Abstract

In this study, we examined the aerodynamic loading on a small caliber rifle (spin stabilized) projectile moving in a muzzle flow field using an element method to analyze the loading and the effect of the angle of attack (for small angles from 0 to 3 deg) on the different components. The temporal pressure distribution on the projectile, which forms the basis of the element method, was computed using a computational fluid dynamics (CFD) analysis combined with a classical interior ballistics model. Then, a high-speed optical experiment was conducted to verify the results of the CFD method and ensure the accuracy of the calculations. The results were as follows: (a) similar to a large caliber projectile, the total axial force, which consisted primarily of the axial forces on the base and boattail, was found to have an inverse exponential relationship with time; (b) the overall lift was a combination of the lift of the base, boattail, cylinder, and nose; and (c) the interaction between the pitch moment of the base and that of the boattail was found to be the primary contributing factor to the total pitch moment. Based on these results, we recommend that the characteristics of the base and boattail be considered when specifying the geometric configuration of a projectile.

References

1.
Ma
,
P.
,
Zhou
,
Y.
,
Shang
,
X.
, and
Yang
,
M.
,
2017
, “
Firing Accuracy Evaluation of Electromagnetic Railgun Based on Multicriteria Optimal Latin Hypercube Design
,”
IEEE Trans. Plasma Sci.
,
45
(
7
), pp.
1503
1511
.10.1109/TPS.2017.2705980
2.
Rajesh
,
G.
,
Kim
,
H. D.
, and
Setoguchi
,
T.
,
2008
, “
Projectile Aerodynamics Overtaking a Shock Wave
,”
J. Spacecr. Rockets
,
45
(
6
), pp.
1251
1261
.10.2514/1.35398
3.
Oswatitsch
,
K.
,
1980
,
Intermediate Ballistics
, Chap. 3,
Springer
,
Aachen, Germany
.
4.
Carlucci
,
D.
, and
Vega
,
J.
,
2007
, “
Empirical Relationship for Muzzle Exit Pressure in a 155 mm Gun Tube
,”
Wit Trans. Modell. Simul.
, 45(2), pp.
225
229
.10.2495/CBAL07
5.
Carlucci
,
D. E.
,
Frydman
,
A. M.
, and
Cordes
,
J. A.
,
2013
, “
Mathematical Description of Projectile Shot Exit Dynamics (Set-Forward)
,”
ASME J. Appl. Mech.
,
80
(
3
), pp.
979
985
.10.1115/1.4023335
6.
Jiang
,
Z.
,
Takayama
,
K.
, and
Skews
,
B. W.
,
1998
, “
Numerical Study on Blast Flowfields Induced by Supersonic Projectiles Discharged From Shock Tubes
,”
Phys. Fluids
,
10
(
1
), pp.
277
288
.10.1063/1.869566
7.
Cler
,
D.
,
2003
, “
CFD Application to Gun Muzzle Blast-A Validation Case Study
,”
AIAA
Paper No. 2003-1142. 10.2514/6.2003-1142
8.
Jiang
,
X.
,
Chen
,
Z.
,
Fan
,
B.
, and
Li
,
H.
,
2008
, “
Numerical Simulation of Blast Flow Fields Induced by a High-Speed Projectile
,”
Shock Waves
,
18
(
3
), pp.
205
212
.10.1007/s00193-008-0155-9
9.
Carson
,
R. A.
, and
Sahni
,
O.
,
2017
, “
Scaling Laws for the Peak Overpressure of a Cannon Blast
,”
ASME J. Fluids Eng.
,
139
(
2
), p.
021204
.10.1115/1.4034639
10.
Carson
,
R. A.
, and
Sahni
,
O.
,
2015
, “
Numerical Investigation of Channel Leak Geometry for Blast Overpressure Attenuation in a Muzzle Loaded Large Caliber Cannon
,”
ASME J. Fluids Eng.
,
137
(
2
), p.
021102
.10.1115/1.4028123
11.
Zhang
,
B.
,
Liu
,
H.
,
Chen
,
F.
, and
Wang
,
G.
,
2012
, “
Numerical Simulation of Flow Fields Induced by a Supersonic Projectile Moving in Tubes
,”
Shock Waves
,
22
(
5
), pp.
417
425
.10.1007/s00193-012-0389-4
12.
Luo
,
Q.
, and
Zhang
,
X.
,
2017
, “
Numerical Simulation of Serial Launch Process of Multiple Projectiles Considering the Aftereffect Period
,”
Int. J. Numer. Methods Heat Fluid Flow
,
27
(
8
), pp.
1720
1734
.10.1108/HFF-04-2016-0151
13.
Yu
,
W.
, and
Zhang
,
X.
,
2013
, “
Numerical Simulation and Analysis of the Muzzle Flow During the Revolving Barrel Gun Firing
,”
ASME J. Appl. Mech.
,
80
(
3
), p.
031602
.10.1115/1.4023338
14.
Zhang
,
X.
, and
Yu
,
W.
,
2010
, “
Aerodynamic Analysis of Projectile in Gun System Firing Process
,”
ASME J. Appl. Mech.
