NASA Technical Reports Server (NTRS) 20180000577: Jig-Shape Optimization of a Low-Boom Supersonic Aircraft Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

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by  NASA Technical Reports Server (NTRS)

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft
Prepared For:
AIAA SciTech 2018
AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
January 8-12, Kissimmee, Florida
Prepared By:
Chan-gi Pak, Ph.D.
Structural Dynamics Group, Aerostructures Branch (Code RS)
NASA Armstrong Flight Research Center
Overview
 Theoretical background (slides 3-10)
 Computational validation (slides 11-28)
 Conclusions (slide 29)
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Theoretical background
Introduction
 Supersonic Commercial Transport Aircraft Design
 Safety
 Light weight airframe can cause strength, buckling, aeroelastic, and aeroservoelasticissues.
 Sonic boom
HSCT
 Supersonic flight of “commercial transport” aircraft allowed only over the ocean.
 Perceived Loudness in decibels
 NASA’s N+2 goal: 75 PLdB
 Concorde: 104 PLdB
Concorde
 High Speed Civil Transport (HSCT): 99 PLdB
 Fuel efficiency
 Light weight airframe
 Reduced drag
 Developing Low Boom Flight Demonstrator (LBFD)
 Lockheed Martin Skunk Works was the prime contractor for preliminary design of X-plane.
 Loudness: 74 PLdB
 Major Issue
 Outer-mold-line configuration of an aircraft is design for the desired aerodynamic Low boom supersonic aircraft
performance. Assume rigid structure.
Cross section of a flat wing
Trim deformation
 Flexibility of the structure changes the aerodynamic performance.
 It has been reported that one degree of the tip twist Trim deflection Deflection due
of a supersonic wing and stabilator under the cruise flight condition to flexible
angle of attack 𝜶
can increase the sonic boom level by 0.2 PLdB and 1.3 PLdB, respectively. 𝑅𝑖𝑔𝑖𝑑
Flow
𝜶
𝐹𝑙𝑒𝑥𝑖𝑏𝑙𝑒
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Jig-Shape Optimization Problem Statement
 Assume unconstrained Optimization
 Optimization Problem Statement
𝑇
 Find design variables: 𝑋 = 𝑋 𝑋 …,𝑋 which
1, 2, 𝑛𝑑𝑣
𝑛𝑠𝑢𝑟𝑓×3
2
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐹 𝑋 = ∆𝑇
𝑗
𝑗=1
 ∆𝑇 ≡ 𝑇 − 𝑇
𝑡 𝑑
 𝑇 = target trim shape at surface GRIDs
𝑡
 Sonic boom level is computed based on target trim shape.
 𝑇 = trim shape based on design jig shape
𝑑
 𝑗𝑖𝑔 𝑇
𝑑 𝑑
𝑡𝑟𝑖𝑚𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠
 𝑗𝑖𝑔 ≡ 𝑗𝑖𝑔 + ∆𝑗𝑖𝑔
𝑑 𝑏
 𝑗𝑖𝑔 = design jig-shape
𝑑
 𝑗𝑖𝑔 = baseline jig-shape
𝑏
 ∆𝑗𝑖𝑔 = jig-shape changes
 ∆𝑗𝑖𝑔 = 𝚽 𝑋
 𝑋 = i-th design variable
𝑖
 𝚽 = 𝜙 𝜙 … 𝜙
1 2 𝑛𝑑𝑣
•
𝜙 = i-th basis function
𝑖

