NUREG/CR-3527

LA-9913-MS

RD

Material Transport Analysis for

Accident-Induced Flow in

Nuclear Facilities

R. A. Martin

P. K. Tang

A. P. Harper

J.. D. Novat

W. S. Gregory

Manuscript submitted: September 1983

Date published: October 1983

Prepared for

Division of Risk Analysis

Office of Nuclear Regulatory Research

US Nuclear Regulatory Commission

Washington, DC 20555

NRC FIN No. A7029

Los Los Alamos National Laboratory

Los Alamos, New Mexico 87545

CONTENTS.

ABSTRACT ..... .......................................................... 1

I. INTRODUCTION ................. ........................................ 1

II. MODULAR STRUCTURE ..................................................... 5

III. MATERIAL CHARACTERISTICS ............................................... 6

A. Existing Capability ............................................ 6

B. Future Improvements ........................................... 10

IV. TRANSPORT INITIATION.............................................. 11

A. Background ................................................... 11

B. Existing Capability ........................................... 12

C. Future Improvements ........................................... 20

V. CONVECTIVE TRANSPORT ................................................... 21

A. Background .................................................. 21

B. Assumptions ........................... 22

C. Continuity Equation ............................................... 23

VI. AEROSOL INTERACTION ............................................. .. 28

A. Background ................. .................................. 28

B. Future Plans ........ .............................................. 29

VII. AEROSOL DEPLETION ........ ........................................ 30

A. Background ........................... ............................. 30

B. Existing Capability .................... ........................... 30

C. Future Improvements ........................................... 32

VIII. FILTRATION ............................................................ 35

A. Background ....... ....... ....................................... 35

B. Filter Model .................................................. 36

C. Filter Plugging ................... ............................... 38

D. Future Improvements ............................................... 40

IX. SAMPLE PROBLEMS USING TORAC....................................... 40

X. SUMMARY ...................................................... ........ 71

REFERENCES ............................................................ 77

V

MATERIAL TRANSPORT ANALYSIS FOR ACCIDENT-INDUCED FLOW IN NUCLEAR FACILITIES

by

R. A. Martin, P. K. Tang, A. P. Harper,

J. D. Novat, and W. S. Gregory

ABSTRACT

This report is a summary of the material transport modeling

procedures developed to support a family of accident analysis computer codes. The material transport modeling areas include transport

initiation, convection, interaction, depletion, and filtration. Except for material interaction, these areas are developed in modular

form in three Los Alamos National Laboratory computer codes: TORAC,

EXPAC, and FIRAC. This flily of codes was developed to provide improved methods of tornado, explosion, and fire accident consequence

assessment, resp'ectively, for the 'nuclear industry. Although the

codes were designed to estimate accident-induced gas-dynamic, ther- mal, and material transport transient phenomena in nuclear fuel cycle

facility ventilatiorffsystems, they are applicable to other facilities

as well. Sample problems using TORAC have been provided to.ilus-.

trate the current material transport capabiloities for a simple system under tornado-induced accident conditions. Some sugge~tions for future improvements to some of these material transport models also are

discussed.

I. INTRODUCTION

Nuclear facilities must be designed to protect the general public from the

consequences of accidents that could result in a release of radioactive material

to the environment. To ensure that nuclear facilities can withstand postulated

accidents, regulatory agencies are responsible for reviewing proposed facility

designs. The degree of conservatism and the related risk assessment also must

1
be evaluated for these accident conditions. The nature..of the hazardous material involved and the potential for accidents require that designers and analysts have methods and supportive experimental data for a systematic approach

to estimating accident effects.

Assessment of the environmental consequences of an accident ultimately involves calculating the atmospheric dispersion of radioactive materials and estimating the radiation dose to the surrounding population. Some uncertainty lies

in the estimate of the nuclear facility source term to be used for atmospheric

dispersion calculations. In current safety analyses, some conservative assumptions are used to assess worst cases. Such assumptions are made to insure that

the consequences are not underestimated. The current program is intended to

improve our ability to more accurately estimate nuclear facility source terms.

Thus, we have undertaken a fuel cycle facility safety analysis program to provide user-oriented tools for making better estimates of accident-induced release

or source-term characteristics at a nuclear, facility's atmospheric boundary.1' 2

These tools are intended 'to be an. improvement over current safety analysis

review techniques. The scope of the program is limited'to only accident-induced

material movement within a nuclear facility.

The types of plants considered in this study include' fuel fabrication,

fuel reprocessing, waste solidification, fuel storage, and UF6 production

facilities. However, the planned. research work will be'applicable to a large

spectrum of facility designs and.processes. The results will apply to current

as well as anticipated Nuclear Regulatory Commission (NRC) licensing and decommissioning actions.

The types of accidents considered in.this study include fires, explosions,

spills, equipment failures, criticalities, and tornados. The highest: priority

will be placed on the analysis of fire hazards. These accidents were specified

by the NRC Research Review Group (RRG) responsible for technical review of this

program.

The fuel cycle safety analysis program is divided into three major

research areas. The first area is defining accidents that could occur and

defining where and how they could occur inside a given facility. This area includes a description of the facility, its,processes or unit operations, process

material'inventories, safety systems, and transport pathways. The second area

is defining the accident energetics and mate'rial release relatively-close to the

accident. Each accident considered will be modeled to describe'-its near-field

•2
effects. The last area is modeling the gas and material fluxes through the

transport pathways up to a containment system or to the atmospheric boundary.

Battelle Pacific Northwest Laboratory (PNL) and Oak Ridge National

Laboratory (ORNL) share responsibility for the first and second research areas;

our responsibility is the third area. Work in the first two research areas will

be to identify the accidents to be considered and also to provide primary

source-term data to be used in the transport models. The Los Alamos National

Laboratory investigation will include developing techniques for estimating

accident-induced transport of material to the nuclear facility's atmospheric

boundaries. The Laboratory's objective in this program is to develop mathematical models and experimental data that will permit prediction of material transport through a complex network of rooms, gloveboxes, ductwork, filtration systems, and other components commonly found in ventilation systems. These models

will require.predicting the accident-induced flow dynamics with special emphasis

on the transport of radioactive material.

Work at Los Alamos in the early stages of this project has resulted in a

family of accident analysis computer codes (TORAC, EXPAC, and FIRAC). TORAC3 is

a computer code that can predict tornado-induced flows, pressures, and material

transport within structures. EXPAC 4 can predict explosion-induced gas-dynamic

transients and material transport within structures. FIRAC5 is designed to predict the simultaneous gas-dynamic, material transport, and thermal transients

that occur in a facility subjected to a fire. TVENT 6 and EVENT 7 are the predecessors of these codes. These codes are directed toward nuclear fuel cycle

facilities and the primary release pathway-the ventilation system. However,

they are applicable to other structures and can be used to model other airflow

pathways within a facility.

The objective of this report is to present the material transport modeling

procedures developed to support the Los Alamos family of fuel cycle safety analysis computer codes. The material transport modeling areas include transport

initiation, convection, interaction, depletion, and filtration. Except for

material interaction, these areas are developed in modular form in TORAC,

EXPAC, and FIRAC.

The material transport-.algorithms in our codes provide an estimate of the

aerosol or gas transport within a nuclear fuel cycle facility. Ultimately, we

would like to predict the quantity and physical and chemical characteristics of

radioactive material that may be released from the facility as a result of an

3
accident. The transport can take place because of airflow through the rooms',

cells, canyons, corridors, gloveboxes, and ductwork installed-in the facility.

In many cases, the entire flow pathway forms a complex network system. Using

the computer codes, we can calculate material concentrations and material mass

flow rates at any location in the network, including the supply and exhaust

ducts of the network system. Most importantly, the codes will perform transport

calculations as a function of time for arbitrary user-specified accident transients imposed on the facil.ity boundaries.. Although our codes can be used to

determine material transport under steady flow conditions if desired, there is

no need to assume steady flow as is required in some material transport codes.

