Configuration Design of AirBreathing

1
Configuration Design of Air-Breathing Hypersonic
Vehicle Considering Fidelity Uncertainty J.
Umakant K. Sudhakar P. M. Mujumdar S.
Panneerselvam
AIAA-2004-4543 10th AIAA / ISSMO
Multidisciplinary Analysis and Optimization
Conference Albany, New York 30th August-1st
September,2004
2
OUTLINE

• Generic Representation of Multidisciplinary
  System
• Disciplinary Fidelity Uncertainty and modeling
• Hypersonic Technology Demonstrator Vehicle
  background
• Engineering Methods for Disciplinary metrics
• Multidisciplinary Design Optimization for HSTDV

3
Generic Representation of Multidisciplinary System
Z f(X, Y) X (xi, i1,2,.k) Vector of
Design Variables Y (Yi, i1,2,.m) Vector of
Disciplinary response Yi (yi1,yi2,.yin) Vector
of responses from discipline i Z (zi,
i1,2,.. p) Vector of System responses
Problem Statement
Minimize F( Z ) subject to Hi(Z) 0 i
1,2,m Gi(Z) ? 0 i 1,2,.n XL ? X ? XU
4
Fidelity Uncertainty in Multidisciplinary System
Preliminary design phase - Medium / Low
Fidelity Analysis

?Y Uncertainty due to lack of fidelity in
disciplinary response ?Z Uncertainty in system
response
Design decisions - Account for disciplinary
fidelity uncertainty on system response
5
Uncertainty Modeling - A Probabilistic Approach
Problem Statement
Maximize P( min F( Z )) subject to P(Gi(Z) ? 0) gt
?i i 1,2,.n ?i specified reliability
level XL ? X ? XU
Steps

• Assessment of Disciplinary Fidelity
• Quantification of Uncertainty Model
• Propagation of Disciplinary Uncertainty to system
  level
• Taking design decisions under uncertainty

6
Assessment of Disciplinary Fidelity Uncertainty
Assume limited high fidelity observations are
available for disciplinary responses
LFA low fidelity analysis HFA high fidelity
analysis CF correlation factor LFA /
HFA
If some CF are ? 1 and some CF are ?
1 Assume Normal Distribution If all the CF are
one sided Assume skewed distributions like
Weibull Distributions
Ref 13 Mantis
7
Quantification of Uncertainty Model
Weibull PDF
t ??
CDF F(x)
W(X) AX B where X ln(x-?) W(X)
ln(-ln(1-F(x)) A ? and B - ?ln ?
Estimate the parameters through linear
regression
Kolmogrov-Smirnov Acceptance Test dmax ? 1.63/?N
for 99 probability dmax ? Fe(x) - Fth(x) ?
8
Propagation of Disciplinary Uncertainty to System
level metric
Input Histogram

• Sample the uncertainty model and do
• Monte-Carlo Simulation
• Record the variation in system metric

Frequency
Multidisciplinary synthesis tool
?Y1i
Zi?Zi
X
AM2
AM1
Y1
Y2?Y2i
Y1?Y1i
i 1,2, N
Output Histogram
N number of simulations
Frequency
System Metric
9
Taking Design Decision under Uncertainty

• Lack of sufficient
• disciplinary fidelity
• introduces risk in
• the design.
• Compromise on the
• system performance provided the reliability
• of achieving the same
• is within acceptable
• risk level of designer.

Reliability
Cumulative Probability
System Metric
System Metric
Database for system metrics at desired
reliability level
Create Metamodel for CDF and Reliability
function - RSM - Kriging
Ref 12 De Laurentis
10
Transforming Probabilistic Optimization to
Deterministic Optimization
Meta-model for P(F) and P(G) with desired
reliability
Maximize P( min F( Z )) subject to P(Gi(Z) ? 0)
gt ?i i 1,2,.n XL ? X ? XU
Minimize F( Z ) subject to Gi(Z) ? 0 i
1,2,.n XL ? X ? XU
11
HYPERSONIC TECHNOLOGY DEMONSTRATOR VEHICLE
(HSTDV)
Cruise Conditions

• Problem Statement
• Design an Air-Breathing Hypersonic Vehicle
  capable of cruising at M6.5 and cruise altitudes
  30-35 km
• Design Constraints
• Dimensional constraints on overall length, height
  and width
• Take-off gross weight
• Intake entry conditions
• Control deflection within allowable values
• Vehicle drag to be less than thrust deliverable

12
HSTDV Discipline Interactions

• Integrated Engine and Airframe
• Entire undersurface of the airframe forms part of
  the engine

Forebody

• Propulsion
• High Static Pressure
• Large air mass flow
• capture
• Minimum total pressure
• loss
• Allowable Intake Entry
• Mach number

