Bernhard H. Anderson

Glenn Research Center, Cleveland, Ohio

Henry D. Baust

Wright Patterson Air Force Base, Dayton, Ohio

Johan Agrell

Swedish Defence Research Agency, Bromma, Sweden

Design-of-Experiments to Reduce Life-Cycle

Costs in Combat Aircraft Inlets

NASA/TM—2003-212017

January 2003

AIAA–2003–0652
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Bernhard H. Anderson

Glenn Research Center, Cleveland, Ohio

Henry D. Baust

Wright Patterson Air Force Base, Dayton, Ohio

Johan Agrell

Swedish Defence Research Agency, Bromma, Sweden

Design-of-Experiments to Reduce Life-Cycle

Costs in Combat Aircraft Inlets

NASA/TM—2003-212017

January 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

41st Aerospace Sciences Meeting and Exhibit

sponsored by the American Institute of Aeronautics and Astronautics

Reno, Nevada, January 6–9, 2003

AIAA–2003–0652
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This report is a preprint of a paper intended for presentation at a conference. Because

of changes that may be made before formal publication, this preprint is made

available with the understanding that it will not be cited or reproduced without the

permission of the author.

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

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

It is the purpose of this study to demonstrate the

viability and economy of Design-of-Experiments (DOE) to

arrive at micro-secondary flow control installation designs

that achieve optimal inlet performance for different mission

strategies. These statistical design concepts were used to

investigate the properties of “low unit strength” micro-effector installation. “Low unit strength” micro-effectors are

micro-vanes, set a very low angle-of-incidence, with very

long chord lengths. They are designed to influence the near

wall inlet flow over an extended streamwise distance. In this

study, however, the long chord lengths were replicated by a

series of short chord length effectors arranged in series over

multiple bands of effectors. In order to properly evaluate the

performance differences between the single band extended

chord length installation designs and the segmented multiband short chord length designs, both sets of installations

must be optimal. Critical to achieving optimal micro-secondary flow control installation designs is the understanding of

the factor interactions that occur between the multiple bands

of micro-scale vane effectors. These factor interactions are

best understood and brought together in an optimal manner

through a structured DOE process, or more specifically

Response Surface Methods (RSM).

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 inlet engine

diffuser system. One method to reduce inlet system LCC is

to reduce its structural weight and volume. Consequently,

advanced compact air vehicle 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 (2)) are characterized by high

distortion and low pressure recovery, which are produced by

extreme wall curvature and strong secondary flow gradients.

These characteristics are further aggravated by maneuvering

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 a

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 effector 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 decision

parameters that are brought into the design process. By

including the HCF effects in the inlet design process, the

aerodynamicist has a total of seven individual response variables that measure various aspects of inlet performance.

These 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 contained in the engine

face distortion pattern. Each of these responses must be maximized, minimized, constrained or unconstrained while

searching for the optimal combination of primary design

variable values that satisfy the mission requirements.

Numerical optimization procedures that have been successful with some aerodynamic problems give little assistance to

the design of micro-scale secondary flow installations. It is

very difficult to incorporate large numbers of independent

factor and response variables into such procedures. Further,

they are very expensive to use if the individual CFD experiments are solutions to the full Navier-Stokes equations in

three dimensions.However, there is a statistical approach to

the problem which combines an optimally sequenced pattern

of Design-of-Experiments (DOE), statistical model building,

and system optimization called Response Surface Methods

(RSM).

In this research study on MSFC for compact

inlet diffusers, three objectives were considered important,

namely: (1) to determine the design characteristics of microscale secondary flow control configurations, (2) to evaluate

the ability of MSFC to manage the aeromechanical effects of

engine face distortion, and (3) to evaluate the effectiveness

DESIGN-OF-EXPERIMENTS TO REDUCE LIFE-CYCLE COSTS

IN COMBAT AIRCRAFT INLETS

Bernhard H. Anderson

Glenn Research Center

Cleveland, Ohio 44135

Henry D. Baust

Wright Patterson Air Force Base

Dayton, Ohio 45433

Johan Agrell

Swedish Defence Research Agency

Bromma, Sweden

NASA/TM—2003-212017 1

National Aeronautics and Space Administration
of robust methodologies to design fixed “open loop” MSFC

installation designs in comparison to adaptive “closed loop”

designs which would require a control system. Anderson and

Keller(3) covers the first two research objectives while Anderson

and Keller(4)-(5) covers the third objective and describes a robust

design methodology whereby the hard-to-control mission

variables can be explicitly included in the design of optimal

MSFC installations. A forth report in this series by Anderson and

Keller(6) evaluates the impact of engine face rake geometry (i.e.

number of rake arms) and its use (i.e. with and without clocking),

on the random and systematic measurement errors associated with

estimating the first five Fourier harmonic 1/2-amplitudes of

engine face distortion. It was concluded in Anderson and

Keller(4)-(5) that micro-scale secondary flow control using multibands of micro-vane effectors were inherently robust, provided

the installations was optimally designed. Robustness in this

situation means that it is possible to design fixed MSFC robust

installations (i.e. open loop) which operates well over the range of

mission variables and is only marginally different from adaptive

(i.e. closed loop) installation designs which would require a

control system. However, this improvement in engine face

distortion came at the expense of total pressure recovery. In order

to overcome the high loss associated with “high unit strength”

micro-vane effectors, the micro-vane angle of incidence was

greatly reduced while compensating for loss of unit strength by

increasing the length of the micro-vane effector units. These

devices, called “low unit strength” micro-vane effectors,

demonstrated excellent robustness properties over the range of

mission variables. “Low unit strength” micro-vane effectors also

demonstrated substantial improvement in inlet total pressure

recovery over “high unit strength” micro-vane effectors,

Anderson, Baust, and Agrell.(6) Therefore effective inlet flow

control management of engine face distortion was achieved by

reducing the unit strength of the vane effector and allowing the

installation design to influence the inlet flow over a longer

streamwise distance.

