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

Management of Total Pressure Recovery,

Distortion and High Cycle Fatigue in

Compact Air Vehicle Inlets

NASA/TM—2002-212000

December 2002
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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

Management of Total Pressure Recovery,

Distortion and High Cycle Fatigue in

Compact Air Vehicle Inlets

NASA/TM—2002-212000

December 2002

National Aeronautics and

Space Administration

Glenn Research Center
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
MANAGEMENT OF TOTAL PRESSURE RECOVERY, DISTORTION

AND HIGH CYCLE FATIGUE IN COMPACT AIR VEHICLE INLETS

ABSTRACT

It is the purpose of this study to demonstrate the viability and economy of

Response Surface Methods (RSM) and Robust Optimization Concepts (ROC) to arrive at microsecondary flow control installation designs that maintain optimal inlet performance over a range

of the mission variables. These statistical design concepts were used to investigate the robustness

properties of “low unit strength” micro-effector installations. “Low unit strength” micro-effectors

are micro-vanes set at very low angles-of-incidence with very long chord lengths. They were

designed to influence the near wall inlet flow over an extended streamwise distance, and their

advantage lies in low total pressure loss and high effectiveness in managing engine face distortion.

To illustrate the potential of economical robust design methodology, 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 to place a constraint on each individual Fourier harmonic

amplitude of Fk/2 < 0.015. For each of these missions strategies, an “Optimal Robust” (open loop

control) and an “Optimal Adaptive” (closed loop control), installation were designed over an inlet

throat Mach number range from 0.30 to 0.70, and angle-of-incidence range from 0.0o to 20.0o.

The “Optimal Robust” installation used economical Robust Design methodology to arrive at a

single design, which operated over the entire throat Mach number and angle-of-incident range

(open loop control). The “Optimal Adaptive” installation optimized all the design parameters at

each throat Mach number and 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

Bernhard H. Anderson

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio

Henry D. Baust

Wright-Patterson Air Force Base

Dayton, Ohio

Johan Agrell

Swedish Defence Research Agency

Bromma, Sweden

NASA/TM—2002-212000 1
designs were found to be marginal. This suggests, that “Optimal Robust” opened loop installation

designs can be very competitive with “Optimal Adaptive” closed loop designs.

Effective inlet flow control management of engine face distortion was achieved by

reducing the unit strength of the micro-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 became very small, and a large overall

performance gain was achieved. In addition, this study demonstrated that optimal “low unit

strength” micro-effector installation designs exhibited the same robustness properties as optimal

“high unit strength” micro-effector installation but without the large total pressure loss. The

design strategy of replacing “high unit strength” micro-effectors with “low unit strength” microeffectors which influence the flow over an extended streamwise distance was therefore found to be

very effective.

INTRODUCTION

The current development strategy for combat air-vehicles 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 Sduct 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 be 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. The design task is further complicated by the existNASA/TM—2002-212000 2
ence of hard-to-control factors that affect inlet performance, i.e. the mission variables. The mission variables that cause the off-design penalty are, for example, inlet throat Mach number

(engine corrected weight flow), angle-of-incidence and angle-of-yaw. While the aerodynamicist

does not know how the pilot is ultimately going to fly the aircraft, it is known how the mission

variables affect 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 Robust Optimization Concepts (ROC) 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, properties of the material, and product

aging. In some applications, the factors measure how the consumer uses or handles the product. In

the aerodynamic design of inlet systems, there is an 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. The variables that cause the off-design penalty are the mission variables,

such as the inlet throat Mach number (engine corrected weight flow), angle-of-incidence and

angle-of-yaw. 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, 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 aerodynamic design. For the first time, the mission

variables can be directly introduced into the aerodynamic 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

NASA/TM—2002-212000 3
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 have been incorporated into an alternate approach, i.e. adapted to the

inlet design problem by Anderson and Keller.(4) The approach taken by Anderson and Keller was

a combined DOE format in which the factor (design) variables and the environmental (mission)

variables were contained in the same DOE. This approached, called the lower order combined

DOE format, led to a very viable and economical methodology to explore the concept of robust

inlet design (Anderson and Keller(5)-(6)). The concept of robust inlet design means that the inlet

mission variables are brought directly into the installation design process, and insensitivity or

robustness to the mission variables becomes a design objective. More importantly, the combined

DOE format allows for conceptual studies to be made of the inlet-engine control system, which

take advantage of the inherent robustness properties that have been built into the installation

design by Response Surface Methods and Robust Optimization Concepts. It is the purpose of this

report to expand the concept of inlet robust installation design to cover both the inlet throat Mach

number and angle-of-incidence mission variable range and to explore the robustness properties of

“low unit strength” micro-vane effector installation designs which exhibit very low total pressure

loss and high effectiveness in managing engine face distortion.

To illustrate the potential of Response Surface Methods and Robust Optimization

Concepts to provide open loop installation designs that exhibit optimal inlet performance over an

extended mission variable range, three different mission strategies were considered for the subject

inlet, namely (1) Maximum Performance, (2) Maximum Engine Stability, 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. For each of three mission strategies, i.e Maximum Performance,

Maximum Engine Stability, and Maximum HCF Life Expectancy mission, an “Optimal Robust”

(open loop control) and an “Optimal Adaptive” (closed loop control) installation were designed to

operate over an inlet throat Mach number range from 0.30 to 0.70, and angle-of-incidence, i.e. αrange from 0.0o to 20.0o

. The “Optimal Robust” installation arrived at a single MSFC installation

which operated optimally over the entire throat Mach number and angle-of-incidence range (open

loop control). The “Optimal Adaptive” installation optimized all the design parameters at each

throat Mach number and 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 of the

three mission strategies, i.e. Maximum Performance, Maximum Engine Stability, and Maximum

HCF Life Expectancy, two approaches to secondary flow control installation design, i.e. “Optimal

Robust” installation design and Optimal Adaptive” 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 throat Mach number and angle-of incidence

range were the Taguchi noise or environmental variables over which each optimal installation had

to be robust.

NASA/TM—2002-212000 4
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 Critical Sector Angle at AIP

QAVE Average Dynamic Pressure at AIP

R Inlet Radius

Rcl Centerline Radius

Ref Engine Face Radius

Rthr Inlet Throat Radius

ROC Robust Optimization Concepts

Re Reynold Number per ft.

RSM Response Surface Methodology

S Standard Deviation

Sclock Standard Deviation over the Rake Clocking Angles

UAV Unmanned Air Vehicle

UCAV Unmanned Combact Air Vehicle

Xcl Axial Distance Along the Duct Centerline

YA Upper 95% Confidence Interval Predicted by DOE Analysis

YCFD Response Predicted by CFD Analysis

YDOE Response Predicted by DOE Analysis

Yi,j Generalized Response Variable

YM,α Generalized Response Variable Summed over Mt and α

Zcl Centerline Offset Displacement

α Inlet Angle-of-Incidence

β Effector Vane Angle-of-Incidence

∆Zcl Inlet Centerline Offset

γ Inlet Angle-of-Yaw

NASA/TM—2002-212000 5
RESULTS AND DISCUSSION

Baseline Flow in the Redesigned M2129 Inlet S-Duct

The redsigned 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)

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 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 shown in Figure (1). The computational grid for the baseline solutions was a single block composed of 61x91x49 grid points in a half cylindrical grid

topology.

A set of cases was run to characterize the performance in the baseline inlet S-duct

over a range of throat Mach numbers from 0.30 to 0.70 and angles-of-incidence from 0.0o to

20.0o. The definition of the baseline cases are presented in Table (1) and were organized as a full

factorial array with two factors at three levels each, i.e. 32 cases. Each of the 9 cases in Table (1)

were run with a Reynolds-averaged Navier-Stokes code.(10) The baseline inlet performance

results are presented in Table (2) and 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 (Fk/2). 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(11). Even though introducing an α-disturbance into the

flow field was not rigorous, it provided a remarkably good approximation in comparison to the

experimental flow field. The data reduction methodology for the total pressure recovery, engine

face distortion and Fourier harmonic 1/2-amplitudes appear in the section entitled Harmonic

Analysis of Distortion.

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—2002-212000 6

R
The inlet was designed such that at 0.70 throat Mach number and 20.0o angle of

incidence the Mach number in the vicinity of the inlet shoulder was just below supersonic conditions. Thus, if either the inlet throat Mach number increases much above 0.70 or the inlet angleof-incidence increases beyond 20.0o

, shock waves will form in the vicinity of the inlet shoulder

which will induce massive flow separation extending upstream of the inlet throat. Over the range

of throat Mach numbers from 0.30 to 0.70 and inlet angles-of-incidence from 0.0o to 20.0o

, the

inlet was separated. The degree of flow separation, i.e. vortex liftoff, is shown in Figure (2). This

type of 3D flow separation results in severe total pressure losses and engine face distortion. In

addition, it may also have very severe consequences with regard to aeromechanical vibration. The

engine face total pressure recovery contours over the range of conditions presented in Table (1)

are shown in Figure (3). Although the baseline flow for the redesigned M2129 inlet S-duct indicated vortex liftoff (flow separation) over the entire mission range defined by Table (1), there is

considerable variation in distortion patterns shown in Figure (3). To augment this visual summary,

the baseline inlet performance is presented in Figures (4) through Figure (9) in terms of the inlet

total pressure recovery (PFAVE), 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, F5/2), and the mean of the

first five Fourier harmonic 1/2-amplitudes (FM/2). Figures (4), (6) and (8) present the effect of

inlet throat Mach number at 0.0o inlet angle-of-incidence on recovery, distortion, and Fourier harmonic 1/2-amplitudes of distortion, while Figures (5), (7) and (9) illustrate the effect of inlet

angle-of-incidence on the same inlet metrics at an inlet throat Mach number of 0.70. The large

variation in inlet performance is evident from these figures. Particularly revealing is the very high

Fourier harmonic 1/2-amplitudes of distortion that can arise at angle-of-incidence conditions. See

Figure (9).

