Eric S. Hendricks

Glenn Research Center, Cleveland, Ohio

Development of an Open Rotor Cycle Model in 

NPSS Using a Multi-Design Point Approach

NASA/TM—2011-217225

October 2011

GT2011-46694
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
Eric S. Hendricks

Glenn Research Center, Cleveland, Ohio

Development of an Open Rotor Cycle Model in 

NPSS Using a Multi-Design Point Approach

NASA/TM—2011-217225

October 2011

GT2011-46694

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Turbo Expo 2011

sponsored by the American Society of Mechanical Engineers (ASME)

Vancouver, British Columbia, Canada, June 6–10, 2011
Acknowledgments

The work presented in this paper was supported by the Subsonic Fixed Wing Project at NASA Glenn Research Center. Special 

thanks to Jeff Berton, Bill Haller, Justin Gray, and Scott Jones of the NASA Glenn Research Center as well as Dr. Dimitri 

Mavris, Dr. Jimmy Tai, Dr. Jeff Schutte, and Chris Perullo of the Aerospace Systems Design Laboratory at the 

Georgia Institute of Technology for their support and guidance in this research.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.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 is a formal draft or working 

paper, intended to solicit comments and 

ideas from a technical peer group.

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2011-217225 1 

Development of an Open Rotor Cycle Model in NPSS 

Using a Multi-Design Point Approach 

Eric S. Hendricks 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

NASA's Environmentally Responsible Aviation 

Project and Subsonic Fixed Wing Project are focused on 

developing concepts and technologies which may enable 

dramatic reductions to the environmental impact of future 

generation subsonic aircraft (Refs. 1 and 2). The open 

rotor concept (also referred to as the Unducted Fan or 

advanced turboprop) may allow the achievement of this 

objective by reducing engine emissions and fuel 

consumption. To evaluate its potential impact, an open 

rotor cycle modeling capability is needed. This paper 

presents the initial development of an open rotor cycle 

model in the Numerical Propulsion System Simulation 

(NPSS) computer program which can then be used to 

evaluate the potential benefit of this engine. 

The development of this open rotor model 

necessitated addressing two modeling needs within 

NPSS. First, a method for evaluating the performance of 

counter-rotating propellers was needed. Therefore, a new 

counter-rotating propeller NPSS component was created. 

This component uses propeller performance maps 

developed from historic counter-rotating propeller 

experiments to determine the thrust delivered and power 

required. Second, several methods for modeling a 

counter-rotating power turbine within NPSS were 

explored. These techniques used several combinations of 

turbine components within NPSS to provide the necessary 

power to the propellers. Ultimately, a single turbine 

component with a conventional turbine map was selected. 

Using these modeling enhancements, an open rotor 

cycle model was developed in NPSS using a multi-design 

point approach. The multi-design point (MDP) approach 

improves the engine cycle analysis process by making it 

easier to properly size the engine to meet a variety of 

thrust targets throughout the flight envelope. A number of 

design points are considered including an aerodynamic 

design point, sea-level static, takeoff and top of climb. 

The development of this MDP model was also enabled by 

the selection of a simple power management scheme 

which schedules propeller blade angles with the freestream 

Mach number. Finally, sample open rotor performance 

results and areas for further model improvements are 

presented. 

Introduction 

Passenger travel by commercial aviation is expected 

to grow at a steady pace over the next 10 to 15 years 

(Refs. 3, 4, and 5). This expected increase in the number 

of passengers will place significant strain on the current 

air transportation system. In addition to creating more 

congestion and delays, the increase in air travel will 

amplify aviation’s impact on the environment (Refs. 4, 6, 

and 7). Therefore, several of NASA’s primary goals for 

the future are the significant reduction of aircraft fuel 

burn, community noise, emissions of nitrogen oxides 

(NOx) and field length for the next generation of 

commercial single aisle aircraft (Ref. 12). These aggressive goals are used to develop technology roadmaps and 

guide technology research efforts across a number of 

research disciplines. 

A technology area of particular interest to NASA and 

the commercial aviation industry is that of advanced 

engine concepts (Ref. 8). One specific concept in this 

research area that is receiving considerable attention is 

the open rotor as it has the potential to dramatically 

reduce aircraft fuel consumption. The open rotor concept 

achieves these reductions by using a large, counterrotating advanced propeller as shown in Figure 1. The 

advanced counter-rotating propeller allows for many of 

the fuel efficiency benefits of a traditional turboprop to be 

achieved without the sacrifice of maximum aircraft speed 

typically required. The open rotor engine concept was 

originally developed during the 1980’s under the NASA’s 

Advanced Turboprop Project (Ref. 9), and demonstrated 

significant fuel burn reductions. However, due to reduced 

fuel prices and several technical challenges facing open 

rotor implementation, the concept was not developed 

further. 
NASA/TM—2011-217225 2 

Figure 1.—Cutaway of a notional open 

rotor concept (Ref. 10). 

