Post on 01-Mar-2022
RECONCILING COMPRESSOR PERFORMANCE DIFFERENCES FOR VARYING AMBIENT INLET CONDITIONS
Natalie R. Smith, Reid A. Berdanier, John C. Fabian, Nicole L. Key Purdue University
West Lafayette, Indiana 47907, USA
ABSTRACT Careful experimental measurements can capture small
changes in compressor total pressure ratio that arise with subtle
changes in an experiment’s configuration. Research facilities
that use unconditioned atmospheric air must account for
changes in ambient compressor inlet conditions to establish
repeatable performance maps. A unique dataset from a three-
stage axial compressor has been acquired over the duration of
12 months in the Midwest United States where ambient
conditions change significantly. The trends show a difference
in compressor total pressure ratio measured on a cold day
versus a warm day despite correcting inlet conditions to sea
level standard day. To reconcile these differences, this paper
explores correcting the compressor exit thermodynamic state,
Reynolds number effects, and variations in rotor tip clearance
as a result of differences in thermal growth.
INTRODUCTION Compressor performance testing is required to verify that
performance goals have been achieved in new designs. Often,
the focus of these studies is aimed at quantifying the effects of
small changes between different configurations, whether it is
blade design, surface roughness, inlet distortion, vane clocking,
or rotor tip clearance, repeatable performance with low
measurement uncertainty is required to ensure confidence in
results. When test or research campaigns extend to multiple
seasons through the year, the effects of ambient inlet conditions
can alter the performance of the compressor and cause
repeatability issues. Traditionally, correcting inlet flow to
standard day reference conditions through rotational speed and
mass flow rate has been sufficient to ensure similarity in
compressor performance measured on different days, but as
measurement uncertainties are reduced, this process must be
refined to include higher order effects which are commonly
neglected.
A similarity analysis provides a fundamental approach for
correcting experimental test data to conditions for a “standard
day.” For turbomachinery applications, textbooks and test codes
specify this correction process to include the temperature and
pressure of the working fluid (e.g., Refs. 1 and 2). Several
authors have extended this discussion to include the effects of
humidity in air [3-5]. By these methods, the rotational speed
and mass flow rate are considered to be independent parameters
of a system by proxy of non-dimensional terms which represent
the blade tip Mach number and the geometry of the machine.
This process assumes that matching these independent
parameters will create a machine operating condition that will
reproduce the correct dependent parameters (notably, total
pressure ratio and efficiency).
In an effort to account for non-equivalent fluid properties
between test days, other compressor performance metrics may
be equated for similarity, as presented by the ASME
performance test code (PTC) for compressors and exhausters
[6]. Previous authors, such as Wiesner [7] and Stub et al. [8],
have applied corrections to flow coefficient, head rise
coefficient, and work coefficient. These corrections relate the
test conditions back to reference conditions.
Reynolds number is a similarity parameter from the
Buckingham Pi analysis that has a second order effect (with
respect to flow and speed) on compressor performance. In
many cases, an experimental test facility will be designed to
operate in a flow regime of comparable Reynolds numbers to
its full-scale or full-speed counterpart. However, some inlet
flow conditions may result in operation at transitional Reynolds
numbers. Analyses of Reynolds number effects in compressors
are often linked in theory to fundamental loss coefficients and
the Moody diagram for turbulent flows in rough pipes. In many
cases, the single-stage compressor performance observations
outlined by Carter et al. [9] are used as a benchmark for
Reynolds number variations. Their results are also cited as an
approved method for correcting compressor performance for
Reynolds number changes by the ASME PTC [6].
In centrifugal compressors, Wiesner [7] observed a
decrease in performance variability once a sufficiently large
Reynolds number was achieved. The same study concluded that
the corrections for Reynolds number prescribed by ASME PTC
Proceedings of the ASME 2015 Power Conference POWER2015
June 28-July 2, 2015, San Diego, California
POWER2015-49102
1 Copyright © 2015 by ASME
10 based on Carter et al. [9] may be inappropriate, a conclusion
which was also reached by Strub et al. [8]. Strub et al. observed
that the changes in flow coefficient and work coefficient with
Reynolds number are functions of efficiency changes and are
similar to a small change in operating speed.
For axial compressors, Wassel [10] determined a
correlation for efficiency based on Reynolds number using test
data collected from several multi-stage axial compressors. This
correlation was further verified using data from additional
multi-stage compressors by Schäffler [11] with added
discussion relating to blade surface boundary layer flow
regimes and separation.
Many sources [12,13] state that the Reynolds number
parameter has a second-order effect on machine performance,
similar to the geometric scaling parameters such as the rotor
tip-to-span ratio. It has been known for decades that changes in
rotor tip clearance affects axial compressor performance [14-
18]. Traditionally, these studies are carried out by modifying
hardware to alter the rotor tip clearance, but tip clearance can
also be affected, albeit in a more subtle manner, if there are
different thermal growth rates between the rotor and casing. For
some facilities, changes in ambient temperature can affect
thermal growth and thus, rotor tip clearance. In general, the
small tip clearance changes which occur with thermal growth
differences due to inlet temperature variations are expected to
be small compared to associated experimental uncertainties.
Walsh and Fletcher [12] explain that the mechanical rotational
speed changes necessary to match corrected speed conditions
also affect the amount of blade growth and thus, tip clearance,
but these differences are usually ignored.
