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Numerical Simulation: Flight Dynamic Stability Analysis Using Unstructured Based Navier-Stokes Solver
2012 Asia-Pacific International Symposium on Aerospace Technology Nov. 13-15, Jeju, KoreaNo.172Numerical Simulation: Flight Dynamic Stability AnalysisUsing Unstructured Based Navier-Stokes Solver ○Yasuhiro NARITA Tokyo Metropolitan University Atsushi HASHIMOTO Japan Aerospace Exploration Agency Masahiro KANAZAKI Tokyo Metropolitan University
Background Dynamic stability analysis using CFD Analysis of free flight condition Simulation for various flight conditionSDMIn several countries USA Development demand of fighter. JapanMany research considers the dynamic stability analysis as key technology. Development demand of HTV-R and so on. Requirement to practical CFD dataCurrent study on dynamic stability analysis using CFD in Japan Many studies has been carried out for subsonic flight w/o shock wave. Next interest is supersonic flight w/ shock wave.3
Objective Investigation of CFD ability for dynamic stability analysis at supersonic flight Dynamic stability analysis using Standard Dynamics Model at supersonic SDM’s configuration and wind tunnel data is opened to public. Investigation of grid dependency and proper number of inner iteration in supersonic condition4
Computational conditions Standard Dynamics Model (SDM)Y M L’ Canopy NX Computational conditions Z （Same as experiment） Reynolds number - 2.95×106 Strake Mach number - 1.05 Mean angles of attack deg. 0.0, 2.5, 5.0 α0 Pitch angle θ， deg. 1.0 Roll angle φ Reduced frequency k - 0.052 where Intake Frequency is lower thanuc the time scale ofk flow.ref ref u c Re M 5 Stability board a u
Overview of SDM experiment Vibration with the constant rotation of pitch angler velocity q and roll angler velocity p at each mean angles of attack α0 q Trend of aerodynamic derivatives are obtained by α0=0.0least square method based on time-series data ofaerodynamic coefficients. q CMq CM α0=2.5 q α0=5.0 [deg]6 *Miwa, Ueno, ”Development of Dynamic Stability Equipment for Transonic Wind Tunnel,”2004.
Computational methods * FAST Aerodynamic Routines developed in JAXA Computations are carried out using unstructured flow solver “FaSTAR”* Governing equation: compressive Navier-Stokes equation Turbulent model: Spalart Allmaras model with rotation correction (SA-R) Time integration is carried out by LU-SGS implicit method. Static analysis → RANS (Reynolds Averaged Navier-Stokes Simulation) Dynamic analysis → URANS (Unsteady Reynolds Averaged Navier-Stokes Simulation) Present URANS employed dual time stepping method using quasi-time. 7
Computational methods Unstructured hexahedral mesh is generated around SDM using HexaGrid. The half span model is used for evaluation of a pitching motion. Coarse 0.3million cells(Coarse),7 million cells (Medium), 23 million cells (Fine) The full span model is used for evaluation Medium of a rolling motion. 0.6 million cells(Coarse), 14 million cells (Medium), 46 million cells (Fine) Fine Moving grid method is used for the dynamic model motion.8
Estimation of aerodynamic derivatives * CZ : Normal force coefficient CM : Pitching moment coefficient CL’ : Rolling moment coefficient CN : Yawing moment coefficient Flow Analysis for stable model α0 [deg] Aerodynamic coefficients CZ CM CL’ CN are obtained. Stiffness derivatives CZα CMα CL’φ CNφ are estimated by central difference by aerodynamic derivatives. （Ex: The stiffness derivatives at α0 = 2.5 deg. are estimated by the results of α0 = 1.5 deg. and α0 = 3.5 deg.) CZ where C Z C M C L C NC Zα C Mα C L C N α α 1.5 2.5 3.5 α 9
Estimation of aerodynamic derivatives q : Pitch angular velocity Analysis for steady rotated model p : Roll angular velocity q pitching motion Flow Analysis based on steady rotation at constant angular velocity q, p Estimated the q0=0, p0 = 0 and q1,p1. Damping derivatives CZq CMq CL’p CNp are estimated by difference.(Ex: In pitching motion, damping derivatives CZq and CMq are estimated fromdifference results of q0=0 and q1=θω.) where q0 q1 C Z C M C L C NC Zq C Mq C L p C Np q q p p These gradients show the CMq.10