In this study, however, the long chord lengths were

replicated by a series of short chord length effectors arranged in

series over multiple bands of effectors. Thus, it is the purpose of

this study to perform a comparative examination between the

single band extended chord length installations of Anderson,

Baust, and Agrell,(6) with the installation made up of multiple

bands of short chord length “low unit strength” micro-effectors

extending over approximately the same streamwise distance. In

order to properly evaluate the performances difference between

the single band extended chord length installation designs and the

segmented multi-band short chord length designs, both sets of

installations must be optimal. Critical to achieving optimal microsecondary flow control installation designs is the understanding of

the factor interactions that occur between the multiple bands of

micro-scale vane effectors. These factor interactions are best

understood and brought together in an optimal manner through a

structured Design-of-Experiments process, or more specifically

Response Surface Methods (RSM).

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

Fk/2 kth 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 Average Inlet Total Pressure at AIP

PAVCRIT Minimum Total Pressure over Angle

QAVE Average Dynamic Pressure at AIP

R Inlet Radius

Rcl Centerline Radius

Ref Engine Face Radius

Rthr Inlet Throat Radius

Re Reynold Number per ft.

RSM Response Surface Methodology

S Standard Deviation

Sclock Standard Deviation over the Clocking Angles

UAV Unmanned Air Vehicle

UCAV Unmanned Combact Air Vehicle

Xcl Axial Distance Along the Duct Centerline

YA Upper 95% Confidence Interval

YCFD Response Predicted by CFD Analysis

YDOE Response Predicted by DOE Analysis

Zcl Centerline Offset Displacement

α Inlet Angle-of-Incidence

β Effector Vane Angle-of-Incidence

∆Zcl Inlet Centerline Offset

γ Inlet Angle-of-Yaw

RESULTS AND DISCUSSION

Baseline Flow in the Redesigned M2129 Inlet S-Duct

The redesigned M2129 inlet S-duct used in this study

was considered similar to the original DERA/M2129 inlet S-duct

defined by AGARD FDP Working Group 13 Test Case 3,(7) using

Lip No. 3 and Forward Extension No. 2. This inlet design was

first proposed by Willmer, Smith and Goldsmith,(8) and has been

used extensively in the US and UK to explore inlet flow control

installation design. The centerline for the redesigned M2129 inlet

is given by the equation

 (1)

while the radius distribution measured normal to the inlet centerline is given by the expression

 (2)

where inches, inches,

inches, and inches. The redesign

of the M2129 inlet was such that the new inlet matches the static

pressure gradients normally found in typical UAV or UCAV

designs. Therefore, the new inlet is more compact than the original M2129 inlet S-duct. As a consequence, supersonic flow will

Zcl ∆Zcl 1 π

Xcl

L ⋅ -------     cos–     –=

Rcl Rthr –

Ref Rthr – -----------------------     3 1

Xcl

L – -------     4

4 1

Xcl

L – -------     3

– 1 +=

thr 2.5355= Ref 3.0=

L 15.0= ∆Zcl 5.401=

NASA/TM—2003-212017 2

R
develop in this inlet when the inlet throat Mach number increases

much above 0.70. The geometry and grid structure for the

resigned M2129 inlet S-duct is described in detail in Anderson,

Baust, and Agrell.(6).

Figure (1): Near wall streamlines in baseline inlet S-duct

Figure (2): Engine face flow field in baseline inlet S-duct.

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 engine face distortion. Figure (2)

presents the engine face total pressure recovery contours and secondary flow velocity vectors for the redesigned 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.

Inlet Flow Control Design Approach

In the secondary flow control concept, micro-scale

actuation is used as an approach called “secondary flow control”

to alter the inlet S-duct inherent secondary flow with the goal of

simultaneously improving the critical system level performance

metrics of total pressure recovery, engine face distortion, and

HCF characteristics. In studying the influence of micro-vane

chord length(1) on inlet performance, it was determined that this

factor was very important parameter in reducing engine face distortion as well as managing the harmonic content of engine face

distortion. While there appear to be limits on the total number

and strength of the individual effector units(1) in managing

engine face distortion, there appear to be no such limits on microvane chord length. By installing multiple bands of micro-effector

units, the chord length can be effectively increased,(5) and engine

face distortion managed. However, this improvement in engine

face distortion came at the expense of total pressure recovery. In

order to overcome the dimensional limit of chord length, the

micro-vane angle of incidence can be greatly reduced while compensating by increasing the length of the micro-vane effector

units. Hence effective inlet flow control management of engine

face distortion can be achieved by reducing the unit strength of

the vane effector and allowing the installation design to influence

the inlet flow over an extended streamwise distance. With this

combination, the total pressure losses associated with micro-vane

effectors become very small, and a large overall performance

gain achieved.(6) In this study, however, the extended chord

lengths were replicated by a series of short chord length effectors

arranged in series over multiple bands of effectors. If discrete

micro-vane effectors arranged in multiple bands perform in a

similar manner as extended chord length single band effectors,(6)

the possible opens that multiple bands of “low unit strength” discrete micro-jets will also perform well. In other words, the effectiveness of “low unit strength” micro-jets may be substantially

improved by multi-band arrangements.

