roll torque prediction in srm: practical applications

63rd International Astronautical Congress, Naples, Italy. Copyright ©2012 by the International Astronautical Federation. All rights reserved.

_____________________________________________ * Dep. of Mech. and Aerospace Eng. University of Rome

“La Sapienza”, Italy, E-mail: [email protected]. t Dep. of Mech. and Aerospace Eng. University of Rome “La Sapienza”, Italy,

E-mail:[email protected]. :t ESA-ESRIN, Italy, E-mail: [email protected]

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IAC-12,C4,2,23,X15674

ROLL TORQUE PREDICTION IN SRM: PRACTICAL APPLICATIONS

F. Stella Department of Mechanical and Aerospace Engineering, Italy University of Rome “La Sapienza”,

Via Eudossiana 18, 00184 Rome (Italy). E-mail: [email protected]

M. Giangi*, F. Nardecchia

t, D. Barbagallo

:t

The production of an unpredicted roll torque, during the launch phase of solid rocket motor (SRM), is not an

uncommon event. One of the possible reason of this phenomenon can be attributed to the complex flow field inside

the combustion chamber. Anyhow, at the moment, the mechanism at the origin of roll torque has not yet been fully

clarified.

Avaliable fligh data, obtained from existing launchers, have shown the presence of a significant roll torque,

expecially when SRM are used. In most cases roll torque is stronger during the initial phase of fligh when slots in

the combustion chamber are still present.

Unfortunately, a model for prediction of roll torque in SRM is not yet clearly established. Analogously, CFD

simulation as a tool for roll torque prediction is not a common tecnique, even if it is not a complete novelty.

Aim of the present work is to investigate and better understand, by means of CFD simulations, the relation between

internal geometry of the combustion chamber of a slotted SRM and the presence of roll torque. The complex

mechanism governing this phenomenon has been reproduced by means of CFD simulation. Several numerical

simulations have be conducted using X-259 Antares II and Castor I as reference motors, showing the basic

mechanism of roll torque generation in SRM. As result, a good agreement in the qualitative behaviour and in

particular in variation with time of roll moment has been found.

I INTRODUCTION

During the launch phase of solid rocket motor

(SRM) the production of an unpredicted roll torque is

not an uncommon event. In the recent past, a strong

roll torque has been observed during the launch of

Mu-V, as reported in [1]. Mu-V is a Japanese solid-

propellant rocket system which has been lunched

seven times from 1997 to 2006. In this rocket roll

torque was observed in all the seven launches during

the early operation period.

Beyond the intensity of the observed roll torque, it

is interesting to remark that the phenomenon presents

a character of repeatability, that made impossible to

ignore its presence. As a consequence few studies

have been conducted on roll torque production, but

unfortunately the mechanism of generation has not

been very well understood. The strength of the torque

in the Mu-V rocket is very large immediately soon

after the launch, but luckily it attenuates gradually

during the ascent phase. In this way the roll-contol

system can handle it without any problem.

However, the problem of roll torque production

cannot be neglected because many modern launchers,

such VEGA and ARES are designed with a solid

rocket motor at first stage.

Going more in the past, the problem of roll torque

induced by the flow inside a solid rocket motor is a

known but still-unresolved topic [2-3]. Available

flight data, show that the presence of roll torque

usually stronger during the initial phase of flight [2-3]

when slots in the combustion chamber are still

present.

Unfortunately, this problem has not been studied,

so far, in its complete details and the few available

flight data are usually incomplete and with large

margin of uncertainty.

