An anti-icing scaling method for wind tunnel tests of aircraft thermal ice protection system

The efficiency of the aircraft Ice Protection Systems(IPSs)needs to be verified through icing wind tunnel tests.However,the scaling method for testing the IPSs has not been systematically established yet,and further research is needed.In the present study,a scaling method specifically designed for thermal IPSs was derived from the governing equation of thin water film.Five scaling parameters were adopted to address the heat and mass transfer involved in the thermal anti-icing process.For method validation,icing wind tunnel tests were conducted using a jet engine nacelle model equipped with a bleed air IPS.The non-dimensional surface temperature and runback ice closely matched for both the reference and scaled conditions.The validation confirms that the scaling method is capable of achieving the similarity of surface temperature and the runback ice coverage.The anti-icing scaling method can serve as an important supplement to the existing icing similarity theory.

Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

A scaled boundary node method applied to two-dimensional crack problems

A boundary-type meshless method called the scaled boundary node method （SBNM） is developed to directly evaluate mixed mode stress intensity factors （SIFs） without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging （MK） interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the 5 function property. This makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.

Dynamic interaction numerical models in the time domain based on the high performance scaled boundary finite element method

Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method （SBFEM） is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.

Determination of the natural frequencies of axially moving beams by the method of multiple scales

The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

An optimal method for the power spectrum measurement

An aliasing effect brought up by mass assignment onto Fast Fourier Transformation （FFT） grids may bias measurement of the power spectrum of large scale structures. In this paper, based on the Beylkin＇s unequally spaced FFT technique, we propose a new precise method to extract the true power spectrum of a large discrete data set. We compare the traditional mass assignment schemes with the new method using the Daub6 and the 3rd-order B-spline scaling functions. Our measurement of Poisson samples and samples of N-body simulations shows that the B-spline scaling function is an optimal choice for mass assignment in the sense that （1） it has a compact support in real space and thus yields an efficient algorithm （2） without any extra corrections. The Fourier space behavior of the 3rd-order B-spline scaling function enables it to be able to accurately recover the true power spectrum with errors less than 5% up to k 〈 kN. It is expected that such a method can be applied to higher order statistics in Fourier space and will enable us to have a precision capture of the non-Gaussian features in the large scale structure of the universe.

Computational multiscale methods for granular materials

The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolves, it is demonstrated to develop computational multiscale methods using discrete particle assembly-Cosserat continuum modeling in micro- and macro- scales,respectively. The computational homogenization method and the bridge scale method along the concurrent scale linking approach are briefly introduced. Based on the weak form of the Hu-Washizu variational principle, the mixed finite element procedure of gradient Cosserat continuum in the frame of the second-order homogenization scheme is developed. The meso-mechanically informed anisotropic damage of effective Cosserat continuum is characterized and identified and the microscopic mechanisms of macroscopic damage phenomenon are revealed. c 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301101]

Scaled radar cross section measurement method for lossy targets via dynamically matching reflection coefficients in THz band

In the terahertz band,the dispersive characteristic of dielectric material is one of the major problems in the scaled radar cross section(RCS)measurement,which is inconsistent with the electrodynamics similitude deducted according to the Maxwell’s equations.Based on the high-frequency estimation method of physical optics(PO),a scaled RCS measurement method for lossy objects is proposed through dynamically matching the reflection coefficients according to the distribution of the object facets.Simulations of the model of SLICY are conducted,and the inversed RCS of the lossy prototype is obtained using the proposed method.Comparing the inversed RCS with the calculated results,the validity of the proposed method is demonstrated.The proposed method provides an effective solution to the scaled RCS measurement for lossy objects in the THz band.

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION AND THE ASYMPTOTICS OF SOLUTIONS(Ⅱ)

This paper is a continuation of part (Ⅰ), on the asymptotics behaviors of the series solutions investigated in (Ⅰ). The remainder terms of the series solutions are estimated by the maximum norm.

THE METHOD OF MULTIPLE SCALES APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A TRUNCATED SHALLOW SPHERICAL SHELL OF VARIABLE THICKNESS WITH THE LARGE GEOMETRICAL PARAMETER

Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.

A MODIFIED METHOD OF AVERAGING FOR SOLVING A CLASS OFNONLINEAR EQUATIONS

In this paper, we studied a method of averaging which decide a uniform validsolution for nonlinear equationand got the ,modified forms for KB ,method (Krylov-Bogoliubov method)and KBMmethod (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and thereby the applied area of the methodof averaging are extended.

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION ANDTHE ASYMPTOTICS OF SOLUTIONS (Ⅰ)

In this paper, the modified method of multiple scales is applied to study the bending problems for circular thin plate with large deflection under the hinged and simply supported edge conditions. Theseries solutions are constructed, the boundary layer effects are analysed and their asymptotics are proved.

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

COMPUTER COMPUTATION OF THE METHOD OF MULTIPLE SCALES-DIRICHLET PROBLEM FOR A CLASS OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .

Multiple scales method for analyzing a forced damped rotational pendulum oscillatorwithgallows

This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.

Performance and uncertainty analysis of a short-term climate reconstruction based on multi-source data in the Tianshan Mountains region,China

Short-term climate reconstruction,i.e.,the reproduction of short-term(several decades)historical climatic time series based on the relationship between observed data and available longer-term reference data in a certain area,can extend the length of climatic time series and offset the shortage of observations.This can be used to assess regional climate change over a much longer time scale.Based on monthly grid climate data from a Coupled Model Inter-comparison Project phase 5(CMIP5)dataset for the period of 1850–2000,the Climatic Research Unit(CRU)dataset for the period of 1901–2000 and the observed data from 53 meteorological stations located in the Tianshan Mountains region(TMR)of China during the period of 1961–2011,we calibrated and validated monthly average temperature(MAT)and monthly accumulated precipitation(MAP)in the TMR using the delta,physical scaling(SP)and artificial neural network(ANN)methods.Performance and uncertainty during the calibration(1971–1999)and verification(1961–1970)periods were assessed and compared using traditional performance indices and a revised set pair analysis(RSPA)method.The calibration and verification processes were subjected to various sources of uncertainty due to the influence of different reconstructed variables,different data sources,and/or different methods used.According to traditional performance indices,both the CRU and CMIP5 datasets resulted in satisfactory calibrated and verified MAT time series at 53 meteorological stations and MAP time series at 20 meteorological stations using the delta and SP methods for the period of 1961–1999.However,the results differed from those obtained by the RSPA method.This showed that the CRU dataset produced a low degree of uncertainty(positive connection degree)during the calibration and verification of MAT using the delta and SP methods compared to the CMIP5 dataset.Overall,the calibrated and verified MAP had a high degree of uncertainty(negative connection degree)regardless of the dataset or reconstruction method used.Therefore,the reconstructed time series of MAT for the period of 1850(or 1901)–1960 based on the CRU and CMIP5 datasets using the delta and SP methods could be used for further study.The results of this study will be useful for short-term(several decades)regional climate reconstruction and longer-term(100 a or more)assessments of regional climate change.

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.