Page 164 - Handbook of Energy Engineering Calculations

FIGURE 18 Economic study plots for life-cycle costs. (Power.)

The curves shown depict the variation in production cost of electricity as a
function of initial investment cost for various levels of thermal efficiency,
loan repayment period, gas-turbine availability, and fuel cost. Each of these
factors is an element in the life-cycle cost model presented here.

This procedure is the work of R. B. Spector, General Electric Co., as
reported in Power magazine.

HRSG TUBE-BUNDLE VIBRATION AND NOISE ANALYSIS

A tubular air heater 11.7 ft (3.57 m) wide, 12.5 ft (3.81 m) deep, and 13.5 ft
(4.11 m) high is used in a boiler plant. Carbon steel tubes 2 in (5.08 cm) in
outer diameter and 0.08 in (0.20 cm) thick are used in inline fashion with a
traverse pitch of 3.5 in (8.89 cm) and a longitudinal pitch of 3 in (7.62 m).

There are 40 tubes wide and 60 tubes deep in the heater; 300,000 lb (136,200
kg) of air flows across the tubes at an average temperature of 219°F
(103.9°C). The tubes are fixed at both ends. Tube mass per unit length = 1.67

lb/ft (2.49 kg/m). Check this air heater for possible tube vibration problems.

Calculation Procedure:

1. Determine the mode of vibration for the tube bundle
Whenever a fluid flows across a tube bundle such as boiler tubes in an
evaporator, economizer, HRSG, superheater, or air heater, vortices are
formed and shed in the wake beyond the tubes. This shedding on alternate

sides of the tubes causes a harmonically varying force on the tubes
perpendicular to the normal flow of the fluid. It is a self-excited vibration. If
the frequency of the Von Karman vortices, as they are termed, coincides with

the natural frequency of vibration of the tubes, then resonance occurs and the
tubes vibrate, leading to possible damage of the tubes.
Vortex shedding is most prevalent in the range of Reynolds numbers from
300 to 200,000, the range in which most boilers operate. Another problem
encountered with vortex shedding is acoustic vibration, which is normal to

both the fluid flow and tube length observed in only gases and vapors. This