Few investigations have been made [2,3,4] in

order to understand both the precise nature of the

vorticity and the resulting changes in the flow-field

evolution inside solid–rocket motors. As described by

Flandro [2], star-shaped cavities are capable of

mailto:[email protected]

https://www.researchgate.net/publication/245436221_Numerical_Investigation_of_Roll_Torque_Induced_by_Solid_Rocket_Motor_Internal_Flow?el=1_x_8&enrichId=rgreq-c5c05278-0977-427a-86cd-b30772dbe661&enrichSource=Y292ZXJQYWdlOzI4MDg0MDk1NjtBUzoyNjEwMDAzMzEwMDE4NTZAMTQzOTIzODczNjA3OQ==

https://www.researchgate.net/publication/269205769_Roll_torque_and_normal_force_generation_in_acoustically_unstable_rocket_motors?el=1_x_8&enrichId=rgreq-c5c05278-0977-427a-86cd-b30772dbe661&enrichSource=Y292ZXJQYWdlOzI4MDg0MDk1NjtBUzoyNjEwMDAzMzEwMDE4NTZAMTQzOTIzODczNjA3OQ==




https://www.researchgate.net/publication/245437277_Roll_torques_produced_by_fixed-nozzle_solid_rocket_motors?el=1_x_8&enrichId=rgreq-c5c05278-0977-427a-86cd-b30772dbe661&enrichSource=Y292ZXJQYWdlOzI4MDg0MDk1NjtBUzoyNjEwMDAzMzEwMDE4NTZAMTQzOTIzODczNjA3OQ==



https://www.researchgate.net/publication/290657536_Roll_torque_induced_by_star-perforated_motor_internal_flow?el=1_x_8&enrichId=rgreq-c5c05278-0977-427a-86cd-b30772dbe661&enrichSource=Y292ZXJQYWdlOzI4MDg0MDk1NjtBUzoyNjEwMDAzMzEwMDE4NTZAMTQzOTIzODczNjA3OQ==


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producing several levels of roll torque, depending

upon the number of star-points. Concerning roll

torque generation historical data reported by Knauber

[3] show that star grain or finned type grain motors

are the best candidates for the production of a

significant roll torque. Knauber [3] identifies four

distinct sources of roll torque generation within solid

rocket motors:

– "Type I", is large chamber vortex generation

usually accompanied by some significant level of

acoustic phenomena;

– "Type II", which is governed by the motor burning

transient, production of roll torque occurs at specific

times during motor live, showing a repeatable

transient. Torque can be either unidirectional or can

exhibit an almost instantaneous reversal in sense;

– "Type III", that is a small unidirectional roll torque

caused by ablative patterns in the nozzle;

– "Type IV", that can be explained by conservation of

angular momentum of spinning rockets due to

changing angular velocity of chamber gases

interacting with the walls of the nozzle.

It has been experimentally observed, as reported by

Knauber [3], that Types I and II sources produce

larger roll torques than the others: unfortunately these

types are, at the present, the less predictable.

Aim of the present work is to investigate and

better understand, by means of CFD simulations, the

relation between internal geometry of the combustion

chamber of a slotted SRM and the presence of roll

torque.

The assumption behind this idea is that the flow-

field in the combustion chamber is influenced by the

presence of slots or fins and this presence produces as

result a roll torque. In the present paper the possible

relation between the internal geometry of propellant

grain and the presence of roll torque in SRM will be

discussed. The complex mechanism governing this

phenomenon has been reproduced by means of CFD

simulation. Several numerical simulations will be

conducted using X-259 Antares and Castor I as

reference motors. The reason of this choice is that for

these type of motor flight data of roll torque are

available from public literature [2]. These motors

have been classified by Knauber [3] as motors that

present roll torque of “Type II”.

As result, a good agreement in the qualitative

behaviour and in particular in variation with time of

roll moment has been found.

II BASIC MECHANISM OF ROLL PRODUCTION

The main mechanism producing roll torque in

slotted motors can be described as follow (Fig.1(a)):

the flow coming from the side slots of SRM merges

near the axes of the motor and because of the weak

stability (or instability) of the axial-symmetric flow

starts rotating in clockwise or anti-clockwise

direction. This rotation is sustained until the final

section of the nozzle and produces a roll torque.

The described phenomenon is, in much smaller scale,

analogous to the instability mechanism that produces

for example rotation in atmospheric cyclones, with

the difference that in our case Coriolis’s forces are

negligible, leaving a-priori undetermined the

direction of rotation.

