Bernhard H. Anderson

Glenn Research Center, Cleveland, Ohio

Dennis J. Keller

RealWorld Quality Systems, Rocky River, Ohio

A Robust Design Methodology for Optimal

Microscale Secondary Flow Control

in Compact Inlet Diffusers

NASA/TM—2001-211278

December 2001

AIAA–2002–0541
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National Aeronautics and

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Prepared for the

40th Aerospace Sciences Meeting and Exhibit

sponsored by the American Institute of Aeronautics and Astronautics

Reno, Nevada, January 14–17, 2002

Bernhard H. Anderson

Glenn Research Center, Cleveland, Ohio

Dennis J. Keller

RealWorld Quality Systems, Rocky River, Ohio

A Robust Design Methodology for Optimal

Microscale Secondary Flow Control

in Compact Inlet Diffusers

NASA/TM—2001-211278 AIAA–2002–0541
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Available electronically at http://gltrs.grc.nasa.gov/GLTRS
ABSTRACT

It is the purpose of this study to develop an

economical Robust design methodology for micro-scale

secondary flow control in compact inlet diffusers. To

illustrate the potential of economical Robust Design

methodology, two different mission strategies were

considered for the subject inlet, namely (1) Maximum

Performance, and (2) Maximum HCF Life Expectancy. The

Maximum Performance mission maximized total pressure

recovery while the Maximum HCF Life Expectancy mission

minimized the mean of the first five Fourier harmonic

amplitudes, i.e. “collectively” reduced all the harmonic 1/2

amplitudes of engine face distortion. Each of the mission

strategies was subject to a low engine face distortion

constraint, i.e. DC60 < 0.10, which is a level acceptable for

commercial engines. For each of these missions strategies, an

“Optimal Robust” (open loop control) and an “Optimal

Adaptive” (closed loop control) installation was designed

over a twenty degree angle-of-incidence range. The “Optimal

Robust” installation used economical Robust Design

methodology to arrive at a single design which operated over

the entire angle-of-incident range (open loop control). The

“Optimal Adaptive” installation optimized all the design

parameters at each angle-of-incidence. Thus the “Optimal

Adaptive” installation would require a closed loop control

system to sense a proper signal for each effector and modify

that effector device, whether mechanical or fluidic, for

optimal inlet performance. In general, the performance

differences between the “Optimal Adaptive” and “Optimal

Robust” installation designs were found to be marginal. This

suggests, however, that “Optimal Robust” open loop

installation designs can be very competitive with “Optimal

Adaptive” close loop designs. Secondary flow control in

inlets is inherently robust, provided it is optimally designed.

Therefore, the new methodology presented in this paper,

combined array “Lower Order” approach to Robust DOE,

offers the aerodynamicist a very viable and economical way

of exploring the concept of Robust inlet design, where the

mission variables are brought directly into the inlet design

process and insensitivity or robustness to the mission

variables becomes a design objective

INTRODUCTION

The current development strategy for combat airvehicles is directed towards reduction in the Life-Cycle Cost

(LCC) with little or no compromise to air-vehicle

performance and survivability. This strategy has been

extended to the aircraft component level, in particular, the

engine inlet diffuser system. One method to reduce inlet

system LCC is to reduce its structural weight and volume.

Consequently, advanced combat inlet configurations are

being made more compact (or shorter) to achieve weight and

volume (and LCC) reduction. However, compact S-duct

diffusers, see figures (1) and (3), are characterized by high

distortion and low pressure recovery, produced by extreme

wall curvature and strong secondary flow gradients. These

characteristics are further aggravated by maneuver

conditions. Since survivability rather than aerodynamic

performance often drives the inlet design, it is expected that

the flow quality entering the turbine engine will present an

additional challenging environment for both fan/compressor

surge margin and aeromechanical vibration. Interest in High

Cycle Fatigue (HCF) research by the US aerospace

community has been spurred by discrepancies between the

expected durability of engine components compared to that

actually experienced in the field. Recognizing that inlet

distortion is a forcing function for vibration in the fan

components, methods for increasing HCF Life Expectancy

can been combined with techniques for inlet recovery and

engine face distortion management. Therefore, to enable

acceptable performance levels in such advanced, compact

inlet diffuser configurations, micro-scale secondary flow

control (MSFC) methods are being developed to manage the

recovery, distortion, and HCF aspects of distortion.(1)-(2)

One of the most difficult tasks in the design of MSFC

installation for optimal inlet operation is arriving at the

geometric placement, arrangement, number, size and

orientation of the effector devices within the inlet duct to

achieve optimal performance.These actuator devices can be

either mechanical or fluidic.This task is complicated not only

by the large number of possible design variables available to

the aerodynamicist, but also by the number of decisions

parameters that are brought into the design process. By

including the HCF effects into the inlet design process, the

aerodynamicist has a total of seven individual response

variables which measure various aspects of inlet

performance. They include the inlet total pressure recovery,

the inlet total pressure recovery distortion at the engine face

and the first five Fourier harmonic 1/2 amplitudes of

distortion. Each of these responses needs to be either

maximized, minimized, constrained or unconstrained while

searching for the optimal combination of primary design

variable values that satisfy the mission requirements. The

design task is further complicated by the existence of hard-tocontrol factors which effect inlet performance, i.e. the

mission variables. The mission variables that cause the offA ROBUST DESIGN METHODOLOGY FOR OPTIMAL

 MICROSCALE SECONDARY FLOW CONTROL

 IN COMPACT INLET DIFFUSERS

Bernhard H. Anderson

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Dennis J. Keller

RealWorld Quality Systems

Rocky River, Ohio 44116

NASA/TM—2001-211278 1
(engine corrected weight flow), angle-of-incidence and angle-ofyaw. While the aerodynamicist does not know how the pilot is

ultimately going to fly the aircraft, it is known how the mission

variables effect inlet performance under wind tunnel conditions.

Traditionally, tolerance or robustness to the mission variables was

accomplished only after the parameter design was completed,

usually by accepting whatever off-design performance was

delivered by the newly designed inlet system. Numerical

optimization procedures that have been successful with some

aerodynamics problems give little assistance to designing robust

inlets since they are point-design procedures, usually with only

one decision parameter. However, there is a branch of statistical

Design-of-Experiments (DOE) methodology which integrates

both traditional Response Surface Methods (RSM) and

Robustness considerations into a single optimization procedure. It

presents new potential for further reduction of Total Quality Cost

over the traditional design approach.

