**Dynamic Analysis of
Piping System:**

**Overview of Dynamic Analysis of Piping System:**

- Dynamic analysis of piping system– Definition
- Comparison of static analysis & dynamic analysis
- Purpose of dynamic analysis
- Basic characteristics of dynamic analysis
- Types of force time profiles
- Types of dynamic analysis

**Definition** of **Dynamic Analysis of Piping System** ** :**

- Dynamic analysis of piping system is a term applied to calculations, which address the dynamic loading resulting from the effects of seismic, equipment vibration, relief valve loads, water hammer loads, etc.,
- Sum of forces and moments in such a system need not be zero & the loads changes quickly with time.

**Comparison of static and dynamic analysis:**

- Static loads are applied slowly in a system, giving it enough time to react & internally distribute the loads. Thus, equilibrium is maintained & the pipe does not move (summation of forces & moments both equal to zero).
- Dynamic load (which changes quickly with time), the system may or may not have enough time for load distribution, resulting in unbalanced forces & moments and, therefore, pipe movement. Since the sum of forces & moments in such a system need not be zero.

**Purpose of dynamic analysis of piping system:**

- To avoid pressure pulsation in compressor system.
- To avoid excessive loads & stresses due to sudden valve closure.
- To avoid excessive low frequency vibration.
- To resist relief valve thrust loads.
- To resist earthquake loads.
- To design a system connected to a table top turbine.
- To design a system for reactions due to slug flow.

**Basic dynamic
characteristics:**

Dynamic motion of any piping system is composed of a time dependant summation of system’s mode shapes.

The mode shape of the cantilever beam are shown below:

A dynamic job must have a preceding static job whenever there are:

- Spring hangers to be designed in the job.
- Single directional restraints in the job.
- Frictional restraints in the job.
- Restraints with gaps in the job.
- Large rotation restraints in the job.

**Consider a simple piping system shown below:**

**Basic Dynamic characteristics:**

- The mode shape and frequency define the system tendency to vibrate.
- The mode shape defines the shape the system would like to take when it vibrates.
- The natural frequency defines the desired speed of vibration.
- For low frequency problems, the user should only consider that there are two degrees of freedom for each non-restrained node.

The absolute magnitude of the displacement in a mode shape computed in an Eigen solution is unknown, only the shape of the mode is known, the max displacement in that mode is indeterminate.

**Types of force vs. Time profile:**

**Random**: The load changes direction and/or magnitude unpredictably with time. (spectrum method)**Harmonic**: With this type of profile, the load changes direction and/or magnitude following a harmonic profile, ranging from its minimum to its maximum over a fixed time. (Harmonic method)**Impulse**: With this type of profile, the load magnitude ramps up from zero to some value, remains relatively constant for a time, and then ramps down to zero again. (time history or force spectrum method)

**Force vs. Time profile:**

**Types of dynamic
analysis:**

**Modal Analysis:**

- Modal analysis simply extracts natural frequency & shapes for system’s modes of vibration.
- A modal extraction performs only an eigen solution.
- The user may process output from a modal analysis in two ways:
- Use of the output processor to review the natural frequencies & mode shapes in report form.
- Animation of the individual mode shape.

**Harmonic Analysis:**

In harmonic analysis the loads or displacements that act on the piping system take a sinusoidal form, i.e.,

F= Fo Sin(wt)

d= do Sin(wt)

Where,

F – Force acting on the piping system as a function of time.

Fo – Amplitude of that force.

w – Frequency of application of the harmonic force.

t – Time, Also:

d – Displacement acting on the piping system as a function of time

do – Amplitude of that displacement

Load may be described by a function of the form:

**F(t)** = A
+ B cos(wt + Q)

- Harmonic analysis is so fast.
- The solutions are directly applicable.
- It is widely used in the area of low frequency field vibrations due either to fluid pulsation, or rotating equipment’s shake.
- A dynamic model that sufficiently correspond to field model is constructed.
- Using best assumption the magnitudes and point of application of dynamic loads are estimated and given to the model.
- The support configuration can be redesigned to eliminate large displacements without rerouting of pipe.
- The restraints limiting dynamic motion should not cause the system to be thermally overstressed.

**Time History Analysis:**

- This is more accurate, more computationally intensive analytical method than response spectrum analysis.
- This is best suited to impulse loadings or other transient loadings where the load time profile

i.e., load variation data w.r.t time at small steps are known.

- It provides a true simulation of the system response throughout the duration of the applied load and subsequent system vibration.
- This method actually calls for solving the dynamic equilibrium equation numerically hence it is time consuming.
- For earthquake time history analysis, values of ground acceleration at time steps (say 0.02sec) have to be given as an input.
- When force vs. time profile is not surely known the solutions won’t be realistic. In those situations, a solution using probabilistic spectrum method is a better option.

**Spectrum Analysis:**

- This method allows an impulse type transient event characterized by a response vs. frequency spectra.
- Each mode of vibration of piping system is related to one response of the spectrum.
- These modal responses are summed together to produce the total system response.
- Ground motion associated with a seismic event is supplied as displacement, velocity or acceleration response spectra which is a uniform inertial loading.
- Another response spectrum application is based on single impulse dynamic loads.
- Relief valve loads, water hammer loads & slug flow loads all cause single impulse dynamic loads.
- For single impulse dynamic loads, dynamic load factor is given instead of velocity or acceleration.
- Usually dynamic load factor of 2 will be given.

**Earthquake analysis:**

- Earthquake loads are defined by defining one or more response spectra and applying them in a specified direction over part or all of the piping system.
- Earthquake produces random ground motions which are characterized by simultaneous but statistically independent horizontal and vertical components.
- Input for this is given from past history.

**Relief valve:**

- Relief valve loadings are due to sudden exhausting of a liquid or a gas.
- More design problems are involved in relieving of gas rather than liquid.
- Two types of destructive dynamic
forces associated with gas relief devices are
- Thrust at valve/atmosphere interface.
- Acoustic shock due to sudden change in fluid moment.

- Thrust at valve/atmosphere interface.

**Water hammer:**

- Water hammer is the effect where mechanical loading occur primarily due to a single traveling pressure wave in a piping system.
- The pressure wave passing through elbow-elbow pairs creates an imbalance force in the system.
- If the distance between the elbows are greater than the water hammer forces will be more.
- Two types of water hammer analysis:
- 3-D water hammer impact & response. (low f)
- 1-D water hammer impact & response. (high f)

- 3-D water hammer impact & response. (low f)

**Slug flow:**

- Slug flow is a flow created by sudden flow of high velocity gas over the surface of a slowly moving fluid in pipe.
- Slugs can cause severe vibrations due to impact on fittings such as elbow and tee connections.
- Slugs can exist due to any one of the following:
- Two-phase flow lines.
- Steam condensate collection in low areas.
- Fire water pumping system.

- Flare system collecting multiple process flows.

- Steam condensate collection in low areas.

- Two-phase flow lines.