Quick reproduction of blast-wave flow-field properties of nuclear, TNT, and anfo explosions

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April 1986

QUICK REPRODUCTION OF BLAST-WAVE FLOW-FIELD PROPERTIES

OF NUCLEAR, TNT, AND ANFO EXPLOSIONS

by

Clinton P. T. Groth

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UTIAS Technical Note No. 259

eN ISSN 0082-5263

QUICK REPRODUCTION OF BLAST-WAVE FLOW-FIELD PROPERTIES

OF NUCLEAR, TNT, AND ANFO EXPLOSIONS

by

Clinton P. T. Groth

Submitted August 1985

April 1986

UTIAS Technical Note No. 259

Acknowledgements

I would like to express my gratitude to Prof. J.J. Gottlieb of UTIAS for providing both direct ion and helpful suggestions in regard to the work in this report.

I would also like to gratefully acknowledge Dr.

e.E.

Needham of S3 (Science, Systems and Software), Albuquerque, New Mexico, for providing the DNA Nuclear Blast Standard and its corresponding computer code.

The assistance and interest received from Dr. G.N. Heppler of UTIAS is also acknowledged with many thanks.

Finally, the interest in this work by Mr. D.V. Ritzei and Mr. R.T. Schmitke and the corresponding financial support from the Defense Research Establishment Suffield, Ralston, Alberta, is much appreciated.

" ,'

Abstract

In many instances, extensive blast-wave flow-field properties are required in gasdynamics research studies of blast-wave loading and structure response, and in evaluating the effects of explosions

on their environment. This report provides a very useful computer

code, which can be used in conjunction with the DNA Nuclear Blast Standard subroutines and code, to quickly reconstruct complete and fairly accurate blast-wave data for almost any free-air (spherical) and surface-burst (hemispherical) nuclear, trinitrotoluene (TNT), or ammonium nitrate-fuel oil (ANFO) explosion. This code is capable of computing all of the main flow properties as functions of radius

and time, as .well as providing additional information regarding air

viscosity, reflected shock-wave properties, and the initial decay of

the flow properties just behind the shock front. Both spatial and

temporal distributions of the major blast-wave flow properties are also made readily available. Finally, provisions are also included

in the code to provide additional information regarding the peak or shock-front flow properties over a range of radii, for a specific explosion of interest.

.

'

1. INTRODUCTION

An explosion, as defined by Baker [1], is "a process by which a pressure wave of finite amplitude is generated in air by a rapid release of energy". The

prediction of the flow-field properties attributed to these pressure (or blast)

waves, and their relationship to the studies of blast-wave loading and the

effects of explosions on their environments, are of accepted importance and have been the subject of a fairly intense gasdynamic research during the past few

decades [1-4]. In assessing explosion effects, the researcher normally must

have available a detailed description of the blast or shock wave and its related flow properties, in order to examine, for example, the dynamic drag response of a simple structure [4].

Today, there exists many published sources of blast-wave flow-field data. The U.S. Army, Navy, and Air Force handbook [5], the American National Standards Institute report [6], and the works of Baker [1], Kinney [7], and Glasstone [8] are all examples of either trinitrotoluene (TNT) or nuclear explosion data, and they are the results of extensive experimental and/or theoretical investiga-tions. The data from these sources are not, however, readily usabie. They are of ten nondimensionalized data, sometimes providing only the shock-front flow parameters, and the results are usually presented in tabular or graphical form,

for one size of explosion and under standard atmospheric conditions. Inter-polation is of ten required to obtain explosion results, and for blasts with different yields or nonstandard conditions, scaling by means of Sachs's modified

scaling laws [1,9] must be employed. It is generally both time consuming and

difficult for nonexperts to obtain meaningful data for an explosion of interest, ~n th is manner.

The blast-wave flow properties at a particular site of interest can, of course, be predicted by using suitable numerical computer codes. These computa-tions involve complicated numerical techniques, sophisticated detonation modeis, and costly high-speed computers to include the relevant explosion processes such as rea I-gas effects, turbulent mixing, afterburning, cratering, and radiation losses. These types of computer codes are not readily available to, or usabie by, a typical scientist, researcher or engineer. Furthermore, without empirical or so-called "fudge" factors, the results are not always in good agreement with experimental data [4].

In an effort to provide accurate and easily accessible explosion data, semi-empirical curve-fit expressions for the various flow properties of both nuclear, TNT, and other explosions have been developed. This report describes a user-friendly computer program package, based upon the results of the DNA Nuclear Blast Standard and its related curve fits [2], designed to quickly provide a researcher with in-depth information regarding the blast wave of nuclear, TNT, and ammonium nitrate-fuel oil (ANFO) explosions. The program package provides the flow properties at specified times and locations, temporal and spatial distributions, peak flow properties as a function of the radius, initial decay rates, and reflected shock properties, for almost any size explosion with various ambient conditions. This program and its capabilities are the subject of this technical report.

The material presented in th is report has been divided into three basic sections, each having one or more subsections. The first part deals with the basic program package used to obtain blast data for a spherical nuclear explo-sion in air. Details and descriptions of the actual subroutines and the output data available from this package are the topics of chapter 2. Then, in an

effort to extend the capabi1ities of this program package, additiona1 curve fits have been inc1uded in this program package, whicb convert the nuc1ear data, and thereby reconstruct blast-wave flow-field data for hemispherica1 nuc1ear exp10-sions and botb spherica1 and hemispherica1 TNT and ANFO exp10exp10-sions. These curve

fits and their re1ated accuracy are discussed in the next section of this report

(see chapter 3). The third section, which appears in chapter 4, consists of the conc1uding remarks. Fina11y, tbe references for the present work fo110w in

chapter 5.

2. BASIC FREE-AIR NUCLEAR BLAST-WAVE PROGRAM

2.1

Subroutine Description

The basic blast-wave program package, deve10ped in this report, consists of a number of fair1y autonomous subroutines all written in standard FORTRAN. Tbere is one main program inc1uded with the package; however, the code bas sufficient flexiblity to afford the us er ease in modifying the program to meet a1most any individua1 requirements. A1though the actua1 computer program listing, also supp1ied with tbis report, contains adequate documentation, what fo110ws here is a detai1ed description of eacb of the subroutines found in tbe package.

a) Subroutine BLAST

Given tbe defining characteristics for an exp10sion (i.e., the exp10sion type, weight of charge, and ambient atmospberic conditions), tbis particu1ar subroutine wi1l either ca1cu1ate all the avai1ab1e flow-field property data for a set of radii and times of interest, or the peak flow properties over a range of distances fr om the blast origin, depending on the va1ue of the variab1e IOUT.

If IOUT equa1s 1, the subroutine provides the flow properties at tbe specified .

radii for the given times, and then produces tbe flow properties at tbe shock-wave front, inc1uding initia1 decay rates and ref1ected shock properties at the

same radii of interest for tbe ca1culated times of arriva1 of the shock fronts.

If IOUT equa1s 4, tben on1y the peak or shock-front properties are computed over

tbe specified range of radii.

The fo110wing input parameters shou1d be set before making a subroutine ca11 to BLAST.

IOUT

ITYPE

IHS

IAMB

Integer va1ue designating tbe type of output needed (1 for flow properties at a set of points of interest, and 4 for peak flow properties over a range of radii). Integer va1ue used to designate the type of exp10sion (1 for nuc1ear, 2 for TNT, and 3 for ANFO).

