Overview and Team Composition Aerodynamics and MDO Andy Ko Joel Grasmeyer* John Gundlach IV* Structures Dr. Frank H. Gern Amir Naghshineh-Pour* Aeroelasticity Erwin Sulaeman CFD and Interference Drag Philippe-Andre Tetrault* Faculty Members Dr. B. Grossman, Dr. R.K. Kapania Dr. W.H.Mason Dr. J.A. Schetz Dr. R.T. Haftka (University of Florida) *Students that have graduated 2
Some History Werner Pfenninger proposes concept by early 195s 1978: AFWAL studies include strut concepts 1996: VPI Starts MDO work under NASA Support 1997: Results look promising Late 1997/early 1998: Internal LaRC study 1998: VPI briefs both Boeing and Lockheed Martin 1998: LMAS contracted by NASA LaRC VPI works as subcontractor to LMAS 1999: Both VPI and LMAS do additional work 1999: NASA/LMAS/VPI Team propose a demonstrator aircraft for the REVCON Program 3
Strut-Braced Wing Advantages The strut increases the structural efficiency of the wing Wing t/c reduced without a weight penalty Lower weight and increased span reduce induced drag Reduced t/c allows less sweep without wave drag penalty Parasite drag is reduced via increased laminar flow Un-sweeping the wing reduces cross-flow instability Higher aspect ratio means smaller chords and smaller Re 4
Description of the MDO Process Updated Design Variables Baseline Design Initial Design Variables Geometry Definition Induced Drag Friction and Form Drag Propulsion SFC Field Performance Stability and Control Structural Optimization Weights Wing bending material weight Range/ Performance Objective Function/ Constraints Aerodynamics L/D Wave Drag Interference Drag Offline CFD Analysis * Structural Optimization includes static aeroelasicity Optimizer 5
MDO Problem Statement Objective: Minimize Takeoff Gross Weight Aircraft Design Variables: Strut Design Variables: Wing Half Span Position of Strut Wing 1/4 Chord Sweep Strut Sweep Wing Chord Strut Offset Cantilever centerline chord = 52 ft. Chordwise Centerline and tip chord for SBW Vertical Wing t/c (3) Strut Chord Wing centerline skin thickness Strut t/c Fuel Weight Strut Force Engine Thrust Altitude Position of engine Under Wing Engine SBW only Vertical Tail Scaling Factor Tip Mounted Engines SBW only 6
MDO Problem Statement Optimization Method: Method of Feasible Directions (DOT) Constraints Range Initial Cruise Rate of Climb Maximum Section Cl Fuel Capacity Engine Out Wing Deflection Second Segment Climb Gradient Balanced Field Length Approach Velocity Missed Approach Climb Gradient Landing Distance Slack Load Factor 7
Design Mission Mach.85 Cruise Mach.85 Climb 14 Knot Approach Speed 11, FT T/O Field Length 75 NMi Range 11, FT LDG Field Length 5 NMi Reserve Two GE-9 Class Engines 325 Passengers 8
Current Designs Cantilever Optimum Fuselage Mounted Engines SBW TOGW Fuel Weight = 67656 lbs. = 221692 lbs. TOGW = 54679 lbs. (1.%) Fuel Weight = 19366 lbs. (14.1%) 9
Current Designs Wing Mounted Engines SBW TOGW = 52123 lbs. (14.3%) Fuel Weight = 185892 lbs. (16.1%) Tip Mounted Engines SBW TOGW = 523563 lbs. (13.8%) Fuel Weight = 185159 lbs. (16.5%) 1
Design Comparisons Mission Profile: 325 Passengers 75 nmi. range + 5 nmi. reserve Cantilever Optimum Fuselage Mounted Engines SBW Wing Mounted Engines SBW Tip Mounted Engines SBW Weights Calculated Takeoff Weight (lb) 67656 54679 52123 523563 Wing Weight (lb) 79196 71571 56629 55554 Fuel Weight (lb) 221692 19366 185892 185159 Zero fuel weight (lb) 385964 356343 335131 33844 Geometry Wing Half-Span (ft) 14.4 16.6 11.8 95.6 Reference Area (ft^2) 462.2 4369.6 477.5 412.3 Aspect Ratio 9.43 1.4 1.17 8.92 Wing 1/4-Chord Sweep (deg) 37.6 32.1 31.5 32.1 Average Wing t/c.1231.95.965.963 Performance Thrust to Weight Ratio.28.26.27.29 Wing Loading (lb/ft^2) 131.5 125.1 127.8 127.6 11
