Joseph P. Veres

Glenn Research Center, Cleveland, Ohio

Axial and Centrifugal Compressor

Mean Line Flow Analysis Method

NASA/TM—2009-215585

November 2009

AIAA–2009–1641
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

 443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
Joseph P. Veres

Glenn Research Center, Cleveland, Ohio

Axial and Centrifugal Compressor

Mean Line Flow Analysis Method

NASA/TM—2009-215585

November 2009

AIAA–2009–1641

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

47th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 5–8, 2009
Acknowledgments

The author thanks Dr. Dhanireddy R. Reddy, Chief of the Aeropropulsion Division at the NASA Glenn Research Center and 

the Subsonic Fixed Wing and the Subsonic Rotary Wing aircraft projects within the NASA Fundamental Aeronautics Program 

for supporting this work. The author would also like to thank Mr. John C. Fabian and Mr. Scott Thorp for their support in 

providing historical data and for managing the refurbishment and buildup effort of the 76-B compressor hardware.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5285 Port Royal Road

Springfi eld, VA 22161

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2009-215585 1 

Axial and Centrifugal Compressor 

Mean Line Flow Analysis Method 

Joseph P. Veres

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

This paper describes a method to estimate key aerodynamic parameters of single and multistage axial 

and centrifugal compressors. This mean-line compressor code COMDES provides the capability of sizing 

single and multistage compressors quickly during the conceptual design process. Based on the 

compressible fluid flow equations and the Euler equation, the code can estimate rotor inlet and exit blade 

angles when run in the design mode. The design point rotor efficiency and stator losses are inputs to the 

code, and are modeled at off design. When run in the off-design analysis mode, it can be used to generate 

performance maps based on simple models for losses due to rotor incidence and inlet guide vane reset 

angle. The code can provide an improved understanding of basic aerodynamic parameters such as 

diffusion factor, loading levels and incidence, when matching multistage compressor blade rows at design 

and at part-speed operation. Rotor loading levels and relative velocity ratio are correlated to the onset of 

compressor surge. NASA Stage 37 and the three-stage NASA 74-A axial compressors were analyzed and 

the results compared to test data. The code has been used to generate the performance map for the NASA 

76-B three-stage axial compressor featuring variable geometry. The compressor stages were 

aerodynamically matched at off-design speeds by adjusting the variable inlet guide vane and variable 

stator geometry angles to control the rotor diffusion factor and incidence angles. 

Introduction 

The mean line flow modeling methodology described in this paper addresses the need for a quick tool 

for conceptual sizing of compressors during the early phases of the design process of gas turbine engines. 

This tool can be used to size axial as well as centrifugal compressors either as single stage, or in 

multistage configurations. The COMDES code which is based on this methodology has a design 

capability feature that can size the blade angles at the rotor inlet and exit, as well as the stator vane angles. 

The work distribution in a multistage compressor can be varied by the user. The mean line code has been 

written to provide rapid evaluation of candidate compressor design concepts. 

The ability to model compressor off-design performance is necessary for system evaluation of 

compressors within gas turbine engines. The off-design performance of the compressor is required to 

enable engine system analyses at several operating conditions throughout the envelope. The mean line 

code can be used to do an initial estimate of the variable geometry reset schedule of a multistage 

compressor that will result in aerodynamically matched stages at off-design compressor speeds. This 

procedure results in the generation of a compressor characteristic map that can be utilized in a 

thermodynamic system model of an engine. The compressor map characteristics can often influence the 

final design of the compressor and therefore compressor sizing, compressor map generation and engine 

thermodynamic system modeling is an iterative procedure. An example where an engine can have 

multiple design points are supersonic vehicles, where at the takeoff condition the engine operates at 

100 percent design corrected speed and flow rate, while at the cruise condition the engine operates at 

reduced corrected speed and flow. By knowledge of the performance at off-design conditions, the 

compressor designer can optimize the configuration to provide acceptable performance in an engine 

system at all operating conditions. Several validation cases from single and multistage research 

compressors that were used during the development of the mean line code are included in this report. 
NASA/TM—2009-215585 2 

Nomenclature 

A Annular area

a Speed of sound 

B Axial distance from hub to tip 

C Absolute velocity 

DF Diffusion factor 

gc Dimensional constant 

H Enthalpy rise 

i Incidence 

M Absolute Mach number 

m Mass flow rate 

P Pressure 

Power Power 

Q Volume flow rate 

 Universal gas constant 

R Radius from centerline of rotor 

T Temperature 

U Rotor peripheral velocity 

W Relative velocity 

 Absolute flow angle 

βF Relative flow angle 

βB Rotor blade angle 

βV Stator vane inlet angle 

δ Rotor slip factor 

η Adiabatic efficiency 

γ Specific heat ratio 

λ Aerodynamic blockage 

Ф Flow coefficient 

σ Solidity 

Subscripts 

1 Rotor leading edge 

2 Rotor trailing edge 

3 Stator vane leading edge 

4 Stator vane trailing edge 

B Rotor blade 

F Flow 

H Rotor hub 

M Meridional component 

R Rotor 

T Rotor tip 

t Total 

S Static 

U Tangential component 

V Stator vane 

Methodology 

The methodology is based on the compressible fluid flow equations in Shapiro (Ref. 1), and the Euler 

equation. The rotor efficiency and stator (or diffusion system) losses at the design point are input items 

into the code. The design point rotor efficiency is modeled at off-design by an empirical correlation with 

rotor incidence. The relative velocity ratio and the diffusion factor (Ref. 2), through the rotor are 

correlated to the onset of stall. The equations and variables used in the mean line methodology are listed 

in the Appendix of this report. 

The compressor code can be run either in the design or in the analysis mode. In either mode, the rotor 

hub and tip radii from the centerline that define the flow path are input at the leading and trailing edges as 

shown in Figure 1. Other input parameters are the inlet total pressure and temperature, shaft rotational 

speed, rotor aerodynamic blockages at the inlet and exit and slip factor. 

Several of the input parameters depend on whether the code is being run in the design or in the 

analysis mode. In the design mode, the design point mass flow rate is input and the blade angles at the 

rotor leading and trailing edges are part of the calculation. The inlet total pressure and temperature are 

input parameters in either case. In addition to the conditions at the rotor mean line, the hub and tip 

conditions are also estimated by the code. In the design mode, the rotor exit pressure at the hub, mean and 

tip are specified as input, and the blade angles at the exit hub, mean and tip are calculated by the code. In 

both the design and the analysis mode, the conditions at the rotor leading edge are solved by a procedure 

that iterates on inlet Mach number and the static pressure and temperature. 

All of the components of the inlet and exit velocity diagram are solved in a similar iterative manner 

whether run in the design or in the analysis mode. The fluid properties are determined at each blade 

leading and trailing edge location from a code named GASPLUS (Ref. 3), which is called as a subroutine 

by the COMDES code. All of the key components of the rotor inlet velocity diagrams are solved 

simultaneously using Equations (1) to (12) listed in the Appendix. These parameters are initially 
NASA/TM—2009-215585 3 

calculated at the mean line radius, followed by estimates of conditions at the end walls. The deviation 

angle is estimated from the exit flow conditions and the input slip factor. The slip factor for axial 

compressors as defined by Equation (22) in the Appendix can be on the order of 0.93 to 0.96 and results 

in the calculation of a rotor deviation angle at the hub, mean, and tip. 

Analysis Mode 

In the analysis mode, the rotor blade angles at the leading and trailing edges are specified at the hub, 

mean, and tip and the mass flow rate and total pressure ratio are calculated parameters. The code 

calculates the mass flow rate iteratively based on the input value of incidence at the mean blade angle of 

the first rotor. By this method the mass flow is varied through the compressor by specifying a range of 

rotor incidences and allowing the code to calculate mass flow rate from choke to stall. Choke is 

determined as the limit of flow where the code fails to converge on the rotor exit velocity triangles. Surge 

has been determined empirically from the NASA Stage 37 and the 74-A compressor data correlated to the 

values of rotor diffusion factor and relative velocity ratios at the tested surge point. At each point along 

each speed line, the iteration begins with solving for the static pressure and temperature at the rotor 

leading edge, based on the available area, incidence, mass flow rate and the inlet total pressure and total 

temperature. Once the inlet Mach number and static pressure and temperature have been solved, all of the 

components of the absolute and relative velocities and flow angles are determined as shown in Figure 2. 