On the opposite side, it is possible that the flow is

perfectly symmetric giving, more or less, the flow

pattern described in Fig.1(b). It is clear that this flow

configuration gives zero roll torque. Obviously, these

are two extreme solutions and other intermediate

combinations can be supposed. Anyhow, it is not

possible or obvious to a-priori determine the right

configuration assumed by the flow-field. CFD

simulations are conducted to overcome and solve this

problem.

(a)

(b)

Fig. 1: flow patterns [4].

Looking the rotation mechanism shown in Fig. 1(a) it

seems obvious that the geometry of the slots and the

combustion chamber have a big importance on roll

generation. Since the geometry of SRM changes

during burning process, expected roll torque changes

during the life of the motor, as expected for roll

torque of type II.







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In the present paper an estimation of roll torque

and thrust will be conducted.

Estimation of roll torque will be done by mean of

the following integral on the nozzle exit section (S):

S

a rdSvρvL

Where is the density of the fluid, va the axial

velocity, v the tangential velocity and r the radial-

coordinate.

This is consistent with the analogous definition of

thrust, that is usually measured by means of:

dSρvTS

2a

In the following also the Knauber number will be

evaluated:

DT

LKn

In the present paper thrust and roll are the results of

CFD simulations and can be averaged or not,

depending on the steadiness (in time) of numerical

solution.

III MODEL SET-UP AND VALIDATION

The governing equations are the three-

dimensional unsteady compressible Navier-Stokes

equations, without any additional equation for

turbulent modeling. Therefore turbulence has not

been approached with an explicit model, like for

example the classic k-. In the present study,

numerical simulations are conducted solving only the

fundamental governing equations: conservation of

mass, momentum and energy. The presence and

effects of turbulence have been approached using

Monotonically Integrated Large Eddie Simulation

(MILES) [5,6]. Basically, the main idea of MILES is

to substitute sub-grid scale models with numerical

viscosity introduced by up-wind schemes. In this

view MILES is usually considered a simplified form

of LES, allowing also the simulation of both turbulent

and laminar flows. In the present paper a second

order up-wind scheme has been adopted. A similar

approach has been used in roll torque prediction by

Shimada et al. [1] adopting a third order upwind

scheme as subscale model. MILES has been also used

in the past by the same and other authors, showing

the capability of resolving fine details of the flow in

unsteady conditions. In particular MILES has been

largely used for the study of pressure oscillation in

Solid Rocket Motors (SRM) [7-10], the same

approach has been also used for non-aerospace

problems with much larger scale [11].

Numerical simulations have been conducted using

a segregated algorithm to solve conservation

equations. Using this approach, the equations are

solved sequentially, but since they are nonlinear and

the phenomenon unsteady, several iterations of the

solution loop must be performed before a converged

solution is obtained for each time step. The

convective terms in the equations for momentum and

energy are discretized using a second-order upwind

scheme. The PISO (Pressure Implicit with Splitting of

Operators) algorithm has been used to achieve the

pressure-velocity coupling and an implicit

discretization of time derivatives has been also

chosen.

All the numerical simulations of the present work

were performed using true transient flow conditions,

considering the propellant geometry as frozen for

each time instant reproduced.

The boundary conditions imposed on the

propellant external surface at the SRM are the so-

called mass flow inlet usually adopted for these type

of problems [12]. Using these boundary conditions a

specific mass flux rate per surface unit is enforced.

Finally a constant pressure is imposed at outlet

section. Actual values adopted in the specific

simulations are extracted from operative conditions

presented in Tables 3, 8 and 11.

The commercial CFD code FLUENT has been

used for all the numerical simulations. FLUENT uses

a control-volume-based technique for discretization

and numerical solution of field equations. For sake of

conciseness we do not report further details of the

numerical code and discrete formulation, the reader

can obtain further information from [12].