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 micro-vane 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 comes 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 for

loss of unit strength 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 a

longer streamwise distance. With this combination, the total pressure losses associated with

micro-vane effectors become very small, and a large overall performance gain achieved.

NASA/TM—2002-212000 7
The micro-vane installations described in the first paragraph function by inducing

a weak set of vortices in a cascade type arrangement within a very thin layer adjacent to the inlet

walls. The weak set of vortices in this thin layer quickly merged to form a secondary flow field

which suppressed the development of the vortex pair that forms in the diffuser, see Figures (2) and

(3). This in turn, substantially reduced engine face distortion. It has been demonstrated that high

unit strength micro-vane effectors with vane heights of 2.0 mm, chord length of 16.0 mm and a

vane angle-of-incidence of 24.0o manage the inlet flow very effectively at a throat Mach number

of 0.70 and over a range of inlet angles-of-incidence from 0.0o to 20.0o

. However, these high unit

strength installation designs exhibited high total pressure loss. In other words, open loop installation designs using high unit strength micro-vane effectors were “Optimal Robust” over a range of

inlet angles-of-incidence and differ only marginally in performance from “Optimal Adaptive”

close loop installation designs.(4) However, the performance penalty paid for high unit strength

“Optimal Robust” installation designs was high total pressure loss. In this study, low unit strength

micro-vane effectors which have low total pressure loss will be examined to determine whether

they exhibit the same robustness properties as high unit strength effectors. However, in this study,

the “Optimal Robust” low unit strength micro-vane effector installation designs will be established over an expanded mission variable range, i.e. throat Mach numbers from 0.30 to 0.70 and

inlet angles-of-incidence from 0.0o to 20.0o.

Inlet Flow Control Installation Design

To manage the flow in the redesigned M2129 inlet S-duct, a single band installation arrangement of micro-scale effectors was placed in the upstream section near the inlet throat.

See Figures (10) and (11). These micro-scale effectors were micro-vanes, 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 co-rotating vortices that would

quickly merge to form a thin layer of secondary flow that will counter the formation of the passage vortex pair. Since the height of the vane effectors were limited to 2.0 mm, a single-band

arrangement of micro-vanes set at 5.0o angle-of-incidence was chosen to investigate the enhancing effect of increasing the vane chord length on distortion management, i.e. allowing the installation design to influence the inlet flow over an extended streamwise distance for a design

advantage

The DOE approach followed directly from the objectives previously stated and

was reflected in the layout of the design factors listed in Table (3). The factor variables were the

number of vane effector units (n), the micro-vane effector height (h), the micro-vane chord length

(c), the inlet throat Mach number (Mt), and the inlet angle-of-incidence (α). Strictly speaking, the

inlet throat Mach number and angle-of-incidence are mission variables and, therefore, the noise

factors that belonged with the environmental variables, i.e. the outer array in a traditional Taguchi-style Robust Parameter Design. However, in this study, the throat Mach number and inlet

angle-of-incidence were combined into the statistical DOE matrix with the control factors. This is

called a combined DOE matrix array, which allowed greater economy than the traditional Taguchi

approach(3). The robust nature of the throat Mach number and inlet angle-of-incidence was investigated during the analysis phase of the data. Table (4) shows the variables that were held constant

during this study. They include the effector vane thickness (t), the geometric angle-of-incidence of

the micro vanes (β), the inlet operating total pressure (Pt) and temperature (Tt), and the inlet

NASA/TM—2002-212000 8
angle-of-yaw (γ). Table (5) 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).

The DOE strategy selected was a Central Composite Face-Centered (CCF) DOE.

This strategy resulted in 27 unique CFD experimental cases that are shown in Table (6). This DOE

construct is called a combined array format because it contains both the factor (design) variables

and the environmental (mission) variables. Notice that these DOE cases covered a substantial

range of possible flow situations over a wide range of throat Mach numbers from 0.30 to 0.70, and

angles-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 27 cases permitted the estimation of both

linear and curvilinear effects as well as two-factor interactive or synergistic effects among the

DOE factors. This CCF DOE strategy is superior to the traditional approach where only changing

one variable at a time does not permit the estimation of the two-factor interactions. It is also more

economical at 27 runs than a full factorial approach where the number of experiments would be 35

or 243 separate CFD cases. It is also more economical than a comparable Taguchi approach

requiring 15 x 3 = 45 runs.

A graphical representation of the Central Composite Face-Centered DOE used in

the study is presented in Figure (12). 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 fractional factorial part and a

quadratic part. The fractional factorial part of the DOE is composed of one-half of the 25 possible

cases, i.e. 32 possible factorial cases, which are represented by the eight corner locations in each

of the four corner-cubes in Figure (12). Because only half the number of possible factorial cases

are actually used in this DOE format (circular symbols), the layout is called a 1/2-fractional of the

full factorial and is composed of 25-1 cases, or 16 separate CFD runs. The remaining cases in Figure (12) 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 27 cases in a Central Composite Face-Centered

DOE with five factor variables. Notice the balanced layout of cases in Figure (12). The factor variables are represented by the axes of the individual cubes, while the environmental variables are

represented by the different cubes. 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 27 cases in Table (6) was run with a Reynolds-averaged Navier-Stokes

code(10) 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 micro-vanes all

had a thickness of 0.138 mm. See Table (4). The computational grid surrounding was developed

such that it reasonably resolved the boundary layer development on both the suction and pressure

surfaces of each micro-vane in the installation. Because wall functions were used in the calculations, the grid resolution for the individual micro-vanes was simplified. However, 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 micro-vanes, and a downstream block. See Figures (10)

and (11). The computational half-plane grid varied in total number of mesh points from about

950,000 to 1,150,000 depending on the micro-vane configuration. All CFD calculations were

NASA/TM—2002-212000 9
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

was first proposed by Ludwig(12) 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 (7).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. A separate

study was initiated by Anderson and Keller(13) 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” AIP 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 separate measurement, the angular orientation of the rake was advanced 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. Using the AIP instrumentation locations for the 80-probe rake, the 27 CFD solutions were interpolated at each of the probe

positions shown in Figure (13a). The span-weighted average total pressure was calculated for the

80-probe rake by multiplying the probe total pressure by the span-weighted coefficients from

Table (7), 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 (6). 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 are presented in Table (8).

Since each F-test exceeded the 95% confidence critical value of F(0.975,9,9) = 4.03, 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

27 = 270 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

NASA/TM—2002-212000 10
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 face distortion descriptor is defined such that it can be determined

from either a computational grid or a standard measurement rake.(14) 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)

The CFD performance results for the Central Composite Face-Centered combined

array DOE format involving both the factor (design) variables and the environmental (mission)

variables are presented in Table (9). The inlet recovery (PFAVE) and the engine face distortion

(DC60) were determined from the computation mesh. The Fourier harmonics 1/2-amplitudes of

engine face distortion listed in Table (9) were determined from a “clocked” engine face rake and

are the mean values over the 10 clocking angles. However, these values were not used in the

regression analysis since weighted regression were required as a result of a lack of constant variance across the design space. Instead, the complete set of 10 x 27 = 270 values together with their

corresponding weighting factors were used in the weighted regression to obtain the response surfaces for each of the Fourier harmonic 1/2-amplitudes of distortion.

Once the response surfaces are determined encompassing the inlet design parameters and mission variables, conceptual studies can be made to the determine the best and most cost

effective method to manage the inlet flow field over the mission variable range. This type of conceptual study is not possible within a traditional Taguchi Robust Parameter Design methodology

because the performance information of that installation over the outer array (mission) variable

range is lost. These two sources of information are combined into a Taguchi signal-to-noise

parameter (S/N) and are not contained in the regression.

Optimal Flow Control Over the Mission Variable Range

To illustrate the potential of RSM and Robust Optimization Concepts to design and

optimize MSFC installations, three mission strategies were considered for the subject inlet,

namely (1) Maximum Performance, (2) Maximum Engine Stability, 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

1/2-amplitudes: Fk/2 < 0.015, k = 1,2...5. For each of three mission strategies, i.e Maximum Performance, Maximum Engine Stability, and Maximum HCF Life Expectancy mission, an “Optimal

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

DC60 ( ) PFAVE PAVCRIT –

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

NASA/TM—2002-212000 11
designed to operate over an inlet throat Mach number range from 0.30 to 0.70, and angle-of-incidence range from 0.0o to 20.0o. The “Optimal Robust” installation arrived at a single MSFC

installation which operated optimally over the entire throat Mach number and angle-of-incident

range (open loop control). The “Optimal Adaptive” installation optimized all the design parameters at each throat Mach number and 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.The

inlet throat Mach number and angle-of incidence range were the Taguchi noise or environmental

variables over which each optimal installation had to be robust. A detailed description of the

robust methodology used in the present study appears in Anderson and Keller,(4) and is termed the

“Lower Order” method, while a lengthy comparison between the “Lower Order”, Taguchi and an

alternative “High Order” method appears in Anderson and Keller.(6)

Maximum Performance Mission - Two different inlet control strategies were

considered for the Maximum Performance mission, an “Optimal Adaptive” and an “Optimal

Robust” strategy. The “Optimal Adaptive” strategy optimized all the design parameters at each

throat Mach number and angle-of-incidence, while “Optimal Robust” strategy arrived at a single

MSFC installation which operated optimally over the entire throat Mach number and angle-ofincident range. To obtain the “Optimal Adaptive” Maximum Performance optimal installation

designs, the inlet duct losses:

 (4)

where minimized at each of the values of inlet throat Mach numbers and each of the

angles-of-incidence to obtained the optimal installation corresponding to that inlet operating condition. This search was subject to the engine face distortion constraint that

 (5)

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

 (6)

where = 1 to 5. In a similar manner, the “Optimal Robust” Maximum Performance installation

design was determined through a search process to locate that installation geometry that minimized the decision parameter:

 (7)

Yi j , = ( ) 1 – PFAVE i j ,

N M Nα

DC60 0.10 ≤

Fk

2

------ ≤ 0.015

k

Y M α,

1

N M

-------- 1

Nα

------- ( ) 1 – PFAVE i j ,

j 1=

Nα

∑

i 1=

N M

= ∑

NASA/TM—2002-212000 12
where is the number of throat Mach number conditions in the set from Mt = 0.30 to 0.70, and

is the number angles-of-incidence α = 0.0 to 20.0o. This search was also subject to the engine

face distortion constraint that

 (8)

and the individual Fourier harmonic 1/2-amplitudes of distortion constraint to

 (9)

Comparisons between the performance results of the “Optimal Robust” and “Optimal Adaptive” installations for the Maximum Performance inlet mission are shown in Figure (14).

