Page 166 - Handbook of Energy Engineering Calculations

FIGURE 19 Strouhl number, S, for inline tube banks. Each curve
represents a different longitudinal pitch/diameter ratio (Chen).

4. Determine the acoustic frequency
As with vortex frequency, we must first determine several variables, namely:
absolute temperature = °R = 219 + 460 = 679°R; sonic velocity, V =
s
0.5
49(679) = 1277 ft/s (389.2 m/s); wave length,λ = 2(w)/n, where w = width
of tube bank, ft (m); n = mode of vibration = 1 for this tube bank; then λ =
2(11.7)/1 = 23.4 ft (7.13 m).
The acoustic frequency, f = (V )/λ, where V = velocity of sound at the gas
a
s
s
0.5
temperature in the duct or shell, ft/s (m/s); V = [(g)(ρ)(RT)] , where R = gas
s
constant = 1546/molecular weight of the gas; T = gas temperature, °R; ρ =
ratio of gas-specific heats, typically 1.4 for common flue gases; the molecular
0.5
weight = 29. Simplifying, we get V = 49(T) , as shown above. Substituting,
s
f = 1277/23.4 = 54.5 cps. For n = 2; f = 54.4(2) = 109 cps. The results for
a
a
Modes 1 and 2 are summarized in the tabulation below.

The tube natural frequency and the vortex shedding frequency are far apart.