Dynamic fluid flow behaviour of a tank draining through a vertical tube

This paper describes the unsteady draining of a sealed tank partially filled with water. The water discharges via a vertical tube into an open tank at atmospheric conditions. The air inflow, compensating for the volume of the discharged liquid, enters the system in an oscillatory manner, much like the “gulping” seen in an upended beer bottle. A mathematical model, based closly on that derived by Dougall & Kathiresan [Chem. Engng Commun. 8, 289–304 (1981)], has been applied to predict the pressure fluctuations in the closed tank. The rate of water discharge from the tank has been predicted and gives a much closer agreement with experimental results than a prediction based on a steady counter-current flooding limitation approach. A drift flux model has been used to describe the two-phase flow effect in the tube and the Wallis flooding criterion has been modified for use in the slug flow regime to describe the boundary conditions at the bottom of the tube. The pressure fluctuations in the sealed tank have been measured and compared with results obtained from the mathematical prediction for a variety of tube diameters.     

Numerical simulation of the flow in a conduit,in the presence of a confined air cushion

A rectangular conduit with a closed end has water flowing in/out at the other end. The water level at the open end has an imposed sinusoidal movement. When this level is higher than the ceiling of the conduit, a certain mass of air is trapped under the ceiling. In a previous article (T.D. Nguyen, La Houille Blanche, No. 2, 1990), it was supposed that this air is flowing out freely through the ceiling, so the relative pressure at the water surface is zero, and the water hammer at the dead end of the conduit was calculated when the conduit was thoroughly filled. In this article, it is supposed that the trapped air is compressed isothermally or adiabatically. The set of equations is resolved (water continuity and movement equations, air state equation) by supposing a regime of flow at each section (section submerged or not), a certain value for the air pressure and by using the sweep method to determine the water flow characteristics. The air volume calculated by iteration must converge, and the calculated regimes at each section (submerged or free) must agree with the supposed regimes. The simulation is performed first with a horizontal conduit then with an inclined conduit. As expected, adiabatic compression gives higher pressure than isothermal compression. The simulation shows also that when there is an air cushion, compared with the case when air is flowing out freely, the shock of the water hammer at the closed end of the conduit is significantly reduced. This method is aimed at calculating the flow with entrapped air in the inlet/outlet tunnel of a hydroelectric plant, or in sewer system pipe when a sudden discharge surge (due to turbin opening/closing or to urban storm) changes a previously free‐surface flow in a mostly full‐pipe flow, but with some air entrapped under the ceiling. Copyright © 1999 John Wiley & Sons, Ltd.     

高速斜入水和水平入水气炮水箱实验系统

为开展模型高速斜入水和水中高速航行的水流场实验研究,研制了立式和卧式气炮与水箱组合的实验系统。通过快速阀和活塞阀控制气炮激发和驱动状态,一级气炮采用高压空气直接驱动弹托和模型,二级气炮采用高压空气驱动重活塞压缩使集气腔中产生高压气体,再驱动弹托和模型达到预定速度。通过调节水箱和发射管角度,使高速模型斜入水或水平入水。其中,立式可变发射角二级气炮可发射质量1～1000 g的模型至2500 m/s最大速度,卧式一级气炮可发射质量1～100 kg的模型至300 m/s最大速度。和小气室、高燃气压力火药驱动方式相比,新型气炮采用大体积、中低驱动压力气室,高压气体更接近等熵膨胀做功,调节高压气体压力,能较好地满足模型质量和速度的宽范围要求。结合光反射通断法测速、高速摄影和阴影流场显示等测量技术,得到立式气炮压缩管重活塞运动速度、压缩管末端压力时间曲线和模型倾斜与水平入水的流场阴影图像。结果表明:重活塞速度在膜片破裂前和理论计算值符合较好,但破膜后差异较大。立式气炮流场阴影图像反映了模型斜入水产生的空中和水中激波以及在气水界面的反射激波、空泡形成和侧向气水界面的破碎与飞溅等现象。从卧式气炮的模型水平入水阴影图像提取气泡轮廓,清楚地看出尾部气泡气水界面的波动和失稳。和商业计算软件Fluent计算结果相比,空泡上游区域基本重合,但尾流区域强湍流导致两者存在明显差异。和水洞实验相比,气炮水箱实验系统近真实地再现高速入水过程伴随的冲击和动态空化等物理现象和模型尺度效应。     

Two‐phase pressure drop caused by sudden flow area contraction/expansion in small circular pipes

