Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.

Quantitative method for evaluating detailed volatility of wind power at multiple temporal-spatial scales

With the increasing proportion of wind power integration, the volatility of wind power brings huge challenges to the safe and stable operation of the electric power system. At present, the indexes commonly used to evaluate the volatility of wind power only consider its overall characteristics, such as the standard deviation of wind power, the average of power variables, etc., while ignoring the detailed volatility of wind power, that is, the features of the frequency distribution of power variables. However, how to accurately describe the detailed volatility of wind power is the key foundation to reduce its adverse influences. To address this, a quantitative method for evaluating the detailed volatility of wind power at multiple temporal-spatial scales is proposed. First, the volatility indexes which can evaluate the detailed fluctuation characteristics of wind power are presented, including the upper confidence limit, lower confidence limit and confidence interval of power variables under the certain confidence level. Then, the actual wind power data from a location in northern China is used to illustrate the application of the proposed indexes at multiple temporal(year–season–month–day) and spatial scales(wind turbine–wind turbines–wind farm–wind farms) using the calculation time windows of 10 min, 30 min, 1 h, and 4 h. Finally, the relationships between wind power forecasting accuracy and its corresponding detailed volatility are analyzed to further verify the effectiveness of the proposed indexes. The results show that the proposed volatility indexes can effectively characterize the detailed fluctuations of wind power at multiple temporal-spatial scales. It is anticipated that the results of this study will serve as an important reference for the reserve capacity planning and optimization dispatch in the electric power system which with a high proportion of renewable energy.

Aerodynamic shape and drag scaling law of a flexible fibre in a flowing medium

The study of a flexible body immersed in a flowing medium is one of the best way to find its aerodynamic shape.This Letter revisited the problem that was first studied by Alben et al.(Nature 420,479–481,2002).To determine the aerodynamic shape of the fibre,a simpler approach is proposed.A universal drag scaling law is obtained and the universality of the Alben-Shelley-Zhang scaling law is confirmed by using dimensional analysis.A complete Maple code is provided for finding aerodynamic shape of the fibre in the flowing medium.

A modified generalized scaling law for the similitude of dynamic strain in centrifuge modeling

Soil strain is the key parameter to control the elasto-plastic deformation and even the failure processes.To overcome the defect that the strain of the model soil is always smaller than that of the prototype in Iai′s generalized scaling law(GSL),a modified scaling law was proposed based on Iai′s GSL to secure the same dynamic shear strain between the centrifuge model and the prototype by modulating the amplitude and frequency of the input motion at the base.A suite of dynamic centrifuge model tests of dry sand level ground was conducted with the same overall scaling factor(λ=200)under different centrifugal accelerations by using the technique of“modeling of models”to validate the modified GSL.The test results show that the modified GSL could achieve the same dynamic strain in model as that of the prototype,leading to better modeling for geotechnical problems where dynamic strain dominates the response or failure of soils.Finally,the applicability of the proposed scaling law and possible constraints on geometry scaling due to the capability limits of existing centrifuge shaking tables are discussed.

EXTENDED SELF-SIMILAR SCALING LAW OF MULTI-SCALE EDDY STRUCTURE IN WALL TURBULENCE

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Scaling laws of compressible turbulence

Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt＇s incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the -5/3 and -2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.

The scaling laws of cabin structures subjected to internal blast loading:Experimental and numerical studies

This paper presents a combination of experimental and numerical investigations on the dynamic response of scaling cabin structures under internal blast loading.The purpose of this study is to modify the similar relationship between the scaled-down model and the prototype of the cabin structures under internal blast loading.According to the Hopkinson’s scaling law,three sets of cabin structure models with different scaling factors combined with different explosive masses were designed for the experimental study.The dynamic deformation process of the models was recorded by a three-dimensional digital imaging correlation(DIC)method and a 3D scanning technology was used to reconstruct the deformation modes of the specimen.In addition,a finite element model was developed for the modification of the scaling law.The experimental results showed that the final deflection-to-thickness ratio was increased with the increase of the model size despite of the similar trend of their deformation processes.The reason for this inconsistency was discussed based on the traditional scaling law and a modified formula considering of the effects of size and strain-rate was provided.