Also presented in Figures (14) is the inlet baseline performance at an inlet throat Mach number of

0.70 for each response. It is apparent from Figure (14) that flow control was able to increase total

pressure recovery substantially above the baseline flow at 0.70 inlet throat Mach number. This

was not the case for the high strength micro-vane effector units.(4)-(5)

The “Optimal Robust” and “Optimal Adaptive” installations provided essentially

the same performance over the inlet throat Mach number range for 0.30 to 0.70 and angle-of-incidence range of 0o to 20o. This is not surprising, since there exists experimental data(11) that demonstrate that a fixed secondary flow control installation optimally designed can provide essentially

the same low DC60 distortion level, i.e. , over a substantial angle-of-incidence

range. Secondary flow control in inlets is inherently robust, provided it is optimally designed. In

addition, “Optimal Robust” and “Optimal Adaptive” installations reduced all the Fourier harmonic 1/2-amplitudes to a value of 0.01 or below, which is extremely low. Although a correlation

between engine face distortion and the Fourier harmonic 1/2-amplitudes can not be established,

reducing the Fourier harmonic 1/2-amplitudes is essentially the same at reducing the engine face

circumferential distortion.

In order to validate the DOE prediction results, a set of nine cases was run using

the “Optimal Robust” installation design determined from the search procedure described. The

validation cases are defined in Table (10) and were organized as a full factorial array with the two

mission variables at three levels each, i.e. 32 cases. Each of the 9 CFD cases in Table (10) were

run with a Reynolds-averaged Navier-Stokes code, and the performance results are presented in

Table (11). More will be said about these performance results later in the report. However, the performance of the “Optimal Robust” installation design were excellent. The engine face total pressure recovery contours for 9 CFD validation cases defined in Table (10) are presented in Figure

(15). The circumferential uniform nature of the engine face distortion patterns over the range of

inlet throat Mach numbers from 0.30 to 0.70 and inlet angles-of-incidences from 0.0o to 20.0o can

clearly be seen in Figure (15).

The near wall streamlines for the baseline solution and the “Optimal Robust”

Maximum Performance installation design are presented in Figures (16a) and (16b) respectively

for an inlet throat Mach number of 0.30 and inlet angle-of-incidence α = 0.0o. A comparison of

these two figures indicates the underlying operational purpose of micro-scale secondary flow

N M

Nα

DC60 0.10 ≤

Fk

2

------ ≤ 0.015

DC60 0.10 ≤

NASA/TM—2002-212000 13
effector devices. In the baseline flow presented in Figure (16a), secondary motion or “overturning” of the fluid, arises through an inbalance between centrifugal force and radial pressure

gradient at wall of the first bend in the S-duct. This inbalance 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.

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-vane effectors into the inlet the “over-turning” in

the inlet boundary is prevented. See Figure (15b). Consequently, the passage vortex will not form

or, at worst, is greatly reduced in strength, which will results 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.

Maximum Engine Stability Mission - To obtain the “Optimal Adaptive” Maximum Engine Stability installation designs, a search was made over the factor variable space to

locate that installation geometry that minimized the decision parameter:

 (10)

at each throat of the inlet throat Mach numbers and each of the inlet angles-of-incidence.

This search was subject to the constraint that each Fourier harmonic 1/2-amplitude of distortion

satisfy the relationship:

 (11)

where = 1 to 5, while no constraint was placed on the inlet total pressure recovery (PFAVE). In

a similar manner, the “Optimal Robust” Maximum Engine Stability installation design was determined through a search process to locate that installation geometry that minimized the decision

parameter:

 (12)

where is the number of throat Mach number conditions in the set from Mt = 0.30 to 0.70, and

is the number of angles-of-incidence α = 0.0 to 20.0o

. This search was also subject to the constraint that

 (13)

Yi j , ( ) DC60 i j , =

N M Nα

Fk

2

------ ≤ 0.015

k

M α,

1

N M

-------- 1

Nα

------- ( ) DC60 i j ,

i 1=

Nα

∑

j 1=

N M

= ∑

N M

Nα

Fk

2

------ ≤ 0.015

NASA/TM—2002-212000 14

Y
while no constraint was placed on the inlet total pressure recovery (PFAVE).

Comparisons between the performance results of the “Optimal Robust” and “Optimal Adaptive” installations for the Maximum Engine Stability inlet mission are shown in Figure

(17). Also presented in Figure (17) is the inlet baseline performance at an inlet throat Mach number of 0.70 for each response. It is apparent from Figure (17) that both the “Optimal Robust” and

“Optimal Adaptive” installations were able to increase total pressure recovery substantially well

above the baseline flow at 0.70 inlet throat Mach number with an unconstrained inlet total pressure recovery (PFAVE) condition during the search procedure. While no correlation can be established between engine face distortion and inlet total pressure recovery, this occurrence suggest

that maximum inlet total pressure recovery occurs when the engine face circumferential distortion

approaches zero.

In order to validate the DOE prediction for the “Optimal Robust” Maximum

Engine Stability installation performance results, a set of nine cases were run using the “Optimal

Robust” installation design determined from the search procedure described. The validation cases

are defined in Table (12) and were also organized as a full factorial array with two mission variables at three levels, i.e. 32 cases. Each of the 9 CFD cases in Table (12) were run with a Reynolds-averaged Navier-Stokes code, and the performance results are presented in Table (13).

More will be said about these performance results later in the report. However, the performance of

the “Optimal Robust” Maximum Engine Stability installation design were excellent. The engine

face total pressure recovery contours for the 9 CFD validation cases defined in Tables (12) are presented in Figure (18). Again, the circumferential uniform nature of the engine face distortion patterns over the range of inlet throat Mach numbers from 0.30 to 0.70 and inlet angles-of-incidence

from 0.0o to 20.0o can clearly be seen in Figure (18).

Presented in Figure (19) are the near wall streamlines for the baseline inlet solution

and “Optimal Robust” Maximum Engine Stability installation design at a throat Mach number of

0.50 and inlet angle-of-incidence, α = 10.0o

. Again, notice the effect of the micro-vane actuators

in preventing the over-turning of the flow adjacent to the inlet walls and thus suppressing the passage vortex formation.

Maximum HCF Life Expectancy Mission -The “Optimal Adaptive” 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

 (14)

at each of the inlet throat Mach numbers and each of the inlet angles-of-incidence. This

defined the “Optimal Adaptive” installation design at each of these inlet operating conditions subject to inlet total pressure recovery (PFAVE) being unconstrained and the following constraint on

the engine face distortion:

 (15)

Yi j ,

1

5

-- Fk

2

------    

i j , k 1=

5

= ∑

N M Nα

DC60 0.01 ≤

NASA/TM—2002-212000 15
and constraint on the individual Fourier harmonic 1/2-amplitudes of distortion

:

 (16)

where = 1 to 5. The “Optimal Robust” Maximum HCF Life Expectancy MSFC installation was

also determined through a search process over the factor variable space to locate that installation

geometry that minimized the decision parameter:

 (17)

where is the number of throat Mach number conditions in the set from Mt = 0.30 to 0.70, and

is the number angles-of-incidence α = 0.0 to 20.0o

. This search was also subject to and

unconstrained inlet total pressure recovery (PFAVE) and the constraint that the engine face distortion satisfy the relationship:

 (18)

and each Fourier harmonic 1/2-amplitude satisfy the expression:

 (19)

Comparisons between the performance results of the “Optimal Robust” and “Optimal Adaptive” installations for the Maximum HCF Life Expectancy mission are shown in Figure

(20). Also presented in Figure (20) is the inlet baseline performance at an inlet throat Mach number of 0.70 for each response. It is apparent from Figure (20) that both the “Optimal Robust” and

“Optimal Adaptive” installations were able to increase total pressure recovery substantially above

the baseline flow at 0.70 inlet throat Mach number with an unconstrained inlet total pressure

recovery (PFAVE) condition during the search procedure. While no correlation can be established

between the Fourier harmonic 1/2-amplitudes and engine face distortion or inlet total pressure

recovery, this occurrence suggest that maximum inlet total pressure recovery occurs when the

Fourier harmonic 1/2-amplitudes of distortion approach zero.

In order to validate the DOE prediction for the “Optimal Robust” Maximum HCF

Life Expectancy installation performance results, a set of nine cases were run using the “Optimal

Robust” installation design determined from the search procedure described. The validation cases

are defined in Table (14) and were organized as a full factorial array with the two mission variables at three levels, i.e. 32 cases. Each of the 9 CFD cases in Table (14) were run with a Reynolds-averaged Navier-Stokes code, and the performance results are presented in Table (15). The

engine face total pressure recovery contours for the 9 CFD validation cases defined in Table (14)

are presented in Figure (21). Again, the circumferential uniform nature of the engine face distorFk

2

------ ≤ 0.015

k

Y M α,

1

N M

-------- 1

Nα

------- 1

5

-- Fk

2

------    

i j , k 1=

5

∑

j 1=

Nα

∑

i 1=

N M

= ∑

N M

Nα

DC60 0.10 ≤

Fk

2

------ ≤ 0.015

NASA/TM—2002-212000 16
tion patterns over the range of inlet throat Mach numbers from 0.30 to 0.70 and inlet angles-ofincidences from 0.0o to 20.0o can clearly be seen in Figure (21).