While the open rotor engine developed during the 

Advanced Turboprop Project demonstrated significant 

reductions in fuel consumption, the lack of development 

over the last two decades has allowed conventional 

turbofans to close the performance gap (Refs. 9 and 11). 

However, many of the technological improvements which 

have been made to turbofans can also be applied the open 

rotor, thereby further improving its performance. In 

addition, advances in computing and design are enabling 

the creation of more advanced counter-rotating propeller 

blades. With these improvements to both conventional 

gas turbine components and counter-rotating propellers, 

there is a need to evaluate the potential improvements 

available in open rotor engines. The development of a 

new analytical cycle model is critical to the evaluation of 

conceptual open rotor aircraft designs such as those 

shown in Figure 2. 

This paper summarizes the development of an open 

rotor engine cycle model with the NPSS computer 

program. NPSS is a variable-fidelity, object-oriented, 

engine cycle analysis tool developed jointly by NASA 

and U.S. industry (Refs. 12 and 13). It is currently the 

accepted, state-of-the-art software for airbreathing engine 

cycle performance analysis for U.S. aerospace industry, 

academia, and NASA. In the next few sections, the 

following topics related to the open rotor cycle model 

development will be addressed: 

 Selection of an open rotor engine architecture and 

implementation in NPSS 

 NPSS model enhancements for counter-rotating 

propeller performance prediction 

 Potential solutions for estimating counter-rotating 

turbine performance in NPSS 

 Implementation of a multi-design point formulation to improve process for creating candidate 

engine models 

Figure 2.—Notional open rotor airplane concepts 

(Refs. 14 and 15). 

 Determination of a power management strategy 

allowing for performance estimation throughout 

the flight envelope 

 Presentation of sample engine performance 

results 

 Areas for further model improvements 

Nomenclature 

A Propeller Annulus Area 

ADP Aerodynamic Design Point 

Alt Altitude 

β Front Blade angle 

CP Net Power Coefficient, P/n3

D5

CT Thrust Coefficient, Fg/n2

D4

D Diameter 

ENET Net Propeller Efficiency, J CT/CP

Fg Propeller Gross Thrust 

FAR Fuel to Air Ratio 

Δh Specific Enthalpy Change 

HP High Pressure 

HPC High Pressure Compressor 

HPT High Pressure Turbine 

ISA International Standard Atmosphere 

J (or J1C) Front Rotor Advance Ratio, V/nD 

LP Low Pressure 

LPC Low Pressure Compressor 

LPT Low Pressure Turbine 

 
NASA/TM—2011-217225 3 

M Mach Number 

MDP Multi-Design Point 

N, n Rotation Speed 

NPSS Numerical Propulsion System Simulation 

PQA Modified Power Coefficient, P/ρn3

D3A 

PQAJ3 Modified Power Coefficient divided by 

Advance Ratio cubed 

PT Power Turbine 

SLS Sea-Level Static 

T Temperature 

T4 Combustor Exit Temperature 

TO Takeoff 

TOC Top of Climb 

TSFC Thrust Specific Fuel Consumption 

TQA Modified Thrust Coefficient, Fg/ρn2

D2A 

UDF Unducted Fan 

NPSS Open Rotor Model Development 

The first task in developing an open rotor engine 

model was selecting an engine architecture. Several 

different architectures for the open rotor engine have been 

proposed which include variations in the location of the 

propellers (pusher vs. tractor), number of shafts, 

gearboxes and turbine design, among other parameters. 

For this study, a gearless, pusher engine configuration 

similar to the GE36 Unducted Fan (UDF) shown in 

Figure 3 was chosen for the initial open rotor model 

development. In this architecture, the engine can be split 

into two distinct sections: the gas generator and propulsor. 

The gas generator is comprised of the low and high 

pressure spools and combustor (in the GE36, the gas 

generator was an F404). The propulsor section contains the 

counter-rotating propellers which are driven by the 

counter-rotating power turbine and the exhaust nozzle. It is 

important to note that these two sections are mechanically 

independent (no shaft connections between sections), but 

are aerodynamically linked by the core engine flow. 

With this architecture selected, an engine model 

could be developed in NPSS. The engine was 

decomposed into a series of components as shown in 

Figure 4. Most of the blocks shown in Figure 4 are blue 

as NPSS already contains analysis capabilities for these 

components. The green blocks, however, identify two 

unique engine components which were not readily 

available in NPSS. As a result, solutions needed to be 

identified for how to model the counter-rotating propeller 

and counter-rotating turbine within NPSS. The next two 

sections will describe the steps taken to estimate the 

performance of the counter-rotating propellers and 

turbine using available performance data. 

Figure 3.—GE36 UDF cross section (Ref. 16).

Figure 4.—Open rotor block diagram. 

Counter-Rotating Propeller Modeling 

Several open rotor propeller configurations were 

designed, built, and tested as part of the Advanced 

Turboprop Project. These configurations were designed 

for optimal operation at different Mach numbers and had 

different blade geometries. Of all the blade geometries 

designed and tested, the most thoroughly documented 

was the F7/A7 rotor set. These propellers were designed 

for Mach 0.72 operation and were used on the GE36 UDF 

demonstrator. Because of available data, the F7/A7 

configuration was selected to provide an initial estimate 

of future open rotor propeller performance for this study. 

