Aftosmis, Michael J.

Nemec, Marian

Spurlock, Wade M.

English

NASA Technical Reports Server

Cartesian Mesh Simulations for the 3rd AIAA  
Sonic Boom Prediction Workshop
AIAA Sci Tech Forum and Exposition  
Orlando, FL
04-05 January 2020
Wade M. Spurlock
Science and Technology Corp.  
Computational Aerosciences Branch  
Moﬀett Field, CA 94035  
wade.m.spurlock@nasa.gov
Michael J. Aftosmis
Computational Aerosciences Branch  
NASA Ames Research Center  
Moﬀett Field, CA 94035  
michael.aftosmis@nasa.gov
Marian Nemec
Computational Aerosciences Branch  
NASA Ames Research Center  
Moﬀett Field, CA 94035  
marian.nemec@nasa.gov
1
https://ntrs.nasa.gov/search.jsp?R=20200000440 2020-03-11T12:39:20+00:00Z
• Cases
• Biconvex - shock/plume interaction
• C608 - full aircraft geometry
• Flow solver & computational resources
• Geometry & grids
• Numerical convergence
• Results
• Challenges
• Conclusions
2020.01.04
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Outline
2
Wind tunnel model setup to examine shock/plume interaction
•
• Extract pressure signal at radial location r = 15 in (0.38 m)
• Model is approximately 22 in (0.56 m) long
Conditions:
• M∞ = 1.6
• Power BC’s at plenum
pt  
p∞
= 8.0,
Tt  
T∞
= 1.768
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Biconvex
3
• Modified version of Low Boom Flight Demonstrator design iteration
• Full aircraft, complex geometry, multiple inflow/outflow BC’s
Conditions:
• M∞ = 1.4, Altitude h = 53,200ft
• Power BC’s at engine nozzle pt /p∞ = 10.0 , Tt /T∞ = 7.0
• Power BC’s at bypass nozzle pt /p∞ = 2.4 , Tt /T∞ = 2.0
• Engine fan inlet pb /p∞ = 2.6 (desired Mach 0.4 flow at engine fanface)
• Environmental Control System vent inlets pb /p∞ = 1.4 (desired Mach 0.35 flow at ECSinlets)
• Extract pressure signal at radial location L
• Model is approximately 1080 in (27.43 m) long
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C608
4
• Flow solver: Cart3D v1.5.5.3
• Steady, inviscid Euler equation solver
• Second-order upwind method
• Domain decomposition, highly scalable
• Multigrid acceleration (4 MG levels)
• 5-stage RK scheme, van Leer limiter
• Automatic meshing
• Multilevel Cartesian mesh with embedded cut-cell boundaries
• Unstructured surface triangulation with component tagging
• Output-driven mesh refinement
• Discrete adjoint solution and local error estimate
• Several diﬀerent adjoint functionals, including pressure signal Δp
• Computing platform
• NASA ARC Electra, 1 Skylake node (40 cores, Intel Xeon Gold 6148)
• Biconvex: 19.9 M cells, 40 min final flow solve, 32 min adaptive meshing (x3 sim’s)
• C608: 29.6 M cells, 60 min final flow solve, 53 min adaptive meshing (x19 sim’s)
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Cart3D Software
5
• Biconvex
• Created surface triangulation from STP and IGS files
• Diagonalized structured grid where possible
• Filled in planar and irregularly shaped areas with unstructured cells
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Geometry
6
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Geometry
• Biconvex
• Created surface triangulation from STP and IGS files
• Diagonalized structured grid where possible
• Filled in planar and irregularly shaped areas with unstructured cells
7
• Issues with leading edge and trailing edge at tip of airfoil
• Cleaned up geometry by projecting LE and TE onto plane of wing tip
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Geometry
tra
ilin
g
ed
ge
8
• C608
• Received unstructured surface triangulation from J. Jensen (NASA ARC)
• 494 k vertices, 987 k triangles
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Geometry
9
• Cartesian cut-cell volume mesh for inviscid flow solver
• Cart3D autoBoom - previous SBPW2 work
• Aligned with Mach angle (with tiny oﬀset to avoid sonic glitch)