Ultimately, a primary goal for experimental research is the
creation of high-quality data sets which can validate and
improve computational models. In the event that measureable
performance changes are observed due to these effects which
are typically considered second-order or negligible, appropriate
steps must be taken to show the reason for their existence and
reduce their potential to adversely affect comparisons between
experiments and computational results. A unique dataset from
a three-stage axial compressor has been acquired over the
duration of 12 months in the Midwest United States where
ambient conditions change significantly. The trends show a
difference in cold day and warm day compressor total pressure
ratio despite correcting inlet conditions to a standard day. To
reconcile these differences, this paper explores correcting the
compressor exit thermodynamic state, Reynolds number
effects, and variations in rotor tip clearance as a result of
differences in thermal growth.
NOMENCLATURE c chord
γ ratio of specific heats
h enthalpy
N rotational speed
P pressure
ρ density
R gas constant
Re Reynolds number
T temperature
U wheel speed
v absolute velocity
w relative velocity
Subscripts
blade condition for the blade
c corrected condition
i inlet
e exit
machine condition for the compressor
o total conditions
ref reference conditions
t rotor tip
test test conditions
0-9 axial measurement planes
Abbreviations RH relative humidity
TC tip clearance
TPR total pressure ratio
TTR total temperature ratio
ANALYTICAL APPROACH To study the effects of higher order similarity parameters
on compressor performance, exit conditions will be corrected to
standard day inlet conditions for density and work coefficient.
Additionally, the potential for Reynolds number effects will be
examined. This section outlines the analysis used for the
density and work coefficient correction, Reynolds number
accounting, and the calculation of thermodynamic properties in
this study. All reference conditions assume dry air with the
following properties:
𝜌𝑜,𝑟𝑒𝑓 =𝑃𝑜,𝑟𝑒𝑓
𝑅𝑟𝑒𝑓𝑇𝑜,𝑟𝑒𝑓
𝑃𝑜,𝑟𝑒𝑓 = 1 atm = 14.7 psi
𝑇𝑜,𝑟𝑒𝑓 = 518.67 oR =288.15K
𝛾𝑟𝑒𝑓 = 1.4
𝑅𝑟𝑒𝑓 = 53.36ft lbf
lbm oR= 287.058
J
kg K .
(1)
A. Calculation of Thermodynamic Properties Air composition varies geographically, particularly with
variations in carbon dioxide levels found in different regions.
For the purpose of this paper, Table 1 summarizes the air
mixture composition that will be used in all calculations.
Different amounts of water content are added to this air mixture
to create a humid air mixture.
2 Copyright © 2015 by ASME
Table 1. Air Mixture Composition [19]
Constituent Mole Fraction
Nitrogen (N2) 0.780869
Oxygen (O2) 0.209409
Argon (Ar) 0.009332
Carbon Dioxide (CO2) 0.000385
Helium (He) 0.000005
REFPROP [20] was used to calculate all thermodynamic
properties used in this paper except for saturation vapor
pressure over water at temperatures below the freezing point.
For those cases, a sixth-order polynomial fit of Wexler’s
expression [21, 22] for saturation vapor pressure over water
was used. In accordance with the World Meteorological
Organization recommendation, the use of saturation vapor
pressure over water is preferred instead of saturation vapor
pressure over ice for this temperature range below the freezing
point [23].
B. Density Ratio Correction Compressor research facilities that use unconditioned
atmospheric air are subject to changes in the fluid properties of
the working fluid with ambient conditions: temperature,
pressure, and humidity. The variations of these atmospheric
conditions make it likely that the compressor will not achieve
the same pressure (or density) rise as it would with the
reference inlet conditions (Eq. 1), because it will begin at a
different initial state on the Mollier Enthalpy-Entropy diagram.
Thus, varying ambient conditions affect the compression
process, including the enthalpy rise (work input) and entropy
rise (losses).
Figure 1 shows the percent difference in total enthalpy, ho,
total density, 𝜌𝑜, and ratio of specific heats, γ, compared to air
at reference conditions for a variety of inlet pressures,
temperatures, and relative humidity values that could occur
throughout a typical year in the Midwest United States. The
effects of temperature alone were calculated over a range of -12
to 32ºC (10 to 90ºF) while holding relative humidity (RH)
constant at the reference condition (0%RH); this is shown in
blue along the bottom axis in Fig. 1. Similarly, the effects of
relative humidity were considered over a range from 0 to
100%RH while holding temperature constant at reference
conditions (15 ºC), and this is shown in black along the upper
axis in Fig. 1. Each of these trends is shown for three pressures:
95.8, 98.6, and 101.4 kPa (13.9, 14.3, and 14.7 psi).
Temperature is the strongest driver of changes in these fluid
properties. At 32.2 ºC (90ºF), dry air has an enthalpy which is
over 20% larger than that for standard day conditions.
Furthermore, high humidity at reference temperature can
increase total enthalpy by 8% over dry air, while pressure has
only a small effect. Density is a weak function of relative
humidity, but a 2.8 kPa (0.4 psi) change in pressure changes the
air density by nearly 3% from reference conditions. These same
changes in ambient conditions affect the ratio of specific heats
by less than 0.5%.
To correct compressor performance for these ambient
condition fluctuations, density ratio and work coefficient will
be held constant between the true test conditions and the ideal
reference conditions, similar to the procedure outlined in the
ASME PTC for compressors and exhauster [6].
