Analysis of Natural Convection During Solidification of a Pure Metal

A numerical study of solidification of gallium in a closed cavity is presented and the influence of natural convection on phase change is investigated.

The mathematical formulation is based on the enthalpy-porosity method, while the equations are discretized on a fixed grid by means of a finite volume technique. Advancing in time is obtained using the SIMPLE algorithm, while the solution of the elliptic equation for pressure correction is obtained by means of a preconditioned BI-CGStab method.

As a test case a square cavity with Ra ranging from 4.68 × 10³ to 9.36 × 10⁵ is adopted. Results will be presented in terms of streamlines, isotherms, solid-liquid interface position and Nu and compared, when possible with available data.     

Stability of Solutal Convection in a Gravity Modulated Mushy Layer During the Solidification of Binary Alloys

The linear stability theory is used to investigate analytically the effects of gravity modulation on solutal convection in the mushy layer of solidifying binary alloys. The gravitational field consists of a constant part and a sinusoidally varying part, which is synonymous to a vertically oscillating mushy layer subjected to constant gravity. The linear stability results are presented for both the synchronous and subharmonic solutions. It is demonstrated that up to the transition point between the synchronous and subharmonic regions, increasing the frequency of vibration rapidly stabilizes the solutal convection. Beyond the transition point, further increases in the frequency tend to destabilize the solutal convection, but gradually. It is also demonstrated that the effect of increasing the ratio of the Stefan number and the solid composition (₀) is to destabilize the solutal convection.     

The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

The effect of rotation and anisotropy on the onset of double diffusive convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. The effect of rotation, mechanical and thermal anisotropy parameters, and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The finite amplitude analysis is performed to find the thermal and solute Nusselt numbers. The effect of various parameters on heat and mass transfer is also investigated.     

The Effect of Rotation on the Onset of Double Diffusive Convection in a Sparsely Packed Anisotropic Porous Layer

The effect of rotation on the onset of double diffusive convection in a sparsely packed anisotropic porous layer, which is heated and salted from below, is investigated analytically using the linear and nonlinear theories. The Brinkman model that includes the Coriolis term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and a dispersion relation are obtained analytically using linear theory. The effect of anisotropy parameters, Taylor number, Darcy number, solute Rayleigh number, Lewis number, Darcy–Prandtl number, and normalized porosity on the stationary, oscillatory and finite amplitude convection is shown graphically. It is found that contrary to its usual influence on the onset of convection in the absence of rotation, the mechanical anisotropy parameter show contrasting effect on the onset criterion at moderate and high rotation rates. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfers. The effect of various parameters on heat and mass transfer is shown graphically. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study.     

Coriolis Effect on the Linear Stability of Convection in a Porous Layer Placed Far Away from the Axis of Rotation

The linear stability theory is used to investigate analytically the Coriolis effect on centrifugally driven convection in a rotating porous layer. The problem corresponding to a layer placed far away from the axis of rotation was identified as a distinct case and therefore justifying special attention. The stability of the basic centrifugally driven convection is analysed. The marginal stability criterion is established as a characteristic centrifugal Rayleigh number in terms of the wavenumber and the Taylor number.     

Effect of Rotation on Thermal Convection in an Anisotropic Porous Medium with Temperature-dependent Viscosity

A linear stability analysis is performed for mono-diffusive convection in an anisotropic rotating porous medium with temperature-dependent viscosity. The Galerkin variant of the weighted residual technique is used to obtain the eigen value of the problem. The effect of Taylor–Vadasz number and the other parameters of the problem are considered for stationary convection in the absence or presence of rotation. Oscillatory convection seems highly improbable. Some new results on the parameters’ influence on convection in the presence of rotation, for both high and low rotation rates, are presented.     

Effect of Radiation Scattering on the Dynamics of the Transitional Zone During Solidification of a Semitransparent Material

The effect of isotropic scattering in a two-phase zone on the velocity of boundaries, thickness of the transitional zone, and distribution of the solid phase over the two-phase zone thickness in the course of solidification of a semitransparent material is considered. A generalized model of phase transition in a semitransparent medium is used. The results of numerical calculations show that radiation scattering can exert a significant effect on the structure and size of the two-phase zone and also on heat transfer (temperature gradient) in the crystal being formed.     

