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1.
Based on the Eulerian spatial averaging theory and the Müller–Liu entropy principle, a two-fluid model for reactive dilute solid–liquid mixtures is presented. Initially, some averaging theorems and properties of average quantities are discussed and, then, averaged balance equations including interfacial source terms are postulated. Moreover, constitutive equations are proposed for a reactive dilute solid–liquid mixture, where the formation of the solid phase is due to a precipitation chemical reaction that involves ions dissolved in the liquid phase. To this end, principles of constitutive theory are used to propose linearized constitutive equations that account for diffusion, heat conduction, viscous and drag effects, and interfacial deformations. A particularity of the model is that the mass interfacial source term is regarded as an independent constitutive variable. The obtained results show that the inclusion of the mass interfacial source term into the set of independent constitutive variables permits to easily describe the phase changes associated with precipitation chemical reactions.  相似文献   

2.
A mathematical model is developed for saturated flow of a Newtonian fluid in a thermoelastic, homogeneous, isotropic porous medium domain under nonisothermal conditions. The model contains mass, momentum and energy balance equations. Both the momentum and energy balance equations have been developed to include a Forchheimer term which represents the interaction at the solid-fluid interface at high Reynolds numbers. The evolution of these equations, following an abrupt change in both fluid pressure and temperature, is presented. Using a dimensional analysis, four evolution periods are distinguished. At the very first instant, pressure, effective stress, and matrix temperature are found to be disturbed with no attenuation. During this stage, the temporal rate of pressure change is linearly proportional to that of the fluid temperature. In the second time period, nonlinear waves are formed in terms of solid deformation, fluid density, and velocities of phases. The equation describing heat transfer becomes parabolic. During the third evolution stage, the inertial and the dissipative terms are of equal order of magnitude. However, during the fourth time period, the fluid's inertial terms subside, reducing the fluid's momentum balance equation to the form of Darcy's law. During this period, we note that the body and surface forces on the solid phase are balanced, while mechanical work and heat conduction of the phases are reduced.  相似文献   

3.
Introduction1 999isthe 90thanniversaryofthepublicationofE .F .Cosserat’sbook“TheoriedesCorpsDeformable”[1],whichwasthefoundationstoneandnowisstillaguidingmonographinthestudyofgeneralizedcontinuumfieldtheories.However,itwasnottillthepublicationofpapersofEricks…  相似文献   

4.
In this paper, we propose a quasi-3D continuum model to study the rate-independent hysteresis phenomenon in phase transitions of a slender shape memory alloy (SMA) cylinder subject to the uniaxial tension. Based on the three-dimensional field equations and the traction-free boundary conditions, by using a coupled series-asymptotic expansion method, we manage to express the total elastic potential energy of the cylinder in terms of the leading order term of the axial strain. We further consider the rate-independent dissipation effect in a purely one-dimensional setting. The mechanical dissipation functions are also expressed in terms of the axial strain. The equilibrium configuration of the cylinder is then determined by using the principle of maximizing the total energy dissipation. An illustrative example with some special chosen material constants is further considered. Free end boundary conditions are proposed at the two ends of the cylinder. By conducting a phase plane analysis and through some calculations, we obtain the analytical solutions of the equilibrium equation. We find that the engineering stress–strain curves corresponding to the obtained solutions can capture some important features of the experimental results. It appears that the analytical results obtained in this paper reveal the multiple solutions nature of the problem and shed certain light on the instability phenomena during the phase transition process.  相似文献   

5.
可侵蚀地表上方含尘大气运动的数值模型   总被引:2,自引:0,他引:2  
王柏懿  陈强  戚隆溪 《力学学报》2004,36(3):265-271
在稀相气固两相流的双流体模型框架下,导出含尘大气运动的基本方程,其中的源项考虑相间双向耦合作用;通过对基本方程进行无量纲化,求得控制气相和弥散相动力学行为的相似准则,包括弗洛德数、罗斯贝数、颗粒雷诺数、颗粒惯性参数、颗粒剪切横移参数、颗粒旋转横移参数和沙尘质量载荷率等. 作为一个模型问题,研究可侵蚀地表上方充分发展湍流大气边界层流动对土壤颗粒的气动卷扬作用,其中计及气动阻力、萨弗曼升力和重力等因素的影响. 为了克服由于沙尘跃移运动轨迹交叉导致流动参数多值性所造成的困难,引进拉格朗日坐标下弥散相连续方程. 对两种不同风速和4种不同粒径条件下的沙尘运动进行数值模拟,给出相应情况中沙尘运动特性和密度分布剖面并讨论风速和粒径等参数的影响,还细致分析了含尘大气边界层中沙尘与气流之间的能量传递过程. 所得的方程、准则和方法可以为土壤风蚀和沙尘暴等自然灾害的预报提供理论基础.  相似文献   

6.
The balance equations of mass, momentum, energy and entropy at a phase boundary imply phase boundary conditions which determine the position of the boundary as a function of temperature. This is true when either the phase boundary is sharp or when it occurs through a transition zone, albeit the latter case seems to require strongly symmetric geometry.  相似文献   

7.
This paper deals with the numerical treatment of Eulerian approach for dilute two-phase compressible flows (gas-particles mixtures) in axisymmetric configurations. For dilute flows, two classes of models depending on the dispersed phase volumetric fraction can be found. The volume occupied by the particles may be considered, that yields a model in which the gas phase and the dispersed phase equations are coupled through the void fraction and the source terms (Delhaye model). The void fraction effects can be neglected, that means the gas phase is a carrier phase for the particles (Ishii model). The mathematical nature of the two models is demonstrated from analysis of characteristic directions. For the Delhaye's model, a centered scheme is used to solve the system of partial differential equations, while an upwind TVD scheme is used for the Ishii's one. Then, it is shown that the problem of symmetry boundary conditions does not depend on the physical approach, as long as the flow remains dilute. However, a classical treatment for symmetry boundary conditions at the geometrical axis leads to large errors. A particular treatment for this boundary is presented: a new class of particles, described by a supplementary system of equations, is required.  相似文献   

8.
In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain. It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in dealing with transport phenomena in deformable porous media.  相似文献   

9.
将精细积分边界元法和界面追踪法相结合求解相变问题。因为边界元法只需要将待求解空间域的边界离散,方便连续追踪移动界面位置和重构网格,所以边界元法适合应用于移动边界问题的模拟。首先,利用精细积分边界元法在固相区域和液相区域分别求解相应的瞬态热传导控制方程,从而求得温度场和边界热流密度。然后,根据固-液相变界面上的能量平衡方程,利用热流密度求得相变界面的移动速度,再采用界面追踪法预测移动相变界面的位置变化。最后,给出了几个数值算例,并通过与参考解的对比验证本文方法的准确性。  相似文献   

10.
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