In Ref. 8, the material transport estimate is obtained in piecemeal fashion using steady flow calculations for rooms and duct segments. Our codes model

the entire network for transient flow and in doing so takersinto account system

interactions. A generalized treatment of material transport under accident con9-15 ditions could become very -complex. Several different types of materials

could be transported, and more than one phase could be involved, including solids, liquids, and gases ýwith phase transitions. Chemical reactions leading to

the formation of new species could occur during transport. Furthermore, there

will be a size distribution function that varies with time and position for each

type of material, depending on the relative importance of effects such as homogeneous nucleation, coagulation (material interaction), diffusion (both by

Brownian motion and. by turbulence), and gravitational sedimentation. We

.know of no computer code that can handle transient-flow-induced material transport in a network system subjected to possibly all of these complications, and

the transport portion of- our codes does not include this- level of generality.

This initial,. basic form of our material transport modeling consists of the

following.

* Gas dynamics decoupled from material transport

* Homogeneous mixture and dynamic equilibrium

* Material transport limited to a single size and species (except for

FIRAC).

* No material interaction during transport

e Material deposition.based on gravitational settling using relationships

from the literature

* Turbulent and Brownian diffusion and phoretic effects neglected

* Phase change, chemical reaction, and electrical migration not allowed

4
9 Material entrainment can be arbitrarily specified using tabular inputs

or calculated using Semi-empirical relationships based on wind tunnel

data

Although the material transport capability is limited in these codes, this

initial version does represent a significant advance for the prediction of material movement within a nuclear facility. The codes are structured in a modular

fashion so that improved modules can be incorporated easily, and this is discussed in Sec. II. Detailed descriptions of the material transport modules now

available within the codes and suggested improvements that can reduce the degree

of conservatism in our current capabilities are included.

II. MODULAR STRUCTURE

The movement of material by a flowing fluid involves several basic mechanisms. The primary mechanism for movement is the flow of the fluid itself; the

other mechanisms involve physical models that could be upgraded as the state of

the art improves. The basic elements of material transport that we will consider in an accident-induced flow environment are listed below.

1. Material characteristics

.2. Transport initiation

S3. Convective transport

4. Transport interaction

5. Aerosol depletion

6. Filtration

Material characteristics and transport initiation are areas that must be considered by the user as he begins to set up a code to solve a given problem. Calculations of convective transport, aerosol depletion, and filtration are performed

automatically by the code. Items 2-6 are actually separate subroutines or modules within the code. Item 3 is a key subroutine that calls on items 2, 4, 5,

and 6 as needed during the course of the calculation. Each of the components

listed above is subject to certain limitations and assumptions that will be discussed below. We also will specify the required user inputs and provide appropriate references for the theory used in each case.

The material transport capability is composed of separate subroutines or

modules that can be added or removed without disturbing other parts of the computer codes (Fig. 1). The purpose of this structure is to allow us to begin

5
Fig. 1.

Material transport modular structure.

with basic material transport modules based on relationships discussed in the

literature. From this initial analysis level 1 we can improve each module so

that a more advanced analysis capability can be achieved. When the module is

complete, we can simply exchange a new module for an old one without disturbing

the rest of the code. With this in mind, we will discuss a number of planned or

possible improvements to our material transport modules in the sections that

follow, starting with user-supplied material characteristics.

III. MATERIAL CHARACTERISTICS

A. Existing Capability

The limitations on material transport in terms-of the physical and chemical characteristics of the material are as follows. For TORAC and EXPAC, the

pneumatically transportable.contaminant material is restricted to a single phase

of a single species. In FIRAC, the contaminant material can consist of any number of aerosol or gaseous species. Thus, multiple-species size distributions

can be simulated in FIRAC. However, no coagulation, phase transitions, or chemical reactions are allowed in' any of the three codes; for example, condensation,

and gas-to-particle conversion are not permitted. If the contaminant is an

6
aerosol (solid particles or liquid droplets suspended in air), then it will be

treated in TORAC and EXPAC as monodisperse (equal-sized) andihomogeneous (uniform density) and with spherical particles or droplets during a given code run.

Both size and density must be specified by the user. If the contaminant is a

gas, it is assumed to be inert. User guidance in the area of aerosol and gas

characteristics is provided below. Some suggestions also are made for describing fuel-grade plutonium and uranium oxide powders.

In applying the material transport capability in our codes, the user must

identify the type (aerosol or gas), quantity, and location of material at risk.

If the material is a solid or liquid aerosol, a characteristic size and density

must be specified. In the simplest case, these parameters may be assumed. For

example, if the user is primarily concerned with the transport of aerosols in

the size range ofD ý 12 vm: and densities of 0.5 < p < 12 g/cm3 , he could run

a code for some assumed cases of (Dp, pp) to determine entrainment or deposition

p p

sensitivity.

In general, the user may wish to characterize a nonideal aerosol contaminant with approximate or idealized values of (Dp, pp). We advise caution here

p'

because there are many different ways to characterize the diameter of aerosols

of irregular shape and nonuniform density. For example, diameters representing

a mean value relative to total count, surface area, volume, weight, or terminal

settling velocity can be estimated based on frequency-of-occurrence data.

For the case of aerosol transport along fuel cycle facility pathways, we

are interested in changes in aerosol concentration resulting from entrainment,

dilution, deposition, and filtration. Entrainment, deposition, and filtration

all depend on the quasi-steady aerodynamic drag characteristics of the aerosol.91 Unless the aerosol is very small (less than 0.5 um), the probability

that a spherical particle or droplet will deposit depends on the magnitude of 10

its terminal settling velocity, us.

us p D 2 pCg/18P , (1)

p p

7
where pF= actual density,

D = diameter,,

p

C = Cunningham slip factor,

g = gravitational acceleration, and

= aerodynamic viscosity..

Most aerosols (spherical or nonspherical) having the same settling velocity will

be distributed-throughout a ventilation system network in a similar manner. The

recommended deposition parameter is the aerodynamic diameter or Stokes

diameter. 10

(1) The aerodynamic diameter Da is the diameter of a sphere of unit density having the same terminal speed as the contaminant.

(2) The Stokes diameter Ds is the diameter of a sphere with the same bulk

density and terminal speed as the contaminant.

These diameters are related by the equation

us ppD&D 2 Csg118p F=p oDa 2Cag18p , (

where Cs andCa are the slip factors associated with Ds and Da, respectively,

and p0 is the unit den.sity.', For the contaminant of interest,. D or Da may have

been -measured directly using such aerodynamic classification devices as impactors, centrifuges, sedimentometers, or air elutriators. (These devices are

suitable for measuring the size of irregularly shaped particles.) If possible,

an aerodynamic diameter measurement should be based on activity. Otherwise, we

recommend using D abased on mass measurements.

If count-frequency data (for exampl~e, based on projected area diameter for

irregularly shaped particles) !are available for the contaminant, they must be

converted to aerodynamic diameter. Such data should be plotted on logprobability paper and fit with a straight line. If this straight-line fit to

the data is acceptable, the size distribution is approximately log-normally

distributed and may be described completely by two parameters, geometric count

median diameter D and geometric.standard deviation 0g* Most fine particle gc.*

systems formed by comminution of a bulk material or grown by accretion have lognormal size distributions, and so this assumption is recommended. -11 16

8
The user can obtain Dgc and a from log-normally distributed countfrequency data. The Hatch-Choate transformation equations now apply. These

equations relate D and a to a number of other median and mean diameters that *gc g

may be important, depending on how the toxic substance or activity is related to

the physical properties of the particle. For example, the activity may be proportional to the total number, total surface area, or total mass of the particles. We chose to work on a mass basis. The user may calculate the geometric

mass median diameter D gm, the volume mean diameter Dv, and the weight mean

diameter Dw from16

2

log Dgm =log Dgc + 6.908 log 9g

logD = log Dgc +3.454 log 2 0 g , and (3)

log Dw =log Dgc + 8.023 log 2 0 g

where the logarithms are calculated using base 10. The median diameters Dgc and

D referred to above divide the count-based and mass-based size distributions

gm

in half. For example, half of the mass of the sample lies above D and half gm

below. A mean diameter is the diameter of a hypothetical particle that is intended to represent the total, number of particles in the sample.