Empirical Scaling Laws of Neutral Beam Injection Power in HL-2A Tokamak

We present an experimental method to obtain neutral beam injection （NBI） power scaling laws with operating parameters of the NBI system on HL-2A, including the beam divergence angle, the beam power transmission efficiency, the neutralization efficiency and so on. With the empirical scaling laws, the estimating power can be obtained in every shot of experiment on time, therefore the important parameters such as the energy confinement time can be obtained precisely. The simulation results by the tokamak simulation code （TSC） show that the evolution of the plasma parameters is in good agreement with the experimental results by using the NBI power from the empirical scaling law.

A scaling law of high-order harmonic generation

Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation （HHG）, a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ）, and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.

Comparison of Coarse Graining DEM Models Based on Exact Scaling Laws

The simulation of a large number of particles requires unacceptable computational time that is the most criticalproblem existing in the industrial application of the DEM. Coarse graining is a promising approach to facilitatethe application of DEM to industrial problems. While the current coarse graining framework is often developedin an ad-hoc manner, leading to different formulations and different solution accuracy and efficiency. Therefore,in this paper, existing coarse graining techniques have been carefully analysed by the exact scaling law which canprovide the theory basis for the upscaling method. A proper scaling rule for the size of particles and samples as wellas interaction laws have been proposed. The scaling rule is applied to a series simulations of biaxial compressiontests with different scale factors to investigate the precision of the coarse graining system. The error between theoriginal system and the coarse system shows a growing tendency as the scale factor increases. It can be concludedthat the precision of the coarse graining system is accepted when applying scaling rules based on the exact scalinglaws.

On the scaling law of ramp structures in scalar turbulence

斜坡结构在标量湍流中广泛存在,指标量的浓度随时间缓慢爬升然后突然下降的现象,它表明湍流并非完全随机的。基于北京市325米气象铁塔的湍流观测数据,本文利用小波分析提取了温度、水汽和二氧化碳序列中的斜坡结构,其上升部分线性拟合的斜率与持续时间存在明显的标度律,三者幂指数相差不大,而且在下降部分也存在类似的规律。同时将斜坡结构上升部分的最大值按时间顺序排列,发现最大值序列依然存在斜坡结构。这表明标量湍流中斜坡结构是自相似的,小尺度的斜坡结构叠加在大尺度的斜坡结构上。

Reinvestigation of the scaling law of the windblown sand launch velocity with a wind tunnel experiment

Windblown sand transport is a leading factor in the geophysical evolution of arid and semi-arid regions.The evolution speed is usually indicated by the sand transport rate that is a function of launch velocity of sand particle,which has been investigated by the experimental measurement and numerical simulation.However,the obtained results in literatures are inconsistent.Some researchers have discovered a relation between average launch velocity and wind shear velocity,while some other researchers have suggested that average launch velocity is independent of wind shear velocity.The inconsistence of launch velocity leads to a controversy in the scaling law of the sand transport rate in the windblown case.On the contrary,in subaqueous case,the scaling law of the sand transport rate has been widely accepted as a cubic function of fluid shear velocity.In order to explain the debates surrounding the windblown case and the difference between windblown and subaquatic cases,this study reinvestigates the scaling law of the vertical launch velocity of windblown transported sand particles by using a dimensional analysis in consideration of the compatibility of the characteristic time of sand particle motion and that of air flow.Then a wind tunnel experiment is conducted to confirm the revisited scaling law,where the sand particle motion pictures are recorded by a high-speed camera and then the launch velocity is solved by the particle tracking velocimetry.By incorporating the results of dimensional analysis and wind tunnel experiment,it can be concluded that,the ratio of saltons number to reptons number determines the scaling law of sand particle launch velocity and that of sand transport rate,and using this ratio is able to explain the discrepancies among the classical models of steady sand transport.Moreover,the resulting scaling law can explain the sand sieving phenomenon:a greater fraction of large grains is observed as the distance to the wind tunnel entrance becomes larger.

