WaterHammer CAESER

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.

BOSfluids Water Hammer Part 3

Copyright © Dynaflow Research Group. Page 1 of 14

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 post-

processing 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.


Page 2 of 14 Copyright © Dynaflow Research Group.

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.



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.

3.1. 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 FileExport. 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

ToolsExternal InterfacesCAESAR 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.



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

FileOpen from the toolbar.

3.2. 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 Description

Pressure 17.2 barg

Pipe material 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



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.

4.1. 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



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:

√( ( ) )

( )



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.

4.3. 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.

4.3.1. 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.



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

0.3657 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



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).

4.3.2. 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 0.005 seconds, see Figure 10.

Figure 10 | Analysis settings



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 ToolsExport 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.



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).

4.3.3. 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



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: 1.0

- 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: 0.03

- Mass Model: Consistent (gives more accurate results)

See also Figure 16.



Figure 16 | Control Parameters

6. Run the dynamic analysis.

4.3.4. 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



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.

WaterHammer CAESER

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