Slug flow and fluid-structure interaction in industrial pipe systems Who are you? When did you do this work? With who did you do this work? Qingzhi Hou

Overview Introduction Two-phase flows Test problems Mathematical models Fluid-structure interaction Conclusions First I will give a brief introduction about the background of this project. Then I will introduce the category of two phase flows. After that, slug flow will be discussed by two test problems. Later on, 1D and 3D models will be talked. Before summary, FSI problems will be explained. It is another important part of this project.

Industrial problems Moving pipes Industrial pipes are widely used in many fields like oil transport, urban water supply, hydropower plants and nuclear industry. They are playing an important role in industry and human’s life. There are two common problems. One is the pipe movement, and another is pipe break. Pipe used to be on the supports, but now fell down; these two pictures are about Alaska oil transport pipelines. Pipeline offset is obvious and supports are destroyed; From this picture we can observe pipe position change.

Broken pipes Here are some pictures about broken pipes Water supply pipes are always under high pressure. When pipe breaks, lot’s of water will be wasted, especially for buried pipes, because it needs a long time to repair. If there is some chemical materials in the pipe, we can imagine what a disaster it will be to the environment. Since pipe damage may cause severe effects to civil life and environment, they are called lifeline system. What is the main reason for these two problems? It’s high velocity liquid slugs.

Two-phase flows Two-phase flow regimes Butterworth & Hewitt 1977 Before talking about slug flow, let me first say something about two phase flows. This picture show us the description and classification of two phase flows in a pipe. It’s well-established by Butterworth & Hewitt in 1977. But here we will focus on slug flow. Because it is the most dangerous two phase flow to the pipeline system.

Test problems Bozkus and Wiggert laboratory set up (1997) water To examine the whole procedure of slug flow, two problems will be tested. The first one is Bozkus and Wiggert laboratory set up. The blue region here is water slug. When this ball valve is open, under high tank pressure, water slug will move very fast and hit on the downstream elbow. Two pressure transducers can record the pressure history. water

Measured pressures at elbow This picture shows us the recorded pressures. Pressure1 is from transducer one. We can see that it has two peaks. Pressure2

Different flow regions Why two peaks? it is because before the slug arrives at the bend, one slug has separated into two liquid mass. It’s shown in this picture. When the first liquid mass hits the bend, we have one peak, and when the second one arrives, we have another one.

Delft experiment (European project) pipe filling and emptying L = 300 m D = 0.25 m Another test problem is pipe filling and emptying experiment. It is set up at Delft Deltas. This is an European project. The first step of it, pipe filling has been finished last month. The scheme is shown in this slide. Since pipe length is more than 300 meters and pipe diameter is 250 mms, this is a large and complex system The water tank is 25 meters high and used to fill the pipe. The volume of air tank is 70 cubic meters. It’s used to empty the system.

Test setup This slide show us the test rig of the experiment. Upstream, pipe bridge (used to initialize), downstream, the middle part and U turn.

Observed two-phase flow These are some test results from one digital camera. From them, we can see most of the two phase flow regimes like stratified flow, wavy flow, annular mist flow, dispersed bubble flow and slug flow.

Delft water-hammer accident When we did the experiment, one accident happened. The downstream valve closed suddenly for some reason. This is the recorded pressures. From it, we can see the maximum of the pressure exceeded the measuring range of transducer, so peaks were cut off. We didn’t expect such a high pressure. From the trend, we can see the maximum pressure is around 6 bar. What is six bar? That means 60 meters high water acted on the pipe. The results can be seen from these pictures. The anchor was lift up, U turn had a big movement, supports were destroyed and leakage was everywhere. The whole system was destroyed. Even worse, one steel bar here was knocked off and fell downstairs. one person was almost injured. Next day, when we did other experiments, no people worked there. Actually, when we think later, we feel lucky. If that guy really hit by the steel bar, it would be a disaster.

1D-models Single phase Water hammer Pipe vibration Here is the model for water hammer. 1D model is widely used for one phase flow. Because it is simple. Except water hammer, another typical one phase flow is pipe vibration. What is water hammer? This can be explained by the following reservoir-pipe-valve system. At he beginning, the valve is open and we have initial velocity V0. When valve is closed suddenly, a pressure oscillation will be generated. The valve is hit by the oscillating pressure. likes a hammer. So this phenomena is usually called water hammer. It’s similar for pipe vibration if we substitute water with steel. But there is some difference. The biggest one is instability may take place when compressive wave is travelling in the pipe. In classical water hammer equations, P is pressure, V is velocity. This figure is the numerical simulation of water hammer.