Taguchi(3) coined the term Robust Parameter Design to

describe an approach to industrial problem solving whereby the

product variation is reduced by choosing levels of the control

factors (design parameters) that make the product insensitive to

the changes in the noise factors that represent sources of

variations. These noise factors in industrial design are often the

environmental variables, such as temperature and humidity

conditions, properties of the material, and product aging. In some

applications, they measure how the consumer uses or handles the

product. In the aerodynamic design of inlet systems, there is a

analogous situation to the industrial design problem. As

mentioned above, the design of inlet systems is usually

accomplished at the cruise condition (the on-design condition)

while variations from the cruise condition are considered as an

off-design penalty. Because the mission variables cause variation

from on-design performance, they can be identified with the noise

factors or environmental variables in the analogous industrial

design problem. Likewise, how the pilot flies the aircraft can be

identified with how the consumer uses or handles the product. In

the industrial problem, the researchers must be able to control the

environmental variables in a laboratory environment, even though

they cannot be controlled at the production level or in the field.

Likewise, the aerodynamic researcher can indeed control the

mission variables in the wind tunnel environment, however these

variables cannot be controlled in flight (in the field). By making

the analogy between the industrial design problem and the

aerodynamic design problem, Robust Parameter Design methods

developed for industrial problem solving can be adapted to the

design of inlet systems, and in particular, design of micro-scale

secondary flow control installations for such inlet systems.

Much has been written and said about the contribution of

Genichi Taguchi to the vastly important area of Product Quality

Enhancement. However, much controversy surrounds Taguchi’s

methodology among statisticians. Many statisticians have pointed

out the apparent flaws in the Taguchi approach. However, it

suffices to say the importance of Taguchi’s contributions lies in

the idea that process or product sensitivity to its environment can

be incorporated into the optimal statistical Design-of-Experiment

and subsequent analysis of data. To the aerodynamicist, it

represents a quantum leap in the area of inlet design. For the first

time, the mission variables can be directly introduced into the inlet

design processes. The inlet system can now be designed to operate

with optimal performance over a range of specified mission

variables. Rigorous application of Taguchi’s Robust Parameter

Design method may not be optimal in the design of micro-scale

secondary flow installations for inlet systems because it can mask

information vital to the aerodynamicist. However, the important

aspects surrounding Taguchi’s approach to Robust Parameter

Design can and have been incorporated into an alternate approach,

i.e. adopted to the inlet design problem. This is the subject of this

report. The present methodology is a more standard method of

statistical Design-of-Experiments, but with a unique data analysis

phase. It provides a good working strategy for aerodynamic

systems. Further, this method overcomes one of the basic

hardships of Taguchi’s method, namely the lack of economy in

the experimental design plan.

Two different mission strategies were considered for the

subject inlet, namely (1) Maximum Performance, and (2)

Maximum HCF Life Expectancy. The Maximum Performance

mission maximized total pressure recovery while the Maximum

HCF Life Expectancy mission minimized the mean of the first five

Fourier harmonic 1/2 amplitudes, i.e. “collectively” reduced all

the Fourier harmonic 1/2 amplitudes of engine face distortion.

Each of the mission strategies was subject to a low engine face

distortion constraint, i.e. DC60 < 0.10, which is a level acceptable

for commercial engines. For each of these missions strategies, an

“Optimal Robust” (open loop control) and an “Optimal Adaptive”

(closed loop control) installation was designed over a twenty

degree angle-of-incidence range. The “Optimal Robust”

installation arrived at a single MSFC installation which operated

over the entire angle-of-incident range (open loop control). The

“Optimal Adaptive” installation optimized all the design

parameters at each angle-of-incidence. Thus the “Optimal

Adaptive” installation would require a closed loop control system

to sense a proper signal for each effector and modify that effector

device, whether mechanical or fluidic, for optimal inlet

performance. For each mission strategy, i.e. Maximum

Performance and Maximum HCF Life Expectancy, the two

approaches to secondary flow control installation design were

compared for the simultaneous management of inlet total pressure

recovery, engine face distortion, and the first five Fourier

harmonic 1/2 amplitudes of distortion. The angle-of incidence

range was the Taguchi noise or environmental variable over

which each optimal installation had to be robust.

NOMENCLATURE

AIP Aerodynamic Interface Plane

c Effector Chord Length

CCF Central Composite Face-Centered

CFD Computational Fluid Dynamics

D Engine Face Diameter

DC60 Circumferential Distortion Descriptor

DOE Design of Experiments

h Effector Blade Height

HCF High Cycle Fatigue

Fi/2 ith Fourier Harmonic 1/2 Amplitude

FM/2 Mean Fourier Harmonic 1/2 Amplitude

L Inlet Diffuser Length

LCC Life Cycle Costs

MSFC Micro-Scale Secondary Flow Control

Mt Inlet Throat Mach Number

n Number of Effector Vanes per Band

PFAVE Inlet Total Pressure Recovery

R Inlet Throat Radius

Re Reynold Number per ft.

RSM Response Surface Methodology

Y Generalized Response Variable

2 NASA/TM—2001-211278 
α Inlet Angle-of-Incidence

β Effector Vane Angle-of-Incidence

βij Coefficients in the Regression Model

γ Inlet Angle-of-Yaw

RESULTS AND DISCUSSION

The basic problem of experimental and CFD analysis

design is deciding what pattern of test cases will best reveal

aspects of the situation of interest. For that reason, the overall

objectives of the study become very important. In the present

study, three objectives were considered important, namely: (1) to

determine the design characteristic (i.e. factor interactions) of

multi-installation. micro-scale secondary flow control configurations, (2) to establish the ability of MSFC to manage the aeromechanical effects of engine face distortion, and (3) to evaluate the

effectiveness of this new methodology for “open loop” microscale secondary flow installations over an angle-of-incidence

range in comparison to fully adaptive “closed loop” designs. The

first two objectives of this overall study on micro-scale flow control are covered by Anderson and Keller(4), while the third objective is covered in detail in Anderson and Keller(5). A third report

in this series by Anderson and Keller(6) evaluates the impact of

rake geometry, specifically the number of rake arms, on the measurement errors associated with estimating the first five Fourier

harmonic 1/2 amplitude of engine face distortion. This paper covers the economical form of Robust Design methodology for

micro-scale secondary flow installation design that appears in

Anderson and Keller(5).

