Eric S. Hendricks and Jonathan A. Seidel

Glenn Research Center, Cleveland, Ohio

A Multidisciplinary Approach to 

Mixer-Ejector Analysis and Design

NASA/TM—2012-217709

September 2012

AIAA–2012–4224
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Eric S. Hendricks and Jonathan A. Seidel

Glenn Research Center, Cleveland, Ohio

A Multidisciplinary Approach to 

Mixer-Ejector Analysis and Design

NASA/TM—2012-217709

September 2012

AIAA–2012–4224

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

48th Joint Propulsion Conference and Exhibit

cosponsored by the AIAA, ASME, SAE, and ASEE

Atlanta, Georgia, July 30–August 1, 2012
Acknowledgments

The work presented in this paper was supported by the Supersonics Project at NASA Glenn Research Center. Special thanks to 

Jeff Berton, Justin Gray and Clayton Meyers of NASA Glenn Research Center for their support and guidance in this research.

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

This report contains preliminary findings, 

subject to revision as analysis proceeds.
NASA/TM—2012-217709 1

A Multidisciplinary Approach to Mixer-Ejector Analysis and Design

Eric S. Hendricks and Jonathan A. Seidel

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

The design of an engine for a civil supersonic aircraft presents a difficult multidisciplinary problem to 

propulsion system engineers. There are numerous competing requirements for the engine, such as to be 

efficient during cruise while yet quiet enough at takeoff to meet airport noise regulations. The use of 

mixer-ejector nozzles presents one possible solution to this challenge. However, designing a mixer-ejector 

which will successfully address both of these concerns is a difficult proposition. Presented in this paper is

an integrated multidisciplinary approach to the analysis and design of these systems. A process that uses 

several low-fidelity tools to evaluate both the performance and acoustics of mixer-ejectors nozzles is 

described. This process is further expanded to include system-level modeling of engines and aircraft to 

determine the effects on mission performance and noise near airports. The overall process is developed in 

the OpenMDAO framework currently being developed by NASA. From the developed process, sample 

results are given for a notional mixer-ejector design, thereby demonstrating the capabilities of the method.

Nomenclature

Cfg nozzle gross thrust coefficient

Cfexp nozzle friction and expansion loss coefficient

H vertical distance between noise source and microphone

L horizontal (sideline) distance between noise source and microphone

R absolute distance between noise source and microphone

Rref reference distance between noise source and microphone

θ polar (yaw) emission angle

φ azimuthal (roll) emission angle

1.0 Introduction

Propulsion design enabling a commercially successful and environmentally acceptable civil 

supersonic transport represents one of the acmes of Multidisciplinary Design, Analysis and Optimization 

(MDAO) application in aerospace. Unlike their subsonic counterparts that always trend toward higher 

bypass ratio (BPR) for Mach ~0.8 cruise fuel economy and thereby enjoy the consequential benefits of 

lower takeoff jet noise, supersonic engines must consider the drag increases associated with higher BPR 

(low specific thrust) cycles when trying to achieve both acceptable cruise performance and regulated 

takeoff noise levels. Similarly, for subsonic aircraft, an optimum-performing inlet and nozzle designed for 

cruise differs little from that designed explicitly for take-off. However, the inlet and nozzle of a 

supersonic aircraft designed for optimum supersonic cruise performance must reconcile diverse inlet 

airflow demands and nozzle expansion ratios to attain successful performance across the larger Mach 

operating regime. Further compounding the MDAO issue for supersonics is the commercial desire for a 

low-sonic-boom vehicle which would enable supersonic overland flight. Such a vehicle typically requires 

a high fineness ratio, which equates to a low diameter-to-length for the propulsion system. This 

supersonics dichotomy between the “optimum” engine for take-off noise and the “optimum” engine for 

cruise efficiency and sonic boom thusly necessitates a compromise in acceptable fuel economy, and/or 

weight, to reconcile these competing trends and achieve commercial acceptability. Research sponsored by 
NASA/TM—2012-217709 2

NASA’s Supersonic Project under the Fundamental Aeronautics Program is aggressively pursuing 

innovative tools, technologies, and concepts that address this dichotomy (Refs. 1 and 2). Mixer-ejector 

nozzle design with engine cycle integration is one such approach being pursued.

Mixer-ejector nozzles have been studied and infrequently used for noise suppression in both subsonic 

and supersonic aircraft applications throughout the previous decades, with one example being shown in

Figure 1 (Refs. 3 and 4). NASA’s High Speed Research (HSR) Program which terminated in 1999 

provides one of the most recent bodies of public data for these types of nozzles and how they may 

potentially benefit civil supersonic aircraft. The basic premise of mixer-ejector nozzle operation is shown 

in Figure 2. In the cruise configuration, the ejector inlet doors are closed resulting in operation as a 

conventional nozzle. The primary flow, which is composed of the mixed airflow from the engine core and 

bypass streams, is depicted by the red arrows entering the mixer then passing through the nozzle. In the 

takeoff configuration, the ejector doors have been opened allowing free stream (secondary) airflow to 

enter the nozzle as shown by the blue arrows. The high-speed primary flow energy entrains secondary 

flow through suction and viscous forces, with the streams partially or completely mixing together before 

exiting the nozzle. When designed correctly, the mixer-ejector will reduce exit jet velocity which 

correlates to reducing jet noise and increases the mass flow through the nozzle which maintains the thrust

produced by the nozzle.

Figure 1.—Alternating lobe mixer-ejector concept (ALMEC) suppressor system installed 

on a Gulfstream G-II aircraft (Ref. 4).

