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transcript
Full-Field Sonic Boom Simulation in
Real Atmosphere
Rei Yamashita
Kojiro Suzuki
32nd AIAA Applied Aerodynamics Conference
AIAA Aviation and Aeronautics Forum and Exposition
(June. 17th, 2014)
○
The University of Tokyo
- Full-Field Sonic Boom Simulation in Real Atmosphere 2
Contents
1. Background
2. Numerical method
3. Numerical results
4. Conclusions
5. Future plan
- Full-Field Sonic Boom Simulation in Real Atmosphere
Sonic Boom
Acoustic phenomenon by shocks
Sound of explosion
Sonic Boom reduction is essential
3
1.Background 1.1 Sonic boom 1.4 Full-field simulation② 1.2 Related research 1.5 Objective 1.3 Full-field simulation 1.6 Waveform parameter method
Depend on many factors
・ Aircraft configuration
・ Flight and atmos. conditions
・ Ground topography
Sonic Boom Intensity
Near field
Middle field
Far field
- Full-Field Sonic Boom Simulation in Real Atmosphere
Concept of Hypersonic Vehicle
(JAXA)
4
1.Background
① Low boom design
To realize supersonic airplane ② Propagation mechanism
To clarify various effects (Molecular relaxation, Atmospheric turbulence etc.) ③ Evaluation method
To predict sonic boom intensity precisely
Related research
It is possible to evaluate
complex phenomena
(Focused sonic boom etc.)
Evaluation method ・Waveform parameter method
・Augmented burgers eq.
・Lossy nonlinear Tricomi eq.
1.1 Sonic boom 1.4 Full-field simulation② 1.2 Related research 1.5 Objective 1.3 Full-field simulation 1.6 Waveform parameter method
- Full-Field Sonic Boom Simulation in Real Atmosphere 5
Full-Field Simulation
・Rigorous model can be solved in full-field simulation
・Necessary to improve the following
Challenging and promising to clarify detailed phenomena (Molecular relaxation, Ground effect, etc.)
① Computational load
② Solution adaptive technique
③ Approach of real atmosphere
1.Background
CFD analysis in whole domain extending from airplane
to ground
1.1 Sonic boom 1.4 Full-field simulation② 1.2 Related research 1.5 Objective 1.3 Full-field simulation 1.6 Waveform parameter method
- Full-Field Sonic Boom Simulation in Real Atmosphere 6
・Yamashita, R. et al, “Numerical Analysis of Sonic Boom Cutoff Phenomena by Direct
Simulation in Whole Domain Extending to Ground Level,” APISAT 2013, No. 02-05-3.
・Potapkin, A. V. et al., “An Advanced Approach for Far-Field Sonic Boom Prediction,”
AIAA Paper 2009-1056, 2009.
Axi-symmetric analysis in r/L (radial distance/Length of body) = 0-1000
⇒ CFD is feasible to predict sonic boom at far-field
1.Background
⇒ Cutoff phenomena can be simulated by 3D Euler analysis in real
(stratified) atmosphere
・ Flight model : Axi-symmetric paraboloid
・ Flight Mach number : M = 1.1
・ Flight altitude : h = 10 km
1.1 Sonic boom 1.4 Full-field simulation② 1.2 Related research 1.5 Objective 1.3 Full-field simulation 1.6 Waveform parameter method
Accuracy of full-field simulation hasn’t been fully confirmed
- Full-Field Sonic Boom Simulation in Real Atmosphere
To investigate accuracy of full-field simulation as
sonic boom prediction method from near-field around
body to far-field (ground).
7
<Full-Field Simulation>
・ Consideration of real (stratified) atmosphere
・ Construction of adaptive grid aligned to shock waves
<Validation>
・ Comparison with ・ D-SEND#1 flight test data by JAXA (JAXA : Japan Aerospace Exploration Agency)
・ Waveform Parameter Method (WPM)
Objective
1.Background 1.1 Sonic boom 1.4 Full-field simulation② 1.2 Related research 1.5 Objective 1.3 Full-field simulation 1.6 Waveform parameter method
- Full-Field Sonic Boom Simulation in Real Atmosphere 8
Waveform Parameter Method (WPM)
Geometric Acoustics Isentropic wave theory
Input Parameter
To approximate shock
by acoustic wave
・ Near-filed pressure waveform
・ Flight condition(Mach number, Flight altitude and etc.)