,
5
(
77
), pp.
769
775
.10.1115/1.4001559
15.
Schmidt
,
E. M.
, and
Shear
,
D.
,
1975
, “
Optical Measurements of Muzzle Blast
,”
AIAA J.
,
13
(
8
), pp.
1086
1091
.10.2514/3.60506
16.
Klingenberg
,
G.
, and
Schröder
,
G. A.
,
1976
, “
Investigation of Combustion Phenomena Associated With the Flow of Hot Propellant Gases-II: Gas Velocity Measurements by Laser-Induced Gas Breakdown
,”
Combust. Flame
,
27
, pp.
177
187
.10.1016/0010-2180(76)90021-3
17.
Schmidt
,
E. M.
,
Gordnier
,
R. E.
, and
Fanslert
,
K. S.
,
1984
, “
Interaction of Gun Exhaust Flowfields
,”
AIAA J.
,
22
(
4
), pp.
516
517
.10.2514/3.48475
18.
Gretler
,
W.
,
1967
,
Intermediate Ballistics Investigations of Wing Stabilized Projectiles
, Chap. 2, Deutsche Versuchsanstalt Für Luft- Und Raumfahrt
Dlr Fb
,
Aachen, Germany
.
19.
Schmidt
,
E. M.
,
Fansler
,
K. S.
, and
Shear
,
D. D.
,
1977
, “
Trajectory Perturbations of Fin-Stabilized Projectiles Due to Muzzle Blast
,”
J. Spacecr. Rockets
,
14
(
6
), pp.
339
344
.10.2514/3.57206
20.
Schmidt
,
E. M.
,
Gion
,
E. J.
, and
Shear
,
D. D.
,
1977
, “
Acoustic Thermometric Measurements of Propellant Gas Temperatures in Guns
,”
AIAA J.
,
15
(
2
), pp.
222
226
.10.2514/3.60620
21.
Qin
,
Q.
, and
Zhang
,
X.
,
2016
, “
Numerical Investigation on Combustion in Muzzle Flows Using an Inert Gas Labeling Method
,”
Int. J. Heat Mass Transfer
,
101
, pp.
91
103
.10.1016/j.ijheatmasstransfer.2016.05.009
22.
Mo
,
G. L.
,
Li
,
Z. X.
, and
Wu
,
Z. L.
,
2018
, “
A Theoretical Model of Non-Deforming Bullets Penetrating Ballistic Gelatin
,”
Int. J. Impact Eng.
,
114
, pp.
105
110
.10.1016/j.ijimpeng.2017.12.004
23.
Silton
,
S.
, and
Howell
,
B.
,
2009
, “
Effect of Spin Variation on Predicting the Dynamic Stability of Small-Caliber Ammunition
,”
AIAA
Paper No. 2009-310.
24.
Jin
,
Z. M.
,
2004
,
Interior Ballistics of Guns
, Chap. 4,
Beijing Institute of Technology Press
,
Beijing
.
25.
ANSYS
, 2014, “
Fluent Theory Guide
,” Chap. 4, ANSYS, Canonsburg, PA.
26.
Richardson
,
L. F.
, and
Gaunt
,
J. A.
,
1927
, “
VIII. The Deferred Approach to the Limit
,”
Philos. Trans. R. Soc. Lond. A
,
226
(
636–646
), pp.
299
361
.10.1098/rsta.1927.0008
27.
Roache
,
P. J.
,
1998
,
Verification and Validation in Computational Science and Engineering
, Chap. 4,
Hermosa
,
Albuquerque, NM
.
28.
Jak
,
E.
, and
Hayes
,
P. C.
,
2008
, “
Procedure of Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.10.1115/1.2960953
29.
Zhou
,
L.
,
Shi
,
W.
,
Lu
,
W.
,
Hu
,
B.
, and
Wu
,
S.
,
2012
, “
Numerical Investigations and Performance Experiments of a Deep-Well Centrifugal Pump With Different Diffusers
,”
ASME J. Fluids Eng.
,
134
(
7
), p.
071102
.10.1115/1.4006676
30.
Corke
,
P.
,
2011
,
Robotics, Vision and Control: Fundamental Algorithms in MATLAB
, Chaps. 10–14,
Springer Publishing Company, Incorporated
,
New York
.
31.
Moffat
,
R. J.
,
1982
, “
Contributions to the Theory of Single-Sample Uncertainty Analysis
,”
ASME J. Fluids Eng.
,
104
(
2
), pp.
250
260
.10.1115/1.3241818
32.
Zhang
,
Z.
,
2000
, “
A Flexible New Technique for Camera Calibration
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
22
(
11
), pp.
1330
1334
.10.1109/34.888718
33.
Moffat
,
R. J.
,
1985
, “
Using Uncertainty Analysis in the Planning of an Experiment
,”
ASME J. Fluids Eng.
,
107
(
2
), p.
173
.10.1115/1.3242452
34.
Abernethy
,
R. B.
,
Benedict
,
R. P.
, and
Dowdell
,
R. B.
,
1985
, “
ASME Measurement Uncertainty
,”
Ann. Occup. Hyg.
,
52
(
6
), pp.
413
417
.10.1115/1.3242450
35.
Kline
,
S. J.
,
1985
, “
The Purposes of Uncertainty Analysis
,”
ASME J. Fluids Eng.
,
107
(
2
), pp.
153
160
.10.1115/1.3242449
36.
Vision Research Inc.,
2018
,
“Data Sheet: The Phantom Ultra High-Speed Camera Line
,” Vision Research Inc., Wayne, NJ, accessed Nov. 4,
2018
, http://www.phantomhighspeed.com/-/media/project/ameteksxa/visionresearch/documents/datasheets/web/wdsuhsfam.pdf?download=1
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