Integer va1ue used to indicate whether tbe exp10sion is eitber spherica1 (free-air) or bemispberica1 (surface-burst), whicbever one is required (i.e.,

1 for spberica1 and 2 for hemispberica1 exp10sions).

Integer value used to indicate ambient conditions for an exp10sion (1 for a U.S. Standard Atmosphere and 2 for special atmospheric conditions to be stated).

HEIGHT - Altitude above sea level (meters). Specify only if IAMB equals 1.

PAMB Ambient pressure. Specify only if IAMB equals 2.

RAMB Ambient density. Specify only if IAMB equals 2.

WEIGHT - Weight of the charge (kilotons). Given in kilotons

for compatibility with the DNA subroutines.

NPT Integer value that represents the number of

combinations of radii and times of interest.

RADIUS - Array containing tbe radii of interest (meters).

TIME Array containing the times of interest (seconds).

Note that input is passed into subroutine BLAST by means of a standard FORTRAN common block statement.

The charge weight for

a

nuclear explosion is specified in kilotons of

TNT, with the ton unit defined as exactly 2,000 pounds. This charge weight, for the particular explosion of interest, is based completelyon an energy equivalence with TNT explosions, and it is the weight of a corresponding TNT explosion that yields the same total explosive energy. Therefore, a 1-kiloton nuclear bomb is one which produces the same amount of energy as a l-kiloton explosion of TNT [3]. In the past, this has been the standard procedure for representing the yield of a nuclear explosion, even tbough nuclear and TNT ex-plosions of the same energy will not produce identical blast waves and effects.

The charge weights for tbe other two explosives, TNT and ANFO, are also entered in kilotons; however, they correspond to the actual weight of the explosive used to generate the blast wave.

The subroutine first calculates the ambient conditions, and then uses these values to determine the modified Sachs's scaling coefficients for scaling the explosion to an equivalent one-kiloton spherical nuclear explosion. Then, using subroutine PEAK from the DNA standard program package, the Sachs's scaling coefficients, and subroutines TARRIV, STATE and VISCY, the pressure, density, temperature, sound speed, equilibrium specific-heat ratio, viscosity, flow velocity, Mach number and Reynolds number per unit length are calculated at the set of given radii for both the shock-front arrival and given times of interest. Next, the shock-front velocity, Mach number, and acceleration are found using

subroutine WFDEFN. A call to subroutine DECAY returns the initial decay rates

of the major flow properties just behind the shock front along constant time and distance curves, as weIl as along the particle path. Finally, the reflected shock-wave properties, including the properties just behind the shock front, are

determined by using subroutine REFLSW. All of the output values generated

with-in subroutwith-ine BLAST are returned from this subroutwith-ine by means of the common block statements.

A few comments should be made regarding the modified Sachs's scaling coefficients. The blast-wave flow properties for explosions, with various yields and ambient conditions, can be obtained by scaling known results from another explosion of the same type, by using the well-known Sachs's scaling

laws [1,9]. These sealing laws are extensions of the rudimentary Hopkinson's 3

scaling laws, and give accurate explosion data over a wide range of distances, ambient conditions, and explosion energies [1]. At distances very close to the origin of the explosion or under very low ambient pressures, the Sachs's sealing

laws no longer apply, because the basic assumptions that the air behaves as a perfect gas without radiation losses and that gravity and viseous effects are negligible are violated. The derivation, validity, and applieation of the

scal-ing laws are given in referenees 1 and 9.

b) Subroutine HIST

Subroutine HIST produces time histories for the pressure, density, temper-ature, sound speed, equilibrium specific heat ratio, viscosity, flow velocity, Mach number, and Reynolds number per unit length, at a specified radius from the blast origin. The tempora 1 distributions start at the time of arrival for the shock front and proceed for a predetermined period depending on the explosion charaeteristies and the loeation of interest. Although all input parameters to subroutines HIST and BLAST are identieal, the first element of the array vari-able RADIUS now need only eontain the radius for the required time histories, IOUT must be set equal to 2, and variables TIME and NPT need not be initialized. Following a similar procedure to subroutine BLAST, this routine calculates the ambient conditions, Sachs's sealing coeffieients, and period of interest for th is time history, and then uses subroutines PEAK, TARRIV, STATE, and VISCY to obtain the major flow properties. The input and output are passed to and from subroutine HIST by means of eommon block statements.

Subroutines capable of producing aetual plots of the spatial and tempora 1 distributions are not supplied in this program package. It was feIt that the variety of plotting software and hardware available to different users would

make it virtually impossible to write generalized p10tting routines. Instead,

all ea1cu1ated va1ues are simply stored in arrays (or alternative1y computer files). Explosion data stored in this form can then be p10tted easi1y by using specific routines deve10ped by the user and tai10red to the avai1able p10tting package and requirements of the individual user.

c) Subroutine SPDIST

Complete spatia1 distributions of the pressure, density, temperature, sound speed, equilibrium speeific-heat ratio, viscosity, flow velocity, Mach number, and Reynolds number per unit 1ength for a specified time af ter burst

initiation can be provided by subroutine SPDIST. The distributions cover a

range of radii, from 10cations near the blast origin out to the radius of the shock front. Again the required input for this subroutine is similar to that required for subroutine BLAST, except that, in this case, the first element of the array variab1e TIME must contain the time of interest for the spatial

distributions, IOUT must now equa1 3, and the variables RADIUS and NPT need not be initialized. Once again, all input and output values are passed through the common b10cks. For ease in plotting, all the data for the distributions are stored in arrays.

d) Subroutine DECAY

This subroutine caleulates the initial decay rates for all major flow properties (i.e., pressure, density, sound speed, and velocity) just behind a

spherical shock-wave front. Using the equations of Sadek and Gottlieb [10], the time and/or distance derivatives of the flow properties along constant time and distance curves, as weIl as along the particle path, are all computed by this subroutine.

Subroutine DECAY requires an input radius, Mach number, and acceleration of the shock front, and the corresponding pressure ratio, density ratio, sound-speed ratio, and flow Mach number for the state just behind the shock, in order to determine the decay rates. All input and output are again passed to and from subroutine DECAY with common blocks.

It should be noted that the expressions for the decay rates depend on the conventional Rankine-Hugoniot equations [10,11], and because of this they do not

include real-gas effects. In turn, this subroutine is valid only for a perfect gas or mixture, for which the specific-heat ratio remains constant across the shock front.

e) Subroutine REFLSW

The pressure loading exerted on a building or structure from an explosion blast wave is of significant importance to explosion-effect studies. Of ten a description of only the flow properties of a blast wave incident on a structure is insufficient, and the reflected blast-wave properties are necessary [3].

