Co-supervisor Ing. Roberto Bertacin Supervisor Prof. Ing. Fabrizio Ponti Graduate Filippo Facciani Study, Development and Application of Solid Rocket Balistic Models
1. Study, Development and Application of Solid Rocket Balistic
Models Graduate Filippo FaccianiSupervisor Prof. Ing. Fabrizio
Ponti Co-supervisor Ing. Roberto Bertacin
2. 1. Introduction: Solid Rocket Motors (SRM) Solid Rocket
Motor: Propulsion system based on the generation of thrust from the
conversion of Enthalpic Energy to Kinetic
EnergyIgniterGrainComponents: Igniter Propellant Grane Case Thermic
Protection NozzleCase and Thermal Protections = is specifically
related to the Nozzle and gives reason of its
performance10/10/2012NozzleStudy, Development and Application of
Solid Rocket Balistic Models2
3. 1. Introduction: Internal BalisticInternal Balistic: Subject
act to study the development of the ducted flow internal to the SRM
Combustion Chamber (CC) CC Gas Mixture: Inert filling gasesMass
Addition: Combustion hot gases Ablation gases Igniter gasesMass
Subtraction: Gases leaving the nozzleGeometric Parameters: CC
Volume 10/10/2012Study, Development and Application of Solid Rocket
Balistic Models3
4. 1. Introduction: Internal Balistic Phases The operative life
of an SRM can be devided in: Ignition transient Quasi steady state
Tail off transient Quasi Steady State: Igniter is off Ablation of
Thermic Protections is negligible Influencing Parameters:
Combustion gases hot flow Nozzle flow = Courtesy of Modeling and
Numerical Simulation of Solid Rocket Motors Internal Ballistics,
Enrico Cavallini Combustion Ratio: = + = = The Combustion Surface
development in time determines the Combustion Gases Mass
Flow10/10/2012Study, Development and Application of Solid Rocket
Balistic Models4
5. 2. Scope: Deisgn and Realization of a Combustion Simulator
Scopo:Realize an SRM Combustion Simulator able to break through the
current limitsKey Parameters: CC Pressure Axial Velocity Combustion
SurfaceFluid dynamic GeometricStato dellarte: Balistic Models 0-D:
parameters are averaged in space and function of time 1-D
Stationary: parameters are function of the axial position only 1-D
non-Stationary: parameters are function of both the axial position
and timeCombustion Surface Regression Models Analytic Based on
Simmetry or Periodicity Isotropic Current Limits: Isotropy forbids
the use of anisotropic inputs from sofisticaded Balistic
ModelsSolution: develop of two cross-linked models, and Internal
Balistic Model and a Regression one, interdependent and able to
work with Anisotropic geometries 10/10/2012Study, Development and
Application of Solid Rocket Balistic Models5
7. 3. 0-D Unsteady Balistic Model Use: L ratios > geometries
where can be neglectedIpothesis: Fluid dynamic parameters are
function of time only Ideal gasses Heat flux through the propellant
grain is negligible No chemical reactions within the control volume
Inviscid Fluid Subsonic Flux = + Continuity Equation Energy
Equation10/10/2012 1 = + + + 2 = + + + 2Study, Development and
Application of Solid Rocket Balistic Models7
8. 3. 0-D Balistic Model: Inputs From the Regression Model: = ,
= = is calculated through analysis of the intersection between the
radius of the Combustion Surface and the Case
profile10/10/2012Study, Development and Application of Solid Rocket
Balistic Models8
9. 3. 0-D Balistic Model: Application to BARIAs initial
Geometry:Analytical Regression:Balistic Prediction: Phase of
Interest: Quasi-Steady-State Good Match Tail Off: discrepancy due
to the Nozzle Physical Model. Such a model just describes sinic
conditions. Qualitative Trend: optimal match with the expected
trend .10/10/2012Study, Development and Application of Solid Rocket
Balistic Models9
10. 3. 0-D Balistic Model: Zefiro 9 Data Provided by AVIO
(Sponsor): Igniter properties () trend (experimental) p() trend
(experimental) HUMP e Scale Factor corrective factors10/10/2012Dati
Found in Literature Therma Protection CharacteristicsData
Calculated from the Mesh every section, in order to calculate
intersections with the Case.Study, Development and Application of
Solid Rocket Balistic Models10
11. 3. 0-D Balistic Model: Zefiro 9 Geometry: Overall results
satisfactory Considerations: the simulation was carried on using an
isotropic approach. Therefore, anisotropies in the cobustion
velocity direction have been considered using an HUMP factor Errore
~ 4% Two deviations from the reference
curve:Regression:10/10/2012Study, Development and Application of
Solid Rocket Balistic Models11
12. 3. 0-D Balistic Model: Zefiro 9 Geometry:Error due to
remeshingRegression:10/10/2012Study, Development and Application of
Solid Rocket Balistic Models12
13. 3. 0-D Balistic Model: Zefiro 9 Geometry: Deviation in the
final part of the Steaty State phase due to the lack of knowledge
about the Thermal ProtectionsRegression:10/10/2012Study,
Development and Application of Solid Rocket Balistic Models13
14. 4. 1-D Non-Stationary Balistic Model Use:geometries where
can not be neglected H ratios < Ip: Properties of the gas
mixture are uniform in a given motor section Velocity components
normals to the motor axis are neglectable Inviscid ideal fluids The
