Table of Content

01 December 2018, Volume 39 Issue 12

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Articles

Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions

Qiang YU, Hang XU

2018, 39(12):  1691-1718.  doi:10.1007/s10483-018-2397-9

Abstract ( 661 )   HTML   PDF (595KB) ( 167 )  

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In this paper, a brand-new wavelet-homotopy Galerkin technique is developed to solve nonlinear ordinary or partial differential equations. Before this investigation, few studies have been done for handling nonlinear problems with non-uniform boundary conditions by means of the wavelet Galerkin technique, especially in the field of fluid mechanics and heat transfer. The lid-driven cavity flow and heat transfer are illustrated as a typical example to verify the validity and correctness of this proposed technique. The cavity is subject to the upper and lower walls' motions in the same or opposite directions. The inclined angle of the square cavity is from 0 to π/2. Four different modes including uniform, linear, exponential, and sinusoidal heating are considered on the top and bottom walls, respectively, while the left and right walls are thermally isolated and stationary. A parametric analysis of heating distribution between upper and lower walls including the amplitude ratio from 0 to 1 and the phase deviation from 0 to 2π is conducted. The governing equations are non-dimensionalized in terms of the stream function-vorticity formulation and the temperature distribution function and then solved analytically subject to various boundary conditions. Comparisons with previous publications are given, showing high efficiency and great feasibility of the proposed technique.

Large eddy simulation of turbulent premixed and stratified combustion using flame surface density model coupled with tabulation method

Zhou YU, Hongda ZHANG, Taohong YE, Minming ZHU

2018, 39(12):  1719-1736.  doi:10.1007/s10483-018-2396-9

Abstract ( 566 )   HTML   PDF (4909KB) ( 109 )  

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Large eddy simulations (LESs) are performed to investigate the Cambridge premixed and stratified flames, SwB1 and SwB5, respectively. The flame surface density (FSD) model incorporated with two different wrinkling factor models, i.e., the Muppala and Charlette2 wrinkling factor models, is used to describe combustion/turbulence interaction, and the flamelet generated manifolds (FGM) method is employed to determine major scalars. This coupled sub-grid scale (SGS) combustion model is named as the FSD-FGM model. The FGM method can provide the detailed species in the flame which cannot be obtained from the origin FSD model. The LES results show that the FSD-FGM model has the ability of describing flame propagation, especially for stratified flames. The Charlette2 wrinkling factor model performs better than the Muppala wrinkling factor model in predicting the flame surface area change by the turbulence. The combustion characteristics are analyzed in detail by the flame index and probability distributions of the equivalence ratio and the orientation angle, which confirms that for the investigated stratified flame, the dominant combustion modes in the upstream and downstream regions are the premixed mode and the back-supported mode, respectively.

Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

Yufeng HAN, Jianxin LIU, Jisheng LUO

2018, 39(12):  1737-1754.  doi:10.1007/s10483-019-2401-9

Abstract ( 527 )   HTML   PDF (505KB) ( 96 )  

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An improved expansion of the parabolized stability equation (iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The iEPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the iEPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the iEPSE. As a local non-parallel stability analysis tool, the iEPSE has great potential application in the e^N transition prediction in general three-dimensional boundary layers.

Conservation relation of generalized growth rate in boundary layers

Runjie SONG, Lei ZHAO, Zhangfeng HUANG

2018, 39(12):  1755-1768.  doi:10.1007/s10483-018-2394-9

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The elementary task is to calculate the growth rates of disturbances when the e^N method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in three-dimensional (3D) flows. In this paper, we study the relation among the wave parameters of the disturbance in boundary layers in which the imaginary parts of wave parameters are far smaller than the real parts. The generalized growth rate (GGR) in the direction of group velocity is introduced, and the conservation relation of GGR is strictly deduced in theory. This conservation relation manifests that the GGR only depends on the real parts of wave parameters instead of the imaginary parts. Numerical validations for GGR conservation are also provided in the cases of first/second modes and crossflow modes. The application of GGR to the e^N method in 3D flows is discussed, and the puzzle of determining growth rates in 3D flows is clarified. A convenient method is also proposed to calculate growth rates of disturbances in 3D flows. Good agreement between this convenient method and existing methods is found except the condition that the angle between the group velocity direction and the x-direction is close to 90° which can be easily avoided in practical application.