Figure (1): Particles traces showing the vortex liftoff (separation) within the DERA/M2129 inlet S-duct, Mt = 0.70, Re =

4.0 x 106/ft., α = 0.0o.

Design of the Experiment

The basic inlet flowpath chosen for this study featured a

compact (L/D =3.0), two turn, or S-duct inlet diffuser, Figure (1).

This S-duct was defined by AGARD FDP Working Group 13

Test Case 3, Willmer, Brown and Goldsmith(7), and was dubbed

the DERA/M2129 inlet. Traditionally, this type of compact inlet

duct would be excluded from design consideration since it is

characterized by severe wall curvature that induces strong secondary flows. These strong secondary flow can cause a flow separation called vortex lift-off. See Figure (1). This type of 3D flow

separation results in severe total pressure losses and severe

engine face distortion. Figure (2) presents the engine face total

pressure recovery contours and secondary flow velocity vectors

for the DERA/M2129 inlet S-duct at a throat Mach number of

0.70. A vortex pair is dominant in the engine face flow field and

this was accompanied by very severe engine face total pressure

distortion.

Figure (2): Baseline engine face solution, Mt = 0.70, Re = 4.0 x

106/ft., α =0.0o.

To manage the flow in the DERA/M2129 inlet S-duct, a

three-band installation arrangement of micro-scale effectors was

placed in the upstream section near the inlet throat. See Figures

(3) and (4). These micro-scale effectors were simple vanes, the

largest height being about the average height of the momentum

layer at the location of band (3), or about 2.0 mm. The purpose of

these simple vanes was to create a set of co-rotating vortices that

will quickly merge to form a thin layer of secondary flow that

will counter the formation of the passage vortex pair(1). Since the

height of the vane effectors were limited to 2.0 mm, a multi-band

arrangement was chosen to investigate the possibility of enhancing the effect of the individual vanes by adding more bands of

effectors.

Figure (3): Location of effector region within the DERA/

M2129 inlet S-duct.

The spacing between the bands is critical since interaction will occur between respective bands of effector units. The

first band was placed at the inlet throat station, X/R = 0.0, while

the second and third bands of effector vanes were placed nominally at X/R = 1.0 and at X/R = 2.0 respectively. See Figure (3).

Nominally, the spacing between the effector vanes was ∆X/c =

(a) Total Pressure (b) Velocity Vectors

Band No. (1), X/R = 0.0 (nominal)

Band No. (2), X/R = 1.0 (nominal)

Band No. (3), X/R = 2.0 (nominal)

Effector Region

3 NASA/TM—2001-211278 
4.0, i.e. about four effector chord lengths as measured between

the half chord stations. See Figure (4).

Figure (4): Micro-scale vane actuator arrangement within

effector region.

The DOE approach followed directly from the three

objectives previously stated and was reflected in the layout of the

design factors listed in Table (1). The design variables (factors)

were the effector vane heights (mm) in the three upstream installation h1, h2, and h3, and the inlet angle-of-incidence α. The

effector vane heights were changed independently and, therefore,

constituted three independent variables. Strictly speaking, the

inlet angle-of-incidence was a mission variable and was, therefore, one of the noise factors that belonged with the environmental variables, i.e. the outer array in the traditional Taguchi-style

DOE design. In this study, however, the angle-of-incidence was

introduced into the statistical design matrix with the control factors which allowed greater economy than the traditional Taguchi

approach.

Table (1): Factors which establish the DOE design matrix.

The robust nature of the angle-of-incidence was investigated during the analysis of the data phase. Table (2) shows the variables

that were held constant during this study. The number of microscale vane effectors ni, i=1,3 was held fixed at 24 in the half-plane,

and were spaced symmetrically around the inlet half-periphery.

Each vane effector was set at a geometric angle-of-incidence βi

,

i=1,3 of 24.0o. In addition, the throat Mach Number (Mt), Reynolds number (Re), and the angle-of-yaw (γ) were set constant at

0.70, 4.0 x 106/ft and 0.0o respectively for this investigation.

Table (2): Variables held constant.

Table (3) displays the response variables for this study. They

were the inlet total pressure recovery (PFAVE), the engine face

distortion (DC60), and the first five Fourier harmonic 1/2 amplitudes of engine face distortion (F1/2, F2/2, F3/2, F4/2, and F5/2).

Table (3): DOE design response.

The DOE strategy selected was a Central Composite

Face-Centered (CCF) DOE plus an additional experiment of special interest to the investigator. This strategy resulted in 26 unique

experimental CFD cases that are shown in Table (4). Notice that

these DOE cases covered a substantial range of possible flow situations over a wide range of angle-of-incidences from 0.0o to

20.0o. This particular DOE, like most DOE strategies, varied

more than one factor at a time. Further, this layout of 26 cases

permitted the estimation of both linear and curvilinear effects as

well as interactive or synergistic effects among the DOE factors.

This is very important in the study of secondary flow control

since very strong interaction effects can develop between separate bands of micro-scale effectors. This CCF DOE strategy is

superior to the traditional approach where only changing one

variable at a time does not permit the estimation of factor interactions. It is also more economical at 26 runs than a full factorial

approach where the number of experiments would be 34 or 81

Factors Range

Installation Vane Height (mm), h1 0.0 to 2.0

Installation Vane Height (mm), h2 0.0 to 2.0

Installation Vane Height (mm), h3 0.0 to 2.0

Inlet Angle-of-Incidence, (degs.), α 0 to 20.0

∆X/c = 4.0 (nominal)

Variable Value

Number of Effectors Units, ni, i=1,3 24

Vane Angle-of-Incidence, (degs.), βi, i=1,3 24.0o

Installation Chord Length (mm), c1, i=1,3 16.0

Throat Mach Number, Mt 0.700

Reynolds Number, x106

 /ft. 4.0

Inlet Angle-of-Yaw, (degs.), γ 0.0o

Design Responses Term

Engine Face Total Pressure Recovery PFAVE

Engine Face Distortion DC60

1st Fourier Harmonic 1/2 Amplitude F1/2

2nd Fourier Harmonic 1/2 Amplitude F2/2

3rd Fourier Harmonic 1/2 Amplitude F3/2

4th Fourier Harmonic 1/2 Amplitude F4/2

5th Fourier Harmonic 1/2 Amplitude F5/2

4 NASA/TM—2001-211278 
separate CFD cases. It is also more economical than a comparable Taguchi approach requiring 3 x 15 = 45 runs. Each of the 26

cases in Table (4) were run with a Reynolds-averaged NavierStokes code(9) that allowed for numerical simulation of microvane effectors without the need to physically embed the vane

effectors within the CFD grid structure.

