A TWO ELEMENT LAMINAR FLOW AIRFOIL OPTIMIZED FOR CRUISE. A Thesis GREGORY GLEN STEEN

A TWO ELEMENT LAMINAR FLOW AIRFOIL OPTIMIZED FOR CRUISE A Thesis by GREGORY GLEN STEEN Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE August 1994 Major Subject: Aerospace Engineering

A TWO ELEMENT LAMINAR FLOW AIRFOIL OPTIMIZED FORCRUISE A Thesis by GREGORYGLEN STEEN Submittedto TexasA&M University in partialfulfillment of the requirements for the degree of MASTER OF SCIENCE Approved as to style and content by: / Leland A. Carlson Kenneth D. Korkan (Co-Chair of Committee) (Co-Chair of Committee) Gerald _/. Morrison (Member) Walter E. Haisler (Head of Department) August 1994 Major Subject: Aerospace Engineering

111 ABSTRACT A Two Element Laminar Flow Airfoil Optimized for Cruise. (August 1994) Gregory Glen Steen, B.S., Texas A&M University Co-Chairs of Advisory Committee: Dr. Leland A. Carlson Dr. Kenneth D. Korkan Numerical and experimental results are presented for a new two element, fixed geometry natural laminar flow airfoil optimized for cruise Reynolds numbers on the order of three million. The airfoil design consists of a primary element and an independent secondary element with a primary to secondary chord ratio of three to one. The airfoil was designed to improve the cruise lift-to-drag ratio while maintaining an appropriate landing capability when compared to conventional airfoils. The airfoil was numerically developed utilizing the NASA Langley Multi-Component Airfoil Analysis computer code running on a personal computer. Numerical results show a nearly 11.75% decrease in overall wing drag with no increase in stall speed at sailplane cruise conditions when compared to a wing based on an efficient single element airfoil. Section surface pressure, wake survey, transition location, and flow visualization results were obtained in the Texas A&M University Low Speed Wind Tunnel. Comparisons between the numerical and experimental data, the effects of the relative position and angle of the two elements, and Reynolds number variations from 8x15 to x16 for the optimum geometry case are presented.

iv ACKNOWLEDGMENTS This material is based upon work supported by the NASA-Langley Research Center under Grant No. NAG-l-1522. Sincere thanks are extended to Dr. Michael F. Card at the NASA Langley Research Center for supporting the effort. Acknowledgment is also due to Mr. Harry L. Morgan, Jr. of NASA Langley for providing a copy of the MCARFA computer code and Mr. Bill Cleary of Ciba-Geigy Corporation for donating the Ren Shape used in the wind tunnel model construction. A great debt of thanks is due to the members of my Advisory Committee Dr. Leland Carlson, Dr. Kenneth Korkan, and Dr. Gerald Morrison. I thank them all for supporting me through the extended period of time required for me to finish this thesis part time and for giving me three outstanding examples of professional success and personal character. I also wish to thank the staff of the Texas A&M University Low Speed Wind Tunnel for their support and friendship through the completion of my education and the start of my professional career. I would especially acknowledge Mr. Oran Nicks, who served not only as my boss, but also as a trusted advisor and friend. I feel extremely fortunate to have had the opportunity to work with and learn from such a truly exceptional man. Finally, I would like to thank my family. I am etemally indebted to my parents Harvey and Ila Steen for teaching me everything really important in life and supporting me in anything I ever chose to do. I would like to close by thanking my wife Kathy and son Kyle whom are my reason for life itself. They have helped, pushed, supported, and loved me more than they will ever know.

V TABLE OF CONTENTS ABSTRACT... iii ACKNOWLEDGMENTS... iv Page TABLE OF CONTENTS... v LIST OF FIGURES... vii LIST OF TABLES... xv NOMENCLATURE... xvi INTRODUCTION... 1 PROBLEM DESCRIPTION... NUMERICAL TOOLS... 5 MCARFA Background... 5 MCARFA Airfoil Geometry Specification... 6 MCARFA Potential Flow Solution... 7 MCARFA Boundary Layer Solution... 9 MCARFA Program Accuracy... 12 PROFIL Background... 16 PROFIL Potential Flow Solution... 17 PROFIL Boundary Layer Solution... 18 PROFIL Accuracy... 19 NUMERICAL RESULTS AND DISCUSSION... 2 Existing Single Element Airfoils... 2 Profile Shape... 22 Relative Position... 2

vi Page RelativeAngle... 57 Modified Profile Shapes... 57 AG91Airfoil... 62 ComparisonWith OtherAirfoils... 75 TransitionLocation... 85 EXPERIMENTAL TOOLS... 88 Wind Tunnel... 88 Airfoil Model... 9 Instrumentation... 94 DataReduction... 96 Flow Visualization... 98 EXPERIMENTAL RESULTSAND DISCUSSION... 1 AG91APrimaryElementAlone... 1 RelativePosition... 16 TransitionLocation... 111 ImprovedWind TunnelModel... 12 UncertaintyAnalysisandDataRepeatability... 16 SpanwiseDragVariation... 141 CONCLUSIONS... 14 REFERENCES... 146 APPENDIXA... 152 VITA... 157

vii LIST OF FIGURES Page Fig. 1 Fig. 2 Fig. Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 1 Fig. 11 Fig. 12 Fig. 1 Fig. 14 Fig. 15 Fig. 16 Fig. 17 Fig. 18 Fig. 19 Fig. 2 Fig. 21 Fig. 22 Concept Airfoil... 2 MCARFA exact test Case A results... 1 MCARFA exact test Case B results... 1 NACA 212 with 212 flap lift coefficient results... 14 NACA 212 with 212 flap drag coefficient results... 15 NACA 212 with 212 flap L/D ratio results... 15 NACA 212 with 212 flap moment coefficient results... 16 NLF(1)-416 airfoil lift coefficient results... 21 NLF(1)-416 airfoil drag coefficient results... 21 NLF(1)-416 airfoil moment coefficient results... 22 NACA 12 airfoil lift coefficient results... 2 NACA 12 airfoil drag coefficient results... 2 NACA 12 airfoil moment coefficient results... 24 NACA 2412 airfoil lift coefficient results... 24 NACA 2412 airfoil drag coefficient results... 25 NACA 2412 airfoil moment coefficient results... 25 NACA 4412 airfoil lift coefficient results... 26 NACA 4412 airfoil drag coefficient results... 26 NACA 4412 airfoil moment coefficient results... 27 NACA 212 airfoil lift coefficient results... 27 NACA 212 airfoil drag coefficient results... 28 NACA 212 airfoil moment coefficient results... 28

.. Vln Page Fig. 2 Secondary element profile effect on lift coefficient results... Fig. 24 Secondary element profile effect on drag coefficient results... Fig. 25 Secondary element profile effect on L/D ratio results... 1 Fig. 26 Secondary element profile effect on moment coefficient results... 1 Fig. 27 Horizontal position effect on lift coefficient at -4% and 8 = 2... Fig. 28 Horizontal position effect on drag coefficient at -4% and 6 = 2... Fig. 29 Horizontal position effect on L/D ratio at -4% and 8 = 2... 4 Fig. Horizontal position effect on moment coefficient at -4% and 8 = 2... 4 Fig. 1 Horizontal position effect on lift coefficient at -% and 6 = 2... 5 Fig. 2 Horizontal position effect on drag coefficient at -% and 8 = 2... 5 Fig. Horizontal position effect on L/D ratio at -% and 8 = 2... 6 Fig. 4 Horizontal position effect on moment coefficient at -% and 8 = 2... 6 Fig. 5 Horizontal position effect on lift coefficient at -2% and 8 = 2... 7 Fig. 6 Horizontal position effect on drag coefficient at -2% and 8 = 2... 7 Fig. 7 Horizontal position effect on L/D ratio at -2% and 6 = 2... 8 Fig. 8 Fig. 9 Fig. 4 Fig. 41 Fig. 42 Horizontal Horizontal Horizontal Horizontal Horizontal position effect on moment coefficient at -2% and 6 = 2... 8 position effect on lift coefficient at -1.5% and 8 = 2... 9 position effect on drag coefficient at -1.5% and 8 = 2... 9 position effect on L/D ratio at -1.5% and 8 = 2... 4 position effect on moment coefficient at -1.5% and 8 = 2... 4 Fig. 4 Horizontal position effect on lift coefficient with NACA 2412... 41 Fig. 44 Horizontal position effect on drag coefficient with NACA 2412... 41 Fig. 45 Horizontal position effect on L/D ratio with NACA 2412... 42 Fig. 46 Horizontal position effect on moment coefficient with NACA 2412... 42

ix Page Fig. 47 Horizontal position effect on lift coefficient at -2% and 8 = 1... 44 Fig. 48 Horizontal position effect on drag coefficient at -2% and 5 = 1... 44 Fig. 49 Horizontal position effect on L/D ratio at -2% and 5 = 1... 45 Fig. 5 Horizontal position effect on moment coefficient at -2% and 5 = 1... 45 Fig. 51 Horizontal position effect on lift coefficient at -2% and _5= 15... 46 Fig. 52 Horizontal position effect on drag coefficient at -2% and 5 = 15... 46 Fig. 5 Horizontal position effect on L/D ratio at -2% and 8 = 15... 47 Fig. 54 Horizontal position effect on moment coefficient at -2% and 8 = 15... 47 Fig. 55 Fig. 56 Fig. 57 Fig. 58 Fig. 59 Horizontal Horizontal Horizontal Horizontal Horizontal position effect on lift coefficient at -2% and 5 = 25... 48 position effect on drag coefficient at -2% and 5 = 25... 48 position effect on L/D ratio at -2% and 8 = 25... 49 position effect on moment coefficient at -2% and 5 = 25... 49 position effect on lift coefficient at -2% and 5 =... 51 Fig. 6 Horizontal position effect on drag coefficient at -2% and _5=... 51 Fig. 61 Horizontal position effect on L/D ratio at -2% and _5=... 52 Fig. 62 Horizontal position effect on moment coefficient at -2% and 5 =... 52 Fig. 6 Horizontal position effect on lift coefficient at -1.5% and _5=... 5 Fig. 64 Horizontal position effect on drag coefficient at -1.5% and t5 =... 5 Fig. 65 Horizontal position effect on L/D ratio at -1.5% and 5 =... 54 Fig. 66 Horizontal position effect on moment coefficient at -1.5% and _5=... 54 Fig. 67 Horizontal position effect on lift coefficient at -1% and 6 =... 55 Fig. 68 Horizontal position effect on drag coefficient at -1% and 6 =... 55 Fig. 69 Horizontal position effect on L/D ratio at -1% and 6 =... 56 Fig. 7 Horizontal position effect on moment coefficient at -1% and 6 =... 56

X Page Fig. 71 Fig. 72 Fig. 7 Fig. 74 Fig. 75 Fig. 76 Fig. 77 Fig. 78 Fig. 79 Fig. 8 Fig. 81 Fig. 82 Fig. 8 Fig. 84 Fig. 85 Fig. 86 Fig. 87 Fig. 88 Fig. 89 Fig. 9 Fig. 91 Fig. 92 Fig. 9 Fig. 94 Relative angle effect on lift coefficient.... 58 Relative angle effect on drag coefficient... 58 Relative angle effect on L/D ratio... 59 Relative angle effect on moment coefficient... 59 Modified profile shapes... 61 Modified primary profile shape effect on lift coefficient... 6 Modified primary profile shape effect on drag coefficient... 6 Modified primary profile shape effect on L/D ratio... 64 Modified primary profile shape effect on moment coefficient... 64 AG91 horizontal position effect on lift coefficient at - 1%... 66 AG91 horizontal position effect on drag coefficient at -1%... 66 AG91 horizontal position effect on L/D ratio at -1%... 67 AG91 horizontal position effect on moment coefficient at - 1%... 67 AG91 horizontal position effect on lift coefficient at -1.5%... 68 AG91 horizontal position effect on drag coefficient at -1.5%... 68 AG91 horizontal position effect on L/D ratio at -1.5%... 69 AG91 horizontal position effect on moment coefficient at -1.5%... 69 AG91 horizontal position effect on lift coefficient at -2%... 7 AG91 horizontal position effect on drag coefficient at -2%... 7 AG91 horizontal position effect on L/D ratio at -2%... 71 AG91 horizontal position effect on moment coefficient at -2%... 71 AG91 airfoil... 74 Reynolds number effect on numerical lit_ coefficient, 6=".... 76 Reynolds number effect on numerical drag coefficient, 6=... 76

xi Page Fig. 95 Fig. 96 Fig. 97 Fig. 98 Fig. 99 ReynoldsnumbereffectonnumericalL/D ratio,5=... 77 Reynoldsnumbereffecton numericalmomentcoefficient,;5=...77 Reynoldsnumbereffecton numericallift coefficient,5=2... 78 Reynoldsnumbereffecton numericaldragcoefficient,;5=2... 78 Reynolds number effect on numerical L/D ratio, ;5=2... 79 Fig. 1 Fig. 11 Fig. 12 Fig. 1 Fig. 14 Fig. 15 Fig. 16 Fig. 17 Fig. 18 Fig. 19 Fig. 11 Fig. 111 Fig. 112 Fig. 11 Fig. 114 Fig. 115 Fig. 116 Fig. 117 Reynolds number effect on numerical moment coefficient, ;5=2... 79 Reynolds number effect on numerical q/z/c a, 5=2... 8 Lift coefficient comparison of various airfoils... 82 Drag coefficient comparison of various airfoils... 82 L/D ratio comparison of various airfoils.... 8 Moment coefficient comparison of various airfoils... 8 Numerical transition location, ;5 =... 86 Numerical transition location, ;5 = 2... 86 TAMU-LSWT facility diagram... 89 Freestream longitudinal turbulence intensity... 91 AG91 pressure port locations... 9 AG91 airfoil installed in TAMU-LSWT... 94 Experimental AG91A lift coefficient results, Re = 7.5x 15... 11 Experimental AG91 A drag coefficient results, Re = 7.5xl 5... 11 Experimental AG91A L/D ratio results, Re = 7.5x15... 12 Expenmental AG91A moment coefficient results, Re = 7.5x 15... 1 Experimental AG91A lift coefficient results, Re = 2.25x16... 1 Experimental AG91A drag coefficient results, Re = 2.25xl 6... 14 Fig. 118 Experimental AG91A L/D ratio results, Re = 2.25x16... 14

xii Page Fig. 119 Fig. 12 Fig. 121 Fig. 122 Fig. 12 Fig. 124 Fig. 125 Fig. 126 Fig. 127 Fig. 128 Fig. 129 Fig. 1 Fig. 11 Fig. 12 Fig. 1 Fig. 14 Fig. 15 Fig. 16 Fig. 17 Fig. 18 Fig. 19 Fig. 14 Fig. 141 Fig. 142 ExperimentalAG91Amomentcoefficientresults,Re= 2.25x16...15 AG91experimentalL/D ratio,94%,-1% position,8=...17 AG91expenmental momentcoefficient,94%,-1%position,8=...17 AG91experimental L/D ratio,94%,-1.5%position,8=...18 AG91experimental momentcoefficient,94%,-1.5%position,8=...18 AG91expenmental L/D ratio, 94%,-2% position,8=...19 AG91experimental momentcoefficient,94%,-2%position,6=... 19 AG91experimental AG91experimental AG91expenmental AG91experimental AG91experimental AG91experimental AG91experimental AG91expenmental AG91experimental AG91experimental AG91experimental AG91experimental AG91 AG91 AG91 AG91 AG91 L/D ratio, 95%, -1% position, 8=... 11 moment coefficient, 95%, -1% position, 8=... 11 L/D ratio, 95%, -1.5% position, 8=... 112 moment coefficient, 95%, -1.5% position, 8=... 112 L/D ratio, 95%, -2% position, 8=... 11 moment coefficient, 95%, -2% position, 8=... 11 L/D ratio, 96%, -1% position, 8=... 114 moment coefficient, 96%, -1% position, 8=... 114 L/D ratio, 96%, -1.5% position, 8=... 115 moment coefficient, 96%, -1.5% position, 8=... 115 L/D ratio, 96%, -2% position, 8=... 116 moment coefficient, 96%, -2% position, 8=... 116 experimental transition location, 8 =... 117 fixed transition effect on lift coefficient, 8 =... 118 fixed transition effect on drag coefficient, 8 =... 118 fixed transition effect on moment coefficient, 8 =... 119 fixed transition effect on L/D ratio, 8 =... 119

oo. Xlll Page Fig. 14 AG91 experimental lift coefficient, 8 =, Re = 8xlO 5... 121 Fig. 144 AG91 experimental lift coefficient, 5 =, Re = lxl6... 121 Fig. 145 AG91 experimental drag coefficient, 5 =, Re = lxl6... 122 Fig. 146 AG91 experimental L/D ratio, c5=, Re = lxl6... 122 Fig. 147 AG91 experimental moment coefficient, 5 =, Re = 1x 16... 12 Fig. 148 AG91 experimental lift coefficient, 5 =, Re = 2x16... 12 Fig. 149 AG91 experimental drag coefficient, 8 =, Re = 2xlO 6... 124 Fig. 15 AG91 experimental L/D ratio, 8 =, Re = 2x16... 124 Fig. 151 AG91 experimental moment coefficient, 5 =, Re = 2x16... 125 Fig. 152 AG91 experimental lift coefficient, _5=, Re = x1 6... 126 Fig. 15 AG91 experimental drag coefficient, 5 =, Re = x16... 126 Fig. 154 AG91 experimental L/D ratio, 8 =, Re = x16... 127 Fig. 155 AG91 experimental moment coefficient, 5 =, Re = x16... 127 Fig. 156 AG91 experimental lift coefficient, 5 = 2, Re = lxl6... 128 Fig. 157 AG91 experimental drag coefficient, 5 = 2, Re = lxlo 6... 128 Fig. 158 AG91 experimental L/D ratio, _5= 2, Re = lxlo 6... 1 Fig. 159 AG91 experimental moment coefficient, 6 = 2, Re = lxl6... 1 Fig. 16 AG91 expenmental lift coefficient, 5 = 2, Re = 2x 16... 11 Fig. 161 AG91 experimental drag coefficient, _5= 2, Re = 2x16... 11 Fig. 162 AG91 expenmental L/D ratio, _ = 2, Re = 2xlO 6... 12 Fig. 16 AG91 expenmental moment coefficient, _5= 2, Re = 2xl 6... 12 Fig. 164 AG91 experimental lift coefficient, 8 = 2, Re = x16... 1 Fig. 165 AG91 experimental drag coefficient, _5= 2, Re = x16... 1 Fig. 166 AG91 experimental L/D ratio, 5 = 2, Re = x16... 14

xiv Fig. 167 AG91experimentalmomentcoefficient,8 = 2, Re= x16...14 Fig. Fig. Fig. Fig. 171 Reynoldsnumbereffectonexperimentalmomentcoefficient...17 Fig. Fig. 17 Uncertaintyanalysisof experimentaldragcoefficient... 18 Fig. Fig. Fig. Fig. Fig. Fig. 179 AG91spanwisedragcoefficient,8= 2, Re = x16... 142 Page 168 Reynoldsnumbereffectonexperimentalift coefficient... 15 169 Reynoldsnumbereffecton experimentaldragcoefficient... 15 17 Reynoldsnumbereffecton experimentall/d ratio... 17 172 Uncertaintyanalysisof experimentalift coefficient... 18 174 Uncertaintyanalysisof experimentall/d ratio... 19 175 Repeatabilityof experimentalift coefficient... 19 176 Repeatabilityof experimentaldragcoefficient... 14 177 Repeatabilityof experimentalmomentcoefficient... 14 178 Repeatabilityof experimentall/d ratio... 141

XV LIST OF TABLES Page Table 1 Table 2 Table Table 4 MCARFA and Williams' exact aerodynamic load results... 14 AG91A airfoil coordinates... 72 NACA 4412 airfoil coordinates... 7 Airfoil comparison at Reynolds number of xl 6... 84

xvi NOMENCLATURE Symbol Cp Title Pressure Coefficient C Total Airfoil Chord (defined as cl + c2 for two element airfoils) c/4 el C2 CA Ca Cd Cl cm Cm CN Cn Quarter Chord Location Primary Element Airfoil Chord Secondary Element Airfoil Chord Total Airfoil Axial Force Coefficient Airfoil Axial Force Coefficient Section Drag Coefficient Section Lift Coefficient Centimeter Section Moment Coefficient About the Quarter Chord Location Total Airfoil Normal Force Coefficient Airfoil Normal Force Coefficient D Drag Force kva Kilo-Volt Amp L Lift Force L/D LSWT m mm NACA NASA Lift to Drag Ratio Low Speed Wind Tunnel Meter Millimeter National Advisory Committee for Aeronautics National Aeronautics and Space Administration

xvii Symbol Pa P Title Pascal Local Pressure Ps Pt Freestream Static Pressure Freestream Total Pressure q Re Dynamic Reynolds Pressure Number R%2 RPM T TAMU U_ U I X y, Z Reynolds Number Based on Boundary Layer Momentum Thickness Revolutions per Minute Longitudinal Flow Turbulence Intensity Texas A&M University Longitudinal Mean Velocity Component Longitudinal Fluctuating Velocity Component Longitudinal Airfoil Coordinate Vertical Airfoil Coordinate Angle of Attack Cto 8, 82 F,y P P Zero Lift Angle of Attack Relative Angle of Secondary Element Circulation Viscosity Density Stream Function

INTRODUCTION Since a wing is the primary source of lift and a major contributor to drag, it is of prime interest in any major attempt to increase aerodynamic performance. A good wing design will provide lift in the most efficient way possible. An important goal in the design of a wing is the selection of an airfoil with a high lift-to-drag ratio, as "the _/" " 9, lift-to-drag ratio is a measure of the aerodynamic emclency... The use of flap systems on airfoils can greatly increase the maximum lift coefficient of the system. The primary use of flaps has been to increase the maximum lift for take-off and landing while maintaining a reasonably small wing for cruise conditions. Many low Reynolds number aircraft, including the new World Class glider 2, have been specifically designed without moveable flap systems. Since they must cruise, take-off, and land with the same wing, design trade-offs must be considered in the selection of an airfoil configuration. The current effort reports on the viability of a two element fixed geometry airfoil designed to provide low drag for cruise conditions and high lift for landing. The airfoil under study consists of two distinct elements arranged similar to wings having external airfoil flaps (Fig. 1). Various combinations of profile shape, element location, and relative angle have been explored. The intent of this research has been to develop a two element airfoil with an L/D greater than that for a comparable single element airfoil at cruise lift coefficients, while providing high lift coefficients for the landing configuration. The final configuration must provide the same stall and cruise speed as comparable fixed geometry single element airfoils. Journal Model is the AIAA Journal of Aircraft.

2 The study has been conducted using widely available numerical tools for multi component airfoil analysis, very fast and accurate numerical tools for single element airfoil analysis, and the Texas A&M University Low Speed Wind Tunnel for experimental verification of the final airfoil design. Fig. 1 Concept Airfoil

PROBLEM DESCRIPTION The original idea for the current study came from experimental data acquired in the early days of airfoil research. National Advisory Committee for Aeronautics (NACA) researchers embarked on a systematic study of various airfoil shapes in the early 194's. The culmination of this work is the classic NACA Report No. 824 titled "Summary of Airfoil Data. ''a'4 Examination of some slotted flap data presented in the NACA report yields an interesting result. Small flap deflections often result in very little increase in drag coefficient but a significant increase in lift coefficient. For example, experimental data from a NACA 6,4-42 airfoil with a 25% chord slotted flap deflected 25 show a nearly 4% increase in cruise L/D over the same airfoil with flap deflection when adjusted for the different maximum lift coefficients. Based on the NACA experimental data, it should be possible to design a new two-element airfoil that will utilize the favorable interactions between the two elements to improve upon the L/D ratio at cruise conditions while maintaining an appropriate take-off and landing capability. Various airfoil configurations, from simple flaps to complex multi-component Fowler flaps have been extensively explored for use as high lift devices, s'16 It has even been mathematically proven that n+ 1 elements are better than n elements for providing maximum lift. 17 However, very little research has been performed on using a multielement airfoil for cruise conditions since the emphasis has always been on increasing lift and not L/D. Bauer did study the two element airfoil problem using hand launched gliders, j8 His glide slope measurement results, although not definitive, provide support to the basic concept of a low drag two element cruise airfoil.

