Tutorial. BOSfluids. Water hammer (part 3) Dynamic Analysis using Caesar II

Transcription

1 BOSfluids Tutorial Water hammer (part 3) Dynamic Analysis using Caesar II 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. The third part of the tutorial describes how unbalanced forces can be exported by BOSfluids and imported in the pipe stress analysis program Caesar II to perform a dynamic stress 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. The 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 this third part of the tutorial, which describes how to export a piping model and unbalanced force results to CAESAR II. Figure 1 3-D model of piping system Typically a thorough investigation of a piping system does not only require a fluid flow analysis, as performed in BOSfluids, but also a static and dynamic stress analysis. To prevent the need to model the same piping system twice, BOSfluids allows the import and export of the complete piping system. Also the results from the fluid flow analysis can be exported. This final part of the Water Hammer tutorial shows how to import a BOSfluids model into the pipe stress analysis package CAESAR II and how the unbalanced force results of a BOSfluids flow analysis can be used in CAESAR II to perform a dynamic stress analysis. Copyright Dynaflow Research Group. Page 1 of 14

3 2. MECHANICAL VIBRATIONS IN PIPING SYSTEMS Mechanical vibrations in piping systems can be created through a variety of different excitation mechanisms. The response of the system depends on the mechanical properties, restraints and geometry. Generally, two types of excitation mechanisms are defined; harmonic excitation and a step/shock excitation. Harmonic excitation is a constant periodic force on a system, while shock/step excitation originates from a sudden impulse force applied to a system. The water hammer event described in this tutorial consists of both excitation mechanisms. Initially a large pressure peak is generated followed by a harmonic pressure force due to the reflection of the pressure waves in the closed system. The initial peak provides the largest force and hence a large mechanical response in the system, while the secondary reflections will have a smaller amplitude, but are still able to generate a large mechanical response if the excitation frequency is close to the mechanical natural frequency of the piping system. Typically a dynamic stress analysis is started by investigating the effect of the largest loads on the most flexible section of the system, since it is generally here where the largest displacements and stress concentrations will occur. At locations where the piping system is constraint by supports, it must be made sure that the supports can sustain the maximum loads. The unbalanced forces in the event of a water hammer are generated by pressure waves traveling through the piping system. The pressure waves generate a pressure difference between two elbows in a straight section of pipe and thereby an axial force. The axial force on this pipe section can be calculated by: With the friction force along the pipe wall, the pressure difference between the two elbows and the internal diameter. Page 2 of 14 Copyright Dynaflow Research Group.

4 3. CREATING THE CAESAR II MODEL It is common for piping engineers to construct the piping model first in a pipe stress package like CAESAR II to determine the locations of restraints and to perform code compliance checks. As a second step, a fluid flow analysis is performed to examine the effect fluid dynamics due to valve closures, pump trips etc. In BOSfluids it is possible to import a piping model from a software package such as CAESAR II Importing the BOSfluids model in CAESAR II For the current water hammer tutorial, the piping model has been created in BOSfluids. To obtain the piping model in CEASAR II, the BOSfluids model can be imported in CAESAR II. 1. Within BOSfluids open the water hammer model from the first part of the tutorial. 2. Select File Export. An Export Model window will appear, requesting a File Name and Type. Select the file type Caesar II Neutral File from the drop down menu and click browse. Select the directory where the file will be saved and name it Hammer.cii. Figure 2 Export the BOSfluids model 3. An Export Options window is shown to select which scenario to export. Also the required units and CEASAR II version can be selected. Note that CEASAR II is not backward compatible, so the neutral file should have a file version equal to or lower than the CEASAR II version the user is currently running. 4. Having created the neutral file, open CEASAR II (version 5.3 will be used in this tutorial). The neutral file can be converted to a CAESAR II input file by selecting Tools External Interfaces CAESAR II neutral file from the toolbar. 5. The Neutral File Generator window will appear. Select Convert Neutral file to CAESAR II Input File, browse to the neutral file created in step 3 and click Convert. Copyright Dynaflow Research Group. Page 3 of 14

5 Figure 3 Convert the neutral file to a CAESAR II input file 6. A CAESAR II model file has now been created and can be opened by selecting File Open from the toolbar Completing the CEASAR II model Having imported the BOSfluids model, some additional modeling is required before the model can be run in CAESAR II. The piping layout, node numbering and pipe properties such as diameter and thickness are all imported from BOSfluids. Non-pipe elements, such as the valve, are imported as ridged elements with a weight of 1 N. Structural boundary conditions and restraints and some additional pipe properties should be added. For this model only rest supports are applied, so maximum flexibility is achieved. Complete the model by adding the following parameters. Table 1 Additional model parameters Parameter Pressure Pipe material Description 17.2 barg A106 B Allowable Stress Code B31.3 Valve weight 1000 N Anchor restraint Nodes: 1, 125 Rest support (+Y) Nodes: 5, 26, 40, 50, 55, 60, 65 70, 80, 95, 100, 105 Page 4 of 14 Copyright Dynaflow Research Group.

