Abstract

Erosion prediction of the solid propellent nozzle is vital for its design process. This erosion is caused by the impingement of agglomerated aluminum/aluminum oxide particles on the nozzle walls. Thus, a multi-phase numerical model is established based on the Eulerian–Lagrangian approach to model the aluminum particles burning inside the combustion chamber and simulate the mechanical erosion of the nozzle. The numerical model is validated against numerical and experimental results from the literature. Then it is simplified by eliminating the aluminum particles burning process as they do not reach the nozzle. The simplified model will be further used in modeling the agglomerates’ breakup and predicting the mechanical erosion for aluminum particles with lower surface tension. The results showed that applying the Reitz–Diwakar breakup model reduces the erosion rate by 6.2–24% depending on the injected droplets. In addition, it was found that a decrease in the erosion rate by 1–4.5% can be achieved by reducing the aluminum additive’s surface tension by 15%.

Issue Section:
Fuel Combustion
Keywords:
solid rocket motor, multi-phase flow, Eulerian–Lagrangian approach, droplet’s breakup, mechanical erosion, surface tension, fuel combustion
Topics:
Aluminum, Combustion, Drops, Erosion, Nozzles, Particulate matter, Surface tension, Rockets, Engines, Motors, Combustion chambers, Computer simulation

References

1.
Braun
,
W. V.
,
1974
,
History of Rocketry & Space Travel
,
Thomas Y. Crowell Co
,
New York
.
2.
Swope
,
L. W.
, and
Berard
,
M. F.
,
1964
, “
Effects of Solid-Rocket Propellant Formulations and Exhaust-Gas Chemistries on the Erosion of Graphite Nozzles
,”
AIAA Solid Propellant Rocket Conference
,
Palo Alto, CA
,
Jan. 29–31
.
3.
Geisler
,
R. L.
,
Beckman
,
C. W.
, and
Kinkead
,
S. A.
,
1975
, “
The Relationship Between Solid Propellant Formulation Variables and Motor Performance
”, AIAA Paper No. 75-1199.
4.
Borass
,
S.
,
1984
, “
Modeling Slag Deposition in the Space Shuttle Solid Rocket Motor
,”
J. Space. Rock.
,
21
(
1
), pp.
47
–
54
.
5.
Wong
,
E.
,
1968
, “
Solid Rocket Nozzle Design Summary
,”
Proceedings of 4th Propulsion Joint Specialist Conference
,
Cleveland, OH
,
June 10–14
.
6.
Amano
,
R. S.
, and
Yen
,
Y.-H.
,
2014
, “
Chapter 19: Experimental Investigation of Molten Alumina Breakup in Gas Flows in a Solid Rocket Chamber
,”
5th International Conference on Chemical Engineering and Applications, IPCBEE
,
Taipei, Taiwan
,
Aug. 26–27
, p.
15
.
7.
Thakre
,
P.
, and
Yang
,
V.
,
2009
, “
Mitigation of Graphite Nozzle Erosion by Boundary Layer Control in Solid Propellant Rocket Motors
,”
J. Propul. Power
,
25
(
5
), pp.
1079
–
1085
.
8.
Thakre
,
P.
, and
Yang
,
V.
,
2008
, “
Chemical Erosion of Carbon–Carbon/Graphite Nozzles in Solid Propellant Rocket Motors
,”
J. Propul. Power
,
24
(
4
), pp.
822
–
833
.
9.
Thakre
,
P.
, and
Yang
,
V.
,
2009
, “
Chemical Erosion of Refractory Metal Nozzle Inserts in Solid-Propellant Rocket Motors
,”
J. Propul. Power
,
25
(
1
), pp.
40
–
50
.
10.
Thakre
,
P.
, and
Yang
,
V.
,
2012
, “
Effect of Surface Roughness and Radiation on Graphite Nozzle Erosion in Solid Rocket Motors
,”
J. Propul. Power
,
28
(
2
), pp.
448
–
451
.
11.
Sutton
,
G. P.
, and
Biblarz
,
O.
,
2001
,
Rocket Propulsion Elements
, 7th ed.,
Wiley-Interscience
,
New York
.
12.
Sabnis
,
J.
