American Institute of Aeronautics and Astronautics1

Thrust Vector Model and

Solid Rocket Motor Firing ValidationsDr. Erland Ørbekk1

Missile Products Division, Nammo Raufoss AS,

N-2831 Raufoss, Norway

Nomenclature

CFD Computational Fluid DynamicCoP Centre of PressureECB Electronic Control BoxECU Electronic Control UnitEoB End of BurnFW Flight WeightHTPB Hydroxyl Terminated PolyButadieneHW Heavy WeightJV Jet VaneJVTVC Jet Vane Thrust Vector ControlRM Rocket MotorSRM Solid Rocket MotorTVA Thrust Vector ActuationTVC Thrust Vector Control6-DOF Six Degree of Freedom

I. AbstractNammo Raufoss AS (Nammo) has several years of experience in design, development and production of different TVC systems for tactical applications.

A thrust vector model has been developed for analysis of rocket motor firings, both with movable nozzle and with jet vanes. The model simulates the commands given by the control section and outputs the thrust response in all thrust directions vs time. The actuator response is simulated and CFD solutions are utilized as input for the thrust model. The model is validated by several rocket motor firings at Nammo Raufoss. The paper will focus on the thrust vector model description and comparison with tests and firings at different motor conditioning temperatures.

The Nammo Raufoss thrust vector control (TVC) tool has been developed during our participation in the Norwegian Propulsion Technology Development Programme.

1 Director Engineering & Development, Missile Products Division, P-O- Box 162 Raufoss Norway, AIAA Member.

44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit21 - 23 July 2008, Hartford, CT

AIAA 2008-5055

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

American Institute of Aeronautics and Astronautics2

II. Introduction

Nammo Raufoss AS (Nammo) has several years of experience in design, development and production of TVC systems for tactical applications and for technology demonstrators. Thrust vector systems are tested and validated by rocket motor firings and a representative thrust vector cycle is often utilized in order to test TVC performance at several conditions vs time, i.e. pitch, yaw and roll at different motor pressures. Performance comparisons are done using a TVC simulation tool with the capability of reproducing the forces and moments in all directions.

This paper describes the thrust vector model developed for analysis of rocket motor firings, both with movable nozzle and with jet vanes. The thrust vector model simulates the commands given to the control section and outputs the thrust response in all directions vs time. The actuator response is simulated and CFD calculations are utilized as input for the thrust vector model. The TVC model is validated by several rocket motor firings at Nammo Raufoss, both movable nozzle and JV firings. The paper will focus on the JVTVC due to its complexity compared to movable nozzle systems.

III. TVC Model Description

A. Overview and brief description of model

The TVC model simulates thrust forces and moment forces at arbitrary motor conditioning temperatures and ambient pressures during the motor burn time. The TVC input is a pre-programmed (user defined) thrust deflection cycle, describing the individual JV positions vs time. This part of the tool represents the commands given by the missile computer. The thrust vector response at rocket motor level is calculated and can be transformed into the missile axis system etc.

The TVC model including different modules is shortly summarized as:

• The SRM module is a model of the theoretical thrust (FTHRUST) without jet vanes at arbitrary soak temperature and ambient pressure condition. This part can be based upon analyses and/or reference firingsat an arbitrary conditioning temperature.

• The TVA module defines the JV response at JV level with respect to angle position, velocity, acceleration and CoP as function of the commanded JV position.

• The TVC function computes the thrust forces and the moment forces at all axes. • A 4TH module that calculates mass, motor inertias and CoG is also included, but not shown as a part of this

paper

The solution algorithm is based upon a simple time stepping process and an outline of the model is seen in Figure 1.

American Institute of Aeronautics and Astronautics3

TVC ModelInput Output

Thrust, Fx (t)

Motor Cond. Temp.

Ambient pressure

δEXi

Propellant Data

Fx0, Fave, Isp,Itot

F0, Itot

Fx,Fy,Fz

Mx,My,Mz

JV Hinge Mom.

JV Aerodynamic Data

JV EoB Erosion Data

JV CoP Data

JV Commands, δcoi(t)

Actuator (ECB) Data

TVAActuatorModule

(Jet VaneDeflection effects)

••δEXi

δEXi

δEXi

•

SRMModule

(Theoretical thrust without JV)

TVC Performance

Module

(Thrust Forces and Moments)

Figure 1 Outline of TVC Model

B. Solid Rocket Motor Module

The motor ballistic input can be based upon analyses or test results at an arbitrary motor conditioning temperature. The SRM module recalculates the ballistic input performance to the desired motor conditioning (firing) temperature and ambient pressure which comply with the TVC test.