Whether run in the analysis or the design mode, the rotor exit deviation angle is taken into consideration 

in the iterative calculations. As in the design mode, the rotor deviation angle is specified as an input item 

in terms of a slip factor as defined by Equation (22) in the Appendix. The code calculates all of the 

components of the rotor exit velocity diagram shown in Figure 2 by solving Equations (13) to (31) in the 

Appendix simultaneously using an iterative technique. In both the analysis and the design mode, all of the 

components of velocity at the rotor trailing edge are derived from the enthalpy rise as calculated from 

Equations (15) and (16) in terms of temperature rise across the rotor, and the Euler equation. 
NASA/TM—2009-215585 4 

The mean line code is run in the analysis mode to estimate the performance of the compressor at offdesign, or part-speed operation. To determine the efficiency at off-design conditions, the compressor rotor 

efficiency at the design point is input. Note that the design point efficiency is that value only at a rotor 

incidence of 6 just ahead of the rotor, not including metal blockage at the leading edge. This design point 

incidence was also determined empirically from analysis of the test data of the two compressor cases in 

this report. The “design point” efficiency is assumed to be the same along all speed lines, and is varied 

only as a function of rotor incidence angle. The losses through the stators due to incidence are not varied 

directly but are lumped into the efficiency calculation, which is a function of rotor incidence as defined by 

Equation (31). This is a simplification which assumes that as the flow rate changes along a speed line, 

both the rotor and the stator experience a change of incidence from their design value, and therefore a 

reduction in efficiency occurs. A model for stator loss variation with incidence that is separate from the 

efficiency deration due to incidence of the rotor is planned for a future version of the code. 

Varying the inlet guide vane setting angle is the first step in aerodynamically matching a multistage 

compressor at part-speed operating conditions. The variable guide vane has a large influence on the flow 

rate into the first rotor. However, variable inlet guide vanes produce a loss of total pressure which is a 

function of setting angle. The model in the mean line code is an empirical correlation that was derived 

from the test data of the NASA 74-A compressor featuring flap type guide vanes and is represented by 

Equation (29).Varying the stator reset angles is the next step in matching multistage compressors, as this 

can be effective in controlling the incidence in the downstream rotor. 

Code Validation Cases 

NASA Stage 37 

The aerodynamic performance of the transonic single stage compressor named NASA Stage 37 

(Ref. 4) was simulated with the mean line methodology. Figure 3 illustrates the Stage 37 compressor test 

data comparison to the mean line model results. The pressure ratio map for a range of speeds and flows 

from choke to surge is compared to test data in Figure 3(a). The stage efficiency comparison is shown in 

Figure 3(b). 
NASA/TM—2009-215585 5 

TABLE 1.—SLIP FACTOR VERSUS DEVIATION ANGLE 

AND STAGE PRESSURE RATIO AT 100 PERCENT 

SPEED AT 21.34 KG/SEC FLOW RATE 

Table 1 illustrates the sensitivity of rotor pressure ratio and rotor exit absolute flow angle to the slip 

factor that is used in the calculation. To obtain agreement with the test data of pressure ratio, a slip factor 

of 0.93 as defined by Equation (22) was selected to estimate the rotor deviation angle. This value of slip 

factor resulted in a reasonable match with the tested pressure ratio data at all speed lines except at the 

100% speed line, where it over predicted the pressure ratio. The design point rotor efficiency at the tip, 

mean and hub were 78.4, 89.4, and 92.9 percent and were input values into the mean line code. The rotor 

mean incidence angle is 5.0 degrees at a flow rate of 21.34 kg/sec. The rotor aerodynamic blockages were 

2 percent at the inlet and 3 percent at the exit. The stator loss coefficient was 6 percent, as defined by 

Equation (27). The slip factor, stator loss and aerodynamic blockages were not varied at off design speeds 

or flow rates in the mean line code. 

The mean line compressor flow code was used to calculate the velocity triangles at the rotor leading 

and trailing edges through a range of flows along each speed line. The pressure ratio versus flow and 

speed are in good agreement with the test data. The efficiency comparison between the mean line model 

and the data is good at the 100 percent speed line, but is slightly less than the data at the reduced speed 

lines. The mean line code output results were analyzed to gain understanding of how the diffusion factor, 

relative velocity ratio and incidences vary with flow along each speed line. 

As one of the key parameters is the variation of mean line rotor incidence along each speed line, 

knowledge of the range of rotor incidence can be important when matching multistage compressor stages, 

at all operating speeds. Figure 4(a) shows the variation of rotor incidence as a function of flow coefficient 

as calculated by the code. The range of rotor incidence is also a function of the corrected speed of the 

rotor as shown in Figure 4(b) with the lowest range occurring at the higher speeds. At 100 percent speed 

Slip factor Deviation angle, 

deg 

Exit absolute flow angle,

deg 

Rotor pressure ratio Stage pressure ratio 

0.90 6.6 47.2 1.99 1.94 

0.93 4.8 49.7 2.09 2.03 

0.96 2.9 51.9 2.18 2.13 
NASA/TM—2009-215585 6 

the rotor is completely transonic from tip to hub and the range of rotor incidence variation is only 2, 

ranging from 5 at choke to 7 at surge. At the lower speeds the tip relative Mach number is reduced and 

ultimately becomes completely subsonic at 70 percent speed and lower. On the 50 percent speed line the 

incidence range is 11 (2 at choke to 13 at surge). The variation of flow coefficient as a function of 

corrected speed is shown in Figure 5(a). As expected the flow coefficient range from choke to surge is also 

dependent on the corrected speed, with the greatest range at low speeds and the narrowest range at the 

higher speeds. The design point output listing of the mean line code (COMDES version 11) is listed in 

Appendix B. 

The stator leading edge metal angle is 42 from the axial direction and remains fixed at all speeds. 

The range of incidence angles at the stator leading edge was analyzed and is summarized in Figure 5(b). 

The stator incidence angle near surge varies from 8 on the 50 percent speed line to nearly 12 on the 

100 percent speed line. The stator incidence at choke varies from 7.6 at 100 percent speed to –25 on the 

50 percent speed line. 
NASA/TM—2009-215585 7 

TABLE 2.—DIFFUSION FACTOR, RELATIVE VELOCITY RATIO 

AND INCIDENCE NEAR SURGE FOR NASA STAGE 37 

rpm, 

percent 

Rotor diffusion 

factor 

Rotor relative 

velocity ratio 

Rotor 

incidence 

Stator 

incidence 

100 0.65 2.06 7.0 12.4 

90 0.63 1.97 9.5 11.5 

80 0.61 1.92 11.0 10.3 

70 0.63 1.89 12.0 9.4 

60 0.59 1.90 13.0 9.6 

50 0.57 1.84 13.0 7.9 

The relative velocity ratio through the rotor from the inlet tip to the exit mean value is a measure of 

the amount of diffusion through the rotor and thus can be correlated to the onset of separation. The rotor 

relative velocity ratio that is calculated in the code is based on the relative velocity at the inlet tip and the 

exit mean line relative velocity. This parameter may be used as a first order guide to determine the 

compressor surge point. Based on analysis with the mean line code, the relative velocity ratio at surge for 

this rotor reaches a maximum of value 2.05 on the 100 percent speed line, while at lower speeds the value 

at surge is near 1.80. However, since the mean line model along the 100 percent speed line shows slightly 

higher pressure ratio and flow than the data, the calculations on the 100 percent speed line may not be 

reliable. The variation of relative velocity ratio through the Stage 37 rotor as a function of speed is shown 

in Figure 6(a). Another key parameter that can be used to determine the stall or surge is the rotor diffusion 

factor. Based on the mean line flow analysis of Stage 37 test data, the diffusion factor at surge on the 

100 percent speed line is 0.63, while at the lower speeds the diffusion factor at surge is 0.58. The rotor 

diffusion factor as a function of rotor speed in Figure 6(b) reaches a value of 0.63 at 100 percent speed. 