・ Atmos. condition(Temperature, wind distributions)
Representative prediction method of sonic boom
To account for nonlinear
waveform distortion
Far-field waveform is obtained by propagation along ray
1.Background 1.1 Sonic boom 1.4 Full-field simulation② 1.2 Related research 1.5 Objective 1.3 Full-field simulation 1.6 Waveform parameter method
- Full-Field Sonic Boom Simulation in Real Atmosphere 9
Contents
1. Background
2. Numerical method
3. Numerical results
4. Conclusions
5. Future plan
- Full-Field Sonic Boom Simulation in Real Atmosphere
-0.8
-0.4
0
0.4
0.8
0 1 2 3 4 5 6 7 8
y, m
x, m
Tail fin
-0.8
-0.4
0
0.4
0.8
0 1 2 3 4 5 6 7 8
y, m
x, m
Tail fin
2.Numerical method
NWM (N Wave Model)
LBM (Low Boom Model)
Designed by Seebass-George-Darden (S-G-D) method
to suppress the pressure fluctuation behind front shock wave
D-SEND#1 model by JAXA
( Darden, C. M., “Sonic-Boom Minimization with Nose-bluntness Relaxation,” NASA TP-1348, 1979. )
LNWM = 5.6 m
LLBM = 8 m
2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
10
- Full-Field Sonic Boom Simulation in Real Atmosphere
2.Numerical method
NWM LBM
Mach number 1.43 1.42
Flight altitude 6.03 km 6.015 km
Computational domain r/LNWM = 0~1100
(r = 6.16 km)
r/LLBM = 0~800
(r = 6.4 km)
Observation point
(D-SEND#1 flight test)
0.5 km altitude
⇒Ground topography has little effect
Numerical condition
Coordinate system
0 1 2 3 4 5 6 7 8
y, m
x, m
x
y
z
r
θ
Flight model
Steady flow
(Steady level flight)
11
2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
O
- Full-Field Sonic Boom Simulation in Real Atmosphere
0
5
10
15
20
200 250 300
Alt
itu
de, k
m
Atmos. Temperature, K
0
5
10
15
20
0 50 100
Alt
itu
de, k
m
Atmos. Pressure, kPa
0
5
10
15
20
0 0.5 1 1.5
Alt
itu
de, k
m
Atmos. Density, kg/m3
Temperature Pressure Density
2.Numerical method
RTp
gdh
dp
・ Atmos. Temperature :
・ Hydrostatic Eq. :
・ Eq. of state of ideal gas :
)75.6( hkmconstT )75.6(0 kmhhTT
Atmospheric Model
05101520
200 250 300
h[k
m]
T∞ [K]
Meteorological data
Atmospheric model
12
2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
- Full-Field Sonic Boom Simulation in Real Atmosphere
・ Convective term : SHUS(Simple High-resolution Upwind Scheme)
+third order MUSCL interpolation
・ Gravity term : Source term
・ Time integration : MFGS(Matrix Free Gauss-Seidel) implicit method
Numerical approach
Governing Equation
2.Numerical method
,,, 2
2
vpE
vw
pv
uv
v
F
upE
uw
uv
pu
u
E
E
w
v
u
Q
ttt
5
4
3
2
1
2
,
0
0
0
,
s
s
s
s
s
S
gv
gS
wpE
pw
vw
uw
w
G CG
t
CG SS
z
G
y
F
x
E
t
Q
Gravity term Correction term (approach is discussed later) 3D Euler Eq.
13
2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
- Full-Field Sonic Boom Simulation in Real Atmosphere
x/L
y/L
0
1100 (NWM)
800 (LBM)
Computational model
Uniform atmosphere
Real atmosphere
1
x 0
y
z
r θ
Flow
Front shock wave Rear shock wave
14
・ 3D grid : rotating 2D grid about x axis(0-180 deg) ・ Each sector : Δ r/L≧4 (8 points overlapping) ・ Change of grid angle : every 5 points ・ Total grid number : 14 million(NWM), 8 million(LBM) points
Computational Grid
2.Numerical method
・ Boundary condition in r direction Special treatment is necessary ⇒ r/L = 0-1 : uniform atmosphere
Model
Axi-symmetric grid at near field
2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
- Full-Field Sonic Boom Simulation in Real Atmosphere 15
2.Numerical method
x/L
y/L
0
1100 (NWM)
800 (LBM)
Computational model
Uniform atmosphere
Real atmosphere
1
x 0
y
z
r θ
Flow
Front shock wave Rear shock wave
B1
B2
B4
B3
① Uniform flow conditions are set
in sector including B1 to B4
② Numerical Fluxes are calculated
③ SC is derived as ∂Q/ ∂t = 0
④ SC = const. in normal calculation
CG SS
z
G
y
F
x
E
t
Q
How to calculate SC
Setup of computational grid
Setup of correction term, Sc
Three dimensional Euler analysis
Move of computational domain
Grid angles are same as shock angles No
Yes
r ≦ rmax
Yes
No
End
Start
2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
- Full-Field Sonic Boom Simulation in Real Atmosphere 16
Model
Closeuup
rmax/L = 1100(NWM),800(LBM)
2.Numerical method 2.1 Numerical model 2.5 Computational grid 2.2 Numerical condition 2.6 Computational procedure 2.3 Atmospheric model 2.7 Overall view of 3D grid 2.4 Governing equation