4 The currentstudytook a systematicapproachto the analysisanddesignof a two-element cruise airfoil. The concept was first explored analytically using widely accepted numerical methods. The final design was experimentally verified using a wind tunnel model of the airfoil. The overall study consisted of five basic steps. First, the accuracy of the numerical tools was studied by comparing results with published experimental and other numerical data. Next, the effects of relative profile, relative angle, and relative position of the two elements in the configuration were numerically studied. Third, a new two element airfoil was designed based on knowledge gained during the parametric variation study. Fourth, a complete numerical database was obtained on the new two element airfoil at various Reynolds numbers corresponding to actual flight conditions. Finally, a wind tunnel model was built and tested to experimentally verify the final numerical results.

NUMERICAL TOOLS The new airfoil under study was designed and initially analyzed using commercially available numerical methods. All numerical studies were performed using an Intel 486 based personal computer running at MHz. The primary numerical tool used for the entire study was the NASA Langley Multi-Component Airfoil Analysis Code (MCARFA). All single element airfoils were also studied using Dr. Richard Eppler's Airfoil Program System (PROFIL) in order to further validate the MCARFA results. MCARFA Background The MCARFA computer code was originally developed under NASA contract to the Lockheed-Georgia Company in the early 197's. 19'2 Major upgrades to the program were completed, again under NASA contract, by the Boeing Company in the late 197's. 21'22 Currently, the NASA Langley Research Center is the prime source for the code and work on incremental improvements and program maintenance as the need arises. The MCARFA code is an analytical model which computes the performance characteristics of multi-component airfoils in subsonic, compressible, viscous flow. z-zs The final converged solution is obtained by successively combining an inviscid solution with a boundary layer displacement thickness. The surface of each airfoil element is approximated by a closed polygon with segments represented by distributed vortex singularities. The boundary layer solution is comprised of mathematical models representing the laminar, transition, turbulent, and confluent boundary layers. The MCARFA program is composed of three main parts: the geometry specification, the potential flow solution, and the boundary layer solution. The

6 program uses an iterative procedure to obtain the viscous solution in five basic steps: 1) compute the potential flow solution for the basic airfoil, 2) compute boundary layer properties based on the potential flow solution, ) construct a modified airfoil by adding the boundary layer displacement thickness to the original airfoil, 4) compute the aerodynamic performance coefficients, and 5) repeat steps 1) through 4) until convergence of the performance coefficients is obtained. Actual convergence is determined by requiring the calculated lift coefficient to converge to within.5 of the previous value. MCARFA Airfoil Geometry Specification The user inputs the desired airfoil element coordinates into the program. Within the program, the element is modeled as a polygon approximation. This polygon consists of N number of corner points with N-1 straight line segments. To obtain accurate results, computational surface points are chosen which may differ in number and location from the input surface coordinates. The total number of computational surface points is an input, as is the number of points on each element. The location of the computational surface points is determined based on local surface curvature. To use this method, the curvature at each user input coordinate is computed with the formula: K

7 where at, a2, and a are taken from a curve fit of the airfoil points. A curvature summation is then computed from the following equation and stored for backward interpolation: Ki = J'tKI ds where: s i =s +x/(x_ - x t) 2 +(zi -zh) 2 The maximum value of K is divided into N equal portions and the s value corresponding to each portion is then determined by backward interpolation between the si and K i arrays. MCARFA Potential Flow Solution The potential flow solution method used in the MCARFA code is a distributed vortex singularity method first formulated by Oellers 26 to compute the pressure distribution on the surface of airfoils in cascade. Instead of working with induced velocities, as is common in many panel method programs, Oellers' method employs stream functions. The stream function for a uniform stream plus that for a vortex sheet is set to be a constant on the airfoil surface. This is mathematically represented by the Fredholm integral equation: $1T U,_x(s) cos_- U,_z(s) sinct V= _n ojy(_)in[r(s'_)]d_=

wherev is the unknown stream function constant, r(s,_) is the distance between the two points on the airfoil surface, x(s) and z(s) are coordinates of a point on the surface, and ),(_) is the vortex strength at a point. By dividing the surface into N segments and assuming constant vortex strength for each segment the above equation becomes: N V- _-_AoTj = U_ (x i cos(x - z i sina) j=l where the influence coefficient A is: sj? Aij= Jln[r(si,_)]d_ By specifying a control point at the midpoint of each segment, the influence coefficient becomes:,t E/t l /t/] Ao : _--n-n[ 2 ln(r2) - t, ln(r,)]- _-n + _-n tan-' - tan-' _- (icj) Ai j = _-_[-As [ln(\-_--)as'l - 1] (i = j) where: As = s j+ I -- Sj ri = (xj - xc,i) 2 + (zj 1 - zc.i) 2 tl= r2 = (x j+, - xc. i )2 + (zi ' _ z_.i )2 (xj - x_.,)(xj+,- xj) + (zj - zo.,)(zj l- zj) As

12 = t = (xj+,- xo.,)(xj+,- xj) + (zj+, - zo.,)(zj+,- zj) As (xj - x.+)(zj+,- zj) + (zj - zo._)(xj+, As -xj) To determine the vortex strength (_) at the intersection of two segments, the following interpolation formula is used: _j= _,j_,(sj - %,) +? j(sj+,- sj) Sj+ I -- S j_ 1 (j IorN) The unknowns in the method are now N-1 number of y's and V, therefore an additional equation is needed to obtain an N by N system of equations. The final equation comes from applying the Kutta condition at the trailing edge. The particular formulation of the Kutta condition used requires that the vortex strengths (_) vary quadratically for the last four segment comers near the upper and lower surface of the trailing edge and that at the trailing edge the upper and lower surface vortex strengths are equal in magnitude but opposite in sign. The N by N system of simultaneous equations is now solved and the incompressible surface velocities are obtained from the resulting values of the vortex strengths and the stream function. The well know Karman-Tsien compressibility correction law is applied to convert the incompressible pressure coefficients to the equivalent answers at the desired freestream Mach number. No stretching of the chord is performed. MCARFA Boundary Layer Solution Using the isentropic flow relations, the local Mach number is computed and input into the boundary layer portion of the program. The boundary layer consists of

1 an ordinaryboundarylayer(nonmergingboundarylayer),anda confluentboundary layer(mergingboundarylayer). The ordinaryboundarylayeris composedof laminar, transition,andturbulentregions. The confluentboundarylayermodelwasdeveloped by Goradia27from the Lockheed-GeorgiaCompanyandis oneof the uniquefeaturesof the MCARFA program. The critical parameters output from the boundary layer routines are the displacement thickness, the momentum thickness, the shape factor, and the skin friction coefficient. The theoretical development of the boundary layer methods used in this program constituted a doctoral dissertation and therefore will only be briefly summarized here. A flat plate boundary layer analysis is performed on each surface of an airfoil element, and the leading edge stagnation point is the plate leading edge. An initial laminar boundary layer region exists from the stagnation point to the point of transition from laminar to turbulent flow. The laminar boundary layer model used is the method of Cohen and Reshotko 2s for a compressible laminar boundary layer with heat transfer and an arbitrary pressure gradient. After computing the laminar boundary layer characteristics at a discrete point a check for transition is made. If transition has occurred, a check for the formation of a long or short transition bubble and for laminar stall is made. An initial check is made to determine if the laminar boundary layer is stable or unstable based on the instability criterion of Schlichting and Ulrich who have solved the Orr-Sommerfeld equation assuming a Polhausen laminar profile. 29 If the boundary layer is unstable, a transition check is made based on an empirically derived transition prediction curve developed by Goradia. 27 If transition has occurred, the initial parameters necessary to start the turbulent calculations are computed. If transition has not occurred, the formation of either a long bubble with laminar stall, or a

ll short bubble with reattachment is determined. The user can also input a fixed transition location, and a check will be made to determine whether this location has been reached. After computing the transition location and initial boundary layer properties, the turbulent boundary layer calculations are made. The turbulent boundary layer model is that of Truckenbrodt. The Truckenbrodt turbulent boundary layer analysis is an incompressible integral method based on the momentum integral equation and the energy integral equation. An additional turbulent boundary layer method as derived by Nash and Hicks 1 is used on the last iteration for the sole purpose of predicting separation. If a slot exit plane is reached during the turbulent boundary layer computations, the confluent boundary layer analysis is initiated. The confluent boundary layer is a result of the mixing from the slot effiux and the wake of the forward element. It can exist from the slot exit to the trailing edge depending on the pressure gradient. The confluent boundary layer model was formulated by Goradia. 27 The model is based on the assumption that the merging fore and aft element boundary layers will have similar profiles ifnondimensionalized in a way analogous to that for a free-jet flow. Several empirical constants were needed to establish the similar boundary layer profiles and were experimentally derived from tests performed by Goradia. None of the boundary layer methods used in this program include curvature effects. All the methods are basically integral methods which are often less accurate than finite-difference methods but require less computer time. No attempt to model separated flow exists, so the numerical results are only valid for cases with very small amounts of separated flow.

12 MCARFA Program Accuracy Studies were performed to document the MCARFA program accuracy on cases similar to the current airfoil design. Williams has developed an exact test case for the plane potential flow about two adjacent lifting airfoils, a2 MCARFA results of Williams' two test cases are presented in Figures 2 and. Test Case A is at an angle of attack of with the flap deflected and test Case B is at an tx of and a flap deflection of 1. The calculated pressure distributions show excellent agreement with the theory. Aerodynamic load data from the exact test case and the MCARFA results are presented in Table 1. Close agreement is obtained for the lift coefficient values, but the MCARFA results show some inaccuracy in the drag coefficient calculations. NACA external airfoil flap data were used to test the viscous MCARFA results on airfoil designs similar to the current study. a'a6 A NACA 212 airfoil with a 2% chord 212 external airfoil flap deflected 2 was tested at a Reynolds number of 1.5xl 6 by NACA researchers. MCARFA lift coefficient results show good agreement overall with the program predicting a 12% higher Clmaxvalue than the experiment (Fig. 4). The Clmaxdifference is due to the program not predicting the slope change in the lift curve at a cl of approximately 1.2 as in the experimental data. The program predicts a higher c d at the lower lift coefficients and a lower c d at the higher c l values than the experimental results show (Fig. 5). The L/D ratio results follow the c d trends (Fig. 6). Moment coefficient results are generally within 5% (Fig. 7). The MCARFA code does not predict a true maximum lift coefficient. It instead continues to predict increasing lift with increasing angle of attack after stall. Comparisons with numerous sets of experimental and other numerical data for both single and multi element airfoils has led to an empirical qmax criterion. The airfoil is

l / 1 R&M :717t)ot, entialflow Exact Test Case Results n =,csr= L -.9 -[ -7 Exacl Airfoil --- Exact Flap MCARFA Air'foil v MCARFA Flap -6 5 C.) Ch -5-4 - -2-1 \ _- _---_r_er -er_ff _ff_ 1..2.4.6 O.g x/c Fig. 2 MCARFA exact test Case A results R&M 717 Pokential Flow Exact Test, Case Resulls a =,csf = 1-4 (_ v -' L Exact Airfoil I Exact Flap MCAREA Airfml / [ v MCARFA Flap I -2 O -1..2.4.6.8 1. 1.2 I 1.4 x/c Fig. MCARFA exact test Case B results

14 Table 1 MCARFA and Williams' exact aerodynamic load results Case A Component ct Cd Exact Main 2.965 -.89 MCARFA Main 2.875 -.686 Exact Flap.82.88 MCARFA Flap.845.86 Exact Total.767 -.1 MCARFA Total.7158.15 Case B Component c_ Cd Exact Main 1.6915 -.898 MCARFA Main 1.6758 -.847 Exact Flap.66.897 MCARFA Flap.45.9 Exact Total 2.281 -.! MCARFA Total 2.19.54 NACA E1E with 2% 212 ExLernal Airfoil Flap 6 = 2 E.E E.O 1._ ----+_-- Re = I 5xlO e', NACA Report No. 57.[1 _-- Re = ] 5xlO 6, MCARFA 1.6 1.4 1.E O 1. 22.8 O. 6.4.2 O. -1-8 -6-4 -2 E 4 6 8 I 1 Angle of Attack Fig. 4 NACA 212 with 212 flap lift coefficient results

15 NA(.A _1 with 2% _'12 E Lcrnol Airfoil Vlap 6 = 2 4 - _w-- Re : 1 5 16, NACA t eporl No 57;/ _-- R(' " I {}SxIO 6, MCARFA i l / O. t- ; /' G, ()()2 _f.1., _, L I I, I, L, i, I, I..2.4.6.8 1. 1.7_ 1.4 1.6 1.8 2. 2.2 Lift CoefficierlL Fig. 5 NACA 212 with 212 flap drag coefficient results NACA 2:_12 wi Lh,_% ') _' 212 ExLer'nal Airfoil Flap 6 = 2 9 8O 7 6O 52 5O 4 2 //_ [ -_ Re = 1 5x16, NACA Report No 57 _ 1..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. L r Lift. CoefficienL Fig. 6 NACA 212 with 212 flap L/D ratio results

16 NACA 2',X) 12 wi th 2% '2',]1'2 Externa] Airfoil 9]ap,,_ = 2-1 -.11 -(1.12 -.1 --4_ Re = ] 5x I 6, NACA Report No 57 ----e-_ Re = 1 5xl(} _, MCARF'A J..J _ O -.14 -.15 -.16 c- -.17 -.18 -.19 -.2 O..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. 2.2 Lift Coefficient Fig. 7 NACA 212 with 212 flap moment coefficient results said to have smiled when the MCARFA code predicts separated flow over more than 1% of the upper surface area on a given element. PROFIL Background The PROFIL computer program is a two dimensional incompressible viscous flow program developed over the last several years primarily by Dr. Richard Eppler of the University of Stuttgart. 7as Because of his lead role in the program development, the code is often referred to as the Eppler code. A major step in the program history occurred when, under collaboration with the NASA Langley Research Center, a User's Manual and program description were published in the early 198's. 9'4 The code is still being continually updated and improved. The latest version is commercially available directly from Dr. Eppler.

17 The PROFIL code has two primary modes of operation: airfoil design and airfoil analysis. In the airfoil design mode, the program solves the inverse design problem through a conformal mapping routine which computes an airfoil geometry based on input velocity distributions. In the airfoil analysis mode, a panel method routine to solve the potential flow and boundary layer effects of a flow field on a given shape is completed. The airfoil analysis portion of the program was all that was used during the current study. Previous experience has shown the program to be an extremely fast and reliable source for performance characteristics of single element airfoils. 41'42 The primary drawback to the PROFIL code is the fact that it only computes results for single element airfoils or airfoils with simple flap systems. No provision is made to analyze complex or multi element airfoils. Because of this limitation, the PROFIL code was used to analyze all single element airfoils and provide a check on the single element results of the MCARFA code, but none of the final two element airfoil cases were examined with the PROFIL code. PROFIL Potential Flow Solution The potential flow airfoil analysis method employs panels with distributed surface singularities. The geometry of the panels is determined by a spline fit of the input airfoil coordinates. The singularities used are vortices distributed parabolically along each panel. The flow condition, which requires the inner tangential velocity to be zero, is satisfied at each input airfoil coordinate. Angles of attack of and 9 are analyzed. The flow for an arbitrary angle of attack is derived by superposition from these two solutions. The numerical method is based upon determination of the velocity vector induced at a point by the vorticity distribution along a straight panel according to the well known Biot-Savart law. 4a

18 PROFIL Boundary Layer Solution An integral method for the calculation of standard boundary layer properties is employed. The standard definitions of the displacement thickness, the momentum thickness, the energy thickness, and the two shape factors are employed as with the MCARFA code. For the laminar boundary layers, some Hartree profiles are used as velocity distributions. 29 Based on these velocity distributions, the critical parameters are calculated using the momentum thickness and the H2 shape factor as the independent quantities. The HI2 shape factor, the skin friction, the transition location, and the separation location are all polynomial fit solutions based on the H2 shape factor. The turbulent boundary layer calculations of the critical parameters are not as straightforward as the laminar boundary layers. Results for the required boundary layer parameters are obtained by empirical relations derived by Wieghardt, Ludwieg- Tillman, and Rotta. 44 Turbulent separation is determined by the value of H2; separation is said to have occurred when H2 is equal to 1.46. Laminar separation is predicted if H2 is equal to 1.5159. One benefit of the PROFIL program is it does continue to model the flow after some separation has occurred, applying an empirical correction based on the amount of separation to both the angle of attack and the lift curve. Transition from laminar to turbulent flow and the corresponding switch in equations is initiated by the following relation: In Rea, 18.4H 2-21.74 -.6r

19 wherer is a roughnessfactorwith a valueof zerocorrespondingto naturaltransitionon a smoothsurface. PROFIL Accuracy Studiessimilar to thoseconductedfor the MCARFA computerprogramwere carriedout to determinethe accuracyof the PROFIL results. This stepalsoservedas a checkof the MCARFA singleelementresultsandasa basisfor the understandingof both computerprograms. Graphicalresultsof all aerodynamicperformancecharacteristicsascalculated by boththe PROFILandMCARFA computercodesandexperimentallytestedby the NACA or NASA arepresentedin theexisting SingleElementAirfoils sectionof this paper. In general,the PROFILcomputecodeagreesvery will throughthe entirelift rangewith the experimentaldata. A shift of the ctvalueof approximately1o is observed between the experimental and PROFIL numerical data. The MCARFA code predicts the low lift coefficient values very well, but slightly overpredicts the lift at higher angles of attack due to the lack of separated flow modeling. Drag coefficient values agree well at the lower lift coefficients for all cases, but the MCARFA code does underpredict the drag at the higher lift coefficients. The PROFIL computer code overpredicts the moment coefficient by about 2% when compared with both the experimental data and the MCARFA computer results.

2O NUMERICAL RESULTS AND DISCUSSION Results for various combinations of profile shape, relative angle, and relative position of the two elements of the new airfoil are presented. Numerical results of the systematic study were obtained at Reynolds Numbers of 8xl 5 through xl 6. Appendix A presents a list of all numerical cases. The MCARFA program was used to analyze all cases. When possible, the PROFIL program was also used to verify MCARFA output. All analytical results were obtained at sea level standard conditions with natural or free transition from laminar to turbulent flow. Existing Single Element Airfoils Numerical results were obtained for a variety of existing single element airfoils for possible use in the initial two element configurations. Examining the single element airfoils afforded the opportunity to examine MCARFA results as compared with the PROFIL answers and published experimental data. 4 Experience in the nuances of the MCARFA numerical method was also obtained in this first step. Five single element candidate airfoils were examined: a NASA NLF(1 )-416, a NACA 12, a NACA 2412, a NACA 4412, and a NACA 212. All cases were performed on an airfoil with a 61 cm chord at a Reynolds number of approximately three million. The NLF(1)-416 airfoil lift coefficient vs. angle of attack results show generally good agreement between the three sources (Fig. 8). The MCARFA program predicts very good results at lower lift coefficients but a slightly higher lift curve slope at the higher angles of attack than experimentally verified. The PROFIL program predicts the shape of the lift curve very well but underpredicts the zero lift angle of attack by about.75. Overall, the drag coefficient results (Fig. 9) show good agreement between all sources, but the MCARFA code does underpredict the drag

21 NI,F(I)-4 16 Airfoil Re = x 1 6 1 el 1.6 1.4 --c_.-- NASA T[ -1B61 Experiment r /_.-/--,.-- - ^ PROFII, I //_ / \ 1._ 1. -- j rj C_.8.6.4 {)._., i _ ] j [ L I, L J I L, I -E a 4 6 el 1 1a 14 1( Angle of ALtack Fig. 8 NLF(1)-416 airfoil lift coefficient results NI,F(1)-416 Re 16 Air'foil._5 NASA TP- 1861 Experiment? MCARFA /_ O.OEO _-- PROFI I, /.15 O. 1 L. O. 5.(] ' O,.2.4.6.8 1. 1.2 1.4 1.6 1.8 Lift CoefficienL Fig. 9 NLF(I)-416 airfoil drag coefficient results

22 coefficient at the higher lift values. Moment coefficient results show excellent agreement between the MCARFA results and the experiment, but the PROFIL code overpredicts the moment coefficient by about 2% (Fig. 1). NLF(1)-416 Airfoil Re x 16 -.O5._ -.6 -O.O7 NASA TP- 1861 Experiment PROFIL l _ MCARFA j _- -8 O -.9 -.1 E o -11 2 bz -. - 12 1 14 - O. 15. i b I.2, I, 1 h I _ I, 1.8 1. 1.2 1.4 1.6 1.8 Lift. Coefficient Fig. 1 NLF(1)-416 airfoil moment coefficient results Results for the NACA 12, 2412, 4412, and 212 airfoils are presented in Figures 11 through 22. Generally good agreement between the two sets of numerical data and the published experimental values were obtained on all cases. Profile Shape Various combinations of existing airfoils were explored for use as a two element airfoil. The NASA NLF(1 )-416 airfoil was chosen for use as the primary

2 NACA 12 Re = x16 Airfoil 1.B 1.6 14 - _-_ NACA Report No fl24 - --4:i_ MCARFA _l PROFIt, // - - r- C 2 CO 1.2 1 O. B.6.4 O. 2 O. -2-4 -6 I L J I -2 2 6 1 1,1 I 1B Angle of Attack Fig. 11 NACA 12 airfoil lift coefficient results NACA O1g Airfoil Re = xlo 6 OOg5 (2 ----_ NACA Report No fl24 MCARFA PROFIL r- _D U k: oo15 C_ L) _:_ [). 1 O5 r2_ [llhl I,IiI,lalblhlll -4-2, 2 4.6 8 1 1.2 1.4 16 1.8 Lift Coefficient Fig. 12 NACA 12 airfoil drag coefficient results

24 NACA 12 Airfoil Re = x 16 5 (I f I -- NACA Report No 8a4 --_--" MCARFA I --_-_-- PROFit, I J.; {)ol c_ -1 CO Q G; -. e- - 5 E o -."7 -.9 o -.11 -o i -o 15,l,l,i,I Ihl_i,,,l,i,I - 4-2 O 2 4.6.8 1 12 1 4 1.6 1.8 Lift Coefficient Fig. 1 NACA 12 airfoil moment coefficient results NACA 2412 Airfoil Re.1x1 6 1.8 1.6 1.4 -+ NACA Report No 824 /._ -_---- MCARFA _/ j._v -/- 1.2. 1..8 O u_ 2_.6.4.2. -O.P_ -4-6 h I i I i I i I i I -2 2 6 t 14, I 18 Angle of ALLacR Fig. 14 NACA 2412 airfoil lift coefficient results

25 NACA 241E Air'foil Re.1xlO 6 25 2 _-- NACA Report No _E4 MCARFA PRQFII, 15 CJ L. [j 1 e'd jjl.5, I I I L i, I, I _ I, I I, ; -4 -.2..2.4.6.8 1. 1. 14 t.6 18 Lift Coefficient. Fig. 15 NACA 2412 airfoil drag coefficient results NACA 41 Airfoil Re =.1xlO 6.5. 8 o.ol _- -.1 O C_ --.- NACA Report No 824 MCARFA PROFIL - -.5 E o -.7-9 o -. I1 --1 -- 15, I, I I, I, I, I, I, I, I I I -4 -.2..2.4.6.8 1 1.2 1.4 1.6 1.8 Lift Coefficient Fig. 16 NACA 2412 airfoil moment coefficient results

26 NACA 44 1E Airfoil Re == "}x 1 6 1.8 1 6 _-- NACA Report No 8:d4 /_;_ 1.4 1. // ja- O. 8 d k_ L_,6,4 O.E -2 -.4 O. -6 I _, [ h [ J I I I -E E 6 1 14 18 Angle of Attack Fig. 17 NACA 4412 airfoil lift coefficient results NACA 441E Re = x1(_ Airfoil 25.2 NACA Report No 8E4 MCARFA PROFIL _ 15 k_ O C) _ 1 r_ O.5 {] i I h I, I i I, I, I, I h I, I h L h I -(}4-2. O.E.4 6.8 1 1 2 14 16 1 8 Lift Coefficient Fig. 18 NACA 4412 airfoil drag coefficient results