Table (4): Central Composite Face-Centered design (plus one

additional case), “Lower Order” Robust Design methodology.

For the present study, however, the individual vanes

were incorporated into the half-plane grid structure, and the

appropriate boundary conditions applied. The half-plane grid

structure was composed of three blocks: an upstream block, a

effector section containing the micro-vanes, and a downstream

block. See Figures (3) and (4). The computational half-plane grid

varied in total number of mesh points from about 750,00 to

1,500,000 depending on the micro-vane configuration. All CFD

calculations were accomplished assuming half-plane symmetry.

It was important to investigate the interactions between the separate effector bands without using the vane model in the code, so

that proper band interaction could be established. This also established a set of baseline validation data to further verify the vane

effector model in the Navier-Stokes code(9) for multi-band flow

control design concepts.

To introduce an angle-of-incidence (α-disturbance) into

the flow analysis, the condition was imposed that the initial station have an angle-of-incidence component that approximated the

measured angle-of-incidence flow field(10). Even though introducing an α-disturbance into the flow field is not rigorous, it provides a remarkable good approximation in comparison to

experimental flow field. The overall intent of introducing an αdisturbance into the flow field in this manner was to economically determine the degree of tolerance of the MSFC installation

design to angle-of-incidence.

Harmonic Analysis of Distortion

The overall methodology used to obtain the harmonic

content of inlet distortion was first proposed by Ludwig(11) and is

currently in use at the Williams International Corporation. This

methodology is characterized by the use of radial weighting factors applied to the total pressure rake measurements. The radial

weighting factors are shown in Table (5).These radial weighting

Table (5): Radial weighting coefficients applied to the total

pressure rake measurements.

factors compress the rake information to a single radius ring of

data samples, where the number of data samples corresponds to

the number of arms of the measurement rake. A separate study

was initiated by Anderson and Keller(6) to evaluate the impact of

rake geometry (specifically the number of rake arms) on the measurement error associated with estimating the first five Fourier

harmonic 1/2 amplitudes of engine face distortion. As a result of

that study, the rake and methodology chosen for this study was

the 80-probe clocked rake because it provided the lowest error in

estimating the first five Fourier harmonic 1/2 amplitudes of

engine face distortion. Using the AIP instrumentation locations

for the 80-probe (virtual) rake, the 26 CFD solutions were interpolated at each of the probe positions shown in Figure (5a). The

Config. h1 h2 h3 α

nvg501 0.0 0.0 0.0 0.0

nvg502 2.0 0.0 0.0 0.0

nvg503 0.0 2.0 0.0 0.0

nvg504 2.0 2.0 0.0 0.0

nvg505 0.0 0.0 2.0 0.0

nvg506 2.0 0.0 2.0 0.0

nvg507 0.0 2.0 2.0 0.0

nvg508 2.0 2.0 2.0 0.0

nvg537 0.0 0.0 0.0 20.0

nvg538 2.0 0.0 0.0 20.0

nvg539 0.0 2.0 0.0 20.0

nvg540 2.0 2.0 0.0 20.0

nvg541 0.0 0.0 2.0 20.0

nvg542 2.0 0.0 2.0 20.0

nvg543 0.0 2.0 2.0 20.0

nvg544 2.0 2.0 2.0 20.0

nvg527 0.0 1.0 1.0 10.0

nvg528 2.0 1.0 1.0 10.0

nvg529 1.0 0.0 1.0 10.0

nvg530 1.0 2.0 1.0 10.0

nvg531 1.0 1.0 0.0 10.0

nvg532 1.0 1.0 2.0 10.0

nvg533 1.0 1.0 1.0 0.0

nvg551 1.0 1.0 1.0 20.0

nvg533 1.0 1.0 1.0 10.0

nvg519 0.0 0.0 0.0 10.0

Ring Number Radial Weighting Coefficient

1 0.05651

2 0.14248

3 0.21077

4 0.26918

5 NASA/TM—2001-211278 
span-weighted average total pressure was calculated for the 80-

probe rake by multiplying the probe total pressure by the spanweighted coefficients from Table (5), and adding the results over

the five probes of the rakes to form a single radius ring of data

samples.

Since the rake at the engine face was “clocked”, a complete set of “repeats” was generated at each experimental run in

Table (4). From the engine face patterns at each of the 10 clocking angles, a Fourier analysis was performed on the sample set of

data and a standard deviation of the “repeats”, Sclock, was deterFigure (5): Total pressure and distortion measurement

arrays.

mined for each of the Fourier harmonic 1/2 amplitudes. In order

to check the constant variance assumption associated with standard least square regression, a simple F-test for comparing the

minimum standard deviation to the maximum standard deviation

(F = S2

max/S2min) was conducted for each of the five responses.

The results are presented in Table (6). Since each F-test exceeded

the 95% confidence critical value of F(0.975,9,9) = 4.03, the

assumption of constant variation across the design space had to

be discarded. This meant that a regression technique known as

weighted least squares regression had to be employed for analyzing the 10 x 26 = 260 data samples in the DOE. The weights in

these regression analyses were set to 1/S2

clock.

Table (6): Fourier Harmonic 1/2 amplitude F-test compliance.

The data reduction for the inlet total pressure recovery

and engine face distortion differed greatly from the harmonic

analysis of distortion described. There exists no generalized

methodology to evaluate the Fourier harmonic 1/2 amplitudes of

engine face distortion for more than five probes in the radial

direction. Hence, both the inlet total pressure recovery and engine

face distortion were calculated directly from the computational

grid at the engine face station. See Figure (5b). This computational mesh was composed of 49 x 121 grid points in the fullplane. The DC60 engine face distortion descriptor(8) is defined

such that it can be determined from either a computational grid or

a standard measurement rake. It is the only recognized distortion

descriptor that has this property, and hence, was chosen for this

study.