• Roll the model geometry for diﬀerent oﬀ-track ɸ angles
• Separate simulation for each oﬀ-track ɸ  on 1 node, can berun simultaneously
• Tested diﬀerent cell aspect ratios in the propagation and spanwise directions
• Adjoint-driven mesh adaptation
• Line sensor at multiple body lengths away
• Objective function is integrated pressure Δp/p∞
• Final grid sizes for data submittal
• Biconvex: 4.5, 8.9, 19.9 million cells for coarse, medium, fine
• C608: 7.1, 14.2, 29.6 million cells for coarse, medium, fine
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Volume Mesh
10
• Adjoint-driven mesh adaptation
• Line sensor at multiple body lengths away
• Objective function is weighted integral of Δp/p∞
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Volume Mesh
Initial mesh
11
Mesh after adaptation (coarse mesh)
• Biconvex
• 550, 600, 700 iterations on coarse, medium, fine grids
• Submitted adapt cycles 05, 06, 07 (ran 2 more out to 09 to check)
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Numerical Convergence
1000 2000 4000 5000 60003000
MG cycles
-4
10 0
-3
10
-2
10
3
10
2
10
1
10
0
10
-1
10G
lo
ba
lR
es
id
ua
l
adapt cycle 00
12
01
02 03 04
05
06 07 08
09
• Biconvex
• 550, 600, 700 iterations on coarse, medium, fine grids
• Adapt cycles 05, 06, 07 (ran 2 more out to 09 to check)
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Numerical Convergence
kk k M M M  M M M M
325.5488.0729.71.3 2.2 4.4 8.7 19.430.8
107.26
10
8
10
7
10
Cells
0.02
0.03
0.04
0.05
Fu
nc
tio
na
l(
J H
)
6
10
7
10
Cells
-4
10
-3
10
10-2
-1
10
Er
ro
r
Error-Indicator, |η|
Error Bars  
Update, ⊗J
1000 2000 3000 4000 5000 6000
Multigrid Cycles
00
0.06
0.05
0.04
0.03
0.02
0.01Fu
nc
tio
na
l(
J H
)
/nobackup/wmspurlo/sbpw3/nearfield/biconvex/off_track_fullSpan/try02_boomSetup/phi000
maxRef = 14
Iterative Convergence
Wed Dec 18 17:06:00 2019
functional  
asymptotic, error 
bars bound J
Good iterative  
behavior
S
13
mooth error  
reduction
• Biconvex
• 550, 600, 700 iterations on coarse, medium, fine grids
• Solutions are well converged by adapt 05, 06, 07 cycles
• Richardson extrapolation used for error estimate
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Numerical Convergence
5 10 15 20 25 30 35 40
Distance along sensor
-0.080
0
-0.060
-0.040
-0.020
0.000
0.020
⊗p
/p
fine  
medium  
coarse
r = 15 in
0.040
5 10 15 20 25 30 35 40
Distance Along Sensor
-0.08
0
-0.06
-0.04
-0.02
0
0.02
0.04
⊗
p/
p ∞
Error Estimate High Confidence  Low Confidence
14
0 1000 3000 40002000
MG cycles
10-3
10-2
10
100
101
102
103
G
lo
ba
lR
es
id
ua
l
• C608
• 400, 500, 550 iterations on coarse, medium, fine grids
• Submitted adapt cycles 03, 04, 05 (ran 1 more out to 06 to check)
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Numerical Convergence
ɸ = 0°
15
adapt cycle 00
-1 01 02 03 04 05
06
• C608
• 400, 500, 550 iterations on coarse, medium, fine grids
• Adapt cycles 03, 04, 05 (ran 1 more out to 06 to check)
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Numerical Convergence
M M M M M M
M  
1.6 2.4 3.6 7.1 14.2 29.6 102.7
6
10
7
10
8
10
Cells
0.015
0.02
0.025
0.03
Fu
nc
tio
na
l(
J H
)
106 710
Cells
-4
10
10-3
-2
10
Er
ro
r
Error-Indicator, |η|
Error Bars  
Update, ⊗J
1000 30002000
Multigrid Cycles
0.03
0.025
0.02
0.015
0.01
0.005
00
Fu
nc
tio
na
l(
J H
)
/nobackup/wmspurlo/sbpw3/nearfield/c608/try04_2deg/phi000
maxRef = 11
Iterative Convergence
Mon Nov 25 17:13:42 2019
0.035
functional  
asymptotic, error 
bars bound J
Good iterative  
behavior
h error  
ction
16
Smoot  
redu
ɸ = 0°
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Numerical Convergence
5 10 15 20 25 30 35 40
Distance along sensor
-0.01000
-0.00750
-0.00500
-0.00250
0.00000
0.00250
0.00500
0.00750
⊗p
/p
fine  
medium  
coarse
h/L=3,
0.01000
• C608