27 NACA 44 12 Air'foil Re x 16,5 _J _D (}'),.; 1 kz '-.- -1 o -.C) ----+_-- NACA Report No 824 _-- MCARFA PROFII, -(/.5 -(I,7 _D - 9 2 co -.11 a- - (_.--,g2_....f -.1 -.15 d L b _ i I, I i L, I h 1 J [, i i L i I 4-2 O.2 4.6 8 1. 1.2 1 4 16 1 8 Lift Coefficient Fig. 19 NACA 4412 airfoil moment coefficient results NACA 212 Re = x 16 Airfoil 1.8 ]. 6 NACA Report No B24 fi] 1.4 1.g I _ PROFIt, c.,/ / *x 5 o 1..8.6.4.2. -.2 --4-6 -2 2 6 1 14 1B Angle of Attack Fig. 2 NACA 212 airfoil lift coefficient results

28 NA(;A 212 Airfoil Re x 1 ()_ J _ ke C_) ()_5 [ [ _ NACA Report No 824 - -',- _CARFA PROFIL V.... o o15 k_ 5, L, m, h, L, m, _, _, m, _, L, m -4-2 O._ 4 6 OP, 1 I E 14 l 6 18 taft Coefficient Fig. 21 NACA 212 airfoil drag coefficient results NACA 212 Re = xlo 6 Airfoil (k5 r_._. O.Ol -l C_ -O --e--_ NAUA Report No 824 _e_-- MCARFA l --*---- PROFIL _ - 5 o -.7 r- -.{)9 )2 -.11-1 -- 1,5, _, _, I _ I, t, /, I, I, I, I,,_ -4-2.._ 4.6 O.B 1. 1.2 1.4 1.6 1.8 Lift Coefficient Fig. 22 NACA 212 airfoil moment coefficient results

29 element in the initial two element configuration. This choice was made for two reasons. First, the NLF airfoil was designed for similar conditions to the two element airfoil under study. 4s It is an unflapped, reasonably high lift laminar flow airfoil designed for light general aviation applications. The second reason for choosing the NLF airfoil was the well documented set of both experimental and numerical data previously published for the airfoil, thus allowing accurate direct comparisons between the current study results and those independently obtained previously. The secondary element profile should be a relatively benign section because of the disrupted flow conditions it will be operating in due to the wake and downwash from the primary element. The NACA 12, 2412, 4412, and 212 airfoils studied previously were determined to be candidates for the secondary profile. Wentz 46 determined the optimum location for the leading edge of a split flap to be 98% chord behind and % chord below the leading edge of the airfoil, this location was used during the initial studies for placement of the secondary airfoil. The NACA found a 25% chord external airfoil flap deflected 2" was the optimum relative size and deflection. 6 Again, these choices were used for initial studies with the two element configuration. Lift coefficient results for the various secondary element profile shapes show the NASA NLF(1)-416 with a NACA 4412 provides the highest qmax (Fig. 2). Drag coefficient results show very little difference between the various secondary element profile shapes at low lift coefficients (Fig. 24). The 4412 case has the lowest drag at a given lift for the higher lift coefficient. Lift to Drag ratio results show the highest L/D values with the 4412 case through the entire el range (Fig. 25). Moment coefficient results show, as expected, higher moment values with increasing camber (Fig. 26). The

O MCARFA Resnlts of Two Element Airfoils c_a = 2 25 NLF(I)-O416 with 257_ NACA 1: z,, I -_-- NI,F( 1)-416 with 25% NACA 24 12 ), /. z! -e, - NI,F(1)-416 with 25% NACA 4412 - _:_ - _" NI,F(1}-416 with 25% NACA 212?7:" f,_ c- 5 1.5 1. 2_ O. 5 O., I L _, _ I l I h l l h b -8-6 -4-2 2 4 6 8 Angle of Attack Fig. 2 Secondary element profile effect on lift coefficient results MCARFA Results of Two Element Airfoils _a = 2. _ N[,I:'(I)-416 with 257, NACA 12 //_/_/_/ O, O2 i,, iiii:iiii.:iii iiiiiiiiiii, C, tj ("5 _-. 1 O, ), ) i _..5 1. 1.5 2. 2.5 Lift Coefficient. Fig. 24 Secondary element profile effect on drag coefficienl results

1 MCAI ["A t _:sulls of Two Element Airfoils de ') 1 _ 1 8 6O 4O 2, _ NL_'I-o.IGw,,h 2_ N.C^2,_ j. I l I d I.5 1. 1.5 2. '2.5 Lift Coefficient Fig. 25 Secondary element profile effect on L/D ratio results MCAkFA Results of Two Element. Airfoils rse : 2 -.15 NLF(I)-416 with 25% NACA 12 ' ---e -- NLF(1)-416 with 25_ NACA 241g CD NLF( 1)-416 with 25% NACA _12 _ NLF(1)-416 with 25_. NACA 4412 L_ q-. U E - g -O25 EJ -- o -- _D/ A _ j_.j" b -. I, I, I, I..5 1. 1.5 2. 2.5 Lift. Coefficient Fig. 26 Secondary element profile effect on moment coefficient results

2 NACA 4412 case has the most negative moment at roughly 2% higher than the 2412 case. Based on the above data, the NACA 4412 profile was chosen for the secondary element. The 2412 was also chosen for further study because of its reasonably high qmax and the significantly lower moment coefficient. Relative Position The optimum relative position of the two elements was studied in detail by varying the horizontal and vertical position independently while holding all other parameters constant. This variation was studied with both the NACA 4412 and 2412 secondary element at second element deflections of 1, 15, 2, 25, and. The primary element size was held constant at 8 centimeters or 75% of the total chord and the secondary element chord was kept at 1 centimeters or 25% of the total chord. Position nomenclature used is the location of the leading edge of the secondary element with respect to the leading edge of the primary element in percent of the primary chord. Lift coefficient results for the 4412 deflected 2 at a vertical position 4% of the primary chord below the primary leading edge show the highest c I values obtained at a horizontal position of 96% behind the primary leading edge (Fig. 27). Drag coefficient results of the same case show the lowest drag coefficient obtained at a secondary horizontal position of 95% (Fig. 28). The maximum L/D ratio was calculated at a position of 95% (Fig. 29). The moment coefficient increased as the secondary element was moved further aft (Fig. ). Similar results were obtained with the secondary element at vertical positions of % below (Figs. 1-4), 2% below (Figs. 5-8), and 1.5% below (Figs. 9-42) the primary element. Results are also presented for a NACA 2412 secondary element deflected 2 and located 2% below the primary element (Figs. 4-46). Again the optimum horizontal position is seen to be 95% behind the primary leading edge.

MCARFA l-_esults of NLP( ] )-4 ] 6 wi t,h 25% NACA 4412 YLE:_ - -4Z el, 5_ 2 2.5 '_ - XLEz - 92% Cl. _S-_ 2. _ 1.5 --_ XI,Ea = 1% cl /_1 - - -.5. i i _ i I, [ I L, ] i I I I I I -8-6 -4-2 2 4 6 8 Angle of Attack Fig. 27 Horizontal position effect on lift coefficient at -4% and 8 = 2 MCARFA Results of NLF(l)-416 with 25? NACA 4412 YLEa = -4%cl,62 = 2. -_ XLE_ = 92_ cl XLEa = 9Z c_ -_ XLE2 = 94% Cl XLEz = 95% cl XLEa = 96N c! XLE2 = 98% ct _/.2 ----It---- XLEa = IOOZ cl / -! --.-- XLE_=1oa_, O L) d5 o.ol l., I, _, B, : i..5 1. 1.5 2. 2.5 Lift Coefficient Fig. 28 Horizontal position effect on drag coefficient at -4% and 8 = 2

4 MCAR.FA bl_sults of NLF(1)-4 16 with 257"o NACA 44 12 YLEz -4%cl,6e = 2 14() 1 1 BO 6O 4 2O /// I --*--- xls o, I '_// I --_--- XLS_- 9_ffo, I // I _ XLE2 96?cl I A/ i _ XLEs lo_el [ -_ XLE2= 1(]2%c' _. I I I J,5 1. 1.5 2. 2.5 Lift Coefficient Fig. 29 Horizontal position effect on L/D ratio at -4% and 8 = 2 M(JARFA Results of NLF(1)-416 with 257 NACA 4412 YLE_ = -4% el, _ : 2 -.15 XLEz = 92% cl r- '5 O -O.EO -_-- XLEe = 9% cl XLEz = 94% c_ XLE_ = 95% Cl /_ XLE:_ = 96% cl / + XLEz = 98% el / + XLE2 = 1% el / _a --.-- xle_:1o2_c,..._.z _ E 2 O -.85 -.:], I _, I, _ I..5 1. 1.5 2. 2.5 Lift Coefficient Fig. Horizontal position effect on moment coefficient at -4% and 8 = 2

5 M(J!Xt4F'A RestJlts of NI,F(1)-4 ] 6 with 25% NA(JA 441_ YI,E2: -% c1, 62 --- 2 2.5 -- ++-- XLE2 = 92%" el _',._<--< _ 2. 1.5 _ 1. L_.5., [ i I i I i I, 1 _ I h I _ i J a -8-6 -4-2 2 4 6 B Angle of Attack Fig. 1 Horizontal position effect on lift coefficient at -% and 8 = 2 MCARFAResultsofNLV(1)-O416wiLh 25% NACA 4412 YLE2 :: -Yo cl, 6a = 2 O. XLEa : 92Z el XLEa = 9% el / _/'/ (L,.2 --_---- + xi.e_ : 95z e, XLEa=aaze_ / / /y,_ ///I --,-4_---- XLE;_ : 9BZ el / Z// )L XLE_= looz_, / 2" ///I. 1., I, I, l, i, i..5 1. 1.5 2. 2.5 Lift CoefficienL Fig. 2 Horizontal position effect on drag coefficient at -% and 8 = 2

6 M(JARFAResultsofNLF(1)-416 YLEa = -% cl, 6a = 2 with 257NACA441a 14 1 EO 1 O P-d] k. 8O 6 v/_/ + XLEa : 9Z el 4 2 _/" ---v---- XLE2 95Z cn / _ XLEa = 96Z ct XLE_ = 98Z cl + XLEa_ loozcs --*---- XLEz = 12% cj O.O.5 1. 1.5 E.O 2.5 Lift CoefficienL Fig. Horizontal position effect on L/D ratio at -% and _ = 2 MCARf,'A ResulLs of NLF(1)-416 with 25% NACA 4412 YLEz = -Z cl, d_ = 2 -.15 ---+e---- glee - 92% cl 5 O -.2 - _ XLEz = 9% cl ---e.---- glee 94Z ct glee = 95Z cl ----_ glee = 96Z ci XLEa = 98Z cl _-a + XLE2= 1ooze2 /fa XLE_= ll]2gcl // _/ ja E r" O -.25 / -., r, I., I, l,..5 1. 1.5 E.O 2.5 Lift Coefficient Fig. 4 Horizontal position effect on moment coefficient at -% and 5 = 2

7 MCARFA Re._ul[s of N[,F(1)-416 with 25E NACA 44 1 YI,E2-2%cl,rSa= 2 2.5 E.O *_-- XhF, z = 9:t% cl ",".--- XhEa = 94% cl I i - c _ --_--- Xl,Ez = 957. cl --_ - XhEz 96% c, /..,,_/..-;'_ y 1.5 T. 1.2.5 D.,,, J _ I, i, i, i, i _ i, i - ] -B -6-4 -,2 2 4 6 8 Angle of Attack Fig. 5 Horizontal position effect on lift coefficient at -2% and 6 = 2 MCARFA Results of NL,F(1)-4 16 with 25% NACA 44 1E YLEa : -2% cl, da 2. LE_ = 9_ el '- (].2 ----- XLE2 = 94_ XL,Ea = 95Z XLE2 = 96_ XLEa : 9BZ k_ J o (,,). 1 O. (), I, I,,..5 1. 1.5 2..5 Lift Coefficient Fig. 6 Horizontal position effect on drag coefficient at -2% and 6 = 2

8 2_ NACA 44 1" MCAt<I"A Re.suits of NLV(1)-4 16 with ( r, YLEe -2% cl, 8e = 2 ] 4 12 1 8 2_ 6O 4 2 ---e--_ XLEu = 9Z c_ XLE_! = 94% c] XLEe - 95Z el XLEz = 96% ct + XLE2 98% el (] O..5 1. 1.5 2. 2.5 Lift, CoefficienL Fig. 7 Horizontal position effect on L/D ratio at -2% and 6 = 2 MCARFA Resu][s of NLF(1)-416 with 25% NACA 4412 YLE2 = -2% cl, 62 = 2 -.15 :S t,.. O L) E O -.2 -.25 -_ XLEz = 92% el XLEz - 9% el XLEz - 94% el ---e---- XLE2 = 95% cl ----e--- XLEz = 96% cl... + XLEz = 98% e1 _- _, -. J I, _,,,.5 1. 1.5 2. 2.5 Lift Coefficient Fig. 8 Horizontal position effect on moment coefficient at -2% and/5 = 2

9 MCARIi'A Results of' N[,F(1)-O416 wilh _% _ YLEe - 1.o/_r'_"c, de :: EO NACA4412 2.5 2. r- rj 1.5 o 1. O. 5. _ I L I L I, t, I i L,,, I L - 1-8 -6-4 -2 2 4 6 8 Angle of AtLack Fig. 9 Horizontal position effect on lift coefficient at -1.5% and 6 = 2 MCARFA Results of NLF(1)-416 wilh 25% NACA 4412 YLEz = -1.5Z el,dz = 2. - _ XLEa = 92Z el ///// XLEz = 94_ c! / J//... LEa = 95_ c, /._ --_---- XLEa = 96X el / //// "_.2 t1).1. L, i, J I,..5 1. 1.5 2. 2.5 Lift- Coefficient. Fig. 4 Horizontal position effect on drag coefficient at -1.5% and 5 = 2

4 X_CAt_t"/\ Re_ult.s of NLP(l)-416 wilh _o_,, =": NACA YLEa=-l.5%cl,de = 2 441,_ 14 1;_O 1(} 6 4O ---_ XLEz = 92% el --_ XLEz 9% cl XLEz = 94_ cl XLEe = 95% cl XLEu 96Z el XLEe 98Z cl --_ 2O O. I, 1 1 1.5 1. 1.5 _. 2.5 LifLCoefficient Fig. 41 Horizontal position effect on L/D ratio at -1.5% and 8 = 2 MCARFAResul[sofNLV(1)-O416with 25% NACA 4412 YLEe -1.5% el, 5e = 2 -.15 r_ ----e---- XLEe 9gZ cl -_+--- XLEz - 9% cl ---_-- XLE2 = 94Z c! XLE2 = 95% cl XLEa = 96Z cl ----_-- XLE2 = 98% cl.j.t] C;..J -.2 E O -O.25 -., I, I, t, _,..5 1. 1.5 2. 2.5 Lift Coefficient Fig. 42 Horizontal position effect on moment coefficient at -1.5% and 8 = 2

41 MCARVA Results of NLV(] )-4 16 with 25% NACA 24 12 YI,E_ -g% cl, cse = 2 2.5 ---_ XI.Ea 92% {:1 2. - _--e---- XLEa = 97. _:l.j:_'5_._/" XLE_ = 98% el j._x'_. / U 1.5 /J 1.,5. i [ _ [, a h [ i [ _ I i [ h I h I -8-6 -4-2 2 4 6 8 Angle of Attack Fig. 4 Horizontal position effect on lift coefficient with NACA 2412 MCARVA Results of NLV(1)-O416 with 25% NACA 2412 YLEe -2% cl, 6a = 2 5,._ ---_ XLE2 = 92% el _a" _ XLE2 = 9% c, //-_/ - _ XL_2 = 94_ el _ /jr -_ Xhgz : 95X c_ //"/_1 XLE2 = 96% ci _/J_ XLE2 _ 96Z el 2' C.) _E e-,.1..5 1. 1.5 2. 2.5 Lift Coefficient Fig. 44 Horizontal position effect on drag coefficient with NACA 2412

42.kl(;AI<FA ]-_.e._ult,_ of NLF(])-4 ] O with 2l) _''" NACA 24 l YI,E_ = -2% cl, _ = 2 O 14 1 () d: _(_ 6[) 4 2O / / ---_-- XLEz, 96% cl _..5 l.o 1.5 2. 2.5 LifL Coefficien[ Fig. 45 Horizontal position effect on L/D ratio with NACA 2412 M()ANFA Results of NLF(1)-416 with 25% NACA 241:2 YLE -2% cl, 6_ :: 2-1 5 o -2 E r_ C-- Z O -O.P_5 XLEz - 92% c_ XLEz = 9% el XLE_ = 94_ cl XLEz = 95% c_ XLEz = 96% c_ XLE_ - 98% cl -.:], _, I, _,..5 1. 1.5 2. 2.5 Lift Coefficien[ Fig. 46 Horizontal position effect on moment coefficient with NACA 2412

4 The best relative position was expected to change with various secondary element deflections due to the changing slot geometry so numerical results were obtained for the NACA 4412 deflected relative angles of 1 through at 2% below the primary leading edge. Lift and drag coefficient results for the 1 deflection case show very small changes with different relative positions (Figs. 47-48). Lift to drag ratio results, however, show a slight L/D improvement with the secondary airfoil located at 9% behind the primary leading edge (Fig. 49). Moment coefficient results, as with previous cases, show the moment increases with the secondary element moved aft (Fig. 5). The 15 deflection cl and c d results show lower lift and higher drag with the 98% position, but no significant change with the other cases (Figs. 51-52). The L/D ratio plot confirms the c I and c d results showing no significant change at the 92% through 95% positions (Fig. 5). Again the moment coefficient increases with the further aft position of the secondary element (Fig. 54). The c I results for the 25 deflection case show the highest Clmaxto be at the 95% and 96% position (Fig. 55). The Ca values are lowest with the 95% and 96% cases (Fig. 56), and the L/D ratio is a maximum for the 95% case through most of the cl range (Fig. 57). Moment coefficient results show the same trends as previously seen (Fig. 58). The L/D results show a spike in the curve near a cl of.75. This spike is calculated because the drag is continuing to drop as the lift is linearly increasing. This drag reduction is accompanied by an increase in the amount of laminar flow calculated on both surfaces. As the angle of attack is increased, more and more laminar flow is calculated on the lower surface of the primary element, but the transition has yet to

94_ 44 MCA {I:'A t{esults of N[,V( 1)-4 ]6 wi th 25% NACA 44 1_2 YLE2-- -2%c1,6_ = 1!r 1 _ 4,-- XI.Ez 9_% (:l I./ 2 i -_ - LE_ 94'Z (:l,[ 1.5 _Z ]. L_.5 [)., i, _, l, I, i, L L, L --6 --4 --2 2 4 6 8 ] I _, Angle of Attack Fig. 47 Horizontal position effect on lift coefficient at -2% and 8 = 1 MCAkVAResults of NLF(1)-O416with25Z NACA4412 YLE2 = -2% c_, (_a = I C). -+ XLEa : 92% cl // -_--- XLEz =: 9Z ci _/ --_-- XLEa el /;z/ a% _. = / -_ U._.1.,,, I, I b,..5 1. 1.5?_. 25 Lift Coefficient Fig. 48 Horizontal position effect on drag coefficient at -2% and 8 = 1

45,.DG NACA 44 1 '_ M(TANt"A ResulL_ of NLF(1)-OdlG wilh ')_,_ YLE_ = -2%Cl,6 1 14 1O _f 25 6 4 2O..5 1. 1.5 2. _.5 Lift Coefficient Fig. 49 Horizontal position effect on L/D ratio at -2% and 8 = 1 MCARVA Resulls of NLF(1)-416 with _5% NACA 4412 YLE -Y_% ci, 6e = 1 -.1 r- 5 -.1 1 XLEe - 92% el.._ XLEz = 9% el /, XLEa = 94Z c: XLEe = 95Z cl.. ---_r'j*_,-. 2 o -.12 E,.9 -O. 1 - :Z -.14 -.15, I, I, L I,,.,5 1. 1.5 g.o 2.5 Lift Coefficient Fig. 5 Horizontal position effect on moment coefficient at -2% and 8 = 1

46 25 -'_ XLE2 : 92% et J_ :_.(),_ I,l:;z 94% c I._/; - - v_ Xldg_ : 95_ ci 5 Z. G O ED,5 1. _...,5., I i, I, I, I, i, _, I -_ -6-4 -g 2 4 6 8 ] Angle of Attack Fig. 51 Horizontal position effect on lift coefficient at -2% and,5 = 15 MCARFA Rost]ll,_ of NLF(1)-O416wiLh 5% NACA4412 YLEa :: -2Zcl,6a = 15 "_.2 XLEa = 9aZ cl //// -_ XLEa = 9Z el, /_/ - _ XLEa = 94% cl // - XLEa = 95% c! //_/ x_,_:7_< :' /// XLEa 98% ct I///// ;-.1., i, i, i, L i..5 1. 1.5 2. 2.5 Lift Coefficient Fig. 52 Horizontal position effect on drag coefficient at -2% and 8 = 15

47 _{CARVA Results of NLV(1)-416 with 25% NACA 44 12 YLEe = -2% cl, _Se 15 14 1 go 1 O -. 8 2 6 4 _////_/! _ XLEe 94%el _//7 i _ XLS_=95_ol J" I -+---.x._ 96_1 _"? _ XLE2 98_ ci 2O., [, [, [, [, i,5 1. 1.5 2. 2.5 Lift Coefficient. Fig. 5 Horizontal position effect on L/D ratio at -2% and 6 = 15 MCARFA Rc._ults of NLF(1)-416 with _.,)_o NACA 4418 YLEe - -2% cl, de = 15 -.1 -,11 _ -(1.12 7- _- -.1 o -.14 ---e---- XLEz = 92% c_ ---e----- XLE2 : 9% cl XLE2 = 94Z cl XLE2 = 95% cl -----_ XLEz : 96Z cl + XLE2 = 98% el -{} 15 ff o -.16 _- -,I7 2 o -.18 a2-19 -,2 O. L h I i L, I.5 1, 1.5 2. I 2.5 Lift. Coefficient Fig. 54 Horizontal position effect on moment coefficient at -2% and 5 = 15

48 MCARF'A [{e._ulls of NI,V(1)-4 16 wilh 25% NACA 44 12 YLF, e... 2% Cl, 6e = 25 2.5 2. -+_--- XLEe 9% cl _:: " ---" XLE 95% t I.- ' +- XLE2 98Z el /_/_" j- "_ 5 1.5 _;./YJ 1..5.,, I, i, l, I L I _, ' -12-1 -8-6 -4-2 _2 4 6 Angle of Attack Fig. 55 Horizontal position effect on lift coefficient at -2% and 8 = 25 MCARFA [{esulls of NLF(1)-416 with 25% NACA 4412 YLEp. -2% cl, tse 25. -_ XLEz = 9X et / /./" XLE2 = 94Z ct jg _,j_o XLEz = 95Z ct / /_.2.1 O. O, _ J, J, L,,..5 l.o 1.5 2. 2.5 Lift Coefficient Fig. 56 Horizontal position effect on drag coefficient at -2% and 8 = 25

49 M(/,;\Rf,'A Results of NLF(])-416 with 857o NACA 441Z_ YLE2 _ -2_ cl, 6_ :- 25 14 12 1 _ k5 6O 4 2 / iiii:iiil, XLEa = 98% {!1 O. L L L 1 L I.5 1, 1.5 2. 2.5 Lift Coefficient Fig. 57 Horizontal position effect on L/D ratio at -2% and 8 = 25 2_)Z NACA 4412 MCARFA Results of NLF(1)-4 16 with r _o. YLE2 -- -2% el, 6a = 25 -,2 O L..; Z E -.21 -.-)2 -. -.2_4 -,25 -,26 [ XLEa = 92% el J XLEa = 9Z c, XLEa= 94%cl ](LEa = 95% c XLEa = 91BY_ cl XLEa = 9BY. cl C -.27 K -.28 -._9 -().>K). I i I, I b I J.5 1. 1.5 2. 2.5 Lift Coefficient Fig. 58 Horizontal position effect on moment coefficient at -2% and 6 = 25