III I MESH SENSITIVITY

Before starting with CFD simulations a mesh

sensitivity analysis has been conducted on X-259

Antares II, this using the propellant configuration

corresponding to t=5.0s. Anyhow, indications

deducted from mesh sensitivity have been used for

other instants of time and for the other motor (e.g.

Castor I).

Three simulations with different spatial

discretization (ranging from 5 million up to 20

million cells) have been performed in order to verify

the grid independence of the numerical solution.

As shown in Table 1, the roll torque obtained

comparing these three grids are quite small. The mesh

B with 9 millions of cells have been adopted for X-

259 at t=5.0s.

An analogous mesh has been adopted for Castor I.

More generally speaking, in all the simulation

conducted, adopted meshes are quite uniformly

spaced along the whole motor, this to guarantee a

uniform accuracy in the whole domain.


https://www.researchgate.net/publication/230605766_Monotonically_Integrated_Large_Eddy_Simulation_of_Free_Shear_Flows?el=1_x_8&enrichId=rgreq-c5c05278-0977-427a-86cd-b30772dbe661&enrichSource=Y292ZXJQYWdlOzI4MDg0MDk1NjtBUzoyNjEwMDAzMzEwMDE4NTZAMTQzOTIzODczNjA3OQ==

https://www.researchgate.net/publication/247351739_Recent_progress_on_MILES_for_high_Reynolds_number_flows?el=1_x_8&enrichId=rgreq-c5c05278-0977-427a-86cd-b30772dbe661&enrichSource=Y292ZXJQYWdlOzI4MDg0MDk1NjtBUzoyNjEwMDAzMzEwMDE4NTZAMTQzOTIzODczNjA3OQ==


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Table 1: Mesh Sensitivity (X-259).

IV PRELIMINARY STUDIES

At the present stage, many doubts are rising from

engineers and scientists working in the propulsion

field concerning the true origin and the basic

mechanism of roll torque and the feasibility at all of

numerical simulation of the phenomenon under

investigation.

Therefore a preliminary study has been

conducted first with the purposes of reproducing and

understanding the behaviors of roll torque production,

and, successively to investigate the possible role of

two of the main believed reasons of roll torque

presence: (1) asymmetry in solid propellant

distribution obtained as result of non appropriate

casting process, (2) presence of strong motor rotation

in rocket trajectory.

IV I BASIC MECHANISM

The first study conducted is devoted to the

understanding of fluid dynamic mechanism behind

roll torque production. As matter of the fact, since

roll torque produced is usually quite small when

compared with other phenomena present in SRM

(e.g. thrust), as also shown from the order of

magnitude of Knauber number that is usually

extremely small (e.g. 10-5

-10-9

), in order to have some

visible effect it is necessary to widely amplify

phenomena that are at the origin of roll torque. For

this reason, flow visualizations and general

understanding of the phenomenon has been

conducted on an ad-hoc 4 SRM, that has been

designed with the purpose of magnifying roll torque

presence.

This conceptual configuration of SRM is

constituted by four, orthogonal, slots placed around

the central combustion chamber of the motor. The

geometry is shown in Figure 2 and 3.

Fig. 2: 4-slot motor - control volume considered and

boundary surfaces.

Fig. 3: 4-slot motor - frontal section geometric

dimensions.

Main geometrical data are reported in Table 2,

while operative conditions are reported in Table 3.

A mesh with ≈ 3 million of cells, whit a typical

mesh size of x ≈ 1cm is adopted during the

numerical simulations.

Motor Length 7.57motorL m

Nozzle Length 1.81nozzleL m

Chamber Diameter 0.727chamberD m

Throat section

Diameter

0.727throatD m

Exit section Diameter 1.96exitD m

Slot Height 0.493sloth m

Slot Span 0.04slotb m

Table 2: 4-slot motor - Geometry.

Mesh N° Cells Typical Size

[mm]

Roll Torque

[Nm]

A 5 x 106 8.5 4.5

B 9 x 106 7.0 4.7

C 20 x 106 5.5 4.7


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Chamber pressure pc = 42 bar

Chamber/inlet

temperature

3387cT K

Mass flow rate 416.7m kg s

Inlet mass flux 1 212.97 kg s m

External pressure 50x10-5

bar

Table 3: 4-slot motor - Operative conditions.