only thermic flux is through exposed PT surfaces No chemical
reactions inside the Control Volume Subsonic flux No abrupt
discontinuities in combustion chamber geometryContinuity Equation
Momentum Equation( ) ( ) + = + + 3 ( ) [(2 + ) ] + = + =1Energy
Equation10/10/2012( ) [ + ] + = + Study, Development and
Application of Solid Rocket Balistic Models14
15. 4. 1-D Balistic Model: Inputs From the Triangular Mesh: To
calculate the mean radius the sart shape is approximated to the
circonference of equivalent area. When the Case surface is exposed,
will be equivalent to the Case radius will be calculated the same
way as per the 0-D case is found by redistributing on the
calculation nodes of 1/3 of the triangular elements adjacent to
every vertex assigned to every specific node10/10/2012Study,
Development and Application of Solid Rocket Balistic Models15
16. 4. 1-D Balistic Model: Cilindrical Geometry Geometry:
Reference curve: results from the 0-D model Analytic regression
Thermic Protection Small size motors Ablation is Short combustion
time neglegible C Qualitative trend in agreement with Expectations
10/10/2012Quantitative values converging to the 0-D model ones for
= 0.01LStudy, Development and Application of Solid Rocket Balistic
Models16
17. 4. 1-D Balistic Model: Star-Aft Geometry Reference values:
results from the 0-D model Inputs: geometry, nozzle throat diameter
evolution in time. The match between the 1-D and the 0-D model is
not good.10/10/2012Study, Development and Application of Solid
Rocket Balistic Models17
18. 4. 1-D Balistic Model: Star-Aft Geometry Complexive trend:
the blue line trend agrees with the one of a cilindric geometry.
Cause: the star-shaped section are reconducted to geometric shapes
with equivalent area10/10/2012Study, Development and Application of
Solid Rocket Balistic Models18
19. 4. 1-D Balistic Model: Star-Aft Geometry Complexive trend:
the blue line trend agrees with the one of a cilindric geometry.
Cause: the star-shaped section are reconducted to geometric shapes
with equivalent area Use of circular sections determines an
underestimation of in the first part of the Quasi Steady State, an
overextimation in the second one.10/10/2012Study, Development and
Application of Solid Rocket Balistic Models19
20. 4. 1-D Balistic Model: Star-Aft Geometry Effect of the
remeshing: 1-D response is delayed compared to the 0-D Late and
incomplete damping10/10/2012Study, Development and Application of
Solid Rocket Balistic Models20
21. 4. 1-D Balistic Model: Star-Aft Geometry Effect of the
remeshing: 1-D response is delayed compared to the 0-D Late and
incomplete damping Cause: the damping factor is artificial and
embedded withing the MacCormack integration method.The artificial
viscosity is triggered by the pressure gradient10/10/2012Study,
Development and Application of Solid Rocket Balistic Models21
22. 4. 1-D Balistic Model: Star-Aft Geometry Effect of the
remeshing: 1-D response is delayed compared to the 0-D Late and
incomplete damping Cause: the damping factor is artificial and
embedded withing the MacCormack integration method.The artificial
viscosity is triggered by the pressure gradient The damping factor
is not reacting to the geometric perturbations, but only to the
pressure gradients induced by it. When these gradiants become low
again, the damping ends indipendently from the permanence of
geometric stimuli. 10/10/2012Study, Development and Application of
Solid Rocket Balistic Models22
23. 5. Conclusions and Future Developments 0-D model: Results
are generally satisfactory Influence of remeshing is localised
Solutions: Improve Remeshing techniques Higher Triangular Mesh
density Filtering of the numeric noise introduced by the geometric
parameters.1-D non-Stationary Model: Good results with analytic
geometries Results are not good with complex geometries due to the
interface and the dynamic behaviour. Solutions: 1. Develop of
algorithms to reorder the sections point cloud: this will allow to
avoid errors introduced by evaluating geometric parameters using
equivalent circular shapes. 2. Modify the Damping term in order to
have it triggered directly from the geometric perturbations
introduced by the remeshing10/10/2012Study, Development and
Application of Solid Rocket Balistic Models23
24. 5. Conclusions and Future Developments Observations: The
1-D non-stationary model highlighted unexpected consequences of
using the Anisotropic Regression Model: the effect of the geometric
noise on the model were not expected, nor met in literature. They
can be bypassed developing an hybrid model, mixin the 0-D and a 1-D
Stationary model. This model will get advantage form the 0-D fast
response and the capability of the 1-D model to calculate axial
distribution along the motor axis for the relevant parameters. At
every iteration, the results from the 0-D model will initialised
the 1-D stationary model. 0-D Model1-D Stationary Model
distributionsThis will allow to limit the remeshin effects while
still being able to achieve distributions for the fluid dynamic
quantities of interest and, therefore, of the combustion
ratio10/10/2012Study, Development and Application of Solid Rocket
Balistic Models24
