Post on 20-Apr-2015
Dr. Jubaraj Sahu,Aerodynamics BranchU.S. Army Research Laboratory
24th International Symposium on BallisticsNew Orleans, Louisiana22 – 26 September, 2008
Numerical Computations of Dynamic Numerical Computations of Dynamic PitchPitch--Damping Derivatives using Damping Derivatives using TimeTime--Accurate CFD TechniquesAccurate CFD Techniques
Projectile AerodynamicsProjectile Aerodynamics
lWind Tunnel testingl Actual flight testing
t Experimental facilities (Aero Range, Transonic Range)t Measure the positions and orientations; get Aero from 6-DOF fits
l Empirical codes (AP, DATCOM, PRODAS etc.) l Computational Fluid Dynamics (CFD)
t Steady-State Aerodynamics
t Unsteady Aerodynamics for Magnus, Roll Damping, Pitch Damping using unsteady rolling and imposed pitching motions (Virtual Wind-Tunnel Method)
l CFD and 6-DOF Rigid Body Dynamics Coupling for “Virtual Fly-Outs” t Simulate actual free flight (integrated unsteady aero/flight dynamics)
t Extraction of aerodynamic coefficients (both static and dynamic) from virtual fly-outs
t Easily extended for computation of dynamic pitch damping moment coefficient using imposed pitching motion– a special case of the virtual fly-out procedure t Roll damping and Magnus moment coefficients also are obtained from time-accurate computations of rolling motion, inherently an integral part of the virtual fly-out method
• Measures projectile orientation and position only
• Pitch, Roll, Yaw• X, Y, Z• 6DOF fit of range data• Limited visualization at a few stations• Aerodynamic coefficients determined• Characterize observed flight dynamics
Digital Virtual Aerodynamic Range
• Computes entire projectile state• Pitch, Roll, Yaw• X, Y, Z• Linear velocities• Pitch, Roll, and Yaw Rates • Unlimited flow visualization• Integrated Aerodynamics and Flight
Dynamics• Predictive capability for new geometries• Outputs wake and pressure contours
Role of HPC in the Development of the Digital Virtual Aerodynamic Range
Aerodynamics Experimental Facility
Multidisciplinary Computational Multidisciplinary Computational TechniqueTechnique
l 3-D Unsteady Navier-Stokes equationsl Higher order turbulence modeling including hybrid RANS/LESl Dual Time-Stepping for transient flow computations
l Two time-stepsl First (outer) global or physical step –usually set to 1/100th of the period of oscillationl Second (inner) step – 5 to 10 inner iterations
l Grid Motion and BC:l Grid moves and rotates as the projectile moves and rotatesl Free stream is preserved for arbitrary mesh and arbitrary mesh velocity
l 6-DOF equations solved at every CFD time-step
l CFD provides aerodynamic forces and moments
l 6-DOF provides the response of the body to the forces and moments
l The response is converted to translational and rotational accelerations
l Integrate the accelerations to obtain translational and rotational velocities
l Integrate once more to obtain linear position and angular orientations
l 6-DOF uses quaternions to define angular orientations
l From the dynamic response, grid point locations and velocities are set
CFD Computational Technique CFD/RBD COUPLING PROCEDURE
TimeTime--Accurate CFD ProceduresAccurate CFD Procedures
STEP 1:“Steady-state” modeNo translation motion
STEP 2:“Uncoupled” mode (Rolling Motion)
Add rotational component (spin, p)
Compute for a few spin cycles until solution converges
STEP 2: “Uncoupled” mode (Pitching Motion)Add the other rotational component (q)
i.e. impose pitching motionPitching motion can be sinusoidal
STEP 1:“Steady-state” modeGrid velocities account only for
translational motionInitial conditions also include the
angular orientations
STEP 2:“Uncoupled” mode (Kinematics)
Add rotational component in X (spin, p)
Compute for a few spin cycles until solution converges
STEP 3: “Coupled mode”Add the other rotational components
(q and r)Full dynamic calculations
Complete Virtual Fly-Out Procedure
Time-Accurate CFD Procedure for Dynamic Derivatives
Virtual Fly-out of a Finned ProjectileInitial Velocity, Mach = 3 (Supersonic)
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
Range, m
Z-C
oord
, m
Experimental DataCFDCFD (Muz)
Z-distance
6-DOF system
φ
θψ
IKr
IJr
Y Z
X
-8.00-7.00-6.00-5.00-4.00-3.00-2.00-1.000.001.002.003.004.005.006.007.008.00
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
Range, m
Thet
a, d
eg
Experimental Data
CFD
Computed positions and orientations (Euler angles) of the projectile match very well with the data measured in actual free flight tests.
