Handbook of Turbomachinery Second Edition Revised - Ventech!

Steady-State Stresses and Thermal Growth
Rotor blades, which are subject to centrifugal force, are one of the principal
elements subject to steady-state stresses. The forces exerted by high-pressure
gases are another stress. Centrifugal stresses can usually be readily estimated
when the surfaces of each blade element lie on radial lines. If a blade is only
slightly twisted, this analysis can be extended to shapes in which the center of
gravity of each element lies on a radial line. (Recall that a blade element now
is defined as the shape generated by the intersection of a blade with a conical
surface.) This configuration has allowed conventional one-dimensional
analysis to be used for estimating the stresses. Conventional techniques have
also been used to assess stresses in the supporting disks and to evaluate stress
concentrations at the junctures of blades with the disks. Chapter 3 of Balje
[19] presents representative simplified procedures for estimating some of the
principal steady-state stress in turbomachines. Such methods have been used
in practice, but their success depends on the designer’s experience with
compressors having similar shapes and applications. Factors of safety must
be employed; too small a factor invites trouble, while too large a one
increases the size, weight, and cost of the unit. The pressure ratio and
efficiency of the compressor could be compromised as well. In general, more
sophisticated methods than those just outlined are advised.
Observe also that the temperatures within compressors increase as the
units are accelerated from rest and that this causes the dimensions of each
element to change. The casing and the tips of the rotor blades move radially
outward. Depending on the relative rates of expansion, these two parts
could rub against each other. The heat from friction then causes additional
growth and possible failure. Since the running clearance at the blade tips
must be small in order to avoid unwanted gas flow between blades and
casing, good estimates of the relative expansions are required.
An alternate design uses solid rings, or shrouds, that are placed
around the blade tips to prevent flow over the tips. A labyrinth seal or some
form of face seal then limits the leakage from the high- to the low-pressure
side of the blade row. The danger of catastrophic failure due to rubbing is
thus reduced, but the centrifugal stresses in the blades are increased. Notice
that shrouds can also limit blade vibrations.
The hub also expands radially outward, but the tips of stator blades
move radially inward. Unless sufficient clearance is provided, the stators
and the rotating hub will contact each other and rub. The heat from the
rubbing exacerbates the interference. Shrouds, with seals, are often placed
under stator tips to mitigate this possibility.
In order to cope with the problems associated with twisted blades and
thermal expansions, designers often rely on computer programs such as
Copyright © 2003 Marcel Dekker, Inc.