First, the density ratios are equated between the test and
reference conditions:
(𝜌𝑜,𝑒
𝜌𝑜,𝑖)
𝑟𝑒𝑓
= (𝜌𝑜,𝑒
𝜌𝑜,𝑖)
𝑡𝑒𝑠𝑡
, (2)
where ρo,e,test and ρo,i,test are calculated stagnation densities at the
compressor exit and inlet, respectively, based on measured
variables during test operation, and ρo,i,ref is the reference
density from Eq. 1. The only unknown in this relation is
𝜌𝑜,𝑒,𝑟𝑒𝑓 , which can be calculated by rearranging Eq. 2,
𝜌𝑜,𝑒,𝑟𝑒𝑓 = 𝜌𝑜,𝑖,𝑟𝑒𝑓 (𝜌𝑜,𝑒
𝜌𝑜,𝑖)
𝑡𝑒𝑠𝑡
. (3)
Figure 1: Effects ambient pressure, temperature and relative humidity changes on the enthalpy, density and ratio of specific heats of air
3 Copyright © 2015 by ASME
Next, the work coefficients are equated between the test and
reference conditions:
(ℎ𝑜,𝑒−ℎ𝑜,𝑖
𝑈𝑡2 )
𝑟𝑒𝑓= (
ℎ𝑜,𝑒−ℎ𝑜,𝑖
𝑈𝑡2 )
𝑡𝑒𝑠𝑡 (4)
where ℎ𝑜,𝑒,𝑡𝑒𝑠𝑡, ℎ𝑜,𝑖,𝑡𝑒𝑠𝑡 , and 𝑈𝑡,𝑡𝑒𝑠𝑡 are calculated directly from
measured variables or through the use of REFPROP with
measured variables as inputs. Similarly for the reference
conditions, ℎ𝑜,𝑖,𝑟𝑒𝑓 and 𝑈𝑡,𝑟𝑒𝑓 may be calculated, leaving
ℎ𝑜,𝑒,𝑟𝑒𝑓 as the only unknown. Equation 4 may be rearranged to
solve for the stagnation enthalpy at the exit based on reference
conditions,
ℎ𝑜,𝑒,𝑟𝑒𝑓 = ℎ𝑜,𝑖,𝑟𝑒𝑓 + 𝑈𝑡,𝑟𝑒𝑓2 (
ℎ𝑜,𝑒−ℎ𝑜,𝑖
𝑈𝑡2 )
𝑡𝑒𝑠𝑡. (5)
Using 𝜌𝑜,𝑒,𝑟𝑒𝑓 and ℎ𝑜,𝑒,𝑡𝑒𝑠𝑡 calculated from Eqs. 3 and 5,
respectively, as input parameters, the total pressure and total
temperature at the compressor exit under reference conditions
may be calculated (using REFPROP),
𝜌𝑜,𝑒,𝑟𝑒𝑓 , ℎ𝑜,𝑒,𝑟𝑒𝑓 → 𝑃𝑜,𝑒,𝑟𝑒𝑓 , 𝑇𝑜,𝑒,𝑟𝑒𝑓 . (6)
And thus, the corrected total pressure ratio,
𝑇𝑃𝑅𝑐𝑜𝑟𝑟 = 𝑃𝑜,𝑒,𝑟𝑒𝑓
𝑃𝑜,𝑟𝑒𝑓 , (7)
and corrected total temperature ratio,
𝑇𝑇𝑅𝑐𝑜𝑟𝑟 = 𝑇𝑜,𝑒,𝑟𝑒𝑓
𝑇𝑜,𝑟𝑒𝑓 , (8)
can be determined.
C. Reynolds Number Reynolds number is a fundamental dimensionless quantity
which is derived from non-dimensionalizing the Navier-Stokes
equation, and it represents the ratio of inertial forces to viscous
forces. To investigate the effect of Reynolds number on
compressor performance, this study considered multiple
definitions of Reynolds numbers with different length scales
and velocities. Smith [24] comments on these choices and
suggests blade chord as the appropriate length scale because it
is related to blade boundary layer development. For this reason,
blade chord was used as the length scale for all Reynolds
numbers defined for this study. Smith also notes that the
velocity should be selected based on the location where viscous
effects are the greatest.
This study considered two Reynolds number definitions.
The first uses rotor tip speed, Ut, and chord, c, for the length
scale,
𝑅𝑒𝑚𝑎𝑐ℎ𝑖𝑛𝑒 = 𝜌𝑈𝑡𝑐
𝜇 . (9)
This definition is commonly used by other authors and is
representative of the machine Reynolds number. However,
when considering loss development on blading, it is more
appropriate to use the inlet velocity to each blade row, v or w
(for absolute or relative frame of reference, respectively), and
chord,
𝑅𝑒𝑏𝑙𝑎𝑑𝑒 = 𝜌𝑣𝑐
𝜇 . (10)
This definition relates more to airfoil performance. Changes of
length scales due to thermal growth are neglected in this
analysis compared to the more significant changes of flow
velocities and fluid properties, leaving chord and radius
constant for all operating conditions.
EXPERIMENTAL APPROACH This section provides details regarding the experimental
research facility and measurement techniques used to acquire
the data presented in this study.