Travel time prediction with viscoelastic traffic model

Yongliang ZHANG, M. N. SMIRNOVA, A. I. BOGDANOVA, Zuojin ZHU, N. N. SMIRNOV

2018, 39(12):  1769-1788.  doi:10.1007/s10483-018-2400-9

Abstract ( 513 )   HTML   PDF (1322KB) ( 83 )  

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Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model (VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang (ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27-41 (2003)) is adopted to predict the travel time through the ring road for providing the counterpart results. When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m, with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.

Phase-field simulation of the coupled evolutions of grain and twin boundaries in nanotwinned polycrystals

Yuanyuan DA, Yuyang LU, Yong NI

2018, 39(12):  1789-1804.  doi:10.1007/s10483-018-2393-7

Abstract ( 485 )   HTML   PDF (3915KB) ( 93 )  

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Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may result in strength drop based on the Hall-Petch law. In this paper, a phase-field model is developed to investigate the effect of coupled evolutions of twin and grain boundaries on nanotwin-assisted grain growth. The simulation result demonstrates that there are three pathways for coupled motions of twin and grain boundaries in a bicrystal under the applied loading, dependent on the amplitude of applied loading and misorientation of the bicrystal. It reveals that a large misorientation angle and a large applied stress promote the twinning-driven grain boundary migration. The resultant twin-assisted grain coarsening is confirmed in the simulations for the microstructural evolutions in twinned and un-twinned polycrystals under a high applied stress.

Semi-analytic solution of Eringen's two-phase local/nonlocal model for Euler-Bernoulli beam with axial force

Licheng MENG, Dajun ZOU, Huan LAI, Zili GUO, Xianzhong HE, Zhijun XIE, Cunfa GAO

2018, 39(12):  1805-1824.  doi:10.1007/s10483-018-2395-9

Abstract ( 561 )   HTML   PDF (660KB) ( 120 )  

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Eringen's two-phase local/nonlocal model is applied to an Euler-Bernoulli nanobeam considering the bending-induced axial force, where the contribution of the axial force to bending moment is calculated on the deformed state. Basic equations for the corresponding one-dimensional beam problem are obtained by degenerating from the three-dimensional nonlocal elastic equations. Semi-analytic solutions are then presented for a clamped-clamped beam subject to a concentrated force and a uniformly distributed load, respectively. Except for the traditional essential boundary conditions and those required to be satisfied by transferring an integral equation to its equivalent differential form, additional boundary conditions are needed and should be chosen with great caution, since numerical results reveal that non-unique solutions might exist for a nonlinear problem if inappropriate boundary conditions are used. The validity of the solutions is examined by plotting both sides of the original integro-differential governing equation of deflection and studying the error between both sides. Besides, an increase in the internal characteristic length would cause an increase in the deflection and axial force of the beam.

Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

Rong WANG, Guohua NIE

2018, 39(12):  1825-1836.  doi:10.1007/s10483-018-2399-9

Abstract ( 449 )   HTML   PDF (223KB) ( 80 )  

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This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

Delay-dependent stability of linear multistep methods for differential systems with distributed delays

Yanpei WANG, Yuhao CONG, Guangda HU

2018, 39(12):  1837-1844.  doi:10.1007/s10483-018-2392-9

Abstract ( 450 )   HTML   PDF (360KB) ( 79 )  

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This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.

Isotropic polynomial invariants of Hall tensor

Jinjie LIU, Weiyang DING, Liqun QI, Wennan ZOU

2018, 39(12):  1845-1856.  doi:10.1007/s10483-018-2398-9

Abstract ( 481 )   HTML   PDF (146KB) ( 82 )  

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The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.