Mass flow inlet boundary conditions have been

imposed, as described in the Section 3, on all the

solid propellant surfaces: inner cylinder, sides and

bottom of lateral slots. The flow coming in to the

lateral slots from side walls is driven from the

geometry of the slots to the core of combustion

chamber.

After a transient, flow becomes oscillatory stable.

Going a bit more into the details of the flow-field, the

flow presents a (modestly) swirling nature: in

particular a single vortex with a certain offset from

the longitudinal axis centerline moves on a nearly

circular trajectory (see Figs. 4-6) with angular

velocity that has been estimated in about 41 rad s-1

,

this correspond to a revolution time of about 0.15 s

and a frequency of about 6.5 Hz.

Also roll torque presents a fluctuating behavior

ranging from 228.3 Nm to 270.3 Nm, with a mean

value of 247.8 Nm and a frequency of about 26 Hz.

This value, being four times bigger than the main

vortex frequency is well correlated with the swirl

effect and seems the obvious result of the interaction

of the rotating vortex with the four slots of the

propellant. Analogously, also thrust presents an

extremely small oscillation (in amplitude) with the

same frequency of roll torque.

Therefore, this result clearly shows that it is

possible to find a roll torque value even starting from

symmetric flow conditions and that CFD simulation

can predict the formation of a flow structure that

produces roll torque.

Trust [kN]

Torque [Nm]

Min value 1025.144 228.3

Mean value 1025.239 247.8

Max value 1025.337 270.3

Table 4: 4-slot motor - Thrust and Torque.

Fig. 4: Contours of vorticity magnitude

(axial station 3.82x m and t=2.55 s).






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IV II MASS FLOW RATE ASIMMETRY

Effects of mass flow rate asymmetry have been

studied on X–259 ANTARES II.

Two simulations with 1% and 5% asymmetry in

mass flow rate on the lateral slot surfaces have been

conducted in order to have a sensitivity of the

influence of this non-uniformity on roll torque. The

non-uniformity is generated increasing the mass flow

rate on one face of the slot and decreasing mass flow

rate on the corresponding face on the same slot, the

same conditions has been applied on all the slots. As

result, overall mass flow rate is preserved.

As shown by the results reported in Table 5 the

values of roll torque are very similar if compared to

that obtained in the standard case.

Therefore mass flow rate symmetry seems not to be

an important source of roll torque.

Case Torque[Nm]

Symmetric (Standard case) 4.7

1% lateral inlet's

asymmetry

4.7

5% inlet asymmetry 4.8

Table 5: X-259 - Effect of mass flow rate asymmetry.

IV III MOTOR ROTATION

Also the effects of motor rotation have been

studied on X–259 ANTARES II.

The effect of motor rotation on the numerical

solution was assessed by performing two different

simulations with 5 °/sec and 10 °/sec moving

reference frame's angular velocity.

Table 6 shows the comparison between the

standard case and the values of roll torque obtained

by imposing the aforementioned motor angular

speeds.

Therefore, also motor rotation seems not to be an

important source of roll torque.

Case Roll

Torque [Nm] Steady motor (Standard case) 4.7

5 grad s-1

motor angular

velocity

4.7

10 grad s-1

motor angular

velocity

4.9

Table 6: X-259 - Effect of motor rotation.

V RESULTS AND DISCUSSION

Numerical simulations have been conducted

using X-259 Antares II and Castor I as reference

motors. It is worthy to note, that the complete set of

ballistic and geometrical data in correspondence of

the instants of time when numerical simulations are

conducted are not easy to collect. Therefore in many

cases the lack of data has been overcome using a

good engineering practice. For example, the internal

geometry of the propellant has been estimated

starting from the initial configuration at t=0s and

assuming a reasonable regression rate. Analogously

mass flow rate and combustion temperature have

been assumed on the basis of reasonable

characteristics of SRM of that time.

