Virtual Laboratory for transient flows

Transcription

1 Ninth LACCEI Latin American and Caribbean Conference (LACCEI 211), Engineering for a Smart Planet, Innovation, Information Technology and Computational Tools for Sustainable Development, August 3-5, 211, Medellín, Colombia. Virtual Laboratory for transient flows Geanette Polanco Simón Bolívar University, Caracas, Dtto. Federal, Venezuela, gpolanco@usb.ve ABSTRACT The consequences of the phenomenon called Water hammer is a series of pressure waves created by a sudden change in flow velocity of a liquid within a pipe system. It is a hazardous condition that could produces fatal consequences at any fluid system, such as breaking down or damages on the security valves. For this reason it is a priority target at design level to avoid its presence or to incorporate dissipation mechanisms that protects the original pipe system. The importance of understanding this phenomenon is significant for every mechanical engineering student. Due to the difficulty that implies to study this phenomenon in actual facilities a portable virtual lab that reproduces the original layout of a real facility located in the Fluid Mechanics Laboratory of Simon Bolivar University is proposed. It covers the solution of different conditions, such as, the aperture of the column and different closing times. This virtual lab will go into a growing field of teaching using new technologies which have been applied in many engineering, for instance the modelling of public transport modelling or Electronic systems fields ((Franco, 23), (Jerez, 28), (Rahman et al., 1992)). Keywords: Virtual laboratory, Fluid Mechanics, Engineering education 1. INTRODUCTION Figure 1. a) Actual lab facility B) Schematic representation of the actual lab facility Medellín, Colombia 9th Latin American and Caribbean Conference for Engineering and Technology WE1-1 August 3-5, 211

2 The facility existing in the Fluid Mechanics Laboratory of the Simón Bolívar University covers an area of 1 m. long per 2 m wide. This facility contains three pipe systems linked each other by tanks, operationally linked to keep the premise of constant level condition. Figure 1 shows the schematic layout of the laboratory facility to do the experience of transient flow in pipe system. Currently students observe the motion of the free surface of the flow at the column trough their transparent wall, at the same time they register the period of time of each motion. The option of instrument the whole system introduces the possibility of design new practical experiences to be performed by the student, at the very same time of the open the possibility of introduce new examples of how this kind of transient systems can be modelled and calculated using the resolution of the governing equation. However, the investments in equipments and measurement instruments can be too high. So the virtual lab appears to be an option manageable at the time. The use of this kind of technology in different fields of engineering and design areas is a current common use. For instance, the modelling of public transport (Escolá et al., 27), electronic systems (Jerez, 28) and fluid mechanics system (Duro et al. 25). 2. REVIEW The transient behaviour of the flow inside pipe system, known as water hammer, in which pressure waves produced by changes in the velocity trough the pipes travel inside the pipe generating a time variation of the whole system, can produce serious damages, as ruptures or collapses of different elements. The change in velocity can obey to the action of valves, starting or stopping of pump, instabilities in the working conditions of pumps, or any other alteration of the pipe system. Transient study involves a special consideration about the compressibility of the fluid, the possibility of the interaction between the fluid and the material of the pipe and or course the variation of the system characteristics in time. The physics of the pressure wave motion can be briefly described using a pipeline connected to a tank with a valve in the downstream extreme. If the system is operating under stationary regime with the valve completely open, then the discharge flow is kept constant as long there is not any change along the whole system. If the valve is closed instantaneously, the kinetic energy of the fluid close to the valve will be transformed into elastic work, the perimeter of the pipe will increase in that point of the pipe, and the fluid will experience a compression with an increase of the hydrostatic pressure. This transformation goes through the whole pipeline with a uniform velocity equal to the speed of the sound in the fluid. When the pressure wave reaches the upstream of the flow the whole pipeline is filled with fluid with no velocity and with high pressure. The necessary time this can be estimated by the distance that the wave must go (length of the pipe) divided by the speed of the wave. Meanwhile in the tank extreme of the pipe the potential energy of the tank is trying to establish the flow again in the initial direction, which happens just after the pressure wave reach that extreme of the pipe. Then a change in the direction in the pressure wave occurs and this goes through the pipe to the opposite extreme with keeping a constant velocity equal to speed of the sound in the fluid coming back to the normal size of the perimeter in the sections, generating the fluid reach the original velocity but in the opposite direction. That situation persists until the wave reaches the extreme of the pipe with the valve. In that moment the whole pipe is filled with fluid with velocity. However, in the extreme suction takes place. This suction also starts to move immediately in direction to the tank with a constant velocity equal to the speed of the sound as a pressure wave. This motion continues until reach the tank and again due to the hydrostatic pressure imposed by the tank the wave goes back to the valve. The whole time of the pressure wave motion is known a period of the cycle of the process and commonly is used as reference time. The period can be computed as 4 times the length of the pipe divided by the constant velocity of the wave. If the system does not suffer any energy dissipation due to friction or any other source, then this cycle will be repeated identically. However, actual systems do have fraction losses, which implies that the cycle will be repeated until the energy is gone and the system stop, which the characteristics that the pressure level of the wave will be decreased for every instant. If the problem studied involves the opening of the valve instead. The pressure at the valve will decrease and a pressure wave will appear, generating the same phenomenon of motion inside the pipe. Medellín, Colombia WE1-2 August 3-5, 211

