NUREG/CR-3719

SAND83-2624

R3

Printed August 1984

Detonation Calculations Using a

Modified Version of CSQII:

Examples for Hydrogen-Air

Mixtures

R. K. Byers

Prepared by

Sandia National Laboratories

Albuquerque, New Mexico 87185 and Livermore, California 94550

for the United States DepartmetfEnergy

under Contract DE-AC04-7600807,89

0~~

ýi kill j I it I

SF 2900-Q(6-82)
NOTICE

This report was prepared as an account of work sponsored by an

agency of the United States Government. Neither the United

States Government nor any agency thereof, or any of their em- ployees, makes any warranty, expressed or implied, or assumes

any legal liability or responsibility for any third party's use, or the

results of such use, of any information, apparatus product or process disclosed in this report, or represents that its use by such

third party would not infringe privately owned rights.

Available from

GPO Sales Program

Division of Technical Information and Document Control

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555

and

National Technical Information Service

Springfield, Virginia 22161

-I
NUREG/CR-3719

SAND83-2624

R3

Detonation Calculations Using a Modified Version of CSQII:

Examples for Hydrogen-Air Mixtures

R. K. Byers

Date Published: August 1984

Sandia National Laboratories

Albuquerque, NM 87185

Operated by

Sandia Corporation

for the

U. S. Department of Energy

Prepared for

Severe Accident Assessment Branch

Division of Accident Evaluation

Office of Nuclear Regulatory Research

U. S. Nuclear Regulatory Commission

Washington, DC 20555

Under Memorandum of Understanding DOE 40-550-75

NRC FIN No. A-1246

k

ABSTRACT

CSQ is a well-tested and versatile wave propagation computer

program, a modified version of which has been used to perform a

number of USNRC-supported analyses of detonations of hydrogen- air mixtures in nuclear reactor containment buildings. The

modifications, from a user's viewpoint, are fairly minor, and

this version of CSQ is being prepared for release to interested

organizations. This report documents the use of CSQ in this form.

as well as certain codes which aid in performing the detonation

calculations.

iii/iv

CONTENTS

Page

I. Introduction 1

I1. Brief Description of CSQ and Related Codes ............ 3

III. Examples and Applications .............................. 5

A. The "Constant Rate - Constant Threshold"

Model . ............................................ 6

B. Ignition-Reaction Examples ........................ 9

C. A Sample Containment Calculation ................ 14

IV. Discussion .............................................. 33

References ............................. ................ ...... 35

Appendix ...................................................... 37

V
LIST OF ILLUSTRATIONS

Figure Page

III.i Ratio of Conversion Rate Constant to Sound Speed

at C-J State for Relation Given by III.1 .............. 8

II1.2 Momentum (above) and Pressure (below) Profiles,

Normalized to C-J Conditions; Conversion Rate

Constant Given by 111.1 . ...................... 10

I11.3 Momentum (above) and Pressure (below) Profiles,

Normalized to C7J Conditions; Conversion Rate

Constant Twice That Given by II.1 ................... 11

111.4 Momentum (above) and Pressure (below) Profiles,

Normalized to q-J Conditions; Conversion Rate

Constant ýialf That Given by III.1.................. 12

111.5 Normalized Pressure Profiles for a Sample

Reaction Model,. ......... ................ ......... 13

111.6 Momentum (above) and Pressure (below) Profiles.

Normalized to C-J Conditions; Reaction Rate

Constants Approximating Results of III.1.......... 15

111.7 Momentum (above) and Pressure (below) Profiles,

Normalized to C-J Conditions; High Reaction Rate

Constant..,................. ...... .................. 16

111.8 Momentum (above) and Pressure (below) Profiles,

Normalized to C-J Conditions; Low Reaction Rate

Constant ............................................ 17

111.9 Computational Geometry for Two-Dimensional

Example Problem ................................... 18'

111.10 Density (above) and Pressure (below) Profiles

in Obstructed Strip, Normalized to C-J Conditions

(Two-Dimensional Reaction Model Example) .......... 19

I114l Density (above) and Pressure (below) Profiles

in Open Strip. Normalized to C-J Conditions

(Two-Dimensional Reaction Model Example).......... 20

iII.12 Boundary Shape for Containment Example.,............ 21

111.13 Density Field at 2 ms in Containment Example ....... 23

111.14 Density Field at 12 ms in Containment Example..... 24

vi
.aie

111.15 Density Field at 16 ms in Containment Example ..... 25

II.16 Density Field at 28 ms in Containment Example ..... 26

111.17 Density Field at 32 ms in Containment Example ..... 27

111.18 Pressure History at Dome Center in Containment

Example ........................................... 28

111.19 Pressure History at Center of Drywell Head in

Containment Example ............................... 29

111.20 Pressure History at Dome - Wall Joint in

Containment Example ............................... 30

111.21 Pressure History about 1.1 m above Bottom of

Wetwell in Containment Example .................... 32

vii/viii
a
ACKNOWLEDGMENT

The author greatly appreciates Jan Frey's efforts in producing this document.

i x/x

I. Introduction

Sandia National Laboratories is engaged in an extensive

program, sponsored by the USNRC, involving many safety-related

aspects of the behavior of hydrogen mixtures in reactor containment buildings [1]. A part of the program is the estimation of

detonation-caused loads on containment structures. CSQ [2], a

well-established computer program which solves continuum

mechanics problems for two-dimensional motion, has been used in

a number of such analyses [3,4,5]. An altered version of the

program was used in order to make use of constitutive relations

for hydrogen-air-steam mixtures which were developed as part of

the overall program [6], and it has been suggested that this

version of the program be released for use outside Sandia. This

report is a brief description of the changes and the way the

resulting code may be used.

CSQ solves finite difference analogs for the partial

differential equations representing the balance of mass,

momentum, and energy, together with constitutive relations for

the materials involved. The code incorporates an accurate

treatment of mechanical and thermal equilibrium of mixtures of

as many as ten different materials. One user option, originally

used for (solid) high explosives, is the detonation of regions

of materials. However, this option requires the use of a single

equation of state for both the undetonated and the detonated

materials. Furthermore, a time and location for the start of

detonation are required input, and these limitations were deemed

inappropriate for the intended use. For this reason, an alternate method of simulating detonations was incorporated in the

code. The method forces a detonation to occur (by converting

unburned to burned material) whenever some quantity (e. g.,

pressure) exceeds a threshold value. This very simple model may,

however, be easily altered as adequate information becomes

available, allowing more accurate treatment of detonation initiation, as well as quenching or transition from deflagration to

detonation.

Section II of this report presents a brief description of

CSQ and the detonation-model modifications, together with

descriptions of ancillary codes which aid in performing CSQ

detonation analyses. Section III describes the effects of

various changes in the detonation model, as well as some results

from a typical calculation of detonation in a containment. The

Appendix contains a description of how the required equation-ofstate information is generated and used to calculate theoretical

detonation conditions.

