In ancient times, dams were built to create reservoirs which could be used as a water source or for irrigation. Today, dams have many uses which have become part of modern life such as water supply, irrigation, flood mitigation, power generation and recreation. In providing water supply, during high levels of stream flow the reservoir is filled up and the reservoir is then used as a water source for both domestic use and irrigation during times when the flow rate is low. For flood prevention, the reservoir is nearly empty during periods of low rainfall so that during heavy rainfall, the storage available in the reservoir can help to prevent flooding. For generating electricity, the storage reservoir provides a head of water upstream of the dam and the potential energy of this water is converted to kinetic then to electrical energy.
If dams are not constructed properly or there are mistakes in the design, they can fail. According to ICOLD (1995) a failure is defined as a collapse or movement of part of the dam or its foundations, so that the dam cannot retain the stored water. In general, a failure results in the release of large quantities of water, imposing risks on the people and/or property downstream. During the 1900-1965 period, about 1% of the 9000 large dams in service throughout the world failed and another 2% suffered serious accidents (De Wrachien and Mambretti, 2009). Dam failures often result in a large flood wave forming which can travel at very high speeds, such an event can have a catastrophic impact on the surrounding areas and communities. The impact force produced by such a wave can be enough to destroy nearby roads, railways, bridges and even demolish buildings. On May 31, 1889, the South Fork Dam in Johnstown, U.S.A failed catastrophically and caused the death of over 2200 people (Coleman et al, 2016). In France, the Malpasset Dam Failure occurred in 1959; the dam failed explosively and released 50 million cubic metres of water. The event caused 384 deaths and 110 people were missing (Zhang et al, 2007). In 1975, Typhoon Nina hit China and caused The Banquiao Reservoir Dam to overflow and fail. The dam failure had a maximum flow rate of 20000m3/s and caused the sudden loss of 18GW of power over the Henan Province. According to the Hydrology Department of Henan Province, approximately 26,000 people lost their lives from the flood and another 145,000 died during later epidemics and famine. The dam break caused roughly 6 million buildings to collapse and over 11 million residents were affected (Zhang et al, 2007). In June 1976, the Teton Dam in the U.S.A failed and inundated 400 million square metres of land which caused 11 deaths and 25,000 to be homeless. The reparation costs for this event are circa 400 million US dollars (Zhang et al, 2007).
There are many other dam breaks which have occurred in the past; the above few demonstrate the importance of modelling the flood wave produced in a dam break, which can then be used to produce emergency evacuation plans. After the Malpasset Dam failure, a European Law on dam breaks was introduced in 1968 which has led to a variety of techniques being used across Europe. The different techniques vary in the type of modelling used (1D, 2D etc.), the extent to which the modelling is carried out, the scale of the modelling and also the assumptions used in the modelling (Morris, 2000).
As real-life field measurements are obviously very hard to make, the vast majority of dam break studies have been carried out in hydraulics laboratories. These experiments are limited by the small spatial scales that can be realistically achieved in laboratories and therefore may not be able to fully capture the long-term flow characteristics. This shows that there is a great need for accurate numerical modelling of dam break waves.
In recent years, there have been many computational 1D,2D and 3D models produced in order to model dam break waves. This project will produce a dam break model and validate the results with accurate experimental results, however in this interim report some initial tutorials will be carried out in order to build confidence using the software (ANSYS Fluent).
Aims and Objectives
The main aim of this report is to build up a sufficient understanding of dam break modelling in order to complete the full report next term. Specific objectives for this report are:
To review the literature available on dam breaks and how they have been modelled
To gain confidence using ANSYS Fluent by building geometries, meshes and simulating simple flows
To develop effective time management skills and to plan the work for next semester efficiently
Methodology
In order to gain confidence using ANSYS Fluent, initial tutorials will be completed and presented in the report. The tutorials completed are as follows:
Tutorial 1
Tutorial 2
Report Outline
The details of the chapters in this report are as follows:
Chapter 1 i.e., this chapter.
Chapter 2 presents a literature review on the relevant methods of modelling dam break waves. Initially, this chapter describes early analytical methods used before computers were available and then goes on to describe more modern techniques including experimental and computational methods.