The near wall streamlines for the baseline inlet solution and “Optimal Robust”

Maximum HCF Life Expectancy installation design at a throat Mach number of 0.70 and inlet

angle-of-incidence of α = 20.0o are presented in Figure (22a) and (22b) respectively. Again,

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 (21).

Comparison of the Optimal Robust Installation Designs

Comparison of the performance of the three “Optimal Robust” installation designs,

i.e. the Maximum Performance, Maximum Engine Stability, and Maximum HCF Life Expectancy

mission designs, are shown in Figures (23) through (25) at a throat Mach number of 0.70 and an

inlet angle-of-incidence of 20.0o

. These figures also include the baseline inlet performance, i.e.

the performance of the redsigned M2129 inlet S-duct without flow control. The low strength

effector units used in these designs achieved a substantial improvement in inlet total pressure

recovery (PFAVE) over the baseline performance. See Figure (23). This differs from the performance of the high strength effector units which never increased the inlet total pressure recovery

above the baseline value(4). Excellent engine face distortion characteristics were also achieved

with the low strength effector units as shown in Figure (24). Although very low engine face distortion was also achieved with the high strength effector units(4), the overall installation reductions

were substantially greater than the present designs. Presented in Figure (25) is a comparison of

the first five Fourier harmonic 1/2-amplitudes for the three “Optimal Robust” installation designs

with the baseline inlet characteristics. Minimizing the mean of the first five Fourier harmonic 1/2-

amplitudes resulted in a substantial reduction in the amplitudes of the first three harmonics 1/2-

amplitudes, and very low amplitudes for the fourth and fifth harmonic components.

By visually comparing the performance of the three “Optimal Robust” installations designs presented in Figures (23) through (25), it is obvious that they are remarkably similar.

This similarity can be established objectively by a statistical comparison between the optimal

CFD performance validations presented in Tables (11), (13) and (15). Since each of the nine CFD

validation cases listed in these tables was run at the same conditions of throat Mach number and

inlet angle-of-incidence, they represent a blocked set of results.

A comparison can be made between the mean or average values of two response

variables, from the i-th data set and for the j-th data set using the t-statistic

 (20)

Here the pooled standard deviation for the two sets of data is calculated from the equation:

Yi Y j

t∗

Yi – Y j

Sp

1

Ni

----- 1

N j

+ ------    

1

2

--

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

NASA/TM—2002-212000 17
 (21)

assuming and are not significantly different base on the F-test. The two standard deviations

used in equation (21) are calculated as follows:

 (22)

and

 (23)

The F-test is based on the ratio and .

Comparison between the standard deviation from data set (i) with the standard

deviation from data set (j) can be made through the expression:

 (24)

where is the larger standard deviation from either data set (i) or (j), and is the

smaller standard deviation from either data set (i) or (j). The standard deviation from the i-th

data set is not statistically different from the standard deviation from the j-th data set at the

95% confidence level if the relationship

 (25)

holds. Likewise, the standard deviation from the i-th data set is statistically different from the

standard deviation from the j-th data set at the 95% confidence level if the relationship

 (26)

Sp

Ni ( ) 1– Si

2 N j 1 )S j2

+ ( ) –

Ni ( ) 1– N j + ( ) 1– ------------------------------------------------------------=

Si

2 S j2

Si

Yi k, – Yi ( )2

k 1=

Ni

∑

Ni 1– = --------------------------------------

j

Y j k, – Y j ( )2

k 1=

Ni

∑

Ni 1– = ---------------------------------------

Si

2 S j2

F∗

Sl er arg

2

Ssmaller

2 ------------------=

Sl er arg Ssmaller

Si

S j

F∗ F 0.975 νi ν j < ( ) , ,

Si

S j

F∗ F 0.975 νi ν j > ( ) , ,

NASA/TM—2002-212000 18

S
is true. In equations (25) and (26), is the 95% percentile of the standard F-distribution F-value with degrees of freedom in the numerator and degrees of freedom in the

dominator. The degrees of freedom from the i-th data set is given by:

 (27)

while the degrees of freedom from the j-th data set is given by:

 (28)

When the difference between the minimum value of the response variable and the

maximum value of the response variable in a DOE is a decade or greater, there often exist a linear

relationship between the mean response and the standard deviation. Under this condition, the logarithm of the response will stabilize the variation over the range of the response. Because this was

the case with DC60 and the Fourier harmonic 1/2-amplitudes over the DOE variable space, the

natural logarithm of the response variable was used in the DOE analysis and in this analysis of

means. However, the inlet total pressure recovery (PFAVE) was not transformed in the DOE analysis and hence was not transformed in this evaluation of means.

Therefore, a direct statistical comparison can be made between the mean values of

the response and of two data set (i) and (j) which have been transformed using a

natural logarithmic function by the t-statistic:

 (29)

where is the number of values in data set (i), the number of values data set (j), and is the

“pooled” standard deviation defined by the relationship:

 (30)

and mean of the transformed response variable for the i-th data set is given by:

 (31)

while the mean of the transformed response variable for the j-th data set is determined from the

expression:

F 0.975 νi ν j ( ) , ,

νi ν j

νi Ni = ( ) 1–

ν j N j = ( ) 1–

Yi ln( ) Y j ln( )

t∗

Yi ln( ) Y j ln– ( )

Sp

1

Ni

----- 1

N j

+ ------    

1

2

--

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

Ni N j Sp

Sp

Ni ( ) 1– Si

2 N j 1 )S j2

+ ( ) –

Ni ( ) 1– N j + ( ) 1– ------------------------------------------------------------=

Yi ln( ) 1

Ni

----- Yi k, ln( )

k 1=

Ni

= ∑

NASA/TM—2002-212000 19
 (32)

The standard deviation from the i-th data set can be determined from the equation:

 (33)

while the standard deviation from the j-th data set can be computed from the equation:

 (34)

where and are obtained from equations (31) and (32).

In comparing the mean values from two data sets (i) and (j), if the expression

 (35)

is valid, the response values from the i-th data set are not statistically different from the response

values from the j-th data at the 95% confidence level. Likewise, the response values from the i-th

data set are statistically different from the response values from the j-th data set at the 95% confidence level if the expression

 (36)

holds. The term is the “pooled” degrees of freedom given by the expression:

 (37)

and is the is the 95% confidence t-value for degrees of freedom.

The results of the t-tests for the comparison of the means and F-tests for comparison of the standard deviations based on the CFD validation cases presented in Tables (11), (13)

and (15) are shown in Tables (16) through (21). The evaluations presented in Tables (16) through

(21) have been organized as three sets of comparisons for mean and standard deviations of two

“Optimal Robust” mission installation designs. In the first comparison, the mean and standard

deviations between the Maximum Performance (data set 1) and Maximum Engine Stability (data

Y j ln( ) 1

N j

------ Y j k, ln( )

k 1=

N j

= ∑

Si

Yi k, ln( ) Yi ( ) ln– ( )

2

k 1=

Ni

∑

Ni 1– = -----------------------------------------------------------

S j

Y j k, ln( ) Y j ( ) ln– ( ) 2

k 1=

N j

∑

N j 1– = ------------------------------------------------------------

Yi ln( ) Y j ln( )

t∗ t 0.975 νp < ( ) ,

t∗ t 0.975 νp > ( ) ,

νp

νp Ni ( ) 1– N j += ( ) 1–

t 0.975 νp () ν , p

NASA/TM—2002-212000 20
set 2) mission cases are evaluated for eight response variables. This comparison is presented in

Tables (16) and (17). In the second comparison set, the mean and standard deviations between the

Maximum Performance (data set 1) and Maximum HCF Life Expectancy (data set 3) mission

cases are evaluated, again for the same eight response variables. This comparison is presented in

Tables (18) and (19). Tables (20) and (21) present the results for the third set of comparisons, i.e.

between the mean and standard deviations of the Maximum Engine Stability (data set 2) and

Maximum HCF Life Expectancy (data set 3) mission cases for the same eight response variables.

The eight response variables evaluated were the inlet total pressure recover (PFAVE), the engine

face distortion (DC60), the first five Fourier harmonic 1/2-amplitudes of distortion (F1/2,F2/2, F3/

2,F4/2,F5/2), and the mean of the first five Fourier harmonic 1/2-amplitudes of distortion (FM/2).

The results of this study indicated that there were no statistical significant differences between the

three sets of CFD validations cases presented in Tables (11), (13), and (15) at the 95% confidence

level. Even though there are differences in the factor variables that define the “Optimal Robust”

installation designs, these factor differences did not translate into statistically significant inlet performance differences over the range of throat Mach Numbers from 0.30 to 0.70 and inlet angle-ofincidences from 0o to 20.0o.

Although the three “Optimal Robust” installation designs were generated from

three very different mission strategies, the performance achieved by these installation designs

were not statistically significantly different over the entire mission variable range. Hence one can

draw overall conclusions with regard to the micro-scale secondary flow control installation

design. Since the common dominator in each of the “Optimal Robust” installation designs was

that the engine face circumferential distortion in each case were all driven to near zero, one can

conclude that this condition represents the most robust operating state of the inlet. In other words,

the inlet is most tolerant to mission variable disturbances when there is no circumferential distortion. Although there is no established correlation between circumferential distortion and any of

the Fourier harmonics 1/2-amplitudes, minimizing the mean of the first five Fourier harmonic 1/2-

amplitudes of distortion results in driving the circumferential distortion to near zero. Likewise,

one can also conclude that the inlet achieves its highest total pressure recovery when the circumferential distortion is also driven to zero, even though there is no established correlation between

total pressure recovery and circumferential distortion. The near zero engine face circumferential

distortion was provided by the three “Optimal Robust” micro-scale secondary flow installation

designs over the entire mission variable range. The “Optimal Robust” installation designs also

provide essentially the same performance as the “Optimal Adaptive” over the same mission variable range.