SBW Savings Based on Cantilever Baseline optimum results Fuselage Mounted Engines SBW Wing Mounted Engines SBW Tip Mounted Engines SBW Weights (%) Calculated Takeoff Weight -1. -14.3-13.8 Wing Weight -9.6-28.5-29.9 Fuel Weight -14.1-16.1-16.5 Zero fuel weight -7.7-13.2-12.3 Geometry (%) Wing Half-Span 2.1-2.4-8.4 Reference Area -5.4-11.7-11.2 Aspect Ratio 1.2 7.9-5.5 Average Wing t/c -22.8-21.6-21.7 Performance (%) Thrust to Weight Ratio -5.6-3.3 4.2 Wing Loading -4.9-2.8-3. 12
Latest Developments Constraint studies Need to know the sensitivity of the designs with respect to constraints Double deck fuselage design Flexible wing sizing Incorporation of passive load alleviation into optimization process Wing buckling Strut imposes compressive forces on the inboard wing. 13
Constraint Studies Need to determine the sensitivity of designs towards design constraints Constraints considered Range Section Cl max Engine out Wing deflection Second segment climb gradient Balanced field length Approach velocity Strut slack load factor Lagrange multipliers used to calculate sensitivities 14
Logarithmic Sensitivity Upper Strut Slack Load Factor (.8) Approach Velocity (14 kts) Balanced Field Length (11 ft) Tip Mounted Engines SBW Wing Mounted Engines SBW Fuselage Mounted Engines SBW Cantilever Baseline Second Segment Climb Grad. (.24) Wing Deflection (2 ft) Engine Out Section Cl Max (.8) Range (75 nmi).1.2.3.4.5.6.7.8 Log Sensitivity 15
Rankings 1 Cantilever Optimum Fuselage Mounted Engines SBW Rankings Wing Mounted Engines SBW Tip Mounted Engines SBW 2 Range Range Range Range 3 Section Cl Max Balanced Field Length Balanced Field Length 4 Approach Velocity Section Cl Max Section Cl Max 5 6 7 Second Segment Climb Balanced Field Length Second Segment Climb Gradient Upper Strut Slack Load Factor Wing Deflection Second Segment Climb Gradient Upper Strut Slack Load Factor Engine Out Second Segment Climb Gradient Wing Deflection Upper Strut Slack Load Factor Section Cl Max 16
Unscaled Sensitivities Constraint Cantilever Optimum Unscaled Sensitivities (lbs/*) Fuselage Mounted Engines SBW Wing Mounted Engines SBW Tip Mounted Engines SBW Range (75 nmi) 57.74 46.12 4.53 41.22 Section Cl Max (.8) -57238.13-23312.63-41368. 85.92 Engine Out... 469357.89 Wing Deflection (2 ft).. -63.55-1197.9 Second Segment Climb Grad. (.24) 1518637.5 452233.33 457766.67 1335883.33 Second Segment Climb Grad. (lbs/deg) 2652.49 7897.51 7994.14 23328.99 Balanced Field Length (11 ft) -.16-6.34-3.51. Approach Velocity (14 kts) -264.71... Upper Strut Slack Load Factor (.8). -556.56-738.5-5411.56 Sensitivities are valid within 5% of the optimum design The SBW is generally less sensitive than the cantilever optimum 17
Double Deck Fuselage Design Probable improvement in TOGW savings due to larger wing-strut separation Seat and cargo layout was investigated to determine dimensions of the fuselage A double bubble design was adopted giving an extra 5 ft of wing-strut separation 18
Double Deck Layout 44 Business Class Seats 84 Economy Class Seats Top Deck Pantry & Galley Lavatories Lavatories Pantry & Galley Main Deck 24 First Class Seats 168 Economy Class Seats Nose Gear Bay Main Gear Bay Bottom Deck 36 LD-3 containers 19
Double Deck Results 6 5 1.1% 13.6% 12.5% Cantilever Fuselage Mounted Engines SBW Wing Mounted Engines SBW Tip Mounted Engines SBW 9.4% Weight (lbs) 4 3 15.1% 18.6% 19.% 7.44% 1.9% 2 1 12.8% 25.3% 18.4% Calculated Takeoff Weight Wing Weight Fuel Weight Zero fuel weight 2
Lift Distribution of the Flexible Wing Wing sizing from rigid lift distribution gives inaccurate results for maneuver spanload (2.5g and -1g) Lift redistribution due to wing deformation Torsional and bending stiffness from hexagonal wing box Calculation of wing deformation Vortex Lattice Method Recalculation of wing weight from flexible wing spanloads 21
