2012 10 30 5 Journal of Northwestern Polytechnical University Oct. Vol. 30 2012 No. 5 710072 NACA 0006 NACA 0012 Basic Finner MissileBFM 1. 58 ~ 2. 5 V211. 3 A 1000-2758201205-0784-05 CFD CFD 1 1-3 2 CFD 3 NACA 0006 NACA 0012 CT5 Baeder CFD Basic Finner MissileBFM 1. 58 ~ 2. 5 vx y = α rx y vx y rx 4 5 1. 1 Euler 6-8 2011-11-12 1 90816008 20070699054 1986
5 785 QdV + t Ω F nds = 0 1 Ω Q = ρ ρu ρv ρw ρe T Ω 1. 4 Ω n F Roe α = α 0 + Δαsinkt * = α 0 + θ 8 LUSGS α 0 Δα k = ωl ref /2V t * 9 1. 2 C m t= C m0 + C θ θ m θ + Cm θ 9 C m0 C θ m V = u - x τ i + v - y τ j + w - z τ k 2 θ Cm 3 u v w x τ y τ z τ t s +T k u' v' w' C m sinkt * dt * C θ t m = s V = u - x τ + u'i + v - y τ + v'j + πδα w - z τ + w'k 3 ts+t C m coskt * dt * θ C t m = s 10 πδα 珓 x τ i + 珓 y τ j + 珓 z τ k = x τ - u'i + y τ - v'j + z τ - w'k V = u - 珓 x τ i + v - 珓 y τ j + w - 珓 z τ k u' 1 = 0 v' 1 = 0 4 z珓 τ = x c - x i ω z - V cosα 0 tanα 0 + Δα+ V sinα 0 7 x i y i z i x c y c z c 2 CFD 1. 3 2. 1 NACA 0006 z 3 Ma = 0. 3 0. 5 0. 65 0. 8 0 w g = 0. 08V 4. 6 dt = 1. 0 w' 1 = V cosα 0 tanα 0 + Δα- V sinα 0 5 α 0 Δα 10-4 s s = 2tV c c 1 Lomax 10 u' 2 = - z i - z c ω z v' 2 = 0 α w' 2 = - x c - x i ω z 6 [ ] 56 C l s = 4 α Ma 1-1 - Ma s 0 s 2Ma Ma 1 + Ma x珓 τ = z i - z c ω z y珓 τ = 0 11
786 30 12 1 2 Ma = 0. 3 2 2. 2 NACA0012 AGARD CT5 α = α 0 + Δαsin2kt * α 0 = 0. 016 Δα = 2. 51 k = 0. 0814 1 /4 3 AGARD CT5 11 C 199 40 4 5 3 CT5 4 AGARD CT5 5 CP 3 BFM 6 7 5. 0dMa = 1. 58 1. 75 1. 89 2. 10 2. 50 k = 0. 003 16 = 1. 5 Δα = 1. 5 8 9 Basic Finner MissileBFM Ma = 1. 58 2 α 0
5 787 10 11 10. 089% 4. 335% 6 BFM 7 BFM 8 Ma = 1. 58 9 Ma = 1. 58 10 C θ m 11 C θ m 4 2 BFM 3 1 1 NACA 0006 NACA 2 0012 3 1.. 2000 224 5-8 Mou BinLiu WeiHuo Zhanghua. Numerical Calculation of Damping-in-Pitch Derivatives for Hypersonic Flow over Sphere- Core. Journal of National University of Defense Technology2000 224 5-8 in Chinese 2Oktay ErdalAkay Hasan U. CFD Predictions of Dynamic Derivatives for Missiles. AIAA-2002-0276 3. CFD. 2005 234 458-463 Yuan XianxuZhang HanxinXie Yufei. The Pitching Static /Dynamic Derivatives Computation Based on CFD Methods. Acta
788 30 Aerodynamic Sinica2005234 458-463 in Chinese 4Parameswaran VasudevBaeder James D. Indicial Aerodynamics in Compressible Flow-Direct Computational Fluid Dynamic Calculations. Journal of Aircraft1997 341 131-133 5Rajneesh SinghJames D Baeder. Direct Calculation of Three-Dimensional Indicial Lift Response Using Computational Fluid Dynamics. Journal of Aircraft1997 344 465-471 6.. 2007 283 527-530 Zhan HaoQian Weiqi. Numerical Simulation of Gust Response for Thin Airfoil. Acta Aeronautica et Astronautica Sinica. 2007283 527-530 in Chinese 7Yang GuoweiObayashi Shigeru. Numerical Analyses of Discrete Gust Response for an Aircraft. Journal of Aircraft200441 6 1353-1359 8.. 2009 262 270-275 Zhan HaoQian Weiqi. Numerical Simulation on Gust Response of Elastic Wing. Chinese Journal of Computational Mechanics 2009262 270-275 in Chinese 9Sitaraman JayanarayananBaeder James D. Field Velocity Approach and Geometric Conservation Law for Unsteady Flow Simulations. AIAA Journal2006 449 2084-2094 10Lomax H T. Indicial Aerodynamics. AGARD Manual of AeroelasticityPart 2NATO. Advisory Group for Aerospace Research and Development1968Chap. 6 11Li JieHuang ShouzhiJiang ShengjuLi Fengwei. Unsteady Viscous Flow Simulations by a Fully Implicit Method with Deforming Grid. AIAA-2005-1221 12Landon R H. NACA0012 Oscillatory and Transient Pitching. AGARD Report 702Compendium of Unsteady Aerodynamic Measurements1982 An Effective Computation Method Based on Field Velocity Approach for Unsteady Flow Simulation and Obtaining Dynamic Derivatives Guo DongXu MinChen Shilu College of AstronauticsNorthwestern Polytechical UniversityXi'an 710072China AbstractSections 1 through 3 of the full paper explain and evaluate the computation method mentioned in the titlewhich we believe is effective. Their core consists ofthe field velocity or grid velocity approach provides a u- nique methodology for directly calculating aerodynamic responses to step change in flow conditionsthe grid time metrics include the velocity caused by the impulsive change in angle of attack but the mesh is not moved accordinglythis approach avoids numerical instabilities and decouples the step change in the angle of attack from a pitch ratebased on this approacha technique is presented to model longitudinal unsteady flow phenomenon by superposing the step change in the angle of attack upon the impulsive change in pitch rate. In Figs. 4 and 5numerical results are validated by comparison with experimental results for NACA 0012 airfoil under forced oscillations. To validate further the applicability for the present methodpitch damping derivativescalculated from the load history of the unsteady flow around a standard research configurationknown as the Basic Finner Missileare presented in Figs. 10 and 11. Predicted results show indeed good agreement with available wind tunnel data. Key wordscomputational fluid dynamicscomputer simulationnumerical methodsstabilityunsteady flow field velocitydynamic derivatives