防波板对罐车模型内液体晃荡影响的试验研究

罐车属于典型的移动式压力容器,在危险化学品运输中占有重要的地位。研究防波板对罐车液体晃荡产生冲击载荷的影响对于罐车的设计、防翻滚等具有重要意义。本文针对典型罐车模型进行试验,研究了载液高度、激励频率、激励幅值对液体晃荡引起的冲击载荷的影响,对比分析了有无防波板时自由液面的形状、罐车端面和防波板位置的冲击载荷峰值。试验结果发现：防波板会改变自由液面的固有频率,自由液面剧烈晃动的激励频率较无防波板时增大;防波板能有效降低相同激励频率和激励幅值下的冲击载荷峰值。在试验的激励频率范围内,中等载液高度时,防波板自由液面处的冲击载荷峰值大于同高度的罐车端面;高载液工况下,在自由液面以下的位置,罐车端面受冲击载荷峰值变化比防波板明显。在本研究基础上,通过实际罐车参数和液体晃动数值模拟,可对罐车和防波板的结构设计和优化提供指导。

     

EXPERIMENTAL INVESTIGATION ON LIFT INCREMENT OF A PLASMA CIRCULATION CONTROL AIRFOIL

利用等离子体激励器发展了新型的环量增升技术,并对二维NACA0012翼型绕流实施控制。由于NACA0012翼型为尖后缘构型,环量增升装置由2个非对称型介质阻挡放电等离子体激励器构成。一个等离子体激励器贴附于翼型吸力面靠近后缘处,其诱导的壁面射流沿来流方向指向下游;另一个等离子体激励器贴附于翼型压力面靠近后缘处,其诱导的壁面射流与来流方向相反指向上游。在风洞中通过时间解析二维PIV系统对翼型绕流流场进行了测量,基于翼型弦长的雷诺数Re=20 000。结果表明在等离子体激励器的控制下,翼型压力面靠近后缘处可以形成一个定常回流区,从而起到虚拟气动外形的作用,因此翼型吸力面的流场得到加速,压力面的流场得到减速,使得翼型压力面的吸力以及压力面的压力都得到增加,进而增加了翼型的环量。风洞天平测力实验进一步验证了该环量增升技术的有效性。在整个攻角范围内,施加控制的翼型的升力系数相比没有控制的工况有明显的提高。     

用Level Set方法求解具有自由面的流动问题

为采用Ｌｅｖｅｌ Ｓｅｔ方法来计算有自由的流动问题提出了一种方案,把自由水面视为水和空气的交界面,两种介质用统一的Ｎ－Ｓ方法求解,在自由面两侧分别采用各自的密度和粘性,并在自由面上给以适当的光滑;采用边界元法求解双调和方程来确定距离函数;Ｎ－Ｓ方程用投影法求解,文中给出了二维水池水面振荡和瞬时溃坝问题的算例,可以看出用ＬｅｖｅｌＳｅｔ方法求解有自由面流动问题是有效的。     

楔形体入水时域解的复边界元数值分析

基于速度势理论,利用复数变量边界元法对二维楔形体常速入水冲击的时域解进行了数值研究。以相似解作为数值计算的初始条件,采用时域解射流线性近似处理方法,利用复数变量边界元法进行求解,以减少计算量和数值误差。深入讨论了扩展坐标系求时域解、射流处理、网格划分和网格更新等关键技术。最后数值计算了不同斜升角楔形体入水时的自由液面隆起、射流飞溅和压力分布,经与相似解结果作比较,自由液面隆起轮廓基本吻合,而压力分布更符合实际情况,从而证明了模型及分析方法的正确性。     

Numerical analysis of the interaction of 3D compressible bubble clusters

Based on the bubble dynamic theory and the compressible two-phase flow solver of the open source software Open FOAM, a numerical simulation study is carried out on the interactions of bubble clusters in a closed volume. The bubble dynamics and interactions of a single bubble, two bubbles, and four bubbles are investigated under the working conditions without and with the presence of a free surface. Through a parametric study, the qualitative patterns of the variations of the bubble collapse period,the volume compressibility, the bubble pressure peak value, and the breakdown, fusion,and separation phenomena with the parameters such as the bubble pressure, the radius size, the bubble spacing, and the distance from the free surface are obtained. The main factors affecting the bubble morphology and the dynamic characteristics are summarized from numerous parameter experiments. It is shown that, in the absence of a free surface,the main factors are the relative size of the bubbles, the pressure of the liquid, and the pressure differences among the bubbles, while in the presence of a free surface, the main factor is the pressure of the liquid between the upper surface of the bubble and the free surface.     

Problem of hydrodynamic pressure on suddenly starting vessel

In this paper,Lagrangian method is applied to discuss the problem of the hydrodynamic pressure on a suddenly starting vessel.The free surface profile and the coefficients of the hydrodynamic pressure on the vessel wall are obtained.And it is verified that the singularity of the pressure near the free surface is only logarithmic.     

