# Piping Vibration Physical Mechanisms

The root cause for piping vibration can be one or many of the following:

• Mechanically-induced vibration
• Fluctuating Line Pressure (LP)
• Flow-induced by variations in Kinetic Pressure (KP)
• Pulsation-driven, i.e. excited by propagating waves in the pipe system

Figure 1. Pressure, Line Pressure, Pulsation and %LP. %LP matters for the generation of shock waves from wave steepening, a topic treated elsewhere in this Learn More section. (Click on figure to expand)

Mechanically-induced vibration tends to be the largest near a machine or perhaps, externally-induced vibration transmitted e.g. via a pipe support, as shown in Figure 2.

Figure 2. Mechanically-induced vibration e.g. from a support. (Click on figure to expand)

Large variation in LP ( for example from opening or closing a valve) can load the entire pipe system. Such loads, though severe, usually have a rather low cycle count as they are infrequent and more transient than steady state vibration, as seen in Figure 3.

Figure 3. Example of a safety valve release and piping displacement relative to its support. (Click on figure to expand)

Flow variation can cause a large pressure variation. As KP does not propagate other than with the flow velocity, KP tends to be localised. To provide some examples of KP:

• Air (1.2 kg/m3) and an ocean storm with 25 m/s (90 km/h) wind speed => 0.5·1.2·(25)2 = 375 Pa
• Natural gas@235 bar (1.7 kg/m3) and 30 m/s flow velocity => 0.5·1.7·(30)2 = 765 Pa (0.0765 bar)
• Water (1000 kg/m3) and 10 m/s flow velocity => 0.5·1000·(10)2 = 50 000 Pa (0.5 bar)

Concentrated jets can lead to higher KP values, but the above example values fall into the higher range for general flow. As can be seen in Figure 1, Line Pressure and Pulsation tend to cause higher pressure variation.

Pulsation differs from LP and KP in that it transmits via wave propagation inside the pipe medium. Pipe systems tend to have little damping and thus, once generated, pulsation has a tendency to distribute across a system. Pulsation is isolated by large changes in diameter, e.g. those found at tanks or headers, and the wave’s power is divided among branches if there are Tees or manifold connections.

Figure 4. Varying Kinetic Pressure (KP). Changing the flow direction causes a load on the pipe system. (Click on figure to expand)

Figure 5. Loading from Pulsation. Pulsation propagates at the wave speed which often is one or two orders of magnitude larger than the flow speed. (Click on figure to expand)

Often, but not always, pulsation is the main culprit among the above-listed phenomena.

Pulsation, Kinetic Pressure and Line Pressure all transmit load to the pipe structure via pressure loading. Pressure couples with pipe structure and cause vibration as:

• Radial expansion/contraction of the cross section, which causes hoop stress on a pipe section and, via Poisson’s ratio, induces an axial stress component.
• Loading of the pipe cross section when there are cross section modes with an uneven number of half wave lengths. This coupling mechanism can be severe at higher frequencies, but tends to be cancelled out at lower frequencies.
• Unbalanced pipe sections are loaded by an unbalanced force, F = P·A, where P is Pressure (LP, KP and/or Pulsation) and A is the pipe’s internal cross section area. Unbalanced force loads arise at pipe bends and at pipe branches.

Figure 6. Symmetric- and A-symmetric loading of the pipe cross-section. Force cancels in the symmetric condition, shown as blue force arrows, while a net reaction force, shown as a red force arrow, is created in the a-symmetric condition. The larger this net reaction force, the larger the unbalanced area and the stronger the pulsation. (Click on figure to expand)

Figure 7. Unbalanced force loading of the pipe cross-section at the pipe bend. This is the most common source of pressure for vibration coupling, as pipe bends are frequent and involve the largest pipe cross section area and as the reaction force F = Pressure·CrossSectionArea. (Click on figure to expand)

Coupling mechanisms for pressure to vibration are:

• Symmetric loading, which causes hoop stress (radial expansion/contraction) and length direction variation due to Poisson’s ratio coupling.
• Unbalanced force at bends, tees, and appurtenance (Small Bore Fittings).
• Force at pipe ends, e.g. at manifolds.

The strongest excitation for low frequency, i.e. frequencies where the pipe cross section is not bending and pulsation is in plane weaves, can be estimated from simple logical reasoning:

• The weakest direction is when the pipe is loaded when bending at full span length, usually loaded by unbalanced force at the end of its span length.
• The second weakest pressure load direction tends to be where there are large unbalanced areas, e.g. tees, manifold walls and appurtenances.

The above suggests that the two primary low frequency piping excitation mechanisms would be vibration via supports and pressure loading at pipe bends. This holds true with one exception, namely that most piping slides on hard supports.

The pipe and pipe-support may or may not be in mechanical contact. Kinetic Pressure excitation can become large in the case of shifting from one pump to the next or opening/closing valves, as this involves momentarily doubling or stopping the flow in the whole system. This leads to a large momentum change. Mechanical excitation can become strong when the pipe hits the support.

The larger this interface force becomes, the larger is the support-pipe gap and the greater is the momentum change in the system. Such hits can be a substantial overload or crack-initiating scenario. That said, the main culprit with many fatigue load cycles tends to be the pulsation loading.

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