Flow
- Full-Field Sonic Boom Simulation in Real Atmosphere 17
Pressure rise : Δp [Pa]
Altitude : h [km]
3.1 Pressure rise
3.2 Pressure waveform(r/L = 1)
3.3 Pressure waveform(h = 0.5 km)
3.4 Closeup of front shock wave
3.5 Maximum pressure rise
Parameter
3.Numerical results
- Full-Field Sonic Boom Simulation in Real Atmosphere 18
Δp max [Pa]
・ NWM : Compression waves arise behind front shock wave
・ LBM : Fluctuations are suppressed behind front shock wave
・ The other configuration of flow field is same in both cases
Pressure rise distribution
3.Numerical results
NWM LBM
Δp max [Pa]
3.1 Pressure rise 3.4 Closeup of front shock 3.2 Pre waveform(r/L=1) 3.5 Max. pressure rise 3.3 Pre waveform(h=0.5km)
NWM LBM
- Full-Field Sonic Boom Simulation in Real Atmosphere
-4
-3
-2
-1
0
1
2
3
-10 0 10 20 30 40
Pre
ssu
re R
ise,
kP
a
Relative Time, ms
Grid Points:171×76
Grid Points:341×151
-4
-3
-2
-1
0
1
2
3
-10 0 10 20 30 40
Pre
ssu
re R
ise,
kP
a
Relative Time, ms
Grid Points:231×76
Grid Points:461×151
19
・ Difference of waveform behind front shock wave
・ Max. pressure rise : 2.5 % (NWM)、0.005 % (LBM)
Grid convergence is adequate to validate sonic boom intensity
Pressure waveform(r/L = 1)
3.Numerical results
NWM LBM
3.1 Pressure rise 3.4 Closeup of front shock 3.2 Pre waveform(r/L=1) 3.5 Max. pressure rise 3.3 Pre waveform(h=0.5km)
- Full-Field Sonic Boom Simulation in Real Atmosphere
-30
-20
-10
0
10
20
30
-10 0 10 20 30 40 50
Pre
ssu
re R
ise,
Pa
Relative Time, ms
CFD (w/o fin)
WPM (w/o fin)
Flight test (w/ fin)
-30
-20
-10
0
10
20
30
-10 0 10 20 30 40 50
Pre
ssu
re R
ise,
Pa
Relative Time, ms
CFD (w/o fin)
WPM (w/o fin)
Flight test (w/ fin)
20
・ NWM : Shape of waveform is almost same in all results
・ LBM : Not N-wave but trapezoid at front shock wave
S-G-D method is effective to reduce sonic boom intensity
Pressure waveform(h = 0.5 km, θ = 0 deg)
3.Numerical results
NWM LBM
3.1 Pressure rise 3.4 Closeup of front shock 3.2 Pre waveform(r/L=1) 3.5 Max. pressure rise 3.3 Pre waveform(h=0.5km)
- Full-Field Sonic Boom Simulation in Real Atmosphere
-5
0
5
10
15
20
25
30
-0.5 0.0 0.5 1.0 1.5
Pre
ssu
re R
ise,
Pa
Relative Time, ms
CFD (w/o fin)
WPM (w/o fin)
Flight test (w/ fin)-5
0
5
10
15
20
25
30
-0.5 0.0 0.5 1.0 1.5
Pre
ssu
re R
ise,
Pa
Relative Time, ms
CFD (w/o fin)
WPM (w/o fin)
Flight test (w/ fin)
21
・ Difference of Δpmax in CFD and WPM : Less than 5 % in both cases
Full-field simulation is feasible to evaluate sonic boom
・ Difference of Δpmax in CFD and Flight test : 6.3 %(NWM),0.03 %(LBM)
Closeup of front shock wave(h = 0.5 km)
3.Numerical results
NWM LBM
3.1 Pressure rise 3.4 Closeup of front shock 3.2 Pre waveform(r/L=1) 3.5 Max. pressure rise 3.3 Pre waveform(h=0.5km)
- Full-Field Sonic Boom Simulation in Real Atmosphere 22
・ Attenuation : Different according to direction of propagation
Effect of atmos. pressure、Convergence effect (by temperature)
・ Max. pressure in LBM is lower than that in NWM all over region
・ Nature of sonic boom propagation is the same in CFD and WPM
Maximum pressure rise(Front shock wave)
3.Numerical results
NWM LBM
0
100
200
300
400
0 1 2 3 4 5 6 7
Pre
ssu
re R
ise,
Pa
Altitude, km
CFD (NWM w/o fin)
WPM (NWM w/o fin)
CFD (LBM w/o fin)
WPM (LBM w/o fin)
Δp max [Pa]
3.1 Pressure rise 3.4 Closeup of front shock 3.2 Pre waveform(r/L=1) 3.5 Max. pressure rise 3.3 Pre waveform(h=0.5km)
Δp max [Pa]
θ = 0 deg
- Full-Field Sonic Boom Simulation in Real Atmosphere 23
1. Nature of sonic boom propagation obtained by full-
field simulation is in good agreement with that by
waveform parameter method
2. Accuracy of full-field simulation is same level of
waveform parameter method
3. Sonic boom intensities at front shock wave obtained
by full-field simulation conform to flight test results
4.Conclusions
- Full-Field Sonic Boom Simulation in Real Atmosphere 24
5.Future plan
・ Full-field simulation is effective to predict sonic boom ・ Full-field simulation can be conducted by rigorous
model based on real physical phenomena
・ Unsteady nature
・ Ground effect
・ Molecular relaxation
・ Thermochemical nonequilibrium and etc.
Full-field sonic boom simulation becomes powerful
tool as accurate evaluation method in the future