A. Facility The experimental data for this study were acquired in the
Purdue Three-Stage Axial Compressor Research Facility. The
compressor geometry is a scaled-up (24-in or 60.69-cm
diameter) version of the rear stages of a high pressure
compressor with a hub-to-tip ratio of 0.833. It operates at
engine-representative Reynolds numbers and Mach numbers
and has a design corrected speed of 5,000 rpm. Rotational
speed is maintained to within 0.1% of the desired speed by
feedback control with an encoder on the motor shaft, and the
mechanical speed was determined as prescribed by Berdanier et
al. [5]. The facility draws atmospheric air through screens into a
large settling chamber, followed by a bellmouth at the entrance
of the 24-in (60.69-cm) diameter inlet duct and a series of flow
conditioning elements. The air passes through an ASME-
standard [25] long-form Venturi nozzle where the mass flow
rate is metered. A nosecone directs the air into the two-inch
(5.08 cm) constant annulus flowpath. After passing through the
compressor, the fluid exhausts to atmospheric conditions
through a sliding-annulus throttle and a collector.
The flowpath described above is shown in Fig. 2. The
compressor consists of an inlet guide vane (IGV) followed by
three stages. The IGV and rotor blades are double circular arc
airfoils, and the stator vanes are NACA 65-series airfoils. The
blading is made from stainless steel, and the outer casing
(shroud) is aluminum. Each vane row is individually indexable
allowing for pitchwise traverses past stationary instrumentation.
Circumferential vane position is measured using precision
string potentiometers.
Three rotor tip clearance (TC) heights have been studied in
this facility. These are nominally 1.5%, 3%, and 4%TC based
on annulus height. The 1.5%TC condition represents the
baseline tip clearance configuration which is nominally
0.030 in. (0.76mm) for “hot” running conditions. Further
4 Copyright © 2015 by ASME
details related to the tip clearance configurations may be found
in Berdanier and Key [18].
B. Instrumentation Steady total pressures and total temperatures are measured
downstream of each blade row, axial stations 1 through 8 in
Fig. 2, using seven-element rakes. Four circumferential
pressure taps at each of these axial stations allow for the
measurement of the casing static pressure. The largest overall
total pressure ratio measurement uncertainty is 0.16%.
Rotor tip clearance is measured during compressor
operation using capacitance probes. Three probes are flush
mounted in the casing circumferentially over the mid-chord of
each rotor. More details on this measurement can be found in
Berdanier and Key [26].
The measurements presented in this paper were acquired
using two methods. The first method consisted of “untraversed”
data representing one pitchwise measurement position for each
of the nine compressor loading conditions (based on corrected
mass flow rate) on the 100% Nc speedline. These data were
acquired several times for each tip clearance configuration
since an untraversed speedline is acquired nearly every time the
compressor is operated. The second method consists of a more
time-intensive 20-point circumferential vane traverse across
one vane pitch to ascertain the area-averaged performance
metrics. This second method was completed at nine points
along the 100% and 90% Nc speedlines for each tip clearance
configuration on a warm day (referred to as ‘Hot’) and a cold
day and is summarized in Table 2.
Table 2. Average conditions for cold and hot days
To,in Po,in RH
°F (°C) psi (Pa) %
Cold 20 (-6.7) 14.4 (99.3) 45
Hot 75 (23.9) 14.25 (98.3) 60
RESULTS After incorporating humidity and real gas effects into
corrected inlet conditions for rotational speed and mass flow
rate, there remain measurable and repeatable discrepancies
between compressor performance on a cold and hot day. This is
shown in Fig. 3 for compressor overall total pressure ratio for
the 3% and 4% tip clearance configurations. Corrected mass
flow rate has been normalized by a nominal loading condition
half way up the speedline. These data represent the average of a
20-point circumferential traverse and are repeatable for the
similar inlet conditions. Data from two rotor tip clearance
heights are presented to show that the trends persist in multiple
hardware configurations. While data will be shown at the 1.5%
tip clearance later in the discussion, traversed speedlines at both
inlet temperatures were not available at the smallest tip
clearance, and thus, it is not included in Fig. 3.
This paper focuses on the differences in total pressure
ratio. The throttle setting was not controlled to ensure that the
corrected mass flow rates between the hot and cold days
matched, and thus, there is no conclusion to be drawn in the
different mass flow rates (the horizontal offset) for the different
temperatures presented in Fig. 3.
The discrepancy between hot and cold day total pressure
ratio is most significant at high loading conditions. The
maximum difference occurs at the near stall operating
condition, the lowest mass flow rate. At the near stall condition,
the TPR difference is 0.0056 (0.417%) for the 3% tip clearance
and 0.0015 (0.113%) for the 4% tip clearance. With a
measurement uncertainty on the order of the differences shown
for the 4% clearance configuration, the discrepancy at the 3%
clearance configuration is about four times larger than the
measurement uncertainty, and it motivates the need to
understand the differences in performance between a hot day
and a cold day.
This section consists of three main parts aimed at
reconciling these pressure ratio differences. The first part
reports the changes in compressor performance by applying the
density and work coefficient correction. The second part
discusses Reynolds number effects. Finally, the last part
discusses the performance effects related to the tip clearance
changes resulting from small deviations in casing thermal
growth due to changes in ambient temperatures.