The subroutine REFLSW computes estimates of the reflected shock-wave prop-erties in air for a given incident wave that is normal to the solid boundary, returning the reflected shock velocity and pressure ratio, as weIl as the

pres-sure and density behind the reflected shock. The incident shock pressure ratio

and the statie pressure, density, specific heat ratio, and flow velocity of the

state just behind the incident shock are required as input to REFLSW. This

sub-routine assumes the shock is incident normallyon asolid boundary, and uses steady one-dimensional flow theory, including the Rankine-Hugoniot equations

[11], in conjunction with the Doan-Nickel equation of state for air [2]. Note that the imperfect gas equation of state for air is embodied in the DNA standard subroutines ENRGYL and AIR.

f) Subroutine STATE

This subroutine makes use of subroutines ENRGYL and AIR, which are part of the DNA standard program package, in order to calculate the temperature and the equilibrium specific-heat ratio for air, given both the pressure and density. This routine incorporates the Doan-Nickel equation of state for air [2], which

includes real gas effects.

g) Subroutine TARRIV

TARRIV returns the time for the shock front of a one-kiloton spherical nuclear explosion to reach a given radius from the origine By using the DNA standard subroutine WFPR2, which gives the shock-front radius as a function of time, the routine applies a bisection root-finding iteration technique to

com-pute the arrival time for the desired location. By scaling these one-kiloton

standard results, using the Sachs's sealing coefficients, the arrival times for other explosions can be estimated.

h) Subroutine WFDEFN

Shock-front velocities and accelerations are important flow properties. The shock-front Mach number, and therefore the velocity, is of ten one of the characteristic values used to define the shock. The acceleration can be used to calculate initial decay rates of flow properties, just behind the spherical shock wave. Subroutine WFDEFN evaluates the shock-front radius, velocity, and acceleration at a specified time for a one-kiloton free-air nuclear explosion. Again, results for other non-standard explosions may be calculated using the modified Sachs's scaling coefficients.

The routine determines the shock radius using the expression from the DNA standard fit relating the radius to the time af ter burst 1n1t1ation. Further explicit differentiation of this expression with respect to time provides both the shock-front velocity and the acceleration.

i) Function VISCY

Values for the viscosity of air used to obtain flow Reynolds numbers are of ten necessary for analyses involving the estimation of viscous forces exerted

on bodies immersed in air flows

[4,12].

Provided with this program package is

a routine which gives the viscosity of air as a function of temperature. VISCY returns the air viscosity for some required temperature by employing the semi-empirical equation of Gottlieb and Ritzei [13] in conjunct ion with the expres-sion of Mazor, Ben-Dor, and Igra

[12],

to provide good accuracy over a large range of temperatures. Note that the first equation is accurate up to only 2400 K, while the second, not so accurate at low temperatures, is very good for temperatures as high as 10,000 K. A weighted average of the two expressions is employed in an overlapping reg ion between 2120 and 2160 K.

j) Subroutine DATIN

All input parameters which are required to define the explosion yield for this package are obtained by a call to subroutine DATIN. This subroutine is a user-friendly routine which prompts the user to enter the all input data for the

program during a short interactive session on the monitor. The explosion type,

charge weight, ambient conditions, and type of desired output are all obtained

by using subroutine DATIN. Subroutines INTCHK, RELCHK, and ERROR are used by

DATIN to help avoid certain input errors.

k) Subroutines INTCHK and RELCHK

During the execution of subroutine DATIN, all of the program input values are initially entered and then assigned to FORTRAN character strings. These strings are then carefully decoded, checking for input errors, before a final input value is assigned to the desired variabie. Subroutine INTCHK is used by DATIN to decode input integer strings, extracting the desired integer variables and flagging incorrect input (real numbers and incorrectly typed alphanumeric characters), without causing any undesirable program execution errors with program termination. Subroutine RELCHK is used in a similar manner to decode

input real-number strings and obtain real number variables. Input error mes-sages from both subroutines are displayed on the monitor and the user is given a new chance to input data in the correct form.

1) Subroutine ERROR

Subroutine ERROR is called by subroutine DATIN and is used to flag the assignment of invalid values to the input parameters of the program package. The error messages are displayed on the monitor.

m) Subroutine OUTI

Explosion data determined from calls to subroutine BLAST are given as

out-put in a listed format by subroutine OUTI. This subroutine can send the output

to a monitor, printer, or designated data file, as specified by the user.

n) Subroutine OUT2

This is another subroutine which merely formats the blast-wave data for output. Subroutine OUT2 produces a table of either the time histories or the spatial distributions, as calculated by either subroutines HIST or SPDIST, respectively. The output information can be sent to the monitor, the printer, or a specified file, whichever the user requests.

0) Subroutine OUT3

Subroutine OUT3 produces a table of the blast-wave peak flow properties over a specified range of distances from the blast origin, as computed by sub-routine BLAST. Again, the output can be sent to the monitor, the printer, or a specified file.

2.2 Program Output

The subroutines described in the previous section (2.1) completes the basic program package, which provides an fairly accurate and complete descrip-tion of the blast-wave flow-field properties for a spherical nuclear explosion. It should be noted that all dimensional values found in the program package are in SI units (i.e. meters, kilograms, seconds), and thus values such as pressure, density, temperature, and velocity have dimensions of kilopascals (kPa) , kilo-grams per cubic meter (kg/m3 ), Kelvin (K), and meters per second

(mIs),

respec-tively. Finally, the complete listing of the single-precision FORTRAN source code is presented in appendix A of this report.

The blast-wave program, as written, is structured to provide four optional types of ouput for a particular explosion of interest. These are as follows: Firstly, a detailed list of all available flow properties, including shock-front properties, reflected shock-wave properties, and initial decay rates can be produced as output for prescribed combinations of radii and times of interest. Secondly, tabulated time histories of the major flow properties at a specified location are also possible. Thirdly, tabulated spatial distributions of the major flow properties for a desired time of interest are available. Finally, the fourth available output format is a tabulated list of some of the blast-wave peak flow properties over a specified range of distances from the blast centre. One of these four outputs is computed, depending on the user's input to the

program (see subroutine DATIN). Samples of each type of output are illustrated

in appendix B for various nuclear, TNT, and ANFO explosions. 7

2.3 The DNA Nuclear Blast Standard

The DNA Nuclear Blast Standard is the work of Dr. C.E. Needham and J.E.

Crepeau, and funded by the Defence Nuclear Agency (DNA), Washington, D.C. It

is based on revisions of Dr. Needham's and others earlier works [14], and it is a direct attempt by the DNA to produce a new american standard for a one-kiloton free-air nuclear explosion that agrees with available experimental data. It is worthwhile noting that the first nuclear explosion standard was provided by the American National Standards Institute [6], and this standard was also based on

Needham's earlier work. Some other researchers objected to this ANSI standard,

claiming that far field data estimates was not in very good agreement with experimental far-field data. Consequently, this new DNA standard includes the latest and most accurate work of Needham, and it is now becoming the recognized standard for nuclear explosion data [3].

The DNA standard is a set of FORTRAN encoded subroutines which represent best fits (of less than 5 percent error) to the explosion results from one- and two-dimensional radiation hydrodynamic and pure hydrodynamic numerical analyses, in Lagrangian and Eulerian coordinates, using first- and second-order differen-cing techniques, as weIl as nonlinear acoustic theory for late times [2]. These first principle calculations were also checked against existing experimental data [2,3]; however, Needham warns of inaccuracies in the results for pressures

greater than 100 MPa. Needham and Crepeau's one-kiloton nuclear standard

sub-routines are the basis of this report's program package for reproducing all explosion data.

The listing of the single-precision computer code for the DNA Nuclear

Blast Standard, with included documentation, is presented in appendix C. For

further details concerning this standard, please refer to the original report of Needham and Crepeau [2].