In the absence of. specific information on the aerodynamic properties of the

aerosol of interest, Stockham1 6 recommends using Dw as an approximation of aerodynamic size. An alternative is to convert Dv to an aerodynamic diameter. (If

we assume -the material density to be uniform, independent of size, and known,

then the mass of the particle with size Dv is a mean mass.) To do -this use

Da = [(61) (pp Po (a 3 /Kr)] 112Dv (4)

where a = volume shape factor and

Kr = resistance shape factor. 1 0

9
The values , of 3 and Kr are given in Ref. 10, where this calculation is

discussed.

We advise caution in estimating aerosol density. The aerosol produced by

accident conditions may .in.fact consist of flocculi and.agglomerates with actual

densities well below the.'theoretical density of the pure parent materials. The

floc densities- may be as much as an order of. magnitude less than the normal

16 density. The user can find pertinent information on fuel-grade powder size

and density in Refs. 2 and 17-30. Useful information on droplet sizes and densities can be found in Ref. 2.

B. Future Improvements

We are interested in removing some -of the idealizations discussed in

Sec. III.A. that impose limitations on our ability to model the transport of

real materials of concern in fuel cycle facilities. In particular, the multiple

species capability currently available in FIRAC5 should be extended to TORAC 3

and EXPAC. 4 This improvement (going from single to multiple species capability)

forms the foundation for transientf calculations of the time- and space-dependent

material size-distributi.on function. Here a multiple-species capability encompasses the ability to model a set of contiguous size intervals representing the

discrete size distribution function of,.-a.,single species.,- Estimates .of -aerosol

mass exchange between. intervals of the size distribution function then depend on

the validity of our physical models for aerosol production (gas-to-particle

conversion, entrainment, or. other mechanism), interaction, and depletion.

Given the capability of modeling aerosol size: distribution, functions, a significant improvement for the user. would be a built-in calculation of the lognormal size distribution function. This distribution is particularly useful in

particle size analysisbecause it is easy to manipulate mathematically and; experimental observations show-that it fits', a wide variety of aerosol populations..

Assuming a log-normal>" distribution for. a given aerosol species, the relative

number. of particles. or droplets having diameters whose logarithms fall .in the.

interval x + dx/2 is given by

1

f(x)dx = exp 2 dx

1.0
where x = In D,

=in aI

•o = in Dgc, and

f(x) = log-normal probability density function.

"In" implies logarithms to base "e". With these expressions and knowing the

total aerosol mass together with pp, Dgc (or Dgm), and ag specified by the user,

our codes could partition the available mass over n increments, such as between

log sizes +.3 ag. This code-calculated distribution of each aerosol would be a

convenient starting point for transient calculations.

IV. TRANSPORT INITIATION

A. Background

To calculate material transport, the analyst must determine or assume the

location, distribution, and total quantity of contaminant material. The contaminant may be located in any or all rooms, cells, gloveboxes, corridors, or rectangular ducts. (An assumption about material distribution is only necessary

when the user wishes to exercise the "calculated aerodynamic entrainment of dry

powder from thick beds" option discussed below.) A total quantity (mass of

material) must be known or assumed.

There are two options for material transport initiation, and they can be

used simultaneously. These are user-specified and calculated aerodynamic entrainment. The user-specified option gives the analyst considerable flexibility.

but requires engineering judgment to specify input to the code. This option

involves preparing a table or graph of material generation rate or mass injection rate (kilograms per second vs time). The data are supplied to the code on

the input deck Material Generation Cards. For example, a given cell can have a

given quantity of fuel-grade uranium or plutonium powder injected at a specified

rate; the injected material also could be a gas. This user-specified option may

be selected to calculate the *consequences of a hypothetical aerosol or gaseous

release, and for reasons discussed below, we recommend using it to handle reentrainment from thin beds (dirty cells or ductwork). Our codes have been developed assuming that accident-induced off-design flows are the primary cause of

source-term initiation. A general-purpose utility code may be used for

11
accidents that do not significantly disrupt the normal ventilation system flow,

such as pressurized releases (if not too severe), spills, and equipment failures. Guidance for user source-term estimation can be found below.

The user may wish to specify a material generation rate vs time for many

accidents. This procedure is the same as that discussed above; that is, a table

or graph of mass injection rates can be specified to simulate the injection of

material associated with the accident.

The calculated entrainment option refers specifically to a subroutine

designed to calculate aerodynamic entrainment of dry powder from:. thick beds.

This subroutine can be useful for analysis of flow-induced material transport

initiation. It uses a new semi-empirical analytical approach that *takes advantage of detailed flow information produced by the gas-dynamics module for calculating entrainment. To arrive at an estimate of the mass of material entrained

at each time step of calculation, this subroutine calculates when the surface

particles will begin to move. Particle, surface, and flow characteristics are

taken into account to do this. It also accounts for the aerodynamic, interparticle (cohesion), and surface-to-particle (adhesion) forces that may be acting.-

This procedure was used previously in Ref. 31 and is discussed more fully there

and below.

The user may use this calculated entrainment option whenever ;powder beds

are known or assumed to be present in rooms, cells, gloveboxes, corridors, or

rectangular ducts. He must provide the code with particle size and density,

total mass of contaminant, and the width and length of the (assumed floor) surface over which the powder is uniformly distributed. If. material transport, is

requested, the user must select at least one of the material transport initiation options. Both options may be used simultaneously.

B. Existing Capability

Our accident analysis. computer codes provide the analyst with two options

for transport initiation: (1) user specification of mass injection rate vs time

and (2).calculated aerodynamic entrainment. These.options are quite different

and require different levels of effort and judgment. from the analyst. In this

section we will provide background information to help the user supply numbers

for source-term initiation using option (1). We will describe in detail the

procedure and equations used with option (2)., The. primary. cause of initiation

is assumed to be transient flow. induced by an accident. Two .examples

illustrating the use of option (1) will be discussed first.

12
As a first example, consider a decomissioned fuel reprocessing facility

with contaminated enclosures. The analyst can estimate the preaccident aerosol

concentrations in these areas using the resuspension factor concept. 2 ,

1 7 , 32 - 34

The resuspension factor K has been used extensively to quantify airborne contamination levels in operational fuel cycle facilities. By definition,

3 K aerosol concentration (g/m K. 2 1/in surface loading (g/m

Sutter 17 has tabulated ranges of K that were compiled from numerous references.

Her tables include values of K derived from measurements of airborne contamination resulting from numerous and varied cases of outdoor wind stresses and indoor mechanical stresses. Sutter's summary tables are useful for obtaining

bracketing or bounding values of K. With assumed or measured values of K and

surface loading, the user can calculate the airborne material concentration subject to transport. Based on the enclosure volume, a quantity or mass of contaminant subject to transport can be calculated from the concentration. This mass

then can be injected at the system node representing the enclosure of interest

using the user-specified option. The mass injection rate-must be specified by

the user.

Healy 3 2 reviewed many measurements and applications of this simplistic resuspension factor concept. Several of its limitations are noteworthy. First,

the measured values of K range over 11 orders of magnitude. For benign conditions where K is most reliable, the uncertainty is at least 2 orders of magnitude. Further, K fails to account for particle, surface, or local flow characteristics except as they existed during a particular measurement. Thus, we

recommend using the resuspension factor only for estimating preaccident airborne

mass subject to transport as suggested by this example.

As a second example, consider a mixed-oxide fuel fabrication facility in

which bulk MOX or "mixed oxide" powder is being protected. The user may elect

to model this facility and run the code for an accidenttransient without material transport. This preliminary run Would supply an estimate of the system

gas-dynamic transients, including flow rates and pressure drops during the

accident. Some controlled areas may be subjected to abnormally high air

13
velocities that could lead to entrainment because of aerodynamic .stress. A

knowledge of theair velocity time history.", wi1: be useful to estimate the

quantity of material made airborne.

We will summarize briefly three methods that can be used to estimate aerodynamic entrainment of aerosol material. Sutter 1 7 has reviewed and compiled

data from numerous papers under the heading "aerodynamic entrainment."' (This

paper is a good source of reference information.) The analyst's objective here

should be to estimate a quantity of material made airborne during the first part

of or during the entire accident transient. This quantity then must be converted to a mass injection rate for input to a code as in the first example.