The performance data reported for the F7/A7 was 

from wind tunnel tests and was presented as shown in 

Figure 5. In the top plot, the modified total power 

coefficient (PQA) is shown as a function of the front 

propeller advance ratio (J1C) and propeller blade angles 

(each line represents a single combination of front and aft 

blade angles). In the bottom plot, the net efficiency of the 

counter-rotating propellers is shown as a function of the 

power coefficient divided by advance ratio, cubed 

(PQAJ3) and propeller blade angles. Plots such as these 

were given as several different Mach numbers to describe 

the semi-installed performance (the effects of the 

upstream nacelle are captured, but not an upstream pylon) 

at several points throughout the flight envelope (Ref. 17). 
NASA/TM—2011-217225 4 

Figure 5.—F7/A7 propeller performance data 

at Mach 0.72 (Ref. 17).

In addition, limited data were provided describing the 

distribution of torque between the blade rows at several 

flight conditions and blade angles. 

Using the reported data, counter-rotating performance 

maps were created for use in the cycle model. These maps 

contain correlations to determine the thrust coefficient, 

power coefficient and power split between the propeller 

blade rows as functions of Mach number, advance ratio 

and front propeller blade angle. Traditional NPSS 

performance maps capture these relationships in multidimensional arrays which are then interpolated or 

extrapolated for points not contained in the table. This 

technique was initially used in the open rotor modeling 

process by creating arrays based on the data reported 

from the F7/A7 wind tunnel experiments. However, 

because of the sparse data provided for the F7/A7, 

extensive extrapolation was required for many flight 

conditions. In this extrapolation process, the values of 

thrust and power coefficient calculated often produced 

unreasonable estimates of propeller efficiency. 

In order to improve the estimation of the thrust 

coefficient, power coefficient and efficiency at 

extrapolated points, the tables were replaced with 

response surface equations (multi-variable regression 

equations) which relate performance to Mach number, 

advance ratio and blade angle. These equations better 

capture the trends in the data in comparison to 

interpolating and extrapolating based on tables. 

Therefore, a set of response surface equations fit to the 

F7/A7 performance data were developed for use in this 

model and are provided in the Appendix. 

With the propeller performance data captured in the 

maps, a counter-rotating propeller element was written 

for NPSS which computes the performance of counterrotating propellers as engine components. The NPSS 

counter-rotating propeller element has a fluid input port 

and fluid output port along with a shaft port for each 

blade row. When the engine is being evaluated in design 

mode, the design blade angle and the propeller diameter 

are determined based on the specified total power 

requirements, rotation speed and disk loading. In offdesign mode, the propeller power required and thrust 

produced are determined from input flight conditions, 

rotation speed and blade angles. 

Counter-Rotating Turbine Modeling 

One of the challenges associated with modeling this 

open rotor configuration is the counter-rotating turbine 

which drives the propellers. A notional schematic of the 

counter-rotating turbine and propellers as used in the 

GE36 UDF is shown in Figure 6. In this configuration, 

the only static blade rows are the inlet and exit guide 

vanes. The remaining blade rows in the power turbine all 

rotate, with odd and even numbered rows rotating in 

opposite directions. This can been seen in Figure 6 as the 

solid blade rows will rotate in one direction, while the 

hatched blade rows will spin in the opposite direction. 

This configuration is unique resulting in little historic 

data and analytical analysis capabilities existing for this 

type of turbine. A partial performance map for the GE36 

counter-rotating power turbine was found as shown in 

Figure 7 giving some insight into the performance. 

However, this overall power turbine map does not include 

information on turbine pressure ratio and mass flow 

limiting its utility. An additional limitation of the map is 

that it is applicable only when there are equal rotation 

speeds for the two propulsor shafts. This lack of data and 

analysis capabilities make it difficult to model the 

counter-rotating turbine in NPSS, requiring exploration of 
NASA/TM—2011-217225 5 

Figure 6.—Schematic of GE36 Power Turbine (Ref. 18). 

Figure 7.—GE36 Overall Power Turbine Performance Map 

(Ref. 19).

several counter-rotating turbine performance estimation 

techniques. 

The first technique examined focused on trying to 

match what would be physically occurring in the counterrotating turbine. Specifically, it was assumed that the 

work being extracted in an alternating fashion for the two 

propulsor shafts was an important characteristic to 

capture. Therefore, a blade row by blade row model was 

implemented in NPSS by placing 12 turbine elements (the 

same as the number of blade rows in the GE36) in series 

and linking their flow ports. These twelve turbines were 

then linked alternately linked to two shaft elements. This 

turbine setup required several additional parameters to 

implement properly. During design, the work distribution 

across the 12 stages needed to be specified and was set to 

values similar to those described in the GE36 Design 

Report (Ref. 19). Furthermore, the performance of each 

blade row at all operating conditions needed to be 

estimated and was done by applying a performance map 

for a traditional, single stage turbine to each blade row. 