Theoretical studies have been made to determine the pressure drops caused by abrupt flow area expansion/contraction in small circular pipes for two‐phase flow of air and water mixtures at room temperature and near atmospheric pressure. Two‐phase computational fluid dynamics (CFD) calculations, using Eulerian–Eulerian model (with the air phase being compressible for pipe contraction case) are employed to calculate the pressure drop across sudden expansion and contraction. The pressure drop is determined by extrapolating the computed pressure profiles upstream and downstream of the expansion/contraction. The larger and smaller tube diameters are 1.6 and 0.84 mm, respectively. Computations have been performed with single‐phase water and air, and two‐phase mixtures in a range of Reynolds number (considering all‐liquid flow) from 1000 to 12 000 and flow quality from 1.2 × 10^?3 to 1.6 × 10^?2. The numerical results are validated against experimental data from the literature and are found to be in good agreement. The expansion and contraction loss coefficients are found to be different for single‐phase flow of air and water, and they agreed reasonably well with the commonly used theoretical predictions. Based on the numerical results as well as experimental data, correlations are developed for two‐phase flow pressure drops caused by the flow area contraction as well as expansion. Copyright © 2010 John Wiley & Sons, Ltd.     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical modelling and computation of fluid pressure transients with air entrainment in pumping installations

In pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in pipelines becomes grossly inaccurate when a constant wave speed is assumed. An accurate numerical model with gas release and absorption has been developed in this paper and used to compute the fluid pressure transients in the pumping mains of selected pumping installations. Free and dissolved gases in the transported fluid and cavitation at vapour pressure are also modelled. When compared with the gas-free case, computations show that entrained, entrapped or released gases amplify the positive pressure peak, increase surge damping and produce asymmetric pressure surges. While the upsurge with air entrainment in the pipelines was considerably amplified, the downsurge was only marginally reduced. The computed results show good agreement with the data available.     

Low and high head flooding for countercurrent flow in short horizontal tubes

Experiments have been carried out discharging water along a horizontal 50 mm bore tube against a countercurrent flow of air. With the water flowrate constant, the air flowrate was slowly increased until waves appeared, restricting the outflow of water. This defined the low head flooding condition which was found to be in good agreement with previous theory for low water discharge rates. A new treatment gives good agreement over the whole experimental range. Once the low head flooding set in, the water head built up up in the water supply tank connected to the horizontal tube and the air flowrate had to be reduced substantially below that required for the initiation of flooding before the water discharge rate was fully reinstated. This is the high head flooding condition and experimental results are in substantial agreement with those of others. Previous theory for high head flooding is derived in a simpler fashion and related to the Kelvin—Helmholtz instability criterion. The theory is shown to be a generalization of the criterion.     

明渠气二相流的双流体模型

从解决平均二相流基本方程的封闭问题出发,分析了水利工程中气水二相流的特点,介绍了据此提出的可用于水利工程稀疏气泡流计算的双流体模型,并对明渠气水二相流进行了算例验证。     

激波与堆积粉尘相互作用的数值模拟

基于双流体模型和测定的堆积粉尘的本构方程 ,利用AUSM+ 格式 ,对激波与堆积粉尘的相互作用进行了数值模拟。计算所反映的流场结构与实验图像一致。此外还对激波强度 ,颗粒材料密度等对流场的影响进行了讨论。     

A modification of the artificial compressibility algorithm with improved convergence characteristics

The artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven‐cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward‐facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical simulation of the flow with contact lines

The paper proposes a physical model for the motion of the contact line and the gas-liquid interface. The local motion of the contact line at the solid wall is assumed and the interface between gas and liquid is traced by a level function. The numerically. The motion of the water column in a vertical pipe is computed and the results are in good agreement with experimental data.     

An investigation of pressure transients in pipelines with two-phase bubbly flow

This paper presents a two-dimensional model for the analysis of the pressure transient of a two-phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air–water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two-phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics.     

非饱和粘性土中气体渗透特征

由于气体的进入形成了非饱和带,饱和土层中的气体渗透实质上是非饱和渗透问题。本文借助基于多孔介质气体渗流理论并考虑气体压缩性的、描述非饱和土中气体渗流运动的本构方程,试验研究了上海地区饱和粘性土层中的气体渗透规律。结果表明,饱水粘性土层中,气体渗透存在起始压力值,数值为100～200kPa, 与上海地区粘土的非饱和进气值较为接近;气体渗透速度与外界所施加的"压力平方差梯度"之间存在明显的分段特征。后者可能与在充满结合水的微孔隙通道中,只有一部分结合水在气压梯度的作用下发生流动,从而形成气体通道,施加的外力越大,形成的气体通道也越大,气体渗流也越明显。非饱和粘性土中气体渗透规律的研究,对于饱和粘土中的气压法施工,具有重要的理论与工程实践意义。     

Validation of a CIP-based tank for numerical simulation of free surface flows

A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows.The numerical simulation is performed by the CIP-based Cartesian grid method,which is described in the present paper.The tangent of hyperbola for interface capturing(THINC) scheme is applied for capturing complex free surfaces.The new model is capable of simulating a flow with violently varied free surface.A series of computations are conducted to assess the developed algorithm and its versatility.These tests include the collapse of water column with and without an obstacle,sloshing in a fixed tank,the generation of regular waves in a tank,the generation of extreme waves in a tank.Excellent agreements are obtained when numerical results are compared with available analytical,experimental,and other numerical results.     

