Energy Dissipation Spectra Research Articles

Adjoint-based variational optimal mixed models for large-eddy simulation of turbulence

An adjoint-based variational optimal mixed model (VOMM) is proposed for subgrid-scale (SGS) closure in large-eddy simulation (LES) of turbulence. The stabilized adjoint LES equations are formulated by introducing a minimal regularization to address the numerical instabilities of the long-term gradient evaluations in chaotic turbulent flows. The VOMM model parameters are optimized by minimizing the discrepancy of energy dissipation spectra between LES calculations and a priori knowledge of direct numerical simulation using the gradient-based optimization. The a posteriori performance of the VOMM model is comprehensively examined in LES of three turbulent flows, including the forced homogeneous isotropic turbulence, decaying homogenous isotropic turbulence, and temporally evolving turbulent mixing layer. The VOMM model outperforms the dynamic Smagorinsky model, dynamic mixed model (DMM), and approximate deconvolution model in predictions of various turbulence statistics, including the velocity spectrum, structure functions, statistics of velocity increments and vorticity, temporal evolutions of the turbulent kinetic energy, dissipation rate, momentum thickness and Reynolds stress, as well as the instantaneous vortex structures at different grid resolutions and times. In addition, the VOMM model only takes up 30% time of the DMM model for all flow scenarios. These results demonstrate that the proposed VOMM model improves the numerical stability of LES and has high a posteriori accuracy and computational efficiency by incorporating the a priori information of turbulence statistics, highlighting that the VOMM model has a great potential to develop advanced SGS models in the LES of turbulence.

Energy level structure of chaotic motion in bouncing ball system

We report our experimental and numerical results on the chaotic dynamics of a ball bouncing on a vertically vibrating plate. It is demonstrated that if the trajectories between collisions are classified according to the rescaled flight time, the chaotic attractor for the bouncing motion of the ball degrades into a regular structure composed of discrete energy levels in the phase space, and the motion states corresponding to these trajectories evolve into separate “microstates” populated on these levels. The probabilities of level transitions and the selection rules for the transitions are discussed. Then, the probability distribution of the energy dissipated during each collision is analyzed. It is found that there are discrete dissipation peaks in the energy dissipation spectrum. The origination of these dissipation peaks is analyzed from the perspective of level transitions.

Role of Complex Surface Tension in the Dispersion Relation of a Capillary Wave

We discuss theoretically the effect of complex surface tension on the dispersion relation of a capillary wave, and we deduce an analytical expression for the attenuation of a capillary wave due to the imaginary part of the complex surface tension. We make use of our recently developed apparent energy dissipation spectroscopy to measure the attenuation of a propagating capillary wave at an air–water interface via a microrheometer based on an atomic force microscope. We show that the revised theoretical expression for the attenuation of a capillary wave can satisfactorily explain the abnormal attenuation of such a wave, which stems from both the apparent energy dissipation spectrum and optical scattering, and we obtain the same value for the imaginary part of the surface tension of water.

Improved Seismic Checking for Pier Based on Seismic Energy Response Method

Based on prophase research work, seismic checking for pier based on energy method is improved. The seismic input energy demand of pier is determined by using the seismic input energy response spectra and hysteretic energy dissipation spectra of sing-degree-of-freedom. Meanwhile, the Pushover Method is used to determine the hysteretic deformation capacity of pier. Then, based on the equilibrium principal between hysteretic deformation capacity and seismic input energy demand of pier, seismic checking for pier is carried on. Then, this improved seismic checking for pier based on energy method is applied in the design examples of piers. Comparing with the calculation of nonlinear time history analyses, it is known that improved seismic checking for pier based on energy method can evaluate the seismic performance of pier effectively. So, these valuable results can provide the meaningful reference for the seismic design of bridge engineering.

On the use of atomic force microscopy for structural mapping of metallic-glass thin films

In this article, we discuss the recent use of the high-resolution dynamic atomic force microscopy (DAFM) in mapping the nano-scale dynamical structural heterogeneity in thin film metallic-glasses (TFMGs). Our focus is laid on the major factors which can influence the structural contrast in the DAFM images, such as tip radius, free-amplitude, set-point amplitude and surface roughness. Finally, through a comparative study of different TFMGs and single-crystal silicon, we demonstrate that the DAFM technique is effective in distinguishing different nanostructures through their energy dissipation spectra.

