Damping Behavior of the Free Liquid Interface Oscillation upon Step Reduction in Gravity

Experiments were carried out to investigate the damping behavior of the reorientation of a free liquid interface in a right circular cylinder, partly filled with a liquid and suddenly exposed to a step reduction in gravity. The damping behavior basically depends on the Ohnesorge number and the static contact angle. This study shows the strong influence of the contact point for low static contact angles.     

Reorientation of Cryogenic Fluids Upon Step Reduction of Gravity

Experiments to observe the surface oscillation of cryogenic liquids have been performed with liquid nitrogen inside a 50 mm diameter right circular cylinder. The surface oscillation is driven by the capillary force that becomes dominant after a sudden reduction of the gravity acceleration acting on the liquid. The experiments show differences from the speculated behavior and enables one to observe new features. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Applicable Boundary Condition at the Moving Contact Line in Case of a Free Surface Reorientation after Step Reduction in Gravity

In this study the sudden change in the acceleration level on a free surface in a right circular cylinder is investigated numerically. The intention to describe the .uid motion encounters the difficulty modelling the moving contact‐line problem. In the numerical simulations the Navier slip boundary condition and a model for the dynamic contact angle are used. The model for the dynamic contact angle γ_d includes the dependence on the Capillary number as well as the contact angle hysteresis. We achieved very good agreement with experimental data.     

Capillary driven Oscillations of a Free Liquid Interface under Non‐Isothermal Conditions

In this study the reorientation behavior of a free liquid interface in a partly filled right circular cylinder upon a step reduction in gravity is investigated experimentally. The experiments focus on the investigation of non‐isothermal boundary conditions on the liquid reorientation. The situation is similar to a spacecraft which enters a ballistic flight after the end of thrust. Heat flux between the liquid propellant and the tank wall occurs and influences the behavior of the liquid reorientation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Experimental/Numerical Investigation on Drag Reduction by Dimples

The paper is concerned with experimental and numerical investigations of the turbulent flow over dimpled surfaces. Shallow dimples distributed regularly over the wall of a plane channel with large aspect ratio are used to study their effect on the skin-friction drag. The resulting pressure drop in the channel was measured for smooth and dimpled walls. In addition to these investigations on internal flows, an external flow study was performed and boundary-layer profiles were measured using a Pitot-tube rake. Complementary to the measurements, direct numerical simulations for the internal flow configuration with and without dimples were carried out for two different grid resolutions and analyzed in detail. The objective was to clarify whether or not dimples cause reduction of the skin-friction drag. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singularities of Steady Axisymmetric Free Surface Flows with Gravity

We consider a steady axisymmetric solution of the Euler equations describing the irrotational flow without swirl of an incompressible inviscid fluid acted on by gravity and with a free surface. We analyze stagnation points as well as points on the axis of symmetry. At points on the axis of symmetry that are not stagnation points, constant velocity motion is the only blowup profile consistent with the invariant scaling of the equation. This suggests the presence of downward‐pointing cusps at those points. At stagnation points on the axis of symmetry, the unique blowup profile consistent with the invariant scaling of the equation is the Garabedian pointed bubble solution with water above air. Thus at stagnation points on the axis of symmetry with no water above the stagnation point, the invariant scaling of the equation cannot be the right scaling. A finer blowup analysis of the velocity field yields that in the case when the surface is described by an injective curve, the velocity field scales almost like and is asymptotically given by with a nonzero constant c₀. The last result relies on a frequency formula in combination with a concentration compactness result for the axially symmetric Euler equations by Delort. While the concentration compactness result alone does not lead to strong convergence in general, we prove the convergence to be strong in our application. © 2014 Wiley Periodicals, Inc.     

冲击波作用下Air/SF6斜界面不稳定性实验和数值模拟研究

开展了Mach数为1.23和1.41的冲击波作用下的Air/SF6斜界面不稳定性激波管实验,并利用王涛等人发展的可压缩多介质粘性流体和湍流大涡模拟程序MVFT(multi-viscous-fluid and turbulence),对该激波管实验进行了数值模拟,二者相比较一致性较好,包括界面图像、湍流混合区TMZ(turbulent mixing zone)宽度、气泡和尖钉位移,确认了该计算代码对界面不稳定性问题模拟的可靠性和有效性.数值模拟再现了冲击波作用下,Air/SF6斜界面的演化过程及流动中复杂波系结构的发展如冲击波的传播、折射和反射.结果还显示冲击波Mach数较大时,冲击波和界面相互作用时混合区获得的能量也较大,扰动界面发展的也更快.     

On the Singular Set of Free Interface in an Optimal Partition Problem

We study the singular set of free interface in an optimal partition problem for the Dirichlet eigenvalues. We prove that its upper (n − 2) -dimensional Minkowski content, and consequently its (n − 2) -dimensional Hausdorff measure, are locally finite. We also show that the singular set is countably (n − 2) -rectifiable; namely, it can be covered by countably many C¹ -manifolds of dimension (n − 2) , up to a set of (n − 2) -dimensional Hausdorff measure zero. Our results hold for optimal partitions on Riemannian manifolds and harmonic maps into homogeneous trees as well. © 2019 Wiley Periodicals, Inc.     