Another Example: Spinning ProjectileInitial Mach = 0.4 (Subsonic Flight)
Z
X
Y
Virtual fly-out technique computes the trajectory of an in-flight spinning projectile; computed results match well with the flight test data
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.0 10.0 20.0 30.0 40.0 50.0 60.0
Range, m
Z-C
oo
rd, m
ARFDAS FitExperimental DataCFDCFD (SM_DT)
Z-distance
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
-10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0
Psi, deg
Thet
a-FP
, deg
Experiment
CFD
Virtual Fly-Out of a Spinning ProjectileInitial Mach = 1.1 (Transonic Flight)
Virtual fly-out technique computes the trajectory of an in-flight spinning projectile; computed results match well with the flight test data.
Z-distance
Z
X
Y
Extraction of Aerodynamic Coefficients from Virtual Fly-Out Simulations
Spinning Projectile
Different Approaches:
1. Aerodynamic coefficients extracted from CFD/RBD virtual fly-out solutions using range reduction software (ARFDAS, for example).
2. PACE - Simple fitting procedure that require a set of short time-histories (virtual fly-outs) at different Mach numbers.
Extraction of All Aerodynamic Coefficients
Virtual fly-outs simulations require only the total aerodynamic forces and moments to fly the projectile.
How do we extract the aerodynamic force and moment coefficients from the virtual fly-out simulations? How good are they?
Pitch-Damping Moment Coeff.
ARFDAS Fit of CFD Generated data Initial M = 1.1
Euler roll angleY-distance
1. Aerodynamic coefficients extracted from CFD using range reduction software, ARFDAS using the virtual fly-out solutions
2. Position (x,y,z) and the orientation (three Euler angles) of the projectile, obtained from the virtual fly-out simulations were provided as input to ARFDAS. Same procedure is used for actual flight measured data.
3.62
3.64
3.66
3.68
3.70
3.72
3.74
0 10 20 30 40 50 60 70 80
X m
Y vs X
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80
X m
Psi vs X
Extracted force and moment coefficients (static and dynamic) from
virtual fly-out simulation
Data Source
Zero-Yaw Axial Force
Coeff.,
0DC
Normal Force Coeff. Deriv.,
αNC
Pitching Moment Coeff. Deriv,
αmC
Pitch Damping Moment Coeff.,
Cmq
Magnus moment Coeff. Deriv.,
αpnC
Roll Damping Moment Coeff.,
lpC
Spark Range
0.359 2.081 4.209 -25.3 1.05 -0.019
CFD 0.335 2.362 4.283 -22.9 0.93 -0.019
Validate using separate unsteady CFD
(Virtual wind tunnel method)
Aerodynamic coefficients extracted from the virtual fly-out method matches very well with those obtained from free flight tests.
Pitch Damping Moment
)C + C( Vd q d SV
21 = MomentDamping Pitch mm
2q α
ρ&
2
)sin(0 tm ωααα +=
Pitching motion imposed:
Cmq = pitch damping moment coefficient due to q= pitch damping moment coefficient due to Cmα& α&
Here,
αmα0α
ω
= instantaneous angle of attack= mean angle of attack= pitch amplitude= pitch frequency, related to reduced
frequency (k =qd/2V)
Virtual wind tunnel method (Imposed pitching motion)
Time-Histories of Normal Force and Pitching Moment coefficients
Mach = 1.1α0 = 1.0, k = 0.1
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50
α (degrees)
C N
CFD - CY1
CFD - CY2
+q
-q
-0.10
-0.05
0.00
0.05
0.10
-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50
α (degrees)C
M
CFD - CY1
CFD - CY2
+q-q
Normal force Pitching moment
Pitch damping moment is obtained directly from the time-history plot of the pitching moment coefficient resulting from the imposed pitching motion.