Analysis with the mean line methodology has yielded the values for key parameters at surge along 

each speed line. Table 2 summarizes the values of rotor diffusion factor, relative velocity ratio and 

incidence, as well as the stator incidence, at the flow where surge was encountered at each speed line for 

NASA Stage 37. 

Since the model slightly over-predicted the pressure rise and mass flow on the 100 percent speed line, 

it is likely that the rotor diffusion factor of 0.65 and relative velocity ratio of 2.06 that the model 

calculated are not an accurate estimate of their real values at surge. On the 90 through 50 percent speed 

lines the values of rotor diffusion factor and relative velocity ratio at surge are reasonably constant near 

0.60 and 1.90, respectively. As there is good agreement between the test data and the mean line model 

along these speed lines, the values of diffusion factor and relative velocity ratio at surge are considered to 

be accurate. The rotor and stator incidences at surge vary on each speed line. 
NASA/TM—2009-215585 8 

NASA 74-A Three Stage Axial Compressor 

The three stage NASA 74-A (Ref. 5), axial compressor was built and tested in the 1980s and is 

illustrated in Figure 7. The design details about this variable geometry multistage compressor are 

described in Reference 5. This compressor was selected in order to validate the capability of the mean line 

code methodology for generating a performance map for a multistage compressor with variable geometry, 

and to improve understanding about matching of multistage compressors at part-speed conditions. 

The 74-A compressor had a variable inlet guide vane (IGV) as well as variable stators in stages 1, 2, 

and 3 as illustrated in Figure 8. There were three builds of the 74-A compressor, with each build having a 

different variable geometry schedule. The current flow analysis of the 74-A compressor is focused on the 

configuration, which had an optimized variable geometry schedule to achieve the best aerodynamic 

efficiency and stage matching at all speed lines. The geometry schedule was optimized on the test stand at 

each speed line. 

As illustrated in Figure 8, the sign convention utilized for the variable geometry reset angles is as 

follows: positive reset angle is in the direction of rotation, and negative reset angle indicating against the 

direction of rotation. This compressor was simulated with the mean line code at all tested rotational 

speeds and the analysis results were compared to the test data as shown in Figure 9. The input slip factor 

for the mean line analysis was 0.96 for all three rotors as this produced the best fit with the pressure ratio 

versus speed and flow test data. The design point efficiency at the tip, mean and hub for the three rotors 

were obtained from the original design report and input into the mean line code as follows: rotor 1: 78.1, 

88.3, and 93.4 percent; rotor 2: 83.5, 90.0, and 92.5 percent; rotor 3: 86.9, 91.1, and 92.2 percent. The 

rotor efficiencies were varied at off-design levels of incidence by the relation in Equation (31). The stator 

loss coefficient utilized in the analysis was 6 percent as defined by Equation (27). The aerodynamic

blockages at the rotor inlet and exit were 2 and 5 percent. The slip factor, stator loss and aerodynamic 

blockages were fixed at off design. Note that while these assumptions are known to be not what actually 

occurs in the compressor, they are considered to be reasonable in order to approximate the values 
NASA/TM—2009-215585 9 

of aerodynamic parameters within the compressor. There is quite good agreement at all speeds in the 

pressure ratio versus flow and speed map of Figure 9(a), but less agreement with the efficiency shown in 

Figure 9(b). The optimized variable geometry schedule obtained by testing is included as a table insert in 

Figure 9. The 74-A compressor test data showed an overall peak adiabatic efficiency near 88 percent or 

above on several speed lines, while the mean line code shows 85 percent as the peak efficiency. It is 

possible that the rotors were more efficient than the values listed in the design report and the stators had 

less loss than the values listed in the design report. The optimized variable geometry reset schedule 

obtained by testing is included as a table insert in Figure 9. Even the build of 74-A referred to as 

“optimized geometry” required extensive fine tuning on the test stand at the 100 percent speed line, by 

adjustments of the variable geometry inlet guide vane and variable stators, as shown in the insert of 

Figure 9(b).

Considering this, the 88 percent peak efficiency that was obtained on test seems high, as the reset 

angles required to aerodynamically match the compressor stages meant that losses must have been 

incurred in the process of matching them. The efficiency achieved on test also seems high considering 

that the 74-A rotors and stators were multiple circular arc blade shapes, which typically provide limited 

control of span wise and stream wise work distribution during the design process. 

The comparison between the mean line model and the data was taken to be adequate in order to 

compare the effects of the variable geometry reset angles. The results from the code were analyzed to 

better understand how rotor incidence and diffusion factor, influence the aerodynamic matching of the 

three stages. 

The mean line analysis provides an understanding of the incidences that were encountered by the 

rotors and stators in build 3 featuring the variable geometry schedule that was optimized during testing. 

Analysis of the code output results shows the range of rotor incidences for each of the three stages from 

choke to surge as a function of percent mechanical rotational speed in Figure 10. 

As illustrated in Figure 10, the range of incidence variation for each of the three rotors from choke to 

surge is from 4 at the 100 percent speed line to 8 at the lower speed lines. This range of rotor incidence 

variation is lower than the rotor incidence range of the previous single stage case (NASA Stage 37), 

especially at the lower speed lines. As shown in Figure 10(a), the first stage rotor experiences a 

continuously increasing incidence at reduced speeds. It is possible that the first rotor may be in stall at the 

50 and 60 percent speed lines as the incidence there exceeds 13 (the level of incidence where surge was 

encountered in Stage 37), and reaches a value of 17 at the surge line. In addition, the test data on the 

compressor map of Figure 9(a) shows a flat pressure rise characteristic near surge on the 60 and the 

50 percent speed lines that may be caused partially by flow separation in the first rotor even before 

compressor surge is encountered. 
NASA/TM—2009-215585 10 
NASA/TM—2009-215585 11 

The rotor incidence angle variation is an aerodynamic parameter that may have a key role in 

aerodynamic matching of multistage compressors at design and at off-design operation. Consequently it 

can be important to consider rotor incidence when determining the variable geometry schedule required 

for matching multistage compressors. However, improved models beyond this mean line methodology are 

likely required in order to optimally match advanced highly loaded compressors featuring arbitrary blade 

shapes. 

The variable geometry stators enable the alignment of the flow with the downstream rotor to achieve 

good rotor incidence and hence good stage matching. During the process of resetting the variable stator in 

order to improve the incidence on the rotor, the stator leading edge itself becomes subjected to incidence 

and additional losses. Note that these additional stator losses incurred due to incidence were not modeled, 

but rather were lumped into the single incidence loss model of Equation (31). Based on the mean line 

analysis of 74-A, it appears that the trend of stator incidence variations seem to track the variation in rotor 

incidence, making the lumped incidence loss assumption a reasonable approximation. An analysis of the 

stator leading edge incidence was done with the mean line methodology at all operating points on the map 

to determine the range of incidence angle variation at each speed line. The range of incidence angle 

variation from choke to surge of stators 1, 2, and 3 as a function of percent shaft mechanical speed are 

shown in Figure 11. 

As shown in Figure 11(a) the incidence range of stator 1 is well balanced from 7 to –8 at all speed 

lines. Stator 2 has an incidence variation of 11 to –9 from choke to surge at all speed lines as shown in 

Figure 11(b). However, the range of incidence for stator 3 as shown in Figure 11(c) is from 5 to –37 and 

appears to be not optimally set for a well balanced range of incidence, particularly at speeds below 

100 percent. As there was no rotor 4 following stator 3, its aerodynamic function was limited primarily to 

efficient pressure recovery of the exit flow from rotor 3, and did not have the additional function of being 

a guide vane for a downstream rotor. It would seem that the pressure recovery of stator 3 might have been 
NASA/TM—2009-215585 12 

improved if it had been reset to minimize incidence at the lower speed lines. However, it should be noted 

that at lower speeds the volume flow through the last stage is typically relatively high and that stator 3 is 

likely to be the first to choke thus limiting the amount of mass flow that could pass through the entire 

compressor. Further analysis of this compressor with a computational fluid dynamic code could improve 

understanding of why the variable geometry schedule that was selected provided the best performance at 

all speed lines, and in particular why the reset schedule of stator 3 was set at such high values of 

incidence especially at the lower speed lines. 