Statistical Comparison of CFD Analysis and DOE Predictions

Extensive CFD validation cases were included in this study and these are presented

in Tables (11), (13) and (15). There are a total of 27 CFD validation cases. They represent the

three “Optimal Robust” installation designs determined by the “Lower Order” Robust design

methodology(4). 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” installaNASA/TM—2002-212000 21
tion designs satisfied the design requirements over the entire mission variable range. In order to

validate the DOE performance prediction procedure, three cases from each of the set of CFD performance validation cases were chosen for statistical comparison with the DOE predictions.

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:

 (38)

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.

As previously discussed, when there exist a functional relationship between the mean values and

standard deviation of the data, the data set does not satisfy the requirement of a normally distributed set. Under this condition, 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, the analysis

of means and variances described in the previous section, and in this evaluation of the DOE

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:

 (39)

must hold. Likewise, if the expression

 (40)

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. For each “Optimal Robust” installation design, the statistical comparisons were made using the diagonal three cases in each set listed in Tables (11),

(13) and (15).

Tables (19) through (21) show the results of this statistical comparison over the

range of throat Mach Numbers from 0.30 to 0.70 and inlet angle-of-incidences from 0o to 20.0o

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

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—2002-212000 22
small to be of practical significance 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 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

and for conceptual studies on the inlet-engine control system design.

CONCLUSIONS

The fundamental importance of Genichi Taguchi’s contribution to RSM over

traditional design approaches lies in the idea that process and product sensitivity to their

environment can be incorporated into the optimal statistical Design-of-Experiment and subsequent

analysis of the data. The Taguchi noise factors that cause variability in industrial design are often

the environmental variables, such as temperature and humidity, properties of the material, and

product aging. In aerodynamic design, the Taguchi noise factors can be identified with the mission

variables, since they produce variation from the design condition. Being able to include the mission

variables directly into the inlet design process represents a major breakthrough in the area of

aerodynamic design of inlets. 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 a significant run size savings over a traditional Taguchi approach,

i.e. 27 CFD experiments as compared to 45 CFD experiments. The combined array DOE format,

in which the factor (design) variables are included with the environmental (mission) variables,

allows for conceptual studies to me made on the inlet-engine control system to determine the most

efficient and cost effective system prior to any experimentation. These conceptual studies on the

inlet-engine control system can not be made using Taguchi’s Robust Parameter Design

methodology.

To illustrate the potential of economical Robust Design methodology, three different

mission strategies were considered for the subject inlet, namely (1) Maximum Performance, (2)

Maximum Engine Stability, 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 (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 amplitudes of Fk/2 < 0.015. For each

of these missions strategies, an “Optimal Robust” (open loop control) and an “Optimal Adaptive”

(closed loop control) installation were designed over an inlet throat Mach number range from 0.30

to 0.70, and angle-of-incidence range from 0.0o to 20.0o

. 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

NASA/TM—2002-212000 23
design parameters at each throat Mach number and 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, that “Optimal

Robust” open loop installation designs can be very competitive with “Optimal Adaptive” close

loop designs.

Effective inlet flow control management of engine face distortion was achieved by

reducing the unit strength of the micro-vane effector and allowing the installation design to influence the inlet flow over an extended streamwise distance by substantially increasing the microvane chord length. With this combination, the total pressure losses associated with micro-vane

effectors became very small, and a large overall performance gain achieved. In addition, this study

demonstrated that optimal “low unit strength” micro-effector installation designs exhibited the

same robustness properties as optimal “high unit strength” micro-effector installation, but without

the large total pressure loss. The design strategy of replacing “high unit strength” micro-effectors

with “low unit strength” micro-effectors which influence the flow over an extended streamwise

distance was therefore found to be very effective.

NASA/TM—2002-212000 24
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., “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., “Optimal Micro-Scale Secondary Flow Control for the Management of HCF and Distortion in Compact Inlet Diffusers”, Proposed NASA TM, 2001.

(6) 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.

(7) AGARD FTP Working Group 13, “Air Intakes for High Speed Vehicles”, AR-270, September

1991.

(8) 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.

(9) Goldsmith, E. L. and Seddon, J. (eds), “Practical Intake Aerodynamics,” Blackwell Scientific

Publications, Oxford, 1993.

(10) 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.

(11) 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.

(12) Ludwig, G. R., “Aeroelastic Considerations in the Measurement of Inlet Distortion”, 3rd

National Turbine Engine High Cycle Fatigue Conference, 1998.

NASA/TM—2002-212000 25
(13) 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.

(14) Goldsmith, E. L., and Seddon, J. (eds), “Practical Intake Aerodynamics,” Blackwell Scientific

Publications, Oxford, 1993.

NASA/TM—2002-212000 26
(a) Baseline Inlet S-Duct Geometry

Figure (1): Geometry and computational grid for redesigned M2129 inlet S-duct.

α

Engine Face (AIP) Station

(b) Baseline Inlet S-Duct Computational Grid

Inlet Throat Station

NASA/TM—2002-212000 27
Table (1): CFD validation cases for the baseline inlet S-duct.

Table (2): Engine face performance results for the baseline inlet S-duct.

Config. Mt α (degs)

nvg301 0.30 0.0

nvg302 0.70 0.0

nvg303 0.30 20.0

nvg304 0.70 20.0

nvg305 0.30 10.0

nvg306 0.70 10.0

nvg307 0.50 0.0

nvg308 0.50 20.0

nvg309 0.50 10.0

Config. PFAVE DC(60) F1/2 F2/2 F3/2 F4/2 F5/2

nvg301 0.99366 0.34109 0.00569 0.00577 0.00451 0.00294 0.00139

nvg302 0.96723 0.45485 0.03589 0.02951 0.01708 0.00498 0.00350

nvg303 0.98949 0.38795 0.00854 0.00747 0.00486 0.00227 0.00049

nvg304 0.95275 0.49219 0.04828 0.03409 0.01384 0.00154 0.00679

nvg305 0.99261 0.35889 0.00710 0.00677 0.00492 0.00270 0.00077

nvg306 0.96439 0.46496 0.03799 0.03052 0.01661 0.00399 0.00430

nvg307 0.98617 0.36363 0.01456 0.01363 0.01015 0.00553 0.00158

nvg308 0.97888 0.42716 0.01968 0.01668 0.01007 0.00379 0.00119

nvg309 0.98400 0.39474 0.01636 0.01490 0.01035 0.00498 0.00105

NASA/TM—2002-212000 28
Figure (2): Near wall streamline traces in the baseline inlet S-duct.

(a) Baseline Condition, Mt = 0.30, α = 0.0o

(b) Baseline Condition, Mt = 0.50, α = 10.0o

(c) Baseline Condition, Mt = 0.70, α = 20.0o

NASA/TM—2002-212000 29
Figure (3): Engine face total pressure recovery contours for the baseline inlet

S-duct over the mission variable range.

(a) Mt = 0.30, α = 0.0o (b) Mt = 0.30, α = 10.0o (c) Mt = 0.30, α = 20.0o

(d) Mt = 0.50, α = 0.0o (e) Mt = 0.50, α = 10.0o (f) Mt = 0.50, α = 20.0o

(g) Mt = 0.70, α = 0.0o (h) Mt = 0.70, α = 10.0o (i) Mt = 0.70, α = 20.0o

NASA/TM—2002-212000 30
Figure (4): Effect of inlet throat Mach number on the engine face total

pressure recovery, baseline inlet S-duct, α = 0.0o

.

Figure (5): Effect of inlet angle-of-incidence on engine face total pressure

recovery, baseline inlet S-duct, Mt = 0.70.

NASA/TM—2002-212000 31
Figure (6): Effect of inlet throat Mach number on the engine face DC60

distortion, baseline inlet S-duct, α = 0.0o.

Figure (7): Effect of inlet angle-of-incidence on engine face DC60 distortion, baseline inlet S-duct, Mt = 0.70.

NASA/TM—2002-212000 32
Figure (8): Effect of inlet throat Mach number on the Fourier harmonic

1/2-amplitudes of engine face distortion, baseline inlet S-duct, α = 0.0o

.

Figure (9): Effect of inlet angle-of-incidence on the Fourier harmonic 1/2-

amplitudes of engine face distortion, baseline inlet S-duct, Mt = 0.70.

NASA/TM—2002-212000 33
Figure (10): Location of effector region within inlet S-duct configuration.

Figure (11): Micro-vane arrangement within inlet S-duct effector region.

Effector Region

NASA/TM—2002-212000 34
Table (3): Factor variables which establish the DOE design matrix.

Table (4): Variables held constant.

Table (5): DOE response variables.

Factor Range

Number of Vane Effectors, n 13 to 27

Effector Vane Height (mm), h 1.0 to 2.0

Effector Chord Length (mm), c 36.0 to 72.0

Inlet Throat Mach Number, Mt 0.30 to 0.70

Inlet Angle-of-Incidence (degs.), α 0.0 to 20.0

Variable Value

Effector Vane Thickness (mm), t 0.138

Vane Angle-of-Incidence (degs), β 5.0

Inlet Total Pressure (lbs/ft2

), Pt 10506.0

Inlet Total Temperature (oR), Tt 517.0

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

NASA/TM—2002-212000 35
Table (6): “Lower Order” Central Composite Face-Centered (CCF) combined array

DOE format involving factor (design) variables and environmental (mission) variables.

