Tutorial. BOSfluids. Water hammer (part 1) Modeling

Transcription

1 BOSfluids Tutorial Water hammer (part 1) Modeling The Water hammer tutorial is a 3 part tutorial describing the phenomena of water hammer in a piping system and how BOSfluids can be used to examine the resulting pressure spike and unbalanced forces in the system. This first part describes the creation of the BOSfluids model and the set-up of the analysis.

2 1. INTRODUCTION A piping system, illustrated in Figure 1, is subject to a sudden valve closure at the pump suction end, resulting in a water hammer. BOSfluids will be used to calculate the pressure rise and the unbalanced forces that result from the closure. The unbalanced force time history results can be exported to a data file, which can be imported by a pipe stress analysis software package such as CAESAR II. This first part of the Water Hammer tutorial describes the model construction, some of the theory of pressure waves and the set-up of the analysis. The second part describes the postprocessing of results and the available output options in BOSfluids. The dynamic analysis of the water hammer event is completed in the third part of this tutorial, which describes how to export a piping model and unbalanced force results to CAESAR II. This program can be used to perform a dynamic stress analysis, to determine the effect of the water hammer on the structural side of the piping system. 2. BUILDING THE MODEL 2.1. Creating the Piping Model Start BOSfluids and create a new model with the filename Hammer, selecting the units Metric (mm). Using the information from Figure 1 and Table 1, define all the piping and valve elements to create the piping system. Figure 1 3-D model of piping system Copyright Dynaflow Research Group. Page 1 of 9

3 Table 1 Element parameters Length(mm) Element X-Dim Y-Dim Z-Dim Description Valve (name: valve1) See note Bend at node Bend at node Bend at node 30 and Bend at node Bend at node Bend at node 85 and Bend at node Note: Specify the transient valve to be open in steady state action and closing in 0.4 seconds in the Valve Actions menu. Starting from 100% at 1.0 sec to fully closed (0% open) at 1.4 sec. Page 2 of 9 Copyright Dynaflow Research Group.

4 2.2. Boundary Condition Theory There are two boundary conditions in this model that need to be defined. One is at the pump suction (node 1). The second boundary condition is at the supply tank (node 125). The boundary condition at the supply tank will reflect the pressure waves coming from the closed valve. How the pressure wave is reflected will affect the solution, so this boundary condition should be modeled correctly. Figure 2 Boundary conditions of hammer model An open ended boundary condition is one where the flow velocity at the boundary is variable. A closed boundary exists where the flow velocity is constant. At these points, incoming pressure waves are reflected just like the system end was closed. So at a pipe end cap, or at a closed valve, where the flow velocity is zero, the system will see a closed boundary condition. For the piping system above, where water is pumped from a supply tank, node 125 will be at an open end. At this location the pressure will be assumed to stay constant. The closed valve at node 5 will act as a closed boundary. So the system will behave like a closed-open system whose natural period is 4L/c where L is the length from node 5 to node 125, and c is the speed of sound in the fluid. Reflections from a closed end pipe will cause a pressure maximum and a corresponding velocity minimum. Closed-closed systems and open-open systems will have a fundamental natural period of 2L/c. This relationship is demonstrated in Figure 3. Figure 3 The natural period of a pressure wave in a pipe with different boundary conditions Copyright Dynaflow Research Group. Page 3 of 9

5 When a frequency analysis is performed for the system, it is expected that the fundamental period displayed will be 4L/c where L is the distance from node 5 to node 125. Note that the actual wave front is shown as a sloped black line in Figure 2 above. Actual wave fronts can be quite long as the total extent of a valve closure wave front equals, where is the valve closure time. If the speed of sound, c, in the system is equal to 1373 m/s, and the valve closure is 0.4 seconds, then the wave front length will be = 549 m, which is longer than the total system length! (The actual wave front length will be some fraction of this distance since the valve closure is not typically a linear function through the closure time duration). With the total system length equaling 83 meters, and the characteristic time scale equal to 2L/c, the reflected wave already returns to the valve and begins cancelling the source before the valve is fully closed. The distance between an elbow pair would have to be equal to or longer than 549 meters to develop the full unbalanced pressure thrust load due to the water hammer. Since the longest distance between elbows in the model is only a fraction of this length, the maximum magnitude of the unbalanced water hammer load will be smaller than that predicted by the famous Joukowski equation: Water hammer and steam hammer waves reflect from both closed and open ends, as well as from changes in diameter. Only five reflections are needed to produce a resonant level response in an undamped piping system. This means that even low magnitude pressure waves can produce large displacements if the characteristic frequency of the fluid dynamics corresponds to a mechanical natural frequency of the system. It is for this reason that some systems are particularly susceptible to acoustic excitation: 1) Hot pipework supported by springs often have low natural frequencies. 2) Any long runs of pipe that is hanger supported typically will often not have inherent horizontal restraint. 3) Any system that is exposed to flow perturbations: Systems attached to reciprocating equipment Systems where valves open or close quickly Systems where boiling or chemical reactions occur Systems containing two phase flow Defining the Boundary Conditions As stated in the previous section, two pressure boundary conditions need to be defined in the model, the pump suction and source pressure. Boundary conditions are defined in the Page 4 of 9 Copyright Dynaflow Research Group.

