Post on 13-Mar-2018
Case 3.1Turbulent Flow over a 2D Multi-Element Airfoil
Summary
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 1/11
The case
Turbulent Flow over a 2D Multi-Element AirfoilM∞ = 0.2α = 16o
Re = 9 × 106
Fully turbulentOur farfield distance is at least 50c
Turbulent working variable contours
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 2/11
The codes
MITDG, SA turbulence model
Farfield 60000c away
UMichDG, SA turbulence model
Farfield 50c away
BergamoDG, k − ω turbulence model
Farfield 50c(?) away
WyomingDG, SA turbulence model
Farfield 120c away
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 3/11
Different reference values
Different farfield boundary locationsDifferent turbulence modelsDifferent parameters (Prandtl number, dynamic viscosity)Numerical errors ...
Group cd clMIT 0.047 4.17UMich 0.054 4.12Bergamo 0.051 4.13Wyoming 0.057 4.13
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 4/11
cd convergence with DOF
10−3
10−2
10−6
10−5
10−4
10−3
10−2
10−1
100
p = 1
|dra
g c
oeffic
ient err
or|
1/sqrt(ndof)
MIT
UMich
Bergano
Wyoming
10−3
10−2
10−6
10−5
10−4
10−3
10−2
10−1
100
p = 2
|dra
g c
oeffic
ient err
or|
1/sqrt(ndof)
MIT
UMich
Bergano
Wyoming
10−3
10−2
10−6
10−5
10−4
10−3
10−2
10−1
100
p = 3
|dra
g c
oeffic
ient err
or|
1/sqrt(ndof)
MIT
UMich
Bergano
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 5/11
cd convergence with WU
102
103
104
105
10−6
10−5
10−4
10−3
10−2
10−1
100
p = 1
|dra
g c
oe
ffic
ien
t e
rro
r|
Work units
MIT
UMich
Bergano
Wyoming
102
103
104
105
10−6
10−5
10−4
10−3
10−2
10−1
100
p = 2
|dra
g c
oe
ffic
ien
t e
rro
r|
Work units
MIT
UMich
Bergano
Wyoming
102
103
104
105
10−6
10−5
10−4
10−3
10−2
10−1
100
p = 3
|dra
g c
oe
ffic
ien
t e
rro
r|Work units
MIT
UMich
Bergano
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 6/11
cl convergence with DOF
10−3
10−2
10−4
10−3
10−2
10−1
100
p = 1
|lift coeffic
ient err
or|
1/sqrt(ndof)
MIT
UMich
Bergano
Wyoming
10−3
10−2
10−4
10−3
10−2
10−1
100
p = 2
|lift coeffic
ient err
or|
1/sqrt(ndof)
MIT
UMich
Bergano
Wyoming
10−3
10−2
10−4
10−3
10−2
10−1
100
p = 3
|lift coeffic
ient err
or|
1/sqrt(ndof)
MIT
UMich
Bergano
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 7/11
cl convergence with WU
102
103
104
105
10−4
10−3
10−2
10−1
100
p = 1
|lift
co
eff
icie
nt
err
or|
Work units
MIT
UMich
Bergano
Wyoming
102
103
104
105
10−4
10−3
10−2
10−1
100
p = 2
|lift
co
eff
icie
nt
err
or|
Work units
MIT
UMich
Bergano
Wyoming
102
103
104
105
10−4
10−3
10−2
10−1
100
p = 3
|lift
co
eff
icie
nt
err
or|
Work units
MIT
UMich
Bergano
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 8/11
Pressure coefficient distribution
Obtained from high-accuracy/reference solutions
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−2
0
2
4
6
8
10
12
x/c
−c
p (
pre
ssu
re c
oe
ff.)
MIT
UMich
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 9/11
Skin-friction coefficient distribution
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−0.04
−0.02
0
0.02
0.04
0.06
x/c
cf (
skin
frictio
n c
oe
ff.)
MIT
UMich
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 10/11
|Skin-friction coefficient| distribution
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−0.02
0
0.02
0.04
0.06
0.08
x/c
cf (
skin
frictio
n c
oe
ff.)
MIT
UMich
Wyoming
1st International Workshop on High-Order CFD Methods, January 7-8, Nashville, TN C2.2 11/11