3 3. STUDY METHODOLOGY The methodology covers two fundamnetal spects as: the undesrtanding of the governing equations of the phenomenon and the premises used in the developing of the numerical representation of the actual system into the work presented here. 3.1 GOVERNING EQUATIONS The governing equations of the transient phenomenon are the momentum balance and continuity, expressed by eqns 1 and 2. The friction factor is assumed equal to the stationary friction factor, which can be calculated using Colebrook relationship or Swamee relationship (Potter & Wiggert, 26). dv dt 1 p + + g senθ + ρ x f V V 2 D = (1) 1 A da dt 1 dρ V + + ρ dt x = (2) The numerical method used to solve the transient equations takes the variable distance and time as independent variables, as pressure and velocity as dependent variables p = p( x, t) V = V x, t (3) ( ) Introducing the definition of the volumetric elasticity of the fluid as: dp K = (4) dρ / ρ An expression of the velocity of the wave can be deducted (Streeter &Wylie, 1998) 2 K / ρ a = 1+ ( K / E)( D / e) (5) p 2 V L1 = ρ a = t x (6) p 2 V L2 = + ρ a = (7) t x These equations must be solved numerically, generating a solving scheme that can be identified as a construction one-dimensional with timing advance (Streeter &Wylie, 1998), as shown at Figure 2.The margins should be set as shown in the following sections. Medellín, Colombia WE1-3 August 3-5, 211

4 Figure 2 Solving schemes of the transient equations 3.2 PREMISES To solve the governing equations was necessary to assume some conditions shown as follows: The preferential direction of the motion of the flow is along the centre axis of the pipe. No flow in the transversal section is allowed. The friction coefficient is estimated as steady state condition for each time. The pipe is fully occupied by the liquid. The pressure level can not achieve the vapour pressure value to avoid the presence of vapour phase inside the pipes. The propagation of the pressure waves is assumed constant. The valve cure must be given by the user to be included in the calculation. The valve only allows the flow of fluid on a direction. The actual conditions presented as limit of the pipe segments are pumps, valves, tanks and others. In all cases, the idea is represent the condition through their mathematical expressions. 4. CASES OF STUDY The virtual lab is proposed to cover different conditions of simulations: Tank connected to rapid closing valves Tank connected to slow closing valves Tank connected to slow-rapid closing valves with a chimney Pumps connected to a tank with valves 5. PROGRAM STRUCTURE The program structure is a lineal structure as shown by Figure 3, basically it contains a module to introduce the required data and the calculation are done in internal part of the program, giving as result of the simulations a series of graphs, such as: pressure variations in time for particular positions, pressure variations along the pipe for particular time and velocity variations pressure in time for particular positions Medellín, Colombia WE1-4 August 3-5, 211

5 Figure 3. Schematic representation virtual lab functioning 6. RESULTS AND ANALYSIS Following a series of results obtained for a schematic system showed in Figure 4, under the conditions of different closing times and different valve behaviour (exponential and linear). Each position identifies as L/X (,.25,.5,.75 and 1) represent a virtual pressure measurement instrument installed in the system. Figure 4. Schematic representation virtual lab functioning There are many different valves types with distinct work range, closing times, behaviors and functionalities. In this virtual lab two parameters are tested. Closing time and closing behaviour can be changed or modified by the user and then, they can observe how those modifications can inside under the pipe system transient behaviour. Figure 5 shows two different valves. The left side shows a valve with exponential closing behaviour meanwhile the right side shows a valve with linear closing behaviour. Note that the total closing time is an independent variable and it can changes for both types of valves. Medellín, Colombia WE1-5 August 3-5, 211