6 sub-tab BCs and Nodes. The specified pressures are fixed pressure boundary conditions and the values are given in Figure 2 and tabulated below. Table 2 Node boundary conditions Node Boundary Condition Value 1 Fixed Pressure P = 16.0 bar 125 Fixed Pressure P = 17.2 bar Go to the BCs and Nodes tab and select Node Group All, to get an overview of all Nodes. Select node 1, and change the Node Type from Simple to Fixed Pressure from the drop-down menu and enter the pressure value. Repeat this for node Unbalanced Forces When a pressure wave runs over a long straight section of pipe with an elbow at each end, there is a difference in pressure at the first elbow with respect to the second elbow. The first elbow already experiences an elevated pressure due to the water hammer event, while the pressure at the second elbow is still at the steady state operating conditions. Consequently, the pressure force on the first elbow is different from the one on the second elbow; hence an overall unbalanced force between the elbow pair. The unbalanced forces that act on the piping system due to the water hammer can interact with the natural mechanical vibration of the system, producing large displacement and stress, leading to pipe rupture or damage to pipe fixtures. Therefore the mechanical vibrations of the piping system need to be examined whenever a large pressure wave or slug is sent through the piping system. Preventing large displacements and stress in the piping system due to water hammer event, requires correct and adequate restraints in the piping system. Users often begin a dynamic mechanical study of a piping system by investigating the effect of the largest water hammer loads on the most flexible axial portion of the system. It is generally here where the largest displacement and stress concentration problems are seen. If the system is restrained, then the user must be sure that the supports providing the rigidity can sustain the maximum value of the dynamic loading. The longest axial sections in the water hammer model are from node 45 to 75 and 90 to 110. BOSfluids is used to determine the magnitude and transient force profile for these two sections. The results are then exported in a data file so they can be imported into CAESAR II, to determine the fluid dynamic loads on the supports. Copyright Dynaflow Research Group. Page 5 of 9

7 3. SETTING UP THE ANALYSIS The analysis is set-up in the sub-tab Analysis. The two main analysis types that are available are a Steady State and a Transient analysis. Since this tutorial deals with a water hammer event due to a valve closure, the results vary in time; hence a transient analysis needs to be performed. To perform a transient analysis, select Analysis Type Transient. Note that a transient analysis usually starts from a steady state. So when a transient analysis is performed BOSfluids first starts with the computation of the steady state. The steady state results are available by reviewing the output at time step t = Adjusting the Analysis Parameters There are several characteristics of the analysis that the user may wish to control. These can be found after selecting Analysis Analysis Type: Transient in the tables Transient and Output, see Figure 4. Some of the important parameters are described in this section. Figure 4 Transient and Output configuration options Page 6 of 9 Copyright Dynaflow Research Group.