5 start moving forward on the upper surface so the net result is a large amount of laminar flow on both surfaces. The point on the L/D curve immediately after the spike is the location where the transition on the upper surface starts to move forward. There is reason to believe this spike in the L/D curve is real. Smith _7 states that the secondary element in a slotted flap system effectively increases the circulation about the primary element and helps to delay the onset of separation. The current data show the secondary element also delays transition. The deflection cj results show little difference in the Clmaxvalue with positions of 95% through 98% (Fig. 59). Drag coefficient data shows the lowest Cd at the 95% and 96% positions (Fig. 6) and therefore the highest L/D is also at the 95% and 96% position (Fig. 61). Moment coefficients are again the highest at the most aft secondary element positions (Fig. 62). The 92% position c m results are quite different than the other position answers with the values the least negative at the lower cfs and crosses over to be the most negative case at the higher Cl conditions. Vertical positions of-1.5% and -1% were also examined for the deflection case because the Clmaxand L/D values for the -2% case proved to be higher than the 2 deflection case earlier. The -1.5% condition c I results show the highest lift values at the 96% condition (Fig. 6) and the c d results show the lowest drag at the 95% position (Fig. 64). The highest L/D for most of the cl range was at the 95% case (Fig. 65). The moment results showed the largest Cmwith the furthest aft position (Fig. 66). The -1% position results are nearly identical to the -1.5% answers (Figs. 67-7). The optimum position of the leading edge of the second element for the 2 and 25 deflection cases was found to be 95% of the primary chord behind and 2% of the primary chord below the leading edge of the secondary element. The deflection

51 MCANF'A Result, s of NLF(])-4 ]6 wit,tl '_'_J,_,,,o NACA 4412 YLE_ = -27o el, /5_ ----s_. XLEz = 92Z ct XLEz = 9% cl ^._._-._ Z 2 L L h [, I L i i L L I _ I, I i _ 4-1 -1-8 -6-4 -2 4 Angle of Attack Fig. 59 Horizontal position effect on lift coefficient at -2% and 8 = MCARF'A Result.s of NLF(l)-416 with o_.,_j _o, NACA 4412 YLE2 = -2% cl, 6z = O.OZ.2 / XLE2 ::92%cl //))v -- -o--- XLE2-9% cl XLE_ = 94Z cl _- XLEz = 95% (:1 XLEz = 9BZ cl / /, XLEz = 98Z cl _.// a) o O.(11 (}.(}, i, ] J 1 2 Lift Coefficient Fig. 6 Horizontal position effect on drag coefficient at -2% and 8 =

52 MCARFA Results of NLP(])-4 16 wit.h 257 NACA 4412 YI,Ee = -2% cl, 6e -- 22 2 18 16 _a--- XLEz 92Z el ----t_--_ XLEa 9% ct Z, i, i!iiiiii --_e,--- XLE2 94% el 14 t. 2_ 12 IO BO 6 4 2, I, I, J 1 E Lifl. Coefficient Fig. 61 Horizontal position effect on L/D ratio at -2% and 6 = MCARFAResulLsofNLF(1)-O416with 257o NACA4412 YLEe = -2% ct, de = -25-26._ -27 -O,2B co -,29 XLEa - g2z c_ - _ XLEz = 9Z el XLE2 : 94Z el XLEa = 95Z ct XLEz = 96% el + + XLEa = 98Z el /.._ a -. E o -.1 tl) -,2 v- o -. K -.4 -O.5 1 2 Lift Coefficient I Fig. 62 Horizontal position effect on moment coefficient at -2% and 8 =

5 MCAI_FA Results of Nt,F(1)-416 with' 27,, _'_ NACA 4412 YLEe -1,5%c1,6e - ----_-- XLEe : 9_ c_..,..f.j_ -_'_--- XLge 95% c '_'_;_. -_ " c D '5 ---_- XI,F,_: = 98% cl _r"r _ j... _>:-... L L_, _, J J L I _ J L, i L I, I,1-1g - 1-8 -6-4 -2 (} ;d 4 Angle of At.Lack Fig. 6 Horizontal position effect on lift coefficient at -1.5% and 8 = MCARF'A ]_esu]ts of NLI_(I)-416 will 25% NACA 44 12 YLEe -l.5%el,6e : O. --_e------ XLE_ = gg c "_ XLEa : 94% c _./ /// XLEa = 96_ cl / // o.2 8 L_ O. 1 (). I, F 1 2 :_ LifL CoefficienL Fig. 64 Horizontal position effect on drag coefficient at -1.5% and 8 =

54 MCARFAResultsofNLF(1)-416wilh;25Z YI,E:_ = -1.5% cl,6s NACA441_ 2_ 2 18 16 ] 4 XLEz = 9Zcl XI,E2 94% cl, -_ LEz : 95% cl + XLEz = 98% cn _ XLE2 : 96% el,_ f% L 2 1 BO 6O 4 2 1, L J I 1 2 Lift. Coefficient Fig. 65 Horizontal position effect on L/D ratio at -1.5% and 6 = MCARFA Results of NLF(1)-O416 with 25% NACA 4412 YLEz = -1.5%c1,6e = -.25.,_ -.26 -.27 '.,- -.28 -----4+-- XLEz 9Z c 1 XLE_ 94Z e: : XLE2-95Z el XLEe - 96% el XLEz - 98_ el -.29 -, o -.1 _, ' -.2 7-, o -. m -.4 -.5, I J,I, i 1 2 Lift Coefficient Fig. 66 Horizontal position effect on moment coefficient at -1.5% and 6 =

55 2/,, NACA 4412 M(TAI_FA Results of NLF(])-4 ] 6 with ' _'" YLF,_ - 1% c i, _ : ' r 1 XLE::' = 94% (I [../_._- "._ L.; 4-12 -1-8 -6-4 - 2. 4 Angle of Attack Fig. 67 Horizontal position effect on lift coefficient at -1% and 8 = MCARFA ResulLs of NLF(1)-4 16 wilh,_t)z NACA 441Le YLEe=-l%cl,6e = O. _- ==IIi: Itl :: //1.2 ;2,.,... Q) _. 1. ) J J _ 1 2 LifL CoeffieienL Fig. 68 Horizontal position effect on drag coefficient at -1% and 8 =

56 MCAt{FA Restllts of NI,F(1)-416 wi [h 2,5% NACA 44 1,? YLEz--1%cl,6z = 22 goo 18 XLEe = 9Z c: + XI,E_' = g4z el 16 _f:,b, 14 12 1 O "i 8O 6 4 2 I I I ] 2. Lift Coefficient Fig. 69 Horizontal position effect on L/D ratio at -1% and 8 = MCARFA Results o1' NLF(1)-4 16 with 25% NACA 441:2 '{LEa: -_Zcl, de= -.25 r_ -.26 U -.27 '.- -.26 C2 -.29 ---'4_ LEa - 9% el XLEz 94% (:_ --_-- XLE:_ - 95% c] ----_-- XLE_ - 96% ct ] J :: -. o -.1 _b _.< -.2 :E o -. -.4 -O5 I J I 1 2 Lift Coefficient Fig. 7 Horizontal position effect on moment coefficient at -1% and 8 =

57 case optimum position was 95% of the primary chord behind and 1.5% of the primary chord below the primary leading edge. Relative Angle The effect of the relative angle on the aerodynamic loads was also studied. The leading edge of the secondary element was positioned 95% of the primary chord behind and 2% below the leading edge of the primary element. The secondary element of NACA 4412 section was deflected from 1 through in 5 increments. The maximum lift coefficient increases with increasing deflection angle so the highest clm_ was obtained with the deflection case (Fig. 71). The lowest drag coefficient was also found at the deflection case for the lower el range (Fig. 72). The highest L/D value at expected cruise conditions was obtained with the deflection case (Fig. 7). The spike in the L/D curve discussed earlier is again present at the 25 and deflection cases; without this spike, the 2 deflection case would have the highest L/D at the cruise case. The 2 deflection case also has the highest L/D through much of the mid c_ range. As expected, the moment coefficient results show the largest moments with the greatest second element deflection, increasing approximately.5 for each 5 deflection increase (Fig. 74). Based on the above study, the deflection case was found to be the best because it had the highest cjmax value and the highest L/D at the expected cruise cj of about.6 at a Reynolds number of x16. The 2 deflection case was also kept for future study based on the more conservative L/D curve and the nearly % lower pitching moment. Modified Profile Shapes The parametric variation study above found the optimum geometry for the new two element airfoil to be made up of a primary element with a NASA NLF(1)-416

58 M(JARFA Results of' NLF(1)-4 16 wit, h g5_ NACA 441 XLEe 957 el, YLEre = -2% cl - _- _ = l(}e JC, G r..o LE -15-1_ -9-6 - 6 9 P Angle of At.Lack Fig. 71 Relative angle effect on lift coefficient MCARFA Result, s of NI,F(1)-416 with E5% NACA 441E XLEe = 95Z cl, YLF:e = -2% cl. O.g O d_.1., I, L 1 2 Lift Coefficient Fig. 72 Relative angle effect on drag coefficient

59 MCARf:'A Re.stilts of NLP(I)-416 with 25?; NACA 44 12 Xt, F]:_ : 95_, el, YLEe = -,_/o')_"el _rj e'-',..- E2 P2) O 18 16 14 12 1 O 8 6 4 2O F I -'_--- 8 = I{} = 15 /ZL,. _ 6 = /... 1 E Lift. Coefficient Fig. 7 Relative angle effect on L/D ratio MCARFA Results of NLF(1)-416 with 25_ NACA 4412, XLEa = 957o cl, YLEa = -2% el -(}.{}5 -_ 6 = G' ---4_-- 6= 15 6 _ = 6 = :25 6 = O -.15 4j_._ jt[ r_ C_-._e a_--_ ---4- O G -.25 r_ -.5 I I I I I 2 Lift Coefficient Fig. 74 Relative angle effect on moment coefficient

6O section 75% of the total chord and a secondary element with a NACA 4412 section 25% of the total chord. The secondary element was deflected with respect to the primary element, although the 2 deflection case was also kept as a candidate. The leading edge of the secondary element was located 95% of the primary chord behind and 1.5% of the primary chord below the primary leading edge. The next task in the study was to design a new two element airfoil based on the experience gained in the parametric study. The relative geometry between the two elements was kept the same as in the parametric variations. In addition, the NACA 4412 secondary profile shape was working well so it was also kept the same. The primary region of possible improvement was in the profile shape of the primary element. In particular, the primary element was operating at a negative angle of attack for the cruise case so the major thrust of the new design was to obtain more laminar flow on the primary element at the cruise cl values. Nomenclature for the new airfoils is GS1 for the first iteration of the two element airfoil configuration. The name followed by an A as in GS1A refers to the primary element only of the two element configuration. The first new primary element, named the GS1 A, attempted to lower the drag of the system by creating a cut-out near the trailing edge of the primary element to shield the secondary element from the freestream (Fig. 75). The second primary element GS2A was an attempt to obtain more laminar flow on the primary element lower surface by thickening the NASA NLF(1 )-416 airfoil from the leading edge back to approximately 85% of the local chord and then faired to meet the old trailing edge. The upper surface remained unchanged from the NLF airfoil. The GSA airfoil lower surface was the same as the NLF airfoil back to about 2% chord and then thicker to the trailing edge. In addition, the trailing edge cusp was removed; the upper surface was again unchanged from the

61 J jj NI,I_1 (/ -416... -_ - { / // (]SO1... f/ _ ":k L._f,/ GS2 _.. _'_\ (/ GS (J J csou / cso4 GS5 / Ij/_" GS6 Fig. 75 Modified profile shapes

62 original NLF shape. The GSUA profile was the same as the GS but a cutout matching the shape of the NACA 4412 leading edge was faired into the last 1% of the lower surface. The GS2A airfoil was further modified by again thickening the lower surface back to about 85% chord and called the GS4A airfoil. The GS5A and GS6A were again thicker modifications of the GS2A airfoil but respectively thinner than the GS4A profile. Numerical results are presented for the various modified profile shapes and the original NLF(1)-416 primary profile, all with a NACA 4412 secondary profile deflected. Lift coefficient results show the lowest Clmaxvalues for the GS1, the GSU, and the GS profiles, with very little difference in the lift curves between the other cases (Fig. 76). The c d results show the highest drag values on the three worst lift cases. The lowest drag was obtained on the GS2 configuration with slight improvements over the other cases (Fig. 77). Lift to drag ratio results show the highest L/D values with the GS2 case at lower lift coefficients but the NLF airfoil case had the best L/D ratio at the highest lift coefficients (Fig. 78). Pitching moment coefficient results were nearly identical for all of the best cases (Fig. 79). AG91 Airfoil Based on the Clmaxvalue and the highest L/D at the lower lift coefficients, the GS2 airfoil was chosen as the final modified profile shape. In order to match the chord in the numerical cases with the wind tunnel results, the numerical case total chord was extended from 51 centimeters in the GS2 case to 61 centimeters for the final shape. The final shape was named the AG91 airfoil for the first (1) Texas A&M University Aggie (AG) airfoil of 199 (9). A small grid varying the relative position of the NACA 4412 secondary element with respect to the AG91A primary element was studied to verify the optimum

6 MCARI,'ARosulks of Primary Airfoils with 25% NACA 4412 XI,E_ = 95% el, YLE2 =: -1.o% cl -----_ NLF( I )-416 t,_ 2 55.- _ 25 1, I, I, I L I _ L, I, I, L, I -1<t -124-1 -1-6 -4 -;2 2 4 Angle of Attack Fig. 76 Modified primary profile shape effect on lift coefficient MCARFA Results of Primary Airfoils with 25% NACA 4412 XLEa 95%cl,YLEe = -1.5%cl /. G -a-- NI,F(1 )-416 GS1A ----e,--_ GSO2A --_+-- GSOA ---_--_- GSAU GSO4A ---_-- GSOSA _ GSO6A.()_ z: Q.1 _-_.(} L i 1 2 Lift Coefficient Fig. 77 Modified primary profile shape effect on drag coefficient

64 MCARVA Rcsult.s of Primary Airfoils with '25% NACA 44 12 XLI22 _: 95Z c J, YI,E2 _: -157o cl 22 2 1 go 16 ----_-- NL["( 1 )-t4 I (i //A \_\I ---_--- C;S4A ///\ _, + CSOSA t_l:j 14 12 1 8 6(1 4O 2 1 2 Lift Coefficient Fig. 78 Modified primary profile shape effect on L/D ratio MCARFA Results of Pri mary Ai rfoi ls wi [h 25% NACA 4412 XLE 95% el, YLEe = -1.57 el -._ c_ -O.EE.E -.24 _- -.26 -_o---- NLF(1)-416 GSO1A GSDBA GSOA + GSOAU + GSO4A + GSO5A GSO6A a) -OgO o -.2 = -.4 2 o -.:6. o. --_-_) _--_V_1 -o.a8 -.4 r 1 _ I I l 2 Lift Coefficient Fig. 79 Modified primary profile shape effect on moment coefficient

65 relative position. The secondary element leading edge was varied from 94% through 96% of the primary chord behind and 1% through 2% below the primary leading edge at a secondary element deflection of and a Reynolds number of xl 6. Lift coefficient results for the secondary element at a vertical position 1% below the primary element show very little change with the different horizontal positions (Fig. 8). Drag coefficient values (Fig. 81) show the lowest Cd through most of the lift range at the 95% position. Lift to drag ratio results, as the c d, show the best L/D through most of the c I range at the 95% configuration (Fig. 82). Moment coefficient values increase with the further aft positioning of the secondary element (Fig. 8). Lift coefficient values for the 1.5% below case show slightly higher cj values for the 95% and 96% cases than the 94% condition (Fig. 84). The lowest c d was obtained at the 95% case (Fig. 85) and, therefore, the highest L/D ratio was observed at the 95% condition as well (Fig. 86). Moment coefficient values again increased with further aft positioning (Fig. 87). The 2% below lift coefficient values again show the highest cl results at the 95% and 96% positions (Fig. 88). Drag coefficients were again the lowest (Fig. 89) and the L/D ratio was the highest (Fig. 9) for the 95% condition. Moment coefficient results were the same as previously observed (Fig. 91). Based on the AG91 position results, the optimum position of the NACA 4412 secondary element leading edge was verified to be 95% of the primary chord behind and 1.5% of the primary chord below the primary element leading edge. The final AG91 profile shape was therefore determined to be a two element airfoil with a primary profile of AG91A section and a secondary element profile of NACA 4412 section. Airfoil coordinates for the AG91A and the NACA 4412 are given in Tables 2 and, respectively. The primary element has a local chord 75% of

66 MCARVAResults of AG91 Airfoil Re = xlo 6,d,YL,E_ -l_ci E.5, [ -_-- XLE_ = 94Z el - _ XLE_ = 95% cl I XLE_ = 96% cl _ (b C_ -.5, i J _ L I _ I, k, I, I _ I 8-16 -14-12 -1 -[ -6-4 -2 Angle of Attack Fig. 8 AG91 horizontal position effect on lift coefficient at -1% MCARFAResultsofAG91 Re = xlo 6,62 =, YLE2 = -1%cl Airfoil.2.O 1.16.14 U O O _1, _.1E.1 O.OOg /.6.4.E. (1 -,5 XLEz = 94% el )_LEz = 95_ ct XLEz = 96% el I., _ l I.5 1.5 E.5 Lift Coefficient Fig. 81 AG91 horizontal position effect on drag coefficient at -1%

I 67 MCARI"A Results of AC91 Airfoil Re - x16, 62, YLE2-1Z el 2EO _1),"d t 8 14O I -----'_- XLE2 : 94% cn [ - =+--- XL+E_ : 95% I +_-- XLEz 96Z el '_ /'\ l () :2 6O 2O ry -_ I 1 I )5 (.5 1.5 2.5 Lift Coefficient Fig. 82 AG91 horizontal position effect on L/D ratio at -1% MCARFA Results of AG9 1 Airfoil Re : xi6 _a =,YLEa = -1Z ci -.2 XLEz = 94% ci -----e_-- XLEz = 95% ct XLEz = 96Z el O G) -.25 E 2 2 _2 -O.O -5 I I i -.5.5 1.5 E5 Lift Coefficient Fig. 8 AG91 horizontal position effect on moment coefficient at -1%

68 MCARFA Results of A(;91 Airfoil Re = xlo_, 6_, YI,_:_ = -1.5% cl,j r_ _ XI,Ez = 94% Cl XLEz ; 95% cl = 1.5 ja_ C9 O. 5 -.5 8-16 -14-12 --1-8 -6-4 -2 Angle of Attack Fig. 84 AG91 horizontal position effect on lift coefficient at -1.5% MCARFA Results of AG91 Air[oil Re = xlo 6,62 =,YLE2 = -1.5%c_.2.1B O. 16 XLEa _ 94% cl XLEz = 95% cl XLEa = 96_ ct - 5.14.12 C9.1 O.OOB.6 4 O.2 OIO -.5 I i I O.5 1.5 2.5 Lift Coefficient Fig. 85 AG91 horizontal position effect on drag coefficient at -1.5%

69 M(TARFA Results of AC91 Airfoil Re xlo 6,62 :_-,'flea -1.5% cl 22O 18O XLEz = 94%cl _-- XLEz = 95% cl XLEz = 96%cl _L 14 rm 1 6C) EO r -2 i i _ l i -O.5.5 1.5 2.5 Lift Coefficient Fig. 86 AG91 horizontal position effect on L/D ratio at -1.5% MCARFAResulLsofAG91 Airfoil Re _ x16,ca =,YLEa = -1.5%el -.2 r_ --_------ XLEz = 94_ cl -----_---- XLEa = 95% cl KLEz = 96% cl o _ r_ o -.25 \ -O.O \ _o o -.5 -.5.5 1.5 2.5 Lift Coefficient Fig. 87 AG91 horizontal position effect on moment coefficient at -1.5%

7O MCARFA Results of A(;91 Airfoil l_(_ [_Xl6, (Sa =, YLEa -277 cl =-**- XLEa - 94_', c_ ----4+-- XLEa = 95Z cl XLEz 96%cl O O O O [r / // -(].5 [4-16 -14-12 -1-8 -6-4 -2 Angle of Attaek Fig. 88 AG91 horizontal position effect on lift coefficient at -2% MC,ARFA Results of AG91 Airfoil Re = xlo 6,6a =, YLEa = -2%cl 2.O 18 O. 16 l l XLE2 = 94_ cl i ] ---R_ XLgz = 95% ct ] / _ XLEz = 96% cl /.O14.O12 t... C) O.1. ()6.6 O. 4.2.(1 -O.5.5 1.5 2.5 Lift Coefficient Fig. 89 AG91 horizontal position effect on drag coefficient at -2%

71 MCARF'A ResulLs of A(;91 Airfoil Re x]o _, cse. =, YLEe = -2% ct 2_ ---_*--- XLEa = 94% cn ]8 ----_-- XLE_ : g5% el I _-- Xl,ge = g6% (:1 14O 1O 6 2-2 -.5 O.5 1.5 2.5 Lift. Coefficient Fig. 9 AG91 horizontal position effect on L/D ratio at -2% MCARFA ResulLs of AG91 Airfoil Re = xlo 6,_a =, YLE2 = -2% cl -O.2 --_+---- XLEa = 94% cl J b ----_-_ XLga = 95% c, -----_-- XLEz = 96_ c, O C -.25 O O Fig. 91 AG91 horizontal position effect on moment coefficient at -2%

72 Table 2 AG91A airfoil coordinates X/C I..5.1.2..4.5.75.1.125.15.2.25..5.4.45.5.55.6.65.7.75.8.85.875.9.925.95.975 1. yup_ c i..154.2178.1484.928.4586.51674.6694.7149.8766.86964.962.11412.166.1217.159.96122.942.8849.76645.69.6118.5277.441.566.278.2529.19857.1996.7467. Ylower/c 1. -.976 -.1944 -.19655 -.2882 -.2767 -.8 -.6594 -.41499 -.4544 -.4864 -.51 O -.55799 -.57221 -.57582 -.56845 -.5478 -.518 -.45551 -.82 -.2982 -.2924 -.12478 -.585 -.72.122.2271.289.286.2872.

7 Table NACA 4412 airfoil coordinates _/C 2..5.1.2..4.5.75.1.125.15.2.25..5.4.45.5.55.6.65.7.75.8.85.875.9.925.95.975 1. Yuppe_C2..1918.19946.28815.5767.4165.4675.575.65712.72659.7847.8786.9296.9676.97999.97486.9588.91916.8727.8148.74756.67117.5861.4922.896.59.2752.2159.1486.7756. Ylower/C2. -.184 -.14175 -.1877 -.21612 -.264 -.25147 -.2754 -.28727 -.2911 -.28998 -.27695 -.25662 -.256 -.298 -.18618 -.1625 -.14126 -.1244 -.195 -.82 -.6688 -.5282 -.41 -.164 -.2766 -.297 -.228 -.1596 -.991.

