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2013年 第34卷 第6期    刊出日期：2013-06-03

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Structure and stability of non-adiabatic reverse smolder waves

袁枋平 卢占斌

2013, 34(6):  657-668.  doi:10.1007/s10483-013-1698-8

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The structure and stability of non-adiabatic reverse smolder waves are investigated numerically. First, the 1D steady-state responses of reverse smolder waves in the presence of convective heat losses are studied with the rate of incoming air flow as the control parameter. Based on the 1D steady solutions, the linear stability and the Lewis number effects on the stability are examined by a numerical normal mode analysis. Finally, the dynamical evolution processes of unstable reverse smolder waves are studied by direct numerical simulations. It is shown that, in comparison with the adiabatic case, the presence of heat losses leads to a backward shift of the extinction limit. For varying Lewis numbers, the extinction limit shifts forward with the increase of the Lewis number while the smolder temperature remains unchanged. Furthermore, results of a linear stability analysis show that the maximum growth rate decreases with the increasing Lewis number, implying that increasing the Lewis number tends to weaken
the thermal-diffusive instability of non-adiabatic reverse smolder waves. Direct numerical simulation results show that, on the fuel-rich branch, the unstable plane reverse smolder wave gradually develops to a regular steady fingering pattern, whereas on the fuel-lean branch, similar to the adiabatic case, vigorous fragmentation instability occurs, and is accompanied by a substantial local temperature rise, which may be sufficiently high to trigger the transition to flaming combustion.

论文

Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux

A. NOGHREHABADI;A. BEHSERESHT;M. GHALAMBAZ

2013, 34(6):  669-686.  doi:10.1007/s10483-013-1699-6

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The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter (Nb), the Buoyancy ratio (Nr), the thermophoresis parameter (Nt), and the Lewis number (Le). The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both
of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.

Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

M. A. HOSSAIN;M. SALEEM;S. C. SAHA;A. NAKAYAMA

2013, 34(6):  687-702.  doi:10.1007/s10483-013-1700-7

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The combined effect of conduction-convection-radiation on natural convection flow of an optically thick Newtonian fluid with gray radiant properties, confined in a porous media square cavity with Darcy-Brinkman-Forchheimer drag is studied numerically. For a gray fluid, Rosseland diffusion approximation is considered. It is assumed that (i) the temperature of the left vertical wall varies linearly with height, (ii) the right vertical
and top walls are at a lower temperature, and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the alternate direct implicit method together with the successive over relaxation technique. The investigation of the effect of governing parameters, namely, the Forschheimer resistance (Γ), the temperature difference (Δ), and the Plank number (Rd), on the flow pattern and heat transfer characteristics is carried out. It can be seen that the reduction of flow and heat transfer occur as the Forschheimer resistance is increased. On the other hand, both the flow strength and heat transfer increase as the temperature ratio Δ is increased.

Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis

I. A. HASSANIEN;H. M. EL-HAWARY;M. A. A. MAHMOUD;R. G. ABDEL-RAHMAN;A. S

2013, 34(6):  703-720.  doi:10.1007/s10483-013-1701-6

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The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic (MHD) micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are determined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spectral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress coefficient, and the Nusselt number are studied.

Vertical two-dimensional non-hydrostatic pressure model with single layer

康玲 郭晓明

2013, 34(6):  721-730.  doi:10.1007/s10483-013-1702-x

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The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pressure assumption. However, they are time-consuming and unstable, which makes them unsuitable for wider application. In this study, an efficient model with a single layer is developed. Decomposing the pressure into the hydrostatic and dynamic components and
integrating the x-momentum equation from the bottom to the free surface can yield a horizontal momentum equation, in which the terms relevant to the dynamic pressure are discretized semi-implicitly. The convective terms in the vertical momentum equation are ignored, and the rest of the equation is approximated with the Keller-box scheme. The velocities expressed as the unknown dynamic pressure are substituted into the continuity
equation, resulting in a tri-diagonal linear system solved by the Thomas algorithm. The validation of solitary and sinusoidal waves indicates that the present model can provide comparable results to the models with multiple layers but at much lower computation cost.

Analytical dynamic model of elastic-plastic pipe-on-pipe impact

闫冬梅 孙玉鑫 杨嘉陵

2013, 34(6):  731-746.  doi:10.1007/s10483-013-1703-9

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The dynamic response of pipe-on-pipe impact is described by an analytical model. The model considers the impact of a whipping pipe with one end hinged and the other end free on a simply-supported target pipe at its midpoint. Combining with the contact theory, the Laplace transformation, and the inverse Laplace transformation method, an analytical model based on the tubular beam theory is proposed to study the elastic-plastic behavior of a target pipe laterally impacted by a whipping pipe. Numerical simulations using the explicit finite element code MSC/DYTRAN are also performed.
The results are coincident with the theoretical prediction.

Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system

胡姝芳 陈传淼

2013, 34(6):  747-760.  doi:10.1007/s10483-013-1704-8

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The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge-Kutta (RK) method is an important part of the former, and the continuous finite element method (CFEM) belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms—the regular method. Finally, numerical
experiments are given to verify the theoretical results.

Frictional contact problem for elastic-viscoplastic materials with thermal effect

M. SELMANI;L. SELMANI

2013, 34(6):  761-776.  doi:10.1007/s10483-013-1705-7

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A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca’s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.

Bifurcation analysis for nonlinear multi-degree-of-freedom rotor system with liquid-film lubricated bearings

于海 陈予恕 曹庆杰

2013, 34(6):  777-790.  doi:10.1007/s10483-013-1706-9

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The oil-film oscillation in a large rotating machinery is a complex highdimensional nonlinear problem. In this paper, a high pressure rotor of an aero engine with a pair of liquid-film lubricated bearings is modeled as a twenty-two-degree-of-freedom nonlinear system by the Lagrange method. This high-dimensional nonlinear system can be reduced to a two-degree-of-freedom system preserving the oil-film oscillation property by introducing the modified proper orthogonal decomposition (POD) method. The efficiency of the method is shown by numerical simulations for both the original and reduced systems. The Chen-Longford (C-L) method is introduced to get the dynamical behaviors of the reduced system that reflect the natural property of the oil-film oscillation.