Flexible Wing Sizing Structural wing model Hexagonal wing box with Optimized area/thickness ratios for spar webs, spar caps, stringers, and skins High accuracy (based on Lockheed wing sizing experience) Piecewise linear load representation Validated with Lockheed C-5B and Boeing 747-1 data Aerodynamic model Vortex lattice method 4 spanwise and 1-1 chordwise vortex panels (single analysis or optimization mode) Consideration of panel twist and dihedral Validated with several standard test cases 22
Hexagonal Wing Box Sectional forces and moments on the wing box L Hexagonal Wing-Box.4.3.2.1 M Airfoil z/c -.1 -.2 -.3 -.4 x/c.2.4.6.8 1 Aerodynamic Center Shear Center (Elastic Axis) N g m Center of Gravity 23
Maneuver Load Alleviation Fuselage mounted engine design Reduction of outboard wing angles of attack due to upward bending (wash-out) Aerodynamic loads are shifted inboard SBW load alleviation weaker due to reduced wing box torsional stiffness Further load alleviation possible by employment of strut moment (chordwise strut offset) CL * c/ cave 2.4 2.2 2 1.8 1.6 1.4 1.2 1.8.6.4.2 Normalized lift coefficients C L c/c ave at 2.5g Rigid wing Flexible wing (strut in elas. axis) Flexible wing (strut at front spar).25.5.75 1 Nondimensionalwing span 24
Flexible Wing Weight Calculation LMAS Configuration (Strut at Wing-Box Front Spar) Spanload C L at Wing Root - Convergence History 2.4 2.3 2.2 2 2.2 1.8 1.6 2.1 CL * c/ cave 1.4 1.2 CL * c/ cave 2 1.8.6.4.2 Rigid Wing Iteration no. 1 Iteration no. 2 Iteration no. 3 Iteration no. 4 Iteration no. 5 1.9 1.8 Root C L *c/c ave.25.5.75 1 Nondimensionalwing span 1.7 1 2 3 4 5 6 7 8 9 1 No. of iterations 25
Z Maneuver Load Alleviation Fuselage mounted engine design (Influence of chordwise strut offset) Wing deformation at 2.5g 5 Wing bending weight convergence -1 5 Y Bending material w eight [l b] 48 46 44 42 4 38 36 34 Strut in wing elastic axis Strut at wing-box front spar Strut at wing-box rear spar Wing without strut 32-2 5 25 X 1 3 28 1 2 3 4 5 6 7 8 9 1 No. of iterations 26
Significance of Flexible Wing Sizing Wing sizing using flexible wing loads is more accurate Impact on MDO results is comparably small Rigid wing sizing gives conservative results for cantilever wing, fuselage mounted and underwing mounted engines SBW But: flexible wing sizing indicates higher wing weights for tip mounted engines SBW 27
Z Z Maneuver Wing Deformation Tip Mounted Engine Case 2.5g (engine C.G. in el. axis) -1g (engine C.G. in el. axis) -1 5 Y -1 5 Y -2 1-2 1 5 25 X 5 2.5g maneuver downward deflection of the outboard wing sections increased outboard wing loading (wash-in!) 25 X 28
Flexible Wing Lift Distribution Normalized lift coefficients C L c/c ave at 2.5g Fuselage mounted engine Tip mounted engine 2.4 2.2 2 1.8 2.4 2.2 2 1.8 Rigid wing Flexible wing (strut and engine in el. axis) Flexible wing (strut in el. axis, engine at -c tip ) Flexible wing (strut at front spar, eng. at -c tip ) CL * c/ cave 1.6 1.4 1.2 1 CL * c/ cave 1.6 1.4 1.2 1.8.8.6.4.2 Rigid wing Flexible wing (strut in elas. axis) Flexible wing (strut at front spar).6.4.2.25.5.75 1 Nondimensional wing span.25.5.75 1 Nondimensionalwing span 29
Wing Bending Material Weight Reduction of wing loading using chordwise engine and strut position Bending material weight lb 5, 49, 48, 47, 46, 45, 44, 43, 42, 41, 4, Rigid wing Engine in el. axis Engine moved forward Engine moved aft.2.4.6.8 1 Chordwise strut position (from LE) Engine offset = ± c tip 3
Tip Mounted Engine 2.5g maneuver spanload convergence Lowest weight configuration 2.4 2.2 2 1.8 1.6 Higher weight configuration 2.4 2.2 2 1.8 1.6 CL * c/ cave 1.4 1.2 CL * c/ cave 1.4 1.2 1.8.6.4.2 Rigid Wing Iteration no. 1 Iteration no. 2 Iteration no. 3 Iteration no. 4 Iteration no. 5 1.8.6.4.2 Rigid Wing Iteration no. 1 Iteration no. 2 Iteration no. 3 Iteration no. 4 Iteration no. 5.25.5.75 1 Nondimensionalwing span.25.5.75 1 Nondimensionalwing span 31