Figure 2.—JT8D-17 20-lobe ejector nozzle showing cruise (left) and takeoff (right) operation.
NASA/TM—2012-217709 3

One of the attractive features of these nozzles is that the “optimum” low BPR engine cycle designed 

for good installed supersonic cruise performance need not be overly compromised for take-off noise 

abatement. The key fluid mechanics at work for secondary entrainment are the overall momentum of the 

primary stream entering the mixing plane, the related local static pressure of the primary stream at the 

primary/secondary mixing plane, and to a lesser degree, the viscous entrainment. These flow parameters, 

established by engine cycle selection and nozzle geometry variables govern the performance, operability, 

and acoustics of the system during operation. As such, MDAO techniques that combine these systemlevel disciplines are paramount in determining the viable design space prior to conducting more detailed 

design and flow analyses. In this paper, an approach to the multidisciplinary analysis of mixer-ejector 

nozzles at the component and aircraft system level is proposed. The multidisciplinary analysis process

first evaluates the mixer-ejector nozzle as an isolated component to determine its performance and 

acoustic characteristics. The determined characteristics are then used as part of a system level analysis 

that includes evaluating the overall engine cycle, the aircraft mission performance, and the noise produced

by the aircraft during takeoff and landing. Following the discussion of the development of this analysis 

capability, sample results are given for a notional mixer-ejector nozzle and associated aircraft to 

demonstrate the trades that can be studied with this new capability.

2.0 Modeling Methodology and Implementation

The challenge of designing a feasible mixer-ejector nozzle is being able to understand the tradeoffs 

that must occur between disciplines. For this study, an analysis process has been developed which 

evaluates the performance and acoustics of mixer-ejector nozzles at both a component level and a full 

vehicle system level. In this process, an initial engine cycle is assumed in order to provide the input flow 

conditions to the mixer-ejector component level analyses. Next, the mixer-ejector geometry is defined,

allowing the performance characteristics of the isolated mixer-ejector nozzle to be determined. As a result 

of this step, a performance map which will be used in the subsequent engine cycle analysis is created and

input parameters are determined for the acoustic assessment of the isolated mixer-ejector. Using these 

input parameters, the acoustic characteristics of the isolated nozzle are determined. The acoustic 

characteristics determined in this analysis will then be used as part of the system level acoustic 

assessment. After the performance and acoustic characteristics have been determined for the isolated 

mixer-ejector nozzle, the characteristics are used to evaluate the overall system-level performance and 

acoustic characteristics of the engine and aircraft.

In setting up this analysis process, it becomes obvious that there is a significant amount of 

information that needs to be passed between each of the discipline analysis tools. While this process of 

passing information can be done by hand for a limited number of designs, a more efficient process would 

be to integrate the discipline analysis tools in a multidisciplinary design, analysis and optimization 

(MDAO) framework. Such a framework would make executing the overall analysis process more 

streamlined by facilitating the passing of information and allowing complex analysis workflows to be 

created. There are numerous tools available for doing this type of code integration and execution. For this 

project, the OpenMDAO framework (Ref. 5) has been selected. OpenMDAO is an open-source, Pythonbased framework for solving MDAO problems. The OpenMDAO framework is currently in development, 

with the development process being led by NASA Glenn Research Center. This framework will serve as a 

key piece of the multidisciplinary analysis process described in the sections below. The following 

sections will describe the individual discipline analyses and how they have been incorporated into the 

overall MDAO process for this study.

2.1 Initial Propulsion Cycle Analyses

A Mixed Flow TurboFan (MFTF) engine cycle configuration was selected as the propulsion system 

for this study. The MFTF is most widely used for military supersonic propulsion systems due to its high 

thrust per unit airflow (specific thrust) performance, affording the most efficient airframe integration and 
NASA/TM—2012-217709 4

installed supersonic cruise thrust specific fuel consumption (TSFC). At increasing supersonic speeds, 

inlet ram, spillage, bleed and bypass drags can severely penalize propulsion system performance. This 

effect is amplified as inlet pressure recovery and mass flow degrade with increasing cruise Mach number, 

further penalizing engine specific thrust and supersonic cruise TSFC. While the high specific thrust of a 

high Fan Pressure Ratio (FPR) and correspondingly low BPR MFTF helps to ameliorate this effect, a 

compromise in BPR and corresponding jet velocity is required to meet commercial noise certification 

rules for takeoff. A superior solution may be possible through the use of mixer-ejector nozzles that can 

improve performance and acoustic characteristics to create a better overall propulsion system.

In order to evaluate the mixer-ejector effects on a supersonic aircraft, a baseline MFTF engine cycle 

was modeled using information resultant from a NASA N+2 systems study contract (Ref. 6). This

baseline cycle represents an aggressive technology MFTF in terms of cycle temperatures, and as such, the 

sea level FPR and BPR for this Mach 1.6 capable engine are 2.2 and 4.3 correspondingly. Per the 

contractor study report, this baseline cycle was intentionally designed to achieve a very low takeoff jet 

velocity while still satisfying the Mach 1.6 supersonic performance requirements, and used only a simple 

convergent-divergent (C-D) nozzle. An attempt was made to replace the simple nozzle for this baseline 

with a mixer-ejector for this current study. However, the baseline nozzle pressure ratio (NPR) for the 

quoted cycle conditions was so close to the critical NPR at the takeoff condition that an ejector solution 

with supersonic primary capable of even minimal part power operation was not possible. While a 

subsonic primary ejector solution is both of interest and analytically possible following the same approach 

outlined herein, this was deemed outside the scope of this initial study. Therefore, for purposes of this 

study, two alternative cycles were developed based on the same aggressive technology levels but

employing higher FPRs (2.8 and 3.4) with correspondingly higher NPRs that enable the use of a mixerejector nozzle with supersonic primary. These two alternative, higher specific thrust cycles were scaled 

down in size to match the baseline cycle thrust at a rolling take-off point of Mach 0.2 sea-level, and 

consequently resulted in similar thrust and TSFC performance throughout the Mach envelope but with 

strikingly different take-off jet velocities. In total, five engine cycles were employed in this study: a 

NASA model of the contractor baseline MFTF with FPR=2.2 and simple C-D nozzle, NASA models of 

FPR=2.8 and 3.4 MFTFs with simple C-D nozzles and sized to the baseline rolling takeoff thrust, and 

NASA models of these same-sized FPR=2.8 and 3.4 MFTFs but utilizing mixer-ejector nozzles.

A mechanical analysis was performed for each of the five engine cycles using NASA’s Weight 

Analysis of Turbine Engines (WATE++) code (Ref. 7) All structural design limits based on materials 

selection and standard NASA design practices were observed, as were required turbine cooling flow 

requirements. Component efficiencies and pressure losses were based on information consistent with the 

contractor baseline, as were the customer bleed and horsepower extractions. A diagram of the MFTF 

cycle architecture is shown in Figure 3, with a sample of the corresponding mechanical flowpath design 

generated from WATE++.