74 the total chord and the secondary element has a local chord 25% of the total. The position of the 4412 leading edge was optimized to be 95% of the primary chord behind and 1.5% of the primary chord below the primary element leading edge. The optimum deflection of the secondary element with respect to the primary element was determined to be, but the 2 case will still be considered because of the somewhat more conservative design. The primary element AG91A is a 16.1% thick airfoil with a chord of 46 centimeters. The final AG91 airfoil, with both the and 2 deflections, is shown in Figure 92. 75% chord j/i _-- r_j jt 2. 25% chord 75% chord jl Fig. 92 AG91 airfoil

75 Numerical results for the final AG91 airfoil with both the and 2 deflection cases are presented for various Reynolds numbers across the entire expected operating envelope. Lift coefficient results for the AG91 deflection case at Reynolds numbers ranging from 8x 15 to x 1 6 show the qmax does not change significantly with the various Reynolds numbers, but the slope of the lift curve does increase, especially at higher ct values, with increasing Reynolds number (Fig. 9). The drag coefficient decreases with increasing Reynolds number as expected (Fig. 94). The L/D ratio (Fig. 95) and the moment coefficient (Fig. 96) also increase with increasing Reynolds numbers. The AG91 2 deflection results are also presented for Reynolds numbers ranging from lxl6 through x16. Results follow generally the same trends as the deflection cases. The lift curve slope increases with increasing Reynolds number with very little change in the Clm_, values (Fig. 97). The drag coefficient decreases with increasing Reynolds number (Fig. 98). The L/D ratio (Fig. 99) and the moment coefficient (Fig. 1) both increase with increasing Reynolds numbers. In addition to the L/D ratio which is critical to the maximum range performance, results are also presented for cln/% which is the driving parameter in the maximum endurance equations for propeller driven aircraft or gliders (Fig. 11). These results also show an increase in performance with an increase in Reynolds number. Comparison With Other Airfoils The AG91 airfoil was compared with three other similar use airfoils. Both the and 2 deflection cases are used for this comparison. The AG91 was compared with the NASA NLF(1)-416 airfoil, the SM71 airfoil, and the Wortmann FX 79-K-144/17 airfoil. The NASA NLF(1)-416 was the profile shape that the

76 MCARVA Results for" AG91 Airfoil XLE_ = 95% el, YLEa - -1.5_ cl. y /;' //-j E.E -_+_ Re = lxlo 6 /_*'_/ ----_-- Re =: exl_ /_./'" r- 1.4 o co O. 6 -O2 -a2-1g -g 8 Angle of Attack Fig. 9 Reynolds number effect on numerical lift coefficient, 8= MCARFA Results for AG91 Airfoil XLEe : 95% cl, YLEa = -1.5% cl C).4 O. ----+_--_ Re = 8xIO 5 + Re = lxlo 6 Re = 2xlO 6 Re = xlo _ # C) O.Og a rm O.C) 1. I, L, a, b -C).g.6 1.4 g.e D Lift Coefficient Fig. 94 Reynolds number effect on numerical drag coefficient, 6=

77 MCARFA Results for' AGO1 Airfoil XLEe= 952cl, YLEe:-- - 5%cl 22 2O 1 _/ 16 14 _h k_ leo 1 8,..-a 6 4 2-2 -.2.6 1.4 2.2. Lifl Coefficient Fig. 95 Reynolds number effect on numerical L/D ratio, 8= MCARFA ResulLs for AG91 Airfoil XLEe = 95% cl, YLEe = -15% el -.25 -.26 + Re = 8x15 -..27 -+ Re = lxlo 6 ] _ Re = 2xLO 6 to C) -O.28 -.29 _P -. r" -.2.a. L x_ -. -.4 -.5 -.2, I e I _ I.6 1.4 2.P_, Lift Coefficient Fig. 96 Reynolds number effect on numerical moment coefficient, 8=

78 MCARFAResults forag91 Airfoil XLE2 = 95% ct, YLE2 = -1.5% ct, 6 = 2 E. t_ Angle of Attack Fig. 97 Reynolds number effect on numerical lift coefficient, 8=2 MCARFA ResulLs for" AG91 Airfoil XLEz = 95%c1, YLE_ = -1.5%c1,6 = 2.O4. -_-_---- Re= lxlo 6 y Re = 2xlO e Re = xlo 8 / O O CD.2.1., _, L, -.2.8 1.8 2.6 Lift Coefficient Fig. 98 Reynolds number effect on numerical drag coefficient, 8=2

79 MCARFA Results for AGg1 Airfoil XLEe = 95% el, YLEe - 1.5% cl, _ 2 14 1EO 1O 76"-,_.z \> ru 8 6 C) 4O EO @ Re = lxlo", /_ + Re = 2xlO Re = 1 _ ] -2 -O,E h I 1 L.8 1.8 [,if[coefficient 2.8 Fig. 99 Reynolds number effect on numerical L/D ratio, 8=2 MCARFA Re, sulks for AG91 Airfoil XLEe 95Z el, YLEe = - 1.5Z c_, 6 2(] C).C) e- (D --Jam-- Re = lxlo a ---+_--- Re = 2xlO a ----_ Re = xlo a t,.. O O..J -.1 _D O -.2 - O K -. -.2 I.8 I 1.8 g.8 Lift Coefficient Fig. 1 Reynolds number effect on numerical moment coefficient, 8=2

8 MCARFAResults for'ag91 Airfoil XLE_ = 95_' el, YLE_ - 1.5% cl, 6 = _()o 18O 16 14 e_ 1 1 O 8O 6O 4 -.2.8 l.8 2.8 Lift Coefficient Fig. 11 Reynolds number effect on numerical Cl/2/Cd,6=2 AG91A was modified from. It was originally chosen for study because it was a reasonably high lift single element airfoil designed for light general aviation applications. The SM71 airfoil is a fixed geometry single element airfoil designed by Mr. Dan Somers and Dr. Mark Maughmer specifically for the new World Class Gliders. 47 The Wortmann FX-79-K-144/17 is a state of the art sailplane cruise airfoil used on many of the current high performance gliders including the Ventus and the Nimbus. 4s It has a 17% chord simple flap deflected -9. for the cruise case. Maximum lift coefficients for all airfoils were taken as the computed values as calculated by the MCARFA computer code. These results are presented with other source values when possible. Cruise lift coefficients were taken as the design c I of.4 for the NLF and the SM71 airfoils. Cruise el values for the AG91 cases and the

81 Wortmannairfoil werecalculatedby requiringthe samestallandcruisespeedfor the AG91andWortmannairfoils asfor the knownnlf(1)-416airfoil. Lift coefficientcomparisons(fig. 12)showthe AG91with the deflection case has the highest Clmaxvalue with the AG91 with the 2 deflection somewhat lower. The SM71, NASA NLF(1 )-416, and FX 79-K-144/17 airfoils all had significantly lower cj,,ax values. Drag coefficient results show the Wortmann airfoil has the lowest c a at the low lift coefficients (Fig. 1). The AG91 2 deflection case had the highest drag at a given lift coefficient for most of the cl range. The AG91 deflection case had a lower drag than the 2 case, but still higher than the other airfoils at a given lift value through most of the el range. The L/D ratio results confirm the ca conclusions that the AG91 cases have lower L/D ratios at a given lift coefficient than the other airfoils (Fig. 14). However, because of the significantly higher Clm_xvalues obtained with the AG91 configurations, the cruise cl values are also higher and therefore the actual cruise L/D ratios are much more competitive. The moment coefficient results show the AG91 deflection case has the highest moment coefficient, followed by the AG91 2 deflection case (Fig. 15). The other airfoils had moment coefficients roughly a third that of the AG91 deflection case. A high moment coefficient is generally considered undesirable in an airfoil because of the trim drag penalty that is usually associated with a higher moment coefficient. This concern is somewhat overblown for fixed geometry airfoils like the AG91 airfoil because the effect of the pitching moment on the aircraft can be greatly reduced, if not eliminated, by proper positioning of the wing on the airframe. This is not possible with variable geometry airfoils for all conditions because, unlike the fixed geometry configurations, the moment coefficient changes

82 MCARI?A Results of Various Airfoils Re = x16 E, 8 / --_--- AG91. g = _ /_; --_--- a_9ol, a = ao / // --*-- sm_1 /,/ --_--- FX 79-K- 144/17 /7' --' NASA NLF(1).-416 / :_/ / U C -15-5 5 15 Angle of Attack Fig. 12 Lift coefficient comparison of various airfoils MCARFA Results of Various Airfoils Re = x 1 6 O. 4 + AC91. = O. --f_---- A_91.6 = 2 SMTO1 + FX 79-K- 144/17 C).2 2_-_ NASA NLF{I)-416,1 I I I.8 1.8 2.8 Lift Coefficient Fig. 1 Drag coefficient comparison of various airfoils

8 MCANFA [ esults of Various Airfoils Re x16 14() 12 1 {) / {} LE 6 4 2 AG91,8 = AG91,_ = 2 SMTOI FX 79-K-[44/17 NASA NLF(1)-416-2 -.2.8 J 1.8 J 2.8 Lift Coefficient Fig. 14 L/D ratio comparison of various airfoils MCARFA Results of Various Airfoils Re = x 16. AC_1, _ = AG91, _ = 2 SMTO1 F_( 79-K- 144/17 NASA NLP(1)-416 --.1 -O.2 O -., I * I J I.8 1.8 2.B Lift Coefficient Fig. 15 Moment coefficient comparison of various airfoils

84 significantly with different flap deflections and therefore the proper positioning for one flap deflection will not be the optimum for a different flap deflection. Table 4 lists the MCARFA results at a Reynolds number of x16 for the various critical parameters associated with the airfoil comparison. Comparisons of the AG91 results with the NASA NLF(1 )-416 airfoil are particularly important comparisons because the NLF airfoil is, with minor modifications, the primary profile in the AG91 configuration so the comparisons are very much that of the effect of adding the secondary element. From the table it is clear that both the AG91 configurations offer significantly higher Clmaxvalues. The deflection case has a nearly 6% higher qmax than the NLF airfoil and the 2 deflection case has an approximately 44% higher Clmaxthan the NLF airfoil. The AG91 deflection configuration has a higher L/D at the cruise case than any of the other airfoils and over 19% higher than the NLF airfoil. The AG91 2 deflection case has a cruise L/D slightly higher than the NLF(1)-416 airfoil. Table 4 Airfoil comparison at Reynolds number of x1 6 Airfoil qmax Clc_isc L/Demise AG91-2.827.6 72.67 AG91-2 2.545.57 61.6 NLF(1)-416 1.77.4 6.92 SM71 1.87.4 67.97 FX 79-K- 144/17 1.4.1 7.18 On the basis of L/D ratio alone, the AG91 airfoil offers significant improvement in the cruise case, but the real benefit is apparent when accounting for the significantly higher C_m_,value as well. The higher C_m_,value allows the wing

85 planformto be significantlysmallerfor the samestall speedthana wing basedonthe otherairfoils. The c_,,,_valueobtainedwith the deflection case for the AG91 airfoil allows a 46% smaller planform than the NASA NLF(1)-416 airfoil. The wing makes up approximately % of the total weight of a sailplane 49 and, in a first order approximation, the wing weight is proportional to the wing planform; therefore, the smaller planform wing will be roughly 46% lighter than the NLF based wing. This corresponds to a nearly 14% lighter aircraft. Since the lift must equal the weight for level flight and the aircraft weighs 14% less, the lift required is also 14% less. This also results in 14% less wing drag at the same L/D ratio. When combining the weight savings and the increased L/D at cruise, a wing based on the AG91 deflection case airfoil will have over 27% less drag at the cruise case than a wing based on the NLF(1 )-416 airfoil. This drag improvement is for a generic sailplane with the same stall speed and the same cruise speed in both cases, the only difference is the wing based on the different airfoils. Following a similar set of calculations, a wing based on the 2 deflection case of the AG91 will have about 11.75% less wing drag at the cruise case than a wing based on the NLF(1 )-416 airfoil. Transition Location Numerical results for the transition location are presented for the AG91 airfoil in the and 2 deflection cases in Figures 16 and 17 respectively. It can be seen that the AG91 deflection case has significantly more laminar flow on the upper surface than the NASA NLF(1)-416 airfoil. The NLF airfoil does have a small amount more laminar flow on the lower surface than the AG91 airfoil. At the cruise lift coefficient the AG91 has approximately 25% laminar flow on the lower surface and 8% laminar flow on the upper surface. No separated flow is calculated on either surface. The AG91 2 deflection case has less laminar flow on the upper surface

86 M( ARVA Transition Location Results Re := x 1 6 1. AG91-() Upper Surface (D X.9 --_-er--- AG91- Lower Surface NASA NI,F{ )-416 tipper I Surface NASA Nt,F( I )-{)4 16 Lower Surface.7 [). 6?..5 _d.4..:2..,-, c" ().E C).1 r,..8 1.8 2.8 Li f[ Coefficient Fig. 16 Numerical transition location, fi = MCARFA Transition Location Results Re = x 1 6 1. AC9! -2 Upper Eurface G O.. AG9:1-2 I,owcr Surface NASA NLP( )-416 tipper l Surface X C).B I o NASA NLP( 1)-416 Lower Surface r,.7,6.5.4..2 O. 1 2.,. O. -2.8 1.8 Lift Coefficient Fig. 17 Numerical transition location, 6 = 2

87 thanthe deflectioncase,but still morethanthe NLF(1)-416airfoil. The2 deflectioncasehasmorelaminarflow on the lower surfacethanthe deflection case,but still lessthanthenlf airfoil at cruiselift coefficients. At the cruiselift condition,theag912 deflectioncasehasapproximately5%laminarflow on the lower surfaceand7%laminarflow on the uppersurface.

88 EXPERIMENTAL TOOLS Experimental surface and wake pressure data, along with flow visualization measurements of transition location, were obtained for various AG91 airfoil configurations in the Texas A&M University Low Speed Wind Tunnel. s Wind Tunnel The wind tunnel is of the closed circuit, single return type. Figure 18 presents a plan view of the wind tunnel circuit. Total circuit length at the centerline is 121. meters. The tunnel cross section is circular and of steel plate construction from the power section at the exit of the diffuser around to the entrance of the contraction section. The maximum diameter of 9.15 meters occurs in the settling chamber. Turning vanes are installed at each corner of the circuit. A single screen is located at the settling chamber entrance and a double screen just upstream of the contraction section to improve dynamic pressure uniformity and to reduce the flow turbulence level. The contraction section which acts as a transition piece from circular to rectangular cross section is of reinforced concrete construction. The contraction ratio is 1.4 to 1 in a length of 9.15 meters. Diffusion takes place immediately downstream of the test section in a concrete diffuser which also returns the flow to a circular cross section. The horizontal expansion angle is 1.4 and the vertical angle is.8 in an overall length of 14.17 meters. The.81 meter diameter, four-blade Curtiss Electric propeller driven at 9 RPM by a 125 kva synchronous electric motor provides the air flow in the wind tunnel. Blade tips are inset into the tunnel wall to minimize tip interference effects.

89!59' i I I Fig. 18 TAMU-LSWT facility diagram Any desired test section dynamic pressure between zero and 5 kilopascals can be obtained by proper propeller blade pitch angle positioning. The rectangular test section is 2.1 meters high,.5 meters wide, and.66 meters long. The corners have 1 centimeter fillets which house fluorescent lamps to provide photographic lighting. Cross sectional area of the test section is 6.2 square meters. Eight centimeter wide vertical venting slots in the side walls at the test section exit maintain near atmospheric static pressure. The test section side walls diverge about 2.5 centimeters in.66 meters to account for boundary layer growth. A turntable 2.1 meters in diameter built into the test section floor rotates with the external balance system to provide remote model positioning. Test section dynamic pressure is measured by a differential pressure transducer accurate to -4-2.4 Pascals. The set dynamic pressure reading is actually the difference

9O betweentwo staticpressurerings;one located in the settling chamber and one just upstream of the test section. A third order calibration curve, obtained by comparison with an accurate pitot-static probe, is then applied to the set dynamic pressure to obtain the uncorrected actual dynamic pressure in the test section. The longitudinal turbulence intensity level was previously measured in the test section at dynamic pressures up to 4.7 kpa. The longitudinal turbulence intensity, in 29 percent, is defined as: %T- U_ xl_ Figure 19 shows the turbulence intensity vs. dynamic pressure as measured by a hot film anemometer system, sl It is seen the turbulence intensity is less than.2% for dynamic pressures less than 1.68 kpa. The turbulence intensity increases to a peak of about.8% at a dynamic pressure near 2.4 kpa, and then decreases with increasing dynamic pressure. The AG91 was tested at four different dynamic pressures corresponding to turbulence intensity levels of approximately:.22%,.19%,.75%, and.65%. A longitudinal turbulence intensity value of.5% is generally accepted as the desired level for good laminar flow airfoil testing. The primary effect of the higher than ideal turbulence intensity values in the TAMU-LSWT was to cause earlier transition from laminar to turbulent flow than would be the case in free air. Airfoil Model A model of the AG91 airfoil was designed and built to experimentally verify the section characteristics predicted by the numerical analysis. The model had a total chord of 61 centimeters. The primary airfoil AG91A had a 46 cm chord and the secondary airfoil NACA 4412 had a 15 cm chord.

91 The primary element was constructed around a 5xl cm steel box beam used as a wing spar. Two steel templates were cut to the final desired profile shape and then one template was welded to the spar. Eighteen 51 mm thick sections of Ren Shape were roughly cut to the profile shape and slid onto the spar and pinned to each other, then the final steel template was welded into place. The center Ren Shape section had sixty-three pressure ports installed by drilling through the rough cut outline and gluing mm steel tubing protruding normal to the surface. Vinyl tubing was then connected to the internal side of the steel tubing and routed through the spar to the transducer location. The final profile was obtained by sanding the Ren Shape down to the steel templates and painting the finished shape. TAMU-LSWT LongiLudinal Turbulence, IntensiLy 1..9.8.7.6 o _J.5.4.._.]...5 1. 1.5 2. _.o= S.O.5 4. 4.5 [ 5. FreestreamDynamicPressure (kpa) Fig. 19 Freestream longitudinal turbulence intensity

92 The secondary element was fabricated similar to the primary element, except due to size constraints, it was not possible to put a solid spar inside the model. The secondary model was, therefore, built of solid Ren Shape with steel templates at the ends and two steel alignment pins connecting each Ren Shape section. Twenty-six pressure ports were installed on the secondary airfoil using the same technique as the primary shape. The vinyl pressure tubing was run through a hole drilled in the Ren Shape and out the bottom of the model. The tubing was then run along the secondary element bracket to the transducer location. The secondary element was connected to the primary by steel brackets at both the top and the bottom of the model. The brackets had fixed mounting holes on the primary element and variable locations for mounting on the secondary element to allow various second element relative positions to be tested. The initial model design called for an accurate profile shape on the center.91 meters of the model and then an approximate shape on the outer.61 meter sections. This was to reduce construction time but still keep a two-dimensional section. Material and mounting problems led to the elimination of the outer.61 m sections, thus making the model effectively a three-dimensional shape with a span of.91 meters. Upon examination of initial wind tunnel data on the model, it was determined that the.91 meter span model was not giving truly two-dimensional results. Circular aluminum endplates 775 mm in diameter were added to the ends of the.91 meter span. Also during initial testing of the AG91 airfoil, the secondary element was observed to deflect under load, effectively closing the gap between the two airfoil sections. Additional brackets were added to the 2 and cases at the 95%, -1.5% leading edge location and the model was re-run for critical conditions.

9 As previouslystated,pressureportswerelocatedon both airfoil sections near the center of the span. Ports were offset 2.5 mm spanwise to eliminate the risk of upstream ports contaminating the data downstream. Sixty-three ports on the primary element and twenty-six ports on the secondary element were distributed based on surface curvature with regions of high curvature having more ports. Figure 11 shows the final profile shapes with pressure port locations. (/ f_ Fig. 11 AG91 pressure port locations The airfoil model was installed with the span vertical in the TAMU-LSWT test section. The LSWT external balance was used as a mounting system allowing the turntable to be utilized for angle of attack changes. The airfoil model was constructed with a steel mounting plate at the base which bolted to the tunnel's Large Base Mount Support. The Base Mount Support was located in the center of the turntable with the top 11 cm below the floor. A two piece floorplate was installed with a small clearance around the spar to eliminate any air transfer between the test section and the balance room below. A rotating pin was used at the ceiling to carry some of the wind load and reduce model deflections. Figure 111 shows a drawing of the airfoil model installed in the TAMU-LSWT test section. The model was aligned with the chord of the primary element parallel to the geometric tunnel centerline. Angle of attack changes were accomplished by rotating

94 F,ndplaLe --N Traversing Mechanism --7-- I AG91Airfoil... \ WakeRake Scanivalve Stepper Model Mounting Plate Fig. 111 AG91 airfoil installed in TAMU-LSWT the turntable in the floor of the test section. All angle of attack values were defined relative to the primary element chord line. Instrumentation All pressures were measured by Validyne pressure transducers on the initial runs. Two ranges of transducers were used. A 2 kpa transducer was used on the upper surfaces of the two airfoils, a 6.9 kpa transducer was used on the lower surfaces

95 of the airfoils, and a 6.9 kpa transducer was used on the wake rake. The TAMU- LSWT 16-bit Preston A/D system was used to convert the analog transducer readings to digital values in the Perkin-Elmer 21 super mini-computer. One thousand samples of analog data were taken at 1 Hz. and averaged to obtain a single pressure reading. A settling time of 2 seconds was used between consecutive pressure readings. Two Scanivalve stepper systems were used to allow multiple pressure readings by a single transducer. Two 48 port heads on the first Scanivalve were installed on the wing spar just below the model base and shielded from the wind by a small fairing. The second 48 port Scanivalve was installed on the tunnel's traversing mechanism near the wake rake. The two heads connected to the airfoil model were of the 1 mm style and the one head measuring the wake rake pressures was of the 1.6 mm style. During the second set of wind tunnel runs, the TAMU-LSWT PSI-84 pressure measurement system was used to measure the wake rake pressures instead of the second Scanivalve system. A forty port total pressure wake rake was used to obtain pressure measurements for the calculation of profile drag. Total port spacing was 6.4 mm between centerlines yielding a 25 mm span. The rake has an additional five static ports evenly spaced along its span to obtain dynamic pressures in the wake. The rake was mounted to the TAMU-LSWT traversing mechanism allowing remote positioning of the rake when desired. The rake was positioned one chord length behind the trailing edge of the airfoil model. A digital optical encoder on the LSWT turntable provided the model angle of attack reading. This reading, the freestream dynamic pressure, and the temperature were read by the Perkin-Elmer D/D system by taking 1 samples of each counter output and averaging to obtain a data point.

96 Data Reduction Pressures were calculated from the measured transducer voltages according to the following equation: p = (V - WOZ) x SLOPE where p is the pressure, V is the transducer voltage, WOZ is the initial transducer voltage with no wind on, and SLOPE is the linear calibration slope obtained on-line by reading a known calibration pressure and corresponding voltage. Pressure coefficients were then obtained from the raw pressures by: where Cp is the pressure coefficient, p is the local pressure, and Pt and Ps are the freestream total and static pressures from a pitot-static probe respectively. The two element drag coefficient was calculated by the momentum loss method from the dynamic pressure wake rake data using the relation: s2 Cd =2j'(_ _/dy C Two-dimensional airfoil normal and axial force coefficients were obtained for each element by integrating the local pressure coefficient data. The two element moment coefficient was also calculated from the surface pressures.by: s2 c n = - x _(Cp, - Cp_ )dx C o

97 l!/ dyud Y/dx c a =- x Cp_ ---Cp, c dx dx J Cm_ ax./ J Two element normal and axial coefficients were calculated from the single element information and using the previously calculated drag coefficient. The lift and chordwise force coefficients were then obtained from the normal, axial, and drag force coefficients by: s cs = c., + (Cn_ X COS52) -- (Ca_ X sin8 2) (c d -(c_ x sin(x)) CA = COS(/, cl = (cn x cos_t) + (c A x sinot) Once the raw force and moment data were obtained, they were corrected for two-dimensional wind tunnel effects by the following procedure: s2 _, =. = I_sb + _wb Cf,m Cr'm = (1 + 2e) ct+( 57"xc ) or= k _x_" xc, +(4XCm) C, = c, x (1 - - 2g)

98 Cm c a = c d X(1--Ssb --2Swb) L D c I c d The angle of attack reading was corrected to account for three-dimensional effects due to the model not entirely spanning the LSWT test section. This correction was: 4 (18x %) for the first set of data without the endplates and: (18 x c_) = _u (n'x 4.64) for the second set of data with the endplates. The aspect ratio correction to angle of attack was obtained by calculating the effective aspect ratio based on the experimental data from the AG91A case at a Reynolds number of7.5x15 and the AG91 2 deflection case at a Reynolds number of 1x 16 respectively and then using this calculated aspect ratio to correct all other wind tunnel data. Flow Visualization Surface flow visualization was performed at various dynamic pressures and model angle of attack settings for the AG91 final configuration. The flow visualization solution was a mixture of white tempera paint and diesel fuel brushed on

99 the airfoil surface. While themixturewaswet,the tunnelwasbroughtup to the desired wind speedandthe mixturewasallowedto dry, leavingthe temperapaintresidueon the surface.this techniqueallowedclearandaccurateassessmentsof the regionsof laminar,turbulent,andseparatedflow, transitionlocations,andseparationbubbles. Photographsweretakenof all testedconfigurationsfor laterusein measuringthe transitionlocationsandflow characteristics.