An equality about the velocity derivative skewness in turbulence

We study velocity derivative skewness S of incompressible homogeneous isotropic turbulence. By using exact relations of isotropic turbulence and various typical models of second-order structure function DLL(r) and energy spectrum E(k), it is found that −S=C(kc/kd)2 when Taylor-microscale Reynolds number Rλ is high. Here, C is a coefficient, kc is the center wavenumber of energy dissipation spectrum, and kd is the Kolmogorov wavenumber. Therefore, the problem of Reynolds number dependence of S becomes the problem of Reynolds number dependence of kc/kd. In the inertial range, we have scaling DLL(r)∼rζ2 and E(k)∼k−(ζ2+1), ζ2 is the second-order inertial-range scaling exponent. Equality −S=C(kc/kd)2 is valid in the case of ζ2>2/3 (intermittency models of Kolmogorov’s 1962 theory) as well as in the case of ζ2=2/3 (Kolmogorov’s 1941 theory).

Hysteretic energy spectrum and damage control

AbstractThe inelastic response of single‐degree‐of‐freedom (SDOF) systems subjected to earthquake motions is studied and a method to derive hysteretic energy dissipation spectra is proposed. The amount of energy dissipated through inelastic deformation combined with other response parameters allow the estimation of the required deformation capacity to avoid collapse for a given design earthquake. In the first part of the study, a detailed analysis of correlation between energy and ground motion intensity indices is carried out to identify the indices to be used as scaling parameters and base line of the energy dissipation spectrum. The response of elastoplastic, bilinear, and stiffness degrading systems with 5 per cent damping, subjected to a world‐wide ensemble of 52 earthquake records is considered. The statistical analysis of the response data provides the factors for constructing the energy dissipation spectrum as well as the Newmark–Hall inelastic spectra. The combination of these spectra allows the estimation of the ultimate deformation capacity required to survive the design earthquake, capacity that can also be presented in spectral form as an example shows. Copyright © 2001 John Wiley & Sons, Ltd.

The use of the discrete element method and fracture mechanics to improve grinding rate prediction

The Discrete Element Method (DEM) is a numerical technique that can simulate the interaction of discrete particles in dynamic environments such as fluidised beds, jigs, flow in bins, screens and mills. This technique has great application potential in comminution modelling at micro-process level. The DEM is being used to determine the grinding rate of ore particles in an Autogenous mill. The frequency of the contact events and the associated energy dissipations derived from the simulation are used to determine the particle failure rate. The probability of particle failure also depends on the inherent fracture properties of a material; hence fracture tests were conducted on an ore sample using a drop-weight impact test machine to obtain a probability fracture model. A second model that uses energy dissipation spectra from the DEM and probability fracture model calculations has been proposed. Though the model tends to over-predict breakage generally, there are indications that the model is responsive to changes in the load behaviour.

Dynamic analysis of automotive clutch dampers

The torsional dynamic characteristics of an automotive clutch are simulated by five lumped parameter linear or nonlinear models. Each nonlinear model includes visco-elastic and dry friction elements. Dynamic stiffness and energy dissipation spectra clearly show excitation amplitude and frequency dependent behavior. Also, dynamic hysteresis curves are predicted and analyzed. The proposed models compare well with limited experimental data. Finally, the utility of such models is illustrated via a transmission rattle simulation program.

Measurements and analysis of high-intensity turbulent characteristics in a turbine-agitated tank

Turbulent flow in the impeller zone and the bulk zone in a turbine-agitated tank was measured by constant temperature anemometry. A split-film probe was used which sensed the directionality of the flow. Turbulent characteristics such as intensity and anisotropy were expressed by statistical moments for all three directions of flow. Turbulent kinetic energy and mean Reynolds stresses were also calculated. The convective velocity was estimated from Taylor's hypotheses as well as from other hypothesis and approximations which considered both the mean velocity and the fluctuations of the flow. The local energy dissipation rates were calculated using three different methods. They were based on energy dissipation spectrum. Kolmogorov's hypotheses and dimensional analysis. The method based on Kolmogorov's hypotheses is suggested here.