Figure 12(a) shows the relative velocity ratio in rotor 1 exceeded the values reached in rotors 2 and 3 

and actually reaches a value of 2.2 before the compressor surges on the 50 percent speed line, indicating 

the possibility that rotor 1 may have been in stall for part of the 80, 70, 60, and 50 percent speed lines. 

Figure 13 shows the range of diffusion factors of rotors 1, 2, and 3 on all speed lines. Figure 13(b) and (c) 

illustrate that rotors 2 and 3 reach their highest values of diffusion factor of 0.59 at the 100 percent speed 

line, a value which is higher than the diffusion factor of rotor 1 at that speed. This indicates the possibility 

that rotor 2 or rotor 3 may have been responsible for initiating surge at the 100 percent speed line. 

Analysis of the NASA 74-A compressor with the mean line methodology has yielded the values for 

rotor diffusion factor, relative velocity ratio and incidence at surge. Table 3 summarizes these values near 

the flow where surge was encountered at each speed line during testing. The design point output listing of 

the 74-A compressor analysis with the mean line code is listed in Appendix C. 

 
NASA/TM—2009-215585 13 

TABLE 3.—DIFFUSION FACTOR, RELATIVE VELOCITY RATIO AND 

INCIDENCE NEAR SURGE FOR THE NASA 74-A COMPRESSOR 

 STAGE 1 STAGE 2 STAGE 3 

rpm, 

percent 

Rotor 1 

DF 

Rotor 1 

W1/W2 

Rotor 1 

Inc 

Stator 1 

Inc 

Rotor 2 

DF 

Rotor 2 

W1/W2 

Rotor 2 

Inc 

Stator 2 

Inc 

Rotor 3 

DF 

Rotor 3 

W1/W2 

Rotor 3 

Inc 

Stator 3 

Inc 

100 0.50 1.84 9.0 1.1 0.58 1.94 10.6 2.8 0.59 1.89 11.4 2.5 

95 0.53 1.87 10.2 2.8 0.56 1.88 10.0 2.7 0.55 1.80 10.0 –0.7 

90 0.53 1.81 11.1 5.0 0.55 1.86 10.1 4.4 0.54 1.77 9.6 –2.8 

85 0.56 1.97 13.1 6.1 0.55 1.86 10.8 8.8 0.56 1.81 10.3 3.8 

80 0.54 1.94 13.1 7.2 0.54 1.84 10.8 10.7 0.55 1.79 10.1 –2.1 

70 0.55 1.98 14.1 4.9 0.48 1.72 10.0 10.1 0.50 1.67 8.8 –7.4 

60 0.57 2.02 15.1 6.3 0.46 1.67 9.8 10.0 0.44 1.57 7.9 –11.5 

50 0.63 2.21 17.0 6.7 0.46 1.68 10.4 7.0 0.38 1.48 7.0 –14.5 

Analysis of the values in Table 3 indicates the stage which might have stalled first and therefore may 

have been the stage responsible for the onset of surge on each speed line. From the analysis it appears that 

on the 100 and 95 percent speed lines, stages 2 and 3 are the first ones to encounter stall as they have the 

highest values of rotor diffusion factor (0.59, 0.58), relative velocity ratio (1.89, 1.94) and incidence 

(11.4, 10.6). At the 95 percent speed line, stage 2 may have stalled first, as it has the highest values of 

rotor diffusion factor (0.56) and relative velocity ratio (1.88). On the 90 percent speed line it appears that 

the second stage initiated stall, as it has the highest values of rotor diffusion factor (0.55) and relative 

velocity ratio (1.86). On the 85 and 80 percent speed lines the diffusion factors are virtually equal in all 

three rotors. On the 70 percent speed line and below it appears that the first stage was the first to stall, as 

the values of rotor diffusion factor (0.56), relative velocity ratio (1.97) and rotor incidence (13.1) are 

higher than in stages 2 and 3. On the 50 and 60 percent speed lines near surge of Figure 9(a) the mean line 

model shows a constantly increasing pressure ratio characteristic, while the test data shows a relatively 

flat pressure rise for nearly half of the speed lines. As there is not good agreement near surge on those two 

speed lines, it is likely that the rotor 1 diffusion factor of 0.63 and relative velocity ratio of 2.21 that the 

model calculated on the 50 percent speed line are not an accurate estimate of their real values at surge. 

Further development of the mean line methodology is planned to improve the accuracy even under 

conditions where one of the compressor blade rows may be in stall, but the compressor is not yet in surge. 

In addition, further analysis of the 74-A compressor is planned with computational flow simulation codes 

at select speed and flow conditions on the map to improve understanding of aerodynamic stage matching. 

NASA 76-B Three Stage Axial Compressor 

The mean line compressor code has been used as a quick tool for aerodynamically matching the 

stages within this multistage compressor at off-design (part-speed) operating conditions by means of 

variable geometry and inter-stage bleeds. This capability can be used as an initial estimate of the variable 

geometry schedule required for safe operation between choke and surge at part-speed operating 

conditions such as during initial startup. The NASA 76-B (Ref. 6), compressor is a three stage research 

compressor designed and built in the 1980s is currently being taken out of storage and is being 

refurbished and readied for testing for the first time. The primary purpose of this test will be to verify the 

integrity of the two bearing running gear under full load, as this facility will be used in the future for 

subsequent advanced multistage compressor testing. The secondary purpose of the test will be to get 

aerodynamic data on the 76-B compressor, as it has not been tested in the past. Similar to the previous 

74-A unit, this compressor was also designed with the Crouse (Ref. 7), axial compressor design program 

which can generate simple blade shapes comprised of multiple circular arc shapes. While the design point 

performance and the variable geometry reset angles at the 100 percent speed line are known from the 

original design simulation, the off-design performance has not been estimated in the past. To avoid 

compressor surge during startup, an accurate estimate of the variable geometry schedule for safe 

operation had to be determined. The cross section for the 76-B compressor is shown in Figure 14. 
NASA/TM—2009-215585 14 

Testing of the 76-B compressor is tentatively scheduled for the summer of 2009 at the NASA Glenn 

Research Center Engine Research Building test cell W7. Whether or not testing will be done will depend 

on results from an ongoing inspection of the compressor hardware. As in the previous case, this highly 

loaded compressor also has variable geometry inlet guide vanes and variable stators 1, 2, and 3 as 

illustrated in Figure 8. There is a need to analytically determine the variable geometry and inter-stage 

bleed schedule that will provide a safe startup operating line so that the initial mechanical shakedown 

tests can proceed free of compressor surge. The mean line flow code was used to predict the performance 

map for this compressor and to determine the variable geometry schedule that would provide a 

recommended operating line for safe startup. This methodology was selected for the initial analysis over a 

higher fidelity computational fluid dynamics analysis (CFD) technique, as it would have been 

computationally expensive to iteratively determine the variable geometry schedule with CFD. However, it 

is planned to verify the reset schedule determined by the mean line analysis with CFD prior to testing. 