3. CONVERTED DATA FOR SURFACE-BURST NUCLEAR AND BOTH TNT AND ANFO EXPLOSIONS

3.1 Eguivalence of Various Explosions: Nuclear vs TNT.

TNT vs ANFO. Spherical vs Hemispherical

There is no actual equivalence between TNT and nuclear explosions. As noted previously, the only real measure of any equivalence between the two is on the basis of the total energy liberated from the explosions [3]. The blast waves and their respective flow-field properties are in fact quite different

for nuclear and TNT events with the same energy release. As Gottlieb points out [3], there are two primary reasons for these differences. Firstly, for nuclear as compared to TNT, the initial energy release is completely different. For nuclear explosions the energy release is much more rapid and also within a markedly smaller space, and the resulting collisional heating of the air, absent in chemical explosive detonations, forms a thermal wave which precedes the for-mat ion of the blast front. This produces much higher higher pressures and temp-eratures at early times for the nuclear explosion. Secondly, about 50% of the energy from the nuclearreaction is lost in the form of thermal radiation which does not contribute much to the blast wave. The TNT explosion, in comparison,

is created by a chemical reaction, and only a small amount of energy is lost in the form of light and heat radiation. ·In general, over 80% of the explosive energy from a TNT burst goes into the production of the blast wave, whereas for the nuclear explosion about 50% of the energy results in the blast wave.

Despite these basic differences, the two types of explosions do seem to exhibit some similar characteristics, especially for late times at larger radii. In fact, it has been shown that a free-air nuclear explosion with twice the total energy release of a free-air TNT explosion produces a blast wave with essentially the same peak overpressure as the TNT explosion, at large distances for the explosion center [3]. This fact is, of course, exploited when convert-ing the spherical nuclear explosion data from this program package to obtain similar explosion data for a spherical TNT explosion.

A similar analogy between TNT and ANFO explosions can also be made. A chemical analysis shows that when 628 tons of ANFO is detonated, this explosive chemical reaction will liberate the same total energy as 500 tons of a TNT

explosive [4,10]. Furthermore, experience has also shown that the SOO-ton TNT and 628-ton ANFO explosions do produce an equivalent blast wave at sufficiently large distances form the explosion center, where their shock trajectories and amplitudes become almost indistinguishable [10]. For these reasons, SOO tons of TNT is of ten considered equivalent to 628 tons of ANFO.

In further comparisons of spherical and hemispherical or free-air and surface-burst explosions, it has been found that the flow-field characteristics for the two again have similar trends, and that a conversion factor between the two may be employed. The assumption that a spherical explosion with twice the yield of a hemispherical explosion will simply produce exactly equivalent blast-wave flow-field properties is generally incorrect [15]. This simple conversion

is not always accurate because the Earth's surface is not a perfectly rigid refleçting boundary, and some explosion energy is lost in cratering processes. However, according to Dewey [15], data for spherical explosions may be scaled, following Sachs's scaling laws, to resembie data for hemispherical explosions. By using a conversion factor in the range of 1.4 to 2.0 for the energy release, depending on the condition of the explosion surface, as weIl as the radii of

interest, spherical explosion data can be converted to hemispherical explosion data for equivalent yields. Reproduction of surface-burst explosion data in th is manner is included in this report's program package.

3.2 Conversion of Nuclear Explosion Data

In order to extend the usefulness of this particular program package, an effort has been made to provide detailed blast-wave data for five explosions, other than surface-burst nuclear events. Guided by the observations of the previous section, this program gives blast-wave information for hemispherical TNT and ANFO, spherical TNT and ANFO, and hemispherical TNT explosions. This is done by using carefully chosen Sachs's cube-root energy scaling factors and other tUne-of-arrival and velocity scaling factors to convert the DNA surface-burst nuclear blast-wave data, thereby making it resembie data for the other

types of explosions. The converted DNA nuclear data attempts to simulate the data for the other explosions by providing the correct peak overpressures, shock-front Mach numbers, time of arrivals, and particle flow velocities.

Generally, a two-step convers ion process is required to convert the DNA surface-burst nuclear data to model the blast-wave properties of one of the five other types of events. In the first step, the charge weight is cube-root scaled by what will be called an energy scaling factor, which is both charge weight and radius dependent. This modified weight enters into the computation of the Sachs's scaling coefficients for the explosion. The value of the factor has been selected so that peak overpressures and shock-front Mach numbers as

computed with these sealing coefficients, in conjunction with the DNA standard curve fits, will agree with data given in other available literature.

In the second step of the conversion process, the cube-root scaled data

is further corrected by using other secondary scaling factors. Large errors

would otherwise occur in the converted arrival times and partiele velocity sig-natures of the cube-root energy scaled nuclear data, which are inherent to the

nature of the data convers ion. The basis for the energy scaling is entrenched

in making the shock-front overpressures and Mach numbers equal for the same radius. Time dependenee is ignored, and this is reflected in the corresponding data. At early times af ter burst initiation, the converted shock-front arrival times and the temporal distributions of flow velocity are incorrect, with errors

in magnitude of up to 30%. However, for later times at larger radii, the

cube-root energy scaled nuclear data tend to agree with the TNT and other explosion data. Thus, additional conversion processes, employing both time-of-arrival

(TOA) and velocity scaling factors, are required. These charge weight, radius, and time dependent factors adjust the computed TOA values and also the computed values of the partiele velocity at a point in time and space behind the blast-wave front, making the converted nuclear data agree with other available

explosion data. Further details concerning the conversion techniques for each of the five types of explosions now follow.

It is worthwhile noting that corrections for the pressure and density signatures were not required, because the difference between the converted and experimental data were not large.

a) Surface-Burst TNT Explosions

The energy, TOA, and velocity sealing factors for TNT and ANFO events were all derived from existing exp1osion data [4,6,10]. For the TNT hemispherical burst, a charge weight and radius dependent energy scaling factor was deve10ped from experimental data of the peak overpressure and shock-front Mach number for

a one-kilogram TNT explosion. The functional form for the radius dependence

was derived by using a seventh order polynomial fitted to actual calculated factors found in comparisons between the TNT and nuclear explosion data, over a wide range of radii. The charge weight dependence was then inc1uded by using the well-established one-third power sca1ing law. The surface-burst TNT energy scaling factor is graphed in figure 1, for a one-kilogram hemispherical charge.

A similar procedure was used to develop the TOA and velocity sealing

factors. The two sealing factors are presented in figures 2 and 3, for a

one-kilogram surfaee-burst TNT explosion. In the case of the velocity sealing,

the sealing depends on both radius and time af ter blast-front arrival. Two speeific radii of 1.5 mand 4.0 mare used to illustrate the time dependence of the velocity sealing factor in figure 3.

b) Surface-Burst ANFO Explosions

The energy, TOA, and velocity sealing factors for a surfaee-burst ANFO explosion are very similar to the sealing factors for a surfaee-burst TNT event, exeept that a few of the equations and their constants have been altered sueh that the converted nuclear data now mode1s the ANFO blast wave and its related flow-field properties. These three sealing factors for an ANFO explosion are

depieted in figures

1, 2,

and

3,

for a one-kilogram TNT-equivalent explosion.

