Detonation waves in gas-filled piping or tubing pose special challenges in analysis and prediction of structural response. The challenges arise due to the nature of the detonation process and the role of fluid-structure interaction in determining the propagation and arrest of fractures. Over the past 10 years, our laboratory has been engaged in studying this problem and developing methodologies for estimating structural response. A brief overview of detonation waves and some key issues relevant to structural waves is presented first. This is followed by a summary of our work on the elastic response of tubes and pipes to ideal detonation loading, highlighting the importance of detonation wave speed in determining flexural wave excitation and possibility of resonant response leading to large deformations. Some issues in measurement technique and validation testing are then presented. The importance of wave reflection from bends, valves, and dead ends is discussed, as well as the differences between detonation, shock wave, and uniform internal pressure loading. Following this, we summarize our experimental findings on the fracture threshold of thin-walled tubes with pre-existing flaws. A particularly important issue for hazard analysis is the estimation of loads associated with flame acceleration and deflagration-to-detonation transition. We give some recent results on pressure and elastic strain measurements in the transition regime for a thick-wall piping, and some remarks about plastic deformation.

1.
Shepherd
,
J. E.
, 2008, “
Detonation in Gases
,”
Proceedings of the Combustion Symposium
, Vol.
32
.
2.
Lee
,
J. H. S.
, 2008,
The Detonation Phenomenon
,
Cambridge University Press
,
Cambridge
.
3.
Thibault
,
P.
,
Britton
,
L.
, and
Zhang
,
F.
, 2000, “
Deflagration and Detonation of Ethylene Oxide Vapor in Pipelines
,”
Process Saf. Prog.
1066-8527,
19
(
3
), pp.
125
139
.
4.
Grossel
,
S. S.
, 2002,
Deflagration and Detonation Flame Arresters
,
Wiley
,
New York
.
5.
Kuznetsov
,
M.
,
Breitung
,
W.
,
Grüne
,
J.
, and
Singh
,
R. K.
, 2005, “
Structural Response of DN15-Tubes Under Radiolysis Gas Detonation Loads for BWR Safety Applications
,”
18th International Conference on Structural Mechanics in Reactor Technology
, Beijing, China, Paper No. SMiRT 18-J09-1.
6.
Krieg
,
R.
,
Dolensky
,
B.
,
Goller
,
B.
,
Breitung
,
W.
,
Redlinger
,
R.
, and
Royl
,
P.
, 2003, “
Assessment of the Load-Carrying Capacities of a Spherical Pressurized Water Reactor Steel Containment Under a Postulated Hydrogen Detonation
,”
Nucl. Technol.
,
141
(
2
), pp.
109
121
. 0029-5450
7.
Naitoh
,
M.
,
Kasahara
,
F.
,
Kubota
,
R.
, and
Ohshima
,
I.
, 2003, “
Analysis of Pipe Rupture of Steam Condensation Line at Hamoaka-1, (I) Accumulation of Noncondensable Gas in a Pipe
,”
J. Nucl. Sci. Technol.
0022-3131,
40
(
12
), pp.
1032
1040
.
8.
OECD
, 2000, “
Flame Acceleration and Deflagration to Detonation Transition in Nuclear Safety
,” OECD Nuclear Energy Agency Technical Report No. NEA/CSNI/R(2000)7.
9.
Roy
,
G. D.
,
Frolov
,
S. M.
,
Borisov
,
A. A.
, and
Netzer
,
D. W.
, 2004, “
Pulse Detonation Propulsion: Challenges, Current Status, and Future Perspective
,”
Prog. Energy Combust. Sci.
0360-1285,
30
, pp.
545
672
.
10.
Florek
,
J. R.
, and
Benaroya
,
H.
, 2005, “
Pulse-Pressure Loading Effects on Aviation and General Engineering Structures
,”
J. Sound Vib.
,
284
, pp.
421
453
. 0022-460X
11.