The performance maps of each blade row were then 

scaled such that the desired total power turbine adiabatic 

efficiency was achieved providing similar performance to 

the GE36 power turbine (Ref. 19). 

The results of implementing this power turbine 

modeling method were mixed. In the region near the 

design turbine design point, the total turbine performance 

map generated by the blade row by blade row model 

provided efficiency contours of similar shape to those 

shown in Figure 7. However, at off-design cases farther 

away from the design point the quality of this modeling 

approach deteriorated as the model often would not 

converge or would converge on a physically infeasible 

solution. The most common observation was that the last 

blade row in the power turbine would act as a 

compressor, absorbing power and raising the pressure 

across the row. The precise cause of this numerical 

phenomenon has not been determined, but there are 

several possible factors that may be contributing. First, 

the performance maps used for each blade row did not 

capture changes to inflow swirl from the preceding stage. 

Therefore, changes to performance from variations in 

rotation speeds of both shafts were not captured. Second, 

the work extraction distribution across the stages which 

was specified at design may be incorrect, resulting in too 

little energy being available in the last stages of the 

turbine. Finally, the power split determined in the 

counter-rotating propeller map (which is based on sparse 

data) may be driving the solution to an unrealistic result. 

Due to these results, the blade row by blade row power 

turbine model was not pursued further, but may be 

considered again in the future. 

Next, two simplified power turbine models were 

considered. First, the power turbine was modeled using 

two conventional turbine components in series. This 

modeling approach eliminates the single blade row map 

and work extraction issues of the blade row by blade row 

model while still allowing both propellers to be driven 

independently. However, the implementation of this 

method in NPSS still did not produce acceptable offdesign performance. These results indicate that there is 

likely an interaction between the counter-rotating 

propeller and power turbine which is not correctly 

addressed with both this method and the blade row by 

blade row turbine model. 

Finally, a single, traditional, low pressure turbine 

NPSS element was used to drive the entire counterrotating propeller system. This method assumes that only 

the total power passed between the power turbine and 

propellers is important (it does not take into account the 

power split between the rotors). The method also forces 

the rotation speed of the propellers to be equal. Therefore, 
NASA/TM—2011-217225 6 

the single NPSS component power turbine model was 

implemented in the NPSS open rotor model. This 

technique was also selected by Bellocq et al. in their 

study of open rotor performance modeling (Ref. 20). 

Multiple-Design Point Formulation 

Through the development of the counter-rotating 

propeller and turbine modeling capabilities in NPSS, a 

complete NPSS model of an open rotor turbine engine 

model was constructed following the block diagram of 

Figure 4. While this block diagram details the layout of 

components within the engine, it does not describe the 

process which will be used to size the engine to meet 

various performance requirements throughout the flight 

envelope. The traditional engine cycle design process 

uses a single design point (cruise or takeoff) to size the 

engine. The off-design performance is then evaluated to 

determine if thrust targets are met at other flight 

conditions. If thrust targets are not met at these other 

flight conditions, the engineer must manually change 

parameters at the design point until all the thrust targets 

are met. This process can be quite tedious, especially for 

unconventional engines such as the open rotor where the 

engineer has little intuition regarding the effect of 

changing design point variables. 

In order to improve the process of sizing the open 

rotor engine to meet multiple thrust targets, the open rotor 

model is being implemented using a multiple-design point 

formulation. In this formulation, the NPSS model is 

constructed so that all critical flight conditions are 

evaluated simultaneously to ensure all thrust targets and 

other design requirements are met. Therefore, each 

designed engine is guaranteed to meet the performance 

requirements specified by the designer. This technique 

was proposed and evaluated in academia for NPSS by 

Schutte (Ref. 21) and is capable of handling a larger 

number of design points. The rest of this section will 

describe some of the details regarding the implementation 

of the open rotor in an MDP formulation. 

First, the design points and their associated thrust 

targets need to be identified. For a typical engine, several 

design points including top-of-climb, takeoff and sealevel static are often considered. Table 1 lists several 

example design points which were considered in the 

development of this open rotor model. The aerodynamic 

design point (ADP) refers to a throttled back operating 

point representative of a cruise condition where the 

turbomachinery components would be designed for best 

TABLE 1.—DESIGN POINTS FOR MDP FORMULATION 

Design point Mach Alt (ft) ΔT (°F) 

(from ISA) 

Net thrust 

(lbf) 

ADP 0.72 35,000 +0 n/a 

TOC 0.72 35,000 +0 4,600 

TO, Hot Day 0.25 0 +27 17,500 

SLS, Hot Day 0.00 0 +27 25,000 

TABLE 2.—NPSS SOLVER VARIABLES FOR 

MDP FORMULATION 

NPSS Independent NPSS Dependent 

TOC Core Mass Flow TO Net Thrust 

TOC FAR TOC Net Thrust 

TO FAR TO T4 Max 

TOC Propeller Power TOC Nozzle Pressure Ratio 

TOC Propulsor Speed TOC Propeller Tip Speed 

performance. For example, this would be the flight condition 

and throttle setting at which the propellers were designed. 