Inlet Flow Control Installation Design

(a) Single Band Micro-Vane Installation Concept

Figure (3): Location of effector region within inlet S-duct

configurations.

To manage the flow in the redesigned M2129 inlet Sduct, an installation arrangement of micro-scale effectors was

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

(3). For the single band installation, the micro-effectors extend

(a) Pressure Recovery (b) Velocity Vectors

Effector Region

(b) Multi Band Micro-Vane Installation Concept

Effector Region

NASA/TM—2003-212017 3
over a streamwise distance of about 72.0 mm., Figure (3a). The

multi band installation extended over the nominally the same

streamwise distance, but was segmented into a six band arrangement of micro effectors. See Figure (3b).The chord length of

individual multi-band installation effectors was about 8.0 mm.,

while the streamwise spacing between the micro-effectors was

nominally 6.0 mm. These micro-scale effectors were microvanes, the largest height being about the average height of the

momentum layer just downstream of the inlet throat or about 2.0

mm. The purpose of these micro-vanes was to create a set of corotating vortices that will quickly merge to form a thin layer of

secondary flow that will counter the formation of the passage vortex pair.

Table (1): Factor variables which establish the DOE design.

Table (2): Variables held constant.

The DOE approach for the multi-band installation

study followed directly from the objectives previously stated and

was reflected in the layout of the design factors listed in Table

(1). The factor variables were the number of vane effector units

per band (n), the micro-vane angle-of-incidence (β) and the

micro-vane effector height (h). Table (2) shows the variables that

were held constant during this study. They included the thickness

of the micro-vanes (t), the micro-vane chord length (c), the nominal streamwise spacing between individual micro-effectors (∆c),

the inlet operating total pressure (Pt) and temperature (Tt), angleof incidence (α), and the inlet angle-of-yaw (γ). Table (3) displays the response variables for this study. They include 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 response variables.

The DOE strategy selected was a Central Composite

Face-Centered (CCF) DOE. This strategy resulted in 15 unique

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

these DOE cases covered a wide range of installation geometries.

This particular DOE, like most DOE strategies, varied more than

one factor at a time. Further, this layout of 15 cases permitted the

estimation of both linear and curvilinear effects as well as twofactor interactive or synergistic effects among the DOE factors.

Table (4): Central Composite Face-Centered (CCF) DOE

design

Factor Range

Number of Micro-Vane Effectors per Band, n 13 to 27

Micro-Vane Angle-of-Incidence (degs), β 0.0 to 8.0

Micro-Vane Effector Height (mm), h 1.0 to 2.0

Variable Value

Micro-Vane Effector Thickness (mm), t 0.138

Micro-Vane Effector Chord Length (mm), c 8.0

Nominal Streamwise Chord Spacing (mm), ∆c 6.0

Inlet Total Pressure (lbs/ft2

), Pt 10506.0

Inlet Total Temperature (o

R), Tt 517.0

Inlet Throat Mach Number, Mt 0.70

Inlet Angle-of-Incidence (degs.), α 0.0

Inlet Angle-of-Yaw (degs), γ 0.0

Response Nomenclature

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

Config. n β h

nvg901 13 0.0 1.0

nvg902 27 0.0 1.0

nvg903 13 8.0 1.0

nvg904 27 8.0 1.0

nvg905 13 0.0 2.0

nvg906 27 0.0 2.0

nvg907 13 8.0 2.0

nvg908 27 8.0 2.0

nvg909 13 4.0 1.5

nvg910 27 4.0 1.5

nvg911 20 0.0 1.5

nvg912 20 8.0 1.5

nvg913 20 4.0 1.0

nvg914 20 4.0 2.0

nvg915 20 4.0 1.5

NASA/TM—2003-212017 4
Figure (4): Graphical representation of the Central Composite Face-Centered (CCF) DOE design.

A graphical representation of the Central Composite

Face-Centered DOE used in the multi-band installation study is

presented in Figure (4). The DOE cases are represented in this

figure by the circular symbols, where the symbol locations on the

cube signify its factor value. This DOE is called a composite

DOE because the organization of cases is composed of a factorial

part and a quadratic part. The factorial part of the DOE is composed of 23 possible cases, i.e. 8 possible factorial cases, which

are represented by the eight corner locations of the cube in Figure

(4). The remaining cases in Figure (4) are the quadratic part of

the DOE. The quadratic cases allow for the evaluation of the curvilinear effects. All together, there are a total of 15 cases in a

Central Composite Face-Centered DOE with three factor variables. Notice the balanced layout of cases in Figure (4). This layout of cases represents the smallest number of CCF DOE cases

that allows for the evaluation of linear and curvilinear effects as

well as all two-factor interactive or synergistic effects.