,
2003
, “
Numerical Simulation of Distributed Combustion in Solid Rocket Motor With Metallized Propellant
,”
J. Propul. Power
,
19
(
1
), pp.
48
–
55
.
13.
Jeenu
,
R.
,
Pinumalla
,
K.
, and
Deepak
,
D.
,
2010
, “
Size Distribution of Particles in Combustion Products of Aluminized Composite Propellant
,”
J. Propul. Power
,
26
(
4
), pp.
715
–
723
.
14.
Grigor'ev
,
V. G.
,
Zarko
,
V. E.
, and
Kutsenogii
,
K. P.
,
1981
, “
Experimental Investigation of the Agglomeration of Aluminum Particles in Burning Condensed Systems
,”
Combust. Expl. Shock Wave.
,
17
(
3
), pp.
245
–
251
.
15.
Son
,
S.
,
Sivathanu
,
Y. R.
,
Moore
,
J. E.
, and
Lim
,
J.
,
2009
, “
Experimental Characteristics of Particle Dynamics Within Solid Rocket Motors Environments
,”
56th JANNAF Interagency Joint Propulsion Meeting, FA9300-08-M-3022
,
Las Vegas, NV
,
Apr. 14–17
, p.
51
.
16.
Carlotti
,
S.
,
Anfossi
,
J.
,
Bellini
,
R.
,
Colombo
,
G.
, and
Maggi
,
F.
,
2019
, “
Particulate Phase Evolution Inside Solid Rocket Motors: Preliminary Results
,”
Proceedings of 8th European Conference for Aeronautics and Aerospace Sciences (EUCASS)
,
Madrid, Spain
,
July 1–4
.
17.
Besnerais
,
G.
,
Nugue
,
M.
,
Devillers
,
R. W.
, and
Cesco
,
N.
,
2017
, “
Experimental Analysis of Solid-Propellant Surface During Combustion With Shadowgraphy Images: New Tools to Assist Aluminum-Agglomeration Modelling
,”
Proceedings of 7th European Conference for Aeronautics and Aerospace Sciences (EUCASS)
,
Milan, Italy
,
July 3–6
.
18.
Butler
,
A. G.
,
1988
, “
Holographic Investigation of Solid Propellant Combustion
,”
Postgraduate thesis
,
Naval Postgraduate School
,
Monterey, CA
.
19.
Xiao
,
Y.
,
Amano
,
R. S.
,
Cai
,
T.
, and
Li
,
J.
,
2005
, “
New Method to Determine the Velocities of Particles on a Solid Propellant Surface
,”
ASME J. Heat Transfer-Trans. ASME
,
127
(
9
), pp.
1057
–
1061
.
20.
Xiao
,
Y.
,
Amano
,
R. S.
,
Cai
,
T.
,
Li
,
J.
, and
He
,
G.
,
2003
, “
Particle Velocity on Solid-Propellant Surface Using X-ray Real-Time Radiography
,”
AIAA J.
,
41
(
9
), pp.
1763
–
1770
.
21.
Xiao
,
Y.
, and
Amano
,
R.
,
2006
, “
Aluminized Composite Solid Propellant Particle Path in the Combustion Chamber of a Solid Rocket Motor
,”
WIT Trans. Eng. Sci.
,
52
, pp.
153
–
164
.
22.
Li
,
Z.
,
Wang
,
N.
,
Shi
,
B.
,
Li
,
S.
, and
Yang
,
R.
,
2019
, “
Effects of Particle Size on Two-Phase Flow Loss in Aluminized Solid Rocket Motors
,”
Acta Astronaut.
,
159
, pp.
33
–
40
.
23.
Majdalani
,
J.
,
Katta
,
A.
,
Barber
,
T.
, and
Maicke
,
B.
,
2013
, “
Characterization of Particle Trajectories in Solid Rocket Motors
,”
Proceedings of 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference
,
San Jose, CA
,
July 14–17
.
24.
Simoes
,
M.
,
Della Pieta
,
P.
,
Godfroy
,
F.
, and
Simonin
,
O.
,
2005
, “
Continuum Modeling of the Dispersed Phase in Solid Rocket Motors
,”
Proceedings of 17th AIAA Computational Fluid Dynamics Conference
,
Toronto, Ontario, Canada
,
June 6–9
.