Baker
,
W. E.
,
Cox
,
P. A.
,
Westine
,
P. S.
,
Kulesz
,
J. J.
, and
Strehlow
,
R. A.
, 1983,
Explosion Hazards and Evaluation
,
Elsevier
,
Amsterdam
.
12.
Bjerketvedt
,
D.
,
Bakke
,
J. R.
, and
van Wingerden
,
K.
, 1997, “
Gas Explosion Handbook
,”
J. Hazard. Mater.
,
52
, pp.
1
150
. 0304-3894
13.
NFPA
, 2002, “
Standard on Explosion Protection Systems
,” National Fire Protection Association Technical Report No. 69.
14.
ASME, 2008, “
Case 2564—Impulsively Loaded Pressure Vessels
,” Supplement 4 of ASME B and PV Code Cases: Boilers and Pressure Vessels, The American Society of Mechanical Engineers, New York, NY.
15.
Duffey
,
T.
,
Rodriguez
,
E.
, and
Romero
,
C.
, 2002, “
Design of Pressure Vessels for High-Strain Rate Loading: Dynamic Pressure and Failure Criteria
,”
Weld. Res. Counc. Bull.
0043-2326,
477
.
16.
Rodriguez
,
E.
, and
Duffey
,
T.
, 2004, “
Fracture-Safe and Fatigue Design Criteria for Detonation-Induced Pressure Loading in Containment Vessels
,”
Weld. Res. Counc. Bull.
0043-2326,
494
.
17.
Pellini
,
W.
, 1973, “
Design Options for Selection of Fracture Control Procedures in the Modernization of Codes, Rules and Standards. Analytical Design Procedures for Metals of Elastic-Plastic and Plastic Fracture Properties
,”
Weld. Res. Counc. Bull.
0043-2326,
186
.
18.
Ciccarelli
,
G.
, and
Dorofeev
,
S.
, 2008, “
Flame Acceleration and Transition to Detonation in Ducts
,”
Prog. Energy Combust. Sci.
0360-1285,
34
(
4
), pp.
499
550
.
19.
Fickett
,
W.
, and
Davis
,
W. C.
, 2001,
Detonation Theory and Experiment
,
Dover
,
New York
.
20.
Tieszen
,
S. R.
,
Stamps
,
D. W.
,
Westbrook
,
C. K.
, and
Pitz
,
W. J.
, 1991, “
Gaseous Hydrocarbon-Air Detonations
,”
Combust. Flame
,
84
(
3
), pp.
376
390
. 0010-2180
21.
Shepherd
,
J. E.
, 1986, “
Chemical Kinetics of Hydrogen–Air–Diluent Detonations
,”
Prog. Astronaut. Aeronaut.
0079-6050,
106
, pp.
263
293
.
22.
Westbrook
,
C. K.
, and
Urtiew
,
P. A.
, 1982, “
Chemical Kinetic Prediction of Critical Parameters in Gaseous Detonation
,”
19th Symposium on International Combustion Processes
, pp.
615
623
.
23.
Reynolds
,
W.
, 1986, “
The Element Potential Method for Chemical Equilibrium Analysis: Implementation in the Interactive Program STANJAN
,” Mechanical Engineering Department, Stanford University, Technical Report.
24.
McBride
,
B.
, and
Gordon
,
S.
, 1996, “
Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications: II. Users Manual and Program Description
,” NASA Reference Publication No. 1311.
25.
Browne
,
S.
,
Ziegler
,
J.
, and
Shepherd
,
J. E.
, 2004, “
Numerical Solution Methods for Shock and Detonation Jump Conditions
,” Graduate Aeronautical Laboratories, California Institute of Technology, Technical Report No. FM2006.006.
26.
Beltman
,
W.
,
Burcsu
,
E.
,
Shepherd
,
J.
, and
Zuhal
,
L.
, 1999, “
The Structural Response of Tubes to Internal Shock Loading
,”
ASME J. Pressure Vessel Technol.
0094-9930,
121
, pp.
315
322
.
27.
Stamps
,
D. W.
,
Slezak
,
S. E.
, and
Tieszen
,
S. R.
, 2006, “
Observations of the Cellular Structure of Fuel–Air Detonations
,”
Combust. Flame
,
144
(
1–2
), pp.