~

---

---

----

---

---c) Surface-Burst Nuclear Explosions

Blast-wave data of surface-burst nuclear events were unavailable for com-parison with the DNA free-air data. Consequently, scaling factors analogous to

the factors developed for spherical TNT and ANFO explosions could not be easily developed. Detailed TOA and velocity conversion factors were not determined, as

it was assumed that the blast-wave characteristics for surface-burst and free-air nuclear explosions resembIe each other in these respects, thereby making these conversions unnecessary.

However, following the aforementioned suggestion of Dewey, a charge weight and radius dependent cube-root energy scaling factor, ranging in value between 2.0 and 1.4, was developed to convert the DNA standard nuclear data to simulate the blast-w?ve data from ground-burst nuclear events. This factor is graphed in figure 1, for a one-kilogram TNT-equivalent nuclear explosion.

d) Free-Air TNT and ANFO Explosions

Spherical TNT and ANFO blast-wave data were also not readily available. However, the program package presented in this report attempts to reproduce data for these particular explosions, by using a cube-root energy scaling factor, computed by dividing the energy scaling factor for a surface-burst TNT or ANFO event, by the energy sealing factor for converting from a free-air to a surface-burst nuclear explosion. The TOA and velocity scaling factors for the spherical TNT or ANFO burst are taken exactly equal to those obtained for the hemispheri-cal burst (see figures 2 and 3). The energy shemispheri-caling factors for both of these explosions are shown in figure 1, for a one-kilogram TNT-equivalent explosion. The FORTRAN functions ENRCON, TOACON, and VELCON are used by the program package in this report to convert the standard nuclear data to provide the blast-wave flow-field data for the desired explosion of interest. Please refer to the computer program listing given in appendix A for further more details concerning the three scaling factors and the entire explosion-data convers ion process.

3.3 Accuracy of the Converted Explosion Data

Using the preceding conversion procedure, it is possible to reconstruct

blast-wave flow field data for the following five explosions: surface-burst

TNT, surface-burst ANFO, surface-burst nuclear, free-air TNT, and free-air ANFO. This section of the report is devoted to discussing both the accuracy and the applicability of the converted DNA standard nuclear data.

A wealth of experimental and theoretical blast-wave flow property data for both surface-burst TNT and ANFO explosions were readily available in the form of tables, graphs, and semi-empirical curve fits. Comparisons of the shock-front flow properties (shock overpressure ratio, shock Mach number, and shock-front arrival time), at different radii for kilogram hemispherical TNT and one-kilogram TNT-equivalent hemispherical ANFO bursts, showed that the data of this program package and those of reference 10 exhibit good agreement. Figures 4, 5, and 6 are examples of the good comparisons obtained for the peak overpressure

ratio, the blast-wave-front Mach number, and the shock-front arrival time. No te

that all three of the flow properties agree to within 5% in the range of radii shown <0.8 to 20 m).

The fact that the peak blast-wave flow properties generated by the program package are forced to agree with other sources of TNT and ANFO explosion data does not mean that the tempora 1 and spatial distributions of the flow properties

will also agree.

An

additional study of the flow-field properties behind the

blast-wave front is needed to establish the accuracy of the converted explosion data. Time histories of the overpressure, density, flow velocity, and sound

speed, for a one-kilogram surface-burst TNT and a 1.256-kilogram surface-burst ANFO exp10sions, as ca1culated from the converted nuclear data, were compared

to tempora 1 signatures for equivalent explosions, as obtained directly from

reference

4.

Figures

7

through

14

illustrate the general results of these comparisons,

providing plots of the time histories of the various flow properties of both surface-burst TNT and ANFO explosions at various radii for the two sources of

data: the converted nuclear data and the TNT and ANFO data of reference 4. The

graphs show that the two sources of TNT and ANFO explosion data are, in fact, in

good agreement. The time histories of the overpressure, density, and velocity

from both sources have nearly similar characteristic shapes and exhibit good agreement. The agreement between the sound speed time histories are not very good for radii near the blast centre, where the nuclear density well can affect the results, but the agreement improves appreciab1y with increasing radii. Furthermore, although the signatures for the converted ANFO data appear to have a longer pulse duration, the signatures are not dramatically extended. In general , it does appear that this. technique for converting nuc lear data, as used in this program package, can for the most part reproduce fair1y accurate

surface-burst TNT and ANFO explosion data.

Two further points should be made concerning the time histories

compari-sons presented in figures

7

through

14.

Firstly, the jumps and discontinuities

observed in these time histories of the converted nuclear data, especially noticeable in the sound speed ratio curves, are produced simply by a lack of

consistency in the matching of the curve fits found in the DNA standard. In

order to remove these discontinuities, the curve fits in the DNA standard would

have to be modified. Secondly, the data comparisons indicate that the user

shou1d exercise caution in handling the converted data for shock-front pres-sures greater than 10 times the atmospheric pressure. Above these prespres-sures, the density-well effects, present in nuclear events but absent in all chemical explosions, may make any converted blast-wave data for chemical explosions quite meaningless.

In regard to the converted data for the other three types of events (TNT and ANFO free-air bursts and nuclear surface bursts), where data are lacking for comparison, the accuracy of the converted blast-wave flow-field properties for these three explosions is untested. It is felt, however, that the program package provides useful first-order estimates to the flow properties for these blast waves.

4. CONCLUDING REMARKS

This present study has presented a complete program package capable of providing fairly accurate and very detailed data for the blast-wave flow-field properties of spherical nuclear explosions in air, of almost any specified yield, and under various atmospheric conditions. The user-friendly package is simp1e and quick to use and provides temporal and spatial distributions of the major flow properties, inc1uding viscosities and Reynolds numbers, as well as

.

'

--- - - - , .

the peak flow properties, initial decay rates, and reflected properties for the

shock front. Furthermore, fairly accurate data for surface-burst TNT and ANFO

explosions were shown to be reproducable by converting and sealing the nuclear explosion data. Furthermore, far-field estimates of hemispherical nuclear and spherical TNT and ANFO bursts were also made available to the program package user.

Contained within the report are descriptions of the program subroutines, summaries of the exp10sion data provided, and the actua1 FORTRAN souree code for the package. It is hoped that this report wi1l prove to be a useful source of nuc1ear, TNT, and ANFO explosion data for many engineers and researchers who require such information.

5. REFERENCES

1. W.E. Baker, "Explosions in Air",> University of Texas Press, Austin, Texas, 1973.

2. C.E. Needham and J.E. Crepeau, "The DNA Nuclear Blast Standard (IKT)", DNA Report No. 5648T, prepared for the Defense Nuc1ear Agency, Washington, D.C., by S3 (System, Science, and Software), Albuquerque, New Mexico, January 1981.

3. J.J. Gottlieb, "Blast-Wave Loading on Darlington Generating Station Power Plant Building in the Event of an Exp10sion at the Nearby Railroad Tracks", contract report prepared for the Nuclear Studies and Safety Department, Ontario Hydro, Toronto, Ontario, by the University of Toronto Institute for Aerospace Studies, DOWDsview ,Ontario, September 1984 (contract report not readi1yavai1ab1e).

4. S.C.M. Lau and J.J. Gott1ieb, "Numerical Reconstruction of Part of an Actual Blast-Wave Flow Field to Agree with Availab1e Experimenta1 Data", UTIAS Technical Note No. 251, University of Toronto Institute for Aerospace Studies, Downsview, Ontario, August 1984.

