Handbook of Turbomachinery Second Edition Revised - Ventech!

Preparation of Maps
Once the losses and energy changes have been established, compressor maps
are conveniently estimated by preparing individual stage curves similar to
those of Fig. 16. Note that the variables selected tend to collapse the curves
for a wide range of rotor speeds into one curve. A set of curves is prepared
for each stage. The abscissa is the flow coefficient: the ratio of the mean axial
component of velocity at the inlet of a stage to a characteristic speed of the
rotor. A diabatic efficiency is the ordinate for one set of curves, and pressure
coefficient is the ordinate for the other. (This coefficient is the ratio of the
useful energy transferred to the gas to the square of a characteristic rotor
speed.)
These curves are created by first selecting the flow coefficients of each
stage being considered. Blade elements for each blade row are then
identified. Allowances for the blockage at the hub and casing are made; then
the gas velocities and incidence angles at the inlet of each element are
determined. Changes in the tangential component of velocity can be
calculated, and the change in enthalpy through a rotor is determined. The
total pressure loss within each blade element is converted into an increase in
entropy. Pressure coefficient and efficiency for each complete stage are then
readily found.
Chapter 10 of NASA SP [1] demonstrates the validity of this
approach. The same reference indicates how these data are used to
synthesize a map for a range of rotating speed and gas flows. A rotor
speed and a gas flow rate at the inlet of the first stage are assumed; the
pressure and temperature changes through the stage are then calculated with
the aid of the estimated stage curves. The flow coefficient of the following
stage is then determined, together with the changes in pressure and
temperature through it. This procedure is repeated for all the stages of the
compressor. The entire routine is also repeated for other gas flow rates and
rotor speeds. This work provides the data necessary to plot the desired map.
Chapter 13 of NASA SP [1] provides a number of examples of this
procedure. Novak [35] contains supplementary information.
Defining the surge point at each speed requires special attention.
Chapter 12 of NASA SP [1] and Bullock et al. [36], Greitzer [37], and
Greitzer [38] present important details about the subject of surging. Note
that surging may occur whenever the pressure ratio being developed at a
fixed rotor speed drops while the flow rate decreases: the slope of the
performance curve for a constant speed is then either positive or
discontinuous. Although the former condition is necessary for surging to
occur, it is not sufficient. The degree to which positive slopes may be
tolerated depends on both the volume and the momentum of the gas within
Copyright © 2003 Marcel Dekker, Inc.