具有可变均压槽的气体静压推力轴承性能研究

具有可变均压槽的气体静压推力轴承,是作者提出的一种新结构轴承.本文建立了这种新结构轴承的性能计算方法,用有限差分法耦合求解气体静压推力轴承的雷诺方程和弹性薄片的变形控制方程,得到轴承的各项性能参数,并通过试验加以对比验证,计算结果与试验具有较好的一致性.结果表明该新型气体静压推力轴承的设计方案能够提高轴承的刚度.     

On the Capillary Problem for Compressible Fluids

Classical capillarity theory is based on a hypothesis that virtual motions of fluid particles distinct from those on a surface interface have no effect on the form of the interface. That hypothesis cannot be supported for a compressible fluid. A heuristic reasoning suggests that even small amounts of compressibility could have significant effect on surface behavior. In an earlier work, Finn took a partial account of compressibility, and formulated a variant of the classical capillarity equation for fluid surface height in a vertical capillary tube; he was led to a necessary condition for existence of a solution with prescribed mass in a tube closed at the bottom. For a circular tube, he proved that the condition also suffices, and that solutions are uniquely determined for any contact angle γ. Later Finn took more complete account of compressibility and obtained a new equation of highly nonlinear character but for which the same necessary condition holds. In the present work we consider that equation for circular tubes. We prove that the necessary condition again suffices for existence when 0 ≤ γ < π, and we establish uniqueness when 0 ≤ γ ≤ π/2. Our result is put into relief by the observation that for the unconstrained problem of a tube dipped into an infinite liquid bath, solutions do not in general exist when γ > π/2. Presumably an actual fluid would in that case descend to the bottom of the tube. This kind of singular behavior does not occur for the equation previously considered, nor does it occur in the present case under the presence of a mass constraint.     

Modified incompressible SPH method for simulating free surface problems

An incompressible smoothed particle hydrodynamics (I-SPH) formulation is presented to simulate free surface incompressible fluid problems. The governing equations are mass and momentum conservation that are solved in a Lagrangian form using a two-step fractional method. In the first step, velocity field is computed without enforcing incompressibility. In the second step, a Poisson equation of pressure is used to satisfy incompressibility condition. The source term in the Poisson equation for the pressure is approximated, based on the SPH continuity equation, by an interpolation summation involving the relative velocities between a reference particle and its neighboring particles. A new form of source term for the Poisson equation is proposed and also a modified Poisson equation of pressure is used to satisfy incompressibility condition of free surface particles. By employing these corrections, the stability and accuracy of SPH method are improved. In order to show the ability of SPH method to simulate fluid mechanical problems, this method is used to simulate four test problems such as 2-D dam-break and wave propagation.     

A finite element analysis of laminar unsteady flow of viscoelastic fluids through channels with non-uniform cross-sections

The effects of non-Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non-uniform cross-section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd-B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two-step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large-scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non-uniform cross-section.     

Three‐dimensional numerical modelling of free surface flows with non‐hydrostatic pressure

A three‐dimensional numerical model is developed for incompressible free surface flows. The model is based on the unsteady Reynolds‐averaged Navier–Stokes equations with a non‐hydrostatic pressure distribution being incorporated in the model. The governing equations are solved in the conventional sigma co‐ordinate system, with a semi‐implicit time discretization. A fractional step method is used to enable the pressure to be decomposed into its hydrostatic and hydrodynamic components. At every time step one five‐diagonal system of equations is solved to compute the water elevations and then the hydrodynamic pressure is determined from a pressure Poisson equation. The model is applied to three examples to simulate unsteady free surface flows where non‐hydrostatic pressures have a considerable effect on the velocity field. Emphasis is focused on applying the model to wave problems. Two of the examples are about modelling small amplitude waves where the hydrostatic approximation and long wave theory are not valid. The other example is the wind‐induced circulation in a closed basin. The numerical solutions are compared with the available analytical solutions for small amplitude wave theory and very good agreement is obtained. Copyright © 2002 John Wiley & Sons, Ltd.