De Equivalent section diameter (pipe or equipment).
fµ Friction factor (viscosity friction).
p Instantaneous pressure.
t Time.
v Instantaneous speed.
Density of fluid.
x Coordinate along axis.
µs Viscosity.
[Z] Pulsation impedance matrix.
{p} Pulsation pressure vector.
{q} Flow vector.
; Variation.
ρ
For this purpose, pulsation impedance (matrix [Z]) is introduced as a complex ratio between pulsation pressures (vector
{p}) and flow (vector {q}) as ( 3) and ( 4) respectively.
Subscripts “u” and “d” are for upstream and downstream of
compressor. All plant facilities and piping can be described
with presented method using matrix transfer. These equations
can be solved for each frequency (harmonic) of pulsation excitations from the machine. Numerical results can be presented and studied in the following two forms: 1. Pulsation
pressure vs. time. 2. Spectra analysis (mainly in the form of
harmonic composition). The first form contains global information and total pulsation effects of all harmonics. The second form presents information about single harmonics.
Pulsation Vessel
Pulsation vessels are the most efficient way to reduce pressure pulsations, shaking forces and vibration. Pulsation vessels
are in the vicinity of the compressor and can be subjected to
high vibrations and shaking forces. API 618 requires top to
bottom flow to cylinders to avoid liquid accumulation. Suction
dampeners are located at the top and need more attention for
support design. The first step is to determine types and sizes
of pulsation vessels. Three common pulsation dampener types
are: 1. Volume bottle without internal. 2. Dampener with
choke tube (one chamber). 3. Dampener with choke tube and
baffle (two chambers).
A good indication for selection of dampener vessel types is
the ratio between frequency of compressor pressure pulsations and natural frequency of the dampener. The most effective arrangement is obtained using vessels without internals
(without choke tube or baffle or similar) and has minimum
pressure drops to avoid possible mechanical problems associated with internals. Generally, low-pass acoustic filters only
may be used when operating conditions are expected to remain unchanged for many years. Low-pass acoustic filter devices may be effective for specific cases but they are less flexible than the bottles without internals to cover operating
condition changes.
For pulsation vessels, a lower length to diameter (L/D) ratio
results in more effective pulsation control effects. However, a
reasonable L/D ratio should be selected for fabrication and
arrangement reasons. Average L/D ratio 3 to 4 is recommended. L/D ratio lower than 5 is necessary to avoid drastically reduced efficiency. Some engineering practices: 1.
Connection: welding neck (WN) (for small connection, integrally forged long welding neck — LWN). 2. All pressure and
integral parts: full penetration welds. 3. For critical applications: nozzle connection with counter suitable for butt weld
and RT/XR test.
The low-cycle fatigue analysis can be carried out following
the procedure described by ASME VIII Division 2 Appendix
5. Adequate stress concentration and safety factors must be
respected (cyclic stress limit can be around 25 Mpa peak
to peak, around eight times less than API cyclic stress limit).
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