From the list provided in Table 1, two design points 

were selected for the current study: top-of-climb and hot 

day takeoff. These two points were selected as they were 

the two primary thrust targets for this engine. There was 

not enough information available regarding the throttled 

back cruise condition to define an aerodynamic design 

point; therefore, the TOC point was used as the ADP of 

the turbomachinery components. Using these two design 

points, the MDP model was constructed by adding the 

parameters in Table 2 to the NPSS solver. Of these five 

independent/dependent pairs, the first three allow the 

sizing of the engine for matching the thrust targets at both 

TOC and TO. The last two independents and dependents 

size the propeller in relation to the gas generator at TOC 

and ensure that the F7/A7 design characteristics are matched. 

Within the NPSS, the solver is varying these 

independent parameters in order to achieve specific 

values of the dependent variables at the appropriate flight 

conditions (in addition to other independents and 

dependents automatically added to the solver). Therefore, 

target values for each dependent must be specified. For 

the first three dependents, the target values are 

determined by the thrust requirements and technology 

assumptions being used by the designer. The propeller tip 

speed target is determined from the propeller design 

process. For the F7/A7, the design front propeller 

tangential tip speed was 780 feet per second. Finally, the 

core nozzle pressure ratio must be specified as it 

determines the relative size of counter-rotating propellers 

and core engine. For this study a nozzle pressure ratio of 

1.25 was selected at TOC. By selecting this value for 

 
NASA/TM—2011-217225 7 

nozzle pressure ratio, almost all the energy is being 

extracted from the core flow to drive the counter-rotating 

propellers. Therefore, almost all the thrust is being 

produced by the high efficiency propellers, lowering the 

engine TSFC. While this value for nozzle pressure ratio is 

low at the TOC design point, it allows enough margin so 

that the pressure ratio remains above unity throughout the 

flight envelope. 

Power Management Strategy 

Another challenge in developing the open rotor MDP 

model was selecting a method for controlling the engine 

at each operating point in the flight envelope. The control 

of the open rotor engine differs from a traditional 

turbofan because both the propeller blade angle and 

combustor fuel flow can be varied. Therefore, a strategy 

for controlling both of these parameters throughout the 

flight envelope was required to allow for the proper sizing 

of engine in the MDP and estimation of performance in 

off-design operation. 

In order to develop the proper power management 

strategy, several brief studies were conducted to 

determine relevant trends in the engine operation. 

Figure 8 below shows a powerhook for the engine at 

cruise with three different blade angles. The figure shows 

that for all three blade angles, the powerhooks are nearly 

identical for most of the operating range. The significant 

difference occurs at the maximum thrust setting for each 

blade angle. The maximum thrust for each blade angle 

differs as a result of other constraints on the engine 

operation such as the maximum combustor exit 

temperature, maximum LPC corrected speed and 

maximum propeller rotation speed. Similar trends are 

observed at takeoff conditions as shown in Figure 9. 

Using the results of these studies, a simple blade 

angle schedule was selected as shown by the green line in 

Figure 10. This characteristic was selected as it passes 

through the known F7/A7 design point and falls within 

the bounds of the reported experimental data at all Mach 

numbers. By selecting a single front propeller blade angle 

at each Mach number, a reasonable prediction of the 

conceptual open rotor performance can be obtained 

throughout the flight envelope. It is recognized that the 

schedule selected in Figure 10 will provide a conservative 

estimate of the maximum thrust available as seen in 

Figure 8 and Figure 9. Following the development of this 

schedule, additional data which covers a larger range of 

Mach numbers was found for the F4/A4 and F5/A5 open 

Figure 8.—Mach 0.72, 35k ft powerhooks. 

Figure 9.—Mach 0.25, sea-level powerhooks. 

Figure 10.—Front propeller blade angle schedule.

 
NASA/TM—2011-217225 8 

rotor blade sets. These blade sets were developed around 

the same time as the F7/A7 for a similar cruise Mach 

number, but had different blade geometry (Ref. 17). 

While this data was not reported in the context of a power 

management strategy, the front blade angle of both blade 

sets follows a linear trend similar to that selected for the 

F7/A7, supporting the use of this schedule for preliminary 

performance evaluation. Future refinement of this 

schedule may allow for improved prediction of maximum 

thrust at each flight condition. 

Several other options for developing a power 

management scheme have also been considered which 

would provide more complex control of blade angle and 

fuel flow. One option is to use an optimizer to select the 

blade angle resulting in the minimum TSFC at a given 

T4. The advantage of this technique is that it would allow 

for the proper blade angle at every point analyzed and the 

scheme would be rapidly adjustable to new designs. 