5. Anon., "Structures to Res ist the Effects of Accidenta 1 Explos ions", Depart-ment of the Army Technica1 Manua1 No. TM-5-1300, DepartDepart-ment of the Navy Publication Report No. NAVFAC-P-397, or the Department of the Air Force Manua1 No. AFM-88-22, U.S. Government Printing Office, Washington, D.C.,

June 1969.

6. Anon., "Airblast Characteristics for Single Point Explosions in Air", ANSI Section S2.20-1983, American Nationa1 Standards Institute, Washington, D.C., 1983.

7. G.F. Kinney, "Exp1osive Shocks in Air", Macmillan Company, New York, 1962; revised in 1985 with K.J. Graham, Springer-Verlag, 1985.

8. S. G1asstone (Ed.), "The Effects of Nuclear Weapons", U.S. Department of Defence and Atomic Energy Commission, Washington, D.C., 1957; revised in 1962; subsequent revision in 1977 with P.J. Do1an (Ed.).

9. R.G. Sachs, "The Dependence of Blast on Ambient Pressure and Temperature", . BRL Report No. 466, United States Ballistic Research Laboratory, Aberdeen Proving Ground, Mary1and, 1944.

10. H.S.I. Sadek and J.J. Gottlieb, "Initial Decay of Flow Properties of Planar, Cylindrical and Spherical Blast Waves", UTIAS Technical Note No. 244,

University of Toronto Institute for Aerospace Studies, Downsview, Ontario, October 1983.

11. M.J. Zucrow and J.D. Hoffmann, "Gasdynamics", Vol. land 11, John Wiley and Sons Inc., New York, U.S.A., 1976.

12. G. Mazor, G. Ben Dor, and O. Igra, "A Simple and Accurate Expression for the Viscosity of Nonpolar Diatomic Gases up to 10,000K", AlAA Journal, Volume 23, Number 4, pp. 636-638, April 1985.

13. J.J. Gottlieb and D.V. Ritzei, "A Semi-Empirical Equation for the Viscosity of Air (U)", Dres Suffield Technical Note No. 454, Defense Research

Estab-lishment Suffield, Ralston, Alberta, July 1979.

14. C.E. Needham, M.K. Havens, and C.S. Knauth, "Nuclear Blast Standard OKT)", AFWL-TR-73-55, both first report and the revised version, United States Air Force Weapons Laboratory, Kirkland Air Force Base, Albuquerque, New Mexico, April 1975.

15. J.M. Dewey, "The Properties of a Blast Wave Obtained fr om an Analysis of the Particle Trajectories", Proceeding of the Royal Society of London (A), Vol. 324,-pp. 275-299, 1971.

.. ~ Cube-root energy sealing factor 7 i,\ I \ H I" !\ H H H ' I ! \

,

: \

,

sb surfaee-burst fa free-air , : \ ! 6 ~" -;H

.. i

"

'

\

"'H.i...

"'l

I \ HHH'H"'HHH' .H.HHHHHHH'_ ~ ... : .\ . . . H . ' ••••••• ; .•.•..••••.••••.••• _ •••••••••••••••••••••••. : ••••.••••••••••.•••••• ,i ••• H"HH'HHHH_ I \ I \ \ ! 5 ~"H" ' H"' \ :H'H"!'H'H" H ' " H •••• • • • • • • • H •••• ' ••• H'HH' HHHHHH.H.H._ LJ 1 _. _.H

o

o

\ !

\:

\

:

,

'H "" ... ' H f\ . \ \ , ... : ... ! ... , ... : ... : 'H' .H.HHH,HHHH_ \ , \. ! H.H.HHHHH'X'H! 'HHH"HH.HH' HHH.H_

~',

I

HHHHHHH_

HH'

>~~,

"

H

'Hi

. ' , ... ...; ANFO (sb)

-

_"

_{-4~-]_-...j_-1}

'

!

~

.~~=~=~.:1~~~-L..;

_~

.

.

.

~

..

~

..

_

....

~

,'

___ _

,

! TNT (sb) ~-:---j--: : : : HHHHHHH" HH.HHHHHHH_ HHHHHH"H HHH'HHHH'HH' HH HH.HHH.H_ --~ HHHHH_ ... ;... . ... ; ... : ···i H"HHH HHH.HHH_ ···i ... . , .HHHHHH.HH._ i i 3 6 9 12 15 Radius (m)

Fig. 1. Cube-root energy sealing factors for converting free-air

nuclear explosion data to reproduee surfaee-burst and free-air TNT and ANFO, as weIl as surface-burst nuelear events. The sealing factors are shown as functions of radius for 1 kg TNT equivalent explosions.

,

_,

,

I I I 1 • ij r .. · .. ·· ~···· ..

l

I : ... ~ ... . Time-of-Arrival sealing factor r--......... . ... 1.... . ... ~. . ...•...•... : I:

,

I

· ..

·l

••••• 1. ! ···l··· ...

-, ... j ... ! .. . ... : ... , ... ····l

·

1

·

·

···

·

· .. ··

-1 • 2 r···

·

·

··

r·

··

·

···r···!···

·

···

·

···

·

, ..

·

·

·

··

·

·

·

···

..

,

.

.

...

.

...

,

...

,

...

.

. ... , ...

-i

,

_,

,

~ !, r· .. ··· .. · ....

:

,

··t

I

_.

"

_\ \ \ \ \ ···1· ... : ... : ... i ... . . ... , ...

-1 j TNT

,

,

I .0

"

'

''F=

't---

t

~;~

+

---

i

--

-

t

_-~I~~~r~~=-r-

..

.

....

..

...

....

j _{···I··············!···· ..}

_··

_·

_·

_·

_····

_·

_·

_·

_·

_{"!··· ..}

_··

_·

_..

_...

_.

_.

_,

... ~. ···i··· ... ! ... j ... -i

0.8

I

i

i

i i 1

I

0

3

6 9 12 15 Radius (m)

Fig. 2. Time-of-arrival scaling factors which make the times of arrival of the cube-root scaled free-air nuclear explosions agree with the times of arrival of TNT and ANFO explosions. The scaling factors are shown as a

~---~~~~~~~~~---. .' ..~ ... ! ... -1-... ,\"""' ...

~

...

~

...

~

... , ... , ... ; ... .

o .

ij ~ ... ~ ... ,\~ ... , ... ; ... , ... ; ... ; ... + ... + ... ~... .-1

~

~""""""".~'"'''''''~''' '",'''''~:'''''''''''.'+'''''''''''''

+

...

.

....

+

...

~

...

+ ... ; ...

-"'~

ANFO 1.5 m)

0.21-

· ..

·

··

..

···

;

· ..

...

+ ... + . ....

1

...

=~~~~--~

__

~

__

~

__

~ ~ ... + ... + ... ; ... j ... ... j ... + ... ~ ... ~ ... + ...

-0.0

L-__ ~ __ ~ __ - L _ _ ~ _ _ ~ _ _ _ _ ~ _ _ ~ _ _ ~ _ _ ~ _ _ ~

o

1 2 3 ij 5

Time af ter blast-front arrival (ms) Fig. 3. Velocity scaling factors wbicb make tbe velocities bebind

the blast-wave front of the cube-root scaled free-air nuclear explosions agree witb the flow velocities of TNT and ANFO explosions. The scaling factors are sbown as functions of the duration af ter tbe shock arrival time, at two specific radii (1.5 mand 4.0 m), for 1 kg TNT equivalent explosions.