6 4. DYNAMIC STRESS ANALYSIS When performing a dynamic stress analysis typically two steps are required. The first step is the determination of the systems modal natural frequencies. The second step is the determination of the pipe stresses due to the dynamic loads. But first a static stress analysis has to be performed Static Stress Analysis Before performing a dynamic stress analysis in CAESAR II a static stress analysis has to be performed. Since the dynamic analysis in CAESAR II uses a linear calculation, the status of non-linear effects such as lift off from supports and friction need to be determined from a static stress analysis. The dynamic analysis uses the results from a static load case as equilibrium situation. For example when the pipe experiences a gap with respect to a support for a certain static load case, this support will not be taken into account during the dynamic analysis, when it uses this static load case as base. When the pipe is restraint by the same support for another static load case and this load case would be taken as base, the pipe would be unable to experience lift off from the support during the dynamic analysis. For our current water hammer model we use the sustained static loads as base for our dynamic analysis. Figure 4 Perform a static analysis 4.2. Modal Analysis Once the static analysis has been performed (where the static loads case should not lead to stresses exceeding the allowable), a modal analysis is performed, see Figure 5. During a modal analysis the various natural vibration modes and associated natural frequencies are calculated. We are primarily interested in the vibration modes that could get excited by the unbalanced forces caused by the water hammer. As explained in the first parts of this Copyright Dynaflow Research Group. Page 5 of 14

7 tutorial the highest forces will occur in the longest stretches of piping, so a first investigation should be made for the modes that show a vibration in axial direction for the pipe sections from node 40 to 75 and from node 90 to 110, see Figure 6. Figure 5 Perform a modal analysis Figure 6 Vibration modes of interest When the results of the modal analysis are examined, the second mode shape that is found shows a vibration along the axis in the pipe section from node 40 to 75. The associated natural frequency is 0.69 Hz. Recall that from the results of the BOSfluids analysis (see part 2 of this tutorial) the water hammer caused an initially a large pressure peak followed by a periodic oscillation of the pressure (pressure waves reflecting from both ends of the piping system). The frequency associated with the periodic oscillation was found to be 4.16 Hz, see Figure 7. A quick estimation of the dynamic load factor for the found mode shape can be made by using the following relation: ( ( ) ) ( ) Page 6 of 14 Copyright Dynaflow Research Group.

8 Figure 7 Frequency spectrum of the pressure results at node 50 A conservative assumption where no dampening is assumed (ζ=0), would lead to a dynamic amplification of: ( ( ) ) So the first structural mode of interest would be excited by the periodic part of the fluid dynamics with an amplification of 2.8%. This means no problems are expected for this dynamic interaction. However the excitation of the higher mode shapes is more complex and should not be dismissed so easily. To get a more thorough understanding of the dynamic response of the piping system under the loads of the water hammer, a dynamic analysis using the time history of the unbalanced forces should be performed Time History Analysis To perform a time history analysis the results of the unbalanced loads are imported in CAESAR II using the Export Forces feature in BOSfluids. But first the output range and resolution are redefined Output Range and Temporal Resolution The output range and temporal resolution was already determined in part 1 of the tutorial before performing the dynamic flow analysis, however the dynamic stress analysis might require some adjustments of the analysis parameters. During the fluid flow analysis the temporal resolution was set automatically by BOSfluids. Investigation of the results showed that it was sufficiently small to capture the initial force peak and the following harmonic oscillations, see Figure 8. Copyright Dynaflow Research Group. Page 7 of 14

9 Figure 8 Force results at node 50 The temporal resolutions used by the solver and used for the output are found by opening the Transient Warning & Messages report. The time step used by the solver is found to be ms and the output interval is 6.0 ms. For the dynamic stress analysis, the temporal resolution should be small enough to capture the highest natural frequency of interest. A conservative approximation would be to choose the temporal resolution to be 10% of the time period of the highest frequency. To determine the highest frequency of interest again the dynamic load factor is used. From Figure 9 it can be seen that for frequency ratios below 0.2 the dynamic load factor remains 1.0 (no amplification). Figure 9 Dynamic load factor Page 8 of 14 Copyright Dynaflow Research Group.