Thermodynamic performance was computed for each cycle using the Numerical Propulsion System 

Simulation (NPSS) (Ref. 8) code, which included identical inlet performance characteristics. NPSS 

nozzle output provided input conditions to the mixer-ejector-specific analyses described in more detail in 

Section 2.2. The nozzle output information included primary nozzle flow conditions (total pressure, total 

temperature and Mach number, mass flow, areas) and downstream exit ambient conditions (static 

pressure). Each of these values changed as a function of the engine’s throttle setting and aircraft flight 

conditions, therefore these relationships needed to be included in the mixer-ejector component 

design/analysis process for producing the parametric nozzle performance used in subsequent cycle, 

mission, and acoustic analyses. Rather than integrating the entire NPSS cycle model into the mixerejector design/analysis process, response surface equations were created that represented primary flow 

conditions into the mixer-ejector nozzle. These equations were used within a module in OpenMDAO 

called “Cycle Parameters” to calculate requisite flow conditions input to the mixer-ejector analyses. 
NASA/TM—2012-217709 5

Figure 3.—MFTF engine components (top) and a cross-section view of the engine (bottom).

2.2 Mixer-Ejector Performance Modeling

The second step in assessing the potential impact of mixer-ejector nozzles is to estimate the 

performance characteristics such as gross thrust coefficient and pumping ratio. The gross thrust 

coefficient and pumping ratio are defined in Equation (1) and Equation (2), respectively. While the 

performance at individual operating points is interesting, the overall goal of this analysis is to produce a 

performance map that covers a wide range of operating conditions. This performance map can then be 

used in later system level assessments to determine the overall benefit of the mixer-ejector.

Cfg = ρu2A+(p−p∞)

ṁ priVideal

(1)

Pumping Ratio = ṁ sec

ṁ pri

(2)

To model the performance of mixer-ejector nozzles, an analysis tool capable of evaluating the 

selected design was needed. The Differential Reduced Ejector/Mixer Analysis (DREA) (Refs. 9 and 10)
NASA/TM—2012-217709 6

program was selected for this study as it provided low-fidelity results with quick execution time. DREA 

was developed to perform conceptual nozzle design using sophisticated flow and energy mathematics 

combined with an implicit 2-D space-marching numerical analysis capturing higher-order resolution. The 

program calculates overall performance characteristics such as secondary flow entrainment, pumping 

ratio, mixed jet properties, and gross thrust coefficient. In addition, the program will produce 2-D velocity 

profiles and mixing properties throughout the length of the ejector. Lastly, DREA is capable of handling a 

variety of mixer operating conditions which range from fully subsonic cases (both primary and secondary 

flow are subsonic) to cases where Fabri choke is encountered (the supersonic primary flow causes the 

secondary flow to also become supersonic in the ejector). All these features make DREA an ideal tool to 

estimate the performance of mixer-ejector nozzles.

In order to produce the performance maps desired for this study, a large number of DREA executions 

would be required to generate sufficient data. While this task could be done by inputting information from 

the Cycle Parameters module by hand, this process would take an extensive amount of time and be prone 

to human error in transferring the inputs. Therefore, the DREA code was incorporated into the 

OpenMDAO framework by creating a code “wrapper.” In the wrapping process, a module with functions 

was developed which would allow the framework to generate the required input files for DREA, execute 

DREA and then parse the output files to record needed data in a usable format.

The OpenMDAO DREA module and the Cycle Parameters module were then integrated into a single 

analysis capability to produce performance maps as shown in Figure 4. In this analysis process, a design 

of experiments (DoE) driver was used to execute the Cycle Parameters and DREA modules for a large 

number of cases. For the design of experiments, six independent variables which were considered most 

critical to the ejector operation were included. These independents were:

• Free stream Mach number

• Flight altitude

• Percent of max engine thrust which defines primary flow total pressure, total temperature and 

Mach number

• Delta from primary flow total pressure which was determined by the Cycle Parameters module

• Delta from primary flow total temperature which was determined by the Cycle Parameters 

module

• Delta from primary flow Mach number which was determined by the Cycle Parameters module

A number of output parameters were recorded from each case executed as part of the design of 

experiments. These outputs included the gross thrust coefficient and pumping ratio which are needed for 

creating performance maps. The data produced using the DoE and OpenMDAO performance environment 

were then used to create maps by establishing the relationship between the independent parameters listed 

above and the output information. Regression equations in the form of second order polynomials were 

created for each of the performance metrics. These equations can then be imported back into the cycle 

analysis process to develop a system level estimate the benefit of the mixer-ejector nozzle.

Figure 4.—Performance analysis 

process in OpenMDAO.
NASA/TM—2012-217709 7

2.3 Mixer-Ejector Acoustic Modeling

In addition to evaluating the performance characteristics of mixer-ejector nozzles, the acoustics 

characteristics need to be determined to understand the potential tradeoffs between the disciplines. For the 

acoustic analysis, the primary concern at the system level is determining the noise levels at each of the 

three certification points that are part of the airport noise metric as shown in Figure 5 (Ref. 11). This task 

is best performed using the Aircraft Noise Prediction Program (ANOPP). However, ANOPP does not 

contain a module capable of modeling the noise from a mixer-ejector. Therefore, an analysis code suitable 

for estimating the acoustic characteristics of mixer-ejector nozzles needed to be identified and then used 

to create input for ANOPP.

The HSRNoise (Ref. 12) computer program was developed during the NASA’s High Speed Research 

Program and is capable of estimating the acoustics of mixer-ejector nozzles. HSRNoise includes two 

unique noise modules for predicting mixer-ejector noise which are not available in other acoustic 

modeling tools. The first method, Boeing’s JN8C4 method, is an empirically-based jet noise prediction 

method which is based on experimental data for a number of 2-D mixer-ejector configurations. The 

second method, the Stone Method, is a semi-empirical correlation for 2-D mixer-ejector jet noise which 

was developed by Modern Technologies Corporation for GE Aircraft Engines. For the examples shown in 

this paper, only the Boeing JN8C4 method is used.