Extracted force and moment coefficients from virtual fly-out
ComputedCMq= -24.0 using virtual wind-tunnel approach
Pitch damping moment extracted from the virtual fly-out method matches very well with that obtained by a separate unsteady CFD approach with prescribed pitching motion.
Data Source
Zero-Yaw Axial Force
Coeff.,
0DC
Normal Force Coeff. Deriv.,
αNC
Pitching Moment Coeff. Deriv,
αmC
Pitch Damping Moment Coeff.,
Cmq
Magnus moment Coeff. Deriv.,
αpnC
Roll Damping Moment Coeff.,
lpC
Spark Range
0.359 2.081 4.209 -25.3 1.05 -0.019
CFD 0.335 2.362 4.283 -22.9 0.93 -0.019
Extraction of Aerodynamic Coefficients from Virtual Fly-Out Simulations
Finned Projectile
Virtual Fly-out of a Finned ProjectileInitial Velocity, Mach = 3 (Supersonic)
ARFDAS Fit of CFD Generated data Initial M = 3.0
Euler roll angleZ-distance
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 10 20 30 40 50 60 70 80 90 100
Range, m
Z, d
eg
CFDARFDAS ResultARFDAS Data Input
-1000
0
1000
2000
3000
4000
5000
0 10 20 30 40 50 60 70 80 90 100
Range, m
Psi,
deg
CFDARFDAS ResultARFDAS Data Input
1. Aerodynamic coefficients extracted from CFD using range reduction software, ARFDAS using the virtual fly-out solutions
2. Position (x,y,z) and the orientation (three Euler angles) of the projectile, obtained from the virtual fly-out simulations, were provided as input to ARFDAS. Same procedure is used for actual flight measured data.
Extracted Aerodynamic Coefficientsfrom Virtual Fly-Out Simulation
DataSource
Mach No. CXo CNa Cma Cmq Clp
SparkRange 3.0 0.221 5.83 -12.60 -196 -2.71
CFD 3.0 0.253 5.88 -12.46 -172 -3.24
Pitch-Damping Moment Coefficient
Time-history of the Pitching Moment with Angle of Attack
Mach = 3.0
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Alpha (degrees)
Cm
CFD - CY1
CFD - CY2
Virtual Wind Tunnel Method
Pitch damping moment is obtained directly from the time-history plot of the pitching moment coefficient resulting from the imposed pitching motion.
Computed Pitch-Damping MomentCoefficient as a function of Mach number
Ø Computed pitch-damping moment coefficients match fairly well with the dataobtained from free flight tests.
Ø Almost identical prediction by both virtual fly-out and virtual wind-tunnel techniques.
-800
-700
-600
-500
-400
-300
-200
-100
0
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
Mach Number
Pitc
h D
ampi
ng M
omen
t Coe
ffic
ient
, Cm
q
AR Test - Single FitAR Test - Multiple FitCFD (virtual wind-tunnel)CFD (virtual fly-out)
Concluding Remarks
l Multidisciplinary CFD/Rigid Body Dynamics Coupling for Virtual Fly-Outs
Ø Integrated unsteady aerodynamics and flight dynamics
ØAll aerodynamic coefficients (static and dynamic) can be easily extracted from the same virtual fly-out solution
ØTechnique easily reduces to the virtual wind tunnel approach for computation of dynamic pitch damping derivatives
l Aerodynamic coefficients extracted (both static and dynamic) match fairly well with the data obtained from free flight tests
l Both virtual fly-out and virtual wind-tunnel methods essentially predict the same dynamic pitch damping moment coefficients