The first method for estimating the quantity of material made airborne by

aerodynamic entrainment is to use the "per cent. airborne" and, 'resuspension

flux",' data measured by Mishima and Schwendiman. 3 0 As-an example, theymeasured

entrainment of uranium dioxide powder -and uranium nitrate solution -at different

air velocities,. (Using these data will require using engineering judgment.) A

second method for :estimating entrainment is to use the ýresults developed by.

Singer et; al. 3 5 ' 3 6 to estimate coal dust entrainment. These results also are

di scussed.by Sutter'. 7

Finally, the analyst may use the resuspension. rate .concept introduced -by

Sehmel. 3 7 Resuspensionrate is defined as a fraction.of the initial mass:'resus--

pended per second. By .definition,

GAt A ' " -. .

where S = resuspension.rate, fraction/s,

A = mass suspended and flowing horizontally

through a given crossýsectional area, g,

G = ground source mass,.g, and

=t duration of sampling, s.

Measurements of S obtained during a number Of atmospheric field tests are tabu17 lated in. Sutter's paper. The user, should becomeý familiar withWthe' l1imitations

of all three of the abovemeth-ods so that; he can apply them,-judiaciously.

S14
Here we will present in detail the procedure and equations used with

option (2), calculated aerodynamic entrainment of dry powder from thick beds.

The entrainment subroutine has the advantage of calculating entrainment automatically. As with the three methods discussed in the second example above, our

objective is to provide the material convection module with an estimate of the

quantity of particulate material that can be entrained from a contaminated surface as a result of accident-induced transient flow conditions. However, the

previous three methods are not suitable for use in a computer code because they

are based on steady-state measurements for specific conditions. Except for

Singer's 35 work with coal dust, they fail to couple unsteady flow (changing velocity) conditions to the amount of material entrained. In addition to local

flow characteristics, the previous methods do not. account for material or surface characteristics in a systematic way. Thus, resuspension factor, resuspension rate, and per cent airborne would have to be measured for innumerable cases

to encompass accident conditions.

The analytical method used in our codes for calculating aerodynamic entrainment was proposed and illustrated in a fuel cycle facility application in

Ref. 31. To estimate the quantity of material entrained, this method considers

the following questions. (1) When does the surface material begin to move?

(2) What criterion determines when material will be suspended? (3) How much

material becomes suspended? A valid answer to question (1) implies that particle, surface, and flow characteristics have been taken into account. Some

account also must be taken of the forces present, namely, aerodynamic, interparticle (cohesion)., and surface to particle (adhesion) forces. This procedure is

similar to the approach taken by Travis,38 who developed a computer model to

predict reentrainment and redistribution of soil contaminants as a result of

eolian effects.

The first question we must answer is "When does material begin to move?"

Before particle motion can occur, a threshold airspeed. must be equalled or exceeded so that the aerodynamic forces will be sufficient to overcome restraining

forces. To relate threshold airspeed to surface effects, we introduce the friction speed equation,

u vT-IT , (5)

15
where t= mean shear stress at the surface and

p =fluid density.

Experimental measurements of threshold friction speed u*t obtained at

of material movement are available for a wide range of material

densities.

*These measurements were plotted in Fig. 2 (from Ref. 39) and are

the following semi-empirical equations. 4 0

the onset

sizes and

fitted by

A = (0.108 + 0.0323/B - 0.00173/B 2 )

(6a)

x (1 + 0.055 /pg D )2 1/2

where A

B

Dp

P p

g

9

= u*t/ [(pp - p)gD/p• 112 ,

- u*tDp/v,

= average particle diameter,

= particle density,

- gravitational acceleration, and

- P/p = fluid kinematic viscosity.

Equation (6a) holds for 0.22 < B < 10. The variable A is the threshold coefficient. The variable B is the particle friction Reynolds number. For the range

B < 0.22, Eq. (6b) applies:

A = 0.266(1 + 0.055/0 pgDp) 11 2

(6b)

x (1 + 2.123B)- 1 12

Equations (6a) and (6b) collapse the threshold friction speed data in the appropriate range of B onto a single curve-with D and p as parameters. Given

p

a particular aerosol size and density, we can calculate u*t from Eq. (6a)

16
170 I

160 Density Diameter

Material (ýg/cm 3 ) (',u.m)

150 -• instant tea 0.21 719

.1Silica geI 0.89 17:169

140 0'Nutshell 1.1 40to359

0. Clover seed 1.3 1290

130 ,0 Sugar 1.59 393

']Gloss 2.42 31 to 48

0 Glass 2.5 38 to 586

120 - s Sand 2.65' 526

D Aluminum 2.7 36 to 204

110 A Glass 3.99 55to 519

E Ci CopperOxide&O 10

100 - V Bronze 7.8 6:6 • 11.35

0 Copper 8.94 12:37

90 90- (ZLead 11.35 8:720

Air density-p=0.01226g/cm 3

Kinematic visc.-/'=0.1464cm% .8 "80 -

03

A 70

U-

"60 3.99

S50 -

2.5

4-,02.42

1.3

30 8 1.59

20

0.0.21

I I I I I

0 5 10 15 20 25 30 35

(Diameter) " (AM.1m

Fig. 2.

Particulate threshold friction speed.

17
and Eq. (6b). An iterative technique is used to i.sollve for u~t because .this

,variable appears implic.itly .onm both sides.,of the equations. The value ofv:.was

assumed to be constant at v =-0.1454,cm2 /s- which corresponds to standard atmospheric conditions.

In u*t we have a measure of when particle motion will occur and when entrainment is possible. Under given flow and surface-conditions, a value of the

friction velocity exceeding the threshold friction velocity can produce entrainment; that is, entrainment can occur only when'u. > u~t. We may relate u. to

the corresponding velocity at the turbulent boundary layer edge using one of the

following two equations. For a smooth surface with a laminar sublayer, 4 1

u(y)/u. =(1/0.41) in (yu*/v) + 5.0 (7)

42 For a rough. surface with no laminar sublayer,

u(y)/u. = (1/k) in (y/yo.) ,(8)

where y.= distance from surfaie,

k.= 0.4 = Von Karman constant,

y R/30 = roughness length, and

.R .= average surface:roughness height,

and where the velocity u(y) is calculated by the gas-dynamics module of the

code. For a duct with fully developed turbulent airflow conditions, the centerline velocity or velocity at the boundary layer edge may be 25% higher than the

average or bulk velocity. This version of the codes uses Eq. (8) for a rough

surface with an assumed boundary layer thickness of y = 10 cm and a roughness

length of yo0 . 0.0104 cm (a moderately rough surface). Our use of Eq. (8) will

lead to higher values of Li. for the same values of~u(y) and.y than Eq. (7). Because entrainment is known to depend on the difference (u. - u*t), our choice of

Eq. (8) will lead to conservative estimates of entrained material.

The next question- is" "What -determines whether particles go into suspension?" That, is, of all the particles, how do we divide those that, could become

18
airborne from those that ,remain: close to the surface? Iversen et'-al. 4 0 have

shown that for particles smalleir than 52 pm, suspension occurs as soon as the

threshold speed is reached. The criterion assumed here-was that suspension will

occur for those particles for which us/u. = 1 and u* > u*t, where us is the particle fall or terminal speed. The friction speed u, is of the same order of

magnitude as the vertical component of turbulence in a boundary layer. Values

Of Dp < 50 um for suspension are in agreement with measurements using soils. 3 8

In each code we have assumed that all of the particles are subject to

suspension.

How much material becomes suspended? Travis 3 8 has suggested the following

expression for qv, the mass of particles per unit area per unit time that go

into suspension.

qv= q U [(u*/u*t) P13 - (9)

where P = mass percentage of suspendable particles, and

Cv, ch = empirical constants (2 x 10-10 and 106, respectively).

In Eq. (9), qh is the mass of material moving horizontally through a vertical

plane perpendicular to the surface per unit width per unit time'and may be determined from4 3

qh= 2.61(p/g)(u, + u*t)2 (u - u*t) .