Moreover, roll torque flight data have been

retrieved from public literature [3] and therefore in

most of the cases measurement methodologies and

related uncertainty are not known.

X-259 ANTARES II The first motor considered is

X–259 ANTARES II. It was used as third stage on

SCOUT LV. This is a motor with four slots placed in

the lower part of the combustion chamber, close to

the nozzle (see Fig.7).

The motor and the nozzle length are Lmotor=2.78m

and Lnozzle=1.12m, while the nozzle exit and throat

area are Ae=0.43m2 and At=0.024m

2.

Figure 7: X–259 ANTARES II

(comb. chamber at t=2.3s).

Main geometrical data are reported in Table 7, while

operative conditions are reported in Table 8.

Motor length 2.78motorL m

Nozzle length 1.12nozzleL m

Chamber diameter 0.109chamberD m

Nozzle exit area 20.43eA m

Nozzle throat area 20.024tA m

Nozzle expansion ratio 17.93e tA A

Table 7: X-259 motor - Geometry.



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Chamber pressure pc = 23.5 bar

Chamber/inlet temperature 2900cT K

Mass flow rate 38.7m kg s

External pressure 50 x 10-5

bar

Table 8: X-259 (t=0s) - Operative conditions.

Several instants of time have been tested in order

to understand if variation in time of roll torque

observed during flight tests is correctly followed by

numerical simulations.

From the mesh sensitivity a nearly uniform mesh

has been adopted with a typical mesh size ranging

from 6 to 8 mm.

Since, due to propellant consumption, the internal

geometry of the combustion chamber changes at the

different instant of time, the size of the adopted grid

ranges from 7 millions up to 10 millions cells.

Several instant of time, and then different

geometries, have been simulated (see Tab. 9). For the

same reason the mass flow rate has been varied from

case to case with the assumption that mass flow rate

per unit area is constant in time.

Main results in terms of thrust and roll torque are

reported in Table 9, it is worthy to observe that there

is a variation of roll torque that, analogously with

flight data, presents an increase between t=0s and

t=5s with a successive decrease.

Time [s] Thrust [kN] Torque [Nm] Knx103

0.0 94.50 0.4 0.01

2.9 94.54 2.7 0.04

5.0 94.46 4.7 0.07

6.1 94.49 4.5 0.06

9.4 94.46 1.4 0.02

10.5 94.48 1.0 0.01

Table 9: X-259 - Thrust, Torque and Kn.

Figure 8 shows the comparison between experimental

data on Antares II's roll torque found in [3] and

results obtained by numerical simulations in the

present study.

First of all, flight data retrieved from [3] present

both data from single flights and an “upper bound”.

Reading [3] it is not possible to clearly understand

how the “upper bound” curve has been obtained from

fly data by the author. One possibility is that this

curve includes part or most of the operative margins,

resulting that “upper bound” curve is usually much

higher than instant values. When we compare CFD

results with the “upper bound” curve, large

differences are obviously found in terms of values,

resulting that CFD data are nearly three times

smaller. Flight data series, from single flights [3],

present several sudden jumps between positive and

negative values. These sudden changes, typical of

unstable phenomena and typical of the “Type II” roll

torque, are probably due to a change in the direction

of the main vortex. Obviously these two opposite

flow configurations are both possible in terms of

internal stability. The origin of these changes are not

reported in [3] and have probably to be found in some

flight maneuver, that, at the present are impossible to

investigate.

Anyhow, following the previous considerations,

it is reasonable not to consider the direction of

rotation of the main vortex and use the absolute

values of flight data. Doing so, the negative part of

the three data series have to be tilted on the positive

side of the diagram.

Comparing the CFD results with this modified

diagram a good agreement with flight data can be

found, with the exception of the very high peak

observed in S-202 at t≈6s.

Also, the general trend is similar with the

maximum located nearly at the same time instant and

both curves smoothly decreasing for larger times.

Fig.8: Roll torque-comparison between flight data [3]

and numerical results (dots).




