Configuration Design of Air Breathing

1
2nd Progress Seminar
22nd August,2003
Configuration Design of Air Breathing Hypersonic
Vehicle using Numerical Optimization
J. Umakant Research Student ( External) Roll No.
01401701
CASDE Dept. of Aerospace Engineering IIT, Bombay
2
Summary of 1st Progress
Seminar September 2002

• Problem Formulation
• Conceived Overall Design process for
  Air-Breathing Hypersonic configuration
• Disciplinary Interactions
• Parameterization of vehicle and Analysis
  Modules
• Review of literature of Aerospace Vehicle Design
  using MDO
• 3 Ph D thesis
• - McQuade Development of CFD based GLA
  factors for 2D scramjet vehicle
• - Guinta VCRSM of HSCT Wing
• - Old Robust design of SSTO vehicle
• 12 Papers from 1990 onwards
• - Bowcutt (1999) MDO Hypersonic Vehicle
  Optimization
• - Design synthesis tools for Launch Vehicles
• - Papers related to approximation strategies
• Fore-body optimization using engineering method
  with FFSQP optimizer
• - two design variables ( fore-body compression
  angles)
• objective function ma / Cd subject to
  constraints on Mintk , L/D , h/l

3
2nd Progress Seminar

I Hypersonic Technology Demonstrator
Vehicle(HSTDV) - Mission -
Vehicle Background II HSTDV Configuration
- Problem Statement -
Parameterization and Trade-Offs -
Engineering Methods for Analysis III
Optimization and Results IV Potential
Improvements in Aerodynamic Prediction code
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HYPERSONIC TECHNOLOGY DEMONSTRATOR
TO DEMONSTRATE AUTONOMOUS SUSTAINED FLIGHT AT
HYPERSONIC SPEED
SCRAMJET TEST
ALTITUDE 32.5 km MACH NO. 6.5 TEST
DURATION 400 s
SCRAMJET MACH NO. 5.5
RAMJET
DUAL MODE TEST
ALTITUDE 20 km MACH NO. 4.5
1 m DIA
5
HSTDV Vehicle Discipline
Interactions

• Integrated Engine and Airframe
• Entire undersurface of the airframe forms part
  of the engine
• Fore-Body
• pre-compressed air to the intake , aerodynamic
  characteristics, volume
• After-Body
• thrust, stability characteristics , after-body
  volume

Optimizer
XD
f , g
Aerodynamic heating, Detailed Modeling of Intake,
Combustor, Nozzle , Trajectory Optimization
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MDO - Implementation Issues

• Mathematical modeling and Computational Expense
• low fidelity methods computationally cheap
  but not sufficiently accurate
• high fidelity methods highly accurate but
  computationally prohibitive

• Optimization Procedures
• problem formulation
• algorithms for global optimization

• Organizational Complexity
• disciplinary expertise is distributed across
  the organization, not available
• centrally
• difficulty in data exchange

