A water hammer is a transient flow in pipes that is created by sudden changes in velocity. This phenomenon can cause strong positive and negative pressures in water conveyance pipes, and usually, it poses pipelines. A water hammer is created by rapidly closing valves, shutting off, or suddenly restarting pumps. It has destructive hydrodynamic effects in pressurized pipelines. This phenomenon cannot be eliminated but can be reduced by using different protection devices. In this study, the pipeline has been modeled using the GAMBIT software. Further, the steady-state pressure drop and governing equations of water hammers are numerically simulated using FLUENT software. The simulation helps the designers to have a good understanding of the water hammer phenomenon and work on ways to reduce it.

iii ACKNOWLEDGEMENT I would like to express my deep sense of gratitude and respect to my supervisor Dr. Seyed Saied for his excellent guidance and Hartha power station. iv List of Figures Figure 2.1 Hydraulic transient at position x in the system 5 Figure 3.1 Gambit model 11 Figure 3.2 Transient analysis water hammer 12 v TABLE OF CONTENTS Address I Abstract Ii Acknowledgments Iii List of Figures Iv TABLE OF CONTENTS v CHAPTER ONE 1 GENERAL INTRODUCTION 1 1.1 Causes of water hammer 2 1.2 Effects of water hammer 3 CHAPTER TWO 4 LITERATURE REVIEW 4 2.1 Introduction to Transient Flow 4 2.2 History of Transient Analysis Methods 6 2.2.1 Arithmetic Method 6 2.2.2 Graphical Method 6 2.2.3 Method of Characteristics 6 2.2.4 Algebraic Method 7 2.2.5 Wave-Plan Analysis Method 7 2.2.6 Implicit Method 7 2.2.7 Linear Methods 7 2.2.8 Perturbation Method 7 CHAPTER THREE 9 Mathematics and governing equation 9 3.1Water Hammer Theory 9 3.2.1 Steady-state analysis 11 3.2.2 Transient analysis 12 CHAPTER FOUR 13 4.1. CONCLUSION 13 vi 4.2 Recommendations 13 Reference 14 1 CHAPTER ONE GENERAL INTRODUCTION Water hammer has been a concern to engineers for almost a century. It has caused serious damage in some engineering applications. One of the important areas where water hammer causes problems. There are instances in which pipes shake, damage the supports and even rupture or leak at pipe welds. After years of research, some causes were identified and design precautions were taken to avoid the problem. These were generally water hammer events that occurred in one phase flow. Water hammer can occur in various other situations [1]. Water hammer is caused by fluid in motion being forced to stop or change direction suddenly. It is a commonly observed phenomenon. It has multiple adverse effects on a system like bending of pipe, damage of equipment, bursting of pipes, etc. Because of these damages large quantity of steam or hot condensate being blowing out which could lead to a serious accident. To overcome these issues there is a need to study water hammers. Hammering sound caused in a pipe containing water when live steam is passed through it. Water hammer analysis is a fundamental part of the design process of piping systems for power plants or water hammer networks. Many types of research work on the causes of water hammers in various industrial applications [2]. Very strong pressure pulses or surges also referred to as water hammers, often occur in fluid-conducting pipes. The stresses on the pipes, valves, and apparatus can be so high that the equipment concerned is damaged or in extreme cases bursts. Before effective measures can be taken to combat this problem, it is important to analyze exactly which kind of water hammer is involved and what causes it [15]. 2 This means that a surge analysis to industry standards has to be performed for every hydraulic piping system at risk from water hammer. Dedicated software is available for this purpose. Using the CFD tool we are making efforts to preview the effect of the water hammer and suggest methods to reduce the same. Through modeling of pipe networks pressure surge analysis for piping systems with different objectives are investigated. [4] 1.1 Causes of water hammer Water hammer is mainly caused due to the sudden closing of valves. When the valve closes, there is high-pressure spikes generation due to which the pipe suffers vibration and thudding sound. [3] Typical events that require transient considerations include

1. Pump startup or shutdown.

2. Valve opening or closing -variation in cross-sectional flow area

3. Changes in boundary pressures e.g. losing overhead storage tank, an adjustment in the water level at reservoirs, pressure changes in tanks, etc.

4. Rapid changes in demand conditions e.g. hydrant flushing.

5. Changes in transmission conditions e.g. main break or line freezing.

6. Pipe filling or draining-air release from pipes.

7. Check valve or regulator valve action. 3 1.2 Effects of water hammer The phenomenon may cause the following problems [5]

8. When the non-return valve or the pump discharge valve closes, depending on the magnitude of the reverse flow already established, a pressure rise occurs, which may exceed the design and test pressure of the pipe.

