Julius Mezaros Lecture
53 Years of Blast Wave Research
A Personal History
by
John M. Dewey
Dewey McMillin & Associates
Professor Emeritus, University of Victoria
MABS21 Israel 2010
The Entropy Problem
G. I. Taylor (1950)
ΔS
ΔS
MABS21 Israel 2010
ΔS
The Entropy Problem
G. I. Taylor (1950)
• In Eulerian co-ordinates the air passing a
fixed measurement point is non-isentropic
MABS21 Israel 2010
The Entropy Problem
G. I. Taylor (1950)
• In Eulerian co-ordinates the air passing a
fixed measurement point is non-isentropic
• The simple thermodynamic relationships
do not apply
MABS21 Israel 2010
The Entropy Problem
G. I. Taylor (1950)
• In Eulerian co-ordinates the air passing a
fixed measurement point is non-isentropic
• The simple thermodynamic relationships
do not apply
• Measured P = f(t)
ρ = f(t)
u = f(t)
T = f(t)
MABS21 Israel 2010
The Solution
• Work in Lagrangian co-ordinates, viz. trace the
physical properties along the particle paths
instead of in x,y,z space.
MABS21 Israel 2010
The Solution
• Work in Lagrangian co-ordinates, viz. trace the physical
properties along the particle paths instead in x,y,z space
• Along the particle paths between the primary and
secondary shocks the entropy is constant and the
simple thermodynamic relationships can be used
P  const . 

P   T
u 
dR
dt
MABS21 Israel 2010
Smoke Tracers on Snowball (500 t TNT, 1964)
MABS21 Israel 2010
Particle Trajectory Analysis
Particle
Trajectories
P PS     S


Time
ΔR
dR 0
a 0 dt
M S  PS ,  S , T S
2

Primary
Shock
P PS     S
 Ms

ΔRo
0
 R0  R0


 R  R
P PS     S

u  dR dt
Radius
MABS21 Israel 2010
The Spherical Piston
G. I. Taylor (1946)
MABS21 Israel 2010
MABS21 Israel 2010
Piston Path compared to gauge
MINOR UNCLE 2 kt ANFO
Hydrostatic pressure
MABS21 Israel 2010
Piston Path compared to gauge
MINOR UNCLE 2 kt ANFO
Dynamic Pressure
MABS21 Israel 2010
SCALING
• For most explosives, the physical
properties of blast waves scale with great
precision over wide ranges of charge
mass and atmospheric conditions using
Hopkinson’s (1915) and Sachs’ (1944)
scaling laws
MABS21 Israel 2010
SCALING
• For most explosives, the physical
properties of blast waves scale with great
precision over wide ranges of charge
mass and atmospheric conditions using
Hopkinson’s (1915) and Sachs’ (1944)
scaling laws
• A 1950s Tripartite (US, UK & Canada)
agreement recommended all blast results
be scaled to a unit charge mass at NTP
MABS21 Israel 2010
Hopkinson’s & Sachs’ Scaling
R 1 R 2  W 1 W 2 
R 1 R 2  W 1 W 2 
1 3
t 1 t 2  W 1 W 2 
1 3
 P02
 P02
P01 
MABS21 Israel 2010
1 3
1
3
P01 
1 3
T 2
T1 
1 2
Scaling Peak Values
TNT Surface Burst
30 kg
100 tonne
Dewey, 1964
MABS21 Israel 2010
Scaling Time Histories
TNT Surface Burst 30 kg
100 tonnes (Dewey, 1964)
MABS21 Israel 2010
Scaling Not Being Used
• Experimenters are not taking
advantage of the scaling laws
MABS21 Israel 2010
Scaling Not Being Used
• Experimenters are not taking
advantage of the scaling laws
• Charge mass, and ambient
atmospheric conditions frequently
are not measured or recorded
MABS21 Israel 2010
Scaling Not Being Used
• Experimenters are not taking
advantage of the scaling laws
• Charge mass, and ambient
atmospheric conditions frequently
are not measured or recorded
• This makes it impossible to
validate results
MABS21 Israel 2010
Shock Reflection (HOB)
PS
PS
RS
TP
H
RS
MS
Regular Reflection
Mach Reflection
MABS21 Israel 2010
Von Neumann 2 & 3 Shock (1943)
MABS21 Israel 2010
Hydrostatic Pressure
1.25 kg TNT at 1.7 m HOB (AirBlast)
MABS21 Israel 2010
Dynamic Pressure
1.25 kg TNT HOB 1.7 m (AirBlast)
10
D ynam ic P ressure (atm )
Transition
1
RR
MR
0.1
0.01
0.1
1
10
G round R adius (m )
MABS21 Israel 2010
100
Over-emphasis on
Hydrostatic Pressure
• Most blast wave properties are expressed
in terms of hydrostatic overpressure
• This was because it was the only physical
property of a blast wave that could be
measured with adequate time resolution
MABS21 Israel 2010
Over-emphasis on
Hydrostatic Pressure
• Hydrostatic pressure is the least sensitive
of all the physical properties e.g. contact
surfaces, boundary layer
MABS21 Israel 2010
Over-emphasis on
Hydrostatic Pressure
• Hydrostatic pressure is the least sensitive
of all the physical properties e.g. contact
surfaces, boundary layer
• Hydrostatic pressure is not the primary
cause of damage by a blast wave. Most
damage and injury is caused by the drag
forces, i.e. drag coeff. x dynamic pressure
MABS21 Israel 2010
Dynamic Pressure
P = ½ ρ u * |u|
D
• Dynamic pressure is a mathematical, not a
physical property of a compressible flow
i.e. it is not directly measureable.
MABS21 Israel 2010
Dynamic Pressure
P = ½ ρ u * |u|
D
• Dynamic pressure is a mathematical, not a
physical property of a compressible flow
i.e. it is not directly measureable.
• Most analyses now use numerical
simulation techniques from which dynamic
pressure is as easily derived as any other
property.
MABS21 Israel 2010
Example: Entrance Labyrinths
& Blast Wave Mitigation
MABS21 Israel 2010
Energy Loss is Minimal
• Energy in a blast wave is essentially
 1
1
2 
    1 OP  2  u 