289
298
. 0010-2180
28.
Pintgen
,
F.
,
Austin
,
J. M.
, and
Shepherd
,
J. E.
, 2003, “
Detonation Front Structure: Variety and Characterization
,”
Confined Detonations and Pulse Detonation Engines
,
G.
Roy
,
S.
Frolov
,
R.
Santoro
, and
S.
Tsyganov
, eds.,
Torus
,
Moscow
, pp.
105
116
.
29.
Austin
,
J.
, 2003, “
The Role of Instability in Gaseous Detonation
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
30.
Pintgen
,
F.
, 2004, “
Detonation Diffraction in Mixtures With Various Degrees of Instability
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
31.
Kaneshige
,
M.
, and
Shepherd
,
J.
, 1997, “
Detonation Database
,” GALCIT Technical Report No. FM97-8.
32.
Dorofeev
,
S.
,
Sidorov
,
V.
,
Kuznetsov
,
M.
,
Matsukov
,
I.
, and
Alekseev
,
V.
, 2000, “
Effect of Scale on the Onset of Detonations
,”
Shock Waves
,
10
(
2
), pp.
137
149
. 0938-1287
33.
Taylor
,
G.
, 1950, “
The Dynamics of Combustion Fronts Behind Plane and Spherical Detonations
,”
Proc. R. Soc. London, Ser. A
,
200
, pp.
235
247
. 0080-4630
34.
Zeldovich
,
Y. B.
, 1942, “
On the Distribution of Pressure and Velocity in the Products of a Detonation Explosion, Specifically in the Case of Spherical Propagation of the Detonation Wave
,”
J. Exp. Theor. Phys.
,
12
(
1
), pp.
389
406
. 1063-7761
35.
Beltman
,
W.
, and
Shepherd
,
J.
, 2002, “
Linear Elastic Response of Tubes to Internal Detonation Loading
,”
J. Sound Vib.
0022-460X,
252
(
4
), pp.
617
655
.
36.
Radulescu
,
M.
, and
Hanson
,
R.
, 2005, “
Effect of Heat Loss on Pulse Detonation Engine Flow Fields and Performance
,”
J. Propul. Power
0748-4658,
21
(
2
), pp.
274
285
.
37.
Edwards
,
D.
,
Brown
,
D.
,
Hooper
,
G.
, and
Jones
,
A.
, 1970, “
Influence of Wall Heat Transfer on Expansion Following a C-J Detonation Wave
,”
J. Phys. D: Appl. Phys.
0022-3727,
3
(
3
), pp.
365
376
.
38.
Noda
,
N.
,
Hetnarski
,
R.
, and
Tanigawa
,
Y.
, 2002,
Thermal Stresses
,
Taylor & Francis
,
London
.
39.
Fickett
,
W.
, and
Davis
,
W.
, 1979,
Detonation
,
University of California Press
,
Berkeley, CA
.
40.
de Malherbe
,
M.
,
Wing
,
R.
,
Laderman
,
A.
, and
Oppenheim
,
A.
, 1966, “
Response of a Cylindrical Shell to Internal Blast Loading
,”
J. Mech. Eng. Sci.
0022-2542,
8
(
1
), pp.
91
98
.
41.
Blevins
,
R. D.
, 1979,
Formulas for Natural Frequency and Mode Shape
,
van Nostrand Reinhold
,
New York
.
42.
Auslender
,
F.
, and
Combescure
,
A.
, 2000, “
Spherical Elastic-Plastic Structures Under Internal Explosion. Approximate Analytical Solutions and Applications
,”
Eng. Struct.
0141-0296,
22
, pp.
984
992
.
43.
Biggs
,
J.
, 1964,
Introduction to Structural Dynamics
,
McGraw-Hill
,
New York
.
44.
Tang
,
S.
, 1965, “
Dynamic Response of a Tube Under Moving Pressure
,”
J. Eng. Mech. Div., Proc. ASCE
,
91
, pp.