A multistage compressor map was created based on the one-dimensional flow methodology. Rotor 

incidence was assumed to be a key parameter for determining the reset angles for the variable geometry 

inlet guide vanes and variable stators for matching of multistage compressors at all operating speeds. As 

such, the variable geometry schedule was determined iteratively using the mean line code by placing 

priority onto the range of incidence of rotors 1, 2, and 3. As the rotor incidence at the peak efficiency used 

in the mean line model is 6, the variable geometry inlet guide vanes and stators were reset manually to 

attempt to provide that level of incidence near the “backbone” of the compressor map. While the rotor 

incidence does vary extensively along a speed line, as has been observed on the previous case analyzed 

(NASA 74-A compressor), the goal of this effort was to minimize the variation in either direction from 

the 6 rotor incidence. This was done concurrently while staying within the empirical stall limits (0.60 

rotor diffusion factor and 1.90 relative velocity ratio) and the choke limit. The choke limit was determined 

by increasing the flow rate until the mean line code no longer converged. 
NASA/TM—2009-215585 15 

Varying the reset angles to control rotor incidence also influenced the levels of diffusion factor and 

relative velocity ratio. As the variable stators were in effect the guide vanes for the downstream rotor, 

they were reset in a manual iterative process until acceptable levels of incidence and diffusion factor were 

obtained on all three rotors. The goal was to control the level of diffusion factor through each rotor not to 

exceed a maximum value of 0.60. Note that the surge line was determined to be where the diffusion factor 

reaches a value of 0.60 in any of the three rotors at a particular operating point. The resultant compressor 

characteristic pressure ratio and efficiency versus flow and speed map and the variable geometry reset 

schedule based on analysis with the mean line code is shown in Figure 15. 

As can be seen in Figure 15(b), the levels of peak efficiency are reduced at the lower speed lines, due 

mainly to the large reset angles of the inlet guide vane. While the suggested variable geometry schedule is 

expected to provide a safe startup line free of compressor stall and surge, it may be at the cost of some 

efficiency, particularly at the reduced speed lines. Figure 15(b) can be compared to Figure 9(b), which has 

been optimized for efficiency on the test stand. It is likely that the variable geometry schedule of the 76-B 

compressor will also need to be fine tuned on the test stand to result in the optimum efficiency at all speed 

lines. 

Note that the performance map for the 76-B compressor is a prediction based on the mean line 

methodology and the off-design models within the code, but the levels of rotor efficiency at the design 

point were input values obtained from the compressor design code originally used to design the 76-B 

compressor as follows: rotor 1: Tip: 78.1 percent, Mean: 88.3 percent, Hub: 93.4 percent; rotor 2: Tip: 

83.5 percent, Mean: 94.0 percent, Hub: 92.5 percent; rotor 3: Tip: 86.9 percent, Mean: 91.1 percent, Hub: 

92.2 percent. Stator losses used in the mean line analysis were 6 percent and slip factor was 0.945 or 

slightly lower than the 74-A machine to be conservative on pressure ratio prediction. Figure 16 shows the 

resulting rotor incidence variations which range from 3 near choke to nearly 11 near surge. The range of 

rotor incidence is in line with or less than that experienced in the 74-A machine. 

As the variable stators were reset to control the incidence variation levels on the downstream rotors, 

the stators’ leading edges also experience incidence variations as shown in Figure 17. At the higher speed 

lines, the level of stator 1 incidence is comparable to that of the 74-A compressor. On the lower speed 

lines, the maximum level of stator 1 incidence is higher than that experienced on the previous 74-A 

compressor. Stator 3 incidence has a much reduced range of variation in comparison to stator 3 in the 

74-A compressor at part speed operation. 

The range of relative velocity ratio on each speed line for the three rotors in the 76-B compressor are 

shown in Figure 18. The rotor 1 velocity ratio is lower than the levels experienced on the previous 74-A 

compressor rotor 1. The maximum relative velocity ratio through rotors 2 and 3 are in line with or lower 

than those of 74-A. 

The range of diffusion factors on each speed line for the three rotors of the 76-B compressor are 

shown in Figure 19. At a maximum value of 0.60 near surge, the rotor diffusion factors for the three 

rotors are also in line with and in some cases lower than the levels experienced on the previous 74-A 

compressor rotors, further increasing confidence in this test achieving the predicted surge line. 

Based on the mean line analyses of the incidence range experienced by the rotors and stators, as well 

as the rotor maximum diffusion factor and relative velocity ratios at the surge line, it is expected that the 

76-B compressor will meet or exceed the predicted flow range shown in Figure 15.

The recommended variable geometry schedule and safe start up line for the 76-B compressor are 

summarized in Table 4. The 76-B compressor mean line flow analysis at the design point is listed in 

Appendix D. 
NASA/TM—2009-215585 16 
NASA/TM—2009-215585 17 
NASA/TM—2009-215585 18 

TABLE 4.—76-B THREE STAGE AXIAL COMPRESSOR STARTUP OPERATING LINE AND VARIABLE GEOMETRY SCHEDULE 

Corrected speed, 

percent 

Corrected mass flow 

lbm/sec 

Pressure 

ratio 

Inlet guide vane 

reset angle 

Stator 1 reset 

angle 

Stator 2 reset 

angle 

Stator 3 reset 

angle 

100 55.77 4.59 0 0 0 0 

95 50.87 3.94 5 0 0 –2 

90 46.34 3.50 10 0 –5 –5 

85 42.13 3.08 15 0 –10 –6 

80 37.90 2.66 20 0 –10 –7 

70 31.66 2.14 25 –5 –10 –9 

60 25.78 1.69 30 –10 –10 –11 

50 20.17 1.36 35 –5 –15 –14 

Conclusion 

The mean line flow analysis code COMDES has been written to provide a quick look at key 

aerodynamic parameters within single and multistage compressors. The design point rotor efficiency and 

stator loss coefficient are input into the code. The off-design performance is determined from models 

within the code based on the level of rotor incidence. Correlations to compressor surge have been 

estimated from the mean line analyses of NASA Stage 37 and NASA 74-A compressors, where rotor 

diffusion factor loading level near 0.60 and relative velocity ratio levels near 1.9 are experienced near 

surge in one or more of the compressor rotors along most of the tested speed lines. However, these values 

appear to be exceeded in rotor 1 of the 74-A unit on the lower speed lines, and perhaps on Stage 37 at the 

100 percent speed line. Note that as the off-design correlations within the code are largely based on 

empirical models derived from Stage 37 and the 74-A compressors, it may not provide accurate 

representations of flow in modern compressors featuring arbitrary blade shapes. The mean line 

methodology has been used to provide some guidance as to how to run the NASA 76-B multistage 

compressor on the test stand by helping to guide the selection of variable geometry schedule which is 

expected to provide a wide range of operation. As the 76-B compressor consists of similar multiple 

circular arc blades as Stage 37 and the 74-A compressors, the performance prediction based on the mean 

line model is considered to be a reasonable approximation. Based on the mean line analysis, a startup 

schedule has been recommended for the 76-B compressor that is expected to provide a surge free start up 

line. However, it is planned that the variable geometry schedule will be fine tuned on the test stand to 

provide optimum efficiency at each speed line. More research is required to determine the relationship of 

incidence, diffusion factor and relative velocity ratio on each blade row to achieve optimum stage 

matching and overall efficiency with acceptable surge margin. The mean line methodology can also be 

used in the conceptual design process to size parameters such as number of stages and to estimate rotor 

inlet and exit blade angles to meet pressure ratio requirements. The mean line code is a research code 

currently under development and improved loss models are planned, including further validation of the 

code for modeling flow in centrifugal compressor stages.
NASA/TM—2009-215585 19 

Appendix A.—Governing Equations 

The rotor annular area is calculated from the hub and tip radii from the centerline by Equation (1). 

The aerodynamic blockage are specified as input parameters at the leading and trailing edges of the rotor 

in the mean line analysis, and is not varied at off-design operating conditions. 

    

1/ 2 1/ 2

2 2

















A    RT  RH RT  RH  B (1) 

The static temperature is a function of the total temperature and the Mach number as shown in 

Equation (2). 

2

2

1 1 M

T

T

S

t     (2) 

The static pressure is a function of the total pressure and the Mach number as shown in Equation (3). 

1

















 

S

t

S

t

T

T

P

P 2 1

2

1 1 







 



     M (3) 

The volume flow rate into the rotor is determined by Equation (4) in terms of the mass flow rate, 

static pressure and temperature. 

S

S C

P

m T g

Q  (4) 

The absolute velocity at the rotor inlet is shown in Equation (5) as a function of volume flow rate and 

inlet area. 

A

Q C  (5) 

The speed of sound is determined from the static temperature and the gas properties as shown in 

Equation (6). 

