Download - Linear Methods Results for AePW-2
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Linear Methods Results for AePW-2
02/Jan/2016
Guilherme Begnini
&
Cleber Spode
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Case 2
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Case 2 – Linear Methods
• AIC-based: NASTRAN & ZTRAN
• NASTRAN with Generalized Aerodynamic Forces from CFD (AERO – Euler_Linearized)
• Time-Domain CFD (AERO – Euler_Linearized)
• Nonlinear Analysis (for comparison):
• Time-Domain CFD
today: AERO – Euler
tomorrow: AERO - RANS
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Case 2 – AIC-Based Methods
• Solvers: Nastran (DLM) – corrected and uncorrected
ZTRAN (TDLM)
• Flutter Prediction: Nastran (PKNL method)
ZTRAN (g-method)
• Set of Reduced Frequencies: 0.03, 0.04, 0.05, 0.06, 0.07
• Panels Aspect Ratio = 2 (No. Chordwise Panels = No. Spanwise Panels)
• Surface Mesh: 40x40 panels
• No Structural Damping considered
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Case 2 – Aerodynamic Meshes
Surface Mesh:
ZTRAN = NASTRAN
Volume Mesh:
ZTRAN only
Airfoil Mesh:
ZTRAN only
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Case 2 – Nastran Aerodynamic Correction
Steady Correction - correction for k=0 used for k≠0
• CLa & Cmy correction (CLa&Cmy)
- matches wing global CLa and Cmy
• Pre-Multiplying Diagonal Matrix (Pre-Diag)
- try to match chordwise dΔCp/da, spanwise Cla and Xac distributions, and global coefficients (factors limited to 3.0)
Unsteady Correction – different corrections for each k
(uses Pre-Multiplying Diagonal Matrix correction)
• Pitch Mode Adjust (Unsteady - Pitch)
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Case 2 – Steady CFD Data for Aerodynamic Correction
• Steady CFD data obtained from CFD++ (medium mesh)
• dΔCp/da distribution computed for a pair of angles of attack: (-0.25 & 0.25 deg.)
• Reference values for global CLa and CMa (30% mac) obtained from the slope of the following curves
0.1000.110
0.1200.1300.140
0.1500.1600.170
0.1800.1900.200
0.2100.2200.230
0.2400.250
-0.50 -0.30 -0.10 0.10 0.30 0.50
Alpha
CL
-0.09
-0.085
-0.08
-0.075
-0.07
-0.50 -0.30 -0.10 0.10 0.30 0.50
Alpha (deg)
CM
y
CLa = 5.075 [1/rad]CMa (30% mac)= 0.351 [1/rad]
12
12
CpCp
d
Cpd
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Case 2 – dΔCp/da Distribution at k=0
• Strip 60%
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Case 2 – dΔCp/da Distribution at k=0
• Strip 95%
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Case 2 – Spanwise CLa Distribution at k=0
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Span (m)
CL
a
CFD
DLM
DLM_Pre_Diag
ZTRAN
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Case 2 – Spanwise Xac Distribution at k=0
CLa
CMaXac
10
12
14
16
18
20
22
24
26
28
30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Span (m)
XC
A (
%) CFD
DLM
DLM_Pre_Diag
ZTRAN
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Case 2 – Aerodynamic Coefficients Verification
Method CLaDifference
CLaCmy (30% mac) Difference Cmy
CFD++ (medium) 5.075 Ref. 0.3508 Ref.