97
122
.
45.
Reismann
,
H.
, 1965, “
Response of a Pre-Stressed Cylindrical Shell to Moving Pressure Load
,”
Eighth Midwest Mechanics Conference
,
S.
Ostrach
and
R.
Scanlon
, eds.,
Pergamon
,
New York
, pp.
349
363
.
46.
Simkins
,
T.
, 1987, “
Resonance of Flexural Waves in Gun Tubes
,” US Army Armament Research, Development and Engineering Center Technical Report No. ARCCB-TR-87008.
47.
Simkins
,
T.
,
Pflegl
,
G.
, and
Stilson
,
E.
, 1993, “
Dynamic Strains in a 60mm Gun Tube—An Experimental-Study
,”
J. Sound Vib.
,
168
(
3
), pp.
549
557
. 0022-460X
48.
Simkins
,
T.
, 1994, “
Amplification of Flexural Waves in Gun Tubes
,”
J. Sound Vib.
,
172
(
2
), pp.
145
154
. 0022-460X
49.
Mirzaei
,
A.
,
Mazaheri
,
K.
, and
Biglari
,
H.
, 2005, “
Analytical Modeling of the Elastic Structural Response of Tubes to Internal Detonation Loading
,”
Int. J. Pressure Vessels Piping
0308-0161,
82
(
12
), pp.
883
895
.
50.
Brossard
,
J.
, and
Renard
,
J.
, 1979, “
Mechanical Effects of Gaseous Detonations on a Flexible Confinement
,”
Prog. Astronaut. Aeronaut.
0079-6050,
75
, pp.
108
121
.
51.
Van de Ven
,
A.
,
Olivier
,
H.
, and
Grönig
,
H.
, 1996, “
Dynamic Structural Response of a Dust Detonation Tube
,”
Seventh International Colloquium on Dust Explosions
, Bergen, Norway, pp.
4.22
4.32
.
52.
Sperber
,
A.
,
Schildber
,
H.
, and
Schlehlein
,
S.
, 1999, “
Dynamic Load on a Pipe Caused by Acetylene Detonations—Experiments and Theoretical Approaches
,”
Shock Vib.
1070-9622,
6
, pp.
29
43
.
53.
Thomas
,
G.
, 2002, “
The Response of Pipes and Supports Generated by Gaseous Detonations
,”
ASME J. Pressure Vessel Technol.
0094-9930,
124
, pp.
66
73
.
54.
Simkins
,
T.
, 1995, “
The Influence of Transient Flexural Waves on Dynamic Strains in Cylinders
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
62
(
1
), pp.
262
265
.
55.
Akbar
,
R.
, 1997, “
Mach Reflection of Gaseous Detonations
,” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY.
56.
Chao
,
T.
, and
Shepherd
,
J.
, 2005, “
Detonation Loading of Tubes in the Modified Shear Wave Regime
,”
Proceedings of the 24th International Symposium on Shock Waves
,
Z.
Jiang
, ed.,
Springer
,
New York
, Vol.
2
, pp.
865
870
.
57.
Chao
,
T. W.
, 2004, “
Gaseous Detonation-Driven Fracture of Tubes
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
58.
Shepherd
,
J. E.
,
Karnesky
,
J.
,
Pintgen
,
F.
, and
Krok
,
J. C.
, 2008, “
Experimental Measurements of Strains and Blast Waves Resulting From Detonations in Tubes
,” Graduate Aeronautical Laboratories, California Institute of Technology, Technical Report No. FM2006.010.
59.
Deiterding
,
R.
,
Cirak
,
F.
,
Mauch
,
S.
, and
Meiron
,
D.
, 2007, “
A Virtual Test Facility for Simulating Detonation-Induced Fracture of Thin Flexible Shells
,”
Int. J. Multiscale Comp. Eng.
1543-1649,
5
(
1
), pp.
47
63
.
60.
Cirak
,
F.
,
Deiterding
,
R.