Figure 2: Compressor flowpath including station numbering
scheme
Figure 3: Difference in TPR between a hot and cold day at 3%
and 4%TC
5 Copyright © 2015 by ASME
A. Density and Work Coefficient Correction The density and work coefficient corrections outlined in
Eqs. (2) through (8) were applied to circumferentially traversed
data at 100% Nc for both a cold day and a hot day. As a result of
this correction process, the differences between the cold and hot
day performance data is reduced, but the shift is small, as
shown in Fig. 4. These data are presented as a function of
corrected mass flow rate which has been normalized by a
nominal loading condition half way up the speedline. The
largest difference between the measured 𝑇𝑃𝑅𝑡𝑒𝑠𝑡 and the
corrected 𝑇𝑃𝑅𝑐𝑜𝑟𝑟 is on the order of 0.065% (or 0.00087 in
TPR). This is smaller than the measurement uncertainty and is
not a discernable shift if shown with the data in Fig. 3.
The combination of ambient temperature, pressure, and
relative humidity on the hot days resulted in densities and work
coefficients similar to that at reference conditions. Therefore,
data acquired on the hot days were corrected significantly less
compared with the data from the cold days. Although it may
appear there is a trend associated with loading condition, the
correction differences from choke to stall are due to a gradual
shift in ambient conditions that occurred while acquiring the
data. Also, the 3% TC cold day data have a jump between 0.9
and 0.95 normalized corrected mass flow rate because this
speedline was acquired on two different days. The four points
closest to stall were acquired on a day with colder ambient inlet
temperature, requiring a larger shift in work coefficient and
density compared to those at higher flow rates.
Although this correction results in a small TPR shift that is
less than the measurement uncertainty, it has been applied to all
data (both overall compressor data and interstage data)
presented in the remainder of the paper to eliminate potential
differences.
B. Reynolds Number Effects Large shifts in ambient conditions can cause the working
fluid properties to change, therefore changing Reynolds
number. Standard compressor testing procedures allow for
Mach number similarity between the test and reference
conditions through a correction process for rotational speed, but
there is no prescribed method to also maintain Reynolds
number similarity. Reynolds number effects are often
considered small, and thus, they are often neglected. However,
deviations from the Reynolds number at reference conditions
can become large on significantly hot or cold days. Previous
authors [6] have defined a Reynolds Index,
Figure 4: Percent difference change in TPR with density and
work coefficient correction on a hot and cold day
Figure 5: Reynolds Number Index on a hot and cold day
6 Copyright © 2015 by ASME
7 Copyright © 2015 by ASME
𝑅𝑒𝑦𝑛𝑜𝑙𝑑𝑠 𝐼𝑛𝑑𝑒𝑥 = 𝑅𝑒𝑡𝑒𝑠𝑡
𝑅𝑒𝑟𝑒𝑓 , (11)
that represents a ratio of the test Reynolds number to the
reference Reynolds number corresponding to standard day
operation. Reynolds Index can be used as a metric to gauge
how far the test Reynolds number has changed from reference
conditions due to differences in fluid properties. Figure 5 shows
the Reynolds Index on the hot and colds days for the data
presented in Fig. 3. The test Reynolds number approaches a
±10% difference from the reference Reynolds number – a value
which could become increasingly important for some
compressors, especially those near the transitional Reynolds
number. The changes in test Reynolds number arise from
varying inlet conditions of temperature, relative humidity, and
pressure. The variations in these ambient inlet conditions and
the resulting Reynolds number experienced over the course of a
year of testing in the Midwest United States are shown in Fig.
6. While relative humidity and pressure affect Reynolds
number, it is actually a strong function of inlet temperature.
Figure 6 shows the changes in both machine and blade
Reynolds number, as defined by Eqs. (9) and (10), as a function
of inlet temperature and relative humidity. The blade Reynolds
number shown here is based on Rotor 1 inlet conditions, using
the relative velocity at Rotor 1 inlet and the Rotor 1 chord. The
blade Reynolds numbers for Rotor 2 and Rotor 3 are similar.
These values should be compared with the loss curves for the
airfoil shape. For these double circular arc airfoils, the profile
loss is not affected by this change in Reynolds number. The
stator inlet Reynolds numbers range from 3.5×105 to 4.5×10
5
and are similar through the compressor whereas the rotor inlet
Reynolds numbers increase slightly through the machine. The
blade Reynolds numbers are all above the critical value (about
2.5×105), and they exist in the minimum-loss region for the
airfoils [27]. Thus, the offset in total pressure ratio shown in
Fig. 3 on cold versus hot days is not associated with a
transitional Reynolds number. Also, Fig. 6 shows that the
choice of blade Reynolds number versus machine Reynolds
number definition does not result in a large difference in
Reynolds number, especially when compared to the differences
in Reynolds number associated with day-to-day variations in
compressor inlet conditions.
C. Temperature Effects on Tip Clearance The differences in total pressure ratio shown in Fig. 3 are
consistent with untraversed data acquired over the course of a
full calendar year at the facility, as shown in Fig. 8 for three
rotor tip clearances. Over the same range of ambient
temperatures, the 4% TC is less affected, compared to the 1.5%
and 3% TC configurations. The two smaller tip clearances have
a general negatively-sloping trend of pressure ratio with
increasing inlet temperature, whereas the 4% TC displays a less
distinct trend with inlet temperature. These TPR data were also
compared with relative humidity and inlet pressure, but did not
display distinct trends like that shown for temperature in Fig. 7.