To execute the JN8C4 module in HSRNoise, information regarding the nozzle geometry, flow 

conditions and nozzle performance need to be supplied. This information is either an input to or output 

from the Cycle Parameters and DREA modules in OpenMDAO. (Note that DREA and HSRNoise use 

different formulas for calculating mixer-ejector nozzle performance requiring additional calculations to 

generate correct input conditions for HSRNoise). Therefore, it was logical to create an OpenMDAO 

module for the HSRNoise analysis code. Again, this OpenMDAO wrapper would generate the required 

input files for HSRNoise, execute HSRNoise and then parse the output files to record needed data.

In addition to collecting the raw data from HSRNoise, several post-processing calculations were 

performed in this OpenMDAO module to prepare the data to be input into ANOPP. The HSRNoise code 

computes acoustic data at a number of microphone locations (θ ranges from 10° to 170°) along a lateral 

sideline as shown in Figure 6. The location of this side line can be changed in HSRNoise by changing the 

parameters H and L in the figure. However, ANOPP requires the acoustic data to be on an arc (typically at 

a 1 ft radius) around the noise source (in this case the nozzle) rather than on a sideline. Therefore, a 

correction needed to be applied to the HSRNoise output in order to produce the input for ANOPP. The 

first part of the correction computes the distance R for each microphone along the lateral sideline using 

Equation (3). That distance is then used to transform the sound pressure level (SPL) values from 

HSRNoise to the SPL values on a 1 ft (Rref = 1 ft) lossless arc needed by ANOPP using the inverse square 

law as shown in Equation (4).

R = √H2+L2

sin(θ) (3) 

SPL1ft = SPLHSRNoise + 20log10 � R

Rref� (4)

After correcting the HSRNoise output data for use in ANOPP, an additional component needed to be 

created to form the final input files for ANOPP. This OpenMDAO module creates input tables for the 

ANOPP’s Acoustic Data Module (ACD) which provides users the ability to input the noise of unique 

components that cannot be predicted by other ANOPP modules. The ACD Generator module created in 

OpenMDAO collects the output of several runs of HSRNoise to create the required tables for the ACD 

module in ANOPP.
NASA/TM—2012-217709 8

Figure 5.—Noise certification points.

Figure 6.—Geometry of acoustic analysis results.

Figure 7.—Acoustic analysis process in OpenMDAO.

Using the HSRNoise and ACD Generator modules as well as the Cycle Parameters and DREA 

modules, an integrated acoustic analysis process was developed in OpenMDAO to produce the ACD 

tables as shown in Figure 7. This analysis process is more complicated than the previous performance 

analysis as it requires a general driver to execute the entire analysis as well as an analysis driver to 

execute a select number of cases through the Cycle Parameters, DREA and HSRNoise modules. As a 

result of this analysis process, ACD tables for ANOPP can be produced for each of the acoustic 

certification points. 
NASA/TM—2012-217709 9

2.4 System Level Performance and Acoustic Assessment

The performance and acoustic modeling capabilities described in the previous two sections can be 

used to supply performance inputs to system level analyses to estimate the impact of using a mixer-ejector 

nozzle on a supersonic aircraft. The systems level analysis process consists of three separate analyses that 

are executed sequentially as shown in Figure 8. 

First, the mixer-ejector performance maps are fed into the engine cycle analysis process. The 

performance maps developed for a mixer-ejector nozzle design are integrated into the final performance 

calculations in NPSS, while the NPSS Nozzle element is used to calculate the primary flow conditions to 

be used as inputs to the maps. This approach allows explicit cycle convergence using the NPSS Nozzle as 

either a fixed-chute mixer-ejector primary or a standard convergent-divergent nozzle, depending on 

whether the ejector is in operation or not. Additional calculations determining secondary mass flow from 

the pumping ratio correlation and its associated ram drag penalties are also included in the final 

performance calculations. A reference viscous and expansion loss (Cfexp) was also represented in the 

cycle as a function of NPR for all five cycles. This loss was assessed in addition to the gross thrust 

coefficient supplied by the mixer-ejector performance maps. For the MFTF cycles where a mixer-ejector 

was not present, a baseline Cfexp versus NPR table was utilized, with a peak Cfexp of approximately 

0.987 which is consistent with the assumptions in the baseline engine. When the mixer-ejector was 

present but not operating, a 1 percent penalty was assumed in addition to the baseline non-mixer-ejector 

Cfexp. This assumption is consistent with the ejector chutes remaining in the low subsonic convergent 

nozzle section, mimicking a “translating throat” design whereby a dedicated throat is established fully 

downstream of the chutes when the ejector is not operating. When the mixer-ejector was present and 

operating, a reference Cfexp=0.95 was assumed. This assumption accounts for the fixed ejector chutes 

now acting as the nozzle throat and passing sonic and supersonic exit flow. At low NPRs (occurring 

during throttle operation below approximately 70 percent engine net thrust conditions), this 0.95 reference 

Cfexp was degraded to 0.80 to represent diffusion and separated flow within the fixed primary nozzle 

chute, which was otherwise allowed to overexpand to a fixed chute exit area. All these calculations and 

assumptions allow for the installed performance of the integrated cycle-nozzle to be determined. As a 

result, the cycle analysis produces engine performance throughout the possible flight envelope which will 

be required for completing the mission analysis.

Next, the mission analysis is conducted to evaluate the overall flight performance characteristics of a 

notional airplane that is using the designed engine. The mission analysis assesses the aircraft performance 

throughout the flight envelope and ensures the vehicle is capable of meeting all performance 

requirements. The baseline aircraft used in this study is a NASA representation of the low sonic-boom, 

small supersonic transport which resulted from the NASA N+2 systems study contract previously cited. 