The calculated aerodynamic entrainment option of the material transport

module is a subroutine that uses Eqs. (6) through (10). The steps can be summarized as follows. At a given time, the gas-dynamics module supplies the velocity u(y) for every room or duct with material subject to aerodynamic entrainment.

This value of u(y) and the turbulent boundary layer velocity profile in Eq. (8)

are used to compute a surface friction velocity u,. A characteristic value of

threshold friction velocity u*t for the input material characteristics is

obtained from Eq. (6). If u, < u*t, no entrainment occurs. [See Eq. (10).] If

19
u, > ut, then semi-empirical entrainment equations [Eqs. (9) and (10)] are used

to estimate the vertical flux of suspendable material . Knowing .qv and the

floor area A over which the contaminant is uniformly distributed, we'can compute

the source term

Mp~qvA , (1)

which has the units kilograms per second. As a source term, Eq. (11) represents

a positive contribution to the Mp term on the right-hand side of Eq. (29) in

Set. V. The floor area A is assumed to be flat and :free of obstacles or

protuberances.

The question of how heavily a surface must be loaded before equations like

Eqs. (6), (9), and (10) are !applicable is debatable. For realistic types of

loadings, such as we expect to find in many locations of a fuel cycle facility,

the empirical constant in Eq. (10) may not be satisfactory because it was

obtained for relatively thick powder beds. Furthermore, the empirical coefficients in Eq. (9) are suspect because they were obtained from experiments with

soil particles.

The recent experimental and theoretical work underlying Eqs. (6) and (10)

is believed to be the best available. 3 9 ' 4 0 ' 4 3 Thus, the basis for predicting

U*t using Eq.. (6) is sound;_ however, the data base to which Eq. (6) was fit is

sparse for. small, heavy particles. In principle, these uncertainties could be

checked and reduced with appropriate experimentation.

C. Future Improvements

We believe that considerable analytical and experimental work is needed to

support the area of material transport initiation. The current fuel cycle facility safety research program1' 2 : is sponsoring investigative work in this area

at both Los Alamos and PNL. At Los Alamo's, one analytical task involves asses-.

sing existing compartment fire models for their ability ( to predict convective

heat release rates.. (or fire compartment gas temperatures) and particulate and

flammable gas mass release rates. In addition, Los Alamos is developing a new

compartment fire model directed specifically at predicting the above parameters

for the case of under-ventilated (oxygen-depleted) fires. 44 Established fire

2•0
models and laboratory oven test methods have not simulated such.fires yet. Future improvements should. consist of coupling a compartment fire model to the

existing FIRAC network analysis capability and obtaining supporting experimental

data from laboratory ovens and compartments.

Additional experimental data are being obtained by Los Alamos in the area

of powder or dust entrainment under simulated accident conditions. 1 Such data

are needed for simulants for radioactive materials under conditions of pulsed

and shock flow for both light and heavy surface loadings. These data can be

used to improve the empirical, coefficients in entrainment equations such as

those in Sec. III.A.

PNL has surveyed source-term information in the areas of fires and explosions. 1'2 It is sponsoring experiments at Factory Mutual Research Corporation

to determine the pyrolysis/combustion characteristics of solid and liquid combustible materials of interest in fuel cycle facilities. 2 In addition, PNL is

conducting experiments to determine source-term quantities of radioactive aerosol under conditions of powder and liquid free-fall spills 4 5 and pressurized

releases.2

V. CONVECTIVE TRANSPORT

A. Background

We have developed a simple material convection model capable of predicting

airborne material distribution in a flow network and its release to the environment. (Radioactive or toxic material release to the environment from an accident is a major concern in nuclear facilities.) The convective transport model

is based on the assumptions that the particle size is small and that its mass

fraction is small relative to the gas mass in the same volume. This allows us

to assume that the material and the gas form a homogeneous mixture and that they

are in dynamic equilibrium. In this case, the gas-dynamic aspect of the problem

is not affected by the presence of the airborne material, and the particulate or

material velocity is the same as the gas velocity. at any location and time.

Consequently, the only relation needed to describe the motion of the material is

the continuity equation. This model and the underlying assumptions are presented in more detail below.

21
B. Assumptions

The usual mathematical, formulation.for the motion of a mui.tiphase, mul1ticomponent material system is based on the concept of conti.nuum mechanics With

some pertinent qualifications.13 We can obtain a set of partial differential

,equations for some macroscopic parameters with a few phenomenological descriptions of the stress, heat flux, and diffusion plus other formulations for the

physical and chemical interactions among phases and components and with the

boundary. Some of the relationships are either incomplete or not known yet.

Depending on the range of interest, an extensive simplification may be necessary.. The following assumptions are made to reduce the complexity of the problem, but they still allow us to meet our simple objective, namely, the capability of handling material transport without disturbing the main gas flow to-any

significant degree.

We define the material as any pneumatically transportable substance in a

ventilation system. The material can be solid, liquid, or even gas other than

the main gas stream. The individual material point is assumed to be quite.small

in size if it is in the condensed phase; a material cloud is an ensemble of

material. Throughout the ventilation system, the main body of the gas and the

material cloud form a mixture. The description of the flow system is based on

the continuum point of view. In Sec. V we will neglect all chemical reactions

and physical processes such as deposition, entrainment, coalescence,, material

break-up, evaporation, and condensation, but most of these processes are considered in other sections of this report. Material generation is a..prescribed

quantity. Once the material cloud is formed and mixed with the main gas stream,

our attention will be on the movement of the material.

Even in a dusty cloud, the volume occupied. by the material is quite small

compared with "the volume of the gas. We !will assume this is the case in our

first model and refer to it as' the disperse condition. A consequence of this

is that the material motion isdominated, by the aerodynamic forces (mainly drag)

but not by the interparticle forces. Furthermore, the material size we most

often encounter in a ventilation system falls into the micron. range. For that

small size, the aerodynamic relaxation time is quite small compared with the

typical residence time. This. means the material ,can respond quickly to the

variation of gas velocity, and most of the'time the material would have'a velocitY nearly identical to the gas at any location and time. Thus, we have 'obtained the dynamic equilibrium condition between the gas and the material cloud,

22
and the only equation that is needed- to find out the material flow rate is the

material continuity equation. We can add one more equilibrium condition (that.

is, the material temperature is the same as the gas), and we have a homogeneous

equilibrium model for the gas and material cloud mixture. This mixture can be

treated as a simple gas with the proper thermodynamic and transport properties

used in all usual gas-dynamic equations. 4 6

In principle, we could proceed to solve the set of gas-dynamic equations

for the mixture. However, the mixture transport properties are not easy to

determine. On the other hand, we still can obtain governing equations for the

main gas stream and the material cloud separately. Some of these equations will

contain terms that express the effect of interaction between the gas stream and

the material. A closer examination of these terms reveals that, if the material

mass fraction is quite small compared with that of the gas, the effect of the

interaction on the gas-phase flow is negligible. This is the disperse condition

for the material cloud relative to the gas mass, and we will assume so. At this

point, we have achieved the complete separation of the gas-phase'flow dynamics

from the material cloud. The gas-dynamic aspect of the material transport problem can be solved first, and then the continuity relation of the material will

be used to determine the material flow. A more complete presentation of various

multiphase,ý multicomponent flow problems is given in the literature. 13 ' 4 6 ' 4 7

All of the above assumptions and steps leading to the final simplification of

the material transport problem are based on the literature cited.

C. :.Continuity Equation

In a volume V, a part of it is occupied by material with mass Mp and volume

Vp and the rest by gas of mass M and volume V Obviously,

V=V p + V . (12)

We define a volume fraction of the material as

a p (13) ap -V

23
and the densities (concentrations) of: the.. material, .and gas.based on"the mixture

volume as

M

p = P

M

and = g ý(14)

which differ from the densities:based:on theivolume of the individual phase,

M

p

and

M

pg

="g (15)

Only pg is related to the

state. The mass fraction of

pressure and temperature through the equation of

the material is defined as

Y Mp p= p + Mg (16).

We can express 'the mass fraction in terms of volume fraction through the

following relation.