9. During the initial down surge phase, the magnitude of the pressure drop may be such that, at an elevated location along the alignment, vapor pressure occurs. This is termed as water column separation, which on cavity collapse create a shock pressure rise, which travels on both sides and may cause the pressure to exceed design and test pressure. For large - diameter steel pipes, the occurrence of vapor pressure is a severe problem.

10. Pump damage.

11. Intense pressure spikes.

12. Bursting of pipes seals.

13. Destroyed meters and gauges. 4 CHAPTER TWO LITERATURE REVIEW 2.1 Introduction to Transient Flow In a water distribution system, system flow control is an integrated part of its operation, for instance, the opening and closing of valves, and starting and stopping of pumps. When these operations are performed very quickly, they can cause hydraulic transient phenomena to come into existence in the water distribution system, which can result in system damage or failure if the transients are not minimized [10]. When the steady-state condition of a flow in a system is altered, the values of the initial flow conditions of the system, characterized by the measured velocity (V) and pressure (P) at positions along the pipeline (x), change with time (t) until the final flow conditions are established in a new steady-state condition. Hydraulic transient evaluation is a complex task and it involves the determination of the values of the functions V(x, t) and P(x, t) during the time interval, T that resulted from a flow control operation performed in a time interval, Δt. In the case of hydraulic transients, density changes of the liquid (normally water) are essential to consider. In the case of surges (mass oscillations), the flow can be considered incompressible [11]. Figure 2.1 depicts what the transient evolution in a system looks like and it represents a view of the transient at a fixed point (x) just upstream of the valve that is being shut. In this graph, the pressure, P is represented as a function of time, t resulting from the operation of a control valve. In the figure, Pi is the initial pressure 5 at the start of the transient, Pf is the final pressure at the end of the transient event, Pmin is the minimum transient pressure, and Pmax is the maximum transient pressure. Figure 2.1 Hydraulic transient at position x in the system [13] 6 2.2 History of Transient Analysis Methods Various methods of analysis were developed for the problem of transient flow in pipes. They range from approximate analytical approaches whereby the nonlinear friction term in the momentum equation is either neglected or linearized, to numerical solutions of the nonlinear system. These methods can be classified as follows: 2.2.1 Arithmetic Method This method neglects friction (Joukowsky, 1904; Allievi, 1925) [6]. 2.2.2 Graphical Method This method neglects friction in its theoretical development but includes a means of accounting for it through a correction (Parmakian, 1963) [7]. Generally, the graphical method is considered to be one of the simplest and most effective ways to calculate the hydraulic transient. Some simplifications must be done to make it possible to apply the graphical method. The transients are normally obtained only at the endpoints of the pipeline and the frictional losses are assumed to be concentrated to only one point (either the inlet or outlet of the pipeline depending on the problem), also the energy losses in the entire pipeline during the transient phase are thus approximated by means of the water velocity in one point (inlet or outlet) although the velocity, in reality, varies along the pipeline. The graphical method can be done freehand or by the use of drawing software (for example AutoCAD), and that of course affects the results because it always depends on the person’s accuracy. 2.2.3 Method of Characteristics This method is the most popular approach for handling hydraulic transients. Its thrust lies in its ability to convert the two partial differential equations (PDEs) of continuity and momentum into four ordinary differential equations that are solved numerically 7 using finite difference techniques (Gray, 1953; Streeter and Lai, 1962) [8]. The graphical method is also based on the method of characteristics. 2.2.4 Algebraic Method The algebraic equations in this method are the two characteristic equations for waves in the positive and negative directions in a pipe reach, written such that time is an integer subscript (Wylie and Streeter, 1993) [9]. 2.2.5 Wave-Plan Analysis Method This method uses a wave-plan analysis procedure that keeps track of reflections at the boundaries (Wood, Dorsch, and Lightner, 1966). 2.2.6 Implicit Method This implicit method uses a finite difference scheme for the transient flow problem. The method is formulated such that the requirement to maintain a relationship between the length interval Δx and the time increment Δt is relaxed (Amein and Chu, 1975). 