NACA 0006 A NACA 0012 CT5

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1 Journal of Northwestern Polytechnical University Oct. Vol No NACA 0006 NACA 0012 Basic Finner MissileBFM ~ 2. 5 V A CFD CFD CFD 3 NACA 0006 NACA 0012 CT5 Baeder CFD Basic Finner MissileBFM ~ 2. 5 vx y = α rx y vx y rx Euler

2 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 * 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 NACA 0006 z 3 Ma = 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 Ma s 0 s 2Ma Ma 1 + Ma x珓 τ = z i - z c ω z y珓 τ = 0 11

3 Ma = NACA0012 AGARD CT5 α = α 0 + Δαsin2kt * α 0 = Δα = k = /4 3 AGARD CT5 11 C CT5 4 AGARD CT5 5 CP 3 BFM dMa = k = = 1. 5 Δα = Basic Finner MissileBFM Ma = α 0

4 % % 6 BFM 7 BFM 8 Ma = Ma = C θ m 11 C θ m 4 2 BFM NACA 0006 NACA Mou BinLiu WeiHuo Zhanghua. Numerical Calculation of Damping-in-Pitch Derivatives for Hypersonic Flow over Sphere- Core. Journal of National University of Defense Technology in Chinese 2Oktay ErdalAkay Hasan U. CFD Predictions of Dynamic Derivatives for Missiles. AIAA CFD Yuan XianxuZhang HanxinXie Yufei. The Pitching Static /Dynamic Derivatives Computation Based on CFD Methods. Acta

5 Aerodynamic Sinica in Chinese 4Parameswaran VasudevBaeder James D. Indicial Aerodynamics in Compressible Flow-Direct Computational Fluid Dynamic Calculations. Journal of Aircraft Rajneesh SinghJames D Baeder. Direct Calculation of Three-Dimensional Indicial Lift Response Using Computational Fluid Dynamics. Journal of Aircraft Zhan HaoQian Weiqi. Numerical Simulation of Gust Response for Thin Airfoil. Acta Aeronautica et Astronautica Sinica in Chinese 7Yang GuoweiObayashi Shigeru. Numerical Analyses of Discrete Gust Response for an Aircraft. Journal of Aircraft Zhan HaoQian Weiqi. Numerical Simulation on Gust Response of Elastic Wing. Chinese Journal of Computational Mechanics in Chinese 9Sitaraman JayanarayananBaeder James D. Field Velocity Approach and Geometric Conservation Law for Unsteady Flow Simulations. AIAA Journal Lomax 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 Landon 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 China 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