6 ,7,7,6,6,5,5,4,4,3,3,2,2,1,1 -, , Figure 5. Schematic representation of valve closing behaviour 18, 18, 16, 16, 14, 14, 12, 12, 1, 1, 8, 8, 6, 6, 4, 4, 2, 2,, , ,8,8,6,6,4 Velocidad (m/s),2 Velocidad (m/s),4, ,2 L/x= L/x=,25 -,4 L/x=,5 L/x=,75 -,2 -,6 Tiempo (s) L/x=1 Tiempos de referencia (L/a) -,4 Tiempo (s) Figure 6. Schematic representation virtual lab results From Figure 6, it is clear that the closing time inside primarily under the amplitude of the pressure wav generated within the pipe. Following the theory that indicates for an instantaneous closing the pressure reaches its maximum value calculated by Jowkosky (Streeter &Wylie, 1998), as the maximum theoretical level using for design, however, the actual limit does not correspond to that limits due to the closing time is always larger that cero, so, Medellín, Colombia WE1-6 August 3-5, 211

7 an instantaneous closing time is a no realistic. Consequently, the calculated value will assure actual information for design purposes. Figure 6 also the transient behaviour of the system in terms of the velocity inside of the pipe. The velocity variations correspond for each instant to the energy conservation principle. So, different level of pressure wave will produce different level of internal velocities. 25, 2, 15, L/x= L/x=,25 1, L/x=,5 L/x=,75 L/x=1 Tiempos de referencia,7 5,,6,5,4,3,2, ,1, -5, Figure 7. Schematic representation virtual lab results for smaller closing time When compared results showed in Figure 7 with result showed in Figure 6 it is clear that the pressure wave amplitude increases for the smaller closing tome, as well as, the registration wave in time suggests that for smaller closing time smaller time steps could be required, so the time step should be base on the spacing and the closing time variable. Presión (Pa) 18, 16, 14, 12, 1, 8, 6, Tiempo = s Tiempo = 4 s Tiempo = 8 s Tiempo = 12 s Tiempo = 16 s Tiempo = 2 s Tiempo = 24 s 4, Tiempo = 28 s 2, Tiempo = 32 s, L/x= L/x=,25 L/x=,5 L/x=,75 L/x=1 Punto sobre la tubería Tiempo = 36 s Tiempo = 4 s Figure 8. Pressure variations along the pipe line and the time It is also possible to observe the pressure behaviour thought the time for the whole length of the pipe studied, which corresponds the global energy distribution along the pipe. Figure 8 contains pressure distributions for 11 Medellín, Colombia WE1-7 August 3-5, 211

8 different times. Note that the line for t = s corresponds to the pressure level calculated by Bernoulli, which means that this pressure is the pressure for stationary condition. Apart from the graphs it is possible obtained a complete file while the variables shown plus extra information as for example friction factors. 7. CONCLUSIONS A virtual lab allows the student to established important design parameters of pipe system as closing times according to avoid water hammer presence, as well as, it allows to understand the influences of each variables as diameters, lengths, material roughness, pumps locations and others. For instance it was shown that for shorter closing time pressure increases and for lineal closing behaviour the system response keeps the same level of pressure, however the transient behaviour changes. Programming the numerical methods to solve engineering problems is a powerful toll at the reach level of student in order to understand basic principles of fluid dynamics and other concepts in other areas. 8. ACKNOWLEDGES To the Fluid Mechanics Laboratory of the Simon Bolivar University for support this work with its installations and computing room. REFERENCES Duro Natividad, Héctor Vargas, Raquel Dormido, Sebastián Dormido, José Sánchez. (25). El sistema de tres tanques: un laboratorio virtual y remoto usando Easy Java Simulations. Universidad Nacional de Educación a Distancia. Madrid. España. Escolá Alba, Arnau Dória-Cerezo & Ramón Costa. (27).Laboratorio virtual para la difusión de los sistemas de gestión energética. El caso del sistema de transporte metropolitano. Institut d Organització i Control de Sistemes industrials (IOC). Universitat Polit`ecnica de Catalunya (UPC). Barcelona Franco, A. (23). Internet en la enseñanza y el aprendizaje de la Física. Revista Española de Física, 17 (5), Jerez Mayorga César Augusto. (28). Laboratorio virtual para el análisis predictivo de fallas en motores de inducción de baja potencia. Universidad de la salle. Facultad de Ingeniería Eléctrica. Bogota. Colombia Potter Merle and David C. Wiggert. (26).Mecánica de los fluidos. Tercera Edición. Prentice Hall. México. Rahman S. U, N. M. Tukur and I. A. Khan. (1992). PC-Based Teaching Tools for Fluid Mechanics. Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran-31261, Kingdom of Saudi Arabia. Streeter Victor y E Benjamin Wylie. (1998). Mecánica de los fluidos. Octava Edición. McGraw Hill. México. Authorization and Disclaimer Authors authorize LACCEI to publish the paper in the conference proceedings. Neither LACCEI nor the editors are responsible either for the content or for the implications of what is expressed in the paper. Medellín, Colombia WE1-8 August 3-5, 211