• Aerodynamic Heating
• Temperature to be within
• specified limits

Forebody Design

• Sizing
• Adequate volume to
• store fuel and other
• onboard equipment

• Aerodynamics
• Lift to drag
• Longitudinal Stability

13
HSTDV Vehicle Discipline
Interactions
Inputs - Fore-body Design - Intake-Combustor
Design
Aftbody
Aftbody Design
Propulsion Functions as nozzle - thrust
characteristics
Sizing -Afterbody volume
Aerodynamics -Cowl drag -Base drag
Trim -Propulsive force and moment
14
Parameterization of HSTDV Body
15
External Configuration Model
Input Variables ?1 , ?2 , ?3 , ?n_plan , ?wc
, wfac_pl , tfac_pl,
Outputs Body discretization
(x,y,z) Wing Tail discretization Internal
Volume Overall Mass (TOGW) Centers of
gravity
External Compression Model (l1,l2,l3
,h1,h2,h3)
External Configuration Model
Planar nature of the vehicles allows use of
Analytical expressions for Sizing properties like
volume, center of gravity. Empirical
correlations for TOGW.
16
Aerodynamics Model
External Configuration Model Vehicle geometry
definition (x,y,z)
Aerodynamics Model Tangent Cone / Tangent Wedge
Method ( local surface inclination )
Overall CN , Cm , CA Control surface characteristi
cs
17
Integrated Airframe and Engine Analysis
Mo, ?, H
output
input
L , D, My P1 , M1 , T1
?1 ,?2 ,?nose wnose ,lmid ,ma
Fore-body Analysis - Oblique shock theory
Intake Entry conditions
?cowl , lcowl ,lint liso , A1 /A3
Dcowl P3 , M3 , T3
Intake and Isolator Analysis -Oblique shock
theory
Combustor Entry conditions
Dcomb , Thcomb P4 , M4 , T4
? , ma ,?comb , lcomb
Combustor Analysis -1D Heat Addition
Nozzle Entry conditions
Dbase , Thnoz Lp , Myp P6 , M6 , T6
After-body Analysis -2D CFD database
?noz ,?noz , lnoz
18
Uncertainties in HSTDV design
19
Fidelity Uncertainty
In this study we consider effect of the fidelity
uncertainty for the disciplinary metric mass
flow capture of air on the system level metric
Thrust deliverable
20
Typical High Fidelity result for Disciplinary
metric
Mass flow capture of air Euler CFD
Iso Mach Contours
Y0
Ps_entry, N\m2
Ps_entry, N\m2
Z-0.6
Top
Center
Side
Bottom
Height of intake, m
Width of intake, m
21
Assessment of Fidelity of Disciplinary
Performance Metric
Few high fidelity observations on the
disciplinary metric are available Correlation
factors ratio of low fidelity observation to
high fidelity observation
Graphical Assessment for Weibull Distribution
Probability
All the CF are one sided Hence Weibull
distribution is assumed
Data
Ref 13 Mantis
22
Quantification of Uncertainty Model
Disciplinary Uncertainty Model for Mass flow
capture of air
Linear Regression
W(X)
Probability
X
Correlation Factor
?6.24 ?0.16 ? 1.0 (assumption)
Kolmogrov -Simrnov Acceptance Test dmax0.132
( to be lt 0.814 for N4)
23
Meta-modeling for System Metric with desired
reliability

• Select pre-determined set of design points
• - Space filling designs like Latin Hypercube
  Sampling

Design space is divided into 8 sub-spaces
40 points in each sub-region
4 points in each sub-region
Total number of pts 32
24
Meta-modeling
Cross-Validation Diagnostic System Metric
Kriging
Thrust Deliverable, kN
Thrust Deliverable, kN
? -1.164 ?1, ?2, ?3 4.736e-03, 3.124e-03,
3.552e-03
25
Meta-modeling
Cross-validation diagnostic plot for disciplinary
metric ma
Data Fusion Input X (?1, ?2, ?3) ma (low
fidelity) Response Y ma ( High fidelity )
Input X (?1, ?2, ?3) Response Y ma ( High
fidelity )
26
 
Multidisciplinary Design Optimization for HSTDV
Problem Statement
Minimize F -(Th_deliv/AF 1) Subject to
G1 MI / 4.2 1 ? 0 G2 ?trim / 20.0
1 ? 0 G3 TOGW / 1200.0 1 ? 0 G4 L /
7.0 1 ? 0 G5 H / 0.8 1 ? 0 Note
Metamodel for CDF of Th_deliv is used
Note assume shock on lip
Optimization variables
Min. Max. Forebody compression angles
?1, ?2 ?3 (deg.) 1.0
6.0 Wing cant angle ?w-cant
(deg.) 0.0 6.0 Wing scale
factor wfac_pl
0.8 1.0 Tail scale factor
tfac_pl,
0.8 1.1 Cruise altitude
Hcruise (kM) 30.0
35.0
Parameters Lmid 2.0m Lab 1.5m ?n_pl chosen
to give body width 0.8m hintk 0.25m wintk
0.5m a/b 2.0
27
Optimizer
Multidiscipline Feasible Formulation
XD
f , g
External Configuration Model
External Compression Model
Forebody length and height
Volume Body Discretization
ma with fidelity uncertainty
Aero Model
Mass C.G.
Thrust Model
Isp
Overall Aero Control data
Adjust Ballast
Metamodel for Thrust deliverable
No
Trim
Thrust Deliverable With desired Confidence level
Yes
Trim deflection , Drag Updated mass
Performance Model
28
Optimization Results
Objective Function
Constraints
Iteration Number
Iteration Number
29
Optimization Results
Note F is computed at the corresponding design
settings using high Fidelity simulation for
disciplinary metric
30
Future Directions
Investigate applicability of alternate methods
for situations wherein high fidelity information
is limited.

• Interval Probability Theory, Dempster-Shafer
  Theory, . . .
• Uncertainty arising out of other analysis
• Increased fidelity of analysis

Thank You