To better understand these differences, interstage data between
a cold and hot day are compared.
The pitchwise total pressures (normalized by compressor
Figure 6: Reynolds number fluctuations with ambient inlet conditions: (a) temperature, (b) relative humidity, and (c) pressure
-10 0 10 20 306.8
7
7.2
7.4
7.6
7.8
8
8.2
8.4x 10
5
Reynold
s N
um
ber
Inlet Temperature, oC
(a)
blade
machine
0 20 40 60 80 1006.8
7
7.2
7.4
7.6
7.8
8
8.2
8.4x 10
5
Reynold
s N
um
ber
Relative Humidity, %
(b)
97 98 99 1006.8
7
7.2
7.4
7.6
7.8
8
8.2
8.4x 10
5
Reynold
s N
um
ber
Inlet Pressure, kPa
(c)
4%TC3%TC
1.5%TC
Figure 7: TPR variations with ambient temperature for three nominal tip clearances (a) 1.5%TC (b) 3%TC and (c) 4%TC
-10 0 10 20 30
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
( T
PR
- T
PR
ma
x )
/ T
PR
ma
x
Inlet Temperature, oC
(a) 1.5%TC
-10 0 10 20 30
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
( T
PR
- T
PR
ma
x )
/ T
PR
ma
x
Inlet Temperature, oC
(b) 3%TC
-10 0 10 20 30
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
( T
PR
- T
PR
ma
x )
/ T
PR
ma
x
Inlet Temperature, oC
(c) 4%TC
7 Copyright © 2015 by ASME
8 Copyright © 2015 by
inlet total pressure) downstream of each blade row at 80%span
at a near-stall loading condition (where compressor pressure
rise was most different) for cold and hot inlet conditions are
shown in Fig. 8. On the cold days, each of the rotors achieves
more pressure rise uniformly across the vane pitch. This trend
is similar for data acquired near the hub and at midspan. The
total pressure measured at the exit of the vane rows is also
similarly higher cold days, but the scale for the stator exit
results is larger than that for the rotor exit results so that the
stator wakes are captured.
Circumferentially averaging these data provides radial total
pressure profiles downstream of each row for a hot and cold
day, Fig. 9. The total pressure ratios have been normalized by
the area-average of the particular dataset at each axial location
to highlight differences in the profile shapes. The profiles are
qualitatively similar, but there are small, yet appreciable
differences near the tip and the hub. On a hot day, the tip region
has less total pressure – a result which is most prominent at
axial measurement planes downstream of Rotor 1 and Stator 2.
This observation suggests differences in tip flows exist between
the cold and hot days.
One of the main parameters that effects flow in the tip
region is the rotor tip clearance. Luckily, rotor tip clearances
were measured during acquisition of these data. The average
rotor tip clearances are shown with the respective average total
pressure ratio at the near stall loading condition in Fig. 10. On
cold days, the rotor tip clearances are a bit tighter for each
nominal tip clearance configuration tested. Figure 8 showed
that on cold days, the rotors produce more pressure rise and the
overall machine total pressure is higher. On hot days, the tip
clearance runs larger, and this is because the aluminum casing
is growing more compared to the thermal and centrifugal
growth of the blade (even for the larger mechanical speeds that
are run on hot days to match corrected conditions).
A 28 ºF (15.6 ºC) change in inlet temperature results in a
change of rotor tip clearance height of approximately 2.4×103
in. (an 8% difference for the baseline 1.5% TC configuration
with a nominal 0.030 in. rotor tip clearance). While Fig. 10
shows the expected result of decreased total pressure ratio with
large increases in nominal rotor tip clearance, it also reveals
that the small change in tip clearance due to changes in ambient
temperature, and the corresponding change in measured total
pressure ratio, follows the same trend.
The radial total pressure profiles at near stall for a cold day
and hot day at all three nominal rotor tip clearances are
compared to see the gradual shift in performance, Fig. 11. Only
the Rotor 1 exit and Stator 2 exit data are shown because they
exhibit the largest differences with tip clearance. The profile
shapes shown in Fig. 11 for the 3% clearance fall between the
1.5% and 4% tip clearance configurations. The cold data have
less total pressure loss at the tip, except for the 4% TC results.