The calculation of thrust over the temperature range utilises the propellant temperature sensitivity and the change in delivered Isp, with motor conditioning temperature, is conserved.

The SRM module, which redefines a calculated thrust curve or a reference-firing curve to a user, specifiedtemperature is validated with several motor firings and comply very well with the measured action times and total impulses.

It should be noted that the reference ballistic curves for this report is based upon the same firing condition as utilised in the TVC firing condition, i.e. scaling is 1:1.

The motor mass, inertias and CoG are also calculated vs time, but are not included in the paper.

C. TVC Aerodynamic Coefficients

The JV aerodynamic performances are defined by CFD calculations representing the rocket motor with TVC at different conditions. The JV aerodynamic performance data are all defined at a reference pressure. The JV performance is characterized from 0° JV deflection to a maximum JV deflection. The maximum JV deflection is normally in the 20-30° region, a JV deflection of 25° is utilized as the maximum value in this paper.

The JV performances are in addition defined at different thrust conditions like pitch/yaw and roll. This since the nozzle exit cone pressure does have influence on the different forces. The wall pressure in the nozzle exit cone is characterized by a low pressure region and a high pressure region for pitch/yaw JV conditions. The effect will reduce the effective lateral thrust performance since the nozzle pressure force is in the opposite direction compared to the JV induced pressure force. The lateral thrust effect of nozzle damping is typically 5-10% for JV's integrated at the optimal position. The damping effect on roll is zero. This effect is implemented in the TVC model as Nozzle damping.

American Institute of Aeronautics and Astronautics4

A CFD calculation of a roll condition is shown in Figure 2 left and a CFD calculation of a yaw condition is shown inFigure 2 right, the high/low pressure region on the nozzle wall is easily seen.

Second order approximations for all aerodynamic constants are implemented. It should be noted that supersonic linear theory can be applied for the definition of JV lift and nozzle damping, i.e. first order approximation possiblefor simplification. The JV lift, nozzle damping and JV drag is at the reference pressure defined as:

)()( 012

2 tAAAALiftJV RREF ++= δδ)()( 01

22 tABBBDampNoz RREF ++= δδ

)()()(0 012

2 tACCCtDDragJV RREF +++= δδ

A typical example plot of the JV lift and nozzle damping is shown in Figure 3. A JV drag example is shown in Figure 4 left. The effect of JV erosion is included in the model by including the effect of increased JV zero drag and reduced (aerodynamic effective) JV area ratio. The JV drag is defined as a zero drag term, D0 increasing with JV erosion see Figure 4 right, and a second order alpha drag part which reduces with JV erosion.

The change in CoP with JV erosion is included for all moment definitions. The effect is normally very small compared to the characteristic lengths utilized in all moment calculations.

VEL: 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750Y X

Z

Figure 2 JVTVC CFD Calulations of Aerodynamic Forces

0.00

0.50

1.00

1.50

2.00

2.50

0 5 10 15 20 25JV Deflection Angle [deg]

(JV

Lift

For

ce)/

(Ref

eren

ce J

V L

ift)

[-]

JV Lift [-]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 5 10 15 20 25JV Deflection Angle [deg]

(Noz

zle

Dam

ping

)/(R

efer

ence

JV

Lift

) [-

]

Nozzle Damping

Figure 3 Left; JV lift. Right; Nozzle damping for pitch/yaw commands

American Institute of Aeronautics and Astronautics5

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25JV Deflection [°]

Indi

vidu

al J

V D

rag

[%]

JV Drag [%]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1Fraction of Motor Burn [-]

Indi

vidu

al J

V D

rag

[%]

JV Zero Drag [%]

Figure 4 Left; Individual JV drag as function of JV deflection, zero drag and alpha drag defined at initial motor burn. Right; Effect of JV Erosion on JV Zero Drag vs motor burn

D. Axis Definition

The JV numbering with JV deflection angle utilised in the model is defined below. The definitions are defined in accordance with Figure 5. Positive JV rotation is defined by clockwise rotation of the JV shaft with definition from top and inward direction, see arrows. The aerodynamic control of pitch, yaw and roll is defined as:

• Pitch: )(2

14321 δδδδη ++−−=

• Yaw: )(2

14321 δδδδζ −++−=

• Roll: )( 4321 δδδδξ ++++=

Figure 5 Definition of JV axis and JV deflection

American Institute of Aeronautics and Astronautics6

E. Actuator Model and Validation

The actuator model, i.e. which simulates the JV positions vs time, is generic and includes the electronic control unit (ECU) and the actuators which are connected to the JV's. The model can be adjusted by tuning of TVA/ECU model constants. The JV movements are defined as individual second-order systems represented by the following equation.

iiii cδδδωζδ

ω=++

••• 212

were

iδ = Individual actuator (JV) angular position

icδ = Individual actuator (JV) angular command

ω = Natural angular frequencyζ = Damping constant

with limit definitions for angular position, angular velocity and angular acceleration, i.e. saturation constants. The equations can be solved by applying a simple forward Euler integration scheme as presented below:

Angular acceleration:•−−

••

×××−−×= 112 2)( ti

ti

ti

ti c δωζδδωδ

Angular limitation:••••

≤ iti δδ (saturation value)

Angular speed: dtt

dtt

ti

ti ∫

−

•••

= δδ

Speed limitation:••

≤ iti δδ (saturation value)

Angular Position: dtt

dtt

ti

ti ∫

−

•

= δδ

Angular limitation: iti δδ ≤ (saturation value)

The integration scheme can be improved if needed by using higher order integration schemes, like RK45 scheme or similar. The TVA/ECU model constants for saturations and the natural angular frequency have to be defined. The only user input is the individual JV deflection command vs time. A JV cycle simulation with measurements of JV positions is shown as an example below in Figure 6. The simulation and comparison is made on a motor with 4 JV's, 2 out of the 4 JV's are shown as an example below. The simulation is in excellent agreement with the measured position data and the overshoot, see Figure 7 zoomed detail, is in excellent agreement with the measurements. The model is validated and is being used in several development programs at Nammo, both for JV applications and for movable nozzle applications.

American Institute of Aeronautics and Astronautics7

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Fraction of Time [-]

Def

lect

ion

Ang

le/M

ax C

omm

and

[-]

Dry Run: PreTestdex1_[deg]dco1_[deg]

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Fraction of Time [-]

Def

lect

ion

Ang

le/M

ax C

omm

and

[-]

Dry Run: PreTestdex3_[deg]dco3_[deg]

Figure 6 Simulation and measurement comparison of JV no 1,3. (dex1,3=JV1,3 simulation, dco1,3=JV1,3 command, Dry Run=JV1,3 measured position)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2

Fraction of Time [-]

Def

lect

ion

Ang

le/M

ax C

omm

and

[-]

Dry Run: PreTestdex1_[deg]dco1_[deg]

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2 0.25

Fraction of Time [-]

Def

lect

ion

Ang

le/M

ax C

omm

and

[-]

Dry Run: PreTestdex3_[deg]dco3_[deg]

Figure 7 Simulation and measurement comparison of JV no 1,3 zoomed details. (dex1,3=JV1,3 simulation, dco1,3=JV1,3 command, Dry Run=JV1,3 measured position)

F. TVC Forces and Moments

Thrust forces and moments are calculated in all 3 directions as function of the individual JV deflections, JV aerodynamic constants, JV erosion and motor thrust/pressure vs time. The response at thrust level is defined to be identical with the individual mechanical JV deflection, i.e. transfer function between mechanical JV deflection and thrust response is 1 to 1.

