Dynamic Analysis of Piping System

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.

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)

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.