部分滑移边界条件下自由液面流动问题研究

数值方法进行相关问题的研究就以圆柱形储液罐为例, 考虑部分滑移边界条件, 对所得的高 度非线性微分方程进行了数值求解, 讨论了贮液腔体内液面接触线和液体高度线, 及部分滑 移条件对流体层微观半径的影响; 所得结论对自由液面晃动问题数值研究中的边界条件处理 有参考意义.     

Surface shapes of fluids in rotating vessels

The shape of the phase boundary of two fluids in systems with a rotational symmetry, and particularly the level of the liquid in a rotating vessel, is studied. The knowledge of the shape of the surface of such a liquid is necessary for centrifugal moulding of optical surfaces. The dimensionless surface equations are formulated, and the solutions of these equations, taking into account the boundary conditions, are discussed.     

液体调谐减振器的分析

本文利用Ｌａｍｂ变换，考虑液体的粘性，略去二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程中的非线性预后，建立了频域内Ｎａｖｉｅｒ－Ｓｔｏｋｒｅｓ方程的边界积分表达式，完整地处理了边界条件（包括自由面边界条件和固壁边界条件）并且给出了液体随结构振动时的附加质量与阻尼的计算表达式。     

Convective structures in a thin layer of an evaporating liquid under an airflow

Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 3–14, July–August, 2007.     

Vapor–Liquid Jump Conditions within a Porous Medium: Results for Mass and Energy

In this paper, we develop the mass and energy jump conditions for a vapor–liquid boundary within a porous medium. The analysis is restricted to a single fluid component and leads to the appropriate jump conditions for an evaporation front. The condition of local thermal equilibrium is assumed to exist in the homogeneous liquid and vapor regions, but not in the boundary region where rapid changes in the saturation occur.     

Refinement of boundary conditions for nematic liquid crystals in the one-constant approximation

The boundary conditions are studied for nematic liquid crystals in the case of weak anchoring. The cases of the general expression and one-constant approximation are considered for the Frank energy of elastic distortions of the director field. It is shown that the one-constant approximation is correct for one-dimensional problems only and, for two- and three-dimensional problems, this model significantly simplifies the boundary conditions and changes their type.     

Linear Stability Analysis of a Viscous Liquid Sheet in a High-Speed Viscous Gas

Air-assisted atomizers in which a thin liquid sheet is deformed under the action of a high-speed air flow are extensively used in industrial applications, e.g., in aircraft turbojet injectors. Primary atomization in these devices is a consequence of the onset and growth of instabilities on the air/liquid interfaces. To better understand this process, a temporal linear instability analysis is applied to a thin planar liquid sheet flowing between two semi-infinite streams of a high-speed viscous gas. This study includes the full viscous effects both in the liquid and gas basic states and perturbations. The relevant dimensionless groups entering the non-dimensional Orr–Sommerfeld equations and boundary conditions are the liquid and gas stream Reynolds numbers, the gas to liquid momentum flux ratio, the gas/liquid velocity ratio, the Weber number and the equivalent gas boundary layer to liquid sheet thickness ratio. Growth rates and temporal frequencies as a function of the wave number, varying the different dimensionless parameters are presented, together with neutral stability curves. From the results of this parametric study it is concluded that when the physical properties of gas and liquid are fixed, the momentum flux ratio is especially relevant to determine the instability conditions. It is also observed that the gas boundary layer thickness strongly influences the wave propagation, and acts by damping sheet oscillation frequency and growth. This is especially important because viscosity in the basic gas velocity profile has always been ignored in instability analysis applied to the geometry under study. This revised version was published online in July 2006 with corrections to the Cover Date.     

The stability of the motion of a liquid,due to thermocapillary forces

A study is made of the stability of the plane-parallel flow of a viscous liquid in a layer with a free boundary, under weightless conditions. The motion of the liquid is due to the dependence of the surface tension on the temperature. An exact solution for an unperturbed boundary is obtained by the same method used in [1], but with a more general boundary condition for the temperature. A study of the stability was carried out by the method of small vibrations, taking account of the perturbation of the free boundary. The article discusses the asymptotic behavior of long waves at small Reynolds numbers, and the conditions for instability are found.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 94–98, November–December, 1971.     

Simulation of liquid sloshing in curved‐wall containers with arbitrary Lagrangian–Eulerian method

There are many challenges in the numerical simulation of liquid sloshing in horizontal cylinders and spherical containers using the finite element method of arbitrary Lagrangian–Eulerian (ALE) formulation: tracking the motion of the free surface with the contact points, defining the mesh velocity on the curved wall boundary and updating the computational mesh. In order to keep the contact points slipping along the curved side wall, the shape vector in each time advancement is defined to modify the kinematical boundary conditions on the free surface. A special function is introduced to automatically smooth the nodal velocities on the curved wall boundary based on the liquid nodal velocities. The elliptic partial differential equation with Dirichlet boundary conditions can directly rezone the inner nodal velocities in more than a single freedom. The incremental fractional step method is introduced to solve the finite element liquid equations. The numerical results that stemmed from the algorithm show good agreement with experimental phenomena, which demonstrates that the ALE method provides an efficient computing scheme in moving curved wall boundaries. This method can be extended to 3D cases by improving the technique to compute the shape vector. Copyright © 2007 John Wiley & Sons, Ltd.     

Vibration effect on convection onset in a system consisting of a horizontal pure liquid layer and a layer of liquid-saturated porous medium

The onset of convection in a system of two horizontal layers (a pure liquid and a porous medium saturated with the same liquid) heated from below under the action of vertical vibration is investigated. For describing the free thermal convection, in the liquid layer the Boussinesq approximation and in the porous layer the Darcy-Boussinesq approximation are used. In the limiting case of a thin liquid layer, effective boundary conditions on the upper boundary of the porous layer with account for convection in the liquid layer are obtained and it is shown that vibration has a stabilizing effect, whereas the presence of a liquid layer leads to destabilization. For an arbitrary liquid to porous layer thickness ratio the onset of convection is investigated numerically. In the case of a thin liquid layer there are two (short-and long-wave) unstable modes. In the case of thick layers the neutral curves are unimodal. Vibration has a stabilizing effect on perturbations with any wave number but affects short-wave perturbations much more strongly than long-wave ones.