Airfoil Design for Mars Aircraft Using Modified PARSEC Geometry Representation
Airfoil Design for Mars AircraftUsing Modified PARSEC Geometry Representation Masahiro Kanazaki Tokyo Metropolitan University Tomoyoshi Yotsuya Tokyo Metropolitan University Kisa Matsushima University of Toyama
Contents 2 Background Objectives Design methods Airfoil representation by modified PARSEC method Evaluation by computational fluid dynamics (CFD) Design optimization by genetic algorithm (GA) Knowledge discovery by scatter plot matrix (SPM) Formulation Results Maximization result of maximum lift to drag ratio (t/c=0.07c, 0.10c) Visualization result by Parallel Coordinate Plot (PCP) Conclusions
Background1 3Image of MELOS ”Mars airplane” is proposed as a part of the MELOS. Technical challenges Propulsion Aerodynamic design Structure ・What kind of airfoil/wing geometry achieves higher performance? ・Ishii airfoil is one of the promising design.
Background2 4Difficulty of flight in the Martian atmosphere gravity density Viscosity Sonic speed atmospheric [m/s2] [kg/m3] [10-5Pa・s] [m/s] constituent The Earth 9.8 1.17 1.86 345 N2，O2The Mars 3.2 0.0118 1.36 258 CO2 1/3 gravity of the earth → Required lift is 1/3. 1% density of the earth → Lift is required to be hundredfold increased. ⇒ Lift of the Mars-airplane have to be about 33rd times lift as much as that of the Earth-airplane. 3/4 speed of sound → Compressibility should be considered even for relative slow flight. Knowledge has to be acquired for unknown design problem. Efficient design method is required for Mars-airplane design.
Background3 5 Airfoil representations for unknown design problem B-spline curve, NURBS Good for use in CAD software Not good for use with data mining PARSEC(PARametric SECtion) method* Parameterization geometrical character based on knowledge of transonic flow Separately definition upper surface and lower surface Easy to introduce automated design method such as genetic algorithm Aerodynamic performances can be explained based on design variables. A few geometrical parameters around the leading-edge*Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998.
Background4 6 Modification of PARSEC representation** Separately defined thickness distribution and camber This definition is in theory of wing section Successful representation of supersonic airfoil Maintain the beneficial feature of original PARSEC A few numbers of design variables Aerodynamic performances can be explained by design variables.** K. Matsushima, Application of PARSEC Geometry Representation to High-Fidelity Aircraft Design by CFD,proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008.
Objectives 7Design exploration of airfoil for Mars-airplane using modified PARSEC airfoil representation Design exploration using CFD and GA Selection of promising designs and comparisons of their performances with baseline (Ishii airfoil) Knowledge discovery by means of PCP
Design methods1 8 Airfoil representation by modified PARSEC method Designed by thickness distribution and camber . The leading edge radius center is always on the camber. The thickness distribution is same as symmetrical airfoil by PARSEC. The camber is defined by a quintic equation. By adding the root term for root camber, the design performance of the leading-edge is improved. Number of design variables is 12.Thickness 6 Camber 2 n1 5 z t an x 2 zc b0 x bn x n n 1 n 1 ＋
Design method2 9Evaluation by CFD Two dimensional Reynolds averaged Navier-Stokes flow solver (RANS) QdV F nds 0 t Time integration : LU-SGS implicit method Flux evaluation : Third-order-accuracy upwind differential scheme with MUSCL method Turbulent model : Baldwin-Lomax model Grid : C-H type structured grid Grid size: 11,651 points Computational grid
Design method3 10 Genetic algorithm (GA) Global optimization Inspired by evolution of life Selection, crossover, mutation Parallel Coordinate Plot (PCP) For the design problem visualization One of statistical visualization techniques from high- dimensional data into two dimensional graph Normalized design variables and objective functions are set parallel in the normalized axis
Formulation1Design problem (Single objective) Maximize maximum L/D subject to t/c=target t/c (t/c=0.07c, 0.10c)Computational condition Martian atmosphere Density=0.0118kg/m3 Temperature=241.0K Speed of sound=258.0m/s Free stream Velocity=60m/s Reynolds number：208,235.3 Mach number：0.233
Formulation2Design space 0.35 for t/c=0.07c 0.50 for t/c=0.10c
Result1 13Convergence history of GA exploration t007c-1 Best design in t007c-2 this generation t010c-1 t010c-2 Worst design in this generation t/c=0.07c t/c=0.10c Population size: 20 15 generations for t/c=0.07c，11 generations for t/c=0.10c (in progress) In each case, solutions are almost converged. (Maximum l/d 45, and 38, respectively.) Four promising solutions are picked up.
Result2 14α vs. l/d t0.07c-1 and -2 achieve better performance than baseline. t0.10c-1/-2 achieve almost same maximum l/d, and better performance at not design point.
Result3 15α vs. Cl t0.07c-1, -2, t0.10c-1, and -2 achieve similar Cl-AoA. l/d is improved because of higher Cl.
