Gas Turbine Handbook : Principles and Practices

Gas Turbine Systems Theory 63
rise associated with the radial/centrifugal field, and the term
W 1 2 – W 2 2 /2g c is associated with the relative velocity of the air
entering and exiting the impeller. The ideal head is defined by the
following relationship:
Head ideal = P m = 1 g c
C u2 U 2 – C u1 U 1 (4-23)
Flow Coefficient φ is defined as =
Q
AU (4-24)
where
Q = Cubic Feet per Second (CFS)
A = Ft 2
U = Feet per sec
rewriting this equation φ = 700Q
D 3 N
(4-25)
where D is diameter, and N is rotor speed.
The flow coefficients are used in designing and sizing compressors
and in estimating head and flow changes resulting as a function
of tip speed (independent of compressor size or rpm). Considering a
constant geometry compressor, operating at a constant rpm, tip speed
is also constant. Therefore, any changes in either coefficient will be
directly related to changes in head or flow. Changes in head or flow
under these conditions can result only from dirty or damaged compressor
airfoils (or impellers). This is one of the diagnostic tools used
in defining machine health.
The thermodynamic laws underlying the compression of gases
are the same for all compressors—axial, centrifugal, and displacement.
However, each type exhibits different operating characteristics
(Figure 4-12). Specifically, the constant speed characteristic curve for
compressor pressure ratio relative to flow is flatter for centrifugal
compressors than for axial compressors. Therefore, when the flow
volume is decreased (from the design point) in a centrifugal compressor,
a greater reduction in flow is possible before the surge line is