7
Broad Strategy for HSTDV Design using MDO
I Overall Vehicle Design using Engineering
Methods ( low fidelity ) - Sizing,
Aerodynamics, Propulsion and Performance
- Identify important design variables
- Build a multidisciplinary analysis tool
- Calibration factors -
Numerical optimization
II Methods to create Approximate Models for
High Fidelity Analysis - Design and
Analysis of Computer Experiments - Data
fusion ( low fidelity high fidelity )
III Global Optimization Strategies using DACE
suggested in Statistical literature.
IV Methods to take into account uncertainties
in approximate model
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Parameterization of HSTDV Body
W_fac
t_fac
XD ?1, ?2, ?3 , ?n_pl , ?wc , wfac_pl,
tfac_pl,,Hcruise
Wing AR0.6, b 1.6m, ?0.4 Tail AR2.3
, b 1.4m , ?0.4 Airframe thickness t 50mm
Lmid 2.5 m
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Fore-body Parameterization 3 Ramp configuration
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After-body Parameterization
?noz
Max pnoz Sin(?noz) s.t 0.2 pnoz/pne
Lab
Mne 1.5 pne 1.1 atm Lab 1.5m 1-D P-M
relations to estimate pnoz ?noz
17
1.0
pnoz/pne
Pnoz labSin ?noz
0.0
0
40
?noz (deg.)
?noz (deg.)
11
Trade-Offs
Parameter Potential Trade
?n_plan higher body width ( volume) vs higher skin friction drag
?1, ?2, ?3 higher f/b height (volume) vs lower intake Mach No., lower Pressure recovery, higher CL CD
lmid higher volume vs higher skin friction drag, higher weight
lab higher a/b volume vs lower nozzle angle ( propulsive force propulsive moment)
w_fac Higher lift, lower trim angle of attack vs higher drag, more space
?w_cant Stability vs higher wave drag
t_fac higher trim deflections vs lower trim deflection, stability
Hcruise higher drag , higher ma vs lower drag , lower ma
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Optimizer
XD
f , g
External Configuration Model
External Compression Model
Forebody length and height
Volume Body Discretization
Mass flow of Air Capture
Aero Model
Mass C.G.
Overall Aero Control data
Adjust Ballast
Thrust Model
Specific Impulse
No
Trim
Yes
Fuel flow rate Thrust Deliverable
Trim deflection , Drag Updated mass
Performance Model
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HYPERSONIC TECHNOLOGY DEMONSTRATOR
-CONFIGURATION
PAYLOAD 400 kg FUEL 250 kg TOTAL WEIGHT
1240 kg
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External Compression Model
M? , ? Input Variables ?1 , ?2 , ?3
Output Fore-body dimensions ( l1
,l2 ,l3 ,h1 ,h2 ,h3 ) Intake Entry
Conditions pintk , Mintk , ma
External Compression Model Oblique shock theory
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Assuming shock on lip condition
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Typical Results from External Compression model
First Ramp Angle 5 deg.
Intake Entry Mach No.

Total Pressure Recovery
Mass flow rate ( Kg/s)
Mass flow rate ( Kg/s)
Calibration factor Mass flow rate based on Euler
CFD calculations is about 30 lower as compared
to the estimate from low fidelity analysis Each
Euler CFD run on a 8node P-III cluster requires
15 hours
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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
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External Configuration Model
Body Discretization

• Input Parameters
• Swid_ntip 0.1m
• Lmid 2.5m
• ?noz 20
• a/b 2.0

Lnoz
Lmid
x0
xfb1_stn
xfb2_stn
xfb3_stn
xmid_stn
xnoz_stn
a
b
w
b
h
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External Configuration Model
Internal volume
body_int vol fb1_v fb2_v fb3_v midbd_v
aftbd_v
Airframe Mass
Mass ?s Swet ?s 20 kg / m2
surface area density
bodyaf_m 1.2 (fb1_m fb2_m fb3_m midbd_m
aftbd_m)
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External Configuration Model
Airframe Center of gravity
Xc.g.
Xc.g.
bodyaf_xcg ( fb1_m fb1_xcg fb2_m fb2_xcg
fb3_m fb3_xcg
midbd_m midbd_xcg aftbd_m aftb_xcg) /
bodyaf_m
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External Configuration Model
equip_m nc_m bal_m obc_m ins_m tm_m
tank_m
wing_m baseline wing mass w_fac
TOGW bodyaf_m equip_m eng_m fuel_m
wing_m tail_m
tm_xcg xfb3_stn 0.25(xmid_stn-xfb3_stn)
tm_zcg 0.5zlh_mid
act_xcg xmid_stn act_zcg zlh_mid
to_xcg ( bodyaf_m bodyaf_xcg
equip_mequip_xcg eng_meng_xcg
fuel_m fuel_xcg wing_m wing_xcg
tail_mtail_xcg) / TOGW
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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
23
Typical Aerodynamic Characteristics of HSTDV
M 6.5
CN
Cm_xcg
?
?
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L/D
ANGLE OF ATTACK (deg.)
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Fidelity of Analysis

• Calibration Factors (Scale factor)
• Use CFD computations to generate calibration
  factors.
• Valid within specified move limits

