Table of Content

01 April 2019, Volume 40 Issue 4

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Articles

Combined effects of topography and bottom friction on shoaling internal solitary waves in the South China Sea

Dalin TAN, Jifu ZHOU, Xu WANG, Zhan WANG

2019, 40(4):  421-434.  doi:10.1007/s10483-019-2465-8

Abstract ( 454 )   HTML   PDF (644KB) ( 116 )  

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A numerical study to a generalized Korteweg-de Vries (KdV) equation is adopted to model the propagation and disintegration of large-amplitude internal solitary waves (ISWs) in the South China Sea (SCS). Based on theoretical analysis and in situ measurements, the drag coefficient of the Chezy friction is regarded as inversely proportional to the initial amplitude of an ISW, rather than a constant as assumed in the previous studies. Numerical simulations of ISWs propagating from a deep basin to a continental shelf are performed with the generalized KdV model. It is found that the depression waves are disintegrated into several solitons on the continental shelf due to the variable topography. It turns out that the amplitude of the leading ISW reaches a maximum at the shelf break, which is consistent with the field observation in the SCS. Moreover, a dimensionless parameter defining the relative importance of the variable topography and friction is presented.

Numerical study of the turbulent channel flow under space-dependent electromagnetic force control at different Reynolds numbers

Daiwen JIANG, Hui ZHANG, Baochun FAN, Zijie ZHAO, Jian LI, Mingyue GUI

2019, 40(4):  435-448.  doi:10.1007/s10483-019-2471-7

Abstract ( 496 )   HTML   PDF (3008KB) ( 131 )  

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In this paper, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with the direct numerical simulation (DNS) methods for different Reynolds numbers. A formulation is derived to express the relation between the drag and the Reynolds shear stress. With the application of optimal electromagnetic force, the in-depth relations among characteristic structures in the flow field, mean Reynolds shear stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The regular quasi-streamwise vortex structures, which appear in the flow field, have the same period with that of the electromagnetic force. These structures suppress the random velocity fluctuations, which leads to the absolute value of mean Reynolds shear stress decreasing and the distribution of that moving away from the wall. Moreover, the wave number of optimal electromagnetic force increases, and the scale of the regular quasi-streamwise vortex structures decreases as the Reynolds number increases. Therefore, the rate of drag reduction decreases with the increase in the Reynolds number since the scale of the regular quasi-streamwise vortex structures decreases.

Unsteady magnetohydrodynamic stagnation point flow-closed-form analytical solutions

T. G. FANG, F. J. WANG, Bo GAO

2019, 40(4):  449-464.  doi:10.1007/s10483-019-2463-7

Abstract ( 432 )   HTML   PDF (521KB) ( 97 )  

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This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic (MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes (NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation, and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.

Melting heat transfer in Cu-water and Ag-water nanofluids flow with homogeneous-heterogeneous reactions

M. IMTIAZ, F. SHAHID, T. HAYAT, A. ALSAEDI

2019, 40(4):  465-480.  doi:10.1007/s10483-019-2462-8

Abstract ( 480 )   HTML   PDF (441KB) ( 95 )  

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This article addresses melting heat transfer in magnetohydrodynamics (MHD) nanofluid flows by a rotating disk. The analysis is performed in Cu-water and Ag-water nanofluids. Thermal radiation, viscous dissipation, and chemical reactions impacts are added in the nanofluid model. Appropriate transformations lead to the nondimensionalized boundary layer equations. Series solutions for the resulting equations are computed. The role of pertinent parameters on the velocity, temperature, and concentration is analyzed in the outputs. It is revealed that the larger melting parameter enhances the velocity profile while the temperature profile decreases. The surface drag force and heat transfer rate are computed under the influence of pertinent parameters. Furthermore, the homogeneous reaction parameter serves to decrease the surface concentration.

Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

K. RAMESH, O. OJJELA

2019, 40(4):  481-498.  doi:10.1007/s10483-019-2464-8

Abstract ( 465 )   HTML   PDF (629KB) ( 111 )  

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The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations (ODEs) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.