1/2

II. Brief Description of CSQ and Related Codes

CSQ solves discrete analogs of the differential equations

representing conservation of mass, momentum, and energy in

two-dimensional motion, in either cylindrical or rectangular

Cartesian coordinates. Constitutive relations ("equations of

state") and initial and boundary conditions are combined with

the three conservation laws to complete the system of equations.

A rectangular grid is used to discretize the spatial region of

interest; various geometric options are used to define which

regions of the grid are occupied by a given material. The available boundary conditions include impermeable boundaries, boundaries which absorb incident stress waves without producing a

reflection and for which the user may choose whether or not to

allow material to enter or leave the mesh, and applied pressure

and velocity boundaries [7]. Sets of connected lines internal to

the mesh may also be defined as impermeable.

The numerical method embodies a "pseudo-viscosity" to smooth

discontinuities, so that the differential equations have solutions which match shock wave solutions near a steady wave

separating regions of constant properties [8]. After advancing

the solution by a timestep using a Lagrangian formulation of the

equations, the code performs a rezone to the original spatial

mesh, so the resulting treatment is essentially Eulerian. The

current version of the program can treat as many as ten different materials in a problem, with any mixtures assumed to be in

mechanical and thermal equilibrium. CSQ incorporates accurate

thermodynamics, has been used on a wide class of problems, and

has produced results which compare well with experimental data.

The standard treatment of detonations in CSQ consists of

releasing the appropriate amount of internal energy in a thin

region (several computational cells) which moves through the

mesh with the detonation velocity. The undetonated material and

the detonation products must be described by the same constitutive relation, and the location and time of initiation must be

specified. In the Sandia hydrogen program, equations of state

were developed for hydrogen--air-steam mixtures and the combustion products of those mixtures, and we wished to make use of

that information. Furthermore, we anticipated a need, as accurate information became available, to analyze phenomena such as

ignition caused by details of a flow field, deflagration-todetonation transitions, and quenching of a detonation front. A

modified version of CSQ already existed [9], in a form that

could be easily adapted to such analyses.

CSQ treats mixed regions by maintaining volume fractions for

each material in the cells of the spatial mesh. The modification

consists of controlling the volume fractions in a way not

entirely determined by the motion and the rezoning process. The

conversion of one material to another (or others) may thus be

3
specified in terms of any of the quantities calculated by the

code, so the requirement that a detonating material be described

by a single equation of state is removed. In addition, complicated chemical processes can, in principle, be modelled in this

way. Finally, zoning complications arise with the standard

method when propagating detonations through complex geometries,

and these complications disappear when it is not necessary to

specify detonation locations and times.

For use in the analyses of interest here, the "tabular"

equation of state (EoS) option is employed. With this option,

CSQ requires a file containing values of the appropriate

thermodynamic variables at points of a temperature-density

"mesh". We adapted a computer code already developed in the

hydrogen program [6] to create such a file. In providing this

information, the principal computational difficulty is in

determining the composition of a given mixture following

combustion. For each temperature and density, the current

estimate of the average molecular weight is used to calculate a

pressure, followed by a Newton-Raphson iteration to find the

mole fractions for the given conditions, assuming mechanical,

thermal and chemical equilibrium of the product species. This

procedure is repeaeed for each temperature-density pair until

the computed pressure on successive interactions has not changed

by ten parts in one million. The EoS surface data for both

unburned and burned mixtures are then used to create the

required file, or added tp an existing one.

CKEOS2 [10] is a computer program which performs various

calculations (e. g., isotherms for a range of densities) using

the same EoS description as is used in CSQ. In order to permit

comparison of CSQ results with other analyses, CKEOS2 has been

modified to allow the calculation of Chapman-Jouguet (C-J)

detonation states (states immediately behind a steady detonation wave), without requiring the original and final states to

share an EoS surface. The steadiness condition requires that the

sum of the material velocity and sound speeds be equal to the

propagation velocity of the wave, and this requirement is used

in the calculation. The modification also produces thermodynamic conditions for an isentrope from the C-J state to the

original density.

4
III. Examples and Applications

General Modelling Approach

In principle, modelling combustion phenomena with CSQ should

be a fairly simple matter. Having the EoS information for the

appropriate mixtures, one must specify some means of describing

the reactions of interest. Reference 1 tabulates 43 reactions

involved in the combustion of hydrogen in oxygen or air, and

offers the opinion that fewer than 20 of them are likely to be

important in determining the overall reaction rate. An attempt

to include this kind of detail in a CSQ calculation would be

very expensive in terms of both computer memory and computing

time, and simpler models are clearly desirable. The approach

used in this study involves only two materials: one represents

the unreacted mixture, and the 'other, the products of complete

combustion of that mixture. Incompletely reacted material is an

appropriate mixture of the two components, and a single equation

prescribes the reaction rate. The modelling of the effects of

the many reactions thus depends on the details of the effective

reaction rate equation. The major modification to CSQ uses such

an equation to prescribe the amount of reacted and/or unreacted

mixture contained in each computational cell.

For reasons connected with the original development of CSQ.

the first material specified in a problem description is treated

separately from the remaining materials, which are combined to

form another material before performing the final cell-averaging

process. The way the code does this calculation makes it most

convenient to require that the undetonated material and its

combustion products be components of the second material; this

is the only input restriction on this version of the code.

An effective reaction rate equation for the mass fraction

(x) of the unreacted mixture may take the form

dx/dt = F(x,T,v),

with T and v being the temperature and specific volume, respectively. In the context of interest here, F is nonpositive for

all values of its arguments, and its magnitude increases with

temperature. In addition, F vanishes unless some ignition

criterion is met (and, of course, if x vanishes). In a particular problem, the form of F, the initial and boundary conditions,

and the course of the calculation will determine which of

several combustion phenomena are calculated. For example, if the

reaction (once initiated) near flame temperatures releases

energy slowly enough that thermal conduction into the unburned

gas can balance it, a stable deflagration can be produced.

Cooling or rapid expansion behind a combustion front may cause a

propagating reaction zone to disappear - i.e., the combustion

quenches. These two processes are not addressed in this report.

5
However, a strong ignition source or flow disturbances could

cause the reaction to proceed rapidly enough that compression

and consequent additional heating occurs behind the front. This

last situation may escalate until a steady shock wave is formed

with a constant-thickness reaction zone immediately behind it,

which is the basis for the Chapman-Jouguet analysis of a detonation.

One other feature of the calculational method differs from

the ordinary formulation, although it is not an explicit modification to CSQ. Because the standard approach does not treat

chemical reactions, there is no requirement that material

energies and entropies be related on an absolute scale. Here,

however, such a requirement is imposed in constructing the EoS

tables for corresponding unreacted and reacted mixtures, in

order to account for the energy available from the reaction. In

the absence of motion and energy transport, the total energy in

a cell must remain constant; at the same temperature and pressure, the EoS treatment assigns a lower internal energy to the

combustion products, so the result must be an increase in

temperature, and hence pressure where the conversion process is

taking place. Thus, no explicit energy source ýis required with

this method.