1 EXPERIMENTAL RESULTS AND DISCUSSION Experimental results were obtained in the Texas A&M University Low Speed Wind Tunnel to verify the AG91 airfoil numerical design. Results were initially obtained for both the primary element alone and the two element combination before improvements were made to the wind tunnel model. Additional experimental values were obtained on the AG91 airfoil with the 2 and secondary element deflection cases after the additional secondary element brackets and endplates were added. Numerical results, of both the design shape and the actual measured and smoothed s4 model profile shape, are included for comparison with the wind tunnel results. AG91A Primary Element Alone Aerodynamic load data were measured on the AG91A primary element alone at Reynolds numbers of 7.5xl 5 and 2.25xl 6 based on the 46 cm chord. Comparisons on this single element airfoil are possible, not only with the MCARFA computer code results, but also the PROFIL computer code analysis. Lift coefficient values at the 7.5xl 5 Reynolds number case show essentially the same Clma_value in both the experiment and numerically predicted data (Fig. 112). The design shape does have a slightly higher Clmaxvalue than the actual constructed shape. The zero lift angle of attack is essentially the same as the MCARFA predicted value. The somewhat non-linear shape of the experimental lift curve suggests the model was not seeing truly two dimensional flow. Numerical and experimental ca values agree quite well with the experimental data slightly higher through most of the ct range (Fig. 11). The L/D ratio results follow the ca values and show generally quite good agreement (Fig. 114). The PROFIL computer code does appear to most

11 Numericaland ExperimentalAG91AAirfoilResulls Re = 7.5x15 1.6 1.4 "Z 1.2 1. L) O.P, a).6 L_ O.d 25.2 TAMU- LSWT ExperLment Measured Shape MCARFA Results. -.2 Measured Shape PROFIL Results Design Shape MCARFA Results Design Shape PROFIL Results I L J -.4-6 I h I h I I _ I I _ I l -4-2 2 4 6 _B 1 12 J 14 Angle of Attack Fig. 112 Experimental AG91A lift coefficient results, Re --- 7.5x1 s Numerical and ExperimenLalAG91AAirfoil Results Re = 7,5x15 TAMU- LSWT Experiment / Measured Shape MCARFA ----v+--- Results / Measured Shape PROFIL Results / Design MCARFA Results }_ Shape.2 i _ Design Shape PROFI L Results L O_ e_ O1 O, I -4-2 i I h I J I _ I i I i I, I i L, I L I..2.4.6.8 1. 1.2 1.4 1.6 1.B Lifk Coefficient Fig. 11 Experimental AG91A drag coefficient results, Re = 7.5x1 s

12 Numerical and E;xpcrimental AG91A Airfoil Results Re = 7.5x15 12 1 O 8O rm 6O 4O 2O f// _ TAMU-LSWTExperiment _ Measured Shape MCARFA Results JJ _ Measured Shape PROFIL Results Design Shape MCARFA Results z - -----e_ Design Shape PROFIL Results -2 -.4 lit', I, L I L, L, I, i, 1-2.O 2 4,6 8 1. 1.2 1.4 1.6, I 18 Lift Coefficient_ Fig. 114 Experimental AG91A L/D ratio results, Re = 7.5x1 s accurately predict the measured values, especially at higher lift coefficients. Moment coefficient results vary substantially between all four types of numerical data and the experimental results (Fig. 115). Similar single element results were obtained on the AG91 at a Reynolds number of 2.25xl 6. Experimental values were only obtained through the cruise lift coefficient range because of model mounting loads and available pressure transducer ranges. Lift coefficient results show generally good agreement with the zero lift angle of attack much closer to the numerically predicted value than at the lower Reynolds number case (Fig. 116). Drag coefficient results again show good agreement with the experimental data slightly higher through the entire cl range (Fig. 117). The experimental L/D ratio values also correspond to the numerically predicted answers, but are somewhat lower because of the higher ca results (Fig. 118). The moment

1 N/_merieal and Experimental A(;91A Airfoil Results Re. = 7.5x1 5 _.- - TAMU-LSWT Experiment -_ Measured Shape MCARFA Results Measured Shape PROFIL Results 5 k_ Design Shape MCARFA Results _-- Design Shape PROFIL Results -.5 em -.1 r_ o (> -,_....- ' -. IF), *, L,, _, r, I,,, L, I, I I -4 -.2 O.2.4.6.8 1. L._ 14 1.6 1.8 Lift Coefficient Fig. 115 Experimental AG91A moment coefficient results, Re = 7.5x15 Numerical and Experimental AG91A Airfoil Results Re = 2.25x16 1.8 1.6 -'._ 1.4 -"d 1.2 1.,.,.. _O :.2.8.6.4.2. -.2 //'_// _/ + Measured Shape IdCARFA Results _ Measured Shape PROF L Results " //._" // v/_/ _ Design Shape MCARFA Results -/ _ Design Shape PROFIt Results / -.4 I, I n I a [ i I n [ _ I J i b t, I -6-4 -2 2 4 6 8 1 1E 14 Angle of Attack Fig. 116 Experimental AG91A lift coefficient results, Re = 2.25x16

14 Numerical and Experimental AG91A Airfoil Results Re = 2.25x16 r-'.2 a) TAMU- LSWT Experiment Measured Shape MCARFA Results Measured Shape PROFIL Results J + Design Shape MCARFA Results? Design Shape PROFIL Results k,. () 1 em, I _ I _ I, I, I, I _ I J I _ I, I i I -4 - g O 2 4.6.8 1. 12 14 16 1B Lift Coefficient Fig. 117 Experimental AG91A drag coefficient results, Re = 2.25x16 Numerical and Experimental AG91A Airfoil Results Re 2.25x16 14 12 1 8 t_ d,.-m 6 4O 2 1 + Measured Shape MCARFA Results _" _ Measured Shape PROFIL Results _ _ De_ARFA Results -2 + Des'_ Shape PROFILResults -4 L I _ i, I _ I, b, I, I, i _ I, I -4 -,2. 2.4.6.8 1. 1.2 1.4 1.6 1 [:1 Lift Coefficient Fig. 118 Experimental AG91A L/D ratio results, Re = 2.25x16

15 coefficient values again vary significantly between the different sources (Fig. 119). The experimental moment is the lowest of any of the types of data. Numeri('al and Experimental AGg'1A Airfoil Results Re = 2.25xI(_ ca TAMU-LSWT g peri rnent Measured Shape MCARFA Results Measured Shape PROFIL Results Design Shape MCARFA Results Design Shape PROFIL Results o -,5 {D r- Z._a r_ -,1-15, i -.4 -.2, J L l i i i [ L I i i J J l..2.4.6 O.B 1. l.g 1.4 1,6 1.B Lift Coefficien_ Fig. 119 Experimental AG91A moment coefficient results, Re = 2.25x16 Overall, the AG91A single element airfoil was experimentally verified. The numerically predicted maximum lift coefficient values were also measured. The drag coefficient was measured higher than predicted, but within the expected range based on the higher turbulence intensity and the model construction techniques. The moment coefficient was also within the predicted range, although really good correlation between any of the sets of moment data were not observed.

16 Relative Position Experimental data was obtained to verify the optimum position of the second element with respect to the first. As with the numerical data, the second element was moved through a grid with the leading edge of the secondary element varied from 94% through 96% behind the leading edge of the primary element and from 1% through 2% below the primary element. Results were obtained through the cruise lift coefficients for the AG91 with the secondary element deflected at a Reynolds number of x1 6 based on the total chord. The experimental L/D results for the 94%, -1% secondary element position show very poor agreement with the numerically predicted values (Fig. 12). Significant differences also exist between the design and constructed shape results at this position. These differences are assumed to be due primarily to the finite trailing edge thickness on the constructed shape and the near zero thickness on the design shape. Moment coefficient results show a experimentally measured moment roughly two thirds that of the predicted case (Fig. 121). Somewhat better correlation between numerical and experimental data was obtained at the 94%, -1.5% position. Lift to drag ratio results still show a significantly lower experimental L/D than predicted (Fig. 122). Moment coefficient results, while again closer, still are significantly different between the numerical and experimental values (Fig. 12). Results very similar to the 94%, -1.5% case were obtained for the 94%, -2% condition. Again, a lower experimental L/D (Fig. 124) and moment coefficient (Fig. 125) were observed. Results at the 95% horizontal position follow the trends observed in the 94% cases. The experimental 1% below L/D results (Fig. 126) and moment coefficient results (Fig. 127) show very poor agreement with the numerically predicted

17 Numerical and ExperimentalAG91 Airfoil Results Re xlo6, XLEe- 94_c1,YLE2=-l_el g2 TA M U- LS'_/T Experiment Measured Shape MCARFA Results _-- Design Shape MCARFA Results 1 4 b.l t"d,,..., 1 25 6O --_, J, I, ] _ a, ] r P, a, t, I _ I _ J -O.g.(}.2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Lift Coefficient Fig. 12 AG91 experimental L/D ratio, 94%, -1% position, 8= Numerical and Experimental AG91 Airfoil Results Re xlo 6, XLEe = 94% el, YLEe = -1% el -.15 -.17 E -.19,.- -.2l G o -.2 Measured Shape MCARFA Results TAMU-LSWTExperiment + e_ -.25 E o -.27 e_j- Design Shape MCARPA Results = -.29 2 o -,).1 -o. --._ 5 ' } I ] ' [ t [ ' ] I _ I [ I I, I, t, I --.2..2.4.6.8 1. 1.2 1,4 1.6 1.8 2. LifL CoefficienL Fig. 121 AG91 experimental moment coefficient, 94%, -1% position, 8=

- () I [ ] 5 18 Numeriealand ExperimentalA(;9'1 Airfoil Results 1_(.' xlo 6, XLE2 94% cl. YLE2 = -1.5% Cl 22 + q'amu-lswt Expetu ment I _ Measured Shape MCARFA Results ] Design Shape MCARFA Results _L 14 r_ 1 O _'_----- -- 6O --2, I I I, :, I, L, I I _ I I, i, I,! I () [E () l() p2.4,6.8 1, 1.E 1.4 1.6 1.8 2. Lift Coefficient Fig. 122 AG91 experimental L/D ratio, 94%, -1.5% position, 8= Numerical and Experimental AG91 AirfoilResults Re x1 6, XLEe = 94% ct, YLEe = -2% cl -.15-17._ -.19 TAMU-LSWT Experiment Shape MCARFA Measured Results Design Shape MCARFA Results --.2 1 o o -.2 _--..._-_ r- -25 E o -.27 C - 29 r-- o -1 - I L I J I, I, r i I i I i I i I h J h I --. 2 1 I2 "4 "6 O'B 1" 12 1"4 1"6 1"8 g'o Lift Coefficient Fig. 12 AG91 experimental moment coefficient, 94%, -1.5% position, 6=

" _ I {} I 1 9 ] " 2 (} " "2 I 4 I 6 I 8 1" 1"2 1'4 1"6 1"8 2" 19 Numerical and ExperimentalAG91 Airfoil Results Re xioq XLEa = 94% el, YLE',e = -222 cl 22O 18 - -'_-*--- TAM LJ- LSWT Experiment _-- Measured Shape MCARFA Results ----,_-- Design Shape MCARPA Results 14 k_ 1 (} 6O 2O -2, I, I, I _ 1, I _ I I, I, I, I, I Lift Coefficient Fig. 124 AG91 experimental L/D ratio, 94%, -2% position, 8= Numerical and ExperimentalAG91 Airfoil Results Re = x16, XLE2 = 94% cl, YLEe = -2% cl -15 C q9 -.1 7 TAMU-LSWT E_peri ment Neasured Shape MCARFA Results Design Shape MCARFA Results a2 _- -O21 O D -.2 r _,_ -.25 E o -.27 g) r.- -.29 2 o -1 K -. -.5 * i, I, i, I, I _ I, I _ l i I L t, I -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Lift Coefficient Fig. 125 AG91 experimental moment coefficient, 94%, -2% position, 8=

11 Ntlmer'i cal and Experimental AG9] Airfoil Resulis Re- x16, XLEa 957.., ci, YLE2 = - I% ci 2<_ 1_ TAMU- LSWT Experiment Measured Shape MCARFA Resul(s Design Shape MCARFA Results 1,1 1 O 22 6O 2 -SO -OE. i l i L J ; ( I i L l, I I I L I.2.4.6 O.g l.o 1.E 1.4 1.6 1.8 E.O Lift. Coeffieient Fig. 126 AG91 experimental L/D ratio, 95%, -1% position, 8= Numerical and ExperimenkalAG9S1 AirfoilResul{s Re = xlo 6, XLEa = 95Z cl, YLEa = -1% Cl 5 TAM U-LSWT Experiment Measured Shape MCARFA Results Design Shape MCARFA Results C) E r- 2 a- Lift Coefficient Fig. 127 AG91 experimental moment coefficient, 95%, -1% position, 8=

111 information. The experimental 1.5% below L/D results (Fig. 128) and moment coefficient results (Fig. 129) and the 2% below answers (Figs. 1-11) show better agreement with the numerical values, but still are significantly lower. The 96%, - 1% position again exhibited very poor agreement with the numerical cases. Both the L/D results and moment coefficient values were significantly lower (Figs. 12-1). The 96%, -1.5% experimental L/D values showed very good agreement with the numerically predicted case (Fig. 14). Moment coefficient values were still measured to be significantly lower than predicted (Fig. 15). Fair agreement was also obtained with the L/D data for the 96%, -2% case (Fig. 16). However, the moment coefficient comparison was still poor (Fig. 17). As previously discussed, the secondary element was observed to significantly deflect under an applied load. It is believed this deflection is the cause of the poor correlation between the experimental and numerical results. The best comparisons came with the largest gap conditions, where deflections would have the least effect. In addition, the significantly lower moment suggests lower lift values on the aft portions of the airfoil, thus further supporting the hypothesis of second element deflection being the cause of the poor agreement. Due to the poor agreement between the experimental and numerical data, the optimum relative position could not be verified. Transition Location The transition location was measured on the primary element of the AG91 airfoil using the flow visualization method discussed earlier. Results for the deflection case of the AG91 airfoil at a Reynolds number of xl 6 show less laminar flow across the entire cl range on the upper surface than predicted (Fig. 18). However, more laminar flow was measured than predicted on the lower surface. This difference

112 Nunlericaland Exper'imentalAG91 Airfoil Resul[s [_.c : [}xlo 6, XLEz = 95% ci, YI,Ez -1.5% Cl 2 18 16 14 _t, 12 1O 8 L2 6O 4 2O Measured Shape NCARFA Results ( Design Shape MCARFA Results -2, I,,, i, L, B,,,, L L,,, -.2..2.4.6.8 l.o 1,2 1.4 1,6 1.8 2. Lift Coefficient Fig. 128 AG91 experimental L/D ratio, 95%, -1.5% position, 6= Numerical and ExperimentalAG91 Airfoil Results Re = xl6,xlez= 95%cl,YLE2 =-1.5%cl -.15 -.17 "7_ --. 19 "- --.21 hape MCARI"A Results o -.2 r- -.25 o -.27 -.29 r- o -.1 _" -. --.5, L, I, I, I, I, I, I, I, L, I i -.2..2 4.6.8 1. 1.2 1.4 1.6 1.8 2. Lift Coefficient Fig. 129 AG91 experimental moment coefficient, 95%, -1.5% position, 6=

11 Nnmerieal and ExperimentalAG91 Airfoil Results Re = xlo 6,XLE_ = 95Zc1,YLE2-2%cl 22O t _ TAMU-LSWT Experiment Shape MCARFA Measured Results Design Shape MCARFA Results 14 _4r... l O L2 6O. / --_,, I, L, I, L L I, I, i L I, I t I -.2..2.4.6.8 1. 1.2 1.4 1.6 1.6 2. Lift Coefficient Fig. 1 AG91 experimental L/D ratio, 95%, -2% position, 8= Numerical and ExperimentalAG91Airfoil Results Re, = :_xlo _, XLEa = 95% el, YLEe = -2% e_ - 15 D -.17 -. I9 -.21 TAMU-LSWT Experiment Shape MCARFA Measured Results Design Shape [_CARFA Results O O...a o -2 -.25 O -.27 -(}.29 O...a -.1 -. -.,q5, i -.2 O L, I, I h I, I _ I l I, I.2.4.6.8 1. t.2 1.4 1.6 1.8 2 Lift Coefficient Fig. 11 AG91 experimental moment coefficient, 95%, -2% position, 8=

114 Nurnericaland ExperimentalAG91 Airfoil Results Re := x16 XLEa -- 96% cl, YLEe = -1% cl EEO TAMU-kSWT Experiment 18 Measured Shape MCARFA Results Design Shape MCARFA Results.I 14 1 6O EO -ao, r, _, L, i, J, i, I, J, _, I, i -O.E. O.E.4.6.8 1. 1.2 1.4 1.6 1./ a.o Lift Coefficient Fig. 12 AG91 experimental L/D ratio, 96%, -1% position, 5= Numerical and ExperirnentalAG91 Airfoil Results Re = xlo 6,XLEa = 96% ci,ylea = -1Zel -.15 c_ -.17 q) U -. I9 ---o_ TAMU- LSWT Experiment ----e---- Measured Shape MCARFA Results Design Shape MCARFA Results -.21 o -.2 r" - 25 o -.27 -.29 u -.1 _J -. -.5, _, i, I, I, I, I, I, i, L, i, I -2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. LifL CoefficienL Fig. 1 AG91 experimental moment coefficient, 96%, -1% position, 6=

115 Numerical and Experimental AG91 Airfoil Results Re.= xlo, XLE2 = 96% {:1, YLE2 = -1.5% (:1 22 1 8 _E ] 4 r, "i 1 (} 6O 2O,/-/L- - - j TAMU- LSWT Experimenl ---o_ Measured Shape MCARFA Results "_ DesiRn MCARFA Results._r / Shape - 2 (} -.2..2.4.6.8 1. 1.2 1 4 1.6 1.B 2. Lift. Coefficient Fig. 14 AG91 experimental L/D ratio, 96%, -1.5% position, 8= Numerical and ExperimentalAG91 Airfoil Results Re. = xlo 6,XLEe = 96%c],YLEe =-1.5%cl -.15 O -.17 -.19 + TAMU- LSWT Experiment + Measured Shape MCARFA Results -_ Design Shape MCARFA Results -.21 (.) -.2 r' E -(/.25 -.27 LE L) _,.o :2 -.29 -.1 -. -.5, L -2. Ikl_lJl,l_lll,l_[ I.2.4.6.8 1 1.2 1.4 1.B 1.8 2. Lift Coefficient Fig. 15 AG91 experimental moment coefficient, 96%, -1.5% position, 6=

116 Numerical and ExperimenLalAG91 AirfoilResulLs [?_c 16, XLEe = 96% el, YLEz = -_Z c_ EEO + TAMU- LS'gT E perlrnent ---_ Measured Shape MCARFA Results 1 _] _ DesiRn Shape MCARFA Results 14 1 6O go -2, J, *, I, :, *, r, f, _, f, _, -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Lift Coefficient Fig. 16 AG91 experimental L/D ratio, 96%, -2% position, 8= Numerical and ExperimenLalAG91 Airfoil Results Re :--:xlo 6, XLEa = 96% el, YLEe = -a% cl --.15 -. l 7 _ -.19,... _ -.21 -.2 + Measured Shape MCARFA ResulLs I _-----a------ TAMU-LSWT Design Experiment MCARFA Shape Results o -.25 5 o -.27 _ -.29 o -.1 _- -. -.5 Jh,IBl,l,ILi,i_Ikiil,l -2 O.2.4,6.8 1. 1.2 1.4 1.6 1.8 2. LiftCoeffieient Fig. 17 AG91 experimental moment coefficient, 96%, -2% position, 8=

117 Nutner'i(:al and ExperimentalAG91 Airfoil Results Re = xlo a, LE2 = 95% ('.I.YLE2 = -15%cl '\ E perlmental Upper Surface E_perimen'tal Lower Surface MCARFA Shape Measured "tipper Surface.- L\ L MCARFA MeastJred Shape Lower Surface,- r_ c_ F-" Lift Coefficient Fig. 18 AG91 experimental transition location, _ = is again likely to be caused by the secondary element deflection. It is possible that the surface finish of the model or the freestream turbulence intensity level in the wind tunnel were also contributing to the differences. Comparisons were made between the experimental wind tunnel data and the numerically predicted values with transition fixed at the experimentally observed locations on the primary element in order to determine the effects of the increased freestream turbulence on the results. Lift coefficient answers show very little change between the numerical fixed and natural transition locations (Fig. 19). Drag coefficient results show a nearly 55% increase in drag coefficient at a q of about.7 with the transition fixed (Fig. 14). Moment coefficient results show very little change with the different transition locations (Fig. 141) and the L/D ratio follows the c o trends with a significantly lower L/D for the fixed transition case (Fig. 142).

118 Numerical and ExperimentalAG91 AirfoilResulls Re = _xl() 6, XLEa 95_ cl, YLEa = -1.5% cl, d 12.5 l. Measured Shape MCARFA Natural Transition o - --_(_ - TAMU-E'_WT Measured ShapeExperi MCARFA ment _, Fixed Transition. - ".8 i y2 ".6.6 I "o _D (1.4 / 9" ().2 O. -.2 b I k I b I I I [ I, J 8-16 -14-12 -1-8 -6-4 Angle of Attack Fig. 19 AG91 fixed transition effect on lift coefficient, 5 = Numerical and ExperimentalAG91 Airfoil Results Re _ xlo 6,XLEa = 95%el,YLEa= -1.5%cl,6 =.5,4 + o _ TAMU-LSWT Experiment Shape MCARFA Measured Natural Transition Measured Shape _ICARFA Fixed Transition o. LD _D.2 " - - _ Q -.1., _,,, I,,, i,,,, -.2..2.4.6.8 1. 1.2 Lift Coefficient Fig. 14 AG91 fixed transition effect on drag coefficient, 6 =

119 Numerical and ExpcrirnenLalAG91 Airfoil Results [?.e = xlo 6, XLEa 95% et, YLE:.e, = -1.5% ct, 6 =. _ -.1 TAMU- LSWT Experimenl Measured Shape MCARFA Natural Transition Measured Shape MCARFA Fixed Transi tion C) -O.E G :g o 9 r_ -.4, _, I, J,,, I I -OE C).O.2.4.6.8 1. I.E Lift Coefficient Fig. 141 AG91 fixed transition effect on moment coefficient, 6 = Numerical and ExperimenLal AG91 Airfoil Results Re = xlo 6, XLE2 =- 95Z cl, YLE2 = -1.5% cl, 6 = "do 1 O 9 rio 7. - c, TAMU-LSWT Experiment / -_ Measured Shape MCARFA Natural Transition -- --n-- Measured Shape MCARFA Fixed Transition t/ _ 6O 5 4 O 2 1 o / _ - 1 -O.E I, I h I, I _ I I,..2.4.6.8 1. Lift Coefficient I I.E Fig. 142 AG91 fixed transition effect on L/D ratio, 6 =

12 Improved Wind Tunnel Model Improvements to the wind tunnel model, as previously discussed, were completed and new aerodynamic load data at Reynolds numbers from lxl 6 through x 16 were obtained for both the and 2 deflection cases of the AG91 airfoil. Results were again compared to both the design and measured shape numerical data from the MCARFA computer code. Lift coefficient data for the AG91 deflection case at a Reynolds number of 8x 15 shows a significant change in the zero lift angle of attack when compared with the numerically predicted data (Fig. 14). The maximum lift coefficient value was also significantly lower at approximately 2.2 rather than the 2.8 predicted. Drag and moment coefficient data were not obtained at this Reynolds number because of the accuracy of the pressure measurement system at reading the extremely low pressures at this condition. Lift coefficient data at the lxl 6 Reynolds number case for the AG91 deflection condition again shows a significant change in the s value (Fig. 144). The experimentally measured Clmaxwas about 2. for this case. Drag coefficient data shows the measured Cd quite a bit higher than predicted (Fig. 145). The numerical and experimental L/D curves generally follow the same trends, but the experimental values are a significant amount lower (Fig. 146). The experimental moment coefficient values are also lower than the numerically predicted case (Fig. 147). The 2x 16 Reynolds number case lift coefficient results show a change in the lift curve slope between the experimental and numerical data (Fig. 148). Experimental drag coefficient values, while following the shape of the curve well, are higher than predicted (Fig. 149). Experimental L/D results (Fig. 15) and moment coefficient values (Fig. 151) are both lower than predicted.