25.
Amano
,
R. S.
, and
Yen
,
Y. H.
,
2016
, “
Investigation of Alumina Flow Breakup Process in Solid Rocket Propulsion Chamber
,”
AIAA 2016 SciTech No. 2318567.
26.
Amano
,
R. S.
, and
Yen
,
Y.-H.
,
2015
, “
Study of Alumina Flow in a Propulsion Chamber
,”
51st AIAA/SAE/ASEE Joint Propulsion Conference
,
Rocket Motor Studies
,
Orlando, FL
,
July 27–29
.
27.
Amano
,
R. S.
,
Yen
,
YH.
, and
Hamman
,
M.L.
,
2014
, “Solid-Fuel Rocket Motor Efficiency Improvement Scheme,”
Novel Combustion Concepts for Sustainable Energy Development
A.
Agarwal
,
A.
Pandey
,
A.
Gupta
,
S.
Aggarwal
, and
A.
Kushari
, eds.,
Springer India
,
New Delhi
, pp.
535
–
560
.
28.
Chen
,
W.
,
Abbas
,
A. I.
,
Ott
,
R. N.
, and
Amano
,
R. S.
,
2020
, “
Investigation of Liquid Breakup Process Solid Rocket Motor Part B: Vertical C-D Nozzle
,”
ASME J. Energy Resour. Technol.
,
142
(
9
), p.
091301
.
29.
Chen
,
W.
,
Abbas
,
A. I.
,
Ott
,
R. N.
, and
Amano
,
R. S.
,
2020
, “
Investigation of Liquid Breakup Process Solid Rocket Motor Part A: Horizontal Converging–Diverging Nozzle
,”
ASME J. Energy Resour. Technol.
,
142
(
5
), p.
052102
.
30.
Abousabae
,
M.
,
Amano
,
R. S.
, and
Casper
,
C.
,
2021
, “
Investigation of Liquid Droplet Flow Behavior in a Vertical Nozzle Chamber
,”
ASME J. Energy Resour. Technol.
,
143
(
5
), p.
052108
.
31.
Abousabae
,
M.
, and
Amano
,
R. S.
,
2022
, “
Air Flow Acceleration Effect on Water Droplet Flow Behavior in Solid Rocket Motor
,”
ASME J. Energy Resour. Technol.
,
144
(
8
), p.
082305
.
32.
Thakre
,
P.
,
Rawat
,
R.
,
Clayton
,
R.
, and
Yang
,
V.
,
2013
, “
Mechanical Erosion of Graphite Nozzle in Solid-Propellant Rocket Motor
,”
J. Propul. Power
,
29
(
3
), pp.
593
–
601
.
33.
Tarey
,
P.
,
Kim
,
J.
,
Levitas
,
V. I.
,
Ha
,
D.
,
Park
,
J. H.
, and
Yang
,
H.
,
2015
, “
Prediction of the Mechanical Erosion Rate Decrement for Carbon-Composite Nozzle by Using the Nano-Size Additive Aluminum Particle
,”
J. Korean Soc. Propul. Eng.
,
19
(
6
), pp.
42
–
53
.
34.
Anson
,
J.
,
Drew
,
R.
, and
Gruzleski
,
J.
,
1999
, “
The Surface Tension of Molten Aluminum and Aluminum-Silicon-Magnesium Alloy Under Vacuum and Hydrogen Atmospheres
,”
Metall. Mater. Trans. B
,
30
(
6
), pp.
1027
–
1032
.
35.
McBride
,
B.
, and
Gordon
,
S.
,
1993
, “Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species,” NASA Technical Memorandum (TM) 4513, Document ID: 19940013151
36.
Reid
,
R. C.
,
Prausnitz
,
J. M.
, and
Poling
,
B. E.
,
1987
,
The Properties of Gasesand Liquids
, 4th ed.,
McGraw-Hill
,
New York
.
37.
Hermsen
,
R.
,
1981
, “
Aluminum Combustion Efficiency in Solid Rocket Motors
,”
19th Aerospace Sciences Meeting
,
St. Louis, MO
,
Jan. 12–15
.
38.
Schiller
,
L.
, and
Naumann
,
A.
,
1933
, “
Ueber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung
,”
VDI Zeits
,
77
(
12
), pp.
