Presentation at 2012 Asia-Pacific International Symposium on Aerospace Technology, APISAT 2012

1. 2012 Asia-Pacific International Symposium on Aerospace Technology
Nov. 13-15, Jeju, Korea
No.172
Numerical Simulation: Flight Dynamic Stability Analysis
Using Unstructured Based Navier-Stokes Solver
○Yasuhiro NARITA Tokyo Metropolitan University
Atsushi HASHIMOTO Japan Aerospace Exploration Agency
Masahiro KANAZAKI Tokyo Metropolitan University

2. Contents
 Background
 Objective
 Computational methods
 Estimation of aerodynamic derivatives
 Results
 Conclusions
2

3. Background
Dynamic stability analysis using CFD
 Analysis of free flight condition
 Simulation for various flight condition
SDM
In several countries
 USA
 Development demand of fighter.
 Japan
Many research considers the dynamic stability analysis as key technology.
 Development demand of HTV-R and so on.
Requirement to practical CFD data
Current 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

4. 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 condition
4

5. Computational conditions
Standard Dynamics Model (SDM)
Y
M
L’ Canopy
N
X 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

6. 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=0.0
least square method based on time-series data of
aerodynamic 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.

7. 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.
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8. 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.
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9. 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 N
C Zα  C Mα  C L'   C N 
α α  
1.5 2.5 3.5 α
9

10. 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 from
difference results of q0=0 and q1=θω.)
where
q0 q1
C Z C M C L C N
C Zq  C Mq  C L ' p  C Np 
q q p p
These gradients show the CMq.
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11. 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.）
cref
C M  C M 0  C M   (C Mq  C M )
 
 0.10
U 0.05
Cm
Cm(fitting)
CM
0.00
where
Aerodynamic derivatives are obtained by least -0.05

square method from estimated aerodynamic 

coefficients. -0.10 t
0 200 400 600 800 1000 1200
Step number
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12. Results
Aerodynamic coefficient
12

13. 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.
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14. Results of motion analysis
Pitching motion
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15. 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  CM
CMα
・
-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.
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16. 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.
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17. 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 )
   cost 
U
Number of inner iteration is influences on CM.
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18. Aerodynamic derivatives
Steady Uniform rotation Unsteady oscillation
Aerodynamic Stiffness Damping Stiffness
Unsteady_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

19. Results of motion analysis
Rolling motion
19

20. Flow visualization
Position of slice
Rolling (Alpha=5deg.) Time variation of Cp distribution
 Flowfield was not affected by rolling motion in present condition.
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21. 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 iterationis 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
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22. 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.
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23. Thank you for your attention.
감사합니다!
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