CN Xcp/d CA m a(Kg/s)
Tangent Cone Method 2.028 3.911 0.431 8.1
CFD (Euler) 1.657 3.507 0.342 5.59
Zeroth order scale factor 20 15
15 30
Higher order scale factors will be used in future
studies
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Trim Model
Basic Body, Wing Tail Aero characteristics Propu
lsive force moment
Evaluate Static stability
Exit with tail size and updated Mass and
C.G ?trim and ?trim and trim drag
Yes
Statically stable
Adjust Ballast weight
No
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Trim Model
?
M?
N
A
?
N Np W Cos ? T A W Sin ?
W
?
0.25T
0.75T
Np 0.25 T / tan ?noz
?noz
Np
Mp Np (to_xcg - x_noz) 0.25T (to_zcg - z_noz)
0.75T (to_zcg - z_noz)
Mtrim Maero_cg Mp_cg 0
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Thrust Model
External Compression Model ma ,
Mintk
Equivalence ratio 1
Thrust Model
Isp (M, H_cr)
Thrust deliverable
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Performance Analysis
Aerodynamics
Performance - 2DOF trajectory simulation
Range R
Propulsion
Sizing
30
 
Multi-disciplinary Design Optimization for HSTDV
Problem Statement

• Minimize f(XD) - (Range)/2000
• g1 MI / 4.0 1 lt 0
  scramjet considerations
• g2 ? / 20.0 1 lt 0
  Aero, control and actuation
• g3 L / 7.5 1 lt 0
• g4 H / 0.85 1 lt 0
  sizing
• g5 W / 0.85 1 lt 0
• g6 TOGW / 1325.0 1 lt 0
  system
• g7 AF / Th deliv 1 lt 0.
  Aerodynamics Propulsion
• ?

Side constraints 3 ? ?1 ? 10 1
? ?2 ? 10 1 ? ?3 ? 10
3 ? ? n_pl ? 6 0 ? ? wc ? 6
0.8 ? wfac_pl ? 1 0.8 ? tfac_pl ? 1.1
30 ? Hcr ? 35
Optimization variables XD ?1, ?2, ?3 , ?n_plan
, ?wc , wfac_pl,tfac_pl,,Hcruise
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Results
?1
?2
?n_pl
?3
Iteration number
Iteration number
32
?w_c
?w_fac
?t_fac
H_cr
Iteration number
Iteration number
33
Cruise Range
g1 MI / 4.0 1 lt 0
Iteration number
Iteration number
g2 ? / 20.0 1 lt 0
g3 L / 7.5 1 lt 0
Iteration number
Iteration number
34
g4 H / 0.85 1 lt 0
g5 W / 0.85 1 lt 0
Iteration number
Iteration number
g6 TOGW / 1325.0 1 lt 0
g7 AF / Th deliv 1 lt 0.
Iteration number
Iteration number
35
Comparison of Initial Configuration Outline with
Optimum configuration
Baseline Optimum

Body Outline
Tail planform
36
XD Initial Design Setting Optimum Design Setting
?1 7.55 5.82
?2 3.88 3.64
?3 2.89 4.14
?n_plan 4.50 4.00
?wc 4.80 6.00
wfac_pl 0.80 0.80
tfac_pl 1.10 1.06
Hcr 31.25 31.65

• Optimum design with respect
• to initial design
• 4 increase in dry weight
• 15 increase in fuel volume
• 1.5 decrease in drag
• 17 increase in cruise range
• Physical constraints on
• Mintk , ? and TOGW are active

37
Sensitivity of objective function with respect to
design variables at initial design point
?R / ? ?1 -66.02
?R / ? ?2 -89.09
?R / ? ?3 93.75
?R / ? ?n_plan 147.85
?R / ? ?wc 23.75
?R / ? wfac_pl 110.5
?R / ? tfac_pl -13.97
?R / ? Hcr 13.46
Optimum configuration has lower values for ?1 and
?2 as compared to initial design. Decreasing
these variables at the initial design point ,
results in a decrease in the objective function
ie, cruise range However, the inter-play
among the design variables has resulted in a net
improvement in objective function.
? ?R / ? Xi 109.69
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Fidelity of Analysis

• Physics Based Corrections
• Improve the accuracy of the Engg. Methods like
  Tangent Cone
• through correlation factors generated using CFD
• Globally valid

Equivalent Body for conical flow calculations
Actual Body
39
Cone Body (semi-included angle 5 )
40
Cone Body (semi-included angle 5 )
?Cp
Angle of attack (deg.)
Error ?Cp Cp (TCM) Cp (CFD) at ? 0
41
Global Correction Factor
?Cp ?/Sin ?
?
Cp (corrected) Cp(TCM) - ?Cp
42
Further course of Action
Focus on methods to include high fidelity
analysis