2.2.7 Linear Methods By linearizing the friction term, an analytical solution to the two PDEs of continuity and momentum may be found for sine wave oscillations. The linear methods of analysis may be placed in two categories: the impedance method, which is steady-oscillatory fluctuations set up by some forcing function, and the method of free vibrations of a piping system, which is a method that determines the natural frequencies of the system and provides the rate of dampening of oscillations when forcing is discontinued (Wylie and Streeter, 1993) [12]. 2.2.8 Perturbation Method With this method, the nonlinear friction term is expanded in a perturbation series to allow the explicit, analytical determination of transient velocity in the pipeline. The 8 solutions are obtained in functional forms suitable for engineering uses, such as determining the critical values of velocity and pressure, their locations along the pipeline, and their times of occurrence (Walski, Chase, Savic, Grayman, Beckwith and Koelle, 2003). 9 CHAPTER THREE Mathematics and governing equation 3.1Water Hammer Theory Water hammer refers to the transient conditions that prevail following rapid system flow control operations. It can be used beneficially, as in the case of a hydraulic ram, which is a pump that uses a large amount of flowing water to temporarily store elastic energy for pumping a small amount of water to a higher elevation. More commonly, the destructive potential of the water hammer is what attracts the attention of water engineers. Governing equations and Turbulence model Steady flow of a Newtonian, incompressible fluid was assumed. The governing equations were solved using the SIMPLE algorithm. The conservation of mass (3-1) and momentum equations (3-2) are: 𝜕𝑢𝜕𝑥+𝜕𝑣𝜕𝑦+𝑤𝜕𝑧=0 )3-1( 𝜌(𝜕𝑣𝜕𝑡+(𝑣∙∇)∙𝑣)=−𝜌𝑔∇ℎ−∇𝑝+∇𝜏 )3-2( Where 𝜏 stands for the divergence of the stress tensor. Considering this term, the number of unknowns turns to be (velocity components v, pressure p, and stress field), which makes the equation above very difficult to be solved. However, calculations are simplified by using the Navier-Stokes equations, which relate the stress field to the fluid viscosity. The unsteady momentum and mass conservation equations are applied to flow in a frictionless, horizontal, elastic pipeline to generate equations describing the water hammer phenomenon. First, the momentum equation is applied to a control volume at the wavefront following a disturbance caused by downstream valve action. The following equation may be developed, which is applicable for a wave propagating in the upstream direction: Δ𝑝=−𝜌𝑎Δ𝑣 )3-3( 10 Δ𝐻=−(𝑎/𝑔)Δ𝑣 )3-4( Where Δp = change in pressure, Pa ρ = fluid density, kg/m3 a = characteristic wave celerity of the fluid, m/s ΔV= change in fluid velocity, m/s ΔH= change in head, m These equations are valid at a section in a pipeline in the absence of wave reflection. They relate a velocity pulse to a pressure pulse, both of which are propagating at the wave speed a in equation (3-4). Assume that an instantaneous valve closure occurs at time t = 0. During the period L/a (the time it takes for the wave to travel from the valve to the pipe entrance), steady flow continues to enter the pipeline at the upstream end. The mass of fluid that enters during this period is accommodated through the expansion of the pipeline due to its elasticity and slight changes in fluid density due to its compressibility. The following equation for the numerical value of a is obtained by applying the equation for conservation of mass. 𝑎=√𝐸𝑣𝜌𝑣1+𝐸𝑣𝐸𝑝∙𝐷𝑒∙𝐶 (3-4) Where and are the volumetric modulus of elasticity of the fluid and the pipe material (Pa) respectively, v, Ep, Ev,ρ is the density of the liquid (Kg/m3), D and e are the internal diameters and the wall thickness (m) of the pipe respectively, and C = constant, which depends on the axial movement of the pipe. In practical calculations, C 1. The continuous differential equation of water hammer is as follow 11 3.2 RESULTS AND DISCUSSION [8, 9] 3.2.1 Steady-state analysis To study the dynamics of flow mathematically, CFD technology is used. Computational Fluid Dynamics or CFD is the analysis of systems involving fluid flow, heat transfer, and associated phenomena such as chemical reactions using computer-based simulation. The technique is very powerful and spans a wide range of industrial and non-industrial applications areas. CFD tool is thus used to analyze the flow through the pipeline to locate critical locations in the pipeline where water hammer is severe. Therefore before installation of protecting devices on pipe, the water hammer and its variation along the pipe is analyzed using the CFD tool. This will reduce the cost and time consumption required to analyze the effect than the practical method. In this analysis we are using the CFD tool- Gambit for pipe modeling and meshing and Ansys Fluent for analyzing the water hammer in figure 3.1. Figure 3.1 Gambit model 3.2.2 Transient analysis as per the steps followed in transient analysis in Figure 3.2, the water hammer phenomenon will be generated. The drastic pressure spikes along the interior of the pipeline are shown by color scheme Dark blue color shows minimum pressure value and red color shows maximum pressure value. Flowing 12 water possesses inertia. When the valve closes, high-pressure waves generated travel to and fro until the pressure is dissipated and is shown by the red color in the graph.