This section describes two reaction - ignition models which

have been used in CSQ detonation calculations, and presents

results from various sample problems. The first model is very

simple, and forces complete conversion to be calculated at a

constant rate. If reasonably good approximations of C-J detonations are to be obtained, the interaction of the model with

CSQ's numerical methods must be considered, and this is also

discussed. A slightly more "realistic" model is; also described,

which does not force complete combustion of the unburned

material; a model of this form is, conceptually, capable of

producing all the phenomena outlined in the previous paragraph.

The final example is an illustration of the use of CSQ in

modelling detonations in reactor containment buildings.

A. The "Constant Rate - Constant Threshold" Model

As stated previously, the simple model we have used to treat

detonations consists of forcing the conversion of one material

into another in every cell for which a specified parameter

exceeds a threshold value. Convenient variables for the

"triggering" quantity are the pressure or temperature; reasonable results are obtained when the threshold value represents a

jump of -1-2% of the corresponding jump to the C-J state. The

detonation may then be initiated by specifying the ignition

region to satisfy the criterion at the beginning of the problem.

As burning proceeds from this region, the original small discontinuity grows, eventually reaching a state approximating the

theoretical steady detonation conditions.

6
The constant rate at which the conversion takes place, as

well as the threshold value, is inserted in the subroutine

TFORM. The mass fraction of unburned material is decreased by

the product of a "burn parameter" (called VDMP in the code) and

the ratio of the timestep to the cell size. The current coding

then places an upper limit of 0.15 on mass fraction change. This

treatment of combustion is obviously quite unphysical, and the

way in which the model parameters interact with CSQ's numerical

techniques and a problem's mesh size has an effect on the

results obtained.

Three simple example problems illustrate the interaction

mentioned in the previous paragraph. The problems all consist of

a one-dimensional detonation wave propagating into a dry

hydrogen-air mixture, and initiated at the edge of the mesh from

a single row of heated cells. The spatial grid is uniform, 10 mm

squares, 3 cells wide and 200 cells in the propagation direction. Each calculation was carried out for approximately 1 ms.

The difference between the calculations lies in the value of the

ratio of the burn parameter (or conversion rate constant) to the

sound speed at the detonated state.

CSQ uses a modified Courant timestep control algorithm,

based upon local velocities and velocity gradients, mesh size,

sound speed, and the artificial viscosity co-efficients. The

timestep chosen for advancement is the minimum of all those

calculated on the mesh. Experience has shown that, in order to

calculate a steady wave which is a reasonable approximation of a

C-J detonation and its associated release wave, several criteria

should be satisfied. One wants -4 cells in the wavefront, the

timestep to be controlled within one cell of the peak, and the

mass fraction increment there to be about its maximum allowed

value. Of course, the calculated peak velocity should also be

about equal to the C-J velocity.

When these criteria are combined with the expression for the

time increment, the ratio (r) of the burn parameter to the sound

speed at the C-J state depends on the Mach number (m) at the C-J

state, and is given by

r = Afm {B1 + (l+.25Bq)m + [ 1 + (B1 + .25mBq) 2 ]1/2}, (111.1)

where B1 and Bq are the linear and quadratic viscosity

coefficients, respectively, and Afm is the maximum allowed

mass fraction increment. The conversion rate ratio is normally

about 0.35, and is shown in Figure II1.1 as a function of

initial hydrogen mole fraction for B1 = .1, Bq = 2, Afm

= .15 (the default values), and two initial temperatures.

7
CONVERSION RATE CONSTANT/SOUND SPEED

3.

3.62',

3.601

0

w

z

0

w

z

0

U.

3.

3.

3.

3.

3.

3.

3.

3.

1.50 2.25 3.00 3.75 4.50 5.25 6.00

x -i0F INITIAL MOLE FRACTION

Figure IIl.1 Ratio of Conversion Rate Constant to Sound Speed

at C-J State for Relation Given by III.1

8
The results of the sample problems described above illustrate the effects of adhering to, and of ignoring, the relation

set forth in the previous paragraph. When VDMP is calculated by

the equation given there, C-J conditions are well approximated

after a propagation distance of 30 - 40 zones, and a fairly good

release wave is obtained, as seen in Figure 111.2. Figure 111.3

displays the results of doubling the burn parameter; the propagation velocity increases and constant peak values are reached

in fewer meshes, but peak values are low compared to C-J values.

Decreasing VDMP by a factor of 2 has the opposite effects, as

shown in Figure 111.4. The reader should note that although the

peak values of pressure, etc., are altered by changing the burn

parameter, the total momentum (or impulse) contained in the wave

is not affected.

B. Ignition-Reaction Examples

It was implied previously that CSQ is capable of a reasonably good treatment of reacting flow, given an accurate model.

In the following examples, this capability is demonstrated by

the use of a model which delays ignition until a "history"

parameter exceeds a given value, and specifies the reaction rate

as a function of the available unburned material and the

temperature. The expressions used are

dH/dt = Max {0,(p-p*)(T - T*)}

and

dx/dt = - klx exp(-k 2 /(T -T

where p and T are the pressure and temperature, respectively,

and x is the mass fraction of the unburned mixture. The ignition

value of the history parameter H, and the values of the constants p* T*, kI, and k2, are arbitrarily chosen to

achieve various results; no claim is made that this model or the

constants used in it are particularly realistic. Note, however,

that simple global models for reaction kinetics are frequently

cast in a similar form.

Apart from the use of the model described in the previous

paragraph, the first example is identical to those described for

the constant threshold - constant rate model, and merely serves

to demonstrate that similar results can be obtained with this

method. As may be seen by comparing Figures 111.5 and 111.2, the

reaction model yields a somewhat smoother release wave behind

the detonation front. The peak pressure is very close to the C-J

pressure because the rate constants were adjusted to match

results of the "good" calculation in the previous section. (Of

9
MOM/MOM(C-J. AT 0.1 MS INTERVALS

2.400

2.200

2.000

1.900

1 .600

1.400

1.200

a 1.000

X.