• Summary of methods adopted for Aerospace Vehicle
  Design
• Various strategies have been used to address the
  issue of
• computational burden associated with high
  fidelity analysis
• Parametric methods with RSM
• Global Local Approximation
• First Order Approximate Model Management
• Variable Complexity Response Surface Method

• Statistical Literature
• Design and Analysis of Computer Experiments

43
Design and Analysis of Computer Experiments
Ref Sacks et.al. 10 Jones et.al. 11
Motivation Given function values Y at sampled
points x , one simple way to create response
surface is through linear regression

• In the above model, the errors are assumed
  independent. This assumption
• is justified for physical experiments.
• Computer experiments are however,
  deterministic.
• Lack of random error in computer experiments and
  any lack of fit is entirely
• due to collection of left out terms in x.
• In DACE model, ?(i) is interpreted as ?(x(i))
  ie., errors are correlated.

44
Further course of Action

• DACE modeling for ma , CN, Cm and CA
• Use data fusion ( low fidelity high fidelity)
  validation
• Optimization Strategies
• Robustness of design through error propagation

45
Design and Analysis of Computer Experiments
The correlation is high if two points x (i) and x
(j) are close and low when the points are far
apart.



(Jones et.al.)
46
Design and Analysis of Computer Experiments
DACE Model
global effect
local effect
(Jones et.al.)
are parameters estimated by maximizing
the likelihood of the sample y ( y(1),, y(n)
)'
47
Design and Analysis of Computer Experiments
RSM model using DACE modeling
ri(x) Corr ?(x), ?(x(i)) , i1,.n
RSM model using regression

48
Design and Analysis of Computer Experiments
Illustration (Jones et.al.)
DACE response surface
Branin test function Contours
Quadratic surface fit
49
Design and Analysis of Computer Experiments
Global Optimization for a 1-D function using DACE
model (Jones et.al.) Expected Improvement
Criteria for selecting additional sample points
50
DACE fit for Pitching Moment Data Predictions are
at the sampled points itself
Cm
?
?

• -45 , -35 , -25 , -15 , -5 , 0 , 5 ,
  15, 25 35 , 45
• ? 0 , 2 , 4, 6,8

51
Mean Squared Error
MSE
?
?
52
Iso-contours of fit surface
Iso-contour of actual function
?
?
? (deg)
? (deg)
53
DACE fit for Pitching Moment Data Predictions are
at untried points
Cm
?
?
54
Mean Squared Error
MSE
?
?
55
Iso-contours of fit surface
Iso-contour of actual function
?
?
? (deg)
? (deg)
56
Review of MDO for Aerospace Vehicles

• McQuade Ph.D thesis Univ. of Washington, 1991
• Aerodynamic optimization of a 2D scramjet
  vehicle using CFD (Euler).
• Fore-body and Nozzle were separately optimized
  to maximize thrust.

• Engg. Models used Oblique Shock theory, 1D
  Heat Addition, MOC
• correction factors based on 2D CFD (Euler)
  analysis (GLA)

57
General Application of Global-Local Approximation
Approximate Problem formulation
Complete Optimization ( 1
iteration)
No
Convergence?
Yes
stop
58
Review of MDO for Aerospace Vehicles
Afterbody Optimization
Objective maximize the net thrust Subject to
constraints on geometric parameters CFD , 1D
isentropic flow, MOC Taylor Series, GLA using
1D, GLA using MOC
59
Review of MDO for Aerospace Vehicles
Afterbody Optimization
Results
Method ? (deg.) ?curve (deg.) Fnet CFD calls Relative Cost/step
Init Design 18.000 0.0050 18.05 - -
CFD 20.541 0.0032 19.71 22 1.0
1-D 26.000 0.0082 18.42 - -
MOC 26.000 0.0082 18.42 - -
Taylor 20.362 0.0031 19.71 7 0.0098
1D GLA 20.850 0.0035 19.71 7 0.0083
MOC GLA 20.563 0.0033 19.70 7 0.0109
60
Review of MDO for Aerospace Vehicles
Fore-body Optimization
Objective maximize the net thrust Subject to
constraints on geometric parameters CFD ,
Oblique shock theory Taylor Series, GLA based on
Oblique shock
61
Review of MDO for Aerospace Vehicles
MDO of Air Breathing Hypersonic Vehicle
Ref Bowcutt J.of Propulsion and Power ,
Nov-Dec,2001
Optimization of Vehicle Configuration for
performance (range) across a specified Mach No.
vs Altitude Trajectory