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CASTOR I Castor I is a larger motor with five slots

going along the length of the motor in a “star”

configuration (see Fig. 9).

Fig. 9: CASTOR I

(combustion chamber at t=0.28s).

The motor and the nozzle length are Lmotor=6.14m

and Lnozzle=1.26m, while the nozzle exit and throat

area are Ae=0.64m2 and At=0.04m

2. The large extent

of the slots is the main reason for the higher values of

roll torque found.

Main geometrical data are reported in Table 10,

while operative conditions are reported in Table 11.

Motor length 6.14motorL m

Nozzle length 1.26nozzleL m

Chamber diameter 0.109chamberD m

Nozzle exit area 20.64eA m

Nozzle throat area 20.04tA m

Nozzle expansion ratio 15.8e tA A

Table 10: CASTOR I - Geometry.

Chamber pressure pc = 37.92 bar

Chamber/inlet temperature 2900cT K

Mass flow rate 105Im kg s

External pressure 50 x 10-5

bar

Table 11: CASTOR I - Operative conditions.

For all the cases simulated a nearly uniform mesh

has been adopted with a typical mesh size ranging

from 6 to 10 mm. Grid dimension ranges from 5

millions up to 7 millions cells.

Fig. 10: CASTOR I – Roll Torque: comparison

between flight data [3] and CFD (dots).

From Figure 10 it is possible to observe that there

is a reasonable agreement between the flight data [3]

of roll torque and the results obtained by CFD. CFD

values are clearly smaller but the time behavior is

similar. The reasons of these differences can be

various, first of all there is a quite large uncertainty

on input data, in some case (e.g. mass flow rate)

assumed on the basis of engineering experience, from

another side the uncertainty on flight data is not

known.

Anyhow, comparison between CFD results and

experimental data seems to indicate that a reasonable

good modeling of roll torque phenomenon and its

variation with internal geometry has been reached.

VI EFFECT OF GEOMETRY

One of the obvious ideas, related to roll torque

production, is that the internal geometry of the

propellant has a fundamental effect. In particular the

aspect ratio of propellant slots seems the major

candidate to be an indicator of the risk of roll

production.

The four geometries studied in the case of Castor

I are reported in Figure 11.

In Tab.12 and Tab.13 the aspect ratio, based on

l/d (with l the depth and d the width of the slot), and

roll torque for the two SRM are reported.

Looking these data, the dependence of roll from

aspect ratio seems quite obvious; in both cases when

aspect ratio goes to zero (i.e. propellant slots

disappear) roll torque decreases. In both cases close

to zero aspect ratio this relation is quite strong and

data have been fitted with an exponential (Figs 11-

12).


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Fig. 11: Castor I – Different geometries studied,

showing variation in time of aspect ratio of the

propellant slot.

t [s] l/d Roll torque

[Nm]

0.28 2.31 59

0.57 2.19 36

2.02 1.70 3

4.12 1.32 1

Table 12: CASTOR I - roll torque as a function of

slot aspect ratio.

t [s] l/d Roll torque

[Nm]

0.0 7.76 0.4

2.9 2.20 2.7

5.0 1.85 4.7

6.1 1.54 4.5

9.4 0.96 1.4

10.5 0.82 1

Table 13: X-259 - roll torque as a function of slot

aspect ratio-

Fig. 11: CASTOR I - data fit of Roll torque as a

function of slot aspect ratio with exponential data-fit.

Fig. 13: X-259 - data fit of Roll torque as a function

of slot aspect ratio (continuous line: exponential data-

fit).

Obviously, there are some remarkable differences

between results shown for X-259 and Castor I, since

X-259 presents a non-monotonic trend with a

maximum around the aspect ratio of 1.85. The

reasons of this differences can be various, between

the others:

Higher values of the aspect ratio in X-259 are not

present in Castor I. These deep propellant slots

with high aspect ratio may work as a driving duct,

stabilizing the flow and reducing the attitude to

produce the circumferential flow

Presence of important three dimensional effects

due to the propellant geometry in X-259

Going back to the relationship between aspect

ratio of propellant slot and roll torque. It is our

opinion that it is not possible to draw a final

conclusion from such limited quantity of data and a

further investigation is required to better assess this

aspect. Anyhow, this relationship seems being

confirmed from the numerical simulations conducted.