However, the inclusion of an optimizer in NPSS model 

substantially lengthens the execution time and often 

results in numerical stability problems. Other power 

management schemes are also being investigated based 

on more detailed studies of the operating characteristics 

of the engine. In this case, it may be possible to use the 

identified characteristics in conjunction with the NPSS 

solver to select the appropriate blade angle and fuel flow 

settings. The difficultly observed with this method to date 

is the operating characteristics of the engine do not appear 

to be consistent throughout the flight envelope making it 

difficult to set up the proper NPSS solver variables. 

Sample Performance Results 

The open rotor modeling enhancements described in 

the previous sections were used to construct a complete 

NPSS model of the gearless, pusher engine. The model 

uses the F7/A7 counter-rotating propeller driven by a 

single power turbine component. The MDP setup 

contains only TOC and TO points with the blade angle 

determined by the simple schedule presented above. 

Using the developed model, a notional open rotor 

engine was created for evaluation. The results presented 

in this section are examples intended to demonstrate the 

capabilities of the model and results which can be 

produced. A summary of the open rotor engine cycle 

parameters used to generate the sample results is provided 

in Table 3. Values for core component design parameters 

were selected to represent advanced technology levels 

while power turbine and counter-rotating propellers 

parameters were selected to represent expected 

improvements over the GE36 Unducted Fan. 

Evaluating the open rotor NPSS model with these 

inputs produces the results given in Table 4. While this 

engine was not designed to exactly match the GE36, it is 

comparable in the overall size and thrust as shown in 

Table 5. The sample engine presented here has a slightly 

smaller propeller diameter and SLS thrust. However, it 

also demonstrates a lower TSFC due to the utilization of a 

modern gas generator. In addition, further improvements 

in the TSFC of the sample open rotor may be possible 

with further design and optimization. 

TABLE 3.—CYCLE DEFINITION AT TOC (* AT TO) 

Component Parameter Value 

LPC Pressure Ratio 2.4 

Adiabatic Efficiency (%) 87.6 

HPC Pressure Ratio 17.7 

Adiabatic Efficiency (%) 87.8 

Burner Exit Temperature (°R)* 3460 

HPT Adiabatic Efficiency (%) 92.1 

LPT Adiabatic Efficiency (%) 94.1 

PT Adiabatic Efficiency (%) 92.0 

CounterRotating 

Propellers 

Net Efficiency (%) 85.0 

Front Tip Speed (ft/s) 780 

Power Loading (shp/D2) 55.5 

TABLE 4.—OPEN ROTOR CYCLE RESULTS 

Parameter (units) Value 

Front Propeller Diameter (ft) 10.9 

TOC Core Mass Flow (lbm/s) 19.6 

TOC Net Thrust (lbf) 4600 

TOC Propeller Thrust (lbf) 4410 

TOC TSFC (lbm/hr/lbf) 0.394 

TO Core Mass Flow (lbm/s) 43.8 

TO Net Thrust (lbf) 17,500 

TO Propeller Thrust (lbf) 16,966 

TO TSFC (lbm/hr/lbf) 0.25 

TABLE 5.—SAMPLE OPEN ROTOR AND 

 GE36 DESIGN CHARACTERISTICS (REF. 9) 

Parameter (units) Sample 

Open 

Rotor 

GE36 

Unducted

Fan 

Propeller Diameter (ft) 10.9 11.7 

OPR 42 27 

SLS Thrust (lbf) 22,119 25,000 

TSFC, M 0.8, 35,000 ft (lbm/hr/lbf) 0.45 0.52 

 
NASA/TM—2011-217225 9 

Conclusion and Future Work 

The renewed interest in open rotor aircraft engines 

due to their capacity to reduce fuel consumption has 

necessitated the development of open rotor cycle models. 

In order to develop such models within NPSS, several 

modeling enhancements were needed to provide analysis 

capabilities for counter-rotating propellers and turbines. 

In addition, the implementation of a multi-design point 

methodology and a simple power management scheme 

allow for rapid cycle design and exploration of the entire 

flight envelope. 

While this work has provided a step forward in open 

rotor cycle analysis capabilities, there still remains room 

for dramatic improvement in open rotor modeling and 

analysis. First, the model presented here is based on a 

limited amount of historic, publicly available counterrotating propeller performance data. Several engine 

companies are currently designing and testing new 

propeller designs. If these performance data are made 

available, the data can be converted into performance 

maps and used in the cycle model. Additionally, if 

analytical counter-rotating propeller performance codes 

are developed or identified, it may be possible to integrate 

(i.e., “wrap”) them into the NPSS framework so that new 

propeller designs can be evaluated. By implementing an 

analytical propeller performance code, a more detailed 

understanding of counter-rotating propeller performance 

and its impact on the cycle design could be achieved. 

Next, further investigation regarding counter-rotating 

turbine performance estimation is needed. While the 

current model using a single turbine element will provide 

reasonable performance estimates for conceptual design, 

it does not allow for more detailed studies of open rotor 

design. A more complete theoretical understanding of 

counter-rotating turbine performance needs to be 

established which will lead to a sophisticated counterrotating turbine model within NPSS. By improving the 

turbine and propeller models, a better understanding will 

be developed regarding the interaction and coupling of 

these components and the limits those effects place on the 

design of such systems. 