Z .8030

E .6000

.4000

.2000

0.000

-. 2000 -

S 0. 00

4q

.400 .000 1.20 1.60

DISTANCE (M)

2.00

P/P(C-J; AT 0.1 MS INTERVALS

I .500

1.400-

1.300

1 .200

1. 100

1 .000

.9000

o .9000

a: .7000

S.6000

.5000

.4000

.3000

.2000

2 000

0.0000-

a I 

0.00

Figure 111.2

.400 .900 1.20 1.60

DISTANCE (Mý

Momentum (above) and Pressure

Normalized to C-J Conditions;

Constant Given by 11I.1

2.00

(below) Profiles,

Conversion Rate

10
MOM/MOM(C-J) AT 0.1 MS INTERVALS

2.400

2.200

2.000

1.800

1.600

1 .400

1.200

1.000

.8000

.6000

C

4,

K

z

w:

.4000

.2000

0.000 H

-. 2000

M) 0.00 .400 .900 1.20 1.60

DISTANCE (M)

2.00

P/P(C-J) AT 0.1 MS INTERVALS

1.500 -

.400

1.300

1 .200

I. 100

1.000

.9000

o .8000

.7000

m .6000

.5000 .4000 4

.3000

.2000

.1000

0.000

a 

0.00

.400 .800 1.20 1.60

DISTANCE (IM

2.00

Figure I11.3 Momentum (above) and Pressure (below) Profiles.

Normalized to C-J Conditions; Conversion Rate

Constant Twice That Given by III.1

11
MOM/MOM(C-J) AT 0.1 MS INTERVALS 2.400

2.200

2.000

1.800

1.600

1.400

1.200

1.000

.8000

.6000

0

4

Z:

z

w

.4000

.2000

0.000 IL

-. 2000 t

M) 0.00 .400 .800 1.20 1.60 2.00

DISTANCE (M)

P/P(C-J) AT 0.1 MS INTERVALS

0

4

wn

Ij.

1.500

1.400

1.300

1.20Q

1.100

1.000

.9000

.8000

.7000

.6000

.5000

.4000

.3000

.2000

.1000

0.000 La 

0.00

.400 .800 1.20 1.60 2.00

DISTANCE (M)

Figure 111.4 Momentum (above) and Pressure (below) Profiles,

Normalized to C-J Conditions; Conversion Rate

Constant Half That Given by III.1

12
P/P(C-J) AT 0.1 MS INTERVALS

1.300

1.200

1. 100

1.000

.9000

.8000

o .7000

IS.6000

w

S.5000

w

0. .4000 -

.3000

.2000

.1000

0.00 .400 .800 1.20 1.60 2.00

DISTANCE (M)

ONED,.22-DRY AIRREACTION MODEL

C80 Is 1 X" 0.

Figure 111.5 Normalized Pressure Profiles for a Sample

Reaction Model

13
course, if the form of the reaction-rate equation, and the

values of the parameters in it, were physically accurate, no

such adjustment would be justified.) In this case, ignition of

the mixture begins at about .01 ms, and the problem ends at

-9 Ms.

Ignition may, obviously, be delayed by adjusting the

"critical" value of the history parameter upward, and this is

the case for the next three sample problems. Instead of a row of

heated cells, a constant velocity is defined at the edge of the

mesh: the state of the material entering the problem is the same

as that of the first "real" cell. A shock of approximately onetenth the strength of a C-J detonation propagates for about 0.6

ms before the detonation begins (Figure 111.6). The detonation

wave overtakes the initial shock at about 0.75 ms, and subsequently reaches fairly steady peak values. Doubling and halving

the rate parameter k, produce the same relative effects as

they do for the "VDMP" model, as may be seen in Figures 111.7

and 111.8.

CSQ may also be used to model ignition caused by local

variations in the flow field. A problem similar to the mediumrate case discussed above illustrates this. The calculation is

made two-dimensional by specifying a centrally located U-shaped

obstacle at .25 m from the velocity boundary, with the open end

facing that boundary (Figure 111.9). When the hitherto onedimensional shock reaches the obstacle at about 0.5 ms, the

history parameter begins accumulating more rapidly near the

obstacle than elsewhere, and ignition begins at approximately

0.64 ms. As is seen by comparing Figures III.10 and III.11, the

resulting flow is still strongly two-dimensional at 0.7 ms; the

rapid buildup of the detonation produces virtually onedimensional wavefronts by 0.1 ms later. (Note that the detonation state values used to normalize the profiles are those for a

wave proceeding into the mixture at its initial state. The

leftward-moving wave exceeds C-J values because it is interacting with the initial shock produced by the velocity boundary

condition.) The same type of behavior could, of course, be

produced with the constant rate - constant threshold model.

C. A Sample Containment Calculation

In order to illustrate the way in which CSQ can be used to

model detonations in containments, some results are presented

for the General Electric Standard Safety Analysis Report (GESSAR)

containment design. The CSQ model for this BWR containment is

axisymmetric, and consists of a large upper compartment with an

ellipsoidal dome and an approximation to the wetwell region

(Figure 111.12). Computational cell size corresponds to 50 cells

on the upper compartment radius, and provides a reasonably

14
"OM/MOMIC-J) AT 0.1 "S INTERVALS 2.400

2.200

2.000

1 .000

1.600

1.400

o 1.200

i 1.000

z .8000

0

K .6000

.4000

.2000

0.000

-. 2000

0.00 .200 .400 .600 .800

DISTANCE (M)

1.00

P/PIC-J) AT 0.2 MS INTERVALS

1.500

1.400

1.300

1 .200

1. 100

1 .000

.9000

o .9000

.7000 7 

= .6000

• .5000

.4000

.3000

.2000

.1000 --

0.000 --

Ef 0.00

Figure 111.6 Mo

.200 .400 .600 .900 1.00

DISTANCE (M)

mentum (above) and Pressure (below) Profiles,

rmalized to C-J Conditions; Reaction Rate

nstants Approximating Results of II.1

No

Co

15
MOM/MOM(C-J) AT 0.1 MS INTERVALS

2.400

2.200

2.000

1.800

1.600

1.400

1 .200

1 .000

.8000

.6000

0

4

z

w

K

0

K

.4000

.2000

0.000

-. 2000

a 0 0.00 .200 .400 .600 .800

DISTANCE (M)

1.00

P/P(C-J AT 0.1 MS INTERVALS

1.500

I.400

1 .300

1.200

1.100

.000

.9000

.8000

o .7000

• .6000

a .5000

.4000

.3000

.2000

. 1000

0.000

gm 0.00

Figure 111.7 MO!

