/MAT/LAW5 (JWL)
Block Format Keyword This law describes the Jones-Wilkins-Lee EOS for detonation products of high explosives. Optional afterburning modeling is available.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW5/mat_ID/unit_ID or /MAT/JWL/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
A | B | R1 | R2 | ||||||
D | PCJ | E0 | Eadd | IBFRAC | QOPT | ||||
P0 | Psh | Bunreacted |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
Tstart | Tstop |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
a | m | n |
Definition
Field | Contents | SI Unit Example |
---|---|---|
mat_ID | Material
identifier (Integer, maximum 10 digits) |
|
unit_ID | Unit
identifier (Integer, maximum 10 digits) |
|
mat_title | Material
title (Character, maximum 100 characters) |
|
Initial
density (Real) |
||
Reference density used in
E.O.S (equation of state) Default = (Real) |
||
A | A parameter of equation of
state (Real) |
|
B | B parameter of equation of
state (Real) |
|
R1 | R1 parameter of equation of
state. (Real) |
|
R2 | R2 parameter of equation of
state. (Real) |
|
parameter of equation of
state. (Real) |
||
D | Detonation
velocity. (Real) |
|
PCJ | Chapman Jouguet
pressure. (Real) |
|
E0 | Detonation energy per unit
volume. (Real) |
|
Eadd | Additional energy per unit volume.
(Real) |
|
IBFRAC | Burn fraction calculation
flag. 3
(Integer) |
|
QOPT | Optional afterburning
model (if Eadd > 0).
(Integer) |
|
P0 | Initial
pressure. (Real) |
|
Psh | Pressure
shift. (Real) |
|
Bunreacted | Unreacted explosive bulk
modulus. 9
10
11 (Real) |
|
Tstart | Start time for additional
energy (QOPT =
0,1,2). (Real) |
|
Tstop | Stop time for additional
energy (QOPT =
0,1,2). (Real) |
|
a | Optional Miller parameter
if QOPT =
3. (Real) |
|
m | Optional Miller parameter
if QOPT =
3. (Real) |
|
n | Optional Miller parameter
if QOPT =
3. (Real) |
Example (TNT)
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/JWL/2/123
TNT - data from example 46 with unit: (g-cm-mus) - Standard JWL , No Afterburning
# RHO_I
1.63
# A B R1 R2 OMEGA
3.7121 .0323 4.15 .95 .3
# D P_CJ E0 Eadd I_BFRAC Q_OPT
.693 .21 .07 0 0 0
# P0 Psh Bunreacted
0 0 0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/123
Miller’s extension unit system
g cm mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comments
- JWL pressure
is:
(1) Radioss then outputs:(2) Where,- Relative volume
- Internal energy per unit initial volume
- with
- Adiabatic constant
- The Jones-Wilkins-Lee Material Law (LAW5) may be used as a boundary for Hydrodynamic Viscous Fluid Material (/MAT/LAW6 (HYDRO or HYD_VISC)) provided the flow direction is from LAW5 to LAW6 (simulation of an explosion), and the gas properties ( ) are similar. Nevertheless, this method is not the most accurate one and multi-material law (/MAT/LAW51 (MULTIMAT)) is recommended instead.
- Detonation Velocity
(D) and Chapman Jouget Pressure
(PCJ) are used in the
burn fraction calculation
. It controls the release of detonation energy
and corresponds to a factor which multiplies JWL pressure.
For a given time:
A lighting time, , is computed by the Starter from the detonation velocity. During the simulation the burn fraction is computed as:(4) Where,
It can take several cycles for the burn fraction to reach its maximum value of 1.00.
Burn fraction calculation can be changed defining IBFRAC flag:
IBFRAC = 0: is the default value
IBFRAC = 1:
IBFRAC= 2:
- Time histories for detonation
time and burn fraction are available through /TH/BRIC with keyword
BFRAC. You can output a function,
, whose first value is detonation time (with
opposite sign) and positive values corresponds to the burn fraction evolution.
- Detonation times can be written in the Starter output file for each JWL element. The printout flag (Ipri) must be greater than or equal to 3 (/IOFLAG).
- If a detonation card is not linked to the material, then instantaneous detonation will be assumed.
- Afterburning can be modeled by introducing an
additional Energy. If Eadd = 0,
then there is no afterburning model and material law becomes a standard JWL EOS.
If Eadd > 0, then the
afterburning model is enabled with the default formulation
QOPT = 0.
Table 1. Available Afterburning Models in Case of Eadd > 0 Modeling Type QOPT Reaction Rate ( ) Time controlled 0 Instantaneous 1 Constant rate for energy release from Tstart to Tstop 2 Linear rate for energy release from Tstart to Tstop Pressure dependent 3 Miller's extension Afterburning energy released is then where . This term is added to JWL energy as described on Equation 1.
- In many publications, Miller’s parameters are often provided in the unit system g, cm, which results in the pressure unit of Mbar. The ‘a’ parameter is also provided with the unit and would require a unit translation if the input unit is different (/BEGIN). To avoid any unit translation, /MAT/LAW5 can be input with g, cm, using the /UNIT option and then the input is automatically translated to the unit defined for the file in the /BEGIN line. Refer to Example (TNT) above for usage.
- When dealing with a multi-material formulation (/MAT/LAW51 (MULTIMAT) or /MAT/LAW151 (MULTIFLUID)), it is mandatory to provide a non-zero value for the bulk modulus Bunreacted of unreacted explosive. It is used to model a linear EOS for the unreacted explosive in order to ensure an equilibrium calculation and numerical stability.
- According to Hayes 1
Bunreacted can be estimated
with the following formula:
Where, is the speed of sound in the unreacted explosive and an estimation for TNT is 2000 m/s.
- The Bunreacted parameter is the same parameter as the parameter in /MAT/LAW51, Iform=10 and 11.