fluid_mechanics

The flow parameter commonly used for compressors is based on the following dimensionless
grouping from dimensional analysis
Rm # 1kRT 01
D 2 p 01
where R is the gas constant, m # the mass flowrate, k the specific heat ratio, T 01 the stagnation temperature
at the compressor inlet, D a characteristic length, and p 01 the stagnation pressure at the
compressor inlet.
To account for variations in test conditions, the following strategy is employed. We set
where the subscript “test” refers to a specific test condition and “std” refers to the standard atmosphere
1 p 0 14.7 psia, T 0 518.7 °R2 condition. When we consider a given compressor operating
on a given working fluid 1so that R, k, and D are constant2, the above equation reduces to
m # std m# test1T 01 testT 0 std
(12.54)
p 01 testp 0 std
In essence, m # std is the compressor-test mass flowrate “corrected” to the standard atmosphere inlet
condition. The corrected compressor mass flowrate, is used instead of flow coefficient. Often,
m # m # std,
std is divided by A, the frontal area of the compressor flow path.
While for pumps, blowers, and fans, rotor speed was accounted for in the flow coefficient,
it is not in the corrected mass flowrate derived above. Thus, for compressors, rotor speed
needs to be accounted for with an additional group. This dimensionless group is
For the same compressor operating on the same gas, we eliminate D, k and R and, as with corrected
mass flowrate, obtain a corrected speed, N std , where
N std
12.9 Compressible Flow Turbomachines 689
a Rm# 1kRT 01
a Rm# 1kRT 01
D 2 p 01
btest D 2 p 01
bstd
ND
1kRT 01
N
1T 01T std
(12.55)
Often, the percentage of the corrected speed design value is used.
An example of how compressor performance data are typically summarized is shown in
Fig. 12.37.
A gas turbine engine
generally consists
of a compressor,
a combustor,
and a turbine.
12.9.2 Compressible Flow Turbines
Turbines that use a gas or vapor as the working fluid are in many respects similar to hydraulic
turbines 1see Section 12.82. Compressible flow turbines may be impulse or reaction turbines, and
mixed-, radial-, or axial-flow turbines. The fact that the gas may expand 1compressible flow2 in
coursing through the turbine can introduce some important phenomena that do not occur in hydraulic
turbines. 1Note: It is tempting to label turbines that use a gas as the working fluid as gas
turbines. However, the terminology “gas turbine” is commonly used to denote a gas turbine engine,
as employed, for example, for aircraft propulsion or stationary power generation. As shown
in Fig. 12.36, these engines typically contain a compressor, combustion chamber, and turbine.2
Although for compressible flow turbines the axial-flow type is common, the radial-inflow type
is also used for various purposes. As shown in Fig. 12.33, the turbine that drives the typical automobile
turbocharger compressor is a radial-inflow type. The main advantages of the radial-inflow
turbine are: 112 It is robust and durable, 122 it is axially compact, and 132 it can be relatively inexpensive.
A radial-flow turbine usually has a lower efficiency than an axial-flow turbine, but lower initial
costs may be the compelling incentive in choosing a radial-flow turbine over an axial-flow one.
Axial-flow turbines are widely used compressible flow turbines. Steam engines used in electrical
generating plants and marine propulsion and the turbines used in gas turbine engines are