8 Force Pairs Double click this parameter to specify the elbow node pairs for which the unbalanced force time history needs to be exported. BOSfluids calculates the unbalanced forces for the complete piping system; these results are available in the Results-tab. However only the results for the node pairs explicitly specified in this parameter are available in the export dialog. After the simulation has been performed the results can then be easily exported to a data file Simulation Time If the simulation time is too short, the maximum pressure, velocity, flow or cavity size during the transient may not be calculated. If the total time is too long then runs may take too much disk space and an inordinate amount of time to post-process or view. The longer the total time the more conservative the resulting calculation. The field for Simulation Time on the dynamic input screen can be left blank. In this case BOSfluids will estimate a required total solution time based on its best estimate of the system transient loading and the acoustic response. In many cases the BOSfluids calculated solution times will be satisfactory. In some cases it will not. It is the user s responsibility to review the transient output and assure that a sufficient total calculation time has been used. A patient review of the animated pressure results along with some quick hand calculations should provide an adequate assurance. In the animated results the pressure wave can be seen as it travels through the piping system. The wave should travel from the source of the disturbance to the end of the system and back again at least two or three times. (In some long pipeline systems only a single return of the pressure wave is required.) The total time should also be long enough for any transient disturbance to stop, and the system to have undergone its worst possible pressure loading scenario. As the user gains more experience with transient fluid solutions, a greater confidence will be gained in the comfortable estimation of an optimum total solution time. Longer times are also required if low frequency data is to be obtained from the time history plots Lowest Frequency This is the lowest mechanical natural frequency of the piping system represented by the fluid model. The parameter can be used during the dynamic analysis of the system to determine the total solution. This is an optional input. If entered, this value will be used as part of the criteria employed to establish the total simulation time. One criteria used for determining the Copyright Dynaflow Research Group. Page 7 of 9

9 total simulation time is that the low frequency harmonic responses due to collective wave reflection must be trapped. The low frequency response is often due to the collective harmonic contribution of multiple reflections Output Interval, Start and End Time The input fields under Output are used to control the volume of the output information from the transient solution. Long transient solutions can easily produce many megabytes and in some cases gigabytes of disk file data if some care concerning output selection is not exercised. The Output Interval is the time step used for the output, which is larger than the time step used in the solver. BOSfluids attempts to set the Output Interval for the user automatically based on system parameters and experience. This is a difficult value to establish however without some prior knowledge of system behavior and the user s desired output. If the only information required from the transient solution is the maximum pressure, or the maximum unbalanced load then the Output Interval can be any value, because the maximum pressure and maximum unbalanced loads for all points in the system are trapped during each time step. If the user wants an accurate depiction of the pressure or load time history then a suitable Output Interval must be used. Accurate time histories are needed when the time history data is to be used in a subsequent mechanical load analysis of the system, or if a frequency decomposition of the time waveform is needed. BOSfluids estimates the Output Interval based on an approximated fundamental acoustic mode, and several experience factors. If the force vs. time function that is produced from BOSfluids is to be used in a CAESAR II analysis then the Output Interval should be set sufficiently small to capture the oscillations with the highest mechanical natural frequency of interest. The user may also specify a starting and stopping time following the Output Interval entered through Output Start and Output End. These input fields tell BOSfluids when to start and stop writing time data to the output data file. This start-stop option for writing time history data is used when the transient phenomena of interest occurs several seconds or minutes into the simulation. An example where this option could be used is when vapor columns form over pipe bridges. In this case it may take several minutes for the vapor column to form, and then only a few more seconds for the bubble to collapse. There is no need to store the solution before the bubble forms. The only interesting part of the simulation occurs when the high pressure spike appears on collapse of the vapor column. The Start and End time can be used to restrict the output to only the time period of interest. The output contains only results for the time window specified. Specifying these parameters is therefore also useful when a start-up transient must be allowed to die-out before the real transient of interest is started. Page 8 of 9 Copyright Dynaflow Research Group.

10 3.2. Defining the Output Parameters for the Hammer Model For the hammer model, a transient analysis is performed to determine the effect of the water hammer. Select Water as the fluid type and define the Simulation Time to 4 seconds, see Figure 4. Since we are interested in exporting the unbalanced forces, we need to define the node pairs of interest. Double click the Force Pair input field and the Force Pairs window appears. In the table, enter the nodes for which the unbalanced force will be calculated, these should be bends. BOSfluids automatically checks whether there is a bend in between the two node pairs entered and will display an error if this is the case, since unbalanced forces should only be calculated for straight sections. Figure 5 Force Pairs window Enter node 45 to 75 and 90 to 110 as displayed in Figure 5. All other analysis settings can be left as default Starting the Simulation All analysis parameters are set and the simulation can be started. Go to the Run tab and click the Run button. (Note that there is only 1 scenario, namely the main model, shown in Scenarios. This is automatically selected. If more scenarios are available, the user can select which scenario to simulate). While the analysis is performed, errors and warnings are displayed in the Messages window. After successful completion of the analysis run, the scenario Main will appear in the list Completed. Proceed to part 2 of the tutorial for the post-processing of the results. Copyright Dynaflow Research Group. Page 9 of 9