Reconciling Compressor Performance Differences for Varying ...

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.


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


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


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


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



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


(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


(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


(c) 4%TC


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


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)


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