Z Z Tip Mounted Engine 2.5g maneuver wing deformation Lowest weight configuration Higher weight configuration -1 5 Y -1 5 Y -2 1-2 1 5 25 X 5 25 X 32
Inboard Wing Buckling Sharp angle between wing and strut Very high horizontal strut force component Inboard wing compressive loading Investigation of inboard wing buckling due to strut force 33
SBW Wing Buckling Analysis Developed a finite element code The code should be fast enough as part of the MDO code Analytical formulation for non-prismatic beam elements to increase the accuracy and CPU time The geometric stiffness matrix for buckling analysis is based on the variational principle approach Sensitivity and optimization for the buckling case Validation of the finite element code Comparison with Nastran 34
Validation 1: Cantilever Beam 4. 3.5 Distributed moment load Error (%) 3. 2.5 2. 1.5 1..5. -.5 Nastran, tip deflection Nastran, tip rotation Proposed FEM 2 4 6 8 Number of elements { 1 r ( y L) } m EI ( y) = EI + / r = 8, m = 1 Method n δ θ Exact 43.381 7.15157 Proposed FEM 1 43.381 7.15157 Nastran 1 41.47918 6.97917 2 42.84853 7.13132 4 43.1138 7.14941 8 43.2988 7.15147 35
Validation 4: Frame Deformations at Point 1 8 z 7 8 5 6 Number of elements used to model y 4 3 the CBEAM Element 26 9 1 2 x 5 elem ents Tx Ty Tz Rx Ry Rz Nastran 1 -.383227-15.2764 5.837361.1785532 7.1299 4.484954 2.7393996-16.3194 6.142943.191991 7.357551 4.86171 4.916125-16.49624 6.194315.1932184 7.415675 4.8651 8.9318146-16.51196 6.198881.193468 7.42843 4.865334 Present FEM 1.9325615-16.51271 6.19997.1934158 7.42189 4.865564 36
Validation 4: Frame 1. -15.2.9325615.916125.9318146-15.2764.8.7393996-15.4 NASTRAN Present FEM.6-15.6.4-15.8 Tx Ty.2-16.. -16.2 NASTRAN -16.3194 -.2 Present FEM -16.4 -.383227-16.51271-16.49624-16.51196 -.4 1 2 3 4 5 6 7 8 9 Number of Elements -16.6 1 2 3 4 5 6 7 8 9 Number of Elements 37
Validation 7: Buckling Analysis P Tapered beam EI = EI o (1+rx/L) r=8 5/16 L 1/4 L 7/16 L Nastran P = 21.45 (16 elements) Present FEM P = 21.449322778195 38
Optimum Beam Stiffness Distribution L k P EI = EA n ; n = 1 = (h root + m x) 2 ; q = k L / P r = h root / h tip 2 = 4P / E E I L The optimum buckling load P optimum = 2 A(x) = = r ln r ( r 1) 4 { 2( q 1) ( r 1) r ln r( q 1) ln r } q 2 2 m 2 h(x) ( )( r 1) 2 m(q 1)(L x) + q h root L + mq m (L x)lnh mid (q 1 qx / L)h tip ln h tip h(x)lnh(x) 39
Variation of the Strut Junction Position Pwing x 1 kipps 1 9 8 7 6 5 4 3 2 1 Required Pwing Wing without strut Wing with Strut Config. SF 811.1.2.3.4.5.6.7.8.9 1 x/l Assume that the changes of the wing/strut junction position stiffness does not change the wing stiffness P buckling increases as the junction moves inboard Additional geometric stiffness matrix of the strut increases the buckling load 4
Offset Length Variation 2.5 2. 1.5 1..5 SF Opt 811 data 1 EI 1 EI 1 EI Config. SF Opt 811, + 2.5 g maneuver h = the offset beam length h reference = h actual = 2.21ft The change of the P buckling is related also to the slope between the strut and wing and the diameter of the fuselage. 1 2 3 4 5 6 7 8 9 1 h / h reference 41
Offset Length and Position Effects 8 7 Spanwise position of the junction y =.65 for 2.5 g maneuver 6 5 4 Move inboard y =.71 y =.76 y =.8 y =.84 y =.9 y =.97 P / Prequired 3 2 1 2 4 6 8 1 Offset length factor h / h actual 42
Future Work u u u We have submitted a proposal together with NASA Langley and Lockheed Martin for the REVCON (Revolutionary Concepts) project REVCON involves building and testing a concept demonstrator within the next three years Program phases Phase 1: 9 months $3, Phase 2: 3 years $2 million 43