MABS21 Israel 2010
Energy Loss is Minimal
• Energy in a blast wave is essentially
 1
1
2 
    1 OP  2  u 


• If the hydrostatic pressure is decreased
then the dynamic pressure must increase
MABS21 Israel 2010
MABS Results
• At the last three MABS, twenty papers
dealt with blast mitigation
MABS21 Israel 2010
MABS Results
• At the last three MABS, twenty papers
dealt with blast mitigation
• Only one discussed the energy
relationship between hydrostatic and
dynamic pressure
MABS21 Israel 2010
MABS Results
• At the last three MABS, twenty papers
dealt with blast mitigation
• Only one discussed the energy
relationship between hydrostatic and
dynamic pressure
• Only two attempted to measure or report
the dynamic pressures
MABS21 Israel 2010
MABS Results
• At the last three MABS, twenty papers
dealt with blast mitigation
• Only one discussed the energy
relationship between hydrostatic and
dynamic pressure
• Only two attempted to measure or report
the dynamic pressures
• Two report that although the side-wall
pressures were reduced the end-wall
pressure was enhanced
MABS21 Israel 2010
Concluding Remarks
• Thanks to my MABS colleagues and
friends
MABS21 Israel 2010
Concluding Remarks
• Thanks to my MABS colleagues and
friends
• Thanks to Spiez Labor for Spiez-base and
the web site.
MABS21 Israel 2010
Concluding Remarks
• Thanks to my MABS colleagues and
friends
• Thanks to Spiez Labor for Spiez-base and
the web site.
• I shall miss the thrill of the count-down and
the smell of detonation products
MABS21 Israel 2010
MABS21 Israel 2010
The Solution
• Work in Lagrangian co-ordinates
• Along the particle paths between the primary and
secondary shocks the entropy is constant and the
simple thermodynamic relationships can be used
P  const . 

P   T
u 
dR
dt
• Thus the measurement of one physical property allows
all the others to be calculated
MABS21 Israel 2010
Rankine-Hugoniot Equations
• Conservation of mass, momentum and
energy for a compressible flow
• Created before the existence of a shock
was known
• More precise than experimental accuracy
• Ms < 3 (OP 7 atm) gamma = 1.401
• Ms > 3 use real gas gamma
MABS21 Israel 2010
MABS Results
• At the last three MABS, twenty papers
dealt with blast mitigation
• Only one discussed the energy
relationship between hydrostatic and
dynamic pressure
• Only two attempted to measure or report
the dynamic pressures
• Two report that although the side-wall
pressures were reduced the end-wall
pressure was enhanced
MABS21 Israel 2010
Energy Loss is Minimal
• Energy in a blast wave is essentially
 1
1
2 
    1 OP  2  u 


• If the overpressure is decreased then the
dynamic pressure must increase
• The energy may also be spread in time
and distance thus decreasing the peak
pressures
MABS21 Israel 2010
Dynamic Pressure
P = ½ ρ u * |u|
D
• Dynamic pressure is a mathematical, not a
physical property of a compressible flow
i.e. it is not directly measureable.
• Most analyses now use numerical
simulation techniques from which dynamic
pressure is as easily derived as any other
property.
• P is better related to the drag forces
which cause most of the damage & injury.
D
MABS21 Israel 2010
Limitation of Scaling
• Cast uncased TNT < about 4 kg
MABS21 Israel 2010
Limitation of Scaling
• Cast uncased TNT < about 4 kg
• Uncased ANFO < several 100 kg
MABS21 Israel 2010
Limitation of Scaling
• Cast uncased TNT < about 4 kg
• Uncased ANFO < several 100 kg
• ANFO yield increases with loading density
MABS21 Israel 2010
Limitation of Scaling
•
•
•
•
Cast uncased TNT < about 4 kg
Uncased ANFO < several 100 kg
ANFO yield increases with loading density
AgN3 valid to 0.5 mg
MABS21 Israel 2010
Limitation of Scaling
•
•
•
•
•
Cast uncased TNT < about 4 kg
Uncased ANFO < several 100 kg
ANFO yield increases with loading density
AgN3 valid to 0.5 mg
Scaling limits for most explosives have not
been reported
MABS21 Israel 2010
Limitation of Scaling
•
•
•
•
•
Cast uncased TNT < about 4 kg
Uncased ANFO < several 100 kg
ANFO yield increases with loading density
AgN3 valid to 0.5 mg
Scaling limits for most explosives has not
been reported
• In the M tonne range, atmospheric
stratification becomes important
MABS21 Israel 2010
Energy Loss is Minimal
• Energy in a blast wave is essentially
 1
1
2 
    1 OP  2  u 


• If the overpressure is decreased then the
dynamic pressure must increase
• The energy may also be spread in time
and distance thus decreasing the peak
pressures
MABS21 Israel 2010