The main forces and moments are calculated at rocket motor level vs time as:

RREFTHRUST

ZPITCH

AFF)BBBAAA(

)BBBAAA(

)BBBAAA(

)BBBAAA(FF

*2/1*)/]()()(

)()(

)()(

)()([)(

0112

12041242

0112

12031232

0112

12021222

0112

120112

12

++−+++

++−+++

++−++−

++−++−=

δδδδ

δδδδ

δδδδ

δδδδ

American Institute of Aeronautics and Astronautics8

RREFTHRUST

YYAW

AFF)BBBAAA(

)BBBAAA(

)BBBAAA(

)BBBAAA(FF

*2/1*)/]()()(

)()(

)()(

)()([)(

0112

12041242

0112

12031232

0112

12021222

0112

120112

12

++−++−

++−+++

++−+++

++−++−=

δδδδ

δδδδ

δδδδ

δδδδ

RCOPREFTHRUST ArFF)AAA(

)AAA(

)AAA(

)AAA(FMxRoll

**)/]()(

)(

)(

)([)(

041242

031232

021222

0112

12

+++

+++

+++

+++=

δδ

δδ

δδ

δδ

RREFTHRUST

REFTHRUST

AFF)CCC(

)CCC(

)CCC(

)CCC(

FFtZDrag

*)/]()(

)(

)(

)([

)/(*)(0*4

041242

031232

021222

0112

12

+++

+++

+++

+++

=

δδ

δδ

δδ

δδ

were

A2,A1,A0: Second order coefficients for JV liftB2,B1,B0: Second order coefficients for nozzle dampingC2,C1,C0: Second order coefficients for JV alpha dragZ0(t): JV Zero drag, linear approximation utilizing the mass flux integralFTHRUST: Thrust Curve of RM without JV's vs timeFREF: Reference Thrust utilized for definition of TVC aerodynamic constantsAR: JV area ratio vs timeδ1,δ2,δ3,δ4: Calculated JV deflection vs timerCOP: Radial distance from RM axis to JV CoP

Additional output such as the aerodynamic hinge moment at JV level is easily derived from the JV lift, JV drag force and JV CoP.

IV. Validation of Model

G. Motor test and simulation of JVTVC with high JV erosion

The simulation model has been tested on several rocket motors and this chapter shows the comparison with a test firing utilizing JV's with high erosion during motor burn. Input data for the analyses are based upon the CFD calculations.

A reference firing, i.e. firing without JV's has been applied as input for the simulation model, see Figure 8 left. The axial thrust of the firing and for the analysis is shown to the right in Figure 8. The difference between the curves to the left and to the right is the caused by the JV induced drag. The measured and calculated axial thrusts are in excellent agreement.

American Institute of Aeronautics and Astronautics9

The comparisons of the side forces, i.e. pitch and yaw are seen in Figure 9, left and right respectively. The analysis is in excellent agreement with the firing results. The measured force in yaw direction, at approx 2 sec, does have some characteristics that are not a part of the commanded JV angles. This can be induced by the test set-up and/or some measurement cross-talks and/or similar.

The calculated and measured thrust deflection angle and the roll moment is seen in Figure 10. There is perfect agreement between the measured and analyzed data. The roll moment prediction accuracy includes in addition to the lift and drag data, the effect of JV CoP position accuracy.

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8

Time [sec]

Thr

ust [

kN]

Analysis, No JV's

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8

Time [sec]

Thr

ust [

kN]

Fx, AnalysisFiring

Figure 8 Reference axial thrust curve, left (no JV's on motor). Axial thrust, firing and analysis comparisonwith TVC, right

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8

Time [sec]

Pitc

h T

hrus

t [kN

]

Fy, AnalysisFiring

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8

Time [sec]

Yaw

Thr

ust [

kN]

Fz, AnalysisFiring

Figure 9 Firing and analysis comparison of side thrust, pitch force left and yaw force right

American Institute of Aeronautics and Astronautics10

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7

Time [sec]

Thr

ust D

efle

ctio

n A

ngle

[°]

DeflAngle_[deg]Firing

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 1 2 3 4 5 6 7

Time [sec]

Rol

l Mom

ent [

kNm

]

FMx_[kNm]Firing

Figure 10 Firing and analysis comparison of thrust angle left and roll moment right

H. Motor test and simulation of JVTVC with low JV erosion

This chapter shows the comparison with a test firing utilizing JV's with low erosion during motor burn. Input data for the analyses are based upon the CFD calculations.

A reference firing, i.e. firing without JV's has been applied as input for the simulation model, see Figure 11 left. The axial thrust of the firing and for the analysis is shown to the right in Figure 11. The difference between the curves to the left and to the right is the caused by the JV induced drag. The measured and calculated axial thrusts are in excellent agreement.

The comparisons of the side forces, i.e. pitch and yaw are seen in Figure 12 left and the resulting thrust angle is shown to the right. The analysis is in excellent agreement with the firing results.