.200 .400 .600 .800 1.00

DISTANCE (M)

nentum (above) and Pressure (below) Profiles.

rmalized to C-J Conditions; High Reaction Rate

nstant

No,

Cot

16
MOH/MOM(C-J) AT 0.1 MS INTERVALS

2.400

2.200

2.000

1 .800

1.600

1 .400

1 .200

1.000

.8000

.6000

0

2

.4000

.2000 -

0.000

-. 2000

f 0.00 .200 .400 .600 .800

DISTANCE (H)

I. 00

P/P(C-J) AT 0.1 MS INTERVALS

1.500

1.400

1.300

1 .200

1.100

1.000

.9000

o .9000

= .7000

.6000

.5000

.4000

.3000

.2000

1I000

0.000-

gm0.00

oWoo .200 .400 .600 .900 1.00

DISTANCE (M)

Figure III.8 Momentum (above) and Pressure (below) Profiles,

Normalized to C-J Conditions; Low Reaction Rate

Constant

17
inc ident

w ave u-shaped

obstacle

Figure 111.9 Computation Geometry for Two-Dimensional Example Problem

18
RHO/RHO(C-Jl AT 0.1 MS INTERVALS

1.500

1 .400

I .300

1.200

I. 100

1.000

.9000

.8000

• .7000

- .6000

z .5000

4000

3000

2000

1000

0.000 O 0.00 1.00 2.00 3.00 4.00

DISTANCE (")

5.00

-I Xl10

P/P(C-J) AT 0.1 MS INTERVALS

i.300

1 .200

1.100

1.000

.9000

.000

.7000

.6000

.5000

.4000

0

w•

U,

.3

.2

.1

Figure 111.10

000 -

000

000

000-

0.00 1.00 2.00 3.00 4.00 5.00

-1

DISTANCE (M) X10

Density (above) and Pressure (below) Profiles

in Obstructed Strip, Normalized to C-J Conditions

(Two-Dimensional Reaction Model Example)

19
RHO/RHO(C-J) AT 0.1 MS INTERVALS

1.500 -

1.400

1.300

1.200

I . 100

1.000

.9000

.8000

.7000

.6000

W .5000

.4000

.3000

.2000

.1000

0.000

an 0.00 1.00 2.00 3.00 4.00

DISTANCE (H)

5.00

X10

P/P(C-J) AT 0.1 MS INTERVALS

1.300

I. 200

1. 100

I .000

9000

.8000

o .7000

" .6000

A .5000

C. .4000

.3000

.2000

. 1000

0.000 -

• 0.00

Figure III.11

1.00 2.00 3.00 4.00 5.00

-1

DISTANCE (M) X10

Density (above) and Pressure (below) Profiles

in Open Strip, Normalized to C-J Conditions

(Two-Dimensional Reaction Model Example)

20
ITIME = 0. CYCLE = 0 TEMP

15 TIM 0. IYCE! IEMP

z

0

I-ý -'4X

2

> -11

I4M1 -24 --

-37

-50 1

i3'

I I I

0 -18 -6 6' 18

RELATIVE HORIZONTAL POSITION (m)

Figure 111.12 Boundary Shape for Containment Example

21
accurate description of the curvature of the dome. The wetwell

region boundaries are made irregular in an attempt to approximate flow restrictions and equipment. Detonation (using the

constant rate - constant threshold model) proceeds from a heated

cell at the center of the boundary representing the drywell head.

The boundaries of the model are treated as rigid (impermeable). CSQ is capable of modelling the response of the materials

which make up the containment structure, but the timestep limitations would be so severe as to make such a calculation prohibitively expensive. For this reason, pressure histories are

maintained at points along the boundary, and may be used to

estimate the effects of the loads on the structure.

The entire model is filled with a mixture of hydrogen and

dry, sea-level air, with an initial hydrogen mole fraction of

0.22 and an initial temperature of 315 K; the resulting pressure

and density for the mixture are 0.142 MPa and 1.250 kg/m 3 , respectively. An isochoric (constant-volume) burn of this mixture reaches a temperature of 2364 K and a pressure of 0.885

MPa. C-J detonation values are 1.842 MPa, 2589 K, and 2.204

kg/m 3 , while an isentrope from the C-J state to the initial

density ends at 2295 K and 0.923 MPa.

As may be seen in Figures 111.13 and 111.14, the square

zones in the CSQ mesh keep the detonation wave from being

perfectly spherical, but it becomes more nearly so as the

calculation proceeds. (The plotted density of dots in the

figures corresponds to the mass density in the calculation.) All

of the mixture in the upper compartment is detonated by about 16

ms, while the wetwell still contains mostly undetonated material

(Figure 111.15). At a later time, the pressure waves from

reflections at the wall interact at the compartment centerline,

producing a region of very high pressure, as seen in Figure

111.16. Figure 111.17 shows the situation still later, when

expansion from the axial high-pressure region results in a

second strong reflection at the centers of the dome and drywell

head.

The phenomena described in the previous paragraph lead to a

common feature of central-point detonations in large compartments: the maximum pressure on the boundary is not the direct

result of the arrival of the detonation wave, but of subsequent

interactions between reflected waves. Figures 111.18 and 111.19

display pressure histories at the dome center and drywell

center, respectively, and clearly show the importance of wave

interactions long after complete detonation has occurred. The

effects of these interactions are also evident where the dome

and vertical wall join (Figure 111.20), but at that location,

the peak pressure does occur when the detonation wave arrives.

22
TIME =- 2.065E-03 CYCLE = 52 DENSITY "-5

f

E

0

L)ILjU

LUL

LU

_J

LUI

2t

-I I

24 f

-37

-50 I I I

-30 -18 -6 6 18 30

RELATIVE HORIZONTAL POSITION (in)

Density Field at 2 ms in Containment Example

Figure 111.13

23
15

TIME = I.204E-02 CYCLE = 147 DENSITY [T I I I

9

E

2

z

0

<I:

> -11

L_1I

-IJ

-LJ

wd

-24

-37

-50

-30 -18 -6 6 18

RELATIVE HORIZONTAL POSITION (mi)

30

Figure 111.14 Density Field at 12 ms in Containment Example

24
TIME = 1.601E-02 CYCLE = 200 DENS ITY

15 TIE = i.0E0 CYL = 20 ESiTY

r=

z

0

LUJ

-J

LU

LUJ

Lii

2

-11

-24

-37

-50 1

-30

I I I I

0 -18 -6 6 18 30

RELATIVE HORIZONTAL POSITION (m)

Figure 111.15 Density Field at 16 ms in Containment Example

25
TIME = 2.809E-02 CYCLE = 336 DENS ITY

15 T IE I.0E0 CYCEI 33 ENIT

E

z

0

-IJ

I-

-J

wj

24

11 1

24 f

-37

-50 i I I I I

30 -18 -6 6 is

RELATIVE HORIZONTAL POSITION (m)

Density Field at 28 ms in Containment Example

30

Figure 111.16

26
I

I TIME = 3.206E-02 CYCLE = 380 DENSITY

E

z

0

ILLJ

-LJ

X

15

2

-11

0

-24 t

-37

-50

-30 0 -18 -6 6 18

RELATIVE HORIZONTAL POSITION (m)

30

a

Figure 111.17 Density Field at 32 ms in Containment Example

27
EULERIAN POINT 9] I 800E-0 I. 7. 740E +00 )

LD

CD

0-

UJ

0:

D

a8.000 I

7.000

6.000

5.000

4.000

3.000

2.000

1.000

0.000

0.00 .400 .800 1.20 1.60 2.00

kTIME (SEC)

GESSAR II.H2-DRY AIR EVERYWHERE(.22)

XIO -1

Figure 111.18 Pressure History at Dome Center in Containment

Example

i

28
EULERIAN POINT 52 ( 1.800E-01. -1.206E+01)

C0

0

5.500

5.000

4.500

4. 000

3.500

3. 000

0j

Ltn

V,)