Steady Natural Convection Flow of a Particulate Suspension Through a Parallel-Plate Channel

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long channel. The walls of the channel are maintained at constant but different temperatures. The two-phase model accounts for particle-phase viscous effects. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Various closed-form solutions for different special cases are obtained. A parametric study of the physical parameters involved in the problem are performed to illustrate the influence of these parameters on the flow and heat transfer aspects of the problem.     

Stefan Number Effect on the Transition from Stationary to Oscillatory Convection in a Solidifying Mushy Layer Subjected to Rotation

The current study investigates the Stefan number effect on the transition from stationary to oscillatory convection in a rotating mushy layer where the near eutectic approximation is applied. It is found that for rotating solidifying systems exhibiting a Stefan number of unit order (i.e., St=1), stationary convection is only possible up to Ta=3. Beyond Ta=3, for St=1, it is found that the oscillatory mode is the most dangerous mode of convection. A map showing the region of occurrence of the oscillatory mode is also presented for a range of Stefan numbers. The map reveals that the oscillatory mode is the most dangerous mode for intermediate values of Stefan number whilst the stationary mode is the most dangerous mode for very small and very large values of Stefan number. It is also demonstrated that increasing the rotation rate serves to render the oscillatory mode as the becoming the most dangerous mode of convection.     

加载速率对6020铝合金材料力学性能影响的实验研究

通过拉伸实验研究了加载速率在1mm/min, 10mm/min, 100mm/min以及200mm/min范围内6020铝合金材料的力学性质,结果表明这种材料有近似于理想弹塑性的性质,应力-应变曲线明显地表现为线弹性和线塑性的特点,而且加载速率对于该铝合金材料的力学性质没有明显的影响.作为对比还测试了45#中碳钢在相同的加载速率条件下的力学特性,得出随着加载速率的增加,无论屈服强度还是抗拉强度均有一定的提高,塑性有了一定的降低.最后,根据实验结果确定了该铝合金材料的本构关系.     

Effect of the Source Term on Steady Free Convection Boundary Layer Flows over an Vertical Plate in a Porous Medium. Part I

The Darcy free convection boundary layer flow over a vertical flat plate is considered in the presence of volumetric heat generation/absorption. In the present first part of the paper it is assumed that the heat generation/absorption takes place in a self-consistent way, the source term q ^′′′≡ S of the energy equation being an analytical function of the local temperature difference T − T _∞. In a forthcoming second part, the case of the externally controlled source terms S = S(x,y ) will be considered. It is shown that due to the presence of S, the physical equivalence of the up- and downflows gets in general broken, in the sense that the free convection flow over the upward projecting hot plate (“upflow”) and over its downward projecting cold counterpart (“downflow”) in general become physically distinct. The consequences of this circumstance are examined for different forms of S. Several analytical solutions are given. Some of them describe algebraically decaying boundary layers which can also be recovered as limiting cases of exponentially decayingones. This asymptotic phenomenon is discussed in some detail.     

Modulated Centrifugal Convection in a Vertical Rotating Porous Layer Distant from the Axis of Rotation

The effect of rotation speed modulation on the onset of centrifugally driven convection has been studied using linear stability analysis. Darcy flow model with zero-gravity is used to describe the flow. The perturbation method is applied to find the correction in the critical Rayleigh number. It is found that by applying modulation of proper frequency to the rotation speed, it is possible to delay or advance the onset of centrifugal convection.     

Solidification and Flow of a Binary Alloy Over a Moving Substrate

We study the solidification and flow of a binary alloy over a horizontally moving substrate. A situation in which the solid, liquid and mushy regions are separated by the stationary two-dimensional interfaces is considered. The self-similar solutions of the governing boundary layer equations are obtained, and their parametric dependence is analysed asymptotically. The effect of the boundary layer flow on the physical characteristics is determined. It is found that the horizontal pulling and the resulting flow in the liquid enhance the formation of the mushy region.     