121 Nurrlericaland Experin_entalAG91 Airfoil Results Rc.: 8 15, XLEa 95% cl, YLEa -- -1.5Z cl, 6 = 2.8 TA_IU L,SWT ElcperirnerR _-- Measured Shape MCARFA Results Design Shape MCARFA Results _.-_'" *_ 1.8 5 (D L_ 25 O. 8 o 1 oi I _f o, t"?" La f._" " -. J I J I, -2 _, - I I Angle of Attack Fig. 14 AG91 experimental lift coefficient, 8 =, Re = 8x1 s Numerical and Experimental AG91 Airfoil Results Rc = lxlo 6, XLEz :: 95Z cl, YLEa = -1.5% cl, 5 : 2.8 -o TAMU-LSWT Experiment [ ---_a.--- Measured Shape MCARFA Results _.._ Design Shape MCARFA Results i J o: "_ 1.8 L).8 -.2-2 -1 1O Angle of Attack Fig. 144 AG91 experimental lift coefficient, 8 =, Re = lxl6

122 Nllnler'i_:al and Experimenlal AG91 Airfoil Result s ble : lxl_,xle2 95%cl, YLEz=-l.5%el,_ =.4. I! _..4-,_ TAIdU- LSWTExperiment Measured Shape IdCARFAResults J _,._ // -- Design Shape MCARFAResulls _.fa/" " N O L.)._ " "\ C. c _-_._ / "///. 1., L, i, i -.2.8 1.8 2.8 Lift Coefficien/ Fig. 145 AG91 experimental drag coefficient, 6 =, Re = lxl6 Numerical and ExperimentalAG91 Airfoil Results Re = lxlo 6,XLE2 = 95%el,YLEa =-1.57oe1,6 = 14 12 1 k_ c-_.2 8 6 4O 2 o _ // o/--" "-o..o y.-.o.. / so" - _ -TAMU--LSWT Experiment 1 _dash pa _AMCARFAResuIt J s MCARFA Results j _, 6 Design Shape -2(1 ).2 1 k l l.8 1.8 2.8 Lift. Coefficient, Fig. 146 AG91 experimental L/D ratio, 6 =, Re = lxl6

12 Numericaland E:xperimen[alAG91 Airfoil Results Re =: 1 1_L XLEe :- 95Z c7, YLEe = -1.5% (.'1, fi = -.1 r- o + TAM U-I,.SWT E periment Measured Shape MCARFA Results [)esign Shape MCARFA Results o o -O.P. o LD o.- - od E o o o o m -. CO -.4, I I -,2.8 1.8 g.8 Lift. Coefficient Fig. 147 AG91 experimental moment coefficient, fi =, Re = lx16 Nunlericaland ExperimentalAG91 Airfoil Result.s Re = 2xlO _, XLEe = 95% cl, YLEe = -15% el, 6 :: 2.8 //,.,..., _ o.8 i c"._i -15-5 5 Angle of ALtaek Fig. 148 AG91 experimental lift coefficient, 8 =, Re = 2x16

124._umcrical m_d F, xperimental AG91 Ai rfoil Nesults Re : _2xlO(L XLE 95%cl, YLEa -1.5%ci,6 O. 4.O c_ TAMLi-LSWT Experiment Measured Shape MCARFA --_---- Results --_---- Design Shape MCARFA ResuLts c, /k c_ L.).2.1 I I I. -.2 O.B 1.8 2.8 LiftCoefficien[ Fig. 149 AG91 experimental drag coefficient, 8 =, Re = 2x16 Numerical and ExperimentalAG91 Airfoil Results Re xlo 6,XLE_ = 95%c1, YLEa=-1.5%cl,6 _ 2 1 BO 16 14 12 c_ 1 O 8 6 4 _ o o 9_ Experiment l Shape MCARFA / /,/ _o + Measured Results _/ Ji-g-n S_l;pe MCARFA Resuits l -2 -.2.8 1.8 2.8 Lift Coefficient Fig. 15 AG91 experimental L/D ratio, 15=, Re = 2x16

125 Nurnc.rict_l and ExperimentalAG91 Airfoil Results Re 2xl(_,XLEa : 95%ez, YLRa=-1.5%cl,5 = -.1 _D TAMI]-LSWT Experiment Shape MCARFA Measured Results, Design Shape MCARFA Results q O ED -. x E _fj r- :E LP -. Lk "_. i_- j - - O. 4 ' a J ' 'J -O.g._ 1.8 2.8 Lifk Coefficient Fig. 151 AG91 experimental moment coefficient, 8 =, Re = 2x16 Lift coefficient results at a Reynolds number ofxl6 show the lift curve slope matches the numerical value well, but again a large shift in o_ value is observed (Fig. 152). The drag coefficient for this case is significantly higher than predicted (Fig. 15) and consequently the L/D results are lower (Fig. 154). Moment coefficient trends do not match the shape of the predicted curve (Fig. 155). Experimental lift coefficient results for the 2 deflection case of the AG91 airfoil at a Reynolds number of lxl6 show fair agreement with the numerically predicted data (Fig. 156). The zero lift angle of attack is shifted approximately 1.5 between the numerical and experimental data. The qmax value was predicted to be 2.6 and measured to be 2.28, some 1% lower. The experimental drag coefficient was higher than numerically predicted through the low cl range, but generally followed the shape of the curve well (Fig. 157). Because of the higher ca, the experimental L/D ratio

126 Numericaland ExperimentalAG91 AirfoilResults Re =_,x1(] s, XLEa - 95% c_, Y[,E2 : -1.5Z ('I, 5 : 2. 1.8 1.6 o TAMU- I_'SWT Experiment s / --_ Meas 1red S ape MCARFA Resu s //x_ -/ -_--- Design Shape MC.4RF,4 Results //_ " 1.4 1.2 ;z. 1..8 LI.6.4 (.2. -.2. -18 J f f _ f _ I * I h f -16-14 -12-1 -8-6 -4 Angle of Attack Fig. 152 AG91 experimental lift coefficient, 6 =, Re = x16 Numerical and ExperimentalAG91 Airfoil Results Re = 'Jxl6, XLEa 95% Cl, YLE2 =-1.5% cl,5 = _.4. / o o - \q z \ / \ / \ / \ o _o - -9. - TAMU-LSWT Experiment Shape MCARFA Measured Results Design Shape MCARFA Results _z _A.2: o C)./.._- _ M/_ /.A. 1., 1, _, i, I, i, I, :, _, I, I, --.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Lift Coefficient Fig. 15 AG91 experimental drag coefficient, 8 =, Re = x16

127 Nun_ericaland Experimental AG91 Airfoil Results Re = _xlo 6, XLE2 95% e_, "flee = -1.5% el, di = () 2 1 8 16O 14 _r, F 1 E l 8 6 4 2 -EO o - - _MU-LSWT Experiment -+ Measured Shape MCARFA / - -_ Results F _ Design Shape MCARFA ResulLs I o- ).2..2.4.6.8 1. 1.2 1.4 1.6 1.g EO Lift Coefficient Fig. 154 AG91 experimental L/D ratio, 6 =, Re = x16 Numerical and ExperimentalAG91 AirfoilResulks Re x16. XLEa=95%cI,YLEa=-l.5%Cl, d = -1 o TAMU- LSWT Experiment + Measured Shape MCARFA Results c- ----e----- Design Shape MCARFA Results -.2 o _ E - c_ P.. -4, I, J, I,,, t, I, I, _, J, L, -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Lift Coefficient. Fig. 155 AG91 experimental moment coefficient, _ =, Re = x16

128 Numerical and ExperimentalAG91 Airfoil Results Re lxlo6, XLEa =9.57._:cI, YLEa = -1.5%el,6 2 E.8 -e - TAMU-LSWT E perilnent -+ Measured Shape MCARFA Results ---_--- Design...Shape MCARFA Results y Z 1.8 o /r_ o 9" LP z_.8 / o / I o /- -2 c -f L I I -2O - 1 1 Angle of Attack Fig. 156 AG91 experimental lift coefficient, 6 = 2, Re = lxl6 Numerical and ExperimentalAG91 AirfoilResulks Re= lxlo6, XLEa 95%cl, YLEa=-l.5%cl,6-2 O.4 Design Shape MCARFA Results // Z. -- -- o _ J t_.2 o _/ o.1., I, ;, I -.2.8 1.8 2.8 Lift Coefficient Fig. 157 AG91 experimental drag coefficient, 6 = 2, Re = lxl6

129 values were lower than predicted, but again the shape of the curves were very similar (Fig. 158). Moment coefficient values show excellent agreement between the numerical predictions and the experimentally measured data (Fig. 159). The 2x 16 Reynolds number lift coefficient data shows the slope of the experimental lift curve to be more shallow than numerically predicted (Fig. 16). The experimental and numerical ot values were very close. Drag coefficient data was again higher experimentally (Fig. 161). The L/D values show reasonably good agreement between the numerical and experimental data (Fig. 162). The moment coefficient data for this Reynolds number case shows the experimental Cmto be lower than the predicted value (Fig. 16). Results at a Reynolds number of x 16 follow the same trends as the 2x 16 case. The experimental lift curve slope is more shallow than predicted but the tx values agree well (Fig. 164). Experimental drag coefficient data is again higher than predicted (Fig. 165). The experimentally measured L/D values again agree quite well with the predicted values (Fig. 166). The moment coefficient was measured to be lower than numerically predicted (Fig, 167). Some evidence still suggests true two-dimensional flow is not being obtained at all lift values even with the endplates installed on the model. The slope of the experimental lift curve changes fairly significantly with different Reynolds numbers. Figure 168 presents the experimental lift curve results for the 2 deflection case of the AG91 airfoil at Reynolds numbers from lxl6 through x16. The lower slope at the higher Reynolds numbers is evidence that the airfoil model is not fully two dimensional. Drag coefficient values did not show a significant change with Reynolds number (Fig. 169). The experimental L/D values were generally the same at different Reynolds number, but the x 16 case did show a somewhat higher L/D curve

1 Numeric.al and ExperimentalAG91 Airfoil Results Rc = lxlo 6, XLEa.- 95% cl, YLEa = -1.57o ('l, 6 = 2 14 12 o I 8 /- _----.. o 6 / /""...2 4 2 / -_ - TAMU-LSWT Experiment Measured Shape MCARFA Results c_ d" _ Design Shape MCARFA Results -2 -.2.8 1.8 2.8 I Lift Coefficient Fig. 158 AG91 experimental L/D ratio, 8 = 2, Re = lxl6 Numerical and ExperimentalAG91 Airfoil Results Re = lxloa, XLEa = 95Z cl, YLEa = -1.5% c1, d = 2. -c. - TAMU- LSWT Experi ment Q) 5 Measured Shape MCARFA Results Design Shape MCARFA Results C. -1 (D E o o -Q o _ o - _ r" rc -._ -., I, L, r -.2.8 1.8 2.8 Lift Coefficient Fig. 159 AG91 experimental moment coefficient, 8 = 2, Re = lxl6

95 11 Nurnericaland ExperimenLalAG91 AirfoilResults Re = 2xlOQ XLE2 "_I {_ e I, YLE2-1.5% cl, 6 2 2 E.B TAMU- LSWT Experiment Measured Shape MCARFA Results 7- Desi_l_ Shape 1.8 _s O L).8 / o" -.2 i I J k i -2-1 1 Angle of Attack Fig. 16 AG91 experimental lift coefficient, 8 = 2, Re = 2x16 Numerical and Experimenka] AG91 Airfoil Results Re = 2xlO 6, XLE2 = 95% el, YLE2 = -1.5% ct, 6 -- 2.4 TAMU-LSWT Experi ment. Measured Shape MCARFA Results Design Shape MCARFA Result,s..o. {b L).2 o o -.1 {}., i, I, J -.2.8 1.8 2.8 Lift CoefficienL Fig. 161 AG91 experimental drag coefficient, 8 = 2, Re = 2x16

12 Numerical and ExperimentalAG91 Airfoil Results Re : 2xlO _,XLEa = 95%c1,YLEa =-1.5%c1,d -- 2 14 leo 1 _to - > ] c_ 6O 4 2O J. '_ o TAMU-L.qWT Experiment Measured Shape MCARFA P _ Results _emgn Shape MCARFA Results K'e <r / e_ -.2./ 1.8 _.8 Lift Coefficient Fig. 162 AG91 experimental L/D ratio, 6 = 2, Re = 2x16 Numerical and ExperimenLalAO91 Airfoil Results Re ExlO6, XLE'_= 95Zcl,YLEe= -I.5%c_,d = 2 O. G.) -o TAMU-LSWT Experi ment Measured Shape MCARFA Results Design Shape MCARFA Results C_ L.) -. I \ "at \ o-a _o -.2 CL Lift Coefficient Fig. 16 AG91 experimental moment coefficient, 8 = 2, Re = 2x16

1 Numerical m_d ExperimentalAG91 AirfoilResults Re x] O(L XLE2 95% cl, YLEa = -1.5% el, 6 2 2.8 _, TAM U- L.SWT Experiment 1. - Measured Design Shape MCARgA MCARFA Results Results J!..f1' i -_+- - Shape,_ OA 5 1. B L_.8 -O.g d, d., L i J -2(1-1 I Angle of Attack Fig. 164 AG91 experimental lift coefficient, 6 = 2, Re = x16 Numerical and ExperimentalAG91 AirfoilResults Re : xlo 6,XLEa-: 95% c1, YLE2 = -1.5%el, d = 2.4 F - c_ TAMU-LSWT Experi ment Measured Shape MCARFA Results,. -_ Design Shape MCARFA Results [ 5 C) cm 2_.2.1 o o_ /" _ \\ o o.o 'o 6.8 1.8 2.8 Lift Coefficient Fig. 165 AG91 experimental drag coefficient, _ = 2, Re = x16

14 Numerical and Exper'iment.al AG91 Airfoil Results Re= xl _, XLE_ = 95% el, YLE2-1.5%c1, d = 2 1 4O 12 1 _1/'1 8 / 6O 4 o / 2 - o TAMU-LSWT Experiment!,- o _ o Measured Shape MCARFA Results Design Shape MCARFA Results o / / -2 -O.E.8 1.[ E.8 Lift Coefficient Fig. 166 AG91 experimental L/D ratio, = 2, Re = x16 Numerical and Experimental AG91 Airfoil Results Re BxlO 6, XLE2 : 95% el, YLE2 = -1.5% Cl, 6 = 2 ). [ TAMU- LSWT Expertment I Measured Shape MCARFA Results Design Shape MCARFA Results r-- C) E r-' r-" -.1 -.2 -(1., _,. L, -O.E.8 1.8 E.8 Lift. Coefficient Fig. 167 AG91 experimental moment coefficient, 8 -- 2, Re = x16

15 [,xp " e rlmentalresulls ' forag91 Airfoil XLE:e :_ 957," cl, YLEa = - 1.5% cl, 6 -- EO ---'+-- Re = lxlo _ -----a---- Re = 2xlO 6 ] _; L -_ Re = xlo _t o 5 o -,2 _ ' -EO -1 1 EO Angle of Attack Fig. 168 Reynolds number effect on experimental lift coefficient Experimental Results for AC91 Airfoil XLEa = 95% el, YLEa = -1.5% el, _ = 2.4 _-- Re = lxlo _. +- Re = 2xlO 8 Re = xlo _ o o CJ j/ J// o o /J" o o _) O.OE 1 t_ o o o o o -.1 --_ [ o.,, i, i, i -2.8 1.8.8 Lift Coefficient Fig. 169 Reynolds number effect on experimental drag coefficient

16 (Fig. 17). The 2x16 and x16 Reynolds number case c m values were lower than the 1x 16 Reynolds number case (Fig. 171). Based on the above data, the AG91 case with the secondary element deflected 2 from the primary element was experimentally verified by fair agreement at all conditions. The deflection case could not be experimentally verified. Neither the numerically predicted Clmaxor the L/D values for this case were observed in the wind tunnel data. Uncertainty Analysis and Data Repeatability An uncertainty analysis as described by Kline and McClintock ss was performed on the wind tunnel data to determine the uncertainty in the force coefficients due to instrumentation and measurement accuracy. Figures 172 through 174 present the cl, ca, and L/D results for the AG91 airfoil2 deflection case at a Reynolds number of lxl6, respectively. It is clear that the uncertainty in the results due to the instrumentation and measurement accuracy is not as large as the apparent scatter in the data. A test of the repeatability of the wind tunnel data was also performed on the AG91 airfoil deflected at a Reynolds number of xl 6. This repeatability check was performed during the initial set of wind tunnel runs before improvements were made to the model. Lift coefficient results show generally good agreement, but definite differences do exist between the two sets of measured data at the same test conditions (Fig. 175). The drag coefficient results show a significant difference between the two sets of experimental data (Fig. 176). Moment coefficient repeatability results show the same trends in both of the experimental cases (Fig. 177), but again definite differences do exist. The L/D ratio results, as the drag coefficient, show significant differences between the two sets of experimental data (Fig. 178). The differences between the two

17 b;xperimental Results forag91 Airfoil XLE_ = 95% el, YLE_ = - 1.5% cz, 6 = 2 ] 4O leo 1O ---_-- Re = lxlo 6 ------*-- Re xlo 6 _z_/] e_ k. 8O /j/ o r-_ 6 o o.2 4 EO a_/" o -2 -.2.8 i [ L I 1.8 2.8 Lift Coefficient Fig. 17 Reynolds number effect on experimental L/D ratio Experilnental Results for AG91 Airfoil XLEa = 95% el, YLEa = -1.5% cl, 6 = 2. Re = lxlo fi T + Re = axlo 6 Re = xlo e O -.1 E _..9 _rj -.2.j_,//o"/Jc_ o o o O -. ' _ ' ' _ ' -O.E.8 1.8 2,8 Lift Coefficient Fig. 171 Reynolds number effect on experimental moment coefficient

18 Numerical and Experimental AG91 Airfoil Results Re = ]x]o6. XLE2 95%c1,YLE_ =-1.5%c_,6 = 2 2.8 r TAMI]-LSWT Experiment /_ ''_'n Measured Shape MCARFA Results /. Design Shape MCARFA Results [ _ r_, q -1o to Angle of Attack Fig. 172 Uncertainty analysis of experimental lift coefficient Numerical and ExperimentalAG91 Airfoil Results Re = lxlo 6, XI.,E_ = 95% el, YLE2 = -1,5% cl, 6 = 2.4 - _- - TAMIJ-LSWT Experiment ] /. o t... o.2.1. ' ' ' _ -.2.8 1.8 2.8 Lift Coefficient Fig. 17 Uncertainty analysis of experimental drag coefficient

19 Numerical and ExperimentalAC-91 Airfoil Results [?.e = lxlo 6, XLEa = 95% cl, YLE_ = -1.5% cl, 6 = EO 14(1 1_ 1 O go j x I c_ 6 4 EO./: c_ TAMU-LSWTExperiment.//_ ---e----- Measured Shape MCARFAResults <4- _ Dem_ln Shape MCARFAResults -2 -O.E I I J.8 1.8 2.8 Lift Coefficient Fig. 174 Uncertainty analysis of experimental L/D ratio Exper'imental AC91 Airfoil Repeakabilit,y Re., xlo 6, XLEu = 95% el, YLEa = -1.5% el, 6 = O. 9.8.7 + Experiment w/o gndplates._ gxperl merit w/o Endplates Repeat j.6.5 O D.4..2 O. 1 O. -.1-16 -15-14 -1 J I J I i I,_ I _ I, I _ I _ I i I i I -1g -11-1 -9-8 -7-6 Angle of Attack j i -5 Fig. 175 Repeatability of experimental lift coefficient

14 Experirnental AG91 Airfoil RepeaLabiliiy Re : xlo O,XLEe:= 95Zc_,YLE2 = -1.57_ci,6 =.4 ----_---- Experi merit w/o Endplates -_q_ Experiment w/o Endplates Repeal. a.2, C.) [...,.1 D.O, I, _, L, _, I I _ I, I I I -.1..1.2..4.5.6,7.8.9 Lift. Coefficient Fig. 176 Repeatability of experimental drag coefficient ExperimentalAG91 AirfoilRepeatabiliLy Re : xlo 6,XLE2 95%c1, YLE2 =-1.5%ei,6 :. C).,..o,,.., E -.1 Experiment w/o Endplates + Experiment w/o Endplates Repeal 2 _ -.2 o o---- --- o --._, t, I i I, t _ I, t, I i l, I -.1..1.2..4.5.6.7.8.9 Lift Coefficient Fig. 177 Repeatability of experimental moment coefficient

141 Experimental AC91 Air'foil RepeatabiliLy Re_ x 16, XLgz = 95% el, YLE2 -- - 1.5% el, _ 5O 4 E)cperi merit w/o Etldplates Repeat _[,, _... 1 I d i L _ L L L L b _ r I I, L I. O. l O.E..4.5.6 /7.8.9 Lift Coefficient Fig. 178 Repeatability of experimental L/D ratio sets of experimental data for all forces and moments are larger than the uncertainty analysis predicts. A likely explanation for the differences is the way the Scanivalve measurement system acquires data. The data is acquired sequentially over a total time of approximately 4 minutes for each data point. Some differences in the freestream conditions can take place during this time, but the freestream total and static pressure readings used in data reduction are only acquired during a discrete time period during the entire 4 minutes. Spanwise Drag Variation Some concern existed over how the experimentally measured drag coefficient would vary at different span stations. This variation could be due to differences in surface finish quality or profile shape. The additional brackets added to reduce the secondary element deflections could also have had an effect on the drag coefficient

142 value. The dragcoefficientwasnormallymeasuredin the centerof the spanof the wind tunnelmodel,but to explorethevariationof the cdwith spanstation,drag measurementsweretakenin five centimeterincrementsfrom 5 cmbelow thecenter spanto 2 cm abovethe centerspanlocation. The additionalsecondaryelement bracketwaslocated18cm from thecenterspanstation. Resultsfor the AG91airfoil with a secondaryelementdeflectionof 2 ata Reynoldsnumberof x16andata lift coefficientof approximately.54showlittle variationin the experimentalcawith span stationat locationsawayfromthe secondaryelementbrackets(fig. 179). An increase in the measuredcdis observednearthe secondaryelementbracket,but this is to be expected. Experiment_al AG91 Airfoil Resulks Re=xlO6, XLE2 95%cl,YLEz=-l.5%ct,6 =2.2.18 l _ Lift Coefficient = 54.16 r-.14.12 _J (.A.1.8 Z_.6.4.2. -6 _ I _ r, r i I i I 6 12 18 24 Span Location (cm) Fig. 179 AG91 spanwise drag coefficient, 6 = 2, Re = x1 6

14 CONCLUSIONS The concept of a two element fixed geometry laminar flow airfoil for the cruise case in an incompressible flight regime has been numerically and experimentally verified. Results show a generic sailplane wing based on the final configuration AG91 airfoil will have a 11.75% reduction in total wing drag when compared with a current general aviation airfoil. The new two element airfoil was numerically designed using the NASA Langley Multi Component Airfoil Analysis Code (MCARFA) and experimentally verified in the Texas A&M University Low Speed Wind Tunnel. Referring back to Table 4, numerical results show the optimum configuration to include the secondary element deflected. With this deflection, the AG91 airfoil has a lift to drag ratio at cruise of 72.67. This is over 19% higher than the NASA NLF(1 )-416 airfoil upon with the AG91 was based. The maximum lift coefficient for this case was calculated to be nearly 6% higher than the NLF(1)-416 airfoil. Overall a 28% reduction in wing drag for a generic sailplane was calculated based on this new case when compared with the NLF(1)-416 airfoil. At the cruise lift coefficient of.6 and a Reynolds number of x16, the new airfoil has 8% laminar flow on the upper surface and 25% laminar flow on the lower surface. While the deflection case numerically showed better performance characteristics, the secondary element deflected 2 also showed good results. The maximum lift coefficient was calculated to be 44% higher than the NLF(1)-416 airfoil and the cruise L/D ratio was slightly higher for the AG91 airfoil. Overall a 11.75% reduction in overall wing drag for a generic sailplane was calculated based on the 2 deflection case when compared to the NLF(1)-416 airfoil. The moment coefficient for the 2 deflection ease was approximately two thirds that of the deflection case.