关于自由面压力脉动与摇板造波的等价性

考虑了一个逆问题，即在浮体运动和自由面压力分布之间是否存在某种等价性？作为这一方向努力的一部分，从二维半无限长水槽摇板造波的特例出发考察了这个问题．基于线性势流理论，导出了自由面压力分布应满足的带复数核的第一类Ｆｒｅｄｈｏｌｍ积分方程，并用正则化方法得到了这类不适定的积分方程的近似正则解．结果表明，自由面压力脉动与摇板造波之间的等价性可以通过解相应的逆问题来解决．     

An asymptotic iteration method for the numerical analysis of near-critical free-surface flows

Satisfying the boundary conditions at the free surface may impose severe difficulties to the computation of turbulent open-channel flows with finite-volume or finite-element methods, in particular, when the flow conditions are nearly critical. It is proposed to apply an iteration procedure that is based on an asymptotic expansion for large Reynolds numbers and Froude numbers close to the critical value 1.The iteration procedure starts by prescribing a first approximation for the free surface as it is obtained from solving an ODE that has been derived previously by means of an asymptotic expansion (Grillhofer and Schneider, 2003). The numerical solution of the full equations of motion then gives a surface pressure distribution that differs from the constant value required by the dynamic boundary condition. To determine a correction to the elevation of the free surface we next solve an ODE that is obtained from the asymptotic analysis of the flow with a prescribed pressure disturbance at the free surface. The full equations of motion are then solved for the corrected surface, and the procedure is repeated until criteria of accuracy for surface elevation and surface pressure, respectively, are satisfied.The method is applied to an undular hydraulic jump as a test case.     

A fully hydrodynamic model for three‐dimensional,free‐surface flows

The hydrostatic pressure assumption has been widely used in studying water movements in rivers, lakes, estuaries, and oceans. While this assumption is valid in many cases and has been successfully used in numerous studies, there are many cases where this assumption is questionable. This paper presents a three‐dimensional, hydrodynamic model for free‐surface flows without using the hydrostatic pressure assumption. The model includes two predictor–corrector steps. In the first predictor–corrector step, the model uses hydrostatic pressure at the previous time step as an initial estimate of the total pressure field at the new time step. Based on the estimated pressure field, an intermediate velocity field is calculated, which is then corrected by adding the non‐hydrostatic component of the pressure to the estimated pressure field. A Poisson equation for non‐hydrostatic pressure is solved before the second intermediate velocity field is calculated. The final velocity field is found after the free surface at the new time step is computed by solving a free‐surface correction equation. The numerical method was validated with several analytical solutions and laboratory experiments. Model results agree reasonably well with analytical solutions and laboratory results. Model simulations suggest that the numerical method presented is suitable for fully hydrodynamic simulations of three‐dimensional, free‐surface flows. Copyright © 2003 John Wiley & Sons, Ltd.     

变深度浅水域中非定常船波

以Green—Naghdi(G—N)方程为基础，采用波动方程／有限元法计算船舶经过变深度浅水域时非定常波浪特性．把运动船舶对水面的扰动作为移动压强直接加在Green-Naghdi方程里，以描述运动船体和水面的相互作用．以Series60 CB＝0．6船为算例，给出自由面坡高，波浪阻力在船舶经过一个水下凸包时变化规律，并与浅水方程的结果进行了比较．计算结果表明，当船舶经过凸包时，波浪阻力先增加，后减少，并逐渐趋于正常．同时发现，当船速小于临界速度时(Fr＝√gh＜1．0)，G—N方程给出的船后尾波比浅水方程的结果明显，波浪阻力也比浅水方程的结果有所提高，频率散射必须考虑．当船速大于临界速度时(Fr＝√gh＞1．0)，G—N方程的计算结果与浅水方程差别不大，频率散射的影响可以忽略．     

An implicit two‐dimensional non‐hydrostatic model for free‐surface flows

An implicit finite volume model in sigma coordinate system is developed to simulate two‐dimensional (2D) vertical free surface flows, deploying a non‐hydrostatic pressure distribution. The algorithm is based on a projection method which solves the complete 2D Navier–Stokes equations in two steps. First the pressure term in the momentum equations is excluded and the resultant advection–diffusion equations are solved. In the second step the continuity and the momentum equation with only the pressure terms are solved to give a block tri‐diagonal system of equation with pressure as the unknown. This system can be solved by a direct matrix solver without iteration. A new implicit treatment of non‐hydrostatic pressure, similar to the lower layers is applied to the top layer which makes the model free of any hydrostatic pressure assumption all through the water column. This treatment enables the model to evaluate both free surface elevation and wave celerity more accurately. A series of numerical tests including free‐surface flows with significant vertical accelerations and nonlinear behaviour in shoaling zone are performed. Comparison between numerical results, analytical solutions and experimental data demonstrates a satisfactory performance. Copyright © 2006 John Wiley & Sons, Ltd.     

