Dynamic Effects on Piping Systems Due to Harmonic Loads

1. SCOPE ……………………………………………………………2. REFERENCE DOCUMENTS
3. DEFINITIONS
4. GENERAL ……………………………………………………….4.1
Pulsation Loading (Reciprocating Compressors)
4.2 Wind Induced Vibration
4.3
Analysis Methods …………………………………………
4.4 Vibration Control
FIGURE
1 Vortices Shed from a Circular Cylinder ………………………

1. Scope
This standard establishes design requirements for piping systems subject to the dynamic effects of
harmonic loads and supplements the requirements for ASME B31.1, ASME B31.3, ASME B31.4, and
ASME B31.8 codes.
2. Reference Documents
Reference is made in this standard to the following documents. The latest issues, amendments, and
supplements to these documents shall apply unless otherwise indicated.
SABIC Engineering Standards (SES)
P01-E01 Design Conditions and Basis for Pressure Piping
P01-E02 Design of Piping Systems for Stress and Pressure Criteria
P01-E03 Flexibility, Support, and Anchoring of Piping Systems
P01-E07 Piping Loads on Equipment Nozzles
American Society of Mechanical Engineers (ASME)
B16.5 Steel Pipe Flanges, Valves, and Fittings
B31.1 Power Piping
B31.3 Process Piping
B31.4 Pipe Line Transportation System for Liquid Hydrocarbons and Other Liquids
B31.8 Gas Transmission Piping Distribution Piping Systems
American Petroleum Institute (API)
API 618 Reciprocating Compressors for Petroleum, Chemical, and Gas Industry Services
3. Definitions
Harmonic Loading. Applied loading that varies sinusoidally with time, t, and has the form: Fi(cos wt + i sin
wt) or Dj(cos wt + i sin wt)
where:
Fi = the maximum amplitude of the harmonically varying force for node “i” in a piping system,
where “i” goes from one to the total number of nodes where dynamic forces are specified.
Dj = the maximum amplitude of the harmonically varying displacement for node “j” in a piping
system, where “j” goes from one to the total number of nodes where dynamic displacements are
specified.
w = omega, the circular frequency of excitation. Applies to all dynamic forces. Each load case
corresponds to a different value of w. (radians/sec)
t = time.
Solutions to harmonic loading problems are generally expressed as:
x(t) = xo cos(wt+Θ)
where:
xo = Maximum displacement amplitude
w = Excitation frequency
= Phase angle
Natural Circular Frequency (w). The number of oscillations or circular revolutions of the radius of an
auxiliary circle per unit of time. Equal to 2πf. (radians/sec)
Natural Frequency (f). The inverse of the natural period. (cycles/sec) or (HZ).
Natural Period (T). The time required for a structure to go through one cycle of free vibration after the
force causing the motion has been removed or has ceased to vary. (Usually expressed in sec.)

T = 2π/w = 2π√(M/k)
where:
M = Mass of the system.
k = Stiffness of the system.
Owner. SABIC
Phase Angle (Θ). A value which relates the timing of one harmonic load or displacement to the other.
Applicable when more than one harmonic load or harmonic displacement is included in the piping system.
Von Ka′rma′n Vortex Condition. A phenomena occuring in cross flow conditions in which vortices are
shed periodically in the wake of a fluid flowing across a body such as a cylinder. The shedding produces
alternating lift forces normal to the cylinder axis and flow (see attachment 1.)
Vortex Shedding Frequency (ws). the frequency corresponding to the alternating lift forces on a body produced
by
vortices
in a
Von
Ka′rma′n
vortex
condition.
ws = S(V/D)
where:
S = Strouhal Number ≈ 0.19
V = Fluid velocity, (ft/sec)
D = Outside diameter of pipe plus insulation, inches
Wavelength (λ). The distance between regions of a compressed gas or rarefaction of a pulsation; (ft). It is
a function of the speed of sound of the gas and the frequency of the pulsation:
c = fλ
where:
c = Speed of sound in the fluid, ft/sec
f
= frequency, cps
4.General
Various examples of harmonic loading can be found in piping systems, such as fluid pulsation loads due to
piston action in reciprocating compressors and pumps, eccentric loading in rotating equipment, and also
wind induced vibration such as vortex shedding.
4.1 Pulsation Loading (Reciprocating Compressors)
4.1.1 The design approach for pulsation and vibration control in reciprocating compressor piping shall be
specified by the engineering contractor and reviewed by the Owner’s representative.
The design approach may consist of an analog acoustical/mechanical study, a digital
acoustical/mechanical study, or any combination thereof but shall follow the requirements given in API 618
Reciprocating Compressors for Petroleum, Chemical, and Gas Industry Services, Par. 3.9.2.
4.1.2 Pulsation suppression devices shall meet the requirements of API 618 Reciprocating Compressors
for Petroleum, Chemical, and Gas Industry Services, Par. 3.9.3.
4.1.3 Supports for pulsation suppression devices shall meet the requirements of API 618 Reciprocating
Compressors for Petroleum, Chemical, and Gas Industry Services, Par. 3.9.4.
4.1.4 Pulsation generated unbalanced forces shall be evaluated in all piping as well as between the
pulsation dampeners and compressor cylinder in a direction transverse to the cylinder.
Forces shall be limited as follows:

Pulsation Dampeners
: 1000 lbs. (peak to peak) (for freq. <30 hz).*
Piping
: (100 lbs. (peak to peak) X nominal line diameter in inches),
(for freq. < 30 hz).* Maximum = 1000 lbs.
Cylinder to dampener
: Vector sum of the forces between suction and discharge
dampener across cylinder shall be 100 lbs. (peak to peak) X
nominal nozzle diameter in inches Maximum = 1000 lbs.
For frequencies greater than 30 hz, the maximum allowable unbalanced forces for dampeners and piping
shall be:
((30/frequency))1/2
X(100 lbs (peak to peak) X Nominal line diameter or nozzle diameter)
4.1.5 For compressors with horsepower ratings greater than 500 HP per cylinder, compressors located on
platforms or at limited access sites, and compressors with overhead piping near the compressor, pulsation
generated unbalanced forces shall be limited to 250 lbs. maximum peak to peak.
4.1.6 For multiple units installations with common piping, the total of the unbalanced forces generated in
that pipe run by any two units shall be within the guideline established in 4.1.4.
4.2 Wind Induced Vibration
4.2.1 Pipe spans which may be suspected of being susceptible to wind driven vibrations, such as piping
routed down from tall vessels or structures, shall be evaluated for Von Ka′rma′n Vortex conditions.
4.2.2 Piping configurations designed for Von Ka′rma′n Vortex conditions shall not have the first or second
harmonic frequency of the span near the Vortex shedding frequency. This may be expressed arithmetically
as follows:
0.5 > W/Wn > 1.3
where:
W = Vortex Shedding Frequency
Wn = Harmonic frequency of the system
4.2.3 W/Wn shall equal 1.3 at wind velocities below 30 mph in order to avoid high amplitude wind
vibrations.
4.2.4 When it becomes impossible to avoid conditions where W/Wn =1, consideration shall be given to
increasing the natural frequency of the system through the addition of restraints, modification of the pipe
span diameter, or in the case of large free-standing discharge stacks, vortex shedders.
4.3 Analysis Methods
4.3.1 Computerized harmonic analysis runs of piping configurations in high pressure systems (pressures
in excess of that allowed by ASME B16.5 PN 420 (Class 2500# rating)) shall incorporate hold down clamp
stiffness values when modelling restraints.
4.3.2 Dynamic stresses calculated by harmonic analysis shall be compared to one half the ultimate fatigue
strength of the piping material. The maximum allowable alternating stress intensity of the material @
1,000,000 cycles shall be reduced by an appropriate fatigue strength reduction factor as follows:
Sdyn < Salt/(SCF)(ERF)
where:
Sdyn = Calculated unintensified dynamic stress in the pipe, psi
Salt = Maximum allowable alternating stress intensity @ 106 cycles, psi
SCF = Stress concentration factor = 4
ERF = Endurance reduction factor = 2
For carbon steel pipe:

Sdyn < 26,000/(4)(2) < 3,250 psi peak to peak
4.4 Vibration Control
4.4.1 For piping systems subject to pulsation loading, all predicted mechanical natural frequencies are to
be a minimum of 30 HZ; or greater than 2.4 times the running speed of the rotating equipment for
double-acting systems and 1.2 times the running speed for single-acting systems.
4.4.2 The following procedure should be utilized in analyzing low frequency field vibrations due to either
fluid pulsations or rotating equipment imbalances:
a. Quantifiable displacements, overstressed points, etc. shall be identified for use in developing the
dynamic model
b. A model of the piping system shall be constructed, with emphasis on accurately modeling mass
components such as flange pairs, valve operators, etc. with additional node points included between
span supports and at the near and far points of bends
c. The frequency, magnitude, location, and direction of the dynamic load shall be estimated
d. The dynamic load shall be modeled in several harmonic analyses using harmonic forces for
pulsation or displacements for vibration. Harmonic resonances shall be identified and the analysis
results shall be compared to field data through an iterative process until agreement is reached
between the mathematical model and actual field measurements
e. The cyclic harmonic stresses from the mathematical run shall be compared to the endurance limit
of the piping material for the purposes of determining if a problem exists with the piping system
f.
If the results in e) indicate a problem exists with the piping system, a modal extraction of the
piping system shall be performed to isolate the mode or modes having a natural frequency close to
the forcing frequency of the applied load
g. The isolated mode in f) shall be eliminated by adding a restraint in the direction of the mode
shape, by adjusting the mass distribution of the system such as relocating valves, flanges, changing
the pipe size, etc., or by altering the forcing frequency of the load
h. The final model with the removed isolated mode shall be reanalyzed statically to determine the
effects of any modifications on the static load cases
4.4.3 Low frequency vibration in piping systems shall be reduced by supporting piping near bends and at
all heavy masses and piping discontinuities.
4.4.4 Vibrations in small bore vents, drains, bypasses, and instrument piping shall be corrected by bracing
the masses (valves, flanges, etc.) to the main pipe.
4.4.5 Supports and structures used to restrain piping vibration must be capable of enduring the continuous
vibration loadings that they are installed to restrain.
4.4.6 The use of U-bolts to restrain piping subject to pulsation loading from reciprocating compressors and
pumps shall be avoided. The use of hold down pipe clamps incorporating belleville washers with a suitable
vibration damping isolating material such as a neoprene fabric pad is preferred. For hot piping
(250 – 350 °F), a neoprene fabric pad with a Teflon belt is recommended. Clamp assemblies shall be
designed to permit axial thermal movement of the pipe without imposing large frictional loads on the piping
system.

Figure 1
Vortices Shed from a Circular Cylinder