validation test cases
2D steady
cylinder
cylinder
3D steady
sphere
sphere
2D steady
NACA0012 airfoil
NACA0012 airfoil
2D steady
NACA63 mean line
NACA63 mean line
3D steady
elliptic wing
elliptic wing
2D unsteady
oscillating flat plate
oscillating flat plate
2D unsteady
oscillating airfoil
oscillating airfoil
3D unsteady
rotor hovering
rotor hovering
3D unsteady
VAWT
VAWT
3D unsteady
NASA SR2 propeller
NASA SR2 propeller
3D unsteady
tiltrotor
tiltrotor
3D steady
light aircraft
light aircraft
3D steady
internal flow
internal flow
3D unsteady
helicopter
helicopter
3D steady
HiLiftPW-1
HiLiftPW-1
3D steady
HiLiftPW-2
HiLiftPW-2
2D steady test case: cylinder - validation for thick non-lifting bodies
Comparison with the analytical solution: $ C_p = 1-(2sin \theta)^2 $
3D model (high aspect ratio)
2D section pressure coefficient
3D steady test case: sphere - validation for thick non-lifting bodies with both quadrilateral and triangular mesh
Comparison with the analytical solution: $ C_p = 1-( {3/\!2} \, sin \theta ) ^2 $
3D model (quad mesh)
3D model (tria mesh)
2D section pressure coefficient
2D steady test case: NACA0012 airfoil - validation of the “Dirichlet” boundary condition for thick lifting airfoils
Comparison with the NACA method (2D analytical solution) at the same 2D lift coefficient
in order to avoid the 3D downwash effect (finite wing, aspect ratio = 24).
solution @ 0deg
solution @ 12deg
2D section pressure coefficient
Comparison with the analytical solution (NACA method) and with experimental data (NACA wind tunnel test @ Re=9.e+6 , M=0.15).
NACA theory 2D Cl-AoA correlation: $ \alpha_{2D} \approx \cfrac{Cl_{2D}}{2\pi (1+ k\tau)} $
PaMS results "2D/3D" correction: $ \alpha_{2D} \approx \cfrac{\alpha_{3D}}{1+2/ AR(1+k\tau)} $
NACA theory 2D Cl-AoA correlation: $ \alpha_{2D} \approx \cfrac{Cl_{2D}}{2\pi (1+ k\tau)} $
PaMS results "2D/3D" correction: $ \alpha_{2D} \approx \cfrac{\alpha_{3D}}{1+2/ AR(1+k\tau)} $
lift coefficient vs angle of attack
lift coefficient vs angle of attack
2D steady test case: NACA63 mean line - validation of the “Neumann” boundary condition for thin lifting airfoil
Comparison with the NACA method (analytical solution) at the same "ideal" angle of attack (1.6deg).
PaMS results "2D/3D" correction: $ Cp_{2D} \approx (1 / 2AR)Cp_{3D} $ , $ Cl_{2D} \approx (1 / 2AR)Cl_{3D} $ (finite wing, aspect ratio = 24)
PaMS results "2D/3D" correction: $ Cp_{2D} \approx (1 / 2AR)Cp_{3D} $ , $ Cl_{2D} \approx (1 / 2AR)Cl_{3D} $ (finite wing, aspect ratio = 24)
solution @ 1.6 deg
2D section delta (lower-upper) pressure coefficient
3D steady test case: elliptic wing - validation for lifting wing
Comparison with the Prandtl lifting line theory (analytical solution):
$ c\,CL=c\,2\pi\, \left( \alpha \cfrac{CL}{\pi AR} \right) $
(wing aspect ratio = 10, section airfoil= NACA0009)
(wing aspect ratio = 10, section airfoil= NACA0009)
solution @ 16deg
lift coefficient per unit span
Comparison with the Prandtl lifting line theory (analytical solution):
$ CL= \cfrac{2\pi\alpha}{1+ 2/AR} $ , $ CD_i= \cfrac{CL^2}{\pi AR} $
(wing aspect ratio = 10, section airfoil= NACA0009)
(wing aspect ratio = 10, section airfoil= NACA0009)
lift coefficient vs angle of attack
induced drag vs angle of attack
Comparison of 3 different wake models in order to verify wake length and doublet panels / vortons conversion.
near wake
doublet wake
vorton wake
lift coefficient time history @ 16deg
2D unsteady test case: oscillating flat plate - validation for oscillating thin lifting airfoil
Comparison with the Theodorsen theory (analytical solution).
PaMS results "2D/3D" correction: $ Cl_{2D} \approx \left( 1+2/AR \right)\,Cl_{3D} $ (finite wing, aspect ratio = 24).
