Chemical Engineering April 2019 - 44

TABLE 1. NON-DIMENSIONAL PERFORMANCE PARAMETERS
Specific volume ratio
Flow coefficient
Machine Mach Number
Machine Reynolds Number
Head coefficient
Work input coefficient
vS / vD = D/S
 = Qs / (ND3 )
Mm = U / as
Rem = Ub / s
 = H / U2
μ =  / 
(S,D) - Fluid density at compressor suction, discharge, kg/m3
QS - Volumetric flowrate at compressor suction, m3/s
N - Rotational speed, rad/s
D - First stage impeller/rotor tip diameter, m
U - First stage rotor tip speed, m/s
aS - Fluid speed of sound at compressor suction, m/s
S - Fluid kinematic viscosity at compressor suction, m2/s
b - Characteristic length: passage exit width of first stage impeller for centrifugal
compressors, chord length at tip of first stage rotor blade for axial
compressors, m
H - Head (can be isentropic or polytropic), J/kg
bine-driven compressors, knowing the fuel composition
and flowrate can be used to determine total energy input.
Centrifugal compressors
A centrifugal compressor uses the rotating energy of an
impeller to impart head to a fluid primarily by first accelerating
the fluid, and then converting the kinetic energy into
potential energy by slowing the fluid. The typical internals
of a centrifugal compressor are shown in Figure 2. Fluid
enters the compressor and is directed in the inlet toward
the rotating impeller. The blades on the impeller are designed
to accelerate the fluid either axially or radially. There
can be a potential energy rise due to the impeller blade geometry,
but the majority of energy increase after exiting the
impeller will be primarily kinetic. In order to convert this energy
into a static pressure, the diffuser section will convert
the kinetic energy into static energy by slowing down the
fluid flow before it is directed to the outlet in the collector.
The design of each of these individual components can
have a significant effect on the compressor performance,
and therefore, must be considered carefully for each specific
application. In addition, a centrifugal compressor
can use multiple impellers in many different configurations
to either increase the operating flow or compression
ratio of the whole unit, with each individual impeller
and diffuser sets of the compressor possibly comprising
different designs.
Field performance testing
One of the first things to consider when planning a performance
test of a centrifugal compressor is the placement
Ambient air: patm
Pressure at meter
Q Pm Tm
Flowrate* Temperature
at meter
Sample line/gas
chromatograph*
Speed of rotation
*Flowrate measurement and gas sample may be on suction or discharge side.
Suction side is recommended.
FIGURE 3. The diagram shows the locations of test instrumentation for a centrifugal
compressor [4]
44
Suction
pressure Suction
temperature
Centrifugal
compressor
Ps Ts
Discharge
pressure
Discharge temp
of sensors for gathering the operating conditions of the
system. The ideal layout of measurements is shown in
Figure 3. Included is a flow-measurement device (preferably
on the suction side of the unit), instruments for measuring
temperature and pressure on both the suction and
discharge sides (although discharge temperature is not
necessary), a means for determining gas composition,
a means of measuring the unit rotational speed, and instruments
to measure atmospheric conditions (mostly to
correct gage-pressure measurements to absolute). Specific
locations of the actual sensors should be selected to
avoid errors due to flow distortion from piping, valves or
upstream sensors. Acceptable locations for sensors are
defined in industry standard documents available in the
references section.
From these measurements, and with the aid of an appropriately
selected and agreed upon EOS, performance
parameters of the compressor unit can be generated,
including power, which is shown in Equation (1).
(1)
Assuming isentropic compression, the efficiency of the
unit can be calculated according to Equation (2).
(2)
Where:
ss = s(ps, Ts)
h(p,T) = enthalpy (heat content) of gas
his(pD, ss) - h(ps, Ts) = isentropic enthalpy change of gas
s(p,T) = entropy of gas (a thermodynamic quantity representating
unvailable energy; Necessarily increases with
turbomachinery process due to frictional losses
m
*
compressor = compressor mass flowrate
Along with selecting the specific measurement sensors
and determining their placement, preparation for the field
performance test should also include the following items:
* Defining the operating conditions to be used for the
test points
* Selecting the approach for data reduction and test
uncertainty. The accuracy of calculated compressor
performance depends on measurement uncertainty
in the inlet and exit pressures and temperatures, gas
composition, and mass flowrate. Uncertainties in performance
can range from less than 0.5% in laboratory
tests [6] to 2-3% or more in field measurements [7].
Overall measurement uncertainty depends on a large
number of factors, including sensor accuracy and calibration,
proper probe installation, signal conditioning,
flow non-uniformity or unsteadiness, and heat loss
from the system.
* Specifying the ultimate objective of the test. For example,
in the case of an acceptance test, the field performance
test results will be used as an acceptance
criterion. In cases where the performance test data will
be used for maintenance scheduling, engineers should
specify how the data will be compared to previous
measurements for equipment aging practices.
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