The aircraft is capable of carrying 30 passengers at a cruise Mach number of 1.6 over a 4250 n mi 

distance using the baseline engine. The NASA Flight Optimization System (FLOPS) code (Ref. 13) was

Figure 8.—System level analysis process.
NASA/TM—2012-217709 10

used to perform the mission analyses. To maintain the low sonic-boom characteristics of the aircraft and 

consistency with quoted thrust requirements, aircraft takeoff gross weight (empty weight plus total 

mission fuel and payload) was held constant at 180,000 lb for all five engines in the study. Resulting 

mission range was used as the figure of merit for assessing changes in engine cycle performance and 

weight, as differences in engine weight were credited or debited to the aircraft as fuel capacity to 

maintaining the 180,000 lb takeoff gross weight.

Finally, the mission-sized cycle performance results and acoustic results can be used to predict a 

system level noise metric for the mixer-ejector nozzle. This metric is the Effective Perceived Noise Level 

(EPNL) at the three certification points located around the runway as shown in Figure 5. ANOPP 

calculates an EPNL value at each point by flying the notional aircraft along a defined flight path. To 

predict the noise of the aircraft, ANOPP uses a variety of modules which represent noise sources such as 

fan noise, core noise, jet noise and airframe noise. For this study, only the noise associated with the mixer 

ejector nozzle is considered and the aircraft is assumed to fly a fixed trajectory. By assuming a fixed 

trajectory, variations in aircraft performance that may result from using a mixer-ejector are removed from 

the analysis, allowing for a direct comparison to be made between mixer-ejector and conventional 

nozzles. 

3.0 Sample Results

The modeling methods and implementations described in the previous sections were used to 

demonstrate the multidisciplinary analysis capabilities for a notional mixer-ejector nozzle. The mixerejector nozzle was selected to match with a sample MFTF engine cycle for a supersonic aircraft. The 

design parameters for the notional mixer-ejector nozzle are given in Table 1. The following sections 

describe the results for performance, acoustics and system level assessment using this configuration. 

TABLE 1.—NOTIONAL MIXER-EJECTOR DESIGN PARAMETERS

Design parameter Value

Primary flow area.................................................................12.0 ft2

Secondary flow area............................................................. 21.0 ft2

Ejector exit area ................................................................. 31.35 ft2

Ejector aspect ratio......................................................................3.0

Ejector length.......................................................................... 8.0 ft

Mixer chute angles.................................................................. 10.0°

3.1 Mixer-Ejector Performance Modeling

Assuming the mixer-ejector nozzle design described above, the performance modeling process 

described previously was exercised. Using the DREA tool that was wrapped in OpenMDAO, a five-level 

full factorial design of experiments was executed. The six variables chosen for this design of experiments, 

along with their minimum and maximum values, are given in Table 2. This design of experiments 

successfully produced over 15,000 data points which were then used to develop performance maps.

TABLE 2.—DESIGN OF EXPERIMENTS VARIABLES AND RANGES

Input parameter Minimum value Maximum value

Free stream Mach number 0.0 0.4

Flight altitude 0 ft 10,000 ft

Percent engine thrust 60 100

Delta of primary flow total pressure from baseline –200 lbf/ft2 +200 lbf/ft2

Delta of primary flow total temperature from baseline –50 °R +50 °R

Delta of primary flow Mach number from baseline –0.1 +0.1
NASA/TM—2012-217709 11

Figure 9.—Performance map correlations to input parameters.

The data produced through the design of experiments process were analyzed to produce performance 

maps. Second order response surface equations were fit to the data points to produce map equations that 

could be used in the system level analysis. Figure 9 shows the correlation of each input variable with each 

of the map performance metric. Essentially, the blue line in each box shows the partial derivative for the 

input/output pair when all other values are assumed to be at the center of the ranges listed in Table 2. 

From Figure 9, it can be seen that only engine percent thrust and flight Mach have a significant effect on 

the gross thrust coefficient (Cfg) as the rest of the partial derivatives have slopes near zero. For the 

pumping ratio, the flight Mach number is clearly the most significant factor as it has the highest slope. 

While the above formulation of the performance maps can be implemented in the system level 

analysis, it was recognized that a different but related set of input variables could be used to formulate the 

map making it easier to integrate in to later analyses. In this formulation, the independent variables 

(inputs) are directly tied to physical parameters that the cycle analysis would easily be able to determine 

(rather than a delta off of some baseline value set by the percent max thrust). These input variables

include:

• Secondary flow total pressure

• Secondary flow total temperature

• Ambient static pressure

• Primary flow total pressure

• Primary flow total temperature

• Primary flow Mach number

These parameters are more commonly used in engine cycle analysis, making the developed map 

easier to integrate into the system level analysis. However, extreme caution needs to be used with these 

equations as it is easy to unknowingly supply combinations of input parameters that are outside the range 

of values used to generate the equation. In this situation, the response surface equation would technically 

be providing an extrapolation outside of the range tested with the design of experiments. The generated 

response surface equations using these input parameters for gross thrust coefficient, pumping ratio and 

secondary mass flow are given in the Appendix.

3.2 Mixer-Ejector Acoustic Modeling

The acoustic analysis process described previously was used to produce acoustic characteristics for 

the notional mixer-ejector nozzle. Acoustic characteristics for the nozzle were needed specifically for the 

three noise certification points previously described. To generate the data for these points, the analysis 

process was executed for the cases described in Table 3. The flyover and approach points each required
NASA/TM—2012-217709 12

one case to be run through the analysis process. These cases assumed a flight Mach number, altitude and 

power setting for the notional aircraft that would use this mixer-ejector nozzle. For the lateral certification 

point, four cases were run again at an assumed flight condition and engine power setting. However, the 

azimuthal angle (φ in Figure 6) was changed for each case so that noise projected in the lateral direction 

could be estimated.

TABLE 3.—INPUT PARAMETERS FOR GENERATING ACOUSTIC 

CHARACTERISTICS AT EACH CERTIFICATION POINT

Certification 

point

Mach Altitude,

ft

Engine net thrust,

%

Azimuthal angle,

°

Flyover 0.28 2000 65 0

Approach 0.20 394 30 0

Lateral 0.25 1000 100 0

Lateral 0.25 1000 100 30

Lateral 0.25 1000 100 60

Lateral 0.25 1000 100 90

Using the cases from Table 3, Acoustic Data Module input tables were created for ANOPP by 

converting the data to a 1-ft, lossless arc as described in a previous section. The SPL data produced in this 

process varied with both emission angle and frequency as shown in Figure 10 for the sideline case at zero 

azimuthal angle (φ). From the figure, it can be seen that the peak SPL values occurred at an emission 

angle (θ) around 150° and at lower frequencies for this operating condition. Plots similar to Figure 10 can 

be created for other cases in Table 3; however the most important information coming from this analysis 

is the Acoustic Data Module inputs which will be used to assess the overall acoustic levels of the mixerejector nozzles in the following section. 

