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Table of Content

    01 May 2018, Volume 39 Issue 5
    Articles
    Asymptotic solution of a wide moving jam to a class of higher-order viscous traffic flow models
    Chunxiu WU
    2018, 39(5):  609-622.  doi:10.1007/s10483-018-2327-6
    Abstract ( 660 )   HTML   PDF (440KB) ( 138 )  
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    The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.

    3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux
    V. NAGENDRAMMA, C. S. K. RAJU, B. MALLIKARJUNA, S. A. SHEHZAD, A. LEELARATHNAM
    2018, 39(5):  623-638.  doi:10.1007/s10483-018-2331-6
    Abstract ( 541 )   HTML   PDF (2599KB) ( 115 )  
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    A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.

    Effects of the particle Stokes number on wind turbine airfoil erosion
    Deshun LI, Zhenxi ZHAO, Yinran LI, Qing WANG, Rennian LI, Ye LI
    2018, 39(5):  639-652.  doi:10.1007/s10483-018-2267-6
    Abstract ( 552 )   HTML   PDF (8630KB) ( 135 )  
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    Under natural conditions, wind turbines are inevitably eroded by the action of sand-wind flow. To further investigate the effects of dust drift on the erosion of the wind turbine blades in sand-wind environments, the effects of the wind velocity, particle diameter, and particle density on the erosion of wind turbine airfoils are studied, and the effects of the particle Stokes number on the airfoil erosion are discussed. The results show that, when the angle of attack (AOA) is 6.1°, there will be no erosion on the airfoil surface if the particle Stokes number is lower than 0.013 5, whereas erosion will occur if the particle Stokes number is higher than 0.015 1. Therefore, there exists a critical range for the particle Stokes number. When the particle Stokes number is higher than the maximum value in the critical range, airfoil erosion will occur. The result is further confirmed by changing the particle diameter, particle density, and inflow speed. It is shown that the erosion area on the airfoil and the maximum erosion rate are almost equal under the same particle Stokes number and AOA. The extent of airfoil erosion increases when the particle Stokes number increases, and the critical particle Stokes number increases when the AOA increases. Moreover, the geometric shape of the airfoil pressure surface greatly affects the airfoil erosion, especially at the curvature near the leading edge.

    Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer
    K. R. RAGHUNATHA, I. S. SHIVAKUMARA, SOWBHAGYA
    2018, 39(5):  653-666.  doi:10.1007/s10483-018-2329-6
    Abstract ( 766 )   HTML   PDF (1389KB) ( 137 )  
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    The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

    Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials
    M. PERALTA, O. BAUTISTA, F. MÉNDEZ, E. BAUTISTA
    2018, 39(5):  667-684.  doi:10.1007/s10483-018-2328-6
    Abstract ( 644 )   HTML   PDF (1291KB) ( 77 )  
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    The pulsatile electroosmotic flow (PEOF) of a Maxwell fluid in a parallel flat plate microchannel with asymmetric wall zeta potentials is theoretically analyzed. By combining the linear Maxwell viscoelastic model, the Cauchy equation, and the electric field solution obtained from the linearized Poisson-Boltzmann equation, a hyperbolic partial differential equation is obtained to derive the flow field. The PEOF is controlled by the angular Reynolds number, the ratio of the zeta potentials of the microchannel walls, the electrokinetic parameter, and the elasticity number. The main results obtained from this analysis show strong oscillations in the velocity profiles when the values of the elasticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.

    One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis
    Peng LI, Feng JIN, Jianxun MA
    2018, 39(5):  685-702.  doi:10.1007/s10483-018-2325-6
    Abstract ( 683 )   HTML   PDF (802KB) ( 136 )  
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    Within the framework of continuum mechanics, the double power series expansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degenerated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic behaviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.

    Improved quadratic isogeometric element simulation of one-dimensional elastic wave propagation with central difference method
    Weibin WEN, Shibin LUO, Shengyu DUAN, Jun LIANG, Daining FANG
    2018, 39(5):  703-716.  doi:10.1007/s10483-018-2330-6
    Abstract ( 601 )   HTML   PDF (724KB) ( 104 )  
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    Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation problems. In the proposed procedures, the lumped matrices corresponding to the isogeometric elements are obtained. The stability conditions of the solution procedures are also acquired. The dispersion analysis is conducted to obtain the optimal Courant-FriedrichsLewy (CFL) number or time-step sizes corresponding to the spatial isogeometric elements. The dispersion analysis shows that the isogeometric quadratic element of the fourth-order dispersion error (called the isogeometric analysis (IGA)-f quadratic element) provides far more desirable numerical dissipation/dispersion than the element of the second-order dispersion error (called the IGA-s quadratic element) when appropriate time-step sizes are selected. The numerical simulations of one-dimensional (1D) transient wave propagation problems demonstrate the effectiveness of the proposed solution procedures.

    Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams
    Bo WANG
    2018, 39(5):  717-732.  doi:10.1007/s10483-018-2322-6
    Abstract ( 688 )   HTML   PDF (685KB) ( 118 )  
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    The dynamic stability of axially moving viscoelastic Rayleigh beams is presented. The governing equation and simple support boundary condition are derived with the extended Hamilton's principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscosity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.

    Quasi-momentum theorem in Riemann-Cartan space
    Yong WANG, Chang LIU, Jing XIAO, Fengxiang MEI
    2018, 39(5):  733-746.  doi:10.1007/s10483-018-2323-6
    Abstract ( 422 )   HTML   PDF (159KB) ( 101 )  
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    The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the nonholonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the RiemannCartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system, the differential equations of motion in its Riemann-Cartan configuration space may be simpler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained problems, which are difficult to be solved by the traditional analytical mechanics method. Three examples are given to illustrate the effectiveness of the method.

    Theoretical analyses on bed topography responses in large depth-to-width ratio river bends with constant curvatures
    Shuxian GAO, Haijue XU, Yuchuan BAI
    2018, 39(5):  747-766.  doi:10.1007/s10483-018-2324-6
    Abstract ( 491 )   HTML   PDF (4055KB) ( 75 )  
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    Bed morphology is the result of a dynamic response to a complex meandering river system. It is an important factor for the further development of river. Based on the meandering river characterized by a large depth-to-width ratio, a theoretical model is established with the coupling of Navier-Stokes (N-S), sediment transport, and bed deformation equations. The flow characteristics and bed response of river are obtained with the perturbation method. The research results show that, under the effect of twodimensional flow disturbance, the bars and pools present the regular response. For a given sinuousness, the amplitude of the bed response can be used as a criterion to judge the bedform stability. The effects of the Reynolds number, disturbance wavenumber, sinuousness, and bed morphology gradient on the bed response development are described.

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