Each of the 15 cases in Table (4) were run with a Reynolds-averaged Navier-Stokes code(11) that allowed for numerical simulation of micro-vane effectors without the need to

physically embed the vane effectors within the CFD grid structure. However, for the present study the individual vanes were

incorporated into the half cylindrical grid structure These microvanes had a thickness of 0.138 mm. See Table (2). The computational grid surrounding each micro-vane effector in the installation was developed such that it reasonably resolved the boundary

layer development on both the suction and pressure surfaces.

Because wall functions were used in the calculations, the grid

resolution for the individual micro-vanes was simplified. The

boundary layer along the micro-vane edges was assumed to be

negligible, and therefore not resolved in the computational grid.

The half cylindrical grid structure was composed of three blocks:

an upstream block, an effector section containing the microvanes, and a downstream block. See Figures (3b) and (4b). The

computational half-plane grid varied in total number of mesh

points from about 950,000 to 1,150,000 depending on the microvane configuration. All CFD calculations were accomplished

assuming half cylindrical symmetry. A two-equation k-l turbulence model was used in this study. The model consists of transport equation for the turbulent kinetic energy and turbulent length

scale. The model includes a near-wall model and compressible

corrections for high speed flows.

Harmonic Analysis of Distortion

The overall methodology used to obtain the harmonic

content of inlet distortion is described in great detail in Anderson,

Baust, and Agrell,(6) and in Anderson and Keller.(7) This methodology is characterized by the use of radial weighting factors

applied to the total pressure rake measurements. These radial

weighting 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. As a

result of that accuracy study in estimating the Fourier harmonic

1/2-amplitudes from an engine face rake,(7) 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.

Clocking the AIP rake means that N separate measurements were

taken, and at each measurement, the angular orientation of the

rake was advanced an by an amount 1/N time the rake angle.The

rake angle is the ratio of 360o divided by the number of arms in

the AIP rake. For example, a standard 80-probe rake has 16-arms.

Hence the rake angle is 22.5o. Therefore total pressure measurements were obtained at each 22.5o/N angular position of the rake.

The span-weighted average total pressure was calculated for the

80-probe rake by multiplying the probe total pressure by the

span-weighted coefficients, 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

determined for each of the Fourier harmonic 1/2-amplitudes. In

order to check the constant variance assumption associated with

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 indicated that the F-test exceeded the 95% confidence critical value of F(0.975,9,9) = 4.03. Hence, the assumption of constant variance 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 15

= 150 data samples in the DOE. The weights in these regression

analyses were set to 1/S2

clock.

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 recognized methodology to evaluate the Fourier harmonic 1/2-amplitudes of

engine face distortion for more than five probes in the radial

direction. Hence, evaluating the Fourier harmonic 1/2-amplitude

directly from the computational mesh had to be discarded. However, both the inlet total pressure recovery and engine face distortion can and were calculated directly from the computational grid

at the engine face station. This computational mesh was composed of 49 x 121 grid points in the full-plane. The DC60 engine

n

β

h

NASA/TM—2003-212017 5
face distortion descriptor 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. The DC60 engine face

distortion descriptor is a measure of the difference between the

engine face or AIP average total pressure (PFAVE) and the lowest

average total pressure in any sector defined by a critical angle of

60o (PAVCRIT), divided by the average dynamic pressure at the

engine (AIP) face. Hence

 (3)

Response Surface Solutions and Factor Interactions

Presented in Figures (6) through (8) is the two way

statistical factor interactions (n*β) between the micro-vane effector bands. Comparisons are made in each figure for the inlet total

pressure recovery (PFAVE), engine face distortion (DC60) characteristics, and the mean of the first five Fourier harmonic 1/2-

amplitudes (FM/2) of distortion. A statistical interaction exists

between two independent factor variables X1 and X2 when the

effect of X1 on response Yi is affected by the value of X2. In

other words, the effect of factor X1 on response Yi is not unique,

but changes as a function factor X2.

Figure (6): Effect of micro-vane number (n) and angle-of incidence (β) on engine face total pressure recovery (PFAVE),

h = 2.0 (mm).

For example, Figures (6) through (8) presents the inlet

performance metrics PFAVE, DC60 and FM/2 as a function the

micro-vane angle-of-incidence (β) at three levels of number of

vane-effectors per band (n). A particularly strong (n*β) factor

interaction exist for the inlet total pressure recovery (PFAVE)

response surface, which can be seen in Figure (6). As the number

of micro-vane effectors per band (n) decreases from 27 to 13,

there is a dramatic increase in total pressure recovery (PFAVE),

and this improvement in recovery is very different at an effector

angle-of-incidence of 0.0o as compared to 8.0o. In other words,

the effect of micro-vane effector angle-of-incidence (β) of

(PFAVE) changes as the number of micro-vane effectors per band

(n) decreases. With 27 micro-vane effectors per band, the optimal

micro-vane angle-of-incidence setting is 4.0o, while for 13

micro-vane effectors per band, the optimal angle-of-incidence

setting is 5.5o. Likewise, (n*β) interactions exist for engine face

distortion (DC60) response, Figure (7), and the mean of the first

five components of the Fourier harmonic 1/2-amplitudes of distortion (FM/2), Figure (8), These (n*β) indurations effect the

response surfaces for (DC60) and (FM/2) in varying degrees.