Figure 10.—Sound pressure levels (SPL, dB) as a 

function of emission angle (degrees) and 

frequency for the lateral case at zero azimuthal 

angle.
NASA/TM—2012-217709 13

3.3 System Level Performance and Acoustic Assessment

The performance maps for the mixer-ejector nozzle were integrated into the propulsion system 

modeling to determine the overall thrust characteristics of these two engine cycles employing these 

nozzles. Figure 11shows the engine TSFC as a function of the installed net thrust at two critical operating 

conditions for all five engine cycles: the NASA model of the contractor baseline MFTF with FPR=2.2 

and simple convergent-divergent nozzle, NASA models of FPR=2.8 and 3.4 MFTFs with simple 

convergent-divergent nozzles and sized to the baseline rolling takeoff thrust, and NASA models of these 

same-sized FPR=2.8 and 3.4 MFTFs but utilizing mixer-ejector nozzles. The resulting engine airflow 

sizes for a rolling takeoff thrust of 41387 lbf at Mach 0.2, sea level was 732 lb/s for the MFTF FPR 3.4 

cycles, 879 lb/s for the MFTF FPR 2.8 cycles, and 1140 lb/s for the baseline N+2 MFTF cycle with 

FPR=2.2. The higher FPR MFTF cycles enable a better rate of climb at a smaller size due to higher 

specific thrust with only modest cruise TSFC penalties. It must be noted that no effort was made to rematch the inlet flow lapse or re-optimize any engine design parameters of these higher FPR cycles. Even 

without this optimization, the higher FPR cycles exhibited only a slightly higher installed TSFC at cruise.

A complete cycle optimization study would likely mitigate this modest increase in cruise TSFC. When 

the mixer-ejectors are added the cruise TSFC of the higher FPR cycles is further degraded, due to the loss 

penalty that was included for having a mixer-ejector on the engine though not operating. For this study, 

the mixer-ejectors where only permitted to operate below 5000 ft. altitude. At the takeoff flight condition, 

the mixer-ejector cycles exhibit increased thrust compared to their equally-sized non-mixer-ejector 

counterparts. Readily apparent in the takeoff performance of the mixer-ejector cycles in Figure 11 is the 

impact from the separated-flow in the fixed chutes at the lower thrust settings (below 70 percent

maximum thrust). While not an issue near max throttle, a more detailed modeling effort is warranted to 

assure safe-operation and adequate performance at reduced power (such as for cutback), and may 

preclude mixer-ejector operation during very low power (such as approach; depending on low-speed 

aerodynamics, thrust required, and acceleration time in case of missed approach).

Figure 11.—Engine TSFC verses net thrust for sample MFTF engines with and 

without mixer-ejector nozzles.
NASA/TM—2012-217709 14

Figure 12.—Aircraft range versus jet velocity for sample MFTF engines with and 

without mixer-ejector nozzles.

Following the development of the engine performance characteristics, the impact of the mixer-ejector 

cycles was evaluated on the overall aircraft performance. Of primary interest in this study was the change 

to the overall range of the aircraft. In Figure 12, the range of the aircraft using each of the five cycles is 

plotted versus the mixed average jet velocity at the nozzle exit for max thrust operation. In this figure, it is 

clear that the mixer ejector nozzles reduce the jet velocity which will reduce the jet noise produced by 

these engine cycles. The results also show that the range of the aircraft is negatively impacted by 

including a mixer-ejector on the engine due to the slightly higher engine TSFC during cruise. Also, 

because the aircraft is assumed to have a fixed maximum takeoff gross weight in this study, the extra 

weight of the mixer-ejector nozzle reduces the amount of fuel that the aircraft can carry further reducing 

the range. However, a more complete engine and aircraft system optimization using additional variables 

may provide comparable range capabilities and will be the subject of future work. 

Finally, the mission performance results and mixer-ejector acoustic characteristics can be combined 

to determine the overall system level noise metrics for the engines cycles. Figure 13 shows a comparison 

of the nozzle only EPNL values from only the jet noise sources at all three certification points for the 

higher FPR engine cycles considered in the cycle and mission analyses. For the conventional convergentdivergent nozzles, the ST2Jet noise method (Refs. 14) is used to compute the noise values. For both the 

FPR = 2.8 and 3.4 cycles, the engine with a mixer-ejector nozzle is more than 10 EPNdB quieter at the 

flyover observer and more than 15 EPNdB quieter at the sideline observer relative to the conventional 

nozzles. This reduction is primarily the result of lower jet velocity exiting the nozzle as displayed in 

Figure 12. However, at the approach observer, the mixer-ejector nozzle is slightly louder than the 

conventional nozzle. While the mixer-ejector nozzles show the potential to significantly reduce jet noise, 

it is noted that the overall EPNL levels are considerably higher than those required to meet certification 

requirements. While there may be several factors leading to these high EPNL values, the most likely 

explanation is that the JN8C4 method is not valid for the mixer-ejector operating conditions considered in 

this study. The JN8C4 method is empirically based and is only valid for designs that lie within the mixer-
NASA/TM—2012-217709 15

Figure 13.—Comparison of mixer-ejector nozzle and conventional nozzle acoustics for two different engine cycles.

ejector designs used to create the model. The advanced cycles used in this study may require mixerejector operation outside of the ranges of validity for the JN8C4 method. Absolute noise levels are 

currently under review along with details regarding constituent source noise modules. 

