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