“Lower Order” Robust Design Methodology

In the traditional Taguchi Robust Parameter Design

methodology, a two tier experimentation strategy is used to solve

the robust design problem. The control factors (design variables)

are studied in their own DOE, called the inner array. A separate

DOE, called the outer array, is constructed using only the environmental or noise variables. For each point in the inner array

DOE, the entire outer array DOE is run and a Taguchi-style signal-to-noise ratio, (S/N) is calculated using the values from the

outer (mission) array matrix. The S/N becomes the response that

is analyzed over the controlled factor variables in the inner array.

Using the regression model, the S/N response is maximized/minimized to find the optimal settings for the inner array variables

that produces the best response that is robust/insensitive to the

outer array variables. Because the outer (mission) array matrix is

run for every point in the inner design array DOE, the setup is

called a product array. While a robust flow control installation

can be established using the traditional Taguchi Robust Parameter Design methodology, the performance information of that

installation over the outer array (mission) variable range is lost.

That information gets rolled into the S/N, i.e. signal-to-noise

parameter. Also, the traditional style Taguchi DOE is expensive.

The total number of experiments is the product of the number of

experiments in the inner array matrix times the number of experiments in the outer array matrix.

Cost saving can be achieved by a DOE in which the

noise factors (mission variables) are introduced directly into the

inner array design matrix with the controlled (design) variables.

This is called a combined array format, which can have significant run-size savings over the traditional Taguchi robust design

methods. Thus, in the new approach to a Robust Design methodology, a single DOE is established composed of both the inner

array (design) variables and outer array (mission) variables. At

each point in the combined DOE, the responses are measured.

Using weighted or ordinary least squares (OLS) regression, a

model is built that is a function of both the inner array (design)

variables and outer array (mission) variables. For the current

study, the resulting regression model for each response was a

subset of the full quadratic model permitted by the DOE, namely:

Y = β0 +β1h1 +β2h2 + β3h3 + β4α

+β11h1

2 + β22h22 +β33h32 + β44α2

+β12h1h2 + β13h1h3 + β14h1α

+β23h2h3 + β24h2α + β34 h3α

To bring to fruition the desired robustness aspect of this study,

this second order model in both the inner array and outer array

was exploited in a unique way during the optimization phase.

Response F = S2

max/S2min F(0.975,9,9)

F1/2 1939.9 4.03

F2/2 53.5 4.03

F3/2 160.0 4.03

F4/2 135.4 4.03

F5/2 47.6 4.03

(a) 80-probe rake (b) Computational grid

6 NASA/TM—2001-211278 
This method has been designated as the economical “Lower

Order” approach.

For comparison purposes, consider a traditional Taguchi

Robust DOE in which the number of required experiments is

much higher (i.e. the number of experiments in the inner array

matrix times the number of experiments in the outer array

matrix). An alternate method of analyzing the data from such a

DOE design is to not lose information by collapsing the outer

array matrix information into a S/N, but to model the actual

response data using an expanded regression model that includes

the outer array variables directly. Such an approach results in the

inclusion of the higher order interactive terms directly into the

regression model. This approach is discussed by Anderson and

Keller(5) and has been termed the “Higher Order” approach to the

analysis of a traditional Taguchi Robust DOE. In the cases studied to date, the less economical Taguchi approach using the introduction of these higher order interactions has resulted in marginal

differences in the final optimal robust results when compared to

the new economical combined “Lower Order” approach.

Flow Control Mission Studies

To illustrate the potential of economical Robust Design

methodology, two different mission strategies were considered

for the subject inlet, namely (1) Maximum Performance, and (2)

Maximum HCF Life Expectancy. The Maximum Performance

mission sought to minimize the inlet duct losses (maximize the

engine face total pressure recovery) subject to the constraint that

the DC60 engine face distortion be less than 0.10, while no

conditions were placed on the first five Fourier harmonic 1/2

amplitudes of distortion. A DC60 distortion level of 0.10 or less is

significant because it would be acceptable for a commercial

engine application. The Maximum HCF Life Expectancy mission

sought to minimize the mean of the first five Fourier harmonic 1/

2 amplitudes, also subject to the constraint that the DC60 engine

face distortion be less than 0.10. In this mission, however, no

constraint was placed upon the inlet total pressure recovery. For

each of these missions strategies, both an “Optimal Robust” (open

loop control) and an “Optimal Adaptive” (closed loop control)

installation were designed using the angle-of-incidence from 0 to

20o as the noise factor. The “Optimal Robust” installation used

economical Robust Design methodology to arrive at a single

design which operated over the entire angle-of-incident range

(open loop control). The “Optimal Adaptive” installation

optimized all the design parameters at each angle-of-incidence

within the search (optimization) routine. Thus, in the “Optimal

Adaptive” system, the factor values were adjusted at each angle of

attack to simulate a closed loop system. Thus the “Optimal

Adaptive” installation would require a closed loop control system

to sense a proper signal for each effector and modify that effector

device, whether mechanical or fluidic, for optimal inlet

performance.

Maximum Performance Mission - Specifically, for the

“Optimal Adaptive” Maximum Performance MSFC installation,

at each angle-of-incidence, the engine face distortion constraint

DC60 < 0.10 was imposed and a search was made over the design

variable space to locate that installation geometry that maximized

PFAVE. For this mission, no constraints were imposed upon the

first five Fourier harmonic 1/2 amplitudes of engine face

distortion. In a similar manner, for the “Optimal Robust” MSFC

installation, the engine face distortion constraint DC60 < 0.10 was

imposed and a search was made over the design variable space to

locate that installation geometry that maximized the optimization

parameter ΣYα

2

/m, where Yα = PFAVE at each of the α = 0.0,

1.0,....,20.0o angle-of-incidences and m = 21. Again, for this

mission no constraints were placed on the first five Fourier

harmonic 1/2 amplitudes of engine face distortion. This procedure

economically defined one installation that was “Optimal Robust”

over the entire range of angle-of-incidence.

Figure (6): “Optimal Robust” Maximum Performance MSFC

installation engine face CFD solution, α = 0.0o.

Table (8): “Optimal Robust” Maximum Performance MSFC

installation inlet CFD performance, α = 0.0o.