• 400, 500, 550 iterations on coarse, medium, fine grids
• Solutions are well converged by adapt 03, 04, 05 cycles
• Richardson extrapolation used for error estimate
ɸ = 0° ɸ = 0°
0 5 10 15 20 25 30 35 40
Distance Along Sensor
-0.01
0.0075
0.005
0.0025
0
-0.0025
-0.005
-0.0075
⊗
p/
p ∞
Error Estimate
0.01
High Confidence  
Low Confidence
17
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Results: Biconvex
18
• Density contours
ɸ = 0°
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Results: Biconvex
19
• Density contours (zoomed in on plume-shock interaction region)
ɸ = 0°
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Results: Biconvex
• Pressure coeﬃcient contours
ɸ = 0°
20
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Results: Biconvex
15 20 25 30 35 40 45 50 55
Distance along sensor
-0.07
-0.05
-0.06
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
dp
 /
p
phi = 0
phi = 15
phi = 30
Pressure signal at r = 15 in
21
• Separate simulation run at oﬀ-track ɸ  every 10° (19total)
• Five line sensors at oﬀsets of Δɸ = [-4, -2, 0, +2, +4]
• Covers full half-cylinder 0 ≤ ɸ ≤ 180° in increments of 2°
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Results: C608
ɸ
22
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Results: C608
ɸ
0°
50°
3000 3500 5000 55004000 4500
Distance along sensor [in]
-0.025
-0.01
-0.015
-0.02
0.015
0.01
0.005
0
-0.005dp
 /
p
phi = 0
phi = 10
phi = 20
phi = 30
phi = 40
phi = 50
23
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Results: C608
ɸ
60°
3000 3500 5000 55004000 4500
Distance along sensor [in]
-0.025
-0.01
-0.015
-0.02
-0.005
0.015
0.01
0.005
120°
0
dp
 /
p
phi = 60
phi = 70
phi = 80
phi = 90
phi = 100
phi = 110
phi = 120
24
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Results: C608
ɸ 130°
180°
3000 3500 5000 55004000 4500
Distance along sensor [in]
-0.025
-0.01
-0.015
-0.02
0
-0.005
0.005
0.01
0.015
dp
 /
p
phi = 130
phi = 140
phi = 150
phi = 160
phi = 170
phi = 180
25
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Results: C608
26
• C608
• Getting outflow BC’s to correct desired Mach number
• Adjusted the back pressure
• Engine inlet from suggested 2.6 to 2.75
• ECS inlets from suggested 1.4 to 2.70
• Consistent closeouts are challenging
• Plume/shock is diﬃcult to capture
• Mesh coarsening farther back in plume can create spurious artifacts in  
pressure signal
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Challenges
27
• Complex geometry increases computational cost
• More features to resolve
• Must take pressure signal farther from body
• Adaptive meshing refines based on solution error and objective function
• Must routinely check for solution quality
• Numerical convergence and adjoint performance
• Grid sequencing with coarse, medium, fine grid pressure signal
• Comparison metrics for multiple oﬀ-track ɸ sim’s: mass flow through  
inflow/outflow boundaries, force & moment coeﬃcients
• Richardson extrapolation shows highest uncertainty in aft portion of signal,  
which is particularly challenging with propulsion and plumes
• Inviscid simulation can eﬀectively capture supersonic flow features of  
shocks, expansions, and coalescence
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Conclusions
28
• James Jensen for workshop C608 geometry
• Melissa Carter and Mike Park for organizing the workshop and for their  
correspondence on the nearfield cases
• ARMD Commercial Supersonic Technology Project for supporting this work
• NASA Advanced Supercomputing Division for computational resources
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Acknowledgements
29
2020.01.04
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Questions?


Cartesian Mesh Simulations for the 3rd AIAA Sonic Boom Prediction Workshop

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