Estimation of aerodynamic derivatives Flow Analysis for unsteady oscillation Vibrate model at (t ) 0 sin(t ) CM can be obtained by following equation. （CL’ is calculated in a same way as CM.） crefC M C M 0 C M (C Mq C M ) 0.10 U 0.05 Cm Cm(fitting) CM 0.00 whereAerodynamic derivatives are obtained by least -0.05 square method from estimated aerodynamic coefficients. -0.10 t 0 200 400 600 800 1000 1200 Step number11
Aerodynamic coefficient Steady Steady rotation Unsteady oscillation Aerodynamic Stiffness Damping Stiffness Damping coefficients derivatives derivatives derivatives derivatives CZ 0.600 C Z CZq 0.020 C Z CZq CZ 0.000 CM 0.400 CM CMq -0.020 CM CMq CM CM 0.200 Cz CL’ 0.000 C L CL p -0.040 C L C L p C L sin -0.060 CN -0.200 0.0 C N 2.5 C Np 5.0 -0.080 0.0 C N C Np C N sin 2.5 5.0 Alpha[deg.] Alpha[deg.]Medium and fine grid are good agreement with the experimental data.⇒ Coarse grid is inadequate for estimating aerodynamic derivatives.13
Aerodynamic derivatives Steady Uniform rotation Unsteady oscillation Aerodynamic Stiffness Damping Stiffness Damping Unsteady_5:Inner iteration is 5. coefficients derivatives derivatives derivatives derivatives 0.000 0.000 CZ C Z CZq C Z -1.000 -0.200 -2.000 CZq CZ -3.000 CMq+CMα ,CMq -0.400 -4.000 CM -0.600 CM CMq -5.000 CM CMq CMCMα ・ -6.000 -0.800 -7.000 CL’ -1.000 C L CL p -8.000 -9.000 -10.000 C L C L p C L sin -1.200 0.0 2.5 5.0 CN C Np 0.0 2.5 5.0 C N C Alpha[deg.] N C Np C N sin Alpha[deg.] Unsteady_5 (Inner iteration is 5) did not agree well.15
Flow visualization Position of slice Pitching (Alpha=5deg.) Time variation of Cp distribution Unsteady wing-tip vortex, wake and shock wave were observed.⇒Convergence at every time step is important by proper inner iteration.16
Influence of inner iteration Inner iteration convergence history of CM. Number of inner iteration is set to 50. 5 cref C M C M 0 C M (C Mq C M ) U θ : Pitch angle cref C M C M 0 C M sin t (C Mq C M ) cost U Number of inner iteration is influences on CM.17
Aerodynamic derivatives Steady Uniform rotation Unsteady oscillation Aerodynamic Stiffness Damping StiffnessUnsteady_5: Inner iteration 5. Unsteady_50: Inner iteration 50. Damping coefficients derivatives derivatives derivatives derivatives 0.000 0.000 CZ C Z C Z -1.000 -0.200 CZq -2.000 CZq CZ CMq+CMα ,CMq -0.400 -3.000 -4.000 CM ・ CMα -0.600 -5.000 -0.800 CM CMq -6.000 -7.000 CM CMq CM -8.000 CL’ -1.000 -1.200 C L CL p -9.000 -10.000 0.0 C L 2.5 C L p C L sin 5.0 0.0 2.5 5.0 ・ C C Alpha[deg.] N Alpha[deg.] N C Np N C C Np C N sin ・ ・Improved accuracy by increasing inner iteration ・Unsteady_50 (inner iteration is 50) result showed good agreement comparing the steady result. ⇒ Large influence of 18
Flow visualization Position of slice Rolling (Alpha=5deg.) Time variation of Cp distribution Flowfield was not affected by rolling motion in present condition.20
Aerodynamic derivatives Unsteady_50: Inner iteration 50. 0.005 Steady Uniform 0.400 rotation Unsteady oscillation 0.000 0.200 CLp+CLβ sinα, CLp Aerodynamic -0.005 Stiffness Damping 0.000 Stiffness Damping coefficients -0.010 derivatives derivatives -0.200 derivatives derivatives -0.015 -0.400 CZ C Z C Z .CLφ -0.020 CZq -0.600 -0.800 CZq CZ -0.025 -1.000 CM -0.030 -0.035 0.0 CM 2.5 5.0 CMq -1.200 -1.400 CM CMq CM 0.0 2.5 5.0 CLangle ofAlpha[deg.] number ofpinner iterationis important. sin ・At high ’ attack,enough C L CL CL Alpha[deg.]C C L p L ・Influence of is small. condition.N C N C Np N C ⇒ Damping can be estimated by steady analysis under this computationalsin C Np C N C 21
Conclusions Investigation of CFD ability for dynamic stability analysis at supersonic flight Pitching motion Unsteady flow was the remarkably observed. Number of inner iteration has to be decided properly in consideration of unsteady flow to estimate correct . Rolling motion At high angle of attack, enough number of inner iteration is important. Unsteady flow was not much observed. Influence of is small in rolling motion. Damping in roll can be calculated by steady in present condition. Obtained results are good agreement with experimental data.22