The “Optimal Robust” Maximum Performance installation was determined to have the following effector vane heights

(mm): h1 = 0.0, h2 =0.0, h3 = 1.9. The inlet CFD solution for the

“Optimal Robust” Maximum Performance installation design at

the engine face is presented in Figure (6) and the CFD performance of the inlet with that installation is shown in Table (8). The

near wall streamlines for the baseline solution and the “Optimal

Robust” Maximum Performance installation design are presented

in Figures (7) and (8) respectively. A comparison of these two

figures indicates the underlying operational purpose of microFactor/Response Range/Constraint Optimal Value

h1 0.0 to 2.0 0.0

h2 0.0 to 2.0 0.0

h3 0.0 to 2.0 1.90

PFAVE Maximized 0.97329

DC60 < 0.10 0.08401

F1/2 Unconstrained 0.00705

F2/2 Unconstrained 0.01636

F3/2 Unconstrained 0.01651

F4/2 Unconstrained 0.00527

F5/2 Unconstrained 0.00106

FM/2 Unconstrained 0.00925

(a) Total Pressure (b) Velocity Vectors

7 NASA/TM—2001-211278 
scale secondary flow control. In the baseline case presented in

Figure (7), the flow in a very thin layer adjacent to the walls “over

turns” as a result of a loss of momentum within the inlet boundary layer. Eventually, this “over-turning” will cause a vortex pair

to form in the inlet passage. This vortex pair results in total pressure loss and severe total pressure distortion at the engine face. It

is not necessary for this vortex to “lift-off” or separate from the

walls for high total pressure loss and distortion to occur (hence

the terminology inlet “secondary flow control” rather than “separation control”). By introducing the micro-actuators into the inlet,

whether vanes or jets, the “over-turning” in the inlet boundary is

prevented. See Figure (8). Consequently, the passage vortex will

Figure (7): Near wall streamlines within effector region, baseline CFD solution, α = 0.0o.

Figure (8): Near wall streamlines within effector region,

“Optimal Robust” Maximum Performance MSFC installation design, α = 0.0o.

not form or, at worst, is greatly reduced in strength, which will

result in a vast improvement in engine face distortion. Therefore,

the entire inlet flow field can be managed by controlling the secondary flow in a thin layer adjacent to the inlet walls. In the

MASC concept, micro-scale actuation is used as an approach

called “secondary flow control” to alter the S-duct’s inherent secondary flow characteristics with the goal of simultaneously

improving the critical system level performance metrics pressure

recovery, engine face distortion, and HCF characteristics.

Figure (9): Comparison between “Optimal Robust” and

“Optimal Adaptive” Maximum Performance MSFC installation designs.

0 2 4 6 8 10 12 14 16 18 20

0.95

0.96

0.97

0.98

0.99

1.00

Inlet Angle of Incidence, α

Engine Face Recovery, PFAVE

Baseline Flow

Optimal Robust MSFC

Optimal Adaptive MSFC

(a) Total Pressure Recovery Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.0

0.1

0.2

0.3

0.4

0.5

Inlet Angle of Incidence, α

Engine Face Distortion, DC60

(b) Engine Face Distortion Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

1st Harmonic 1/2 Amplitude, F1/2

(c) 1st Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

2nd Harmonic 1/2 Amplitude, F2/2

(d) 2nd Fourier Harmonic 1/2 Amplitude Characteristics.

8 NASA/TM—2001-211278 
Figure (9): Comparison between “Optimal Robust” and

“Optimal Adaptive” Maximum Performance MSFC installation designs, cont.

Comparisons between the performance results of the

“Optimal Robust” and “Optimal Adaptive” installations for the

Maximum Performance inlet mission are shown in Figures (9a)

to (9g). Also presented in Figures (9a) to (9g) are the baseline

flow solutions, i.e. the inlet performance without flow control, for

each response. It is apparent from Figure (9a) that flow control

was unable to increase total pressure recovery above the baseline

flow. A recovery improvement could not be demonstrated for this

case. The losses resulting from the micro-vanes actuators, which

were included in the CFD analysis, were somewhat greater than

improved efficiency of the flow process as a result of the vane

installation. This is not always the case, since experimental evidence exists that clearly demonstrates that substantial improvement in recovery is achievable under severe vortex lift-off

conditions.(2) It is important, however, that a vane model in a full

Navier-Stokes includes a loss term associated with the microvanes.

Essentially, the “Optimal Robust” and “Optimal Adaptive” installations were the same configuration based on their performance over the angle-of-incidence range of 0 to 20o

. This is

not surprising, since there exists experimental data(9) that demonstrate that a fixed secondary flow control installation can provide

essentially the same low DC60 distortion level, i.e. DC60 < 0.10,

over a substantial angle-of-incidence range. Secondary flow control in inlets is inherently robust, provided it is optimally

designed. By comparing Figure (9c) with Figure (9e) an interesting feature of this mission can be seen. There was the shift in the

peak amplitude from the first Fourier harmonic 1/2 amplitude to

the third Fourier harmonic 1/2 amplitude as a result of secondary

flow control. With micro-scale secondary flow control, a dominant “# per rev” frequency may thus be shifted to avoid the natural resonance frequency of the engine fan blades. This shift is

usually to the higher “# per rev” frequency range.

For the “Optimal Adaptive” Maximum HCF Life

Expectancy MSFC installation, at each angle-of-incidence, the

engine face distortion constraint, DC60 < 0.10, was imposed and

a search was made over the design variable space to locate that

installation geometry that minimized ΣFj/5, the mean of the first

five Fourier harmonic 1/2 amplitudes present in the engine face

distortion profile. For this mission, no constraint was placed on

the inlet total pressure recovery.

Maximum HCF Life Expectancy Mission - In a similar manner, for the “Optimal Robust” Maximum HCF Life

Expectancy MSFC installation, the engine face distortion constraint, DC60 < 0.10, was imposed and a search was made over

the design variable space to locate that installation geometry that

minimized ΣYα

2/m, where Yα = ΣFj/5, the mean of the first five

Fourier harmonic 1/2 amplitudes present in the engine face distortion profile at each of the α = 0.0,1.0,....., 20.0o angle-of-incidence and m =21. Again for this mission, no constraints were

placed on the inlet total pressure recovery. This procedure economically defined one installation that was “Optimal Robust”

over the range of angle-of-incidence.

Figure (10): “Optimal Robust” Maximum HCF Life Expectancy MSFC installation engine face CFD solution, α = 0.0o

.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

3rd Harmonic 1/2 Amplitude, F3/2

Baseline Flow

Optimal Robust MSFC

Optimal Adaptive MSFC

(e) 3th Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

4th Harmonic 1/2 Amplitude, F4/2

(f) 4th Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

5th Harmonic 1/2 Amplitude, F5/2

(g) 5th Fourier Harmonic 1/2 Amplitude Characteristics.