318
–
320
.
39.
Ranz
,
W. E.
, and
Marshall
,
W. R.
,
1952
, “
Evaporation From Drops–Part I and II
,”
Chem. Eng. Prog.
,
48
(
3
), p.
141
.
40.
STAR-CCM+, Ver 2020.2, CD-adapco Ltd
,
2022
, http://www.cd-adapco.com
41.
Neilson
,
J. H.
, and
Gilchrist
,
A.
,
1968
, “
Erosion by a Stream of Solid Particles
,”
Wear
,
11
(
2
), pp.
111
–
122
.
42.
Neilson
,
J. H.
, and
Gilchrist
,
A.
,
1968
, “
An Experimental Investigation Into Aspects of Erosion in Rocket Motor Nozzles
,”
Wear
,
11
(
2
), pp.
123
–
143
.
43.
Stiesch
,
G.
,
2003
,
Modeling Engine Spray and Combustion Processes
,
Springer,
Berlin
, p.
154
.
44.
Reitz
,
R. D.
, and
Diwakar
,
R.
,
1986
, “
Effect of Drop Breakup on Fuel Sprays
,”
SAE
Paper No.
860469
.
45.
Reitz
,
R. D.
, and
Diwakar
,
R.
,
1987
, “
Structure of High-Pressure Fuel Sprays
,”
SAE
Paper No.
870598
.
46.
Khalil
,
E. E.
,
ElHarriri
,
G.
, and
Abousabaa
,
M.
,
2018
, “
Heat Transfer Enhancement in Parabolic Trough Absorption Tube Using Twisted Tape Inserts
,”
2018 Joint Thermophysics and Heat Transfer Conference
,
Atlanta, GA
,
June 25–29
.
47.
Selim
,
O. M.
,
Elgammal
,
T.
, and
Amano
,
R. S.
,
2020
, “
Experimental and Numerical Study on the Use of Guide Vanes in the Dilution Zone
,”
ASME J. Energy Resour. Technol.
,
142
(
8
), p.
083001
.
48.
Salem
,
A. R.
,
Nourin
,
F. N.
,
Abousabae
,
M.
, and
Amano
,
R. S.
,
2021
, “
Experimental and Numerical Study of Jet Impingement Cooling for Improved Gas Turbine Blade Internal Cooling With In-Line and Staggered Nozzle Arrays
,”
ASME J. Energy Resour. Technol.
,
143
(
1
), p.
012103
.
49.
Hasan
,
A. S.
,
Abousabae
,
M.
,
Salem
,
A. R.
, and
Amano
,
R. S.
,
2021
, “
Study of Aerodynamic Performance and Power Output for Residential-Scale Wind Turbines
,”
ASME J. Energy Resour. Technol.
,
143
(
1
), p.
011302
.
50.
Elgammal
,
T.
,
Selim
,
O. M.
, and
Amano
,
R. S.
,
2021
, “
Enhancements of the Thermal Uniformity Inside a Gas Turbine Dilution Section Using Dimensional Optimization
,”
ASME J. Energy Resour. Technol.
,
143
(
10
), p.
102102
.
51.
McBride
,
B.
, and
Gordon
,
S.
,
1996
, “Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications II. User's Manual and Program Description,” NASA Reference Publication 1311, Document ID: 19950013764.
52.
Salita
,
M.
,
1988
, “
Quench Bomb Investigation of Al2O3 Formation From Solid Rocket Propellants (Part II): Analysis of Data
,”
25th JANNAF Combustion Meeting
,
Huntsville, AL
,
Oct. 24–28
, pp.
185
–
197
.
53.
Madabhushi
,
R. K.
,
Sabnis
,
J. S.
,
de Jong
,
F. J.
, and
Gibeling
,
H. J.
,
1991
, “
Calculation of Two-Phase Aft-Dome Flowfield in Solid Rocket Motors
,”
J. Propul. Power
,
7
(
2
), pp.
178
–
184
.
54.
Ketner
,
D. M.
, and
Hess
,
H. S.
,
1979
, “
Particle Impingement Erosion
,”
15th Joint Propulsion Conference
,
Las Vegas, NV
,
June 18–20
.
Copyright © 2023 by ASME
You do not currently have access to this content.