Yp = [1+ (±jp) (!)] -1 (17)

Because the material-phase density of liquids or solids is usually so much larger than the gas-phase density, the disperse. condition (a <<1) does not imply p

the dilute condition (Y « <1) unless

p

<< -

p. pp

(18)

24
which is a more stringent condition.ý' We will assume this is the case in:.'the

current material convection model.

The velocity of a mixture is defined as follows.

= (P; Up + pg Ug) /P (19)

with

p IP g+ ' (20)

p is the density of the :mixture. M, Up, and u represent the mixture velocity, _9

material velocity, and gas velocity, respectively; they are vector quantities.

Using.the mass fraction Yp, we have

p = Qpp + (1-Yp)Ug . (21)

If u and ug are of the same order of magnitude and for the dilute

condition,

u -1 M g . (22)

The mixture velocity is dominated by the gas velocity. Also from Eq. (20), the

mixture density is roughly the same as the gas density... We expect this should

be the case for alight loading situation. From now on, we. will drop the

subscript g for all quantities associated with .the gas phase.

47 The continuity equation for any phase or component in a mixture is

aJpdV f p; Up d5 + Mp (23)

V JS p

25
The, time derivative term on the left-hand side represents the change, of the

material density inside a control volume V. .The first term on the right-hand

side is the material flow through the boundary 5 of the volume V, and the last

term is the material source. Assuming pý is uniform over the control volume

and using the same representation we have for the gas continuity. equation,,

Eq. (23) becomes

dPI

V =P.Ep~i Upi Ai + M . (24)

Here we drop the vector notation for the velocity but add the subscript i to

indicate the flow path connecting to that volume. Ai is the flow area, and

U is the flow velocity normal to the area. The positiveness of the flux

term is referred to as the flow into the volume. Again we introduce Yp into

Eq. (24),

V a• [ypp] =Z. p. upi A. + Mp , (25)

[p Pi *i up1 1

or

dY 1r

V d pi P Ai" +1 Mp- p p Vdt (26)

The last term in Eq. (26)*is the gas density change and is determined by the-gas

continuity equation.

Under the dynamic equilibrium condition, the material velocity is almost

identical to the gas velocity everywhere and at any instance, namely,

u p(27)

26
u i represents the gas velocity in pathway i. Substituting that into Eq.r(26)

and recalling the gas mass flow in branch i,

m =i ui A i (28)

we obtain

p i p p dt (29)

Equation (29) is a differential equation for the unknown Yp. Once the gasdynamic quantities p and ri are known, Eq. (29) can be integrated to obtain Yp

at a new time. The advantage of using Y instead of p as the unknown is that

Y is not subject to theeffect of compressibility as is pp Once Y is calcup Pp

lated, the material density concentration can be obtained through

p y . (30)

Yp p

The quantity mass fraction. (or molar fraction) has been used extensively in

fluid flow with chemical reaction. In the TORAC code, we expect the air density

variation to be small, so we use Eq. (24) in the numerical calculation directly

without referring to the mass fraction step.

Finally, we must emphasize again that the assumptions that are made about

the dilute condition of the material enable us to solve the gas-dynamic problem

independently. The validity of the assumptions depends on the individual case

that we are facing. However, we do believe that this simple model will cover a

broad range of problems related to material movement in nuclear facilities.

27
VI. AEROSOL INTERACTION

A. Background

One goal of the fuel cycle facility safety analysis program is to predict

the quantity and physical and chemical characteristics of radioactive material

that could be transported to a plant boundary. Unfortunately, the quantity and

physical and chemical characteristics of the material can be changing, especially during the course of an accident. In particular, the aerosol mass in the

respirable size range at the time of exhaust at a facility boundary can be quite

different from that produced near the accident. An intermediate need is.to predict the quantity and characteristics of aerosols that reach the nuclear filtration systems (or other engineered safeguards.) because this can affect the filter

plugging behavior. Further, aerosol characteristics are needed to model transport processes because size and density play a role in determining what type of

deposition mechanisms will be important as well as in determining the magnitude

of the deposition flux or aerosol depletion (Sec. VII). Thus, aerosol interaction dynamics are an essential aspect of material transport. 9 This is especially true for conditions of high aerosol concentration (106 particles/cm3 or

greater). In nuclear fuel cycle facilities, high aerosol concentrations could

result from the accidents under study (particularly fires). For explosions',

high concentrations are more likely to occur in the near-field, that is,. close

to the actual explosion.

The general dynamic equation' (GDE) is a nonlinear, partial i'ntegrodifferential equation that models the-time rate of change of the size distribution of an aerosol. 9 ' 4 8 The GDE: can be formulated for continuous or discrete

size distribution functions.49 The continuous GDE may be written for aspatially and chemically homogeneous system consisting of a single aerosol species

Ain the absence of convection. 9 ' 48

•n~v~t) .;) . .j v/2 .• .

an-(v -t) - I(vt)n(v,t) + f (v-u,u)n(v-u.,t)n(u,t)du

vd S0n , (31) n nvt) o,(v, u)n(u,.t)du + S [n(v, t),v

28,
where n(v,t) is the size distribution density function so that n(v,t)dv is the

number of particles per unit volume of fluid with volumes in the range v to

v + dv. In Eq. (31), I(v,t) = dv/dt, the rate of change of the volume of a particle of volume v by transfer of material between the particle and the fluid

phase, s(v,u) is the coagulation coefficient for particles of volumes v and u,

and S is the net rate of addition (or removal if S < 0) of particles into the

system. Equation (31) states that during a process, mass is conserved throughout the aerosol population size distribution.

The first term on the right-hand side of Eq. (31) represents the rate of

growth or shrinkage of particles by gas-to-particle conversion (including gasphase chemical reactions and condensation). The second term represents the

coagulation gain of particles in the size range (v,v + dv) by collision of two

particles of volumes v - u and u to form a particle of volume v. The third term

represents the coagulation loss of particles in the size range v + dv by collision with all other particles. Finally, the last term represents all particle

sources and sinks.

B. Future Plans

The current versions of TORAC, EXPAC, and FIRAC do not allow material

interaction, but future versions should provide this capability using existing

physical models' for the terms in Eq. (31). However, although solutions -to

Eq. (31) are difficult to obtain, analytical solutions to a few simple forms of

the initial condition [I(v,t), s(v,u), and S] are available. Some analytical

solutions are reported in Refs. 9 and 48, including cases of coagulation alone

and simultaneous coagulation plus removal, coagulation plus growth, and turbulent diffusion and growth. Although the analytical solutions to Eq. (31) may

not correspond directly to realistic physical condition's, they may be useful as

first approximations and also serve to check the accuracy of numerical

solutions.50,51

There is a major step from single-species models to multispecies models.

References 52 and 53 present the analytical and numerical developments currently

being used in the multicomponent aerosol computational technique MAEROS, which

was developed by F. Gelbard. These techniques are being assessed for possible

use in this program. Research in the area of aerosol dynamics currently is very

active.

29
VII. AEROSQL.DEPLETION

A.- Background

Because the flow Reynolds number based on the enclosure or duct hydraulic

diameter and fluid bulk velocity will be greater than about :2100 for all cases

of interest here, the flow always will be turbulent. We will assume that all

flows are developed fully so that boundary layer or duct velocity profile shapes

are constant with distance. This will be true sufficiently far from inlets (20

to,50 hydraulic diameters) so that entrance effects are unimportant in our

cal cul ations.

Under these conditions, not all of the material that is made airborne at

the location of material transport initiation, will survive convective transport

to the filtration systems or facility boundary. Depending on the aerosol aero-

.dynamic characteristics and passage geometry, there may be a sizable reduction

in aerosol concentration. As such, an enclosure or duct acts as an aerosol

filter.

B. Existing Capability

Once. the user has chosen to exercise material transport, he can calculate

aerosol losses caused by gravitational sedimentation in rooms, cells,. and horizontal .rectangular ducts in this version of our codes. *This module can. be

turned on for rooms and horizontal ducts and turned off for vertical ducts by

.adjusting input flags. Aerosol depletion may be calculated throughout the network during transient flow. The theory is based on quasi-steady-state settling

with the terminal settling velocity, corrected by the •Cunningham slip factor..