Chapter 3 presents the software used in the report, ANSYS Fluent. The governing equations used to solve fluid problems are described. At the end of the chapter, the method used to complete the Fluent tutorials is described.
Chapter 4 presents the results and discussion from the Fluent tutorials.
Chapter 5 presents a summary of the report. Finally, future work for next semester will be discussed.
Literature review
Introduction
This chapter presents a review of the work done in the field of solving dam breaks analytically, experimentally and computationally. This chapter helps to provide a base knowledge for the project.
The dam break problem has been an area of interest in research for over 100 years, this is due to the potential severe damage that could occur if a dam were to fail. The solutions to the problem have developed substantially over the years, starting with early analytical solutions with some broad assumptions to advanced 3D CFD solutions in the modern day.
Early Analytical Methods
The dam break problem is generally defined as a rapidly moving column of water generated by the instantaneous release of a given volume of water confined in a rectangular channel (Crespo et al, 2008). To the authors knowledge, the first solution to the dam break problem is Ritter (1892) who solves it by applying expressions of Saint Venant, often called the non-linear shallow water equations. Ritter’s solution is based on an inviscid fluid on a dry bed and friction is also neglected. The solutions provide a parabolic water surface profile that is concave upward. The front travels downstream with a wave speed, c=2√(gd_(0)), where g=acceleration due to gravity, and d0=initial quiescent water depth behind the dam (Crespo et al, 2008). This solution has been found to agree well with experimental values, except from the leading tip of the wave which is significantly affected by friction (reference comparing ritter to experimental). Dressler (1952) introduces the dam break problem as a highly unsteady flow, with a forward positive wave advancing over the channel and a back disturbing wave propagating into the still water above the dam. The case investigated is a 2D, horizontal dry bed, with the water in the dam at rest. Dressler (1952) argues that hydraulic resistance caused by stream bed friction and the resultant turbulence dominate the propagation of the dam break wave and therefore concludes that the solution provided by Ritter (1892) is unrealistic as it neglects this term. Dressler (1952) adds the Chézy resistance term to the shallow water equations and calculates the discharge rate, flow velocities and the locus of critical flow. Dressler (1952) confirms that the front tip region of the wave where the slope is vertical needs to be analysed separately. Whittam (1955) investigates this tip region and finds that the water near the tip builds up and is pushed along by the water behind at a speed significantly less than predicted in previous solutions such as Ritter (1892). Whittam (1955) defines the front tip region as a definite boundary layer and uses an adaptation of the Polhausen method to calculate the velocity at the tip of the wave as a function of time. The Polhausen method is based on the Von Kármán momentum theorem and is well known for its application to boundary layer problems. The velocity at the tip of the wave is found as a function of time and is found to be accurate in comparison with experimental results, however as t (time) gets large the solution starts to disagree but it is noted that a dam does not have an infinite volume so solutions for large t can be ignored.
Experimental Methods
As real-life dam break data is obviously very hard to make, experimental methods are very important in order to validate both analytical and computational methods.
Martin and Moyce (1952) carried out a series of tests including the 2D collapse of rectangular and semi-circular sections, and the 3D axial collapse of right circular cylinders over an initially dry horizontal bed. The velocity of spread of fluid and the rate of fall of the top of the water column are explored in the experiment. For each of the experimental cases, the apparatus was similar. The fluid column was constrained by a very thin waxed paper diaphragm held in position by a thin film of beeswax on a metal strip forming part of the fluid reservoir. A bank of car batteries was used to short the circuit with the metal strip, causing the waxed paper to be free and the therefore allow the dam break to begin (Martin and Moyce, 1952). The theoretical solutions assume that the dam break is instantaneous, so the removal of the dam is a vital part in ensuring the experimental data is accurate. It has been found through experiments that if the removal of the dam is <0.1s then it can be assumed to be an instantaneous release (Bellos et al, 1992). This rule was established after these experiments were done, so it is not possible to see if this is an efficient dam removal method. Martin and Moyce (1952) found the wave front velocity to be proportional to the original water column height which is in agreement with Ritter (1892). Dressler (1954) carried out a series of experiments to confirm his 1952 solution. Dressler (1954) carries out the experiments in a horizontal glass flume, 65m in