The trends at 4% TC are less clear, which is consistent with
Figure 8: Total pressure wakes at 80%span for 3% TC at near stall loading conditions, hot and cold days
0 20 40 60 80 1001.108
1.11
1.112
1.114
1.116
1.118Rotor 1 Exit
Po
,3 /
Po
,in
0 20 40 60 80 100
1.06
1.08
1.1
1.12
Stator 1 Exit
Vane Position, %vp
Po
,4 /
Po
,in
0 20 40 60 80 1001.23
1.235
1.24
1.245
1.25Rotor 2 Exit
Po
,5 /
Po
,in0 20 40 60 80 100
1.18
1.2
1.22
1.24
Stator 2 Exit
Vane Position, %vpP
o,6
/ P
o,in
0 20 40 60 80 1001.345
1.35
1.355
1.36
1.365Rotor 3 Exit
Po
,7 /
Po
,in
0 20 40 60 80 1001.28
1.3
1.32
1.34
1.36Stator 3 Exit
Vane Position, %vp
Po
,8 /
Po
,in
cold
hot
Figure 9: Radial total pressure profiles from traversed data downstream of each row for a cold and hot day for the 3% TC
0.99 1 1.0110
20
30
40
50
60
70
80
90
Radia
l P
ositio
n,
%span
Normalized Po,3
/ Po,in
Rotor 1 Exit
0.99 1 1.0110
20
30
40
50
60
70
80
90
Normalized Po,4
/ Po,in
Stator 1 Exit
0.99 1 1.0110
20
30
40
50
60
70
80
90
Normalized Po,5
/ Po,in
Rotor 2 Exit
0.99 1 1.0110
20
30
40
50
60
70
80
90
Normalized Po,6
/ Po,in
Stator 2 Exit
0.99 1 1.0110
20
30
40
50
60
70
80
90
Normalized Po,7
/ Po,in
Rotor 3 Exit
0.99 1 1.0110
20
30
40
50
60
70
80
90
Normalized Po,8
/ Po,in
Stator 3 Exit
cold
hot
8 Copyright © 2015 by ASME
the observations from Fig. 7 where there was a less distinct
trend in TPR with ambient temperature. This could be because
a 2.4×103 in. change in tip clearance is less significant for a
0.080 in. nominal rotor tip clearance than for a 0.030 or 0.060
in. rotor tip clearance. The trends at 3% TC are nearly as strong
as those at 1.5% TC, an observation which could suggest the
3% TC configuration represents a critical point in the loss
development with increased tip clearance. For example, for the
Stator 2 exit profiles in Fig. 11, the 3% TC is near the point
where the profiles shift from having more loss in the hub to
more at the tip.
CONCLUSIONS Compressor research facilities that operate with
unconditioned ambient air and are exposed to ambient
temperature conditions may record different compressor
performance as a result of these changing conditions. To
achieve high-quality experimental data for comparison to
computational predictive models, careful consideration must be
given to the overall effects that can cause measurable
performance changes. A correction procedure for density and
work coefficient was imposed for data collected from the
Purdue Three-Stage Axial Compressor Facility with two
different tip clearance configurations. Applying this correction
procedure for data collected with cold and hot ambient inlet
conditions reduced measured differences by only 0.05%, which
was less than half of the measurement uncertainty.
Reynolds number trends with respect to the machine and
blade rows were also assessed. These assessments showed
ambient conditions representing typical seasonal variations in
the Midwest United States can cause large changes (10%
different) in Reynolds numbers. However, for this range of
Reynolds numbers, the airfoils in the Purdue Three-Stage
Compressor operate in a regime which is independent of
Reynolds number, far above the transitional Reynolds number.
The changes in overall total pressure ratio with ambient
conditions were, therefore, attributed to the small changes
measured in rotor tip clearance. The tip clearance changes due
to ambient temperature changes can exceed 0.1% span. On hot
days, the tip clearance runs larger, and this is because the
aluminum casing is growing more compared to the thermal and
centrifugal growth of the blade (even for the larger mechanical
speeds that are run on hot days to match corrected conditions).
The performance changes associated with these different
clearances fall within the expected trend. This was verified by
comparing data from several clearances acquired on hot and
cold days. As a result, this tip clearance change due to day-to-
day variations in thermal growth, which is typically considered
in literature to be a negligible effect, is not only measurable, but
it is significant.
Quantifying these second-order effects on compressor
performance required significant testing of the same
compressor with different rotor tip clearances throughout the
year to provide quality datasets on both hot and cold days. This
type of dataset is rarely available or presented in the literature.
These results also highlight the necessity of measuring
operating rotor tip clearances to accompany performance data,
especially when measurement campaigns will extend over days
with varying inlet conditions.
ACKNOWLEDGMENTS This material is based upon work supported by NASA
under the ROA-2010 NRA of the Subsonic Fixed Wing project
and in part by the National Science Foundation Graduate
Research Fellowship Program under Grant No. DGE-1333468.
The authors would also like to thank Rolls-Royce for the
permission to publish this work.
Figure 10: TPR trends with measured rotor 1 tip clearance at a
near stall operating condition
1 1.5 21.315
1.32
1.325
1.33
1.335
1.34
1.345
1.35
1.355
1.36
Rotor 1 Tip Clearance, mm
Overa
ll T
PR
Cold
Hot
1.5%TC
3%TC
4%TC
Figure 11: Radial profiles for three nominal tip clearances on a
hot and cold day
0.99 1 1.01 1.0210
20
30
40
50
60
70
80
90Rotor 1 Exit
Radia
l H
eig
ht,
%span
Normalized Po,3
/Po,in
0.99 1 1.01 1.0210
20
30
40
50
60
70
80
90Stator 2 Exit
Radia
l H
eig
ht,
%span
Normalized Po,6
/Po,in
TC = mm
0.79 (cold)
0.90 (hot)
1.53 (cold)
1.65 (hot)
2.15 (cold)
2.24 (hot)
9 Copyright © 2015 by ASME
REFERENCES [1] Cumpsty, N.A., 2004, Compressor Aerodynamics,
Krieger, Malabar, FL, pp. 11-21.
[2] Dixon, S.L., 2005, Fluid Mechanics and
Thermodynamics of Turbomachinery, Elsevier,
Burlington, MA, pp. 16–20.