2. 500

2. 000

1 500

1 000

.5000

0.000

0.00 .400 .800 1.20 1.60 2.00

IT TIME (SEC)

GESSAR II.H2-DRY AIR EVERYWHERE(.22)

X]O -1

Figure 111.19 Pressure History at

Containment Example

Center of Drywell Head in

29
4

EULERIAN POINT 73 ( 1.746E+01. 9.OOOE-01)

3.750

LD

+

o 3.500

X

3.250

3.000

2.750

2.500

2. 250

2. 000

- 1 .750- -

0-

1 .500

S1 .250

U,

.7500

.5000

2500

0.000 i

0. 0 .400 .800 1. 20 1. 60 2.00

TIME (SEC) XlO

GESSAR II.H2-DRY AIR EVERYWHERE(.22)

Figure 111.20 Pressure History at Dome - Wall Joint in

Containment Example

30
(The theoretical value of reflected pressure for the detonation

wave is greater than 4 MPa; the lower calculated value is caused

by the finite zone size.) As expected, the pressure histories in

the wetwell, exemplified by Figure 111.21, show much more rapid

early variations, because of the more complicated geometry of

the boundary. Pressures are still fairly high when the calculation is terminated at 200 ms, since no flow is allowed out of

the problem.

Because of the complicated spatial and temporal variations

in loads produced in calculations like the one described above,

the CSQ results frequently provide only an indication of whether

analyses using other methods should be performed. For example,

dynamic structural calculations could be carried out using the

pressure histories, or approximations of them, as boundary conditions, if the CSQ results seem severe enough to warrant such

an investigation.

31
EULERIAN POINT 6 ( 1.386E+01. -2.934E+01)

I . 400 ,

- I .300

X

1 .200

EIERA 10 PON ( .8EO. 294+

1.000

. 9000

.BOO

0.3000

.6200

.5000

.4000

.8000

.2000

.1000

0.00 400 4000 1.20 1060 2.0

TIME (SEC) X o

GESSAR II.H2-DRY AIR EVERYWHERE(.22)

Figure 111.21 Pressure History about 1.1 m above Bottom of

Wetwell in Containment Example

32
IV. Discussion

The example results presented in this report show that a

modified version of CSQ can make use of equation-of state

information to calculate detonations without the requirement

that the unburned material and the combustion products be

described by the same constitutive relations. The examples

presented all deal with calculations involving tabular EoS

descriptions of dry hydrogen-air mixtures, but this is not a

necessary restriction. Three examples also demonstrate that,

given adequate models for ignition criteria and reaction

kinetics, analyses of reasonable sophistication could be carried

out. Finally, calculations with CSQ can yield reasonably

accurate estimates of dynamic loads exerted on reactor containment boundaries in the event of internal detonations.

33/34

References

1. M. P. Sherman, et al.. The Behavior of Hydrogen During

Accidents in Light Water Reactors, SAND8O-1495

(NUREG/CR-1561), Sandia National Laboratories, Albuquerque,

NM. August 1980.

2. S. L. Thompson, CSQII - An Eulerian Finite Difference

Program for Two-Dimensional Material Response - Part I.

Material Sections, SAND77-1339, Sandia National

Laboratories, Albuquerque, NM, January 1979.

3. W. B. Murfin, et al., Report of the Zion/Indian Point Study:

Volume 1, SAND8O-0617/1 (NUREG/CR-1410), Sandia National

Laboratories, Albuquerque. NM, August 1980.

4. R. K. Byers, CSQ Calculations of H2 Detonations in the Zion

and Sequoyah Nuclear Plants. SAND81-2216 (NUREG/CR-2385).

Sandia National Laboratories. Albuquerque, NM, July 1982.

5. J. C. Cummings, et al.. Review of the Grand Gulf Hydrogen

Igniter System, SAND82-0218 (NUREG/CR-2530), Sandia National

Laboratories, Albuquerque. NM, March 1983.

6. M. Berman, ed., Light Water Reactor Safety Research Program

Quarterly Report, July-September 1980, SAND8O-1304

(NUREG/CR-1509). Sandia National Laboratories, Albuquerque,

NM, March 1981.

7. J. M. McGlaun, Improvements in CSQII: A Transmitting

Boundary Condition, SAND82-1248, Sandia National

Laboratories, Albuquerque, NM, June,1982.

8. R. D. Richtmeyer and K. W. Morton, Difference Methods for

Initial Value Problems, Interscience Publishers (1967).

9. S. L. Thompson. Sandia National Laboratories, private

communication.

10. S. L. Thompson, CKEOS2 -- An Equation of State Test Program

for the CHART/CSQ EOS Package, SAND 76-0175, Sandia National

Laboratories. Albuquerque. NM. May 1978.

11. D. R. Stull and H. Prophet. JANAF Thermochemical Tables,

Second Edition, NSRDS-NBS37, National Standard Reference

Series. United States National Bureau of Standards,

Washington D. C., June 1971.

35
12. IMSL Library Reference Manual, Edition 9. LIB-0009,

International Mathematical and Statistical Libraries. Inc..

Houston. TX, June 1982.

13. S. L. Thompson, RSCORS - A Revised Scors Plot Program. ,

SAND77-1957. Sandia National Laboratories, Albuquerque, NM.

May 1978.

36
APPENDIX

The standard CSQ code package includes the following programs, listed with their purpose:

1. CSQGEN - Initialize new problem or rezone an existing

calculation

2. CSQ - Main analysis program

3. CSQLINE - Produce 1-Dimensional plots

4. CSQPLT - Produce 2-Dimensional (plane) plots

5. CSQSURF - Produce 3-Dimensional plots

6. CSQHIST - Produce plots and edits of point histories

7. CSQTAP - Produce edits of CSQ output tape

8. CHDCSQ - Couple output from the I-D Lagrangian code CHARTD

to CSQGEN

9. PRECSQ - Preprocess size data to calculate storage array

sizes consistent with problem

Programs 3 through 6 employ the RSCORS [13] plot routines.

which is available from Sandia National Laboratories. The first

five codes in the list use the preprocessor's output to acquire

common block statements via CDC UPDATE. Complete information on

the codes and their use will be found in the primary reference

[2].

37
Equation-of-State (EoS) Tables and Calculations

The code package described above has been expanded to

include a tabular EoS file which describes 65 gases, the last of

which is dry air (EoS number 1885). The remaining tables correspond to unburned and burned mixtures of hydrogen and dry air,

with initial hydrogen mole fractions spanning the range .18-.58.