Slug flow – 1D model Moving slug Slug Hold-up Downstream Gas Upstream Gas This picture shows us the 1D model for slug flow. It consists of four regimes. For the moving slug, it can be taken as a rigid body. But when it hits the bend, its compressibility has to be considered to account for water hammer. Ideal gas state equation is employed to describe the upstream gas dynamics. The downstream gas is usually ignored because the pipe is open to the atmosphere. When the time of the slug motion is short, the hold-up doesn’t play an important role. That is say, there’s not too much mass loss during the slug motion.

Slug impact at the elbow - 1D model Dynamic pressure Under high upstream pressure, the slug will be accelerated and move like a bullet When this bullet hits on the bend, orifice or partially opened valve, huge impact force will be generated. And because of that, pipe will shake, break or even explode.

Italian experiment (slug flow in vertical pipe) Filling through orifice (Giuseppe D.M 2008) For slug flow in vertical pipe, 1D model is also widely used, because the interface of water and air can remain flat when it is moving. The main thing here is the flow column moves and impacts the orifice after open the ball valve. The right two figures are the pressure history. We can see high pressure peaks generated on the orifice. But for slug flow in horizontal pipes, can we still assume that the interface is vertical and keeps unchanging? The answer is no. It can be seen from former two phase flow regimes. So more complex model has to be employed.

3D-models Smoothed particle hydrodynamics (SPH) Lucy (1977) and Monaghan (1977) Advantages: easy to deal with free surfaces, moving boundaries, high velocity impacts, explosions and large deformations. Kernel approximation Particle approximation We already have many different 3-D models for fluid problems like FVM, FEM and BEM. But these models are difficult to solve two phase flows, because problems like moving interface, free surface are difficult to be treated. Now days, mesh free methods like SPH, LBM are becoming more and more popular. SPH is one of the oldest and true mesh free method. It's established by Monaghan and Lucy in 1977 to solve astrophysics problems. Now it has been applied to many other fields, and fluid problem is the most popular one. The most important two steps of SPH are kernel approximation and particle approximation. In kernel approximation, a function can be approximated by its integral representation. And the same holds on its spatial derivative form. In the particle approximation, a function can be discretized into a form of summation over all the nearest neighboring particles

Conservation laws Lagrangian form Continuity equation Momentum equation Energy equation We will use the discritization of Navier stokes equations to illuminate the procedure of this method. The largrangian form of conservation laws are expressed by three equations. Here I have to mention alpha and beta denote the components and can be x, y or z. Sigma has two parts, one is pressure and another is shear stress. If we neglect the shear stress, this will change into the Euler form of Navier-Stokers equation.

SPH Mass Summation density Continuity density For density evolution, there are two popular forms. One is summation density, and the other is continuity density. For continuity density, there are three forms, but the last two are more popular because symmetric velocity is used.

SPH Momentum This is also held for momentum evolution. Here p is pressure, F is external force flux, epsilon is shear strain, delta is the Dirac delta function.

SPH Energy For energy evolution, there are also two popular forms. It is worth noticing that all variables are or can be symmetric in SPH evolution equations. This can save lots of computation time.

Fluid-structure interaction (FSI) Forces on pipes and anchors Vibration of pipes Except slug flow, another important part of this project is fluid-structure interaction. Fluid-structure interaction was driven by the nuclear industry in the 1970s. For waterhammer, we assume pipe doesn’t move. But in fact, it’s impossible. Under such forces as transient pressure, dynamic impact, pipe will have some response like expansion, movement and vibration. For example, If the force is very high, pipe will break or explode, pipe support will be also destroyed. So it’s necessary to consider FSI

FSI Basic modes of vibrations Coupling mechanisms There are several different basic modes of flow induced vibrations like radial motion, axial motion, lateral motion, torsional motion and junction motion. Junction motion is usually observed in complex pipe systems, and it involves all the basic modes. to be included in model

Summary Performed tasks Coming half year Final goal Literature review Delft experiment 1D modeling FSI in frequency domain Coming half year Data analysis of experiment 1D modeling (two phase flow) SPH modeling Final goal Simulation tool for filling of pipelines

References Bozkus Z, Wiggert D.C (1997). Liquid slug motion in a voided line. Journal of Fluids and Structures, 11, 947-963. Butterworth D, Hewitt G. F (1977). Two-Phase Flow and Heat Transfer. Oxford: Oxford University Press. Doyle J.F (1997). Wave Propagation in Structures. New York: Springer Press. Giuseppe D.M, Nicola F, and Maurizio G (2008). Transient Flow Caused by Air Expulsion through an Orifice. Journal of Hydraulic Engineering, 134(9), 1395-1399. Liu G.R, Liu M.B (2003). Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific Publishing Co Pte Ltd. Lucy L.B (1977). Numerical approach to test the fission hypothesis. Astronomical Journal, 82: 1013-1024. Gingold R.A, Monaghan J.J (1977). Smoothed particle hydrodynamics: theory and application to non-spherical stars. Royal Astronomical Society, 181: 375-389.