Combined effects of axial load and temperature on finite deformation of incompressible thermo-hyperelastic cylinder

Jie XU, Xuegang YUAN, Hongwu ZHANG, Zhentao ZHAO, Wei ZHAO

2019, 40(4):  499-514.  doi:10.1007/s10483-019-2466-8

Abstract ( 436 )   HTML   PDF (729KB) ( 81 )  

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A finite deformation problem is examined for a cylinder composed of a class of incompressible thermo-hyperelastic Mooney-Rivlin materials under an equal axial load at its two fixed ends and a temperature field at its lateral boundary. Firstly, a thermomechanical coupling term is taken into account in the strain energy density function, and a governing equation of the problem is obtained. Secondly, an implicit analytical solution is derived by using the incompressibility and the boundary conditions. Significantly, numerical examples show that the middle portion of the cylinder undergoes almost a uniform radial deformation. However, the deformation near the two ends varies remarkably along the axial direction for relatively large axial loads. In addition, the rising temperature can increase the deformation of structures, and its influence is linear approximately. Specially, in the case of tensile load, the jump increase of the axial deformation may occur.

Deep postbuckling and nonlinear bending behaviors of nanobeams with nonlocal and strain gradient effects

Bo ZHANG, Huoming SHEN, Juan LIU, Yuxing WANG, Yingrong ZHANG

2019, 40(4):  515-548.  doi:10.1007/s10483-019-2482-9

Abstract ( 478 )   HTML   PDF (1076KB) ( 99 )  

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In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale parameters which describe the stiffness-softening and stiffness-hardening size effects of nanomaterials, respectively. By applying Hamilton's principle, the motion equation and the associated boundary condition are derived. A two-step perturbation method is introduced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically. Afterwards, the influence of geometrical, material, and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed. Numerical results show that the stability and precision of the perturbation solutions can be guaranteed, and the two types of size effects become increasingly important as the slenderness ratio increases. Moreover, the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.

Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method

Qiang LYU, Jingjing LI, Nenghui ZHANG

2019, 40(4):  549-562.  doi:10.1007/s10483-019-2470-8

Abstract ( 481 )   HTML   PDF (513KB) ( 116 )  

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The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the governing equations for the beam are presented. Second, an extended differential quadrature method (DQM) in the spatial domain and a differential method in the temporal domain are combined to transform the integro-partial-differential governing equations into the ordinary differential equations. Third, the accuracy of the present discrete method is verified by elastic/viscoelastic examples, and the effects of thermal load parameters, material and geometrical parameters on the quasi-static and dynamic responses of the beam are discussed. Numerical results show that the thermal function parameter has a great effect on quasi-static and dynamic responses of the beam. Compared with the thermal relaxation time, the initial vibrational responses of the beam are more sensitive to the mechanical relaxation time of the thermoviscoelastic material.

Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis

R. KARROUBI, M. IRANI-RAHAGHI

2019, 40(4):  563-578.  doi:10.1007/s10483-019-2469-8

Abstract ( 494 )   HTML   PDF (898KB) ( 104 )  

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The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material (FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded (FG), the material properties vary along the thickness direction as one innovation of this study. Applying the first-order shear deformation theory (FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations (PDEs) using Hamilton's principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material (FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.

Path integral solution of vibratory energy harvesting systems

Wenan JIANG, Peng SUN, Gangling ZHAO, Liqun CHEN

2019, 40(4):  579-590.  doi:10.1007/s10483-019-2467-8

Abstract ( 477 )   HTML   PDF (993KB) ( 86 )  

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A transition Fokker-Planck-Kolmogorov (FPK) equation describes the procedure of the probability density evolution whereby the dynamic response and reliability evaluation of mechanical systems could be carried out. The transition FPK equation of vibratory energy harvesting systems is a four-dimensional nonlinear partial differential equation. Therefore, it is often very challenging to obtain an exact probability density. This paper aims to investigate the stochastic response of vibration energy harvesters (VEHs) under the Gaussian white noise excitation. The numerical path integration method is applied to different types of nonlinear VEHs. The probability density function (PDF) from the transition FPK equation of energy harvesting systems is calculated using the path integration method. The path integration process is introduced by using the GaussLegendre integration scheme, and the short-time transition PDF is formulated with the short-time Gaussian approximation. The stationary probability densities of the transition FPK equation for vibratory energy harvesters are determined. The procedure is applied to three different types of nonlinear VEHs under Gaussian white excitations. The approximately numerical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulation (MCS).