10 The highest natural frequency of interest could therefore be estimated by: Using this relation with an excitation frequency of 4.16 Hz, the highest frequency of interest becomes 20.8 Hz. The required output interval to capture this frequency can be estimated by. The output range should be long enough to capture at least 2 periods of the smallest natural frequency of interest. This frequency was found in the modal analysis to be 0.69 Hz. This would mean the output range should be approximately 4 seconds (where an extra 1.2 seconds was taken for the initial transient) Rerun the Simulation and Export the Results from BOSfluids The new parameters for the output range and interval can entered in the analysis settings. Since the valve in the water hammer case closes after 1 second the Output Start Time is taken to be 1 second, the End Time and the Simulation Time are increased to 5 seconds and the output interval is set to seconds, see Figure 10. Figure 10 Analysis settings Copyright Dynaflow Research Group. Page 9 of 14

11 Rerun the simulation in the Run tab. Change to the Results tab and check the output data by re-generating the unbalanced force plot for node 50 as in Figure 8. The start time, end time and time step should be changed according to the new analysis settings. The unbalanced forces can be exported by selecting Tools Export Forces. By selecting File Type : Caesar II, the time history results for each node pair (these were defined in part 1) are stored in separate files, see Figure 11. Figure 11 Export the unbalanced forces CAESAR II will always start its dynamic stress analysis at zero seconds, so when a data file does not start at zero seconds CAESAR II will still perform calculations for the time between zero and the output start time using a zero force input. BOSfluids can shift the output data so the first data point starts at zero seconds by ticking the Start at Zero option, this will reduce computation times during the CAESAR II dynamic analysis. Click Export to generate the data files. Page 10 of 14 Copyright Dynaflow Research Group.

12 The data files consist of simple ascii based text and can be opened by any text editor. Before importing the files in CAESAR II confirm that the correct units are used for the time history results (force in Newton and time in milliseconds) Importing the Data File in CAEAR II When the data files are made, store the data files in the same directory as the CAESAR model. The time history data files can now be imported in CAESAR by selecting Time History from the Analysis Type drop down menu. Multiple data files can be imported and solved in a load case, however the user should be carefully evaluate the sign of the applied forces. The forces on different pipe sections should work against each other in such a way the resulting deformation represents the worst case scenario in terms of resulting stresses. Since the current tutorial is primarily written to provide an example for the import/export of BOSfluids models/results, only one data file is imported in CAESAR II. The other file and the combined case are left for the user to carry out themselves. The unbalanced force results for the pipe section from node 45 to 75 are imported in the CAESAR II dynamic stress module by following the steps below: 1. In the first tab Time History Definitions the time history file is referenced by typing #<file name> in the name field. Delete all default input lines, untick the comment (Cmt) checkbox for the first line and use the input parameters as shown in Figure 12. Figure 12 Time History Definitions 2. Select the Force Sets tab. Add a force set in the X-direction at a node anywhere on the pipe section of interest except for the bend nodes, in this case on Node 50. The magnitude is set at 1.0, since the actual magnitude of the forces is defined by the data file. Define a force set with number 1 as shown in Figure 13. Figure 13 Force Sets Copyright Dynaflow Research Group. Page 11 of 14

13 3. Select the Time History Load Cases tab. This tab links the time history profile set in the first tab with the force set in the second tab. Define one load case as shown in Figure 14. Figure 14 Time history load cases 4. Select the Static/Dynamic Combinations tab. According to the code the dynamic loads (occasional loads) should be combined with the static sustained loads in a combined load case and tested against the allowables. Create one static/dynamic load case combination combining the static sustained load case (S2) with the dynamic time history load case (D1), as shown in Figure 15. Figure 15 Static/Dynamic Combinations 5. Select the Control Parameters tab. Define the following parameters: - Static Load Case for Nonlinear Restraint Status: 2 (the sustained static load case) - Stiffness Factor for Friction: Frequency Cutoff: 20Hz - Time History Time Step: 5ms - Load Duration: 6.5 sec (the total time of the time history 5 sec + one period of the lowest natural frequency 1.5 sec) - Damping ratio: Mass Model: Consistent (gives more accurate results) See also Figure 16. Page 12 of 14 Copyright Dynaflow Research Group.

14 6. Run the dynamic analysis. Figure 16 Control Parameters Results The results of the dynamic analysis show the highest stress, 136MPa occurs at node 90. This stress is still below the allowable (74% of the allowable), see Figure 17. The largest displacements are found in the pipe section where the force was applied, see Figure 18. These large displacements of 212 mm are caused by the lack of horizontal supports. Figure 17 Dynamic Output: Stress report Copyright Dynaflow Research Group. Page 13 of 14

15 Figure 18 Dynamic Output: Displacement report 4.4. Conclusion This concludes the Water Hammer tutorial, where the fluid dynamics and the structural dynamics of a water hammer event on a piping system were investigated. This tutorial is not written with the intention to give a thorough overview of the CAESAR II dynamic module. For a more elaborate overview of all the functions of the CAESAR II dynamic module you are referred to the CAESAR II user manual. For more BOSfluids tutorials you are referred to the BOSfluids website. Page 14 of 14 Copyright Dynaflow Research Group.