• Sizing
• Aerodynamics
• Stability Control
• Propulsion
• Trajectory

Optimization variables nose angle, engine
axial location,
engine cant, cowl length and
chine length

62
Review of MDO for Aerospace Vehicles
Key changes in the Optimized vehicle configuration

• Engine location moved forward by 6 of vehicle
  length
• Engine cant reduced by 2 deg
• Engine cowl length reduced by 5 of vehicle
  length
• Chine length reduced by 80 of vehicle length

The optimized vehicle, flying the same M-q
trajectory as the baseline, achieved 46
greater air-breathing range 9 improvement in
effective specific impulse 13 reduction in trim
drag over the baseline configuration

63
Review of MDO for Aerospace Vehicles
Aerodynamic Lessons

• Wind tunnel testing and CFD analysis was
  performed on the
• Optimized vehicle
• HABP like Engg. Codes overpredicted lower surface
  pressures in
• the aft region of the vehicle.
• Vehicle range reduced by 6 based on W/T
  Aerodynamics.
• Vehicle instability levels in terms of negative
  static margin increased
• resulting in reduction in max. flight dynamic
  pressure at which the
• vehicle could operate.

64
Review of MDO for Aerospace Vehicles
Hall mark of MDO
Range sensitivities to the five vehicle design
parameters
Parameter Derivative
A variation that is detrimental by itself can be
beneficial when working in concert with many
coupled variations.
65
Review of MDO for Aerospace Vehicles

• John Robert Olds , Ph.D. thesis NCSU, 1993
  
  
• Advanced Space Transportation Vehicle optimized
  for minimum weight.
• Taguchi methods was used to select initial
  experimental arrays. Parametric
• methods were used to determine the settings
  for design variables which
• minimized weight. The effect noise
  variables on the objective function was
• included to ensure a robust design .
• Central Composite Design was used for the
  final design variables .
• Quadratic Response surface was created using
  RSM
• Non-linear optimizer was used to optimize the
  quadratic surface
• Remarks
• Parametric methods are useful only for very
  early design stages where the
• number of design variable are very few.
• Initial problem size 8 design variables
• Final problem size 3 design variables
• Inclusion of design constraints in the frame
  work is not easy.

66
Review of MDO for Aerospace Vehicles

• Giunta , Ph.D thesis VPI SU , 1997
• HSCT configuration optimized for TOGW.
• Variable Complexity Response Surface Modeling.
• Low fidelity methods used to screen the original
  design space.
• Response Surfaces (polynomial based) using
  medium fidelity analysis created
• for the reduced design space.
• RSMs were used for function evaluations in the
  optimizer.
• Preliminary investigation on the use of Design
  of Computer Experiments
• (Kriging) for creating response surfaces was
  also carried out.

• Remarks
• RSM help to smoothen out the numerical noise in
  analysis methods. This ensures that
  the gradient calculations (search directions )
  are not affected.
• Constraints from aerodynamics, propulsion,
  stability, performance.
• Methodology demonstrated for problem sizes of 5
  to 20 design variables.
• Curse of dimensionality limits the problem size.
• Further studies are needed to investigate the
  capabilities of DACE modeling.

67
Review of MDO for Aerospace Vehicles

• Summary
• Various strategies have been used to address the
  issue of
• computational burden associated with high
  fidelity analysis
• Parametric methods with RSM
• Global Local Approximation
• First Order Approximate Model Management
• Variable Complexity Response Surface Method

68
Review of MDO for Aerospace Vehicles

• 
  
  Summary
• For problems at complete vehicle level, RSM
  based on linear regression has
• been widely used to overcome the challenge of
  computational cost.
• Once the response surface is available, in most
  of the cases, an optimizer
• has been used to find the minimum of the
  surface
• Issues
• It may be difficult to predict the form of the
  linear regression.
• Restriction on the number of design variables
  is a serious limitation.
• Sample points to construct the RSM are chosen
  based on DoE. These
• may not necessarily be in the region of
  interest.
• Multiple starts are required in the
  optimization, to verify if the solution
• is not a local minima.
• Conceptual problem is reported on the use of
  RSM based on linear
• regression for computer simulation
  experiments.