PaMS results "2D/3D" correction: $ Cl_{2D} \approx \left( 1+2/AR \right)\,Cl_{3D} $ (finite wing, aspect ratio = 24).
pitching motion: $ \alpha(t)=10°\sin \left( \omega t + \pi / 2 \right) $
heaving motion: $ h(t)=0.25 \left[ m \right] \sin \left( \omega t \right) $
frquency: $ \omega =0.3925 \left[ rad / s \right] $
reduced frquency: $ \omega_r = \cfrac{\omega c}{2 V_{\inf}} = 0.19625 $
lift coefficient time history
2D unsteady test case: oscillating airfoil - validation for oscillating thick lifting airfoil
Comparison with the analytical solution (Theodorsen theory) and the experimental data (NASA wind tunnel test, M=0.3, Re=3.9e+6, NACA0012 airfoil)
Theodorsen theory thickness correction: $ Cl_{\tau \neq 0} = \left( 1+k\tau\right)Cl_{\tau = 0} \approx 1.09 Cl_{\tau = 0} $
Exp data Prandtl-Glauert compressibility correction: $ Cl_{M=0}=\sqrt{1-M^2}\, Cl_{M\neq0} $
PaMS results "2D/3D" correction: $ Cl_{2D}\approx \left( 1+2/AR \, \left( 1+k \tau \right) \, Cl_{3D} \right) $ (finite wing, aspect ratio = 24)
pitching motion: $ \alpha(t)=2.64°+10.16°\sin \left( \omega t + \pi / 2 \right) $
frquency: $ \omega =0.198 \left[ rad / s \right] $
reduced frquency: $ \omega_r = \cfrac{\omega c}{2 V_{\inf}} = 0.099 $
lift coefficient time history
Aerodynamic interference
lift coefficient time history
3D unsteady test case: rotor hovering - validation for wake models
Comparison with experimental data (NASA wind tunnel test - M=0.46, Retip=2.5e+6).
(blade pitch angle = 8deg, rotational speed = 1250 rpm, static CT = 0.0046)
(blade pitch angle = 8deg, rotational speed = 1250 rpm, static CT = 0.0046)
experimental model
fully free wake model
no roll-up wake model
thrust coefficient time history
tip vortex position
blade span lift coefficient
3D unsteady test case: Vertical Axis Wind Turbine - validation for lifting wing and wake-body interference
Comparison with experimental data (SANDIA towing tank test – M=0, Re= 6.7e+4).
Tip Speed Ratio ( $ TSR = V_{\inf} / \omega R $ ): 5.1, 7.6
Tip Speed Ratio ( $ TSR = V_{\inf} / \omega R $ ): 5.1, 7.6
experimental and numerical test model
vorton wake - blade interference
TSR = 5.1
tangential force time history
1 revolution tangential force
TSR = 5.1
normal force time history
1 revolution normal force
TSR = 7.6
tangential force time history
1 revolution tangential force
TSR = 7.6
normal force time history
1 revolution normal force
3D unsteady test case: NASA SR2 propeller - validation for wing-propeller configuration
Comparison with experimental data (NASA wind tunnel test – M=0.7, Re=5.0e+6) at the same propeller
thrust coefficient (CT=0.245) and at zero angle of attack
experimental and numerical (far wake, near wake) model
pressure coefficient (upwash side)
pressure coefficient (downwash side)
spanwise section Cl
3D unsteady test case: tiltrotor - validation for wing-propeller configuration @ angle of attack up to 90deg
Comparison with experimental data (NACA wind tunnel test – M=0, Mtip=0.58, ReMAC=0.8e+6
at the same propellers thrust (100.5 N).
experimental and numerical model
propeller pitching moment and normal force vs angle of attack
longitudinal and lift model force vs angle of attack
3D steady test case: light aircraft - validation for wing-fuselage configuration
Comparison with experimental data (Partenavia wind tunnel test – M=0, Re=7.4e+5).
PaMS results corrected with the experimental drag coefficient at zero lift.
PaMS results corrected with the experimental drag coefficient at zero lift.
experimental and numerical test model
darg coefficient vs lift coefficient
3D steady test case: internal flow - validation of the boundary conditions for internal flows
Comparison with a numerical solution (Fluent - finite volume Euler solver) with the same surface grid.
bend pipe
pressure coefficient (sym plane)
bend pipe with internal sphere
pressure coefficient (sym plane)
3D unsteady test case: helicopter - validation for the aerodynamic interaction between a helicopter rotor and an airframe
Comparison with experimental data (US Army Research - 6deg nose down, speed 16 m/s).
experimental and numerical models
time history thrust coefficient
time history pressure coefficient
3D steady test case: High Lift Prediction Workshop 1 (HiLiftPW-1) - 1st AIAA CFD High Lift Prediction Workshop - validation for slat-main-flap "Config. 1"
Comparison with experimental data (NASA LaRC wind tunnel test – M=0.2, Re=4.3e+6) from -2.6deg to 23.3deg.
experimental and numerical models (numerical model without fuselage)
Comparison with experimental data (NASA LaRC wind tunnel test – M=0.2, Re=4.3e+6) from -2.6deg to 23.3deg.
lift, drag (PaMS induced drag only) and moment coefficient vs angle of attack
result @ 10.922deg
pressure coefficient distribution @ 17% span
result @ 10.922deg
pressure coefficient distribution @ 41% span
result @ 10.922deg
pressure coefficient distribution @ 65% span
result @ 10.922deg
pressure coefficient distribution @ 85% span
result @ 10.922deg
pressure coefficient distribution @ 95% span
3D steady test case: High Lift Prediction Workshop 2 (HiLiftPW-2) - 2nd AIAA CFD High Lift Prediction Workshop - validation for wing-body DLR F11 "Config. 4"
Comparison with experimental data (Airbus B-LSWT wind tunnel test – M=0.176, Re=15.1e+6) from -3.2deg to 24.2deg.
experimental and numerical models
lift, drag (PaMS induced drag only) and moment coefficient vs angle of attack