144 The 2 deflection case has 7% laminar flow on the upper surface and 5% laminar flow on the lower surface and the cruise lift coefficient of.57 and a Reynolds number of xl6. Experimental results show the 2 deflection case values agree fairly well with the numerically calculated answers. The measured drag coefficient was higher than numerically predicted, but the shape of the curve agreed well. The numerically calculated values at the deflection case could not be experimentally verified. Significantly higher drag and lower lift were measured than numerically predicted. Based on the experimental verification, the lower moment coefficient, and the somewhat more conservative design, the final configuration for the AG91 airfoil uses the 2 secondary element deflection. The final configuration of the AG91 airfoil is made up of two distinct components; the primary element is a modified profile named the AG91A based on the NASA NLF(1 )-416 airfoil and the secondary element is a NACA 4412 airfoil. The primary component chord is 75% of the total chord and the secondary element chord is 25% of the total. The leading edge of the secondary element is located 95% of the primary chord length behind and 1.5% of the primary chord length below the leading edge of the primary element. The secondary element is deflected down 2 with respect to the primary element. The most likely location for future improvement to the two element cruise airfoil concept is the lower surface of the primary element. Results show slightly less laminar flow on the lower surface of the AG91 airfoil than on the original NASA NLF(1)-416. This is largely due to the negative angle of attack of the primary element at the cruise case. Further design, without decreasing the Clmaxvalue, of the lower surface should increase the cruise performance.

145 Anotherpossibility for future studywouldbe thevariationof the secondary elementdeflectionangleduringflight. Thecurrentstudyexploredtheconceptof a fixed geometryairfoil, but the increasedcomplexityof a variablegeometry configurationis often determinedto be of netvalue. This possibilitywould not bea significantchangefor the AG91airfoil becauseof the pre-existingstructureto supportthe distinctsecondaryelement.

146 REFERENCES IAnderson, J.D., Jr., Introduction to Flight, Second Edition, McGraw-Hill Book Company, New York, 1985. 2Schweizer, P.A., "An International One-Design Class and the Olympics," Technical Soaring, Vol XIII, No. 2, April 1989, pp. 42-44. Abbott, I.A., von Doenhoff, A.E. and Stivers, L.S., "Summary of Airfoil Data," NACA Report No. 824, 1945. 4Abbott, I.A. and von Doenhoff, A.E., Theory of Wing Sections, Dover Publications, New York, 1959. 5Duddy, R.R., "High-Lift Devices and Their Uses," Journal of Royal Aeronautical Society, Vol. 5, 1949, p. 859. 6Gad-el-Hak, M., "Control of Low-Speed Airfoil Aerodynamics," AIA,,I Journal, Vol. 28, No. 9, 199, pp. 157-1552. 7Liebeck, R.H., "A Class of Airfoils Designed for High Lift in Incompressible Flow," Journal of Aircraft, Vol. 1, No. 1, 197, pp. 61-617. 8Liebeck, R.H., "Design of Subsonic Airfoils for High Lift," Journal of Aircraft, Vol. 15, No. 9, 1978, pp. 547-561. 9McGhee, R.J., Viken, J.K., Pferminger, W., Beasley, W.D. and Harvey, W.D., "Experimental Results for a Flapped Natural-Laminar-Flow Airfoil with High Lift/Drag Ratio," NASA TM-85788, 1984. l Morgan, H.L., "High-Lift Flaps for Natural Laminar Flow Airfoils," Laminar Flow Aircraft Certification, NASA CP-241, 1985.

147 llmurri, D.G., McGhee,R.J.,Jordan,F.L., Davis,P.J.,andViken, J.K.,"Wind Tunnel Resultsof the Low-SpeedNLF(1)-414FAirfoil," Research in Natural Laminar Flow and Laminar-Flow Control, NASA CP-2487 Part, 1987. 12rmsbee, A.I. and Chen, A. W., "Multiple Element Airfoils Optimized for Maximum Lift Coefficient," AIAA Journal, Vol. 1, Dec. 1972, pp. 162-1624. 1Page, F.H., "The Handley Page Wing," The Aeronautical Journal, June 1921, pp. 26-289. 14Somers, D.M., "Design and Experimental Results for a Flapped Natural- Laminar-Flow Airfoil for General Aviation Applications," NASA TP-1865, 1981. lsspitzmiller, T., "Flaps and Their Effects," Air Progress, Vol. 54, May 1992, pp. 4-6. 16Viken, J.K., Viken, S.A., Pfenninger, W., Morgan, H.L., and Campbell, R.L., "Design of the Low-Speed NLF(1)-414F and the High-Speed HSNLF(1)-21 Airfoils with High-Lift Systems," Research in Natural Laminar Flow and Laminar- Flow Control, NASA CP-2487 Part, 1987. 17Smith, A.M.O., "High-Lift Aerodynamics," Journal of Aircraft, Vol. 12, No. 6, 1975, pp. 51-5. lsbauer, A.B., "The Laminar Airfoil Problem," Eighth Annual Symposium of the National Free-Flight Society, 1975, pp. 4-45. 19Stevens, W.A., Goradia, S.H., and Braden, J.A., "Mathematical Model for Two-Dimensional Multi-Component Airfoils in Viscous Flow," NASA CR-184, 1971. 2 Stevens, W.A., Goradia, S.H., Braden, J.A. and Morgan, H.L., "Mathematical Model for Two-Dimensional Multi-Component Airfoils in Viscous Flow," AIAA Paper 72-2, San Diego, CA, Jan. 1972.

148 21Brune,G.W. andmanke,j.w.,"an ImprovedVersionof the NASA- Lockheed Multielement Airfoil Analysis Computer Program," NASA CR-1452, 1978. 22Brune, G.W. and Manke, J.W., "A Critical Evaluation of the Predictions of the NASA-Lockheed Multielement Airfoil Computer Program," NASA CR-14522, 1978. 2Morgan, H.L., "A Computer Program for the Analysis of Multielement Airfoils in Two-Dimensional Subsonic, Viscous Flow," Aerodynamic Analyses Requiring Advanced Computers, NASA SP-47 Part II, 1975, pp. 71-747. 24Smetana, F.O., Summey, D.C., Smith, N.S. and Carden, R.K., "Light Aircraft Lift, Drag, and Moment Prediction - A Review and Analysis," NASA CR-252, May 1975. 2SAllison, D.O. and Waggoner, E.G., "Prediction of Effects of Wing Contour Modifications on Low-Speed Maximum Lift and Transonic Performance for the EA- 6B Aircraft," NASA TP-46, 199. 26Oellers, H.J., "Incompressible Potential Flow in a Plane Cascade Stage," NASA TT F-1,982, 1971. 27Goradia, S.H., Confluent Boundary Layer Flow Development With Arbitrary Pressure Distribution, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA, 1971. 28Cohen, C.B. and Reshotko, E., "The Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient," NACA Rep. 1294, 1956. 29Schlichting, H., Boundary-Layer Theory, McGraw-Hill, New York, 1987.

149 Truckenbrodt,E. "A Methodof Quadraturefor Calculationof the Laminar and Turbulent Boundary Layer in Case of Plane and Rotationally Symmetric Flow," NACA TM-179, 1955. 1Nash, J.F. and Hicks, S.G., "An Integral Method Including the Effects of Upstream History on the Turbulent Shear Stress," Computation of Turbulent Boundary Layers, AFOSR-IFP-Stanford Conference, August 1968. 2Williams, B.R., "An Exact Test Case for the Plane Potential Flow About Two Adjacent Lifting Aerofoils," R&M No. 717, Aeronautical Research Council, London, 197. Platt, R.C. and Abbott, I.H., "Aerodynamic Characteristics of NACA 212 and 221 Airfoils with 2-percent-chord External-airfoil Flaps of NACA 212 Section," NACA Report No. 57, 196. 4Wenzinger, C.J. and Delano, J.B., "Pressure Distribution over an NACA 212 Airfoil with a Slotted and a Plain Flap," NACA Report No. 6, 198. SWenzinger, C.J., "Pressure Distribution over an NACA 212 Airfoil with an NACA 212 External-airfoil Flap," NACA Report No. 614, 198. 6Wenzinger, C.J. and Harris, T.A., "Wind-tunnel Investigation of an NACA 212 Airfoil with Various Arrangements of Slotted Flaps," NACA Report No. 664, 199. 7Eppler, R., Airfoil Program System User's Guide, Universit_t Stuttgart, Stuttgart, Germany, March 27, 1991. SEppler, R., Airfoil Design and Data, Springer-Verlag, Berlin, 199. 9Eppler, R. and Somers, D.M., "A Computer Program for the Design and Analysis of Low-Speed Airfoils," NASA TM-821, 198.

15 4 Eppler, R. and Somers, D.M., "Supplement To: A Computer Program for the Design and Analysis of Low-Speed Airfoils," NASA TM-81862, 198. 41Nicks, O.W., Steen, G.G., Heffner, M. and Bauer, D., "Wind Tunnel Investigation and Analysis of the SM71 Airfoil," Technical Soaring, Vol. XVI, No. 4, Presented at the XXII OSTIV Congress, Uvalde, Texas, 1991, pp. 19-115. 42Reed, R.C., "Wortmann FX 79-K-144/I 7 Airfoil Low Speed Wind Tunnel Test," Report No. TR-921, Aerospace Engineering Division, Texas Engineering Experiment Station, Texas A&M University System, November 1992. 4Carlson, L.A., "Derivation of the Biot-Savart Law," AERO 472 Class Notes, Texas A&M University, 1978. 44Eppler, R., "Direct Calculation of Laminar and Turbulent Bled-Off Boundary Layers," NASA TM-7528, 1978. 4SSomers, D.M., "Design and Experimental Results for a Natural-Laminar-Flow Airfoil for General Aviation Applications," NASA TP- 1861, 1981. 46Wentz, W.H. and Ostowari, C., "Additional Flow Field Studies of the GA(W)-I Airfoil with -Percent Chord Fowler Flap Including Slot-Gap Variations and Cove Shape Modifications," NASA CR-687, 198. 47Somers, D.M. and Maughmer, M.D., "The SM71 Airfoil: An Airfoil for World Class Sailplanes," Presented at the XXIII OSTIV Congress, Uvalde, Texas, August 1991. 48Jolmson, R.H., "Flight Testing/Performance Improvements Through Wing Profile Correction," Technical Soaring, Vol. XIII, No., pp. 84-89. 49Roskam, J., Airplane Design Part V: Component Weight Estimation, Roskam Aviation and Engineering Company, Ottawa, Kansas, 1985.

151 S "LowSpeedWind TunnelFacility Handbook,"AerospaceEngineering Division, TexasEngineeringExperimentStation,Texas A&M University System, 1985. 5_Haffermalz, D.S. and Steen, G.G., "Freestream Turbulence Intensity Measurements in the Texas A&M University Low Speed Wind Tunnel," Report No. TR-9211, Aerospace Engineering Division, Texas Engineering Experiment Station, Texas A&M University System, July 1992. S2Rae, W.H. and Pope, A., Low-Speed Wind Tunnel Testing, Second Edition, John Wiley and Sons, New York, 1984. SAnderson, J.D., Jr., Fundamentals of Aerodynamics, Second Edition, McGraw-Hill, Inc., New York, 1991, pp. 7-71. S4Morgan, H.L., Jr., "Computer Programs for Smoothing and Scaling Airfoil Coordinates," NASA TM-84666, 198. 55Kline, S.J. and McClintock, F.A., "Describing Uncertainties in Single-Sample Experiments," Mechanical Engineering, Vol. 25, No. 1, Jan. 195.

152 APPENDIX A CASE LIST

15 Cn$c I 2 4 7 8 9 1 11 12 1 14 15 16 Primry Airfoil 717 A 717 B 6,4-42 6,4-42O 6,4-42 Primary Hinge Primary Size, 1, 1.824, -.187 212 1.2,-.54 i 212 (I)-416 (I)-416 (1)-16.98, -..98, -. (I)-416.98, -. (1)-416.92,-. i (1)-16.9,-. (I)-416.94,-. (1)-416.95,-. (1)-416.96,-. 17 (I)-416 1.,-. 18 19 2 21 22 2 24 25 26 27 28 29 1 2 4 5 6 7 8 9 4 41 ;_2 (1)-416 (1)-16 (I)-416 (1)-416 (1)-16 (i)-416 (I)-416 (1)-16 )-416 (1)-416 (1)-16 (i).416 (I)-416 (1)-16 (i)-416 )-416 (1)-16 (1)-416 (I)-416 (1)-416 (I),416 (!)-416 12 2412 4412 1.2, -O.9,-.2.94,-.2 i.95,-.2.96,-.2.98,-.2.92,-.2.98,-..92,-.4.9,-.4.94,-..95,-.4.96,-..98,-.4 1._ -.4 i.2,-.4.92,-.15.9,-.15.94,-.15.95,-.15.96,-.15.98,-.15.8.8-2 1.25 1.25 1.25 1.25 1.25 i.25 1.25 1.25!.25 1.25 1.25!.25 1.25!.25 i.:,5 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 i.25 1.25 1.25 1.25 1.25 1.25 i.25 2 2 2 Second Airfdl Second Hinge 717 A, 717 B 6,4-42 6,4-42 6,4-42,.824, -. 187.824, -. 187.824, -. 187 212.25,-.1 212.25,-.1 12, 2412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 212, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, Delta Second ] Flap.5.5.5 o_1667.1667.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167,4167.4167.4167.4167.4167.4167.4167 1 25 25 25 2 2 2 2O 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2o 2 2 2 2 2 2 2 2 2 2 2 2 2 Freestream Alpha O, I,1-1 to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-8 to 8, del = 2-6 to 8, del = 2-4 to 12, del = 2-1 to 8, del = 2-1 to 8, del =2-1 to 8, del = 2 -I to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2 -I to 8, del = 2-1 to 8, del = 2-1 to 8, dei = 2-1 to 8, del = 2-1 to 8, del = 2 - I to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-8 to 8, del = 2-1 to 8, del = 2-8 to 8, del = 2-1 to 8, del = 2-1to 8, del =2 -I to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-1 to 8, del =2 -l O to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-1 to 8, del = 2-8 to 8, del = 2-6 to 8, del = 2-41o 14, del = 2-4 to 14, del = 2-4 to 12, dei = 2 I RN.5.5 i 6 T 1 1.5.1 4 44 45 46 47 48 212 (1)-416 (1)-16 (I)-416 (1)-416 (1)-16,92,-.2.9,-.2.94,-.2 I 2 1.25 1.25 1.25 1.25 2412,.4167 2412,.4167 2412,.4167 2412,.4167 2412,.4167 i 2O 2 2 2 2-4 to 14, del = 2-1 to 8, del = 2-1 to 8, del = 2-1 to 8, del =2 - I to 8, del = 2-1 to 8, del = 2

154 Primary Second Second, Second Delta Freestream Case 49 5O 51 52 5 54 56 5 58 59 6 61 62 6 64 65 66 67 68 69 7 71 72 7 74 75 76 77 78 79 8 81 82 8 84 85 86 87 Airfoil (1)-416 (I)-416 (I)-416 )-o416 (1)-416 (I)-416 (1)-o41/, (1)-416 (-416 (1)-o416 (-416 (1)-416 (1)-416 (1)-416 (i)-416 (1)-416 (I)-416 (1)-416 (1)-416 (J)-416 (1)-416 (1)-416 (I)-416 )-o416 (1)-o416 (I)-416 (1)-416 (1)-416 (I)-416 (1)-o416 (1)-416 (!)-416 (1)-416 (I)-416 (1)-o416 (1)-416 GS1A GS2A GSA Primary Hinge I Primary Size.98, -.2, 1.25.92,-.2! 1.25.9,-.2 i 1.25.94, -.2. 1.25.95, -.2 I 1.25.92, -.2 1.25.9, -.2 1.25.94, -.2 1.25.95, -.2 1.25.96, -.2 1.25.98, -.2 1.25.92, -.2 1.25.9, -.2 1.25.94, -.2 1.25.95, -.2 1.25'.96, -.2 i.25.98, -.2 1.25.92, -.2 1.25.95, -.2 1.25.9, -.2 1.25.94, -.2 1.25.96, -.2 1.25.98, -.2 1.25.96, -.2 1.25.9, -.15 1.25.94, -.15 1.25 r.95, -.15. 1.25 _96_ -.15 1 1.25.98, -.15 i 1.25.9, -.1 i.25.95, -.1 1.25.94,-.1.96, -.1 l 1.25 1.25.95, -.15 1.25.95, -.15 1.25.95, -.15 1.25.9799,-.8 1.25.95,-.15 1.25.95,-.15 1.25 1 Airfoil Hinge 2412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412, 4412 O, 4412, 4412.155,.1 4412, 4412, S_e Flap.4167 2.4167 1.4167 1.4167 1.4167 1.4167 15.4167 15.4167 15.4167. 15.4167 15.4167 15.4167 25.4167 25.4167 25.4167 25.4167 25.4167 25.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167.4167,4167 ' Alpha -1 to 8, del = 2-6 to 12, dcl = 2-6 to 12, del = 2-6 to 12, del = 2-6 to 12, del = 2-8 to 1, del = 2-8 to 1, del = 2-8 to 1, del = 2-8 to 1, del = 2-8 to 1, dcl = 2-8 to 1, dcl -- 2-12 to 6, del =2-12 to 6, del = 2-12 to 6, dei = 2-12 to 6, del = 2-12 to 6, dcl = 2-12 to6, dcl=2-14 to 4, del = 2 -! 4 to 4, del = 2-14 to 4, do = 2-14 to4, del =2-14 to 4, del = 2-12 to 4, del = 2-15 to -6, del = i -14 to4, del =2-14 to 4, del =2-14 to 4, d l = 2-14 to 4, del = 2-14 to4, del = 2' -14to4, del=2-14 to4, del = 2-14 to4, del = 2-14 to 4, del = 2-18 to -9, del -- 1-8 to 1, del = I 2to 11, del-- 1-14 to2, del --4-14 to 4, del =2-14 to 4, del ---2 ' RN 88 89 9 91 GSAU (I)-416 (1)-416 GS2A.95,-.15!.25.95, -.15 1.25 2.95, -.15 1.25 4412, 44'i2 O, 4412,.4167.4167.4167 -i to 4, del = 2-14 to4, del =2-4 to 12, dcl = 2-18 to -9, del = 1 1 I 92 9 94 95-96 GS2A OS2A GS4A GS5A GS6A '.95, di15 1.25.95, -.15 i.25.95,..15 I 1.25.9_5, -.15 I 1.25.95, -.15 i 1.25 4412, 4412, 4412, 4412, 4412,,4167.4167,4167.4167 A167 i -8 to 1, del = i 2 to il, del = I -14 to 4, del = 2-14 to 4, del = 2-14 to 4, del = 2

155 Pdmary Second Second Second Delta Freestream Cllse i Airfoil Primary Hinge ] Primary Size Airfoil Hinge Size Flap Alpha RN 97 GS2A.94,-.15 J 1.25 4412,.4167-14 to 4, del = 2 98 GS2A.96, -.15 I 1.25 4412,.4167-14 to 4, del = 2 99 GS2A.94, -.1 1.25 4412,.4167-14 to 4, d l = 2 1 GS2A.95, -.1 1.25 4412,.4167-14 to4, del -- 2 11 GS2A.96, -.1 1.25 4412,.4167-14 to 4, del = 2 12 GS2A.94, -.2 1.25 44-12,.4167t -14 to 4, d l = 2 1 GS2A.95, -.2 1.25 4412, -14 to 4, d l = 2 14 15 GS2A.96, -.2 1.25 GS2A.95, -.15 1.25 4412, 4412,.4167.4167!.4167-14 to 4, d l -- 2-18 to-9, del --- 1 1 16 17 GS2A.95, -.15 1.25 GS2A.95, -.15 i.25 4412, 4412,.4167 1.4167-8 to 1, del = 1 2to I1, del = I 1 I 18 GS2A.95, -.15 1.25 / 4412,.4167-17 to -9, del = 1.75 19 11 111 GS2A.95,-.15 I!.25 GS2A.95, -.15 I i.25 GS2A.95,-.15 ] 1.25 4412 I 4412, 4412,,.4167.4167.4167-8to 1, del= I 2to II, del= 1-18 to -9, del = 1.75.75 2 il2 11 114 GS2A.95, -.15 l 1.25 4412 GS2A.95, -.15 ] 1.25 4412, SM71 _ 2,.4167.4167-8 to 1, del = I 2toll, del=l -4 to 14, d l = 2 2 2 115 79-K-144 2-4 to 14, d l = 2 GS2A.95,-.15 1.25 4412,.4167 2-8 to 8, del = 2 117 AG91 A-ACT!.4967-4 to 12, d l = 2.79-118 AG91 A-ACT 1.4967-4 to 12, del = 2 2.2 119 AG91A-ACT.96,-.2!.4967 4412-ACT,.4967-17 to -2.14 12 ACO1A-ACT.96,-.15 1.4967 4412-ACT,.4967-17 to -2.74 121 AG91A-ACT.96,-.1 1.4967 4412-ACT,.4967-17 to -2.22 122 AC,-91A-ACT.95,-.2 1.4967 4412-ACT,.4967-12 to -2 2.98 12 AG91A-ACT.95,-.15 1.4967 4412-ACT,.4967-17 to -2 2.96 124 AG91A-ACT.95,-.1 i.4967 4412-ACT ',.4967-16 to -2 2.929 125 AG9iA-ACT.94,-.2 1.4967 4412-ACT,.4967-17 to -2 2.91 126 AG91A-ACT.94,-.15 1.4967 4412-ACT..4967-17 to -2 2.9 127 AG91A-ACT.94,-.1 i.4967 4412-ACT,.4967-14 to -2 2.919 --128 AG-91A-ACq _.95,-.15 1.4967 4412-ACT, 129 AG91A-ACT.95,-.15 1.4967 4412-ACT,,4967 I.4967 2-9 to 4-15 tog.79.81 1 AG91A-ACT.95,-.15 1.4967 4412-ACT,.4967-16 to 7 1.7 11 AG91A-ACT.95,-.15 1.4967 4412-ACT,.4967-17 to 6 2.6 12 AG91A.96,-.2 1.5 4412,.5-17 to -2 1 AG91A.96,-.15 1.5 4412,.5-17 to -2 14 AG91A.96,-.1 1.5 4412,.5-15 to -2 15 AC,-91A.95,-.2 1.5 4412,.5 -i 7 to -2 16 AG91A.95,-.15 1.5 4412,.5-18 to -2 17 AG91A.95,-.1 1.5 4412,.5-18 to -2 18 AG91A.94,-.2!.5 4412,.5-18 to -2 19 AG91A.94,-.15 1.5 4412,.5-18 to-2 14 AG91A.94,-.1 1.5 4412,.5-16 to -2 141 AG91A.95,-.15!.5 4412,.5 2-1 to2 142 AG91A.95,-.15 l 1.5 4412,.5 O -18 to 8.8 14 144 AG91A.95,-.15 i 1.5 4412, AG91A.95,-.15 1.5 4412,.5.5 I -19to7-21 to 6 1 I2

156 Primary Primary Primary Second Second Delta Freestream Case Airfoil Hinge Size Airfoil Hinge Size Flap Alpha RN 145 AG91A 1.5-4 to 12, del = 2.75 146 AG91A 1.5-4 to 12, del = 2 2.25 147 AG91A.95,-.15 1.5 4412 t,.5-19 to 6 148 AG91A-ACT.95,-.15 1.4967 4412-ACT,.4967-17 to 7 2.96 149 AG91A.95,-.15 1.5 "4412,.5 2-14 to 11.8 15 AG91A.95,-.15 1.5 4412,.5 2-15 to 1! 151 AC_,-91A.95,-.15 1.5 4412,.5 2-1419 2 15 AG91 A-ACT 152 i AG91A 154 AG91 A-ACT 155 AG91A-ACT.95,-.15.95,-.15.95,-.15.95,-.15 1.5 1.4967 1.4967 1.4967 4412 4412-ACT i 4412-ACT 4412-ACT,,,,.5.4967.4967.4967 2 2 2 2-14 to 9-8 to II -8 to 9-9 to 9.9!.9 2.9

157 VITA Gregory Glen Steen was bom July 8, 1966 in Great Falls, Montana. Mr. Steen graduated from Helena High School in Helena, Montana in the spring of 1984. Mr. Steen entered Texas A&M University in the fall of 1984 and graduated with his Bachelor of Science in Aerospace Engineering degree in December of 1988. During college, Mr. Steen participated in the University's Cooperative Education program working three work terms at the Texas A&M University Low Speed Wind Tunnel. After graduation, Mr. Steen accepted a position as a Research Specialist at the Low Speed Wind Tunnel. He entered the Master's program in Aerospace Engineering on a part time basis in the fall of 1989. Mr. Steen is married to the former Kathy Boeckman and has one son. He may be reached through his parents Harvey and Ila Steen at 75 Sixth Avenue in Helena, Montana 5961.