Figure (7): Effect of micro-vane number (n) and angle-of incidence (β) on engine face distortion (DC60), h = 2.0 (mm).

Figure (8): Effect of micro-vane number (n) and angle-of incidence (β) mean Fourier harmonic 1/2-amplitude (FM/2),

h = 2.0 (mm)

In general, it is quite remarkable that very small

angles-of-incidences are required to achieve large improvements

in performance using multiple bands of short chord length microeffectors. When the angle-of-incidence is set to 0o, the microvanes act as fences and perform very poorly. With very small

angle-of-incidences, large increases in total pressure recovery

(PFAVE) were achieved, and substantial decreases in DC60

engine face distortion and the mean Fourier harmonics 1/2-

amplitudes (FM/2) were realized. See Figures (6), through (8).

DC60 ( ) PFAVE PAVCRIT –

QAVE --------------------------------------------------------=

012345678

0.966

0.968

0.970

0.972

0.974

Micro-Vane Angle-of-Incidence (degs), β

Engine Face Recovery, PFAVE

Number of Micro-Vanes, n = 13

Number of Micro-Vanes, n = 20

Number of Micro-Vanes, n = 27

012345678

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Micro-Vane Angle-of-Incidence (degs), β

Engine Face Distortion, DC60

Number of Micro-Vanes, n = 13

Number of Micro-Vanes, n = 20

Number of Micro-Vanes, n = 27

012345678

0.000

0.005

0.010

0.015

0.020

0.025

Micro-Vane Angle-of-Incidence (degs), β

Mean Harmonic 1/2 Amplitude, FM/2

Number of Micro-Vanes, n = 13

Number of Micro-Vanes, n = 20

Number of Micro-Vanes, n = 27

NASA/TM—2003-212017 6
Optimal Flow Control Installations Designs

To illustrate the potential of RSM to design and optimize MSFC installations, three mission strategies were considered for the subject inlet, namely (1) Maximum Performance, (2)

Maximum Engine Stability mission, and (3) Maximum HCF Life

Expectancy. The Maximum Performance mission minimized the

inlet total pressure losses, the Maximum Engine Stability mission

minimized the engine face distortion, 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, and a constraint on each individual Fourier harmonic amplitudes of Fk/2 < 0.015, k = 1 to 5.

Maximum Performance Mission - To obtain the optimal Maximum Performance installation design, a search was made over

the factor variable space to find that installation that minimized

the inlet duct losses

 (3)

This search was subject to the engine face distortion constraint

that

 (4)

while the individual Fourier harmonic 1/2 amplitudes of distortion were each constrained to

 (5)

where k = 1 to 5. The resulting optimal values of the DOE factors

were n =13, β = 5.6o, and h = 2.0 mm.

Maximum Engine Stability Mission - To obtain the optimal

Maximum Engine Stability installation designs, a search was

made over the factor variable space to locate that installation

geometry that minimized the decision parameter:

 (6)

subject to inlet total pressure recovery (PFAVE) being unconstrained, while the constraint on each Fourier harmonic 1/2

amplitude of distortion satisfy the relationship:

 (7)

where k = 1 to 5. The resulting optimal values of the DOE factors

were n =13, β = 5.6o, and h = 2.0 mm.

Maximum HCF Life Expectancy Mission -The optimal Maximum HCF Life Expectancy MSFC installation was determined

through a search process over the factor variable space to locate

that installation geometry that minimized the mean of the first

five Fourier harmonic 1/2 amplitudes of distortion, i.e

 (8)

This search was subject to the inlet total pressure recovery

(PFAVE) being unconstrained and the following constraint on the

engine face distortion:

 (9

and constraint on the individual Fourier harmonic 1/2 amplitudes

of distortion:

 (10)

where k = 1 to 5. The resulting optimal values of the DOE factors

were n =13, β = 5.6o, and h = 2.0 mm.

CFD Validation Test Cases - In order to validate the DOE prediction for the optimal Maximum Performance, Maximum

Engine Stability, and Maximum HCF Life Expectancy installation designs, a set of three cases were run using the optimal factor

values determined from the search procedure described. Each of

the three CFD cases were run with a Reynolds-averaged NavierStokes code, and the performance results were tabulated in Table

(5). The engine face total pressure recovery contours for the three

CFD validation cases are presented in Figure (9). Again, the circumferential uniform nature of the engine face distortion patterns

for the three optimal installation designs can clearly be seen in

Figure (9).

Table (5): Engine face performance CFD solutions for optimal micro-scale secondary flow control installation designs.

Y = ( ) 1 – PFAVE

DC60 0.10 ≤

Fk

2

------ ≤ 0.015

Y DC = ( ) 60

Fk

2

------ ≤ 0.015

Factor/

Response

Max. Perf. Max. Stability Max. HCF Life

n 13 22 19

β 5.6 6.4 5.2

h 2.0 2.0 1.70

PFAVE 0.97292 0.97162 0.97178

DC60 0.04603 0.02983 0.03447

F1/2 0.00539 0.00184 0.00308

F2/2 0.00414 0.00827 0.00745

F3/2 0.00521 0.00479 0.00548

F4/2 0.00480 0.00258 0.00278

F5/2 0.00385 0.00520 0.00446

FM/2 0.00468 0.00454 0.00465

Y 1

5

-- Fk

2

------    

k 1=

5

= ∑

DC60 0.01 ≤

Fk

2

------ ≤ 0.015

)

NASA/TM—2003-212017 7
Figure (9): Comparison of total pressure recovery contours

for the optimal micro-scale secondary flow control installation CFD solutions.

