Page 165 - Handbook of Energy Engineering Calculations

occurs when the vortex shedding frequency is close to the acoustic frequency.
Excessive noise is generated, leading to large gas pressure drops and bundle
and casing damage. The starting point in the evaluation for noise and
vibration is the estimation of various frequencies.
Use the listing of C values shown below to determine the mode of

vibration. Note that C is a factor determined by the end conditions of the tube
bundle.

Since the tubes are fixed at both ends, i.e., clamped, select the mode of
vibration as 1, with C = 22.37. For most situations, Mode 1 is the most
important case.

2. Find the natural frequency of the tube bundle
4
4
0.5
2
Use the relation, f = 90 C[d – d ]/(L – M ). Substituting, with C = 22.37,
o
n
i
2
4 0.5
4
0.5
f = (90)(22.37)[2 – 1.84 ] /(13.5 − 1.67 ) = 18.2 cycles per second
n
(cps). In Mode 2, f = 50.2, as C = 61.67.
n
3. Compute the vortex shedding frequency
To compute the vortex shedding frequency we must know several factors, the
first of which is the Strouhl number, S. Using Fig. 19 with a transverse
pitch/diameter of 1.75 and a longitudinal pitch diameter of 1.5, we find S =
3
3
0.33. Then, the air density = 40/(460 − 219) = 0.059 lb/ft (0.95 kg/m ); free
2
2
gas area = 40(3.5 − 2)(13.5/12) = 67.5 ft (6.3 m ); gas velocity, V =
300,000/(67.5)(0.059)(3600) = 21 ft/s (6.4 m/s).
Use the relation, f = 12(S)(V)/d = 12(0.33)(21)/2 = 41.6 cps, where f =
c
c
o
vortex shedding frequency, cps.