The flow in ducts, and rooms is assumed to be well-mixed so that the aerosol concentration is uniform within the volume. More detail and references may be

found below. The user must supply only the aerosol, diameter and density to this

model, and the aerosol may Consist of solid particles or liquid droplets.....

Future versions of the material transport module will account for combined

molecular and turbulent diffusion as well as aerosol interactions, but the current version is restricted to gravitational sedimentation. The particle flux.J

....-resulting from gravitational sedimentation is9

J usn. , (32).

30
where the units of J are particles per unit area per unit time, us is the terminal settling velocity or transfer coefficient for sedimentation, and n is the

local aerosol number concentration in particles per unit volume for the homogeneous aerosol.' If we multiply both sides of Eq. (32) by the homogeneous particulate mass mp, then

J u sp , (33)

where the units of J are mass per unit area per unit time and p= nmp is the

aerosol mass concentration per unit volume. The terminal settling velocity is

calculated from9

2 8

u= p D gC/I18 , (34)

s p p

where p p = aerosol density,

D = aerosol diameter,

p

g = gravitational acceleration,

C = Cunningham slip correction factor, and

= fluid dynamic viscosity.

The code input variables for material depletion are p p and D . These variables

may be assumed by the user. We recommend that the user select aerodynamic diameter with unit density or Stokes diameter with the material bulk density.' This

selection was discussed in Sec. VII.A above. To calculate the slip correction.

factor, the code uses 9

C = 1 + (2L/Dp)(A + A2 exp(- A3 Dp/L)) (35)

31
where L is the molecular mean free path and the A's are dimensionless constants

based on experimental measurements of small particle drag.. The code uses

L = 0.065 um,

A1 = 1.257,

A2 = 0.400,

A3 = 0.550,

2

g = 981 cm/s2, and

p = 0.0001781 g/cm-s,

where L, p, and g are taken at standard sea-level conditions.

We know p' from the material transport mass balance calculation for the

previous time step for each node (volume or duct). Then, knowing us and the

projected floor area for sedimentation A, we can compute the sink term using

Eq. (33),3

• |.

M =-J'A=-UpA , (36)

which has the units kilograms per second. Becausel aerosol depletion is a sink

term, we-have used a minus sign in Eq. (36).. This equation represents a negative contribution to the M term on the right-hand side of. Eq. (29). Aerosol

p

depletion by sedimentation may be selected for all volumes and ducts and is calculated in the same manner.

C. Future Improvements

Aerosols moving through passages that are horizontal (or not exactly vertical) can be deposited because of gravitational settling. However, a number

of other processes that can cause aerosol depletion and contribute to:a material

transport sink term should be considered. 9 1 1 ' 1 4 Particles that come sufficiently close to surfaces can be intercepted mechanically and stuck. Particles

with enough inertia can deviate from the flow streamlines, impact, and stick to

rough elements, obstacles, or bends. Particles less than about 1 pm in size can

be transported to surfaces by both turbulent (eddy) and molecular (Brownian)

32
diffusion. Particles greater than about 1 pm in size-and being transported parallel to surfaces can be deposited because of the fluctuating velocity components normal to the surface (turbulent inertial deposition). Lower flow velocities enhance deposition-caused by molecular diffusion and sedimentation. Unless

the surfaces are sticky, the net rate of deposition will depend on the relative

rates of transport and reentrainment. Except for fibrous particles or very

light particles, interception may be neglected because particles large enough to

be intercepted will most likely be deposited as a result of inertial effects or

sedimentation.

Under certain conditions, other effects may become important for the

smallest particles. These effects include thermophoresis, diffusiophoresis, and

electrical migration. The latter three effects are discussed in Refs. 9 and 14.

They are believed to be relatively unimportant here compared with other effects.

Friedlander's book 9 provides an excellent introduction to deposition by convective diffusion . and inertial deposition. Here the concept of aparticle

transfer coefficient k is introduced such that

J =k no , (37)

where J is the particle deposition flux (particles per square centimeter-second)

at a given location in a tube and n0 is the local average particle number concentration (particles per cubic centimeter) in the mainstream at that cross

section. Thusý, the transfer coefficient k has units of centimeters per second

and may be considered an effective deposition velocity. 'Experimental measurements of k for liquid droplets and solid particles were obtained for turbulent

flow in vertical tubes at Reynolds numbers up to 50 000. Several theories for predicting k for turbulent deposition are based on the "diffusion freeflight" model. Particles are assumed to be transported by turbulent diffusion

to within one "stopping distance" from the wall, at which point the particles

make a "free flight" to the wall. The stopping distance is

S2-

s T pp DpV/18 , (38)

p p

33
where T is the particle relaxation time and v is the assumed free-flight

velocity.

Beal 56 has developed a method of analysis for predicting k for turbulent

flow in vertical tubes. Beal's method combines the approaches taken in Refs. 54

and 57 and applies them to particles ranging from molecule size to about 100 pm.

This theory accounts for the deposition mechanisms of Brownian and turbulent

diffusion and turbulent inertial deposition but not gravitational settling.

Beal's approach is to integrate the particle flux equation

J= (D 0)dn (39)

across the concentration boundary layer. Here D is the particle coefficient of

molecular diffusion, and c is the particle eddy diffusivity (both with units of

square centimeters per second). In the derivative, y represents distance in

centimeters perpendicular to the surface. In the paper Bea1 5 6 states his assumptions for v and £ in specific regions of the turbulent boundary layer and

derives equations for k.

The authors of Ref. 58 have developed a method for predicting k for

turbulent flow in horizontal tubes. This method applies to particles with a

size greater than about 1 pm because it accounts for the deposition mechanisms

of turbulent diffusion and gravitational settling but does not account for

Brownian diffusion. Reference 58 also considers the. effect of pipe wall roughness and provides experimental verification for particles with sizes from about

1 to 4 um.

The equations for k presented in Refs. 56 and 58 were incorporated into a

computer code called DUCT 8 that estimates aerosol depletion under steady flow

condition's in a given duct segment. We propose to include these equations as an

improvement to the aerosol depletion modules in TORAC, EXPAC, and FIRAC.

Experimental data are needed to check'aerosol depletion calculations for

losses encountered in larger scale facilities, particularly for fire conditions.

Such data are being sought in the current fuel cycle safety program. Another

area needing improvement is accounting for the effects of other ventilation system components (besides filters) such -as blowers, dampers, bends, and flow

restrictions on aerosol removal.

34
VIII. "FILTRATION

A. Background

A phenomenological approach to filter loading is used. The filter: gasdynamic performance can be changed by the accumulation of airborne material on

the filter, which in turn causes an increase in resistance. A linear model is

used in which the increase in resistance is linearly proportional to the amount

of material on the filter. The proportionality constant is a function of both

material and filter properties. The user supplies the filter efficiency and

plugging factor; however, the information for the latter is not readily available in the literature.

Experimental evidence 5 9 indicates that the pressure drop acrossý filters

commonly used for air cleaning in the chemical and nuclear industries increases

nonlinearly at high-speed flow. This contrasts with the linear relationship

that we generally observe in a relatively low-speed flow region for normal or

near-normal applications. 6 We can take an entirely experimental approach to

determine all of the influence coefficients on filter and flow properties, or we

can model the filter flow bas2d on the principle of flow through porous media

and determine the relationship between the flow rate and the pressure drop with

most (if not all) pertinent parameters explicitly included. Even so, some

empirical constants still are needed.; for practical purposes, we can combine

some filter properties into these constants and- determine them by experimental

means. The number of coefficients with proper filter modeling is much less than

that obtained through direct empirical methods. We will review some theoretical

works and present a model that is suitable for our system.

The purpose of air filters in a ventilation system is to remove airborne

material in the air stream and to prevent hazardous, material from being released

to.the environment. Experience shows that the accumulation .of material, usually

in the condensed phase, will cause the pressure drop across a filter to increase

for the same flow rate. In the case of a fire or an explosion, rapid flow

resistance increases as the result of large amounts of material caught by. a

filter. This is commonly called filter plugging or clogging. After reviewing

analytical work on the development of filter models, we will review filter

plugging phenomena briefly and eventually propose a semi-empirical formulation

to describe this condition.