4.0 Conclusion

The design of an engine for a supersonic aircraft presents a difficult multidisciplinary problem to 

propulsion system engineers. The engine must be capable of supplying the required thrust throughout the 

flight envelope while also minimizing the noise it produces during takeoff and landing. The mixer-ejector 

nozzle is one technology that may be able to positively impact both of these metrics by reducing takeoff

jet velocities while enabling the use of smaller, higher specific thrust, higher FPR engine cycles. In order 

to evaluate the potential impact of mixer-ejector nozzles, a multidisciplinary analysis process has been 

developed and presented in this paper. The process uses low fidelity disciplinary analysis codes to predict 

the performance and acoustics of the isolated mixer-ejector nozzles. The results from these analysis tools 

are then used to estimate the overall system level performance of an aircraft and engine using these 

nozzles. Execution of the entire analysis process is facilitated by the use of an MDAO framework, 

OpenMDAO.

Using the analysis process above, a notional mixer-ejector was analyzed and applied to two different 

mixed flow turbofan engine cycles. The results of this study demonstrate the need for the 

multidisciplinary approach to evaluating the mixer-ejector nozzle as part of the overall aircraft system.

The mixer-ejector nozzle provides improved thrust and fuel burn characteristics of the engine in portions 

of the low speed operation. However, at cruise the presence of the ejector in the non-operating condition 

slightly decreased the performance of the engine. As a result of this decreased performance during cruise 

and the higher weight of the mixer-ejector over a conventional nozzle, the range of the aircraft was 

negatively impacted for both higher FPR engine cycles relative to their conventional convergentdivergent nozzle counterparts. While the range of the aircraft was decreased by the presence of the mixer-
NASA/TM—2012-217709 16

ejector, the inclusion of this technology provides a significant reduction in the jet noise during takeoff.

More than a 10 EPNdB reduction in jet noise is predicted at both the flyover and sideline noise 

certification points. These results for aircraft range and noise when using the higher FPR cycles with the 

mixer-ejector nozzles present an opportunity for further multidisciplinary optimization to create a better 

engine system compared to the baseline MFTF cycle.

The results above indicate there are potential benefits of mixer-ejector nozzles on future supersonic 

civil aircraft. However, it is important to note that these results are for a notional mixer-ejector design and 

may change in future studies as improved assumptions and analysis capabilities are included. The new 

mixer-ejector multidisciplinary analysis capability described in this paper presents many opportunities for 

future design studies. In this study, the mixer-ejector nozzle geometry was assumed fixed throughout the 

analysis. However, there are a number of design parameters including length, aspect ratio and primary to 

secondary area ratio that could be varied, resulting in a better nozzle in terms of both performance and 

acoustics. Furthermore, the integrated analysis process developed in this study can be used to explore the 

engine design trade space to find the best combination of cycle design parameters and mixer-ejector 

nozzle design parameters to meet the mission and acoustic requirements.
NASA/TM—2012-217709 17

Appendix

The equations below are the second order response surfaces for gross thrust coefficient (Cfg), 

pumping ratio and secondary mass flow that were described in Section 3.1.

Cfg = −1.88080401145108 + 0.00251022043776385 ∗ PPRI − 1.22482971829852 ∗ MPRI

+ 0.000155788672122014 ∗ TPRI − 0.0158594605411259 ∗ Pstatic

+ 0.0164531481665035 ∗ TSEC − 0.00858760307179354 ∗ PSEC + PPRI ∗ PPRI

∗ 0.000000005275137024 + PPRI ∗ MPRI ∗ −0.0000319371657122326 + MPRI

∗ MPRI ∗ 0.306888290022466 + PPRI ∗ TPRI ∗ 0.0000000138347388952 + MPRI

∗ TPRI ∗ 0.000026511421123294 + TPRI ∗ TPRI ∗ 0.0000000085918829761

+ PPRI ∗ Pstatic ∗ 0.0000002254714307732 + MPRI ∗ Pstatic

∗ −0.0000321189079163447 + TPRI ∗ Pstatic ∗ 0.0000000933851943275

+ Pstatic ∗ Pstatic ∗ −0.0000000834284540801 + PPRI ∗ TSEC

∗ −0.0000062821538778467 + MPRI ∗ TSEC ∗ 0.00154609008925985 + TPRI

∗ TSEC ∗ −0.0000006695017074581 + Pstatic ∗ TSEC

∗ 0.0000405979956527768 + TSEC ∗ TSEC ∗ −0.0000016661850914034 + PPRI

∗ PSEC ∗ 0.0000001136496197052 + MPRI ∗ PSEC ∗ −0.0000015046671232206

+ TPRI ∗ PSEC ∗ −0.0000000706233098087) + Pstatic ∗ PSEC

∗ −0.0000020829077799803 + TSEC ∗ PSEC ∗ 0.0000094224046104911 + PSEC

∗ PSEC ∗ 0.0000004213243901684

Pumping Ratio

= 3.1414646977946 + 0.00412871844662116 ∗ PPRI − 2.26912258893189

∗ MPRI − 0.000507940546247807 ∗ TPRI − 0.0246422375967092 ∗ Pstatic

− 0.00772996926454509 ∗ TSEC − 0.0243449494600919 ∗ PSEC + PPRI ∗ PPRI

∗ −0.0000000357338008477 + PPRI ∗ MPRI ∗ −0.00011439202748741 + MPRI

∗ MPRI ∗ 1.20824408067919 + PPRI ∗ TPRI ∗ −0.0000000307792041218 + MPRI

∗ TPRI ∗ 0.000135286298718735 + TPRI ∗ TPRI ∗ −0.0000001748357911165

+ PPRI ∗ Pstatic ∗ 0.0000002821656147195 + MPRI ∗ Pstatic

∗ 0.0000159440514023688 + TPRI ∗ Pstatic ∗ −0.0000001491504671946

+ Pstatic ∗ Pstatic ∗ −0.0000006123118201233 + PPRI ∗ TSEC

∗ −0.0000100596302346047 + MPRI ∗ TSEC ∗ −0.000493241108138516 + TPRI

∗ TSEC ∗ 0.0000024069638960806 + Pstatic ∗ TSEC ∗ 0.0000699824563572073

+ TSEC ∗ TSEC ∗ 0.0000507567295994289 + PPRI ∗ PSEC

∗ 0.0000004311270428131 + MPRI ∗ PSEC ∗ 0.00018809302632975 + TPRI

∗ PSEC ∗ 0.0000000897750488695 + Pstatic ∗ PSEC

∗ −0.0000028544127821669 + TSEC ∗ PSEC ∗ 0.0000274525391964286 + PSEC

∗ PSEC ∗ 0.0000000134435295003

Sample of secondary mass flow results, regressed for user verification
NASA/TM—2012-217709 18