VII CONCLUSIONS

Numerical simulations conducted in three

different cases have show that the phenomenon of roll

torque in SRM can be successfully reproduced using

CFD simulation.


IAC-12,C4,2,23,X15674 of 10

The analysis of obtained results have shown, for

the considered cases, that the driven mechanism of

roll torque production is the presence of a main axial

vortex in the combustion chamber. Also the

importance of propellant grain geometry for

generation of this vortex structure has been, in some

of its aspects, enlightened.

Going to numerical results, tests conducted have

shown a good qualitative agreement between CFD

simulation and flight data in terms of variation of

predicted roll torque with time, showing the

importance of propellant geometry for the production

of internal vortex structure in SRM.

Obtained results show that the enlargement and

successive disappearance of propellants slots is one

of the main reasons of decreasing of roll torque for

late time instant.

Finally the detailed quantitative comparison of

predicted roll torques with flight data shows some

meaningful differences. Anyhow it is worthy to note

that the presented study is an initial attempt for roll

torque prediction using CFD and represents an

improvement to the state of the art.

VIII REFERENCES

[1] T. Shimada, N. Sekino and Fokunaga M.,

Numerical Investigation of Roll Torque induced by

Solid Rocket Motor Internal Flow (AIAA 2008-

4891), 44th AIAA/ASME/SAE/ASEE Joint Prop.

Conf. & Exhibit 21-23 July 2008, Hartford, CT.

[2] G. A. Flandro, Roll Torque and Normal Force

Generation in Acoustically Unstable Rocket Motors,

AIAA Journal, 2, 1964.

[3] R. N. Knauber, Roll Torque Produced by Fixed–

Nozzle Solid Rocket Motors, J. Spacecraft and

Rockets, 33 (6) 1996.

[4] T. Shimada, Roll Torque Induced by Star-

Perforated Motor Internal Flow, 58th Int.

Astronautical Congress, Hyderabad, 24-28 September

2007.

[5] C. Fureby and F.F. Grinstein, Monotonically

Integrated Large Eddie Simulation of free shear

flows, AIAA Journal 37, 544, 1999.

[6] F.F. Gristen, C. Fureby, Recent progress on

MILES for high Reynolds number flows, Journal of

Fluid Engineering, 124 848-861, 2002.

[7] F. Paglia, Oscillazioni di pressione in presenza di

singolarità geometriche, Ph.D. Thesis, University of

Rome “La Sapienza”, 2004.

[8] F. Stella, F. Paglia, M. Giangi, M. D’Ascenzi,

Numerical simulation of pressure oscillation in SRM:

definition of assessment and methodology, Avio

Technical Report, 2005.

[9] F. Stella, F. Paglia, “Pressure Oscillations In Solid

Rocket Motors: Effect of Nozzle Cavity”,

Aerotecnica Missili & Spazio, Vol. 88 (1-2) pp.31-

41, 2009.

[10] D. Scherrer, F. Chedevergne, P. Grenard,, J.

Troyes, A. Murrone, E. Montreuil, F. Vuillot, N.

Lupoglazoff, M. Huet, B. Sainte-Rose, P. Thorigny,

N. Bertier, J.-M. Lamet, T. Le Pichon, E. Radenac, A.

Nicole, L. Matuszewski, M. Errera, Recent CENDRE

Applications, The Onera Journal AerospaceLAB

(www.aerospacelab-ournal.org) Issue 2, 2011.

[11] Peter Brady, An investigation free surface

hydraulic structures using large eddy simulation and

CFD, Ph.D. Thesis, University of Technology

Sydney, 2010.

[12] FLUENT 6.3 User's Guide.





















roll torque prediction in srm: practical applications

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