(a) Total Pressure (b) Velocity Vectors

9 NASA/TM—2001-211278
Table (9): “Optimal Robust” Maximum HCF Life Expectancy MSFC installation inlet CFD performance, α = 0.0o.

The “Optimal Robust” Maximum HCF Life Expectancy

installation design was also determined through a search process

to have the following effector vane heights and chord lengths

(mm): h1 = 0.0, h2 = 0.0, h3 = 2.0. The inlet CFD solution for the

“Optimal Robust” Maximum HCF Life Expectancy installation

design at the engine face is presented in Figure (10) and the performance of the inlet with this installation is presented in Table

(9).

Figure (11): Near wall streamlines within effector region,

“Optimal Robust” Maximum HCF Life Expectancy MSFC

installation design, α = 0.0o.

Presented in Figure (11) is the near wall streamlines for

the “Optimal Robust” Maximum HCF Life Expectancy installation design for α = 0.0o. Again, notice the effect of the microvane actuators in preventing the over-turning of the flow adjacent

to the inlet walls and thus suppressing the passage vortex formation. Once again, there was a vast improvement in engine face

distortion. Figures(12a) through Figure (12g) shows that the differences between the “Optimal Adaptive” and “Optimal Robust”

secondary flow installation design were again minimal for the

Maximum HCF Life Expectancy mission. Requiring the mean of

the first five Fourier harmonic 1/2 amplitudes present in the

engine face distortion profile to be minimized does not necessarily mean that all the amplitudes will be reduced relative to the

baseline flow. Figures (12c) through (12f) show that the first

through the fourth Fourier 1/2 harmonic amplitude all decreased

relative to the baseline flow. However, the fifth Fourier harmonic

1/2 amplitude increased above the baseline case at the higher

angle-of-incidences. See Figure (12g). The important conclusion

is that both the “Optimal Adaptive” and “Optimal Robust” mission strategies resulted in installation designs that are able to

reduce the Fourier harmonic 1/2 amplitudes of distortion, while

maintaining a very low engine face DC60 distortion.

By comparing the “Optimal Robust” Maximum Performance installation design shown in Table (8) and the Maximum

HCF Life Expectancy installation shown in Table (9), it can be

seen that the two optima are almost identical (h3 = 1.90 versus h3

= 2.0). This will not in general be the case in all future studies.

The different approaches to optimization can (and most probability) lead to different optima.

Figure (12): Comparison between “Optimal Robust” and

“Optimal Adaptive” Maximum HCF Life Expectancy MSFC

installation designs.

Factor/Response Range/Constraint Optimal Value

h1 0.0 to 2.0 0.0

h2 0.0 to 2.0 0.0

h3 0.0 to 2.0 2.00

PFAVE Unconstrained 0.97377

DC60 < 0.10 0.08216

F1/2 Minimized 0.00708

F2/2 Minimized 0.01517

F3/2 Minimized 0.01583

F4/2 Minimized 0.00523

F5/2 Minimized 0.00102

FM/2 Minimized 0.00887

(a) Total Pressure Recovery Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.95

0.96

0.97

0.98

0.99

1.00

Inlet Angle of Incidence, α

Engine Face Recovery, PFAVE

Baseline Flow

Optimal Robust MSFC

Optimal Adaptive MSFC

(b) Engine Face Distortion Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.0

0.1

0.2

0.3

0.4

0.5

Inlet Angle of Incidence, α

Engine Face Distortion, DC60

10 NASA/TM—2001-211278 
Figure (12): Comparison between “Optimal Robust” and

“Optimal Adaptive” Maximum HCF Life Expectancy MSFC

installation designs, cont.

Figure (12): Comparison between “Optimal Robust” and

“Optimal Adaptive” Maximum HCF Life Expectancy MSFC

installation designs, cont.

CONCLUSIONS

The fundamental importance of Genichi Taguchi’s

contribution to Total Quality Design over traditional design

approaches lies in the idea that process and product variability can

be incorporated into the optimal statistical Design-of-Experiment

and subsequent analysis of data. To the aerodynamicist, it

represents a major breakthrough in the area of aerodynamic

design of inlets, since the effect of the mission variables can be

directly introduced into the design process. The inlet system can

now be designed to operate with optimal performance over a

range of specified mission variables.Taguchi’s Robust Parameter

Design method, however, may not be optimal in the design of

secondary flow installations for inlet systems because: (a) it loses

information vital to the aerodynamicist and, (b) it is costly.

Fortunately, the important aspects surrounding Taguchi’s

approach to Robust Parameter Design can and have been

incorporated into an alternate economical approach and adapted

to the inlet design problem. This alternate inlet design method,

using a combined array approach to economical Robust Design,

had significant run size savings over a traditional Taguchi

approach, i.e. 26 CFD experiments as compared to 45 CFD

experiments.

To illustrate the potential of economical Robust Design

methodology, two different mission strategies were considered

for the subject inlet, namely (1) Maximum Performance, and (2)

Maximum HCF Life Expectancy. The Maximum Performance

mission maximized total pressure recovery while the Maximum

HCF Life Expectancy mission minimized the mean of the first five

Fourier harmonic 1/2 amplitudes. i.e. “collectively” reduced all

the harmonic 1/2 amplitudes of engine face distortion. Each of the

mission strategies was subject to a low engine face distortion

constraint of DC60 < 0.10, a level acceptable for commercial

engines. For each of these missions strategies, an “Optimal

Robust” (open loop control) and an “Optimal Adaptive” (closed

loop control) installation was designed over a twenty degree

angle-of-incidence range. The “Optimal Robust” installation used

a new economical approach to Robust installation design to arrive

at a single installation which operated over the entire angle-ofincident range (open loop control). The “Optimal Adaptive”

installation optimized all the design parameters at each angle-ofincidence. Thus the “Optimal Adaptive” installation would

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

1st Harmonic 1/2 Amplitude, F1/2

Baseline Flow

Optimal Robust MSFC

Optimal Adaptive MSFC

(c) 1st Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

2nd Harmonic 1/2 Amplitude, F2/2

(d) 2nd Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

3rd Harmonic 1/2 Amplitude, F3/2

(e) 3rd Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

4th Harmonic 1/2 Amplitude, F4/2

(f) 4nd Fourier Harmonic 1/2 Amplitude Characteristics.