Sec. Mass Flow

= 67.6231994429525 + 0.024494624200508 ∗ PPRI + 6.31620091246409

∗ MPRI + 0.00387069632721205 ∗ TPRI − 0.136239682255964 ∗ Pstatic

− 0.375261798528971 ∗ TSEC − 0.194570803130727 ∗ PSEC + PPRI ∗ PPRI

∗ −0.0000006796934734726 + PPRI ∗ MPRI ∗ −0.000125870951948597 + MPRI

∗ MPRI ∗ 3.75768601776597 + PPRI ∗ TPRI ∗ −0.0000005644944364664 + MPRI

∗ TPRI ∗ 0.000891281224394572 + TPRI ∗ TPRI ∗ 0.0000003420719319794

+ PPRI ∗ Pstatic ∗ 0.0000030619921930288 + MPRI ∗ Pstatic

∗ −0.00157908232678972 + TPRI ∗ Pstatic ∗ 0.0000010110121793826 + Pstatic

∗ Pstatic ∗ −0.0000110293437669869 + PPRI ∗ TSEC

∗ −0.0000530976230405342 + MPRI ∗ TSEC ∗ −0.0351492856826302 + TPRI

∗ TSEC ∗ −0.0000143918607364096 + Pstatic ∗ TSEC ∗ 0.000413365237851738

+ TSEC ∗ TSEC ∗ 0.00084503570989837 + PPRI ∗ PSEC

∗ 0.0000023795336151179 + MPRI ∗ PSEC ∗ 0.00363542442357027 + TPRI

∗ PSEC ∗ 0.00000018453226691 + Pstatic ∗ PSEC ∗ −0.0000080553812376122

+ TSEC ∗ PSEC ∗ 0.000222651261613385 + PSEC ∗ PSEC

∗ −0.000004272658852365
NASA/TM—2012-217709 19

References

1. Thirumurthy, D. and Jones, J., “Experimental Investigation and Computation of a Supersonic Ejector 

Nozzle with Clamshells,” AIAA-2010-4725, 40th Fluid Dynamics Conference and Exhibit, 28 June-1 

July 2010, Chicago, Illinois.

2. Thirumurthy, D., Blaisdell, G., Anastasios, S., and Sullivan, J., “Preliminary Design and 

Computational Analysis of and Ejector Nozzle with Chevrons,” AIAA-2011-918, 49th AIAA 

Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 4-7 

January 2011, Orlando, Florida.

3. Pratt & Whitney West Palm Beach, Florida, and General Electric Aircraft Engines Cincinnati, Ohio, 

“Critical Propulsion Components, Volume 3: Exhaust Nozzle,” NASA/CR—2005-213584, Vol. 3, 

May 2005.

4. Presz, W., Reynolds, G., and Hunter, C., “Thrust Augmentation with Mixer/Ejector Systems,” AIAA2002-0230 40th AIAA Aerospace Sciences Meeting & Exhibit, 14-17 January 2002, Reno, NV.

5. Heath, C. and Gray, J., “OpenMDAO: Framework for Flexible Multidisciplinary Design, Analysis 

and Optimization methods,” AIAA-2012-1673, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics and Materials Conference and 20th AIAA/ASME/AHS Adaptive Structures 

Conference, 23-26 April 2012, Honolulu, Hawaii.

6. Welge, H.R., et al., “N+2 Supersonic Concept Development and Systems Integration,” NASA/CR—

2010-216842.

7. Onat, E., and Klees, G., “A Method to Estimate Weight and Dimensions of Large and Small Gas 

Turbine Engines,” NASA-CR-159481, 1979. 

8. 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.

9. Dechant, L. J., “Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes 

Equations for Aerodynamic Ejector/Mixer Nozzle Flows,” NASA/CR—1998-207406.

10. Dechant, L. J. and Nadell, S., “A User’s Guide for the Differential Reduced Ejector/Mixer Analysis 

“DREA” Program: Version 1.0,” NASA/TM—1999-209073.

11. U.S. Code of Federal Regulations, Title 14, Chap. I, Part 36, Noise standards: Aircraft Type and 

Airworthiness Certification.

12. Rawls, J. and Yeager, J., “High Speed Research Noise Prediction Code (HSRNOISE) User’s and 

Theoretical Manual,” NASA/CR—2004-213014, November 2004.

13. McCullers, L.A., “Aircraft Configuration Optimization Including Optimized Flight Profiles,” 

Proceedings of the Symposium on Recent Experiences in Multidisciplinary Analysis and 

Optimization, NASA CP–2327, April 1984.

14. Stone, J.R., Krejsa, E.A., Clark, B.J., and Berton, J.J., “Jet Noise Modeling for Suppressed and 

Unsuppressed Aircraft in Simulated Flight,” NASA/TM—2009-215524, 2009.
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14. ABSTRACT

The design of an engine for a civil supersonic aircraft presents a difficult multidisciplinary problem to propulsion system engineers. There 

are numerous competing requirements for the engine, such as to be efficient during cruise while yet quiet enough at takeoff to meet airport 

noise regulations. The use of mixer-ejector nozzles presents one possible solution to this challenge. However, designing a mixer-ejector 

which will successfully address both of these concerns is a difficult proposition. Presented in this paper is an integrated multidisciplinary 

approach to the analysis and design of these systems. A process that uses several low-fidelity tools to evaluate both the performance and 

acoustics of mixer-ejectors nozzles is described. This process is further expanded to include system-level modeling of engines and aircraft to 

determine the effects on mission performance and noise near airports. The overall process is developed in the OpenMDAO framework 

currently being developed by NASA. From the developed process, sample results are given for a notional mixer-ejector design, thereby 

demonstrating the capabilities of the method. 

15. SUBJECT TERMS

Ejector; Multidisciplinary design optimization; Nozzle design; Acoustics 

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