Finally, if improved models for the counter-rotating 

propellers and turbines are implemented, the power 

management scheme will need to be reevaluated. This 

will be especially necessary if the new models demonstrate a high degree of coupling between the two systems 

as the performance characteristics may change. 

The development of the new capabilities described in 

this paper will make possible future open rotor cycle 

studies and aircraft design studies. NASA is interested in 

evaluating several different open rotor configurations, 

specifically tractor/pusher and geared/ungeared variations. Many of the developments described in this paper, 

including the propeller performance modeling, multidesign point sizing and power management strategy, will 

be applicable to the modeling of all these open rotor 

engine architectures. The evaluation of these open rotor 

configurations will also be conducted at the vehicle level 

so that a meaningful comparison can carried out between 

open rotors, high-bypass ratio turbofans and geared 

turbofan engines. 

NASA/TM—2011-217225 11 

Appendix—Counter-Rotating Propeller Response Surface Equations 

Thrust coefficient for cruise Mach numbers: 

ܥ் ൌ 0.477858888468182 ൅ 7.06020237179521 ൈ ܯ ൅ 0.106298212735099 ൈ ߚ െ 4.2264950825376 ൈ ܬ

െ 3.66227236419897 ൈ ܯଶ െ 0.135610213199312 ൈ ܯ ൈ ߚെ0.000855628477643638 ൈ ߚଶ

൅ 1.56685453798423 ൈ ܯ ൈ ܬ ൅ 0.0712347127445022 ൈ ߚ ൈ ܬ െ 0.315151540318393 ൈ ܬଶ

Thrust coefficient for takeoff Mach numbers: 

ܥ் ൌ െ2.82997954389849 ൅ 0.180742434146289 ൈ ߚ െ 1.1579348683331 ൈ ܬ ൅ 0.0158989848771736 ൈ ߚ

ൈ ܬ െ 0.158269167605173 ൈ ܬଶ െ 0.00172659713577937 ൈ ߚଶ

Power coefficient for cruise Mach numbers: 

ܥ ௉ൌ 19.799023228925 ൅ 18.4702389814161 ൈ ܯ െ 0.590047973770211 ൈ ߚ െ 9.99634088349976 ൈ ܬ

െ 10.0200863814251 ൈ ܯଶ െ 0.367383133097003 ൈ ܯ ൈ ߚ ൅ 0.00635741314998766 ൈ ߚଶ

൅ 4.60880216127912 ൈ ܯ ൈ ܬ ൅ 0.185060516036581 ൈ ߚ ൈ ܬെ1.08805807929953 ൈ ܬଶ

Power coefficient for takeoff Mach numbers: 

ܥ ௉ൌ െ3.87744594552613 ൅ 0.167892520010464 ൈ ߚ െ 0.0438743949610855 ൈ ܬ െ 0.0215083034537208

ൈ ߚ ൈ ܬെ0.237242660435654 ൈ ܬଶ

NASA/TM—2011-217225 13 

References 

1. National Aeronautics and Space Administration. 

Subsonic Fixed Wing - Research Overview. 2009. 

<http://www.aeronautics.nasa.gov/fap/sfw_research

_overview_feature.html>. Accessed 26 Oct 2010. 

2. Collier, F., Overview of NASA’s Environmentally 

Responsible Aviation (ERA) Project. < 

http://www.aeronautics.nasa.gov/pdf/asm_2010_coll

ier_508.pdf>. Accessed 2 Nov 2010. 

3. Boeing. Current Market Outlook 2010-2029. 

<http://www.boeing.com/commercial/cmo/pdf/ 

Boeing_Current_Market_Outlook_2010_to_2029.pd

f> Accessed 1 Nov 2010. 

4. Federal Aviation Administration, FAA Flight Plan 

2009-2013,2008. <http://www.faa.gov/about/ 

plans_reports/media/flight_plan_2009-2013.pdf>. 

Accessed 1 Nov 2010. 

5. Federal Aviation Administration, Capacity Needs in 

the National Airspace System 2007-2025, 2007. 

<http://www.faa.gov/airports/resources/publications/ 

reports/media/fact_2.pdf>. Accessed 1 Nov 2010. 

6. Luther, L., Environmental impacts of airport 

operations, maintenance, and expansion, 

Congressional Research Service, RL 33949, April 

2007. <http://www.policyarchive.org/handle/10207/ 

bitstreams/3205.pdf>. Accessed 11 Nov 2010. 

7. United States Environmental Protection Agency, 

Evaluation of Air Pollutant Emissions from Subsonic 

Commercial Jet Aircraft, EPA420-R-99-013, 1999. 

8. National Aeronautics and Space Administration. 

Subsonic Fixed Wing – Energy Efficiency. 2009. < 

http://www.aeronautics.nasa.gov/fap/sfw_energy_eff

iciency.html>. Accessed 26 Oct 2010. 