Peak position of dissipation spectrum in turbulent boundary layers.

The peak locations of energy dissipation spectrum (y(+)(kp)) are investigated experimentally in the low Reynolds number (R(theta)<5000) zero-pressure-gradient turbulent boundary layers. These peaks are scaled by the relation y(+)(kp)=2(u(*)delta/nu)(1/2)=2R(1/2)(*), where u(*) is friction velocity and delta is the boundary layer thickness. They are located close to the peak positions of the Reynolds shear stress (y(+)(p)), that is, y(+)(kp) approximately equal to y(+)(p). This result predicts that the small-scale structures residing in high-energy dissipation regions concentrate around y(+)(p).

Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients

The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.

Spatiotemporal intermittency and instability of a forced turbulence

The time development of an infinitesimal disturbance and the relation to the spatiotemporal intermittency of a developed turbulence is studied by solving numerically the Navier–Stokes equation and its linearized form. A high-symmetric flow is integrated by the use of the spectral method with 3403 effective modes to realize a developed turbulent field with Reynolds number of about 186 which is in statistically stationary state. Energy transfer in the wave-number space is not uniform in time but quiescent and active periods of energy transfer and of the energy dissipation rate occur repeatedly in a large-scale eddy-turnover time. Vorticity tends to be concentrated in long thin tubelike regions and the energy dissipation field forms double peaks around a tube, which resembles a flow around a nonaxisymmetric Burgers vortex. Both the energy and the enstrophy of the disturbance field increase exponentially in time with growth rate comparable to the reciprocal of the time scale of the peak wave number of the energy dissipation spectrum. The energy spectrum of the disturbance field shows an equipartition of energy at small wave numbers including the inertial range. The disturbance vorticity field has a dipole structure at the position of a vorticity concentrated tube. The direction of this dipole structure is orthogonal to that of the energy dissipation field.

An Experimental Study on Axisymetric Turbulence. (6th Report. Turbulent Energy Transfer Mechanism in Wavenumber Space).

A cigar-shaped axisymmetric turbulence field is experimentally investigated. The equivalent integral scale and the scale of the maximum energy-dissipation rate estimated for the axisymmetric turbulence were almost equal to the scales of isotropic turbulence, which shows that they are valid for determining the characteristic wavenumber range in the spectrum of nonisotropic turbulence, such as the range of energy-containing eddies, the inertial subrange and the energy dissipation range. Energy spectra were measured and the energy dissipation spectra and energy transfer spectra were calculated. The aspects of their streamwise evolutions suggest that it is indispensable to recover the isotropy of the large energy-containing eddies before the turbulence energy begins to be steadily supplied into the dissipation range from the inertial subrange.

Superconducting and anelastic effects in Pb-doped BiSrCaCuO ceramics

The resistivity, shielding and anelastic effects in Pb-doped Bi 2− x Pb x Sr 2Ca 2Cu 3O y ceramics, where x = 0-0.6, have been studied. The best superconducting properties have been achieved for x = 0.4. The chemical analysis shows that the real Pb content is lower than the nominal. Energy dissipation spectra show no maximum around the transition temperature. A sharp peak at 215 K has been interpreted as being due to a first order antiferromagnetic transition.

Characterization of the two‐phase systems in airlift tower–loop bioreactors during the cultivation of E. coli

During the cultivation of E. coli in an airlift tower-loop bioreactor, the following properties were measured: transverse profiles of Sauter bubble diameter, d(S); local relative gas holdup, E(G); bubble rise velocity, u(BS); local mean velocity, ū turbulence intensity, u'; macrotime scale, T(EL); dissipation time scale, tau(E); power spectrum, E(n); and energy dissipation spectrum D(n) at different distances from the aerator. The influence, distance from the aerator, absence and/or presnece of cells, and batch and/or continuous-culture operation on the behavior of the two-phase system are discussed on the basis of these properties.