Nastran4.450 -12.3% 0.3499 -0.3%
Nastran - Unsteady-Pitch
Nastran - Cla&Cmy 5.075 0.0% 0.3508 0.0%
Nastran - Pre-Diag 5.070 -0.1% 0.3932 12.1%
ZTRAN 4.183 -17.6% 0.3596 2.5%
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Case 2 – dΔCp/da Distribution at k=0.03
• Strip 60%
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Case 2 – dΔCp/da Distribution at k=0.03
• Strip 95%
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Case 2 – Generalized Aerodynamic Forces
• Real Part
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Case 2 – Generalized Aerodynamic Forces
• Imag Part
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Case 2 – Flutter Results: V-g-f Plots
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
0 50 100 150 200 250
q (psf)
Fre
qu
en
cy (
Hz)
DLM
DLM
DLM - Cla&Cmy
DLM - Cla&Cmy
DLM - Pre-Diag
DLM - Pre-Diag
DLM - Unsteady-Pitch
DLM - Unsteady-Pitch
ZTRAN
ZTRAN
AERO - QHH
AERO - QHH
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0 50 100 150 200 250
q (psf)
Aero
dyn
am
ic D
am
pin
g
DLM
DLM
DLM - Cla&Cmy
DLM - Cla&Cmy
DLM - Pre-Diag
DLM - Pre-Diag
DLM - Unsteady-Pitch
DLM - Unsteady-Pitch
ZTRAN
ZTRAN
Experiment
AERO - QHH
AERO - QHH
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Case 2 – Flutter Results
Method
Flutter
Frequency
(Hz)
Difference
(Freq)
Flutter
Dynamic
Pressure
(psf)
Difference
(Dyn. Pres.)
Experiment 4.30 Ref. 168.8 Ref.
Nastran 4.28 -0.5% 165.0 -2.2%
Nastran - Cla&Cmy 4.28 -0.5% 144.8 -14.2%
Nastran - Pre-Diag 4.37 1.7% 131.5 -22.1%
Nastran - Unsteady-Pitch 4.13 -4.0% 159.1 -5.8%
ZTRAN 4.31 0.2% 160.7 -4.8%
AERO – Euler_Linearized Qhh 4.14 -3.8% 175.1 3.7%
AERO – Euler_Linearized Time Domain 4.11 -4.4% 179.2 6.2%
AERO – Euler Nonlinear Time Domain 4.09 -4.9% 176.8 4.7%
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Case 2 – Effect of DLM Mesh Refinement
& Structural Damping
• Analysis Default: Mesh = 40 x 40, g=0
150
152
154
156
158
160
162
164
166
168
170
10x10 20x20 30x30 40x40 50x50
Mesh Refinement
Qf
(psf) DLM (g=0)
DLM (g=0.2%)
Experiment
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Flutter Results – Additional Cases
Ref: Heeg, J. et al., Plans and Example Results for the 2nd AIAA Aeroelastic Prediction Workshop,
SciTech 2015.
80
100
120
140
160
180
200
0.4 0.5 0.6 0.7 0.8 0.9
Mach
Flu
tter
Dyn
am
ic P
ressu
re (
psf)
Experimental - AoA: -0.3-0
DLM
Experimental - AoA = 1.3
Experimental - AoA: 5.3-5.5
• Mesh = 50 x 50, g=0.2%
• Most results within 5% error (except those for AoA ~ 5)
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Flutter Results – Time Domain Simulations
Euler linearized around Static Aeroelastic position for each Q
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Flutter Results – Time Domain Simulations
Euler around Static Aeroelastic position for each Q
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Flutter Results – Time Domain Simulations
CPU time consumed
(wall time)
Euler = 8200 s
Euler Linearized = 700 s
168 CPUs
1,867,297 Tetra elements
432,456 nodes
Embraer mesh.
Perturbed in pitch mode velocity
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Flutter Results – Time Domain Simulations
Euler flutter Q = 176.8 psf
Euler Linearized flutter Q = 179.2 psf
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Flutter Results – Time Domain Simulations
Euler flutter Q = 176.8 psf
Euler Linearized flutter Q = 179.2 psf
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Flutter Results – Time Domain Simulations
Euler flutter Q = 176.8 psf
Euler Linearized flutter Q = 179.2 psf
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Flutter Results – Time Domain Simulations
Euler flutter Q = 176.8 psf
Euler Linearized flutter Q = 179.2 psf
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Flutter Results – Time Domain Simulations
Euler flutter Q = 176.8 psf
Euler Linearized flutter Q = 179.2 psf