, and
Mauch
,
S. P.
, 2007, “
Large-Scale Fluid-Structure Interaction Simulation of Viscoplastic and Fracturing Thin Shells Subjected to Shocks and Detonations
,”
Comput. Struct.
,
85
(
11–14
), pp.
1049
1065
. 0045-7949
61.
Liang
,
Z.
,
Karnesky
,
J.
, and
Shepherd
,
J.
, 2008, “
Detonations in C2H4–O2
. Experimental Measurements and Validation of Numerical Simulations for Incident and Reflected Waves,” Graduate Aeronautical Laboratory, California Institute of Technology, Technical Report No. FM2006-009.
62.
Shepherd
,
J. E.
,
Teodorcyzk
,
A.
,
Knystautas
,
R.
, and
Lee
,
J. H.
, 1991, “
Shock Waves Produced by Reflected Detonations
,”
Prog. Astronaut. Aeronaut.
0079-6050,
134
, pp.
244
264
.
63.
Liang
,
Z.
,
Karnesky
,
J.
, and
Shepherd
,
J.
, 2006, “
Structural Response to Reflected Detonations and Deflagration-to-Detonation Transition in H2–N2O Mixtures
,” Graduate Aeronautical Laboratory, California Institute of Technology, Technical Report No. FM2006-003.
64.
Shepherd
,
J.
,
Schultz
,
E.
, and
Akbar
,
R.
, 2000, “
Detonation Diffraction
,”
Proceedings of the 22nd International Symposium on Shock Waves
,
G.
Ball
,
R.
Hillier
, and
G.
Roberts
, eds., Vol.
1
, pp.
41
48
.
65.
Thomas
,
G. O.
, and
Williams
,
R. L.
, 2002, “
Detonation Interactions With Wedges and Bends
,”
Shock Waves
,
11
, pp.
481
491
. 0938-1287
66.
Liang
,
Z.
,
Curran
,
T.
, and
Shepherd
,
J. E.
, 2008, “
Structural Response of Piping Components to Detonation Loading
,” Graduate Aeronautical Laboratories, California Institute of Technology, Technical Report No. FM2006.008.
67.
Liang
,
Z.
,
Curran
,
T.
, and
Shepherd
,
J. E.
, 2008, “
Structural Response to Detonation Loading in a 90-deg Bend
,”
Proceedings of the 26th International Symposium on Shock Waves
, Göttingen, Germany, Jul. 15–20, 2007,
K.
Hannemann
and
F.
Seiler
, eds.,
Springer
,
New York
.
68.
Naitoh
,
M.
,
Kasahara
,
F.
,
Kubota
,
R.
, and
Ohshima
,
I.
, 2003, “
Analysis of Pipe Rupture of Steam Condensation Line at Hamoaka-1, (II) Hydrogen Combustion and Generation
,”
J. Nucl. Sci. Technol.
0022-3131,
40
(
12
), pp.
1041
1051
.
69.
Chao
,
T. -W.
, and
Shepherd
,
J. E.
, 2005, “
Fracture Response of Externally Flawed Aluminum Cylindrical Shells Under Internal Gaseous Detonation Loading
,”
Int. J. Fract.
0376-9429,
134
(
1
), pp.
59
90
.
70.
Chao
,
T. W.
, and
Shepherd
,
J. E.
, 2004, “
Comparison of Fracture Response of Preflawed Tubes Under Internal Static and Detonation Loading
,”
ASME J. Pressure Vessel Technol.
0094-9930,
126
(
3
), pp.
345
353
.
71.
Lam
,
A.
, and
Zielonka
,
M.
, 2002, “
Fracture Response of Externally Flawed Thin-Walled Plastic Tubes to Gaseous Detonation Loading
,” Graduate Aeronautical Laboratories, California Institute of Technology, Report No. Ae104c.
72.
Brossard
,
J.
, and
Charpentier de Coysevox
,
N.
, 1976, “
Effects d’un confinement souple sur la détonation des mélanges gazeux
,”
Acta Astronaut.
,
3
, pp.
971
981
. 0094-5765
73.