  1/ 2

a    TS gC (6) 

The Mach number is determined from the total velocity and the speed of sound as shown in 

Equation (7). 

a

M  C (7)

The meridional velocity is determined from the total velocity and the tangential component of 

absolute velocity as shown in Equation (8). 
NASA/TM—2009-215585 20 

  1/ 2

2 2 CM  C CU (8) 

The flow function of the rotor is defined by Equation (9) in terms of the axial component of velocity 

and the rotor peripheral speed. 

T

M

U

C   (9) 

The tangential component of absolute velocity is determined from the absolute velocity and the inlet 

swirl angle as shown in Equation (10). 

CU  C Tan (10) 

The relative flow angle is determined by Equation (11). 





 



    

C

U CU

F Tan 1 (11) 

The rotor incidence angle is defined as the difference between the relative flow angle and the blade 

angle at the rotor leading edge just upstream of the blade by Equation (12). 

   iR = F B (12) 

The relative velocity at the rotor leading edge is determined by Equation (13). 

  Cos F

C

W   (13) 

The rotor total-to-total adiabatic efficiency is defined by Equation (14). 

1

1

1

2

1

1

2



 















 





t

t

t

t

T

T

P

P

(14) 

The enthalpy rise is calculated in terms of temperature rise across the rotor by Equation (15) and the 

Euler Equation (16) which is based on the change in tangential velocity from inlet to exit. 

  P C Tt2 Tt1 H = J c g  (15) 

H  U2 CU 2 U1 CU1 (16) 

The meridional component of velocity is determined from the density, mass flow rate and area as 

shown in Equation (17). 
NASA/TM—2009-215585 21 

2 2

2

2 P A

m R T

C =

S

S

M (17) 

The relative velocity at the rotor exit is determined from Equation (18). 

   1/ 2

2

2

2 W 2= U2 CU 2  CM (18) 

The absolute flow angle at the rotor exit is determined from the relation shown in Equation (19). 

















  

2

1 2

2 Tan

M

U

C

C (19) 

The absolute velocity at the rotor exit is determined from Equation (20). 

 

1/ 2 2

2

2 C2  CU 2  CM (20) 

The tangential component of relative velocity at the rotor exit is determined from Equation (21). 

 

1/ 2 2

2

2 WU 2  W2 CM (21) 

The slip factor is the difference between the theoretical and absolute fluid tangential velocities 

normalized with blade peripheral speed as described by Equation (22). The slip factor is an input item and 

is typically from 0.93 to 0.96 for axial compressors. For centrifugal compressors the slip factor can be on 

the order of from 0.80 to 0.90, depending on number of blades and exit blade angle. 

 

2

2 C 2 Tan B2

U

C

= U  M 

 (22) 

In the design mode, the rotor exit blade angle is determined from Equation (23) in terms of the slip 

factor, rotor peripheral velocity and the absolute tangential and meridional velocities. 

 





 



     

2

2 2 1

2 Tan

M

U

B C

U C

(23) 

The relative flow angle at the rotor exit is determined from Equation (24). 

 





 



    

2

1 2 2

2 Tan

M

U

F C

U C (24) 

The rotor diffusion factor at the root-mean-square radius is calculated by Equation (25). 

     

   

1 2 1

1 1 2 2

1

2 1

R R W

R C R C

W

W DF U U (25) 
NASA/TM—2009-215585 22 

The incidence at the stator vane leading edge can be estimated by Equation (26). 

V V i  2   (26) 

The stator loss coefficient is defined by Equation (27). 

2 2

4 2

t S

t t

V P P

P P



   (27) 

The power required to drive the compressor is calculated from Equation (28). 

c g

H m

= 550 Power



(28) 

The inlet guide vane setting angle versus loss of total pressure that is used by the code was 

determined empirically from the NASA 74-A compressor which has a flap style variable inlet guide vane, 

and is shown in Equation (29). As such, these losses are considered a good approximation for the 76-B 

compressor, which also has similar flap style inlet guide vanes. Note that these losses would likely be 

different for other types of variable guide vane configurations and may not provide an accurate 

representation of losses. 

2 3 P 0.0059374 .00055463747 S .00007424 S .000000458487 S  t     (29) 

The total pressure at the exit of the variable inlet guide vane is obtained from Equation (30). 

  Pt  Pt  Pt 1 exit inlet (30) 

The efficiency of the rotor as a function of incidence shown in Equation (31) was determined 

empirically from the Stage 37 and 74-A compressors analyzed in this report and is currently the model in 

the compressor code for estimating the off-design efficiency. This same model is used on all speed lines 

for rotor efficiency deration versus incidence. 

0.0006 0.0185 0.1699 0.5187 3 2   iR  iR  iR  (31)

 
NASA/TM—2009-215585 23 

Appendix B.—NASA Stage 37 Axial Compressor (100 Percent rpm) 

********************************************************************* 

**************** AXIAL & CENTRIFUGAL COMPRESSOR BLADE DESIGN 1-D   

** ******************* COMDES Version 11. ************************ 

********************************************************************* 

 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 1 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 46.95 17188.699 14.613 518.670 0.850 0.860 0.980 

 (21.34131 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 46.95 17189.197 1.402 0.249 53.349 36.000 0.030 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 1 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 9.93 0.00 -0.02 588.32 -0.20 588.32 0.54 

 MEAN 8.59 0.00 -0.02 692.14 -0.24 692.14 0.64 

 HUB 7.00 0.00 -0.02 595.24 -0.20 595.24 0.55 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 68.46 62.28 6.18 1489.95 1602.08 11.99 490.04 1.47 

 MEAN 61.77 56.62 5.15 1288.88 1463.18 11.04 478.66 1.36 

 HUB 60.46 52.33 8.13 1050.00 1207.16 11.93 489.37 1.11 

 

 ROTOR EXIT CONDITIONS, STAGE 1 

 B2 axial THK AeroBl 

 0.30 0.030 0.970 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 9.65 872.72 571.32 659.72 1190.07 0.73 

 MEAN 8.59 927.93 707.79 600.06 1195.32 0.78 

 HUB 7.38 1034.19 820.66 629.34 1177.45 0.88 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1447.20 1096.54 875.88 0.92 

 MEAN 1288.18 834.82 580.39 0.70 1.83 

 HUB 1106.55 691.23 285.89 0.59 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 27.42 1.88 19.17 651.54 1.26 587.99 0.77 

 MEAN 31.71 2.17 21.28 665.19 1.28 593.32 0.88 

 HUB 32.48 2.22 19.65 664.59 1.28 575.37 0.91 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 40.89 53.01 49.55 3.46 0.93 0.45 1.29 

 MEAN 49.71 44.05 39.22 4.83 0.93 0.59 1.49 

 HUB 52.52 24.43 18.28 6.15 0.93 0.62 1.83 

 

 STAGE EXIT CONDITIONS, STAGE 1 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.06 0.834 29.909 2.047 1.273 220.863 1.712 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 882613.25 0.421 2341.782 1037233.750 

 

 OVERALL EXIT CONDITIONS; ALL 1 STAGES 

Del Enthalpy GHP EFFICIENCY PR TR 

 882613.25 2341.7822 0.8264 2.0346 1.2733 

 

NASA/TM—2009-215585 25 

Appendix C.—NASA 74-A Three Stage Axial Compressor 

(100 Percent rpm Geometry Reset Optimized) 

********************************************************************* 

**************** AXIAL & CENTRIFUGAL COMPRESSOR BLADE DESIGN 1-D   

** ******************* COMDES Version 11. ************************ 

********************************************************************* 

 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 1 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 63.74 16042.000 14.467 518.670 0.850 0.860 0.980 

 (28.97464 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 63.74 16042.465 1.402 0.249 53.349 28.000 0.030 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 1 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 10.08 15.00 15.16 493.78 133.79 475.31 0.45 

 MEAN 7.94 15.00 15.16 580.92 157.40 559.19 0.53 

 HUB 4.93 15.00 15.16 499.59 135.37 480.90 0.45 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 68.87 64.30 4.57 1411.69 1369.98 12.60 498.51 1.24 

 MEAN 58.65 52.40 6.25 1110.91 1116.53 11.91 490.48 1.03 

 HUB 47.96 42.20 5.76 689.46 746.07 12.56 498.03 0.68 

 