14. Inlet Due to sudden valve closure, there is negative pressure generation i.e. vacuum is created. This variation is shown by blue color at the inlet section.

15. Middle section as the pressure wave’s progress, there is pressure variation as shown.

16. Outlet For 0.1 sec the high-pressure spikes do not reach the outlet yet. As a result, the pressure at the outlet is minimum but greater than vacuum pressure at the inlet. By contour plot, critical vacuum and high-pressure regions are detected so that protection devices are chosen and installed accordingly. Figure 3.2 Transient analysis water hammer 13 CHAPTER FOUR 4.1. CONCLUSION The water hammer phenomenon cannot be completely eliminated but it can be minimized by using various protection devices like zero velocity valve, air valve, surge vessel, surge tank, etc. In steady-state analysis, we get the pressure distribution along with the interior of the pipeline i.e. working pressure. When a water hammer occurs, due to the sudden closure of the valve, the water due to inertia travels forward and a vacuum is created as there is no further supply of water. Flow reversal occurs due to the slope and bangs on the valve creating high surge waves. If the pressure due to these waves is greater than a particular limit then it may cause severe damage to the pipeline and its accessories. To avoid this, analysis is done to identify the critical locations of positive high pressures and negative low pressures, and accordingly, protection devices can be installed. 4.2 Recommendations The following recommendation is given for the continuation of this research 1-Extended the work to all pipes of the system. 2- Use a computer with a new program to analyze and give fast results. 3- A case study in the operational conditions of pumps and valves with a change in operating conditions (cold or hot operation) 14 Reference [1] Erentürk, Murat. The simulation of passive water hammer in pipes. Diss. Massachusetts Institute of Technology, 1996. [2] Jadhav, S. G., et al. "Water Hammer in Engineering Application: A Review." [3] Wood, Don J. "Water hammer analysis—essential and easy (and efficient)." Journal of Environmental Engineering 131.8 (2005): 1123-1131. [4] Bhutta, Muhammad Mahmood Aslam, et al. "CFD applications in various heat exchangers design: A review." Applied Thermal Engineering 32 (2012): 1-12. [5] Hoang, My Lan, et al. "Analysis of the airflow in a cold store using computational fluid dynamics." International Journal of Refrigeration 23.2 (2000): 127-140. [6] Tijsseling, Arris S., and Alexander Anderson. "A precursor in water hammer analysis–rediscovering Johannes von Kries." Intl. Conf. on Pressure Surges, Chester, United Kingdom. 2004. [7] Streeter, Victor L., and Chintu Lai. "Closure to “Water-Hammer Analysis Including Fluid Friction”." Journal of the Hydraulics Division 89.3 (1963): 307-313. [8] Yasar, Muhammad, Muhammad Waseem, and Ghulam Nabi. "Sensitivity Analysis of Hydraulic Parameters for Water Hammer in Penstock Design." HYDROPOWER. 2017. [9] Axworthy, David H. Water distribution network modeling: from steady-state to water hammer. University of Toronto, 1998. [10] Itissam, A., et al. "Sizing the Protection Devices to Control Water Hammer Damage." World Academy of Science, Engineering and Technology International Journal of Civil, Architectural Science and Engineering, 415â 420 (2014). [11] Ghidaoui, Mohamed S., et al. "A review of water hammer theory and practice." Appl. Mech. Rev. 58.1 (2005): 49-76. [12] Jung, Bong Seog, and Bryan W. Karney. "Eigenvalue Approach for Unsteady Friction Water Hammer Model." Water Engineering Research 5.4 (2004): 177-183. [13] Viel, Antoine. "Strong coupling of Modelica system-level models with detailed CFD models for transient simulation of hydraulic components in their 15 surrounding environment." Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical University; Dresden; Germany. No. 063. Linköping University Electronic Press, 2011. [14] Kaushal, D. R., et al. "CFD modeling for pipeline flow of fine particles at high concentration." International Journal of Multiphase Flow 43 (2012): 85-100. [15] Saemi, Simindokht, et al. "Computation of laminar and turbulent water hammer flows." WCCM-ECCM-ECFD 2014 Congress: 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) 20/07/2014-25/07/2014. 2014.