The near wall streamlines for the baseline inlet solution and optimal Maximum HCF Life Expectancy installation

design for a throat Mach number of 0.70 are shown in Figures

(10) and (11). In the baseline flow presented in Figure (10), secondary motion or “over-turning” of the fluid, arises through an

imbalance between centrifugal force and radial pressure gradient

at wall of the first bend in the S-duct. This imbalance displaces

high-speed fluid towards the outer (concave) wall and low-speed

fluid towards the inner (convex) wall and leads to a generation of

longitudinal vorticity which tend to congregate on the inner (convex) wall of the first bend. This forms the vortex pair in the inlet

S-duct, which eventually “lifts-off”. See Figure (2). This vortex

pair results in total pressure loss and severe total pressure distortion at the engine face.

Notice the effect of the micro-vane actuators in preventing the

over-turning of the flow adjacent to the inlet walls. This suppresses the formation of the passage vortex, thus resulting in the

engine face distortion patterns displayed in Figure (9).

(a) Optimal “Maximum Performance” Solution

(b) Optimal “Maximum Engine Stability” Solution

(c) Optimal “Maximum HCF Life Expectancy” Solution

Figure (10): Baseline Inlet Solution

Figure (11): Optimal “Maximum HCF Life Expectancy”

installation solution.

NASA/TM—2003-212017 8
Comparison of the Optimal Installation Designs

Presented in Figure (12) is a comparison between the

optimal pressure recovery performance for the single-band

micro-vane installation designs, Figure (12a), and the multi-band

micro-vane installation designs, Figure (12b). For the single-band

and multi-band installation arrangement, the optimal Maximum

Performance, Maximum Stability, and Maximum HCF Life

Expectancy designs were compared with the baseline solution.

For each band arrangement, micro-vane secondary flow control

improved the pressure recovery performance in comparison to

the baseline solution. However, there was substantially more total

pressure recovery improvement for the single-band installation

than for the multi-band concept. Thus, the greater number of discrete vortices induced by the multi-band arrangement generated

higher losses relative to the single-band concept, although

improvement over the baseline solution was still achieved.

(a) Optimal Single Band Micro-Vane Installation Designs

(b) Optimal Multi Band Micro-Vane Installation Designs

Figure (12): Effect of optimal micro-scale secondary flow

installation designs on engine face total pressure recovery,

(PFAVE).

Shown in Figure (13) is the effect of the optimal

micro-scale secondary flow installation designs of engine face

(DC60) distortion. Again for each band arrangement, the optimal

Maximum Performance, Maximum Stability, and Maximum

HCF Life Expectancy designs were compared with the baseline

solution. In general, both the single-band and multi-band

arrangement of micro-vane effectors substantially improved the

inlet distortion characteristics over the baseline solution. See Figure (13a) and (13b). In addition, no strong conclusions can be

reached as to the differences between the band arrangements with

regards to managing engine face distortion.

(a) Optimal Single Band Micro-Vane Installation Designs

(b) Optimal Multi Band Micro-Vane Installation Designs

Figure (13): Effect of optimal micro-scale secondary flow

installation designs on engine face distortion, (DC60).

Presented in Figure (14) is a comparison between the

optimal harmonic 1/2 amplitude characteristics for the singleband micro-vane installation designs, Figure (14a), and the multiband micro-vane installation designs, Figure (14b). In general,

both the single-band and multi-band arrangement of micro-vane

effectors substantially improved the first five Fourier harmonic 1/

2 amplitude characteristics over the baseline solution. See Figure

(14a) and (14b). In addition, no strong conclusions can be

reached as to the differences between the band arrangements with

regards to managing the first five Fourier harmonic 1/2 amplitudes of engine face distortion

NASA/TM—2003-212017 9
(a) Optimal Single Band Micro-Vane Installation Designs

(b) Optimal Multi Band Micro-Vane Installation Designs

Figure (14): Effect of optimal micro-scale secondary flow

installation designs on engine face Fourier harmonic 1/2

components of distortion, (Fi/2).

Comparison of CFD Analysis and DOE Prediction

Validation cases were included in this study and these

are presented in Table (7), There are a total of three CFD validation cases. They represent the three “Optimal Robust” installation designs. The CFD validation performance results for

“Optimal Robust” Maximum Performance, Maximum Engine

Stability installation, and Maximum HCF Installation designs

included all the response variables important for this study, i.e.

inlet total pressure recovery (PFAVE), engine face distortion

(DC60), and the first five Fourier harmonic 1/2-amplitudes of

distortion (F1/2, F2/2, F3/2, F4/2, and F5/2). These results indicate that the three “Optimal Robust” installation designs satisfied

the design requirements over the entire mission variable range. In

order to validate the DOE performance prediction procedure, the

three CFD performance validation cases were chosen for statistical comparison with the DOE predictions for all of the eight

responce variables.