Result4 16α vs. Cd In t=0.07c design, drag was increased 5% compared with baseline. In t=0.10c design, drag was increased 10% compared with baseline. Drag minimization also have to be considered for next step.
Result5 17Geometry and flowfield (t/c=0.07c) t007c-1(AoA=2.9deg.) t007c-2(AoA=3.0deg.) Cp distributions when the airfoil achieves maximum l/d obtained from t007c case Thickness distribution is similar to baseline. LE radiuses of t007c-1/-2 are smaller than that of baseline. Cambers of t007c-1/-2 are larger than that of baseline. Baseline (AoA=4.0deg.) Pressure recoveries on the upper surfaces of t007c-1/-2 are relaxed.
Result6 18Geometry and flowfield (t/c=0.07c) t010c-1(AoA=3.2deg.) t010c-2(AoA=3.3deg.) Cp distributions when the airfoil achieves maximum l/d obtained from t010c case. LE radiuses of t007c-1/-2 are smaller than that of baseline. Cambers of t007c-1/-2 are larger than that of baseline. Pressure recoveries on the upper surfaces of t010c-1/-2 are also relatively relaxed. Baseline (AoA=4.0deg.)
Result7 Comparison of parameters among solutions and baseline Modified PARSEC represents Ishii like airfoil by parameter identification. t007c-1 t007c-2 t010c-1 t010c-2 Ishii like airfoil dv1 LE radius (rle) 0.0040 0.0042 0.0042 0.0053 0.0086 x-coord. of maximum ・x coordinate (dv7) of maximum camber dv2 thickness (xt) 0.2891 0.2891 0.3322 0.3333 0.2000 LE radius small comes up to LE. dv3 z-coord. of maximum thickness (zt) 0.0350 0.0350 0.0500 0.0500 0.0350 ・ LE camber (dv6), maximum camber,(dv8) -0.5837 dv4 curvature at maximum thickness (zxxt ) -0.5275 -0.5276 -0.5841 -0.4600 and TE camber (dv11) tend to be large. dv5 angle of TE (βte) 7.9650 7.9649 8.7658 8.7707 5.0000 dv6 camber radius at LE (rc) 0.0024 0.0024 0.0033 0.0023 0.0016 x-coord. of maximum camber dv7 (xc) 0.3276 0.3244 0.3124 0.3123 0.5200 z-coord. of maximum camber dv8 (zc) 0.0352 0.0332 0.0375 0.0379 0.0200 curvature at maximum camber dv9 (zxxc) -0.0269 -0.0212 -0.0049 -0.0077 -0.2500 dv10 z-coordinate of TE (zte) -0.0045 -0.0087 -0.0007 -0.0008 0.0000 dv11 angle of camber at TE (αte) 9.3007 9.1802 10.2644 11.2638 4.5000
Result8 20Visualization of design problem (t/c=0.07c) Baseline l/d>43.0 All solutions obtained by GA Pick up individuals which achieve better L/D than 43.0
Result8 21Visualization of design problem (t/c=0.07c) Baseline l/d>43.0 To obtain better maximum l/d, Smaller LE radius (dv1), and curvature (dv4) Closer maximum camber position xc (dv7) to LE Larger angle of TE (dv5) Larger curvature maximum camber (dv9) Larger camber angle at TE (dv11) Almost same thickness at 25% chord and 75% cord compared with baseline
Result9 22Visualization of design problem (t/c=0.10c) Baseline l/d>4370 All solutions obtained by GA Pick up individuals which achieve better L/D than 37.0
Result9 23Visualization of design problem (t/c=0.07c) l/d>37.0 To obtain better maximum l/d, Smaller LE radius (dv1), and curvature (dv4) Closer maximum camber position xc (dv7) to LE Larger angle of TE (dv5) Larger curvature maximum camber (dv9) Larger camber angle at TE (dv11) Almost same thickness at 25% chord and 75% cord compared with baseline
Result10 24Comparison between two cases (t/c=0.07c and t/c=0.10c) t007c-1 Green: t/c=0.07 Purple: t/c=0.10 t010c-1 Almost same design variables (except for thickness) showed better objective function compared with two cases.
Conclusions 25 Design exploration of airfoil for Mars-airplane Design optimization using CFD and GA Selections of promising designs and investigations of their performances Improvement of maximum l/d in t/c=7% case Acquirements of airfoils which achieves relaxed pressure recovery on the upper surface Higher Cl, but higher Cd than baseline Knowledge discovery by means of ANOVA and SPM to obtain better maximum l/d Smaller LE radius, and uppersurface curvature Closer maximum camber position xc to LE Larger angle of TE Larger curvature maximum camber Larger camber angle at TE Further study: Consideration of Cd minimization
Acknowledgement 26We thank members of the Mars-airplane working group in ISAS/JAXA for giving their experimental data and their valuable advices. Thank you very much for your kind attention.