Unburned mixtures have an odd EoS number from 1 to 6.3; the

corresponding combustion products are described by the next

larger EoS number. EoS numbers 1-10 describe mixtures with

initial mole fractions from .18 to .26, .02 apart. With one

exception, the range .27-.34 is covered by EoS numbers 11

through 40 in increments of .005; EoS numbers 21 and 22 refer to

a stoichiometric mixture with an initial hydrogen mole fraction

of 0.29524. The r-emaining 12 pairs revert to a mole fraction

increment of .02. The tables for the mixtures cover a density

range of .0001 to 100 kg/m3. and a temperature range of 300 to

4000 K.

The release package also includes a FORTRAN program which

produces the EoS tables (on file TAPE12) for hydrogen-steam-air

mixtures. This code reads unformatted input, one variable to a

line. Input consists of, in order, initial steam and hydrogen

mole fractions, reference temperature (K), and integers defining

the EoS numbers for unburned and burned mixtures. Following

these quantities with -1 causes the code to expect input for

another mixture. EoS numbers should be placed on the file in

ascending numerical order. When the last input set is followed

by 1, the code will insert the new tables at the appropriate place in an EoS file from TAPE66. The program is based on the

JANAF tables [11], 1and uses routines from the IMSL library [12].

CKEOS2 [10] is a program which performs various thermodynamic calculations with the EoS data used by CSQ, including

the tabular data described above. An input parameter selects the

type of calculation (e.g., an isotherm for a range of densities),

and its value is less than 8 for curves in a plane of 2 thermodynamic variables. As in aid in interpreting CSQ results, a need

exists for computing Chapman--Jouguet states connecting two

separate materials, and this is provided in a modified version

of CKEOS2. In order to exercise this option, the user must

request at least one calculation for the unburned mixture,

followed by a request for a calculation for the burned mixture,

with the curve type parameter equal to the standard value plus

10. When the code processes the first request for the burned

material, it first produces the standard calculation: these

results are followed by a set of C-J detonation data. Each point

on the last curve for the unburned material is used as an

initial state for the detonation calculations. The results also

include temperatures and pressures for isentropes from the C-J

38
states to the initial density. The EoS routines will extrapolate

to values outside the range of the tables. However, because of

the reference point used for the entropy, peculiar results may

be obtained for that quantity if the extrapolation distance is

very large. The CKEOS2 reference should be consulted for a

complete set of input instructions.

39/40

Division of Technical Information

and Document Control

NRC Distribution Contractor

U.S. Nuclear Regulatory Commission

15700 Crabbs Branch Way

Rockville, MD 20850

275 copies for R3

U. S. Bureau of Mines

Pittsburgh Research Center

P. 0. Box 18070

Pittsburgh, PA 15236

Attn: M. Hertzberg

U. S. Nuclear Regulatory Commission (6)

Office of Nuclear Regulatory Research

Washington, DC 20555

Attn: G. A. Arlotto

R. T. Curtis

J. T. Larkins

L. C. Shao

K. G. Steyer

P. Worthington

U. S. Nuclear Regulatory Commission (5)

Office of Nuclear Regulatory Research

Washington, DC 20555

Attn: B. S. Burson

M. Silberberg

J. L. Telford

T. J. Walker

R. W. Wright

U. S. Nuclear Regulatory Commission (6)

Office of Nuclear Reactor Regulation

Washington, DC 20555

Attn: J. K. Long

J. F. Meyer

R. Palla

K. I. Parczewski

G. Quittschreiber

D. D. Yue

U. S. Nuclear Regulatory Commission (6)

Office of Nuclear Reactor Regulation

Washington, DC 20555

Attn: V. Benaroya

W. R. Butler

G. W. Knighton

T. M. Su

Z. Rosztoczy

C. G. Tinkler

41
U. S. Department of Energy

Operational Safety Division

Albuquerque Operations Office

P.O. Box 5400

Albuquerque, NM 87185

Attn: J. R. Roeder, Director

Swedish State Power Board

El-Och Vaermeteknik

Sweden

Attn: Eric Ahlstroem

Berkeley Nuclear Laboratory

Berkeley GL 139PB

Gloucestershire

United Kingdom

Attn: J. E. Antill

Gesellschaft fur Reakforsicherheit (GRS)

Postfach 101650

Glockengasse 2

5000 Koeln 1

Federal Republic of Germany

Attn: Dr. M. V. Banaschik

Battelle Institut E. V.

Am Roemerhof 35

6000 Frankfurt am Main 90

Federal Republic of Germany

Attn: Dr. Werner Baukal

UKAEA Safety & Reliability Directorate

Wigshaw Lane, Culcheth

Warrington WA34NE

Cheshire

United Kingdom

Attn: J. G. Collier (3)

S. F. Hall

A. J. Wickett

British Nuclear Fuels, Ltd.

Building 396

Springfield Works

Salwick, Preston

Lancs

United Kingdom

Attn: W. G. Cunliffe

42
AERE Harwell

Didcot

Oxfordshire OX1l ORA

United Kingdom

Attn: J. Gittus, AETB (2)

-J. R. Matthews, TPD

Kernforschungszentrum Karlsruhe

Postfach 3640

75 Karlsruhe

Federal Republic of Germany

Attn: Dr. S. Hagen (3)

Dr. J. P. Hosemann

Dr. M. Reimann

Simon Engineering Laboratory

University of Manchester

MI39PL,

United Kingdom

Attn: Prof. W. B. Hall

Kraftwerk Union

Hammerbacher strasse 12 & 14

Postfach 3220

D-8520 Erlangen 2

Federal Republic of Germany

Attn: Dr. K. Hassman (2)

Dr. M. Peehs

Gesellschaft fur Reaktorsickerheit (GRS mbH)

8046 Garching

Federal Republic of Germany

Attn: E. F. Hicken (2)

H. L. Jahn

Technische Universitaet Muenchen

D-8046 Garching

Federal Republic of Germany

Attn: Dr. H. Karwat

McGill University

315 Querbes

Outremont, Quebec

Canada H2V 3W1

Attn: John H. S. Lee (3)

AEC, Ltd.

Whiteshell Nuclear Research Establishment

Pinawa, Manitoba, Canada

Attn: D. Liu (2)

H. Tamm

43
National Nuclear Corp. Ltd.

Cambridge Road

Whetestone, Leicester, LE83LH

United Kingdom

Attn: R. May

CNEN NUCLIT

Rome, Italy

Attn: A. Morici

Director of Research, Science & Education

CEC

Rue De La Loi 200

1049 Brussels

Belgium

Attn: B. Tolley

Bechtel Power Corporation

15740 Shady Grove Road

Gaithersburg, MD 20877

Attn: D. Ashton

Northwestern University

Chemical Engineering Department

Evanston, IL 60201

Attn: S. G. Bankoff

Brookhaven National Laboratory

Upton, NY 11973

Attn: R. A. Bari (2)

T. Pratt

Westinghouse Hanford Company

P. 0. Box 1970

Richland, WA 99352

Attn: G. R. Bloom (3)

