NASA Technical Memorandum 110394 Numerical Study of Steady and Unsteady Canard-Wing-Body Aerodynamics Eugene L. Tu August 1996 National Aeronautics and Space Administration NASATechnicalMemorandum110394 Numerical Study of Steady and Unsteady Canard-Wing-Body Aerodynamics Eugene L. Tu, Ames Research Center, Moffett Field, California August 1996 National Aeronautics and Space Administration Ames Research Center Moffett Field, California 94035-!000 TABLE OF CONTENTS Page Nomenclature ............................................................................. xv Summary. .................................................................................. 1 Chapter 1 Introduction ........................................... ......................... 3 1.1 Motivation ...................................................................... 3 1.2 Background ..................................................................... 4 1.3 Previous Studies ................................................................ 4 1.4 Objectives ...................................................................... 6 1.5 Geometry ....................................................................... 6 Chapter 2 Computational Modeling ....................................................... 9 2.1 Numerical Method .............................................................. 9 2.1.1 Turbulence modeling .................................................. 10 2.1.2 Code performance ..................................................... 10 2.2 Geometry Modeling ............................................................ 11 2.3 Static Grid Generation ......................................................... 12 2.3.1 Surface grids .......................................................... 12 2.3.2 Flowfield grids ........................................................ 12 2.4 Dynamic Grid Generation ...................................................... 14 2.5 Boundary Conditions ........................................................... 14 2.6 Zonal Interfacing ............................................................... 15 2.7 Dynamic Stability Analysis ..................................................... 16 Chapter 3 Effect of Canard on Steady-State Aerodynamics ............................... 31 3.1 Experimental Validation: Coplanar Canard ..................................... 31 3.1.1 Baseline grid .......................................................... 31 3.1.2 Refined grid ........................................................... 33 3.2 Aerodynamic Performance ...................................................... 34 3.2.1 Canard vertical position ............................................... 34 3.2.2 Canard deflection angle ............................................... 35 iii 3.3 Canard-WingVortexInteraction............................................... 36 3.3.1 Coplanarcanard...................................................... 36 3.3.2 Canardverticalposition............................................... 37 3.3.3 Canarddeflectionangle............................................... 39 3.4 Effectof Canardon Wing \,%rtexBreakdown................................... 40 Chapter4 Effectof Fixed Canardon UnsteadyAerodynamics............................ 69 4.1 Pitch-Up RampMotion ........................................................ 70 4.1.1 Aerodynamicperformance............................................. 71 4.1.2 Spatialand temporalconvergence..................................... 71 4.1.3 Canard-wingvortexinteraction........................................ 72 4.2 Pitch Oscillation............................................................... 73 4.3 DynamicStabilit3............................................................... 74 4.3.1 Effectof canard....................................................... 75 4.3.2 Reducedfrequency.................................................... 95 Chapter5 UnsteadyAerodynamicsof MovingCanards................................... 95 5.1 CanardPitch-UpRampMotion................................................ 95 5.1.1 Unsteadylift andpitchingmoment.................................... 96 5.1.2 Canard-wingvortex interaction........................................ 98 ,5.2 CanardPitch Oscillation....................................................... 98 5.2.1 Unsteadylift andpitchingmoment.................................... 99 5.2.2 Canardand wingvortexstructures................................... 127 Chapter6 Conclusions.................................................................. 127 6.1 Validationof the Computationalblethod...................................... 127 6.2 Canard-Wing-BodySteadyFlowfield.......................................... 128 6.3 Canard-Wing-BodyUnsteadyFlowfield........................................ 129 6.4 Recommendationsfor FutureStudies.......................................... 135 AppendixA GoverningEquations....................................................... 131 AppendixB NumericalAlgorRhm....................................................... 137 AppendixC Turbulence Modeling ....................................................... 143 References 147 iv List of Tables Page 2.1 Surface and flowfield grid data for coplanar, vertical-offset and deflected canard configurations .................................................. 18 List of Figures Page 1.1 Sketch of the leading-edgevortexstructureof a canard or wing ................... 7 1.2 Crossflow plane sketch of the leading-edge vortex ................................. 7 1.3 Schematic of the typical steady-state canard-wing vortex interaction for a configuration at moderate angles of attack ............................ 8 1.4 Close-coupled canard-wing-body geometry (pitch axis. moment center, and canard vertical locations shown) ....................................... 8 2.1 Schematic diagram of the grid generation procedure for static canard configurations with various canard vertical positions and deflections ....... 19 2.2 Baseline surface grid for the wing-body configuration with and without an undeflected mid-canard ................................................ 20 2.3 Refined surface grid for the wing-body configuration with and without an undeflected mid-canard ................................................ 20 2.4 Schematic of the procedure for generating a vertical-offset canard configuration from a baseline undeflected mid-canard configuration ........ 21 2.5 Perspective view of the surface grid for wing-body configuration with a high-canard (y/g = 0.185) .......................................... 21 2.6 Schematic of the procedure for generating a deflected canard configuration from a baseline undeflected mid-canard configuration ........ 22 2.7 Perspective view of the surface grid for wing-body configuration with a deflected canard (_c = 10 deg) ......................................... 22 2.8 Flowfield grid topology and expanded near-body grid for the undeflected mid-canard configuration ...................................... 23 2.9 Comparison of the baseline and refined near-body flowfield grids for the undeflected mid-canard configuration .................................. 24 2.10 Algebraic redistribution of the flowfield grid ................................... 25 2.11 Flowfield grid at the mismatched interface surface for the high-canard configuration ............................................................. 26 2.12 Flowfield grid at the mismatched interface surface for the deflected canard configuration ...................................................... 26 2.13 Schematic illustrating the integration of dynamic grid generation and zonal interface computation into the time-iterative solution 27 process ................................................................... 2.14 Types of velocity boundary conditions at the surfaces of the canard. wing and body ............................................................ 28 2.15 Schematic illustrating the interfacing of two adjacent zones .................... 28 2.16 Example of a local search procedure for improved efficiency in dynamic zonal interface computations .................................. 29 3.1 Comparison of computed and experimental steady-state surface pressure coefficients for the baseline grid with and without mid-canard. M_c = 0.90, a _ 4 deg, Re_ = 1.52 million ............... 41 vii 3.2 Comparisonof computedandexperimentalforcecoefficients for thebaselinegrid with andwithout mid-canard. M_ = 0.90, Ree = 1.52 million ......................................... 42 3.3 Comparison of component force coefficients for the baseline grid with and without mid-canard. (Lift and moment curves are given for shaded regions of the geometry). Moo = 0.90, Ree = 1.52 million ....................................................... 43 3.4 Comparison of baseline and refined grid surface pressure coefficients with experiment. Moc = 0.90, ct = 8.21 deg, Ree = 1.52 million ....................................................... 44 3.5 Comparison of baseline and refined grid surface pressure coefficients with experiment. 2lI_ = 0.90, a = 12.38 deg, Ree = 1.52 million ....................................................... 44 Comparison of baseline and refined grid force coefficients with experiment. M,c = 0.90, Ree = 1.52 million ............................ 45 Comparison of computed and experimental surface pressure coefficients for the refined grid with and without mid-canard. 5/c_ = 0.90, a _ 12 deg, Rec = 1.52 million ..........................