Peak overpressure ratio

\l

.. "\1.".; ... , ... ; ... .

20

.~, ~

.

_. ""

.... , ...

,

...

~

..

.

\~\

,

~

\

lOr- -. - . " .~\ ... ... . u r-' 7" •• • ~ .. ~.. ... u • • • • • •

~

...

~

.

~

:.:.

'.

~,

.

..

~

::::::u

... u

....

.

~

,

+++

! ! ! ! ! ,

ANFO (converted nuclear) . ..

-ANFO (Sadek

&

Gottlieb)

TNT (converted nuclear)

..-TNT (Sadek

&

Gottlieb)

. ...

-, ...

-. -.-.-.-.-.-.-.-.

-...

-5 :

.

..

~

.

...\~\:

... : .... : .

. :.:::: ...

:

.: ...

::

...

,

'

.u.:: ...

.

.

.;

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..

.

..

.

.. , ...

.

... , ...

.

...

,

...

.

..

,

..

..

.

..

~

_{... _}

_...

_.

_....

_.

_...

_.

_.

... ~ + ~. ." ... , ... ! ... +.···+···!···~···!i··· i···+··· .... , ... ,

~

,

\

~

..

+

u.u.... ... ~ ~.\.l\

..

..

...

uu~ ... u .. ; ... ~ ... u .. " ... ; ... ; ... ~ ... ; 2 ~ ... + ... { ... uu... :" ~ ... ; ... + ... +-.... + ... , ;

~~

uu .. uu ... _

~ ~

r ' ... _. . ... :... . ... . 1 t ·.·.·.·.-_:,: ... -.:... ... .. ...

u.: .

•

,

•.

..

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~

...

,

...

,

..

.

..

t.:::::::::.'I::::"::':]:::::'::

O. 5 0

~

~I.;~I

~?~~~

'"

,

...

-...

-~ .. + ..

+

...

0.20

: ,

f·

~lIo

...

"

~

... , ... , ... ; ...

-" , t )

i

I

·

-

·

i ~ .... ;~ ... r ... -1 O. 10

0.05

~:···t···f···

... ::::::::: .. ::::::

:

::::: ...

::::!:. . ... : :.: ... : ... :.: ... ::.;: .... :.: ... :.:.:.:.:.:.! ... -: ···i···j···r··· L ::::'.'. ::::::-_~, ::::::::::. . . . u u . . . .. ;... _ .. ···7···t···:····r .. u ... " - ... .:... ···t···~···;···r···· ...

-. -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-...

-...

-~····+···f··· ···t··· r- +"+" r ····f···i··· ... ( ... . 1 2 ... j ... ! ... ! ... ! ... ····!··· .. !·· .... ··l···t ... . ... -u .... u.!

···

l

··

·

·

....

.

... "H·t····

H.; ... -:-.... ! ... y... .

-··r

..

···

H

·1

_{·······rH··_·~····+·······!·····l······t"""······· ... I} 5 10 Radius (m)

20

Fig. 4. Comparison between the peak overpressure ratios of surface-burst TNT and ANFO explosions as predicted from the curve fits of Sadek and Gottlieb and the converted DNA nuclear data representation of this program package (1 kg TNT-equivalent explosions).

Shock-front Mach number

5

2 1 1

+++

-11 -11 -11 \ uu.uuu.lr.; r._l, : ... uu \ ' \

...

' \

:

~

2 ANFO ANFO TNT TNT 5 (converted nuclear) (Sadek

&

Gottlieb) (converted nuclear) (Sadek

&

Gottlieb)

10 Radius (m)

Fig. 5. Comparison between the shock-front Mach numbers of surface-burst TNT and ANFO explosions as predicted from the curve fits of Sadek and Gottlieb and the converted DNA nuclear data representation of this program package(l kg TNT-equivalent explosions).

Shock-front arrival time

(ms)

50~,,---r---.---.--.-.--r-..-r---~

+++

ANFO (converted nuclear) ANFO (Sadek

&

Gottlieb)

TNT (converted nuclear)

6 6 6 TNT (Sadek & Gottlieb)

20

.

.

.

_

.

.

,

....

10 5 .... ~ .... :,. ... ,:.. ... . .... .;. ... , ... -... ~. . . ... ! ... ! ... . ····t···t,. . ... : ···i, ... ! ... . .... ~. . , ... -... ,-... . . ... -, ... i

···r·

····j···+···1 .... ,.~ ... -: ... : ,

i

···1 ... ~ .. ···1· 2 ... _ ... , ... _···l i 1

...

:

...

!

.,:...

: ... ; ....

...

. ;

.

.

.

.

...

~

.. .

... ~. ···1 ··· .. ··!···r .... ··· .. 1· .... · .. ·i· .... ···:···~· . ... _ ... ··· .. ·~· .. ···l···r···t· : : ... <-... " ... .. ... · .. ·· .. ···!· .. ··· · .. ·!·· .... ·· ..

···r

.... · ....

f ····L.! .... : ... ~ ... ... ; ... _ ... .

0.5

... ... : ... 4 . . .

1

...

-!-... ? ... ~ ... . . ... ..1 ... 1 .. , ... ; ... .:.,

0.2

~~---~----~--~--~~--~~~---~ 2

5

10 Radius (lP)

Fig. 6. Comparison between the shock-front arrival times of surface-burst TNT and ANFO explosions as predicted from the curve fits of Sadek and Gottlieb and the converted DNA nuclear data representation of this program package (1 kg TNT-equivalent explosions).

3. 0

.----...,..---,---~----,

-1

o

1 2

Time (ms)

a) Overpressure ratio lip/PI

converted nuclear Lau

&

Gottlieb

2.5

H ···

2.0

1.5

1. 0 ~ ... .

0.5

o

--

... ~. 1 Time (ros) b) Density ratio _{p/p l} 2 1.5.---r---~----.---, 1.5.---...,..---,---~----.

1.LJ

1.3

1.2

"

'\ . .\ ... . . d .d \ i . -'\I .... ~',. ....

',i'...:.

I ..•..•.•.••.•.•..•...•••..•.• ? ....••..•. ! .• "!fI ... ... ... . ... _ ... .

1.2

0.9

0.6

1 • 1 ... :

_0.3

... ~.... . ... ! ... ~ .... .

1.0'----...L.---'---L----'

0.0

o

1 2

o

1 Time (ms) Time (ms)

c) Sound-speed ratio a/al d) Flow velocity ratio u/al

Fig. 7. Comparison between the blast-wave signatures of surface-burst TNT explosions as predicted by the work of Lau and

Gottlieb and the converted DNA nuclear data from this program package (1 kg TNT explosion, radius of 1.629 m).

3 1-... ....

-2 ... ; .... ....

-\

i··· ...

-_

... ...

i

i

1

_

...

~

-

"-o

---

.--1 i

o

2 Time (ms) a) Overpressure ratio 6P/Pl 1.

25

... ~ .... ! ... ! ... j ... . 1.20 ... . 1. 15 ... ~ ... . ... !

"

. 1. 1 0 .... ···;··\··,· .... :-,\;t ··· ... + ... "' ... 1 ' - .... - t:'"

----+-1.

0 5

1-... ; ... " ... ~ ... ; .. . 1. 00 L _ _ L-_---1 _ _ .-L _ _ ...L._...:::=..J

o

2 Time (ms)

c) Sound-speed ratio a/al

2. 5

~-~T---T""":

---,!..---"T

!