L. Muhlstein

R. D. Peak

UCLA

Nuclear Energy Laboratory

405 Hilgard Avenue

Los Angeles, CA 90024

Attn: I. Catton

Argonne National Laboratory

9700 South Cass Avenue

Argonne, IL 60439

Attn: H. M. Chung

44
Sandia National Laboratories

Directorate 6400

P. 0. Box 5800

Albuquerque, NM 87185

Attn: R. Cochrell (20)

Sandia National Laboratories

Organization 6427

P. 0. Box 5800

Albuquerque, NM 87185

Attn: G. Shaw (20)

University of Wisconsin

Nuclear Engineering Department

1500 Johnson Drive

Madison, WI 53706

Attn: M. L. Corradini

Los Alamos National Laboratory

P. 0. Box 1663

Los Alamos, NM 87545

Attn: H. S. Cullingford (4)

R. Gido

G. Schott

J. Travis

Battelle Columbus Laboratory

505 King Avenue

Columbus, OH 43201

Attn: P. Cybulskis (2)

R. Denning

Power Authority State of NY

10 Columbus Circle

New York, NY 10019

Attn: R. E. Deem (2)

S. S. Iyer

Offshore Power System (2)

8000 Arlington Expressway

Box 8000

Jacksonville, FL 32211

Attn: G. M. Fuls

D. H. Walker

Electric Power Research Institute

3412 Hillview Avenue

Palo Alto, CA 94303

Attn: J. J. Haugh (3)

K. A. Nilsson

G. Thomas

45
Fauske & Associates

627 Executive Drive

Willowbrook, IL 60521

Attn: R. Henry

Mississippi Power & Light

P. 0. Box 1640

Jackson, MS 39205

Attn: S. H. Hobbs

General Electric Co.

175 Curtner Avenue

Mail Code N IC157

San Jose, CA 95125

Attn: K. W. Holtzclaw

NUS Corporation

4 Research Place

Rockville, MD 20850

Attn: R. Sherry

Duke Power Co.

P. 0. Box 33189

Charlotte, NC 28242

Attn: F. G. Hudson (2)

A. L. Sudduth

Westinghouse Corporation

P. 0. Box 355

Pittsburgh, PA 15230

Attn: N. Liparulo (3)

J. Olhoeft

V. Srinivas

General Physics Corporation

1000 Century Plaza

Columbia, MD 21044

Attn: Chester Kupiec

TVA

400 Commerce

W9CI57-CD

Knoxville, TN 37902

Attn: Wang Lau

EG&G Idaho

Willow Creek Building, W-3

P. 0. Box 1625

Idaho Falls, ID 83415

Attn: Server Sadik

46
Department of Aerospace Engineering

University of Michigan

Ann Arbor, MI 47109

Attn: Martin Sichel

Dr. Roger Strehlow

505 South Pine Street

Champaign, IL 61820

Applied Sciences Association, Inc.

P. 0. Box 2687

Palos Verdes Pen., CA 90274

Attn: D. Swanson

Purdue University

School of Nuclear Engineering

West Lafayette, IN 47907

Attn: T. G. Theofanous

Acurex Corporation

485 Clyde Avenue

Mountain View, CA 94042

Astron

2028 Old Middlefield Way

Mountainview, CA 94043

Attn: Ray Torok

Bechtel Power Corporation

P. 0. Box 3965

San Francisco, CA 94119

Attn: R. Tosetti

Thompson Associates

639 Massachusetts Avenue

Third Floor

Cambridge. MA 02139

Attn: Timothy Woolf

Factory Mutual Research Corporation

P. 0. Box 688

Norwood, MA 02062

Attn: R. Zalosh

47
Sandia

1131

1131

1512

1513

1513

2512

2513

6400

6410

6411

6411

6411

6411

6420

6421

6422

6422

6425

6425

6427

6427

6427

6427

6427

6427

6427

6427

6427

6427

6427

6427

6440

6442

6444

6444

6445

6449

8024

8513

8523

8523

8523

3141

3151

Distribution:

W. B. Benedick

J. Fisk

J. C. Cummings

S. N. Kempka

A. C. Ratzel

V. M. Loyola

J. E. Shepherd

A. W. Snyder

J. W. HickmAi

V. L. Behr

A. L. Camp

S. E. Dingman

F. E. Haskin

J. V. Walker

J. B. Rivard

D. A. Powers

A. R. Taig

W. J. Camp

W. Frid

M. Berman (3)

K. P. Guay

J. Kotas

M. S. Krein

B. W. Marshall. Jr.

L. S. Nelson

0. Seebold

M. P. Sherman

S. R. Tieszen

G. Valdez

M. J. Wester

C. C. Wong

D. A. Dahlgren

W. A. von Riesemann

R. K. Cole. Jr.

S. L. Thompson

E. H. Richards

K. D. Bergeron

M. A. Pound

W. J. McClean

W. T. Ashurst

K. D. Marx

B. R. Sanders

C. M. Ostrander (5)

W. L. Garner

48
A

NRC FORM 335 US NUCLCAR REGULATORY COMMISSION REPORT NUMBER (Asused by TIOC add Vol No. d ncy)

16.3)

BIBLIOGRAPHIC DATA SHEET SAND83-2624

NUREG/CR-3719

2 Leave Diank

3 TITLE AND SUBTITLE 4 RECIPIENTS ACCESSION NUMBER

Detonation Calculations Using a Modified Version

of CSQII: Examples for Hydrogen-Air Mixtures 5 DATE REPORT COMPLETED

MONTH MYEAR March 1984

6. AUTHORISI 7 DATE REPORT ISSUED

MONTH IYEAR

R. K. Byers August 1984

9 PROJECT, TASK /WORK UNIT NUMBER

8 PERFORMING ORGANIZATION NAME AND MAILING ADDRESS fInclude ZJp COde)

Sandia National Laboratories

P. 0. Box 5800 10 FIN NUMBER

Albuquerque, NM 87185 • A-1246

Division 6444

11 SPONSORING ORGANIZATION NAME AND MAILING ADDRESS (Include Zio Cod.) 12a TYPE OF REPORT

Severe Accident Assessment Branch

Division of Accident Evaluation Technical

Office of Nuclear Regulatory Research 12b PERIOD COVERED linclusIi° des)

U. S. Nuclear Regulatory Commission

Washington, DC 20555

13 SUPPLEMENTARY NOTES

14 ABSTRACT (200 words or less)

CSQ is a well-tested and versatile wave propagation computer

program, a modified version of which has been used to perform a

number of USNRC-supported analyses of detonations of hydrogenair mixtures in nuclear reactor containment buildings. The

modifications, from a user's viewpoint, are fairly minor, and

this version of CSQ is being prepared for release to interested

organizations. This report documents the use of CSQ in this form.

as well as certain codes which aid in performing the detonation

calculations.

15a K.EY WORDS AND DOCUMENT ANALYSIS 15 blFRl fl0

16 

AVAILABILITY 

STATEMENT

I6 AVAILABILITY STATEMENT

-49-