 ROTOR EXIT CONDITIONS, STAGE 1 

 B2 axial THK AeroBl 

 0.30 0.030 0.950 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 9.83 860.00 583.39 631.86 1156.82 0.74 

 MEAN 8.09 901.83 635.16 640.21 1138.83 0.79 

 HUB 5.85 1168.69 933.72 702.86 1113.16 1.05 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1376.41 1013.96 793.02 0.88 

 MEAN 1132.52 810.70 497.36 0.71 1.62 

 HUB 818.96 712.17 114.76 0.64 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 23.50 1.62 16.27 617.33 1.19 555.61 0.78 

 MEAN 23.52 1.63 15.55 606.14 1.17 538.29 0.89 

 HUB 26.93 1.86 13.40 626.52 1.21 512.89 0.94 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 42.72 51.45 49.40 2.05 0.96 0.38 1.35 

 MEAN 44.77 37.84 35.20 2.64 0.96 0.40 1.72 

 HUB 53.03 -9.27 -11.90 2.63 0.96 0.26 2.76 

 

 STAGE EXIT CONDITIONS, STAGE 1 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.07 0.825 23.980 1.658 1.189 308.916 2.395 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 610056.13 0.322 2197.571 1531257.125 

 

 
NASA/TM—2009-215585 26 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 2 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 63.74 16042.000 23.980 616.663 1.000 1.000 0.980 

 (28.97464 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 42.61 14712.716 1.401 0.249 53.349 32.000 0.030 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 2 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 9.76 10.00 10.16 601.47 107.79 591.73 0.50 

 MEAN 8.29 10.00 10.16 601.47 107.79 591.73 0.51 

 HUB 6.49 10.00 10.16 601.47 107.79 591.73 0.50 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 64.44 63.49 0.95 1365.63 1394.24 20.16 586.78 1.17 

 MEAN 60.24 53.48 6.76 1159.89 1211.88 20.13 586.48 1.02 

 HUB 53.09 47.87 5.22 908.69 1001.60 20.16 586.78 0.84 

 

 ROTOR EXIT CONDITIONS, STAGE 2 

 B2 axial THK AeroBl 

 0.30 0.030 0.950 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 9.57 887.70 641.26 613.84 1265.09 0.70 

 MEAN 8.35 900.20 651.89 620.81 1251.86 0.72 

 HUB 6.91 1070.36 852.40 647.36 1239.25 0.86 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1339.31 929.55 698.05 0.73 

 MEAN 1168.35 807.55 516.46 0.65 1.75 

 HUB 967.63 657.54 115.23 0.53 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 39.74 1.66 28.60 730.80 1.19 665.09 0.84 

 MEAN 39.08 1.63 27.68 718.77 1.17 651.19 0.91 

 HUB 42.25 1.76 25.96 733.24 1.19 637.77 0.93 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 46.25 48.67 46.37 2.30 0.96 0.48 1.25 

 MEAN 46.40 39.76 37.09 2.67 0.96 0.49 1.47 

 HUB 52.78 10.09 6.70 3.39 0.96 0.55 1.88 

 

 STAGE EXIT CONDITIONS, STAGE 2 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.07 0.852 39.450 1.645 1.180 236.419 1.833 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 691788.00 0.386 2491.989 1210194.250 

 

 
NASA/TM—2009-215585 27 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 3 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 63.74 16042.000 39.450 727.603 1.000 1.000 0.980 

 (28.97464 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 28.13 13544.696 1.400 0.250 53.349 39.000 0.050 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 3 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 9.52 10.00 10.16 583.18 104.52 573.73 0.45 

 MEAN 8.46 10.00 10.16 583.18 104.52 573.73 0.45 

 HUB 7.25 10.00 10.16 583.18 104.52 573.73 0.45 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 64.60 64.76 -0.16 1332.87 1359.76 34.38 699.59 1.04 

 MEAN 61.64 53.80 7.84 1184.74 1227.59 34.33 699.31 0.95 

 HUB 57.37 49.35 8.02 1015.23 1081.43 34.38 699.59 0.83 

 

 ROTOR EXIT CONDITIONS, STAGE 3 

 B2 axial THK AeroBl 

 0.30 0.050 0.950 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 9.36 922.28 692.41 609.23 1368.77 0.67 

 MEAN 8.46 912.86 668.46 621.67 1356.01 0.67 

 HUB 7.46 1052.63 840.28 634.01 1350.57 0.78 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1310.05 867.55 617.64 0.63 

 MEAN 1184.73 808.10 516.28 0.60 1.74 

 HUB 1044.49 666.09 204.21 0.49 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 63.76 1.62 47.04 850.32 1.17 779.57 0.87 

 MEAN 61.28 1.55 45.24 834.39 1.15 765.08 0.91 

 HUB 65.67 1.66 43.97 850.92 1.17 758.78 0.92 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 48.66 45.39 42.83 2.56 0.96 0.54 1.21 

 MEAN 47.08 39.71 37.00 2.71 0.96 0.51 1.36 

 HUB 52.96 17.85 14.32 3.53 0.96 0.60 1.59 

 

 STAGE EXIT CONDITIONS, STAGE 3 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.07 0.863 62.302 1.579 1.162 188.703 1.463 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 735914.31 0.429 2650.942 1010580.875 

 

 OVERALL EXIT CONDITIONS; ALL 3 STAGES 

Del Enthalpy GHP EFFICIENCY PR TR 

 2037758.50 7340.5020 0.8131 4.2382 1.6296

 

NASA/TM—2009-215585 29 

Appendix D.—NASA 76-B Three Stage Axial Compressor 100 Percent rpm 

(Performance Estimate) 

********************************************************************* 

**************** AXIAL & CENTRIFUGAL COMPRESSOR BLADE DESIGN 1-D   

** ******************* COMDES Version 11. ************************ 

********************************************************************* 

 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 1 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 55.49 16085.000 14.583 518.670 1.000 1.000 0.980 

 (25.22451 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 55.49 16085.466 1.402 0.249 53.349 28.000 0.030 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 1 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 9.98 21.37 21.74 623.08 248.48 571.39 0.57 

 MEAN 8.23 9.70 10.07 623.08 110.67 613.17 0.58 

 HUB 6.01 0.00 0.37 623.08 4.05 623.06 0.57 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 61.59 65.35 -3.76 1400.31 1309.56 11.67 486.56 1.20 

 MEAN 59.20 54.74 4.46 1155.92 1216.87 11.64 486.24 1.12 

 HUB 53.41 49.21 4.20 843.47 1045.40 11.67 486.56 0.96 

 

 ROTOR EXIT CONDITIONS, STAGE 1 

 B2 axial THK AeroBl 

 0.30 0.030 0.950 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 9.58 1046.03 701.61 775.84 1124.66 0.93 

 MEAN 8.14 1002.22 760.33 652.95 1155.38 0.87 

 HUB 6.37 1119.57 900.43 665.33 1144.52 0.98 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1345.01 1007.91 643.40 0.90 

 MEAN 1142.05 756.34 381.72 0.65 1.62 

 HUB 894.14 665.36 6.29 0.58 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 22.93 1.57 13.11 614.37 1.18 523.37 0.75 

 MEAN 27.12 1.86 16.60 637.62 1.23 553.85 0.85 

 HUB 29.43 2.02 15.94 647.46 1.25 543.02 0.90 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 42.12 39.67 36.25 3.42 0.94 0.36 1.30 

 MEAN 49.35 30.31 26.01 4.30 0.94 0.55 1.57 

 HUB 53.54 -0.54 -4.80 4.26 0.94 0.57 2.16 

 

 STAGE EXIT CONDITIONS, STAGE 1 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.06 0.806 25.819 1.770 1.221 258.935 2.007 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 712698.81 0.394 2235.032 1262908.750 

 

 
NASA/TM—2009-215585 30 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 2 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 55.49 16085.000 25.819 633.150 1.000 1.000 0.980 

