MABS21 Israel 2010

Julius Mezaros Lecture

53 Years of Blast Wave Research

A Personal Historyby

John M. Dewey

Dewey McMillin & Associates

Professor Emeritus, University of Victoria

MABS21 Israel 2010

The Entropy ProblemG. I. Taylor (1950)

ΔS ΔS ΔS

MABS21 Israel 2010

The Entropy ProblemG. I. Taylor (1950)

• In Eulerian co-ordinates the air passing a fixed measurement point is non-isentropic

MABS21 Israel 2010

The Entropy ProblemG. 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 ProblemG. 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

.constP

TP

dt

dRu

MABS21 Israel 2010

Smoke Tracers on Snowball (500 t TNT, 1964)

MABS21 Israel 2010

Particle Trajectory Analysis

SSPP

R

R

R

R

0

2

0

0

SSPP

Radius

Tim

e

PrimaryShock

ParticleTrajectories

ΔRo

ΔR

dtdRu

SSPP

sMdta

dR

0

0

SSSS TPM ,,

MABS21 Israel 2010

The Spherical PistonG. I. Taylor (1946)

MABS21 Israel 2010

MABS21 Israel 2010

Piston Path compared to gaugeMINOR UNCLE 2 kt ANFO

Hydrostatic pressure

MABS21 Israel 2010

Piston Path compared to gaugeMINOR 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

31

2121 WWRR

310102

312121 PPWWRR

2112

310102

312121 TTPPWWtt

MABS21 Israel 2010

Scaling Peak Values

Dewey, 1964

TNT Surface Burst

30 kg 100 tonne

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)

H

RS

RS

PS

PS

MS

Regular Reflection Mach Reflection

TP

MABS21 Israel 2010

Von Neumann 2 & 3 Shock (1943)

MABS21 Israel 2010

Hydrostatic Pressure1.25 kg TNT at 1.7 m HOB (AirBlast)

MABS21 Israel 2010

Dynamic Pressure

Ground Radius (m)

0.1 1 10 100

Dyn

amic

Pre

ssur

e (a

tm)

0.01

0.1

1

10

1.25 kg TNT HOB 1.7 m (AirBlast)

RR

MR

Transition

MABS21 Israel 2010

Over-emphasis onHydrostatic 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 onHydrostatic Pressure

• Hydrostatic pressure is the least sensitive of all the physical properties e.g. contact surfaces, boundary layer

MABS21 Israel 2010

Over-emphasis onHydrostatic 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 PressurePD = ½ ρ u * |u|

• Dynamic pressure is a mathematical, not a physical property of a compressible flowi.e. it is not directly measureable.

MABS21 Israel 2010

Dynamic PressurePD = ½ ρ u * |u|

• Dynamic pressure is a mathematical, not a physical property of a compressible flowi.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

2

2

1

1

1uOP

MABS21 Israel 2010

Energy Loss is Minimal

• Energy in a blast wave is essentially

• If the hydrostatic pressure is decreased then the dynamic pressure must increase

2

2

1

1

1uOP

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

• Thus the measurement of one physical property allows all the others to be calculated

.constP

TP

dt

dRu

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

• 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

2

2

1

1

1uOP

MABS21 Israel 2010

Dynamic PressurePD = ½ ρ u * |u|

• Dynamic pressure is a mathematical, not a physical property of a compressible flowi.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.

• PD is better related to the drag forces which cause most of the damage & injury.

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

• 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

2

2

1

1

1uOP