原位自生TiC对低合金马氏体钢磨料磨损性能的影响

以新型含TiC马氏体钢Ti60和商用不含碳化物马氏体钢JFE400为研究对象,通过三体磨料磨损试验机研究在纯煤粉和纯煤粉掺杂40%(质量分数)石英砂为磨料下,TiC硬质相对低合金马氏体钢磨料磨损性能的影响及其作用机理. 结果表明:在纯煤粉环境下,Ti60钢的磨损体积大于JFE400钢;但在纯煤粉掺杂40%(质量分数)石英砂环境下,Ti60钢的磨损体积却小于JFE400钢. 根据磨痕表面的形貌,上述结果是由以下几方面综合作用造成的. 首先,两种环境下材料的磨损机制均主要是犁削磨损;其次,煤粉颗粒的层状结构及低硬度的特性,使得TiC硬质相对其犁削行为起不到阻碍作用,而块状结构且具有高硬度的石英砂颗粒的犁削行为则受到TiC硬质相的阻碍. 所以在纯煤环境下,基体硬度较大的JFE400钢,相对于基体硬度较小的Ti60钢,呈现出较优的抗磨料磨损的性能. 而在纯煤粉掺杂40%(质量分数)石英砂环境下,Ti60钢的抗磨粒磨损性能却优于JFE400钢.      

润滑条件下铜锌合金表面粗糙度对磨损率的影响

采用基于原位全息显微技术和放射性核素技术的试验装置对润滑条件下的Cu Zn36和100Cr6进行了摩擦磨损试验,分析了Cu Zn36在试验过程中的摩擦磨损特性,以及摩擦系数、磨痕表面粗糙度和实时磨损率之间的关系,进而建立了关于表面粗糙度的磨损模型,并通过拟合优度方法对磨损模型进行了评价.结果表明:在试验磨合的初始阶段,Cu Zn36表面平整性被迅速破坏而产生了较高的磨损率,随着试验的进行,磨痕表面的强化层逐渐形成,表面粗糙度和实时磨损率逐渐降低并趋于稳定.磨损模型的拟合优度R2的计算结果为90.23%,说明建立的磨损模型能够对给定工况下的实时磨损率进行较为准确的预测.     

Effect of Vertical Modulation on the Onset of Filtration Convection

The present paper examines the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal layer of fluid saturating a porous medium. A constant temperature distribution is assigned on the rigid boundaries, so that there exists a vertical temperature gradient. The mathematical model is described by equations of filtration convection in the Darcy–Oberbeck–Boussinesq approximation. The linear stability analysis for the quasi-equilibrium solution is performed using Floquet theory. Employment of the method of continued fractions allows derivation of the dispersion equation for the Floquet exponent σ in an explicit form. The neutral curves of the Rayleigh number Ra versus horizontal wave number α for the synchronous and subharmonic resonant modes are constructed for different values of frequency Ω and amplitude A of vibration. Asymptotic formulas for these curves are derived for large values of Ω using the method of averaging, and, for small values of Ω, using the WKB method. It is shown that, at some finite frequencies of vibration, there exist regions of parametric instability. Investigations carried out in the paper demonstrate that, depending on the governing parameters of the problem, vertical vibration can significantly affect the stability of the system by increasing or decreasing its susceptibility to convection.      

The Effect of Strong Heterogeneity on the Onset of Convection in a Porous Medium

The effect of strong heterogeneity on the onset of convection induced by a vertical density gradient in a saturated porous medium governed by Darcy’s law is discussed. The general case, where there is heterogeneity in both the vertical and horizontal directions, and where there is heterogeneity in permeability, thermal conductivity, and applied temperature gradient, is considered. A computer package has been developed to implement an algorithm giving a criterion for instability. This package is applied to the case of a cube partitioned into octants and to the cases where the permeability and thermal conductivity vary continuously across a cube in either a linear or a quadratic manner.     

The Effect of Pulsating Deformation on the Onset of Convection in a Porous Medium

A linear instability analysis has been performed for the onset of convection in a horizontal layer of a porous medium whose permeability pulsates with time as a result of vertical movement of one of the boundaries. It was found that, to a first-order approximation in the pulsation amplitude, the effect of deformation is destabilizing for disturbances whose period is of the order of the thermal diffusion time scale. The effects of the average porosity, pulsation amplitude, and pulsation frequency were investigated.