White
,
D. A.
, 1957, “
On the Existence of Higher Than Normal Detonation Pressures
,”
J. Fluid Mech.
0022-1120,
2
, pp.
513
514
.
74.
Craven
,
A. D.
, and
Grieg
,
T. R.
, 1968, “
The Development of Detonation Over–Pressures in Pipelines
,”
Inst. Chem. Eng. Symp. Ser.
,
25
, pp.
41
50
. 0022-1120
75.
Shepherd
,
J.
, 1992, “
Pressure Loads and Structural Response of the BNL High-Temperature Detonation Tube
,” Brookhaven National Laboratory Technical Report No. A-3991.
76.
Boyack
,
K.
,
Tieszen
,
S.
, and
Stamps
,
D.
, 1993, “
Internal-Pressure Loads Due to Gaseous Detonations
,”
Proc. R. Soc. London, Ser. A
,
443
(
1918
), pp.
343
366
. 0013-7812
77.
Kogarko
,
S. M.
, 1958, “
Invetigation of Pressure at the End of a Tube in Connection With Rapid Nonstationary Combustion
,”
Sov. Phys. Tech. Phys.
,
3
(
9
), pp.
1875
1879
. 0038-5662
78.
Chan
,
C. K.
, and
Dewitt
,
W. A.
, 1996, “
DDT in End Gases
,”
27th Symposium (International) on Combustion
,
The Combustion Institute
,
Pittsburgh, PA
, Vol.
2
, p.
2679
.
79.
Zhang
,
F.
,
Thibault
,
P. A.
, and
Murray
,
S. B.
, 1998, “
Transition From Deflagration to Detonation in Multi-Phase Slug
,”
Combust. Flame
,
114
, pp.
13
24
. 0010-2180
80.
Duffey
,
T.
, and
Mitchell
,
D.
, 1973, “
Containment of Explosions in Cylindrical Shells
,”
Int. J. Mech. Sci.
,
15
, pp.
237
249
. 0020-7403
81.
Benham
,
R. A.
, and
Duffey
,
T.
, 1974, “
Experimental-Theoretical Correlation on the Containment of Explosions in Cylindrical Vessels
,”
Int. J. Mech. Sci.
,
16
, pp.
549
558
. 0020-7403
82.
Hodge
,
P. G.
, 1956, “
The Influence of Blast Characteristics on Final Deformation of Circular Cylindrical Shells
,”
ASME J. Appl. Mech.
,
284
, pp.
617
624
. 0021-8936
83.
Duffey
,
T.
, 1971, “
Approximate Solutions of an Impulsively Loaded Long Cylinder Governed by an Elastic-Plastic Material Law
,”
Acta Mech.
,
11
, pp.
45
57
. 0001-5970
84.
Duffey
,
T.
, and
Krieg
,
R.
, 1969, “
Effects of Strain Hardening and Strain Rate Sensitivity on the Transient Response of Elastic-Plastic Rings and Cylinders
,”
Int. J. Mech. Sci.
0020-7403,
11
, pp.
825
844
.
85.
Fanous
,
F.
, and
Greiman
,
L.
, 1988, “
Simplified Analysis for Impulsively Loaded Shells
,”
J. Struct. Eng.
0733-9445,
114
, pp.
885
899
.
86.
Young
,
W.
, and
Budynas
,
R.
, 2002,
Roark’s Formulas for Stress and Strain
,
7th ed.
,
McGraw-Hill
,
New York
.
87.
Pintgen
,
F.
, and
Shepherd
,
J. E.
, 2007, “
Elastic and Plastic Structural Response of Tubes to Deflagration-to-Detonation Transition
,” Explosion Dynamics Laboratory, California Institute of Technology, Technical Report No. FM2006-005.
88.
Koslowksi
,
M.
, and
Lew
,
A.
, 1999, “
Plastic Response of Thin Tubes to Gaseous Detonation Waves
,” Graduate Aeronautical Laboratories, California Institute of Technology, Report No. Ae104c.
You do not currently have access to this content.