低重环境下俯仰运动圆柱贮箱中液体非线性晃动

在低重力环境下,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数,并将速度势函数在自由液面处作波高函数的级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;最后用四阶Runge-Kutta法求解非线性方程组。计算结果表明,随俯仰激励频率的逐渐变化,由于面外主模态和次生模态同时失稳,致使整个系统各阶模态和波高函数由稳态运动过渡为不稳定运动。     

Finite element study of free surface turbulent flow in rotating channels

Under certain conditions of liquid flow through rotating channels, the Coriolis force can induce a free surface to be formed. This problem is of practical importance in a Coriolis wear tester, which is used for determining the sliding wear coefficient of wear materials in slurry handling equipment. A deforming Galerkin finite element method is presented for predicting two‐dimensional turbulent free surface mean flow in rotating channels. Reynolds‐averaged Navier–Stokes (RANS) equations are cast into weak(algebraic) form using primitive variables (velocity and pressure). Eddy viscosity is determined via a mixing length model. Velocity is interpolated biquadratically, while pressure is interpolated bilinearly. The kinematic condition is used to form the Galerkin residual for the free surface. The free surface is represented by Hermite polynomials of zeroeth order for continuity of position and slope. Combined Newton's iteration is used to simultaneously solve for the free surface and the field variables. Results of velocity and pressure fields, as well as the free surface are shown to converge with mesh‐size refinement. There is excellent respect for mass conservation. Results are presented for various values of Rossby number (Ro) and height‐based Reynolds number (Re_H). Parameter continuation in Ro and Re_H space is used to compute solutions at higher values of flow rate and angular velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

非线性流固耦合问题的ALE分步有限元数值方法

推导了一种基于ALE（Arbitrary Lagrangian-Eulerian,即任意的拉格朗日-欧拉）描述下的带有自由液面不可压液体与运动结构非线性耦合问题的一种有限元数值计算方法,在时间域上采用分步格式计算,这种方法与混合插值方法比较其优点是速度和压力可使用同阶线性插值,给数值计算带来很大方便,将所得到的方法应用到结构与TLD（调谐式（液体阻尼器）装置之间的耦合问题,数值计算结果验证了本文所推导的方法。     

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4 π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demonstrated in our calculation results.     

实践十号卫星项目——热毛细对流振荡特征的地面研究

上部开口环形液池在水平径向温度梯度作用下会出现内部温度和自由面的振荡,本文研究了二者发生的临界条件.环形液池内柱加热外壁制冷,以0.5℃/min的速率线性升温得到水平径向温差,T型热电偶测量液层内部单点温度,高精度激光位移传感器测量液层自由面某点形变.随两端温差增加,当超过某一临界温度ΔTct时,开始出现振荡.实验结果表明,对同一种硅油,两种振荡的临界条件随液层厚度具有相同的变化趋势.对不同普朗特(Prandtl)数(Pr)的硅油,振荡临界条件临界马兰哥尼数(Macr)随着邦德数(Bo)的增加而变大.本文工作是中国科学院科学先导专项SJ-10返回式科学实验卫星项目-热毛细对流表面波空间实验研究的地面研究结果,该工作为空间实验提供前期的基础科学研究数据和实验保障.     

Vibrations of an ice sheet with crack under a time-periodic load

The analytic solution of the problem of vibrations of an ice sheet with a rectilinear crack floating on the surface of an ideal incompressible fluid of shallow depth under the action of a local zone of the time-periodic pressure is obtained. The ice sheet is simulated by two thin viscoelastic semiinfinite plates of different thickness. Various conditions on the crack edges are considered. Far field asymptotics are investigated and it is revealed that the predominant directions of wave propagation at an angle to the crack can be distinguished in the far field in the case of contact of two plates of different thickness. In the case of contact of identical plates, a waveguide mode propagating along the crack is excited. It is shown that the waveguide mode is the same for the plates with the free edges and the free overlap since the part of the solution symmetric about the crack is the same while the difference between the solutions is caused by the antisymmetric part of the solution.     

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids.     

混凝土高压状态方程实验与数值模拟研究

为研究高压下混凝土冲击压缩特性以及确定HJC本构模型状态方程参数,采用$\varnothing $58 mm火炮加载技术和多普勒探针系统（Doppler probe system,DPS）测速技术,对抗压强度为26.5 MPa（C25）和42.1 MPa（C40）的混凝土进行反向平板撞击实验研究与数值模拟。DPS探针记录TU1无氧铜靶自由面粒子速度历史,根据一维应变弹塑性波理论,计算撞击压力,拟合得到2～11 GPa高压条件下混凝土波速与粒子速度（u_s-u_p）、压力与体积应变（p-μ）关系。实验结果表明：高压条件下,混凝土波速-粒子速度呈线性关系;两种初始密度、孔隙率相近,强度不同的混凝土波速-粒子速度、压力-体积应变关系存在明显差异,相同压力下,混凝土试件强度越高,体积应变越小。基于实验结果,确定了两种强度混凝土HJC本构模型状态方程参数,利用LS-DYNA动力有限元分析软件对平板撞击实验进行了数值模拟,靶板自由面粒子速度历史与实验曲线吻合较好,仿真结果表明混凝土中冲击波的追赶卸载现象仅存在于低速撞击条件下。