Config. n h c Mt α

nvg701 13 1.0 36.0 0.30 20.0

nvg702 27 1.0 36.0 0.30 0.0

nvg703 13 2.0 36.0 0.30 0.0

nvg704 27 2.0 36.0 0.30 20.0

nvg705 13 1.0 72.0 0.30 0.0

nvg706 27 1.0 72.0 0.30 20.0

nvg707 13 2.0 72.0 0.30 20.0

nvg708 27 2.0 72.0 0.30 0.0

nvg709 13 1.0 36.0 0.70 0.0

nvg710 27 1.0 36.0 0.70 20.0

nvg711 13 2.0 36.0 0.70 20.0

nvg712 27 2.0 36.0 0.70 0.0

nvg713 13 1.0 72.0 0.70 20.0

nvg714 27 1.0 72.0 0.70 0.0

nvg715 13 2.0 72.0 0.70 0.0

nvg716 27 2.0 72.0 0.70 20.0

nvg717 13 1.5 54.0 0.50 10.0

nvg718 27 1.5 54.0 0.50 10.0

nvg719 20 1.0 54.0 0.50 10.0

nvg720 20 2.0 54.0 0.50 10.0

nvg721 20 1.5 36.0 0.50 10.0

nvg722 20 1.5 72.0 0.50 10.0

nvg723 20 1.5 54.0 0.30 10.0

nvg724 20 1.5 54.0 0.70 10.0

nvg725 20 1.5 54.0 0.50 0.0

nvg726 20 1.5 54.0 0.50 20.0

nvg727 20 1.5 54.0 0.50 10.0

NASA/TM—2002-212000 36
Figure (12): Graphical representation of the “Lower Order” Central Composite Face-Centered (CCF) combined array DOE format involving factor

(design) variables and environmental (mission) variables.

n n n

n n n

n n n

Mt=0.30

Mt=0.50

Mt=0.70

α=0.0o α=10.0o α=20.0o

c c c

c c c

c c c

h h h

h h h

hh h

NASA/TM—2002-212000 37
Table (7): Radial weighting coefficients applied to the total pressure rake measurements.

Figure (13): Total pressure and distortion measurement arrays.

Table (8): Fourier Harmonic 1/2-amplitude F-test compliance

Ring Number Radial Weighting Coefficient

1 0.05651

2 0.14248

3 0.21077

4 0.26918

5 0.32106

Response Nomenclature S2

max/S2min t(0.95,9,9)

1st Harmonic 1/2-Amplitude F1/2 1939.9 4.03

2nd Harmonic 1/2-Amplitude F2/2 391.6 4.03

3rd Harmonic 1/2-Amplitude F3/2 1681.0 4.03

4th Harmonic 1/2-Amplitude F4/2 153.9 4.03

5th Harmonic 1/2-Amplitude F5/2 292.3 4.03

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

NASA/TM—2002-212000 38
Table (9): Engine face performance results for the Central Composite Face-Centered

(CCF) combined array DOE format involving design (factor) variables and mission

(environmental) variables.

Config. PFAVE DC(60) F1/2 F2/2 F3/2 F4/2 F5/2

nvg701 0.98892 0.07588 0.00067 0.00263 0.00107 0.00052 0.00052

nvg702 0.99460 0.03610 0.00279 0.00155 0.00176 0.00025 0.00022

nvg703 0.99451 0.04464 0.00345 0.00182 0.00140 0.00048 0.00039

nvg704 0.99053 0.03336 0.00320 0.00230 0.00201 0.00077 0.00085

nvg705 0.99498 0.03660 0.00282 0.00152 0.00143 0.00040 0.00012

nvg706 0.99072 0.03273 0.00293 0.00180 0.00200 0.00057 0.00035

nvg707 0.99138 0.04374 0.00369 0.00195 0.00128 0.00073 0.00053

nvg708 0.99489 0.07689 0.00594 0.00286 0.00122 0.00020 0.00065

nvg709 0.97405 0.19080 0.01753 0.01474 0.00622 0.00085 0.00386

nvg710 0.96183 0.24010 0.02856 0.01960 0.00421 0.00442 0.00613

nvg711 0.96431 0.20937 0.02096 0.01503 0.00553 0.00039 0.00423

nvg712 0.97633 0.04567 0.00412 0.01193 0.00858 0.00240 0.00339

nvg713 0.96250 0.27487 0.02827 0.02212 0.00933 0.00043 0.00413

nvg714 0.97727 0.05010 0.00034 0.00910 0.01055 0.00322 0.00121‘

nvg715 0.97850 0.02916 0.00492 0.00842 0.00572 0.00352 0.00288

nvg716 0.96591 0.04687 0.00581 0.00303 0.00606 0.00484 0.00701

nvg717 0.98674 0.01487 0.00148 0.00242 0.00285 0.00147 0.00098

nvg718 0.98665 0.03322 0.00485 0.00539 0.00441 0.00095 0.00121

nvg719 0.98636 0.02689 0.00097 0.00243 0.00429 0.00201 0.00040

nvg720 0.98646 0.03927 0.00643 0.00581 0.00309 0.00072 0.00138

nvg721 0.98647 0.02511 0.00232 0.00371 0.00392 0.00108 0.00047

nvg722 0.98703 0.03559 0.00580 0.00538 0.00340 0.00057 0.00107

nvg723 0.99309 0.04708 0.00391 0.00228 0.00150 0.00028 0.00037

nvg724 0.97462 0.04156 0.00031 0.00891 0.00843 0.00257 0.00172

nvg725 0.98807 0.03531 0.00503 0.00536 0.00358 0.00060 0.00069

nvg726 0.98277 0.02139 0.00138 0.00305 0.00355 0.00131 0.00100

nvg727 0.98684 0.02975 0.00416 0.00478 0.00374 0.00085 0.00073

NASA/TM—2002-212000 39
Figure (14): Comparison of “Optimal Robust” and “Optimal

Adaptive” Maximum Performance inlet mission 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 (degs.), α

Engine Face Recovery, PFAVE

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

Engine Face Distortion, DC60

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

NASA/TM—2002-212000 40
Figure (14): Comparison of “Optimal Robust” and “Optimal Adaptive” Maximum Performance inlet mission installation designs, continued.

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 (degs.), α

1st Harmonic 1/2 Amplitide, F1/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

2nd Harmonic 1/2 Amplitide, F2/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

3rd Harmonic 1/2 Amplitide, F3/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

4th Harmonic 1/2 Amplitide, F4/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

5th Harmonic 1/2 Amplitide, F5/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

Mean Harmonic 1/2 Amplitide, FM/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

NASA/TM—2002-212000 41
Table (10): “Optimal Robust” Maximum Performance inlet mission CFD validation

cases.

Table (11): “Optimal Robust” Maximum Performance inlet mission CFD validation

results.

Config. n h c Mt α

nvg728 22 1.95 72.0 0.70 0.0

nvg729 22 1.95 72.0 0.70 10.0

nvg730 22 1.95 72.0 0.70 20.0

nvg731 22 1.95 72.0 0.50 0.0

nvg732 22 1.95 72.0 0.50 10.0

nvg733 22 1.95 72.0 0.50 20.0

nvg734 22 1.95 72.0 0.30 0.0

nvg735 22 1.95 72.0 0.30 10.0

nvg736 22 1.95 72.0 0.30 20.0

Config. PFAVE DC(60) F1/2 F2/2 F3/2 F4/2 F5/2

nvg728 0.97803 0.04904 0.01070 0.01262 0.00543 0.00104 0.00289

nvg729 0.97585 0.02144 0.00289 0.00392 0.00383 0.00200 0.00194

nvg730 0.96629 0.04842 0.00634 0.00190 0.00431 0.00473 0.00777

nvg731 0.98835 0.04936 0.00867 0.00629 0.00295 0.00057 0.00124

nvg732 0.98722 0.04412 0.00804 0.00610 0.00329 0.00080 0.00129

nvg733 0.98304 0.02739 0.00533 0.00502 0.00374 0.00168 0.00201

nvg734 0.99432 0.07512 0.00587 0.00288 0.00117 0.00030 0.00066

nvg735 0.99337 0.07170 0.00566 0.00275 0.00134 0.00034 0.00061

nvg736 0.99081 0.05397 0.00468 0.00250 0.00154 0.00054 0.00068

NASA/TM—2002-212000 42
Figure (15): Engine face total pressure recovery contours for the “Optimal

Robust” Maximum Performance inlet mission installation CFD solutions.

(a) Mt = 0.30, α = 0.0o (b) Mt = 0.30, α = 10.0o (c) Mt = 0.30, α = 20.0o

(d) Mt = 0.50, α = 0.0o (e) Mt = 0.50, α = 10.0o (f) Mt = 0.50, α = 20.0o

(g) Mt = 0.70, α = 0.0o (h) Mt = 0.70, α = 10.0o (i) Mt = 0.70, α = 20.0o

NASA/TM—2002-212000 43
Figure (16): Comparison of near wall streamlines for baseline and

“Optimal Robust” Maximum Performance installation CFD solution,

Mt = 0.30, α = 0.0o.

(a) Baseline Inlet Solution

(b) Optimal Robust “Maximum Performance” solution

NASA/TM—2002-212000 44
Figure (17): Comparison of “Optimal Robust” and “Optimal

Adaptive” Maximum Engine Stability inlet mission 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 (degs.), α

Engine Face Recovery, PFAVE

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

Engine Face Distortion, DC60

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

NASA/TM—2002-212000 45
Figure (17): Comparison of “Optimal Robust” and “Optimal Adaptive” Maximum Engine Stability inlet mission installation designs, continued.

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 (degs.), α

1st Harmonic 1/2 Amplitide, F1/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

2nd Harmonic 1/2 Amplitide, F2/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

3rd Harmonic 1/2 Amplitide, F3/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

4th Harmonic 1/2 Amplitide, F4/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

5th Harmonic 1/2 Amplitide, F5/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

Mean Harmonic 1/2 Amplitide, FM/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

NASA/TM—2002-212000 46
Table (12): “Optimal Robust” Maximum Engine Stability inlet mission CFD validation cases.

Table (13): “Optimal Robust” Maximum Engine Stability inlet mission CFD validation results.