---.

converted nuclear Lau

&

Gottlieb

..

-2 . 0 1-1 ... ;; ... i ... ; ... + ... -i 1. 5

~\\

... :... . . i ... ; ... +-... -1 \ , ... i .. ... ; ... ; ...

-1.0 .... ... ~

:

~~~~---~

~ ... ! ... -... ~ ... ~.:;;.:::.:. - -

r

-i i

l

i

0.5

L-____ ~ ____ ~ ____ ~ ____ - L ____ ~

o

2

ij 1.0 0.8

0.6

0.4

0.2

.

0.0 Time (ms) b) Density ratio p/p₁ ... ! , .. .. ~... . ... ! ... . .••... , .... ···l···r··· l··· ... . ···r···················· .. ( ... .

···l

·

····

·

···i

>i~---0.2

L -_ _ ~ _ _ _ _ ~ _ _ ~~ _ _ ~ _ _ _ _ _

o

2 Time (ms)

d) Flow velocity ratio u/al Fig. 8. Comparison between the blast-wave signatures of

surface-burst TNT explosions 8S predicted by the work of Lau and

Gottlieb and the converted DNA nuclear data from this program package (1 kg TNT explosion, radius of 2.007 m).

•

1.6

1.2

0.8

0.4

o.

0 ~ ... ; ... . - 0 • y L..-_----1 _ _ ---L-_ _ - - ' -_ _ ....L..-_---'

o

2 4 Time (ms) a) Overpressure ratio 6P/Pl

1.2

~--~----~---.---r----ï

1.1

1. 0

L - _ - L _ _ -'--_---JL...-.._-.;.:-::.=.;-"----'

o

2 4 Time (ms)

c) Sound-speed ratio a/al

2.0

converted nuclear

1.8

_{Lau & Gottlieb}

1.6

1.4

1.2

1.0

O. 8 L-_--L-_----L _ _ L-_=:c::=::::d

o

2 Time (ms) b) Density ratio p/p₁ y

0.8

~--~--,--~---.--~

0.4

o .

2 ~ ... ~ ... " ... : ... : ... ! ... .

o .

0 ~ ... u.u.; ... ; ... ; ... ~., .... ..:~i.o.:::

-0.2

L - _ - L _ _ L - _ - L _ _ ~_~

o

2 y Time (ms)

d) Flow velocity ratio u/al

Fig. 9. Comparison between the blast-wave signatures of surface-burst TNT explosions as predicted by the work of Lau and

Gottlieb and the converted DNA nuclear data from this program package (1 kg TNT explosion, radius of 2.529 m).

o .

6 ..---,..---..---r----r--,

1.l!.---r----r---,----r---,

0.5

O.l!

0.3 0.2 O. 1 0.0

- O. 1

o

2 Time (ms) a) Overpressure ratio 6P/P1 converted nuclear

Lau

&

Gottlieb

1.3

,

1.2

... ,-...

.

~ ... . ···r

1.1

.. H::::]

1.0

····ot·· ... ! ; ····t

···IH

0.9

L - _ - L _ _ L - _ - L _ _ ~_~

o

2 Time (ms) b) Density ratio p/p₁

1. 08

.---r----r---~--,.---_,

O.l!

~----..---~--~---r--,

1. 06

1. Ol!

1.

02

1. 00

"\ \ ... , . . . ... ~\" •. 1 ... ~ ... 1 ... -1

,

_,

...H ... "HH.j .. :'!.,""" ~ ... ; ... 1 ... . ! " , :

... H.'..H ..

'

...

.>~". , ' .... , ! ~

...

... ~.. . ... j... . ... ~ ... ···'·1···~ ... ··· ... ~

...

...

..

....

:...

'1

...H .. HHT· ... :... . ... ; 0.3 ... ~ ... . 0.2 ... ... ~.. ... . ... ···i ···~···1

o.

1 ... ~ ... .

o.

0 ... ~ ... :-... . . ... ! ··i···

0.98

L - _ - L _ _ L - _ - L _ _ ~_~ -0. 1

o

2

o

2 LJ Time (ms) Time (ms)

c) Sound-speed ratio a/al d) Flow velocity ratio u/al

Fig.

10.

Comparison between the blast-wave signatures of surface-burst TNT explosions as predicted by the werk of Lau and Gottlieb and the converted DNA nuclear data from this program package

(1

kg TNT explosion, radius of

4.021

m).

I

8

~---r---r---.----~ I.J 6

3

I.J

2

2 1

o

... ! ... ! ... ···t· .. · - 2 L..-_ _ _ _ ---J.. _ _ _ _ _ _ . l -_ _ _ _ ...J... _ _ _ _ - . . l 0

o

2 0 Time (ms) a) Overpressure ratio Óp/Pl

2.0

r---~----~----~~----~

_2.0

1.8

1.6

1.2 1. 6 w··· .. ··· .. ···;····

0.8

1.1.J O.I.J 1.2

0.0

1. 0 '---_ _ -'--_ _ - - L - _ _ - - ' - _ _ - - - ' - 0 • I.J

o

2 I.J 0 Time (ms)

c) Sound-speed ratio a/al

b)

,..

converted nuclear

Lau

&

Gottlieb

---2 Time (ms) Density ratio p/p₁ ....

_--

.... _{..,.. ...} Time (ms)

d) Flow velocity ratio u/al

Fig. 11. Comparison between the blast-wave signatures of surface-burst ANFO explosions as predicted by the work of Lau and

Gottlieb and the converted DNA nuclear data from this pro-gram package (1.256 kg ANFO explosion, radius of 1.570 m).

5

-1

1.1.J

1.3

1.2

1.1

---o

2 Time (ms) a) Overpressure ratio 6P/Pl ... ! _···t \ \ .. \ \ \ ... L ... , ... . " !

" '<1' ,.

_"

_{" \}

:

: ...

.. ···· .. ·r··· ..

'<·~

....

! .... . ... ":'.

!

···t·· ... ?.... ... ... ··· .. ···i ... ~. 3. 0

r----..,.---...,....----.----,

converted nuclear

-Lau & Gottlieb

2.5 : .

...

...

...

...

:! ... . . ...

-2.0

1.5

1.0

~\

: :: ... \ ... + ... .. ...

\

,

.

,

~···

..

·

....

····

.. ··

..

·· ..

..

r

...

·

' ... ---

:

___

:

--...

I I - - -,---;...

0.5

~--~--~--~--~

o

2 Time (ms) b) Density ratio p/p l

1.6.---r---.---,---,

1.2

0.8

~\

.::::::" \ ... " ... + ... + ... + ...

-~I~

·...i .. ·~r

.... ;.;;:;

..

:·:+~

__ ... _

O.I.J 0.0 r-.... . ... ~ ... . ... -... ···i -.- ... (. ... .

1.0L---L---L---.L..---'

-O.I.J

o

2 I.J

o

2 Time (ms) Time (ms)

c) Sound-speed ratio a/al d) Flow velocity ratio u/al

Fig. 12. Comparison between the blast-wave signatures of surface-burst ANFO exp1osions as predicted by the werk of Lau and

Gott1ieb and the converted DNA nuc1ear data from this pro-gram package (1.256 kg ANFO exp1osion, radius of 1.971 m).