Eigen vector based on jig shape

Eigen vectors are normalized as Max deflection = 1 inch.
Structural Dynamics Group Chan-gi Pak-5
Update Jig-Shape Module: using shape_change.exe
 Shape_change.exe: Change jig shape using design
variables and basis functions.
From O3 tool Template input file Static input file  𝑗𝑖𝑔 ≡ 𝑗𝑖𝑔 + 𝚽 𝑋
𝑑 𝑏
 Input
 Design variables file 𝑋 : basis functions for
𝑋 Design variables file
Update trim input deck
Static analysis
the shape optimization (basis_functions.dat)
 Basis functions file 𝚽 : design variables of
𝚽 Basis functions file
the current optimization step (design_var)
Trim input file
Static output file  Baseline grid shape file 𝑗𝑖𝑔 : grid
𝑗𝑖𝑔 Baseline grid shape file 𝑏
𝑏 information of the baseline configuration
(grid_base.bdf; a template file)
Trim analysis
Updated jig-shape Trim deflection  Output
 Updated grid shape file 𝑗𝑖𝑔 : grid
𝑑
information of the updated configuration
External loads file
𝑗𝑖𝑔 Updated grid shape file (grid_update.bdf)
𝑑 Surface grid shape file
Trim output file
Modal input file
𝑇 Target grid shape file Objective function
𝑡
Modal analysis
𝑛𝑠𝑢𝑟𝑓×3
2
𝐹 𝑋 = ∆𝑇 Objective function file
𝑗
Modal output file 𝑗=1
System mass matrix file To O3 tool
Change jig shape using design variables & basis functions.
Structural Dynamics Group Chan-gi Pak-6
Modal Analysis Module: using MSC/NASTRAN solution 103
 Perform modal analysis using MSC/NASTRAN
solution 103 to change system mass matrix
From O3 tool Template input file Static input file
file (MGH matrix), weight, moment of inertia,
and CG location for trim analysis.
𝑋 Design variables file  Compute six rigid body modes.
Update trim input deck
Static analysis
𝚽 Basis functions file
Trim input file
Static output file
𝑗𝑖𝑔 Baseline grid shape file
𝑏
Trim analysis
Updated jig-shape Trim deflection
External loads file
𝑗𝑖𝑔 Updated grid shape file
𝑑 Surface grid shape file
Trim output file
Modal input file
𝑇 Target grid shape file Objective function
𝑡
Modal analysis
𝑛𝑠𝑢𝑟𝑓×3
2
𝐹 𝑋 = ∆𝑇 Objective function file
𝑗
Modal output file 𝑗=1
System mass matrix file To O3 tool
Change mode shapes, weight, moment of inertia, & CG location for trim analysis.
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Trim Analysis Module: using ZAERO & change_trim.exe
 Change_trim.exe: Update input deck for ZAERO
trim analysis.
From O3 tool Template input file Static input file
 Input
 Template input file: file for ZAERO based trim
𝑋 Design variables file analysis (Lbfd_trim.bdf)
Update trim input deck
Static analysis
 Modal output file: f06 file from MSC/NASTRAN
 Output
𝚽 Basis functions file
 Trim input file: updated ZAERO input file to be
Trim input file
Static output file used for trim analysis (trim.bdf)
𝑗𝑖𝑔 Baseline grid shape file
𝑏
 Perform trim analysis using ZAERO
 Input
Trim analysis
Updated jig-shape Trim deflection  Trim input file: Trim.bdf
 Output
 External loads file: aerodynamic load + inertial
External loads file
𝑗𝑖𝑔 Updated grid shape file
𝑑 Surface grid shape file load (Extload.dat)
 Trim output file: ZAERO output (trim results)
Trim output file
Modal input file
𝑇 Target grid shape file Objective function
𝑡
Modal analysis
𝑛𝑠𝑢𝑟𝑓×3
2
𝐹 𝑋 = ∆𝑇 Objective function file
𝑗
Modal output file 𝑗=1
System mass matrix file To O3 tool
Compute external load using ZAERO code.
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Objective Function Module: using MSC/NASTRAN solution 101, shape.exe, & differ.exe
 Perform static analysis using inertia relief.
(MSC/NASTRAN sol. 101)
From O3 tool Template input file Static input file  Input
 Static input file: external loads file and
updated grid shape file are included in this
𝑋 Design variables file
Update trim input deck
Static analysis file
 Output
𝚽 Basis functions file
 Static output file: MSC/NASTRAN output
Trim input file
Static output file file, ~f06 file.
𝑗𝑖𝑔 Baseline grid shape file
𝑏  Trim_deflection.exe: read deflected shape.
 Input
Trim analysis
 Static output file: MSC/NASTRAN output
Updated jig-shape Trim deflection
from sol. 101
 Trim output file: ZAERO output file (read
External loads file trim results)
𝑗𝑖𝑔 Updated grid shape file
𝑑 Surface grid shape file  Output
Trim output file  Surface grid shape file: grid geom. + rigid
Modal input file
rotation + deformed shape (@ all grids;
𝑇 Target grid shape file Objective function Shape.dat)
𝑡
 Differ.exe: compute objective function value
Modal analysis
 Input
𝑛𝑠𝑢𝑟𝑓×3
2  Surface grid shape file
𝐹 𝑋 = ∆𝑇 Objective function file
𝑗
Modal output file 𝑗=1  Target grid shape file: 𝑇 @ surface grid
𝑡
 Output
System mass matrix file To O3 tool  Objective function file: performance index
for objective function; 𝐹 𝑋
Compute trim deformation using MSC/NASTRAN solution 101 using inertia relief.
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Compute Starting Design Variables: Using Least Squares Surface Fitting Technique
∆𝑇
 ∆𝑇 ≡ 𝑇 − 𝑇
𝑡 𝑡 𝑏 𝑡
 𝑇 = target trim shape at surface GRIDs
𝑡
 𝑇 = trim shape based on the baseline jig-shape
𝑏
 𝑗𝑖𝑔 𝑇
𝑏 𝑏
𝑡𝑟𝑖𝑚𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠
 Fitting ∆𝑇 surface using perturbed shapes ∆𝑇 , 𝑖 = 1,2,…,𝑛dv
𝑡 𝑖
 Perturb baseline jig-shape using basis functions 𝚽
 𝑗𝑖𝑔 ≡ 𝑗𝑖𝑔 + 𝚽 𝑋
𝑑 𝑏
 Where, 𝜙 = i-th basis function
𝑖
 𝑗𝑖𝑔 + 𝜙 𝑇
𝑏 𝑖 𝑖
𝑡𝑟𝑖𝑚𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠
 ∆𝑇 ≡ 𝑇 − 𝑇 (i-th perturbed shape)
𝑖 𝑖 𝑏
 Define a matrix: 𝜳 = ∆𝑇 ∆𝑇 … ∆𝑇
1 2 𝑛𝑑𝑣
 𝜳 𝑋 = ∆𝑇
𝑡
 𝜳 𝑇 𝜳 𝑋 = 𝜳 𝑇 ∆𝑇
𝑡
 𝜳 𝑇 𝜳 −1 𝜳 𝑇 𝜳 𝑋 = 𝜳 𝑇 𝜳 −1 𝜳 𝑇 ∆𝑇
𝑡
 Starting design variables: 𝑋 = 𝜳 𝑇 𝜳 −1 𝜳 𝑇 ∆𝑇
𝑡
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