[3] Fishbeyn, B.D. and Pervyshin, N.V., 1970,
“Determination of the Effect of Atmospheric Humidity
on the Characteristics of a Turbofan Engine,” Foreign
Technology Division, Wright-Patterson AFB, OH, Paper
NO. FTD-HT-23-290-68 (AD 715232).
[4] Bird, J. and Grabe, W., 1991, “Humidity Effects on Gas
Turbine Performance,” International Gas Turbine and
Aeroengine Congress and Exposition, Orlando, FL, June
3-6, ASME Paper No. 91-GT-329.
[5] Berdanier, R.A., Smith, N.R., Fabian, J.C., and Key,
N.L., 2015, “Humidity Effects on Experimental
Compressor Performance—Corrected Conditions for
Real Gases,” Journal of Turbomachinery, 137(3),
031011 (10 pages).
[6] American Society of Mechanical Engineers, 1997,
“Performance Test Code on Compressors and
Exhausters,” ASME New York, Standard No. PTC 10.
[7] Wiesner, F.J., 1979, “A New Appraisal of Reynolds
Number Effects on Centrifugal Compressor
Performance,” Journal of Engineering for Power,
101(3), pp. 384–392.
[8] Strub, Bonciani, Borer, Casey, Cole, Cook, Kotzur,
Simon, and Strite, 1987, “Influence of the Reynolds
Number on the Performance of Centrifugal
Compressors,” Journal of Turbomachinery, 109(4), pp.
541–544.
[9] Carter, A.D.S., Moss, C.E., Green, G.R., and Annear,
G.G., 1957, “The Effect of Reynolds Number on the
Performance of a Single-Stage Compressor,” Ministry of
Aviation, Aeronautical Research Council, London, UK,
Reports and Memoranda No. 3184, pp. 1-26.
[10] Wassel, A.B., 1968, “Reynolds Number Effects in Axial
Compressors,” Journal of Engineering for Power, 90(2),
pp. 149–156.
[11] Schäffler, A., 1980, “Experimental and Analytical
Investigation of the Effects of Reynolds Number and
Blade Surface Roughness on Multistage Axial Flow
Compressors,” Journal of Engineering for Power,
102(1), pp. 5–12.
[12] Walsh, P.P. and Fletcher, P., 2008, Gas Turbine
Performance, Blackwell Science, Oxford, UK, pp.
149,168,407.
[13] Shepherd, D.G., 1956, Principles of Turbomachinery,
MacMillan Publishing Co., New York, NY, pp.39-47.
[14] Jefferson, J.L. and Turner, R.C., 1958, “Some Shrouding
and Tip Clearance Effects in Axial Flow Compressors,”
International Shipbuilding Progress, 5, pp. 78–101.
[15] Wisler, D.C., 1985, “Loss Reduction in Axial-Flow
Compressors Through Low-Speed Model Testing,”
Journal of Engineering for Gas Turbines and Power,
107(2), pp. 354–363.
[16] Freeman, C., 1985, “Effect of Tip Clearance Flow on
Compressor Stability and Engine Performance,” VKI
Lecture Series 1985-05.
[17] Tschirner, T., Johann, E., Müller, R., and Vogeler, K.,
2006, “Effects of 3D Aerofoil Tip Clearance Variation on
a 4-Stage Low Speed Compressor,” ASME Paper No.
GT2006-90902.
[18] Berdanier, R.A. and Key, N.L., 2015, “Tip Leakage Flow
Effects on Multistage Compressor Performance for
Small Core Engine Applications,” Submitted to Journal
of Turbomachinery.
[19] Wright, J.D., 2010, “Properties for Accurate Gas Flow
Measurements,” 15th
Flow Measurement Conference
(FLOMEKO), Taipei, Taiwan, Oct. 13-15.
[20] Lemmon, E. W., Huber, M. L., and McLinden, M. O.,
2013, NIST Standard Reference Database 23: Reference
Fluid Thermodynamic and Transport Properties—
REFPROP, Version 9.1, National Institute of Standards
and Technology, Standard Reference Data Program,
Gaithersburg, MD.
[21] Wexler, A., 1976, “Vapor Pressure Formulation for Water
in Range 0 to 100 ºC. A Revision,” J. Res. Natl. Bur.
Stand., 80A(5), pp. 775–785.
[22] Wexler, A., 1977, “Vapor Pressure Formulation for Ice,”
J. Res. Natl. Bur. Stand., 81A(1), pp. 5–20.
[23] WMO, 1966, International Meteorological Tables, S.
Letestu, ed., World Meterological Organization, Geneva,
Switzerland, Report No. 188 TP 94, Table 4.3, pp. 3–4.
[24] Smith, L.H., 1964, “Some Comments on Reynolds
Number,” Journal of Engineering for Power, 86(3), pp.
225–226.
[25] American Society of Mechanical Engineers, 2004, “Flow
Measurement,” ASME New York, Standard No. PTC
19.5, pp. 19–27.
[26] Berdanier, R.A. and Key, N.L., 2015, “Experimental
Investigation of Factors Influencing Operating Rotor Tip
Clearance in Multistage Compressors,” International
Journal of Rotating Machinery, Article ID 146272, 14
pages.
[27] NASA, 1965, “Aerodynamic Design of Axial-Flow
Compressors,” ed. Johnsen, I.A. and Bullock, R.O.,
Washington, D.C., NASA SP-36, pp. 206.
10 Copyright © 2015 by ASME