to 48543. Empirical equations have been developed for the relative mean Nusselt number that related to Reynolds number and dimensionless frequency with about uncertainty of 10% rms.The support of both King Fahd University of Petroleum and Minerals and Cairo University for this research is acknowledged.     

Dynamic study of gelatin gels by creep measurements

We have investigated the dynamical properties of gelatin gels using creep measurements. A commercial apparatus (Carrimed CSL500) was modified in order to increase the deformation of the gel and to take advantage of the inertia of the system. When a step stress is applied, the very first response of these materials is an oscillating strain owing to a coupling of the high elasticity of the gelatin gels and the inertia of the apparatus. From these damped oscillations, we have extracted the elastic and loss moduli as a function of frequency, which allows us to widen the frequency range (toward high frequencies) of measurement. After subtraction of the oscillations, we have obtained the compliance funtion from which, using Ferry's formalism, we can calculate the relaxation time distribution function over a very large time range (10^–3–10⁴ s). We show that the dynamics of gelatin gels is governed by two very different characteristic times. We interpret the faster relaxation time as relaxation at the scale of the gel network mesh-size, while the slower time we assign to relaxations involving the lifetime of the gelatin gel cross-links. It is now possible to use creep measurements as an alternative to the forced oscillatory function determination, as the same data can be obtained but, more quickly, and over a large frequency range. This gives us more indication of the gel's structure (gel network behaviour, kinetics of ageing) than all the laborious methods previously necessary.     

Characterization of long time fluctuations of forces exerted on an oscillating circular cylinder at KC=10

Flow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier-Stokes equations. The Keulegan-Carpenter number is held constant at KC=10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80≤Re≤100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150≤Re≤280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.