(c) 5st Fourier Harmonic 1/2 Amplitude Characteristics.

0 2 4 6 8 10 12 14 16 18 20

0.000

0.010

0.020

0.030

0.040

0.050

Inlet Angle of Incidence, α

5th Harmonic 1/2 Amplitude, F5/2

Baseline Flow

Optimal Robust MSFC

Optimal Adaptive MSFC

11 NASA/TM—2001-211278 
require a closed loop control system to sense a proper signal for

each effector and modify that effector device, whether mechanical

or fluidic, for optimal inlet performance.

In general, the performance differences between the

“Optimal Adaptive” and “Optimal Robust” installation designs

were found to be marginal. This suggests, however, that “Optimal

Robust” open loop installation designs can be very competitive

with “Optimal Adaptive” close loop designs. Secondary flow

control in inlets is inherently robust, provided it is optimally

designed. Therefore, the new methodology presented in this

paper, combined array “Lower Order” approach to Robust DOE,

offers the aerodynamicist a very viable and economical way of

exploring the concept of Robust inlet design, where the mission

variables are brought directly into the inlet design process and

insensitivity or robustness to the mission variables becomes a

design objective.

REFERENCES

(1) Anderson, B. H., Miller, D. M., Yagel, P. J, and Traux, P. P., “A

Study of MEMS Flow Control for the Management of Engine

Face Distortion in Compact Inlet Systems”, FEDSM99-6920, 3rd

ASME/JSME Joint Fluids Engineering Conference, San Francisco, CA, July 18-23, 1999.

(2) Hamstra, J. W., Miller, D. N., Truax, P. P., Anderson, B. H.,

and Wendt, B. J., “Active Inlet Flow Control Technology Demonstration”, ICAS-2000-6.11.2, 22nd International Congress of the

Aeronautical Sciences, Harrogate, UK, August 27th-September

1st, 2000.

(3) Taguchi, G and Wu, Y, “Introduction to Off-Line Quality Control,” Central Quality Control Association, 1980.

(4) Anderson, B. H. and Keller, D. J., “Optimal Micro-Scale Secondary Flow Control for the Management of HCF and Distortion

in Compact Inlet Diffusers”, Proposed NASA TM, 2001.

(5) Anderson, B. H. and Keller, D. J., “Robust Design Methodology for Optimal MicroScale Secondary Flow Control in Compact Inlet Diffusers”, NASA/TM— 2001-211278.

(6) Anderson, B. H. and Keller, D. J., “Considerations in the Measurements of Engine Face Distortion for High Cycle Fatigue in

Compact Inlet Diffusers”, Proposed NASA TM, 2001.

(7) Willmer, A. C., Brown, T. W. and Goldsmith, E. L., “Effects of

Intake Geometry on Circular Pitot Intake Performance at Zero

and Low Forward Speeds”, Aerodynamics of Power Plant Installation, AGARD CP301, Paper 5, Toulouse, France, May 1981, pp

51-56.

(8) Goldsmith, E. L. and Seddon, J. (eds), “Practical Intake Aerodynamics,” Blackwell Scientific Publications, Oxford, 1993.

(9) Bender, E. E, Anderson, B. H., and Yagle, P. J., “Vortex Generator Modeling for Navier Stokes Code”, FEDSM99-69219, 3rd

ASME/JSME Joint Fluids Engineering Conference, San Francisco, CA, July 18-23, 1999.

(10) Gibb, J. and Anderson, B. H., “Vortex Flow Control Applied

to Aircraft Intake Ducts,” Proceedings of the Royal Aeronautical

Society Conf., High Lift and Separation Control, Paper No. 14,

Bath, UK, March, 1995.

(11) Ludwig, G. R., “Aeroelastic Considerations in the Measurement of Inlet Distortion”, 3rd National Turbine Engine High

Cycle Fatigue Conference, 1998.

12 NASA/TM—2001-211278 
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AIAA–2002–0541

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18

A Robust Design Methodology for Optimal Microscale

Secondary Flow Control in Compact Inlet Diffusers

Bernhard H. Anderson and Dennis J. Keller

Propulsion; Flow control

Unclassified -Unlimited

Subject Category: 07 Distribution: Nonstandard

Prepared for the 40th Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and

Astronautics, Reno, Nevada, January 14–17, 2002. Bernhard H. Anderson, NASA Glenn Research Center, and

Dennis J. Keller, RealWorld Quality Systems, 20388 Bonnie Bank Boulevard, Rocky River, Ohio 44116. Responsible

person, Bernhard H. Anderson, organization code 5850, 216–433–5822.

It is the purpose of this study to develop an economical Robust design methodology for microscale secondary flow control in compact inlet diffusers.

To illustrate the potential of economical Robust Design methodology, two different mission strategies were considered for the subject inlet, namely (1)

Maximum Performance, and (2) Maximum HCF Life Expectancy. The Maximum Performance mission maximized total pressure recovery while the

Maximum HCF Life Expectancy mission minimized the mean of the first five Fourier harmonic amplitudes, i.e., “collectively” reduced all the

harmonic 1/2 amplitudes of engine face distortion. Each of the mission strategies was subject to a low engine face distortion constraint, i.e., DC60 ≤

0.10, which is a level acceptable for commercial engines. For each of these missions strategies, an “Optimal Robust” (open loop control) and an

“Optimal Adaptive” (closed loop control) installation was designed over a twenty degree angle-of-incidence range. The “Optimal Robust” installation

used economical Robust Design methodology to arrive at a single design which operated over the entire angle-of-incident range (open loop control).

The “Optimal Adaptive” installation optimized all the design parameters at each angle-of-incidence. Thus, the “Optimal Adaptive” installation would

require a closed loop control system to sense a proper signal for each effector and modify that effector device, whether mechanical or fluidic, for

optimal inlet performance. In general, the performance differences between the “Optimal Adaptive” and “Optimal Robust” installation designs were

found to be marginal. This suggests, however, that “Optimal Robust” open loop installation designs can be very competitive with “Optimal Adaptive”

close loop designs. Secondary flow control in inlets is inherently robust, provided it is optimally designed. Therefore, the new methodology presented

in this paper, combined array “Lower Order” approach to Robust DOE, offers the aerodynamicist a very viable and economical way of exploring the

concept of Robust inlet design, where the mission variables are brought directly into the inlet design process and insensitivity or robustness to the

mission variables becomes a design objective.