The calculated and measured roll moment is seen in Figure 13. There is perfect agreement between the measured and analyzed data. The roll moment prediction accuracy includes in addition to the lift and drag data, the effect of JV CoP position accuracy. The pitch, yaw, and roll fractions as defined in chapter D is shown to the right.

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6

Time [sec]

Sid

e T

hrus

t [kN

]

THRUST no JV's, Analysis

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6Time[sec]

Axi

al T

hrus

t [kN

]

Fx, AnalysisFx, Firing

Figure 11 Reference axial thrust curve, left (no JV's on motor). Axial thrust, analysis and firing comparison with TVC, right

American Institute of Aeronautics and Astronautics11

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5Time[sec]

Sid

e T

hrus

t [kN

]Fy, AnalysisFz, AnalysisFy, FiringFz, Firing

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5Time [sec]

Thr

ust A

ngle

[deg

]

Alpha, AnalysisAngle, Firing

Figure 12 Firing and analysis comparison of side thrust, pitch and yaw, and resulting thrust angle right

-0.1

0

0.1

0.2

0.3

0 1 2 3 4 5 6Time [sec]

Rol

l Mom

ent [

kNm

]

FMx, AnalysisMx, Firing

-1.25

-0.75

-0.25

0.25

0.75

1.25

0 1 2 3 4 5 6

Time [sec]

Pitc

h,Y

aw,R

oll F

ract

ions

[-]

YawFrac_[-]RollFrac_[-]PitchFrac_[-]

Figure 13 Firing and analysis comparison of roll moment left and the pitch, yaw and roll fraction vs time to the right

V. Conclusion

The TVC model has successfully been implemented and validated in several rocket motor tests with TVC at Nammo, both for JVTVC and for movable nozzle TVC's.

• The TVC model is in excellent agreement with the firing results and is an important tool for both pre- and post predictions.

o The JV drag model is in agreement with the rocket motor firing results, both with and without JV deflection. The induced zero drag with JV erosion is in agreement with the firing results. The overall alpha drag is also influenced by the JV erosion and is in agreement with the firing results.

o The side thrust is en excellent agreement with the firing results and the implemented nozzle damping comply with test results.

o JV CoP and the resulting roll moment is in agreement with the test resultso Pitch and yaw moments are not presented in the paper since it is a function of the side forces and

the distance between JV CoP and missile CG. These moments are less sensitive than the roll moment due to the difference in characteristic moment distances.

• The tool can be used for actuator definition with respect to performance and actuator loading.• The tool provide very accurate TVC input for missile 6-DOF flight simulations

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The technology work on TVC systems, movable nozzle and JV’s, has been important in order to increase the technology competence for TVA systems in general and Nammo has established tools for defining the TVC actuator needs for solid propulsion rocket motors.

Acknowledgments

This work has been financed by our participation in the Norwegian Propulsion Technology Development Program, and through internal funding at Nammo Raufoss Missile Propulsion Division.

References

[1] Crowe, C. T., “Drag Coefficient of Particles in a Rocket Nozzle”, AIAA Journal, 5, 1021-1022, 1967.

[2] Hermsen, R. W., “Review of Particle Drag Models,” JANNAF Performance Standardization Subcommittee, 12th

Meeting Minutes, January 1979.

[3] Schaff, S., P. Chambre, “Flow of rarefied Gases,” in Fundamentals of Gas Dynamics, Princeton Series, Vol. III, Princeton University Press, 1958.

[4] B. McBride, S. Gordon, M. Reno, CETPC/93, “ Chemical Equilibrium with Transport Properties, 1993”, COSMIC Program # LEW-16017, Lewis Research Center, Cleveland, Ohio.

[5] SPP, A Computer Program for the Predictions of Solid Propellant Rocket Motor Performance, Software and Engineering Associates Inc., Carson City, Ne

[6] Erland Orbekk, "SuperSonic Split Line TVC Technology and Testing at Nammo Raufoss AS," AIAA-2006-4940

[7] Erland Orbekk et al., "Novel TVC system utilizing guide vanes with jet flap’s into a high efficiency compact nozzle ," AIAA-2005-4499

[8] Erland Orbekk et al., "Internal Flow Analysis Of A Technology Demonstrator Rocket Motor With New CFD Code," AIAA-1998-3967