Vibration Abatement of Piping Systems

Vibration is a serious risk to piping systems causing fatigue and other issues that could result in unscheduled shutdown, downtime, fires and explosions. Common causes of pipe vibration are fluid/structure interactions, internal (induced by flow) and external (induced by wind) vortex shedding, pressure pulses due to abrupt opening/closing of valves, as well as pulsation in discontinuous flow generating machines such as piston pumps and reciprocating compressors attached to piping systems. In addition to pulsation, discontinuous flow generating machines such as reciprocating compressors generate other dynamic forces including, but not limited to, ‘cylinder gas forces’. Some of these perturbations, e.g., pulsation forces, can be mitigated by fluidic/acoustic solutions such as pulsation dampers. But the mechanical perturbations such as ‘cylinder gas forces’ need to be addressed in mechanical design, with attention to dynamics, of the piping system.

Natural Frequencies and Modes of Vibration

As in other structures, piping systems have the tendency to vibrate at certain frequencies, called natural frequencies with their corresponding associated shapes/patterns, called mode shapes. The natural frequencies and modes depend on the distribution of mass and stiffness of the piping system.

Excessive pipe vibrations are frequently caused by coincidence between the pulsation frequency and the mechanical natural frequency of the piping. It is essential to either avoid this resonance condition or abate resonant vibration by adding damping to the piping system.

When a piping system is excited by a dynamic perturbation with a frequency that coincides with one of its natural frequencies, the system with its low inherent damping undergoes great displacements and stresses. This phenomenon which is known as resonance, causes excessive vibration, even fatigue and subsequently failure, in systems with low mechanical damping.

Flow-induced vibration caused by high flow velocities and turbulence at discontinuities in pipes (branch connections, bends and similar) is a common scenario that could resonate piping systems. In a gas compression plant with a train consisting of a gas turbine operated centrifugal compressor and an after-cooler package, the after-cooler discharge piping was found to vibrate excessively in one direction. The magnitude of vibration was found to increase with mass flow rate delivered by the compressors, and exceeds the plant’s acceptability criteria.

Vibration induced by cylinder gas forces in reciprocating compressors, caused by the oscillatory motion of each cylinder, is another example of perturbations that could resonate piping systems attached to the compressor.

In an applications, two natural gas lines fed by compressors in a power plant exhibited such resonant vibration in all three directions. The measured time and frequency domain acceleration traces of Figure 1 show the extent of vibration measured, in different directions, at one location on the pipe.

 

Figure 1 Time and frequency domain pipe acceleration measured at one location

 

In another application, two 6” piping systems carrying a two-phase solution in a petroleum refinery were subject to flow and process-induced perturbation, so that every 30 seconds or so, a short burst of random force was setting the pipes to vibrate, with most of vibration energy at their first natural frequencies.  Figure 2 shows the time and frequency domain acceleration of the pipe in vertical direction measured at one location on one of the pipes.

Figure 2 Time and frequency domain pipe acceleration measured at one location

Recommendations and Solutions

A common solution to alleviate pipe vibration subject to harmonic perturbation is to create a mismatch between the excitation frequency and the piping natural frequency by either increasing the diameter of the piping and/or more extensive support configuration for the piping. The former solution increases the weight and cost of piping and the latter solution could have adverse impact on thermal stresses. For example, a stiff piping system with many supports (such as U-bolts, clamps, etc.) may stiffen the piping system and increase its natural frequencies but thermal stresses and reaction loads might become too high, exceeding the acceptable limits.
Adding mechanical damping to a piping system is an attractive alternative solution. This can be done by either targeting a single mode of vibration and adding tuned damping to it or incorporating broadband damping which can add damping to multiple modes of vibration. In the following section, tuned mass dampers for providing tuned damping and viscous dampers for providing broadband damping are described and their damping effectiveness are demonstrated, numerically. Moreover, the advantages and disadvantages of each damping solution are presented.

a) TUNED MASS DAMPERS
Tuned mass dampers (TMDs) which are made up of an inertia element (mass) suspended by energy dissipating (damping) and resilient (restoring) elements, are highly effective narrowband vibration treatment devices commonly used for dampening the vibration of a structure at a particular resonant frequency.

Figure 3 Two TMDs installed underneath two 6” pipes

TMDs are appended to the vibrating structure at locations where they can most effectively couple with the target mode(s).   Figure 3 shows two TMDs installed on a pair of piping systems.  One major advantage of TMDs is that they need to be connected to the vibrating structure at one end only and do not need to be anchored to an abutment at their other end.  The free ends of the TMDs depicted in Figure 3 is a testament to this very attractive and desirable feature of TMDs.

b) Viscous and Visco-Elastic Dampers

Viscous dampers are broadband damping devices and do not need to be tuned to a particular resonant frequency.  Viscous dampers are more straightforward and less costly than tuned mass dampers.  Because of their broadband nature, a single viscous damper can add damping to multiple modes of vibration whereas multiple TMDs, each tuned to one natural frequency (normally the first one) of the piping system, are needed to treat multiple modes of vibration.

Contrary to tuned mass dampers which are single-point devices and need to be connected to the vibrating structure at one end only with their other end free, viscous dampers are two point damping devices and need to be attached to the vibrating structure at one end and anchored to a rigid support (abutment) at the other end; note that two point damping devices transmit vibration from the vibrating structure to the support structure.

Viscous and visco-elastic dampers are commonly used for lowering resonant vibration of piping systems. Viscous dampers require rigid abutments (support points) which might not be available.  In the absence of support points, tuned mass dampers can be used to abate the vibration problems in these piping systems.

Damping Effectiveness of TMDs

Figure 4(a)   Schematic of a TMD appended to a structure (piping system)

Figure 4(b)   Frequency response functions of one of the structure without and with TMD

To demonstrate the effectiveness of the tuned damping solution, the 9 Hz mode of vibration of a piping system, with the modal mass of 400 lbs, is modeled using a one degree of freedom mass-spring-damper M1K1C1. A TMD (made up of mass-spring-damper M2K2C2) tuned to the natural frequency of the piping system’s target mode is numerically appended to this model shown in the schematic of Figure 4(a).

Frequency response functions of the structure without (blue trace) and with (red trace) the TMD are shown in Figure 4(b). Comparison of the two frequency response functions of Figure 4(b) clearly shows the effectiveness of the TMD in lowering the magnitude of vibration at the natural frequency of the pipe the TMD is tuned to.

 

Refer to the technical note ‘Vibration Abatement of a Natural Gas Piping System Using Tuned Mass Dampers’ for more on the effectiveness of tuned damping in quieting piping systems’ vibration.

Piping systems possess negligible amount of mechanical damping and as such have the potential to resonate (vibrate excessively) when perturbed by flow turbulences, pressure pulsation or mechanical equipment. Introducing damping into the piping system abates resonant vibration. This can be done by either incorporating viscous dampers or tuned mass dampers into the piping installation. Both devices can effectively add damping to the piping system. Tuned mass dampers offer the added installation advantage of being a single-point device, i.e., they only needs to be attached to the piping system. Viscous dampers, on the other hand, are two-point devices; they need to be attached to the piping system and be anchored to a rigid abutment which may not be available in some applications.