 (25.22451 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 34.91 14558.812 1.401 0.249 53.349 40.000 0.030 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 2 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 9.35 20.00 20.37 614.91 228.34 570.94 0.51 

 MEAN 8.12 11.00 11.37 614.91 123.68 602.35 0.51 

 HUB 6.66 10.00 10.37 614.91 112.55 604.52 0.51 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 60.44 62.78 -2.34 1312.72 1246.60 21.64 601.92 1.03 

 MEAN 58.82 53.47 5.35 1139.67 1187.59 21.60 601.61 0.99 

 HUB 53.22 50.73 2.49 935.13 1027.02 21.64 601.92 0.85 

 

 ROTOR EXIT CONDITIONS, STAGE 2 

 B2 axial THK AeroBl 

 0.30 0.030 0.950 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 9.07 1110.87 838.37 728.80 1254.74 0.89 

 MEAN 8.06 1018.00 758.18 679.34 1262.15 0.81 

 HUB 6.90 1206.90 973.60 713.24 1248.12 0.97 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1272.58 848.34 434.20 0.68 

 MEAN 1131.00 774.92 372.83 0.61 1.60 

 HUB 968.96 713.26 4.64 0.57 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 43.43 1.68 26.08 756.14 1.19 653.41 0.83 

 MEAN 43.57 1.69 28.39 748.03 1.18 661.69 0.89 

 HUB 48.01 1.86 26.34 767.52 1.21 646.31 0.92 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 49.00 30.79 26.53 4.26 0.94 0.51 1.28 

 MEAN 48.14 28.76 24.55 4.21 0.94 0.53 1.47 

 HUB 53.77 -0.37 -4.68 4.31 0.94 0.54 1.80 

 

 STAGE EXIT CONDITIONS, STAGE 2 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.06 0.838 43.921 1.701 1.196 198.773 1.541 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 774043.25 0.478 2427.408 1048406.375 

 

 

 
NASA/TM—2009-215585 31 

 COMPRESSOR INLET CONDITIONS - ANALYSIS, STAGE 3 

 W act RPM act Pt Tt 'POTS POTH AeroBl 

 55.49 16085.000 43.921 757.232 1.000 1.000 0.980 

 (25.22451 Kg/sec) 

 

 W cor RPM cor GAMMA Cp 'R NBLAD THK 

 22.44 13312.652 1.399 0.250 53.349 56.000 0.050 

 

 ROTOR LEADING EDGE CONDITIONS, STAGE 3 

 R1 Stator Alfa C1 CU1 Cm1 Abs MACH 

 TIP 8.94 24.00 24.37 603.96 273.61 538.43 0.45 

 MEAN 8.06 15.00 15.37 603.96 166.04 580.69 0.46 

 HUB 7.07 17.00 17.37 603.96 188.94 573.64 0.45 

 

 BetaFlo BetaBlade Incid U1 W1 Ps1 Ts1 Rel Mach 

 TIP 58.38 58.70 -0.32 1254.61 1152.01 38.11 727.21 0.87 

 MEAN 57.96 51.14 6.82 1131.25 1138.60 38.06 726.92 0.86 

 HUB 53.08 49.97 3.11 992.68 1005.37 38.11 727.21 0.76 

 

 ROTOR EXIT CONDITIONS, STAGE 3 

 B2 axial THK AeroBl 

 0.30 0.050 0.950 

 

 R2 C2 Cu2 Cm2 Ao2 Mach2 

 TIP 8.80 1139.71 903.45 694.79 1362.96 0.84 

 MEAN 8.03 1047.10 814.34 658.23 1371.41 0.76 

 HUB 7.18 1245.44 1032.40 696.61 1355.86 0.92 

 

 U2 W2 Wu2 Mach Rel2 Ws1/W2 

 TIP 1235.80 770.18 332.35 0.57 

 MEAN 1127.28 728.84 312.94 0.53 1.57 

 HUB 1007.14 697.07 25.26 0.51 

 

 Pt2 PR Ps2 Tt2 TR Ts2 Eff2 

 TIP 70.10 1.60 44.34 880.66 1.16 772.80 0.88 

 MEAN 69.79 1.59 47.45 873.79 1.15 782.71 0.92 

 HUB 75.43 1.72 43.72 893.27 1.18 764.52 0.93 

 

 Alfa2 Beta FLO Beta BLADE Deviat Slip F. Diff Fct Solidity 

 TIP 52.44 25.56 20.81 4.75 0.94 0.54 1.31 

 MEAN 51.05 25.43 20.85 4.58 0.94 0.56 1.45 

 HUB 55.99 -2.08 -6.65 4.57 0.94 0.56 1.66 

 

 STAGE EXIT CONDITIONS, STAGE 3 

 DIFF LOSS Effic Pdisch PR TR Ns Ns nondim 

 0.06 0.864 70.177 1.598 1.166 162.820 1.262 

 

 Del Enthalpy Del_H/U^2 GHP Reynolds# 

 785293.56 0.514 2462.690 895235.375 

 

 OVERALL EXIT CONDITIONS; ALL 3 STAGES 

Del Enthalpy GHP EFFICIENCY PR TR 

 2272035.50 7125.1299 0.8039 4.7739 1.7016 
NASA/TM—2009-215585 32 

References 

1. Shapiro, A.H., “The Dynamics and Thermodynamics of Compressible Fluid Flow, Volume I,” The 

Ronald Press Co., 1953, pp. 83–88. 

2. Lieblein, Schwenk, Francis, Broderick, “Diffusion Factor for Estimating Losses and Limiting Blade 

Loadings in Axial Flow Compressor Blade Elements,” NACA RM E53D01, 1953. 

3. Fowler, J.R., “GASPLUS User’s Manual,” NASA LEW15091, 1994. 

4. Reid, L., Moore, R.D., “Design and Overall Performance of Four Highly Loaded, High-Speed Inlet 

Stages for an Advanced High-Pressure-Ratio Core Compressor,” NASA Technical Paper 1337, 1978. 

5. Steinke, R.J., “Design of 9.271 Pressure Ratio Five Stage Core Compressor and Overall Performance 

for First Three Stages,” NASA Technical Paper 2597, Figure 22 page 11, 1986. 

6. Fabian, J.C., Thorp, S.A., Veres, J.P.,“NASA 76-B Three Stage Axial Compressor Design,” NASA 

Technical Memorandum, (to be published). 

7. Crouse, J.E., Gorrell, W.T., “Computer Program for Aerodynamic and Blading Design of Multistage 

Axial-Flow Compressors,” NASA TP 1946, 1981. 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-11-2009 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Axial and Centrifugal Compressor Mean Line Flow Analysis Method 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Veres, Joseph, P. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 561581.02.08.03.21.03 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-16825 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA; AIAA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2009-215585; AIAA-2009-

1641

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 07, 02, and 05 

Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

This paper describes a method to estimate key aerodynamic parameters of single and multistage axial and centrifugal compressors. This 

mean-line compressor code COMDES provides the capability of sizing single and multistage compressors quickly during the conceptual 

design process. Based on the compressible fluid flow equations and the Euler equation, the code can estimate rotor inlet and exit blade 

angles when run in the design mode. The design point rotor efficiency and stator losses are inputs to the code, and are modeled at off design. 

When run in the off-design analysis mode, it can be used to generate performance maps based on simple models for losses due to rotor 

incidence and inlet guide vane reset angle. The code can provide an improved understanding of basic aerodynamic parameters such as 

diffusion factor, loading levels and incidence, when matching multistage compressor blade rows at design and at part-speed operation. Rotor 

loading levels and relative velocity ratio are correlated to the onset of compressor surge. NASA Stage 37 and the three-stage NASA 74-A 

axial compressors were analyzed and the results compared to test data. The code has been used to generate the performance map for the 

NASA 76-B three-stage axial compressor featuring variable geometry. The compressor stages were aerodynamically matched at off-design 

speeds by adjusting the variable inlet guide vane and variable stator geometry angles to control the rotor diffusion factor and incidence 

angles. 

15. SUBJECT TERMS

Compressors; Turbocompressors; Simulation; Computational fluid dynamic; Turbomachinery 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

36 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18