阶梯折算法的收敛条件及其一般格式

叶开沅教授创造了阶梯折算法[1].利用这个方法求解非均匀弹性力学问题,所得到的解可以用解析式表达,并具有计算量小、精度高的优点.本文通过数学上的推导,给出了阶梯折算法的收敛条件,并证明了当收敛条件满足时,所得到的解可一致收敛于精确解.文中还给出了阶梯折算法的一般格式及误差估计.由于采用矩阵形式表达,避免了以往冗长的数学表达式,使得解的形式非常简洁.文末给出算例,算例表明运用本文的理论,可以得到阶梯折算法的正确模式.     

A Regularity Result for the Incompressible Euler Equation with a Free Interface

We address the local existence of solutions of the 2D and 3D water wave problems. For the space dimension three, we consider the irrotational datum u ₀ and prove that the local in time existence holds for initial velocities belonging to H ^2.5+δ , where δ>0 is arbitrary. For the space dimension two, the data does not need to be irrotational. We prove the local in time existence when u ₀ belongs to H ^2+δ and $\operatorname{curl}u_{0}$ to H ^1.5+δ , where δ>0 is arbitrary.     

二流体系统中自由面及界面上的二阶椭圆余弦波*

本文考虑[1]中所建立的模式,采用约化摄动法及PLK方法,求得了自由面及界面上的二阶椭圆余弦波。在退化情况下与文[3]和[4]的结果符合。     

Some Properties of Free Boundary for Solution of Porous Medium Equation with Gravity Term in One-dimension

Consider the degenerate parabolic equation (porous medium equation with gravity term): u_t = (u^m)_{xx} + (u^n)_x, -∞ < x < ∞, t > 0, m > 1 u(x, 0) = u_0(x), -∞ < x < ∞ The main results consist of the estimation of t^∗_i called waiting time, the behavior of pressure V = \frac{m}{m-1}u^{m-1} near a vertical or a nonvertical part of ς_i(t) and a condition of that ς_i(t) is continuously differentiable.     

Free Cavitational Deceleration of a Circular Cylinder in a Liquid after Impact

The problem is considered about the vertical continuous impact and subsequent free deceleration of a circular cylinder semi-immersed in a liquid. The specificity of this problem is that, under certain conditions, some areas of low pressure near the body appear and the attached cavities are formed. The separation zones and the motion law of the cylinder are unknown in advance and have to be determined in solving the problem. The study of the problem is conducted by a direct asymptotic method effective for small spans of time. Some nonlinear problem with unilateral constraints is formulated that is solved together with the equation defining the law of motion of the cylinder. In the case when the space above the external free surface of a liquid is filled with a gas with low pressure (vacuum), an analytical solution of the problem is constructed. To determine the main hydrodynamic characteristics (the separation point and acceleration of the cylinder), we derive a system of transcendental equations with elementary functions. The solution of this system agrees well with the results obtained by the direct numerical method.     

Free Oscillations of a Two-Layer Liquid in a Rotating Basin of Variable Depth

The problem of free oscillations of a two-layer liquid in a rotating basin of variable depth is formulated and solved. The results are used to model the natural motions of large bodies of water, specifically in the example of the Black Sea.     

Investigation upon the performance of piezoelectric energy harvester with elastic extensions

Piezoelectric vibration energy harvesters have attracted much attention due to its potential to replace currently popular batteries and to provide an sustainable power sources. Many researchers have proposed ways to increase the performance of piezoelectric energy harvesters like bandwidth, working frequency and output performance. Here in this contribution, we propose the method of using elastic extensions to tune the performance of a piezoelectric energy harvester. Mathematical model of the proposed device is derived and analyzed. Numerical simulations are done to investigate the influences of the derived parameters, like length ratio λ_l, bending stiffness ratio λ_B, and line density ratio λ_m. Results show that the elastic extension does change the motion of the proposed device and help tune the performance of piezoelectric energy harvesters.     

Numerical Investigation of Particulate Flow over a Backward‐Facing Step

Flow separation and recirculation caused by a sudden expansion in the channel geometry in the form of a backwardfacing step (BFS) appear in numerous practical applications. Additionally, BFS flow has been used as a generic test case to study fundamental flow properties, such as separation or re‐attachment. In the present work, BFS flow laden with dispersed particles is investigated by numerical simulations using a spectral element method [1]. The motion of the dispersed particles is computed by Lagrangian particle tracking. In a first step, only the influence of the flow on the particles is accounted for, while possible effects of the particle motion on the flow are neglected. Spatial distribution of the particles is investigated, and effects of different wall‐particle interaction models on the computational results are examined.     

计及表面波的圆环形贮液容器的弯曲自由振动*

本文研究考虑表面波作用的圆环形贮液容器的弯曲自由振动问题,导出了贮液容器与液体耦联振动的振型函数和固有频率的精确计算公式,结果可借助于计算机求解.分析表明,水对容器的振动效应可等效于在内外环体上分别附着一不同的广义分布质量.     

炉液倾动重心近似计算的数学分析

为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考.