Config. n h c Mt α

nvg737 24 2.0 70.2 0.70 0.0

nvg738 24 2.0 70.2 0.70 10.0

nvg739 24 2.0 70.2 0.70 20.0

nvg740 24 2.0 70.2 0.50 0.0

nvg741 24 2.0 70.2 0.50 10.0

nvg742 24 2.0 70.2 0.50 20.0

nvg743 24 2.0 70.2 0.30 0.0

nvg744 24 2.0 70.2 0.30 10.0

nvg745 24 2.0 70.2 0.30 20.0

Config. PFAVE DC(60) F1/2 F2/2 F3/2 F4/2 F5/2

nvg737 0.97784 0.05082 0.01110 0.01303 0.00570 0.00074 0.00287

nvg738 0.97576 0.04369 0.00896 0.01219 0.00648 0.00149 0.00328

nvg739 0.96619 0.04643 0.00571 0.00304 0.00557 0.00491 0.00738

nvg740 0.98835 0.05149 0.00899 0.00638 0.00290 0.00030 0.00124

nvg741 0.98722 0.04643 0.00835 0.00623 0.00326 0.00052 0.00129

nvg742 0.98305 0.03018 0.00575 0.00537 0.00387 0.00135 0.00177

nvg743 0.99871 0.07797 0.00603 0.00208 0.00114 0.00017 0.00065

nvg744 0.99337 0.07384 0.00583 0.00278 0.00129 0.00020 0.00061

nvg745 0.99081 0.05620 0.00486 0.00258 0.00154 0.00041 0.00063

NASA/TM—2002-212000 47
Figure (18): Engine face total pressure recovery contours for the “Optimal

Robust” Maximum Engine Stability inlet mission installation CFD solutions.

(a) Mt = 0.30, α = 0.0o (b) Mt = 0.30, α = 10.0o (c) Mt = 0.30, α = 20.0o

(d) Mt = 0.50, α = 0.0o (e) Mt = 0.50, α = 10.0o (f) Mt = 0.50, α = 20.0o

(g) Mt = 0.70, α = 0.0o (h) Mt = 0.70, α = 10.0o (i) Mt = 0.70, α = 20.0o

NASA/TM—2002-212000 48
Figure (19): Comparison of near wall streamlines for baseline and

“Optimal Robust” Maximum Engine Stability installation CFD solutions, Mt = 0.50, α = 10.0o

.

(a) Baseline Inlet Solution

(b) Optimal Robust “Maximum Engine Stability”solution

NASA/TM—2002-212000 49
Figure (20): Comparison of “Optimal Robust” and “Optimal

Adaptive” Maximum HCF Life Expectancy inlet mission 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 (degs.), α

Engine Face Recovery, PFAVE

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

Engine Face Distortion, DC60

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

NASA/TM—2002-212000 50
Figure (20): Comparison of “Optimal Robust” and “Optimal Adaptive” Maximum HCF Life Expectancy inlet mission installation designs, continued.

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 (degs.), α

1st Harmonic 1/2 Amplitide, F1/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

2nd Harmonic 1/2 Amplitide, F2/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

3rd Harmonic 1/2 Amplitide, F3/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

4th Harmonic 1/2 Amplitide, F4/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

5th Harmonic 1/2 Amplitide, F5/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

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 (degs.), α

Mean Harmonic 1/2 Amplitide, FM/2

Baseline Perf., Mt = 0.70

Optimal Robust, Mt = 0.30

Optimal Robust, Mt = 0.50

Optimal Robust, Mt = 0.70

Optimal Adaptive, Mt = 0.30

Optimal Adaptive, Mt = 0.50

Optimal Adaptive, Mt = 0.70

NASA/TM—2002-212000 51
Table (14): “Optimal Robust” Maximum HCF Life Expectancy inlet mission CFD

validation cases.

Table (15): “Optimal Robust” Maximum HCF Life Expectancy inlet mission CFD

validation results.

Config. n h c Mt α

nvg746 19 1.70 63.0 0.70 0.0

nvg747 19 1.70 63.0 0.70 10.0

nvg748 19 1.70 63.0 0.70 20.0

nvg749 19 1.70 63.0 0.50 0.0

nvg750 19 1.70 63.0 0.50 10.0

nvg751 19 1.70 63.0 0.50 20.0

nvg752 19 1.70 63.0 0.30 0.0

nvg753 19 1.70 63.0 0.30 10.0

nvg754 19 1.70 63.0 0.30 20.0

Config. PFAVE DC(60) F1/2 F2/2 F3/2 F4/2 F5/2

nvg746 0.97813 0.04366 0.00631 0.01173 0.00647 0.00124 0.00238

nvg747 0.97585 0.03636 0.00374 0.01040 0.00688 0.00204 0.00290

nvg748 0.96591 0.07454 0.01207 0.00299 0.00231 0.00331 0.00586

nvg749 0.98864 0.03958 0.00653 0.00588 0.00355 0.00097 0.00119

nvg750 0.98740 0.03481 0.00589 0.00555 0.00376 0.00121 0.00126

nvg751 0.98323 0.02144 0.00289 0.00392 0.00383 0.00200 0.00194

nvg752 0.99470 0.06192 0.00490 0.00279 0.00148 0.00048 0.00061

nvg753 0.99356 0.05861 0.00469 0.00262 0.00162 0.00055 0.00058

nvg754 0.99091 0.04134 0.00365 0.00224 0.00174 0.00071 0.00063

NASA/TM—2002-212000 52
Figure (21): Engine face total pressure recovery contours for the “Optimal

Robust” Maximum HCF Life Expectancy inlet mission installation CFD solutions.

(a) Mt = 0.30, α = 0.0o (b) Mt = 0.30, α = 10.0o (c) Mt = 0.30, α = 20.0o

(d) Mt = 0.50, α = 0.0o (e) Mt = 0.50, α = 10.0o (f) Mt = 0.50, α = 20.0o

(g) Mt = 0.70, α = 0.0o (h) Mt = 0.70, α = 10.0o (i) Mt = 0.70, α = 20.0o

NASA/TM—2002-212000 53
Figure (22): Comparison of near wall streamlines for baseline and

“Optimal Robust” Maximum HCF Life Expectancy installation CFD

solutions, Mt = 0.70, α = 20.0o.

(a) Baseline Inlet Solution

(b) “Optimal Robust” Maximum HCF Life Expectancy solution

NASA/TM—2002-212000 54
Figure (23): Effect of “Optimal Robust” installation designs on total pressure recovery, Mt = 0.70, α = 20.0o

.

Figure (24): Effect of “Optimal Robust” installation designs on engine face

DC60 distortion, Mt = 0.70, α = 20.0o.

NASA/TM—2002-212000 55
Figure (25): Effect of “Optimal Robust” installation designs on the Fourier

harmonic 1/2-amplitudes of engine face distortion, Mt = 0.70, α = 20.0o.

NASA/TM—2002-212000 56
Table (16): Statistical comparison of the mean between “Optimal Robust” Maximum

Performance (data set 1) and Maximum Engine Stability (data set 2) installation

CFD results.

Table (17): Statistical comparison of the standard deviation between “Optimal

Robust” Maximum Performance (data set 1) and Maximum Engine Stability (data

set 2) installation CFD results.

Response t* t(0.975,16) Comment

PFAVE 0.983311 0.984589 0.274126 2.120 Not Diff.

DC60 -3.104553 -2.972547 0.880060 2.120 Not Diff.

F1/2 -5.070342 -4.957721 0.773155 2.120 Not Diff.

F2/2 -5.423593 -5.288741 0.461401 2.120 Not Diff.

F3/2 -5.840606 -5.799162 0.144458 2.120 Not Diff.

F4/2 -6.940625 -7.367960 0.867452 2.120 Not Diff.

F5/2 -6.403719 -6.475028 0.177812 2.120 Not Diff.

FM/2 -5.644880 -5.604631 0.191506 2.120 Not Diff.

Response S1 S2 F* F(0.975,8,8) Comment

PFAVE 0.009538 0.010004 1.048857 4.43 Not Diff.

DC60 0.430507 0.283570 1.386064 4.43 Not Diff.

F1/2 0.395277 0.281970 1.401939 4.43 Not Diff.

F2/2 0.595343 0.628281 1.139752 4.43 Not Diff.

F3/2 0.551444 0.628052 1.138923 4.43 Not Diff.

F4/2 0.936279 1.082130 1.155777 4.43 Not Diff.

F5/2 0.823936 0.859715 1.043424 4.43 Not Diff.

FM/2 0.386132 0.466342 1.207726 4.43 Not Diff.

Y1 ln( ) Y2 ln( )

NASA/TM—2002-212000 57
Table (18): Statistical comparison of the mean between “Optimal Robust” Maximum

Performance (data set 1) and Maximum HCF Life Expectancy (data set 3) installation CFD results.

Table (19): Statistical comparison of the standard deviation between “Optimal

Robust” Maximum Performance (data set 1) and Maximum HCF Life Expectancy

(data set 3) installation CFD results.

Response t* t(0.975,16) Comment

PFAVE 0.983311 0.984249 0.209142 2.120 Not Diff.

DC60 -3.104553 -3.141833 0.219665 2.120 Not Diff.

F1/2 -5.070342 -5.264171 1.084849 2.120 Not Diff.

F2/2 -5.423593 -5.402603 0.073190 2.120 Not Diff.

F3/2 -5.840606 -5.797130 0.158285 2.120 Not Diff.

F4/2 -6.940625 -6.762864 0.437173 2.120 Not Diff.

F5/2 -6.403719 -6.544794 0.364755 2.120 Not Diff.

FM/2 -5.644880 -5.723091 0.382118 2.120 Not Diff.

Response S1 S3 F* F(0.975,8,8) Comment

PFAVE 0.009538 0.009453 1.067896 4.43 Not Diff.

DC60 0.430507 0.370320 1.123346 4.43 Not Diff.