9. Hager, R. D. and Vrabel, D. Advanced Turboprop 

Project. NASA-SP-495. 1988. 

10. Flight Global. Web. 26 Oct 2010. 

<http://www.flightglobal.com/blogs/runwaygirl/2008/03/engine-rd-boost-begs-political1.html#more>. 

11. Guynn, M.D., Berton, J.J., Fisher, K.L., Haller, W.J., 

Tong, M.T., and Thurman, D.R. “Engine Concept 

Study for an Advanced Single-Aisle Transport.” 

NASA-TM-2009-215784. 

12. Claus, R.W.; Evans, A.L.; Lytle, J.K., and Nichols, 

L.D.: “Numerical Propulsion System Simulation,” 

Computing Systems in Engineering, Vol. 2, No. 4, 

pp. 357-364, 1991. 

13. NPSS User Guide Software Release: NPSS_1.6.5. 

14. http://sitelife.aviationweek.com/ver1.0/Content/imag

es/store/11/14/2b30674c-cd2f-47ae-be63-

63bf3434132f.Large.jpg 

15. Airbus, Global Market Forecast 2009-2028. 

<http://www.airbus.com/en/gmf2009/>. 

16. GE Aircraft Engines, “Full Scale Technology 

Demonstration of a Modern Counterrotating 

Unducted Fan Engine Concept: Component Test.” 

NASA-CR-180868. Dec. 1987. 

17. Hoff, G.E. et al., “Experimental Performance and 

Acoustic Investigation of Modern, Counterrotating 

Blade Concepts.” NASA-CR-185158. Jan. 1990. 

18. Reid, C. “Overview of Flight Testing of GE Aircraft 

Engines UDF Engine.” AIAA-88-3082. 

19. GE Aircraft Engines, “Full Scale Technology 

Demonstration of a Modern Counterrotating 

Unducted Fan Engine Concept: Design Report.” 

NASA-CR-180867. Dec. 1987. 

20. Bellocq, P., Sethi, V., Cerasi, L., Ahlefelder, S., 

Singh, R., and Tantot, N., “Advanced Open Rotor 

Performance Modeling for Multidisciplinary 

Optimization Assessments.” Proceedings of 

GT2010, ASME Turbo Expo 2010: Power for Land, 

Sea and Air, 2010, Glasgow, UK. Paper: GT2010-

22963. 

21. Schutte, Jeffrey S. Simultaneous Multi-design Point 

Approach to Gas Turbine On-design Cycle Analysis 

for Aircraft Engines. Atlanta, Ga.: Georgia Institute 

of Technology, 2009. 
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)

01-10-2011 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Development of an Open Rotor Cycle Model in NPSS Using a Multi-Design Point Approach 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Hendricks, Eric, S. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 561581.02.08.03.13.11 

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-17908 

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 

11. SPONSORING/MONITORING 

 REPORT NUMBER

NASA/TM-2011-217225 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 07 and 64 

Available electronically at http://www.sti.nasa.gov 

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

13. SUPPLEMENTARY NOTES

14. ABSTRACT

NASA's Environmentally Responsible Aviation Project and Subsonic Fixed Wing Project are focused on developing concepts and 

technologies which may enable dramatic reductions to the environmental impact of future generation subsonic aircraft (Refs. 1 and 2). The 

open rotor concept (also referred to as the Unducted Fan or advanced turboprop) may allow the achievement of this objective by reducing 

engine emissions and fuel consumption. To evaluate its potential impact, an open rotor cycle modeling capability is needed. This paper 

presents the initial development of an open rotor cycle model in the Numerical Propulsion System Simulation (NPSS) computer program 

which can then be used to evaluate the potential benefit of this engine. The development of this open rotor model necessitated addressing 

two modeling needs within NPSS. First, a method for evaluating the performance of counter-rotating propellers was needed. Therefore, a 

new counter-rotating propeller NPSS component was created. This component uses propeller performance maps developed from historic 

counter-rotating propeller experiments to determine the thrust delivered and power required. Second, several methods for modeling a 

counter-rotating power turbine within NPSS were explored. These techniques used several combinations of turbine components within 

NPSS to provide the necessary power to the propellers. Ultimately, a single turbine component with a conventional turbine map was 

selected. Using these modeling enhancements, an open rotor cycle model was developed in NPSS using a multi-design point approach. The 

multi-design point (MDP) approach improves the engine cycle analysis process by making it easier to properly size the engine to meet a 

variety of thrust targets throughout the flight envelope. A number of design points are considered including an aerodynamic design point, 

sea-level static, takeoff and top of climb. The development of this MDP model was also enabled by the selection of a simple power 

management scheme which schedules propeller blade angles with the freestream Mach number. Finally, sample open rotor performance 

results and areas for further model improvements are presented.

15. SUBJECT TERMS

Counter-rotating propellers; Propellers; Turboprop engines; Gas turbine engines 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

17 

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