length and 22.5cm in width. Three different initial water column heights were investigated: 22cm, 11cm and 5.5cm. Three different bed surfaces with varying roughness and obeying Manning’s law were also investigated. A system of springs was used to lift the aluminium gate to allow the motion to start; from photographs, it can be seen that there is no motion in the water until the gate has been completely removed. It was found that there was a bigger disagreement between theoretical and experimental results for smoother channel beds. Dressler (1954) concludes that it can be assumed with high probability that the Chézy resistance function is not wholly adequate to describe highly dependent flows, such as the dam break wave. Dressler (1954) states that the reason it cannot be completely concluded is because his solution (1952) is not an exact solution but only an approximation. Bellos et al (1992) investigate 2D dam break induced flow in a converging-diverging flume. To avoid 3D flow effects flat bottom, vertical side walls and mild side wall contractions and expansions were used. Bellos et al (1992) assume the channel geometry and the bed roughness to be constant throughout and investigate the effect of changing the channel bed slope in the flow direction, the upstream water depth and the initial water column height, on the flow. As expected, the flood routing is faster for larger bed slopes, the wave depression travels faster for larger initial water column heights and the wet bed conditions result in a reflected wave travelling upstream (Bellos et al, 1992). Stansby et al (1998) carried out a rigorous series of dam break experiments over dry and wet beds. The experiments were carried out in a 15.24m long, 0.4m wide and 0.4m high flume and the dam gate is released using a pulley system. For the dry-bed case a horizontal jet forms for small t (time) and for the other cases a mushroom-like jet occurs, neither of which had been observed previously (Stansby et al, 1998). The results are compared with Stoker’s (1992) solution and for small times, the differences between them are quite significant. However, after a bore has formed downstream due to highly complex flow interactions, the results agree extremely well (Stansby et el, 1998).
There is a lack of data in the aforementioned dam break flow experiments
regarding the flow dynamics. Lobovský et al (2014) provide a detailed insight into the dynamics of the dam break wave over a dry horizontal bed under controlled laboratory conditions. Lobovský et al (2014) used a purposely built polymethyl methacrylate prismatic tank with internal dimensions of 1610mm long, 600mm high and 150mm wide. A similar pulley system to Stansby et al (1998) is used to remove the gate, however further detail is added by Lobovský et al (2014) regarding experimental accuracy such as replacing the steel wire because it had plastically deformed due to the high shock from the pull. As this is an important part of the experiment, Lobovský et al (2014) carry out an analysis of the gate removal time and find that 95% of cases fall within the range <0.06s;0.10s>. Lobovský et al (2014) add extra information that has not been included in previous dam break experiments such as preheating the water to 25˚C before each run, which means the water can be considered Newtonian with a density of 997kgm-3, kinematic viscosity of 8.9 x 10-7 and surface tension of 0.072Nm-1. Five pressure sensors were used and arranged with 4 on the centre line of the back wall at varying heights and 1 offset from the centre line. The experiment has been carried out for initial water column heights of 300mm and 600mm, the test has also been repeated 100 times in order to provide statistically sound data. This repetition had not been done before in previous experiments and adds a level of accuracy to the data. On the downstream wall, the peak pressure values are found to be spread out. For the larger initial water column height, 600mm, the scattering in the peak pressure values is found to be significantly larger (Lobovský et al, 2014). A linear relationship is found between the initial water column height and the impact pressure load for the sensor nearest to the channel bed which was subjected to the largest load. The relationship between the other sensors is not linear but it is found that a higher initial water column height corresponds to a higher impact pressure force (Lobovský et al, 2014). The pressure forces are compared with the results of Lee et al (2002) and the results from Lee et al (2002) are found to be outside the 95% confidence interval produced by Lobovský et al (2014) during the impact event. Lobovský et al (2014) suggest that the reason for this is that Lee et al (2002) used pressure sensors with a larger diameter and did not account for the unpredictable nature of only carrying out the experiment once. The results from Lobovský et al (2014) are extremely robust and surpass the accuracy of previous experiments by a significant margin. Lobovský et al (2014) also address the pressure forces due to a dam break in which the literature is lacking. For these reasons as well as the data being easily available online, the results from Lobovský et al (2014) will be used as validation for the model produced in ANSYS Fluent later in the project.