F1/2 0.395277 0.419342 1.577729 4.43 Not Diff.

F2/2 0.595343 0.605094 1.021587 4.43 Not Diff.

F3/2 0.551444 0.576764 3.045711 4.43 Not Diff.

F4/2 0.936279 0.689089 2.133706 4.43 Not Diff.

F5/2 0.823936 0.798711 1.110372 4.43 Not Diff.

FM/2 0.386132 0.445898 1.104159 4.43 Not Diff.

Y1 ln( ) Y3 ln( )

NASA/TM—2002-212000 58
Table (20): Statistical comparison of the mean between “Optimal Robust” Maximum

Engine Stability (data set 2) and Maximum HCF Life Expectancy (data set 3) installation CFD results.

Table (21): Statistical comparison of the standard deviation between “Optimal

Robust” Maximum Engine Stability (data set 2) and Maximum HCF Life Expectancy (data set 3) installation CFD results.

Response t* t(0.975,16) Comment

PFAVE 0.984589 0.984249 0.071929 2.120 Not Diff.

DC60 -2.972547 -3.141833 1.088837 2.120 Not Diff.

F1/2 -4.957721 -5.264171 1.819320 2.120 Not Diff.

F2/2 -5.288741 -5.402603 0.391603 2.120 Not Diff.

F3/2 -5.799162 -5.797130 0.007148 2.120 Not Diff.

F4/2 -7.367960 -6.762864 1.414981 2.120 Not Diff.

F5/2 -6.475028 -6.544794 0.178357 2.120 Not Diff.

FM/2 -5.604631 -5.723091 0.550795 2.120 Not Diff.

Response S2 S3 F* F(0.975,8,8) Comment

PFAVE 0.010004 0.009453 1.120069 4.43 Not Diff.

DC60 0.283570 0.370320 1.705428 4.43 Not Diff.

F1/2 0.281970 0.419342 2.211722 4.43 Not Diff.

F2/2 0.628281 0.605094 1.186619 4.43 Not Diff.

F3/2 0.628052 0.576764 1.185756 4.43 Not Diff.

F4/2 1.082130 0.689089 2.466089 4.43 Not Diff.

F5/2 0.859715 0.798711 1.158589 4.43 Not Diff.

FM/2 0.466342 0.445898 1.093797 4.43 Not Diff.

Y2 ln( ) Y3 ln( )

NASA/TM—2002-212000 59
Table (22): Statistical comparison between CFD analysis and DOE prediction for the

“Optimal Robust” Maximum Performance mission installation design.

Response Mt α (degs) CFD DOE t t* Comments

PFAVE 0.30 0.0 0.99432 0.99522 2.10090 0.73005 Not Diff.

DC60 0.07512 0.05562 2.10090 0.54532 Not Diff.

F1/2 0.00587 0.00450 1.96942 0.55327 Not Diff.

F2/2 0.00288 0.00336 1.96917 0.28857 Not Diff.

F3/2 0.00117 0.00123 1.91931 0.83415 Not Diff.

F4/2 0.00030 0.00018 1.96935 1.30110 Not Diff.

F5/2 0.00066 0.00038 1.96917 0.88946 Not Diff.

FM/2 0.00217 0.00193 1.96924 0.34888 Not Diff.

PFAVE 0.50 10.0 0.98835 0.98803 2.10090 0.27666 Not Diff.

DC60 0.04936 0.02052 2.10090 1.73825 Not Diff.

F1/2 0.00867 0.00729 1.96942 0.39272 Not Diff.

F2/2 0.00629 0.00311 1.96917 1.33491 Not Diff.

F3/2 0.00295 0.00317 1.91931 1.47962 Not Diff.

F4/2 0.00057 0.00114 1.96935 1.72954 Not Diff.

F5/2 0.00124 0.00116 1.96917 0.10854 Not Diff.

FM/2 0.00394 0.00317 1.96924 0.77457 Not Diff.

PFAVE 0.70 20.0 0.96629 0.96575 2.10090 0.43803 Not Diff.

DC60 0.04824 0.06511 2.10090 0.54417 Not Diff.

F1/2 0.00634 0.00363 1.96942 1.32794 Not Diff.

F2/2 0.00190 0.00401 1.96917 1.41370 Not Diff.

F3/2 0.00431 0.00671 1.91931 7.28503 Diff.

F4/2 0.00473 0.00192 1.96935 2.27527 Diff.

F5/2 0.00777 0.00352 1.96917 1.26278 Not Diff.

FM/2 0.00501 0.00397 1.96924 0.50478 Not Diff.

NASA/TM—2002-212000 60
Table (23): Statistical comparison between CFD analysis and DOE prediction for the

“Optimal Robust” Maximum Engine Stability mission installation design.

Response Mt α (degs) CFD DOE t t* Comments

PFAVE 0.30 0.0 0.99871 0.99517 2.10090 2.06018 Not Diff.

DC60 0.07797 0.05595 2.10090 0.60221 Not Diff.

F1/2 0.00603 0.00507 1.96942 0.36478 Not Diff.

F2/2 0.00208 0.00360 1.96917 1.02288 Not Diff.

F3/2 0.00114 0.00127 1.91931 1.56370 Not Diff.

F4/2 0.00017 0.00016 1.96935 0.14723 Not Diff.

F5/2 0.00065 0.00046 1.96917 0.55175 Not Diff.

FM/2 0.00217 0.00211 1.96924 0.09142 Not Diff.

PFAVE 0.50 10.0 0.98835 0.98803 2.10090 0.27666 Not Diff.

DC60 0.05149 0.02049 2.10090 1.82491 Not Diff.

F1/2 0.00899 0.00764 1.96942 0.37888 Not Diff.

F2/2 0.00638 0.00309 1.96917 1.37007 Not Diff.

F3/2 0.00290 0.00319 1.91931 1.85829 Not Diff.

F4/2 0.00030 0.00132 1.96935 3.79089 Diff.

F5/2 0.00124 0.00136 1.96917 0.14981 Not Diff.

FM/2 0.00396 0.00332 1.96924 0.68769 Not Diff.

PFAVE 0.70 20.0 0.96619 0.96580 2.10090 0.31636 Not Diff.

DC60 0.04643 0.06454 2.10090 0.59760 Not Diff.

F1/2 0.00571 0.00353 1.96942 1.17945 Not Diff.

F2/2 0.00304 0.00371 1.96917 0.37769 Not Diff.

F3/2 0.00557 0.00668 1.91931 3.27779 Diff.

F4/2 0.00491 0.00277 1.96935 1.47449 Not Diff.

F5/2 0.00738 0.00399 1.96917 0.97422 Not Diff.

FM/2 0.00532 0.00413 1.96924 0.59630 Not Diff.

NASA/TM—2002-212000 61
Table (24): Statistical comparison between CFD analysis and DOE prediction for the

“Optimal Robust” Maximum HCF Life Expectancy mission installation design.

Response Mt α (degs) CFD DOE t t* Comments

PFAVE 0.30 0.0 0.99470 0.99480 2.10090 0.08472 Not Diff.

DC60 0.06192 0.05192 2.10090 0.33963 Not Diff.

F1/2 0.00490 0.00075 1.96942 4.11884 Diff.

F2/2 0.00279 0.00238 1.96917 0.30153 Not Diff.

F3/2 0.00148 0.00137 1.91931 1.34198 Not Diff.

F4/2 0.00048 0.00025 1.96935 1.62933 Not Diff.

F5/2 0.00061 0.00022 1.96917 1.61994 Not Diff.

FM/2 0.00205 0.00093 1.96924 1.62058 Not Diff.

PFAVE 0.50 10.0 0.98864 0.98738 2.10090 1.12168 Not Diff.

DC60 0.03958 0.02416 2.10090 1.01040 Not Diff.

F1/2 0.00653 0.00182 1.96942 3.18509 Diff.

F2/2 0.00588 0.00337 1.96917 1.05658 Not Diff.

F3/2 0.00355 0.00351 1.91931 0.23523 Not Diff.

F4/2 0.00097 0.00113 1.96935 0.39917 Not Diff.

F5/2 0.00199 0.00081 1.96917 1.47013 Not Diff.

FM/2 0.00362 0.00213 1.96924 1.47694 Not Diff.

PFAVE 0.70 20.0 0.96591 0.96488 2.10090 0.87609 Not Diff.

DC60 0.07454 0.09673 2.10090 0.50252 Not Diff.

F1/2 0.01207 0.00135 1.96942 5.14994 Diff.

F2/2 0.00299 0.00668 1.96917 1.52274 Not Diff.

F3/2 0.00231 0.00747 1.91931 3.54417 Diff.

F4/2 0.00331 0.00135 1.96935 1.91215 Not Diff.

F5/2 0.00586 0.00290 1.96917 1.13662 Not Diff.

FM/2 0.00531 0.00395 1.96924 0.68737 Not Diff.

NASA/TM—2002-212000 62
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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E–13672

WU–708–53–13–00

68

Management of Total Pressure Recovery, Distortion and High Cycle Fatigue in

Compact Air Vehicle Inlets

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

Aerodynamics; Propulsion; Fluid dynamics

Unclassified -Unlimited

Subject Category: 07 Distribution: Nonstandard

Bernhard H. Anderson, NASA Glenn Research Center; Henry D. Baust, Wright-Patterson Air Force Base, Dayton,

Ohio 45433; and 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 Response Surface Methods (RSM) and

Robustness Design Concepts (RDC) to arrive at micro-secondary flow control installation designs that maintain optimal

inlet performance over a range of the mission variables. These statistical design concepts were used to investigate the

robustness properties of "low unit strength" micro-effector installations. "Low unit strength" micro-effectors are

micro-vanes set at very low angles-of-incidence with very long chord lengths. They were designed to influence the near

wall inlet flow over an extended streamwise distance, and their advantage lies in low total pressure loss and high

effectiveness in managing engine face distortion.