Scaling law of single ion–atom impact ionization cross sections of noble gases from He to Xe at strong perturbative energies

We extend our previous work of a classical over-barrier ionization （COBI） model to calculate the single ionization cross sections of noble gases ranging from He to Xe at strong perturbative energies. The calculation results are in good agreement with extensive experimental data. The scaling law of single ion-atom impact ionization cross sections of noble gases on projectile charge q and energy E, also on target ionization energy I is drawn from the model.

Scaling Laws for Plasma Focus Machines from Numerical Experiments

Numerical experiments carried out systematically using the Lee Model code unveil insightful and practical wide-ranging scaling laws for plasma focus machines for nuclear fusion energy as well as other applications. An essential feature of the numerical experiments is the fitting of a measured current waveform to the computed waveform to calibrate the model for the particular machine, thus providing a reliable and rigorous determination of the all-important pinch current. The thermodynamics and radiation properties of the resulting plasma are then reliably determined. This paper provides an overview of the recently published scaling laws for neutron (Yn) and neon soft x-ray, SXR (Ysxr) yields: Yn = 3.2x1011 Ipinch4.5;Yn = 1.8x1010 Ipeak3.8;Ipeak (0.3 to 5.7), Ipinch (0.2 to 2.4) in MA. Yn^E02.0 at tens of kJ to Yn^E00.84 at MJ level (up to 25MJ) and Ysxr = 8.3x103 Ipinch3.6;Ysxr = 6x102 Ipeak3.2;Ipeak (0.1 to 2.4), Ipinch (0.07 to1.3) in MA. Ysxr^E01.6 (kJ range) to Ysxr^E00.8 (towards MJ).

SCALING LAW OF IRREGULAR EUTECTIC IN DIRECTIONAL SOLIDIFICATION

The profile features of the solidifying interface of the irregular Al-Si eutectic during directional solidification are studied by numerically solving a nonlinear coupling equation of directional solidification of this eutectic.The critical splitting point of the solidifying interface coincides with the maximum value of its position and corresponds to the marginal stability point.Argument is presented that the interlamellar spacing for local regular structure selects the critical splitting state of the α(Al)-liquid interface as its operating point,and the oper- ating point of the average interflake spacing for the irregular structure is the critical splitting state of the β(Si)-liquid interface.The scaling laws derived,which have the more general forms than the classic Jackson-Hunt scaling,gained support from the experimental results.

Experimental researches for scaling laws of low-order structure function in boundary layer

Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.

EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.

Studies on convergence and scaling law of Thomson backscattering spectra in strong fields

With the saddle point analysis method for the Bessel function structure and property, the convergence problem and the scaling laws of Thomson backscattering spectra are solved and studied in both cases that are for the plane wave laser field without and with applied external constant magnetic field. Some unclear points appeared in previous work are clarified. The extension of the method to a general situation for the laser field with an arbitrary polarization is discussed. We also make a simple analysis and discussion about the optimal spectra dependence of field parameters and its implication to practical applications.

Scaling Law of s-Wave Valence Proton Distributions

Inthe framework of the single-particle potential model, the root-meamsquare radii of s-wave valence proton distributions for P and S isotopes have been systematically calculated. The scaling law of s-wave valence proton distributions is obtained by analyzing the relation between radii and separation energies. Necessary condition for the occurrence of 2sl/2-state proton halos is deduced from the scaling law. Quantitative condition derived from this work can to some extent serve as reference for proton halo search.

Mobile user forecast and power-law acceleration invariance of scale-free networks

This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.