A direct statistical comparison can be made between

the optimal responses predicted by the DOE models (YDOE) and

the actual CFD predicted performance values (YCFD) through the

expression:

 (11)

where YA is the upper 95% confidence interval for the individual

predicted response YDOE from the regression model, and

t(0.975,N-p) is the 95% confidence t-value for N-p degrees of

freedom.

When the span of the response data covers a decade or

more, there often exist a functional relationship between the

mean values and standard deviation of the data. Under these conditions, the data does not satisfy the requirement of a normally

distributed set. Therefore, a transformation is often used to stabilize the variation over the response variable range. Because this

was the case with DC60 and the Fourier harmonic 1/2-amplitudes, the natural logarithm of these responses were used in the

DOE analysis and in this evaluation of the DOE regression

model. Since all the response parameters except for PFAVE were

analyzed using a natural log transformation, the natural log of the

response (Y) was used in the statistical comparison of those

response variables. For a statistically significant difference to

exist between the DOE model predicted response (YDOE) and the

CFD validation response prediction (YCFD), the expression:

 (12)

must hold. Likewise, if the expression

 (13)

is valid, the YCFD is not statistically different from YDOE. Therefore, for no significant statistical difference to exist between the

DOE model predicted response YDOE and the CFD analysis

response YCFD, the CFD response prediction must fall within the

95% confidence interval of the DOE model prediction for that

response.

Table (7) shows the results of this statistical comparison at an inlet throat Mach Number of 0.70 and inlet angle-ofincidences of 0o for the Maximum Performance, Maximum

Engine Stability, and Maximum HCF Life Expectancy missions.

In general, the number of incidences when the comparisons were

statistically different was somewhat above 5%, which is remarkably good. All the cases in which a statistical difference were

indicated involved in the evaluation of the Fourier harmonic 1/2-

amplitudes of distortion. In these particular cases, the differences between the CFD analysis and DOE prediction were to too

small to be of practical significance, i.e. there was no “meaningful statistical difference” This indicates that the DOE prediction

results are not substantially different from the CFD analysis

results (i.e. the CFD analysis predictions fell within the 95%

confidence interval of the DOE performance predictions). It also

indicates that the optimal installations determined by the DOE

t∗

YCFD ln( ) Y DOE ln– ( )

Y A ln( ) Y DOE ln– ( )

t( ) 0.975, N p – -----------------------------------------------

---------------------------------------------------------=

t∗ > t( ) 0.975, N p –

t∗ < t( ) 0.975, N p –

NASA/TM—2003-212017 10
models were a statistically valid optima when compared to the

actual CFD installation analyses. The accuracy of the response

surfaces determined from the DOE analysis was therefore more

than adequate for use in determining an installation optimum.

Table (7): Statistical comparison between CFD analysis and

DOE prediction for the optimal installation designs.

CONCLUSIONS

It is the purpose of this study to demonstrate the viability and economy of Design-of-Experiments (DOE) to arrive at

micro-secondary flow control installation designs that achieve

optimal inlet performance for different mission strategies. These

statistical design concepts were used to investigate the properties

of “low unit strength” micro-effector installation. “Low unit

strength” micro-effectors are micro-vanes, set a very low angleof-incidence, with very long chord lengths. They are designed to

influence to near wall inlet flow over an extended streamwise

distance. In this study, however, the long chord lengths were replicated by a series of short chord length effectors arranged in

series over multiple bands of effectors. In order to properly evaluate the performances difference between the single band

extended chord length installation designs and the segmented

multi-band short chord length designs, both sets of installations

must be optimal. Critical to achieving optimal micro-secondary

flow control installation designs is the understanding of the factor

interactions that occur between the multiple bands of micro-scale

vane effectors. These factor interactions are best understood and

brought together in an optimal manner through a structured

Design-of-Experiments process, or more specifically Response

Surface Methods (RSM).

To illustrate the potential of Response Surface Methodology to determine optimal micro-scale secondary flow installation designs, three different mission strategies were considered

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

Maximum Engine Stability, and (3) Maximum High Cycle

Fatigue Life Expectancy. The Maximum Performance mission

minimized the inlet total pressure losses, the Maximum Engine

Stability mission minimized the engine face distortion (DC60),

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, and a constraint on each

individual Fourier harmonic amplitude of Fk/2 < 0.015.

Comparison of the optimal single-band and multiband installation design concepts for the Maximum Performance,

Maximum Engine Stability, and Maximum High Cycle Fatigue

Life Expectancy missions indicated that micro-scale flow controlled improved performance over the baseline solution. However, the multi-band installation concept had greater total

pressure losses relative to the single-band arrangement. The

larger number of individual vortices generated by the multi-band

concept also generated greater losses. In comparing the optimal

single-band and multi-band installation design concepts for the

Maximum Performance, Maximum Engine Stability, and Maximum High Cycle Fatigue Life Expectancy missions relative to

engine face DC60 distortion and the first five Fourier harmonic 1/

2 amplitude of engine face distortion, no strong conclusions can

be reached as to which arrangement is better. Therefore, the

multi-band concept provided a viable concept for improving performance over the baseline performance. However, the penalty

paid for the greater number of vortices generated by the multiband arrangement were larger losses relative to the single-band

design concept.

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.

Response Mission CFD DOE t t* Comments

PFAVE Max. Perf. 0.97292 0.97358 2.26216 0.96721 Not Diff.

DC60 0.04603 0.05202 2.26216 0.32502 Not Diff.

F1/2 0.00539 0.00367 1.97681 0.76907 Not Diff.

F2/2 0.00414 0.00347 1.97681 0.31881 Not Diff.

F3/2 0.00521 0.00392 1.97669 2.07258 Diff.

F4/2 0.00480 0.00337 1.97669 0.80030 Not Diff.

F5/2 0.00385 0.00295 1.97669 0.81048 Not Diff.

FM/2 0.00468 0.00369 1.97681 0.84656 Not Diff.

PFAVE Max. Stability 0.97126 0.97059 2.26216 1.07561 Not Diff.

DC60 0.02983 0.02936 2.26216 0.04364 Not Diff.

F1/2 0.00184 0.00197 1.97681 0.14992 Not Diff.

F2/2 0.00827 0.00479 1.97681 1.01101 Not Diff.

F3/2 0.00479 0.00398 1.97669 1.34175 Not Diff.

F4/2 0.00258 0.00269 1.97669 0.09433 Not Diff.

F5/2 0.00520 0.00368 1.97669 0.88621 Not Diff.

FM/2 0.00454 0.00319 1.97681 1.26802 Not Diff.

PFAVE Max. HCF Life 0.97178 0.97178 2.26216 0.00636 Not Diff.

DC60 0.03447 0.03844 2.26216 0.30853 Not Diff.

F1/2 0.00308 0.00348 1.97681 0.26243 Not Diff.

F2/2 0.00745 0.00336 1.97681 1.47714 Not Diff.

F3/2 0.00548 0.00338 1.97669 3.55215 Diff.

F4/2 0.00278 0.00105 1.97669 2.28369 Diff.

F5/2 0.00446 0.00239 1.97669 1.61631 Not Diff.

FM/2 0.00465 0.00306 1.97681 1.49557 Not Diff.

NASA/TM—2003-212017 11
(3) Anderson, B. H. and Keller, D. J., “Optimal Micro-Scale Secondary Flow Control for the Management of HCF and Distortion

in Compact Inlet Diffusers”, NASA/TM-2002-211686, July

2002.

(4) Anderson, B. H. and Keller, D. J., “A Robust Design Methodology for Optimal Micro-Scale secondary Flow Control in Compact Inlet Diffusers”, AIAA Paper No. 2002-0541, Jan. 2002.

(5) Anderson, B. H. and Keller, D. J., “Robust Design Methodologies for Optimal Micro-Scale Secondary Flow Control in Compact Inlet Diffusers”, NASA/TM-2001-211477, March 2001.

(6) Anderson, B. H., Baust, Henry D., and Agrell, Johan: “Management of Total Pressure Recovery, Distortion, and High Cycle

Fatigue in Compact Air Vehicle Inlets”, Proposed NASA TM,

2002.

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

Compact Inlet Diffusers”, NASA/M-2001-211476, March 2001.

(8) AGARD FTP Working Group 13, “Air Intakes for High Speed

Vehicles”, AR-270, September 1991.

(9) 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.

(10) Goldsmith, E. L. and Seddon, J. (eds), “Practical Intake

Aerodynamics,” Blackwell Scientific Publications, Oxford, 1993.

(11) 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.

NASA/TM—2003-212017 12
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NASA TM—2003-212017

AIAA–2003–0652

E–13720

WBS–22–708–92–21

18

Design-of-Experiments to Reduce Life-Cycle Costs in Combat Aircraft Inlets

Bernhard H. Anderson, Henry D. Baust, and Johan Agrell

Aerodynamics; Propulsion; Fluid dynamics

Unclassified -Unlimited

Subject Category: 07 Distribution: Nonstandard

Prepared for the 41st Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics

and Astronautics, Reno, Nevada, January 6–9, 2003. Bernhard H. Anderson, NASA Glenn Research Center;

Henry D. Baust, Wright Patterson Air Force Base, Dayton, Ohio 45433; Johan Agrell, Swedish Defence Research

Agency, Bromma, Sweden. Responsible person, Bernhard H. Anderson, organization code 5850, 216–433–5822.

It is the purpose of this study to demonstrate the viability and economy of Design-of-Experiments (DOE), to arrive at

micro-secondary flow control installation designs that achieve optimal inlet performance for different mission strategies.

These statistical design concepts were used to investigate the properties of “low unit strength” micro-effector installation. “Low unit strength” micro-effectors are micro-vanes, set a very low angle-of incidence, with very long chord

lengths. They are designed to influence the neat wall inlet flow over an extended streamwise distance. In this study,

however, the long chord lengths were replicated by a series of short chord length effectors arranged in series over

multiple bands of effectors. In order to properly evaluate the performance differences between the single band extended

chord length installation designs and the segmented multiband short chord length designs, both sets of installations must

be optimal. Critical to achieving optimal micro-secondary flow control installation designs is the understanding of the

factor interactions that occur between the multiple bands of micro-scale vane effectors. These factor interactions are best

understood and brought together in an optimal manner through a structured DOE process, or more specifically Response

Surface Methods (RSM).