35
B. Filter Model

60 The pioneering work of D'Arcy6 established the foundation of the principle

of fluid flow through porous media. His experimental results indicated a linear

relationship between the flow rate and the pressure drop that is proportional to

an empirical constant, permeability. This parallels quite well HagenPoiseille's conclusion of fully developed laminar flow through a pipe. 4 2 It is

not surprising to find that many theoretical models of flow through porous media

are based on D'Arcy's concept but with different qualifications. The most successful one among them is the Kozeny model. 6 1 According to his theory, the

porous medium is represented by an assemblage of channels of various crosssections and a definite length. The flow through the channels is determined by

the Navier-Stokes equations, and the permeability is expressed in terms of viscosity and the properties of the porous medium. However, an empirical constant

is needed to include the effect of the tortuous characteristic of the medium. A

modification of the Kozeny model by Carman 6 2 defined the constant, which is

called tortuosity, in a more explicit way. This new model still requires an

empirical coefficient to account for the uncertainty of determining various

porous medium properties.

Another point of view on the pressure-drop relationship of flow through a

porous medium is based on drag theory with the dragging obstacles being particles or fibers. A model using fibers as a porous medium leads to a permeability

that is weakly dependent on flow rate. 63 Because of the actual complexity of

the medium, some empirical adjustment is needed for this model.

So far we have discussed D'Arcy's law and its derivatives, which are adequate only when the flow velocity is low; that is, at conditions where the pressure drop is proportional to the viscous dissipation by the porous medium. For

channel flow with flow velocity increasing, the dissipation mechanism changes

from a viscous to a turbulent effect, and the pressure drop then is proportional

to the kinetic energy of the stream.42 Following the reasoning of Kozeny in

modeling porous media as channels, we can establish a quadratic relation between

the pressure drop and flow rate at high velocity. 6 4 Again, an empirical coefficient equivalent to the resistance factor in pipe flow under turbulent conditions is introduced. 'The summation of viscous effects and turbulent dissipation

leads to an equation proposed by Ergun. 65

36
2

Ap : (1-C) 2 hUm +.1.75 (Ž-) PUm (40)

ed d

p p

with

Ap = pressure drop,

= bed length,

g = gravitational constant,

c = void fraction,

= viscosity,

dp = effective porous medium particle size,

p = fluid density, and

ur = superficial velocity.

Superficial velocity is the flow velocity approaching the packed bed and not the

average flow velocity in the interstitial region. Equation (40) is written in

centimeter-gram-second units but also can be expressed in a different form,

ap =KL Q + K p2 (41)

A31 2A

where Q and A represent volume flow rate and the frontal area of the packed

column. It can be easily identified that

u Q (42) m A

Ku 150 AA'12 (42)

L3 2 (343)

p

37
and

KT = 3.5 ( 9p (44)

KL and KT are dimensionless and are dependent on-the properties of the porous

medium. Equation (41) is identical to the Reynolds' expression on pipe flow in

laminar and turbulent regions. 6 6

As we mentioned earlier, the theoretical model that we ultimately choose

will use some empirical coefficients and must be included to account for the

complexity and uncertainty of the porous medium. It does not matter if we

obtain KL and KT first from Eqs. (43) and (44) and then add experimental corrections later. We can determine the effective KL and KT directly from experiment.

This task is not more difficult than finding the correction factors alone

because. there are only two unknowns involved as presented in Eq. (41). From now

on we will use Eq. (41)*as the foundation of our filter model regardless of the

filtration medium we use as long as we can determine the two coefficients

through experimental or analytical means.

A subroutine using Eq. (41) to represent a filter branch has been added to

the TORAC code because we expect very high flow rates in the system if a

tornado-induced depressurization occurs. The turbulence coefficient KT must be

read in through the input file; if it is zero, then only the laminar-dependent

portion will be used. The laminar coefficient KL can be input or calculated for

a given pressure drop and flow rate; the former approach is preferred. This

subroutine has been checked out successfully. However, reliable data on KT have

not been obtained, and more extensive experimental work is needed in that area.

C. Filter Plugging

The physical phenomena involving the capture of an aerosol under flow con67,68 ditions by a filtration medium are complicated. The porous material provides various locations for material retention--bed grain surfaces, crevices,

constrictions, or pore cavities. The normal pressure of the fluid, friction,

interparticle forces, and the chemical bonding force give the required means of

.holding the material at a given location. The mechanisms for the suspended material reaching a retention site include gravity, inertia, hydrodynamic forces,

38
interception, and Brownian motion. Attempts to relate the overall filter efficiency with the aforementioned mechanisms without any experimental coefficient

is not practical.' A more useful approach is phenomenological; that is, we assume some form of dependence of filter efficiency on the total amount of aerosol

retained. We note that experimentation indicates a small increase in the efficiency for increasing retention. For normal operating conditions, we assume

that filter efficiency remains constant and does not significantly affect the

system flow conditions.

The same conclusion cannot be drawn about the flow resistance of the filter

when a large amount of material is retained on it. The increase in resistance

can be quite substantial and should be dealt with properly. The plugging is

related to material size, shape, phase, filter structure, and the quantity of

captured material. Using the Carman-Kozeny filter model,62 we can see that the

material retention reduces the specific surface, which is defined as the total

surface of the bed grain per unit filter volume and thus increases the effective

resistance. 5 3 We can express the general relation as follows.

AP = f(Ma .(45)

LP)o a

where (Ap) 0 is the pressure drop for a clean filter, shown in Eq. (41), and f is

a monotonically increasing function of material mass Ma on the filter. Clearly,

f(M =) = 1. For a light loading condition, f is a linear function of Ma:

f(M) =1 + aM , (46)

where a is a coefficient dependent on filter and material properties. 6 8 More

recent work of Bergman69 using the fibrous drag model of Davies70 concludes that

a depends on the fiber volume fraction, fiber size, and particulate size.

However, the foundation of Davies' model is still empirical. For the time

being, we will postulate the phenomenological relation of Eq. (46) with a being

determined by experiment. As future data warrant, we will modify the equation

and include more explicit relations.

39
D. .Future Improvements

We. have presented the nonlinear filter and filter plugging models used in

the TORAC computer code. The background physics, simplification, and mathematical formulation have been discussed and evaluated. We would not stop our effort

here, -and therefore, we are continuing to modify the codes and are adding various features to them as needed. We will complement our analytical effort with

extensive experimental investigations to determine the effects of material

type, moisture, and heat on a in Eq. (46) and on the form of the function f in

Eq. (45).

IX. SAMPLE PROBLEMS USING TORAC

TORAC is an acronym for the Tornado Analysis Code. The code. can predict

tornado-induced flows, pressures, and material transport within structures.

This computer code is primarily the TVENT computer code, 6 but it has been modified to include material transport, particularly the transport. of radioactive

material. This code is the first of a number of versions that will evolve into

more refined and improved codes, and it is one code in a family of computer

codes that is designed to provide improved methods of safety analysis for the

nuclear fuel cycle industry.

TORAC solves steady-state and transient pressures and gas and material flow

distributions in complex airflow pathways within structures. System pressures,

flows, and material transport in this version of the code are based on the

following assumptions.

* ,Isothermal flow

0 Lumped-parameter formulation

* Incompressible flow with compressibility at nodes

0 Gas dynamics decoupled from material transport

e No material interaction, phase change, or chemical reaction allowed

.. during transport

0 Homogeneous mixture and dynamic equilibrium

*1 Material deposition only by the mechanism of gravitational settling

* Material entrainment based on resuspension factor and other concepts

for rooms and semi-empirical entrainment rate equations and wind

tunnel data for ducts

A single file containing the input for all the sample problems.appears as a

subroutine at the end of the TORAC 3 source program. The user' may execute this

40
file "as is" to run the "Tornado at Exhaust" condition. Nine other sample probl-ems can be run from this same file by following the instructions given in comment statements at the end of the file. The hypothetical ventilation system

used in these problems is shown in Fig. 3. It consists of a supply and exhaust

blower, a large room, dampers, a filter plenum, a long duct, and an exhaust

stack. The corresponding computer model is shown schematically in Fig. 4. The

purpose of these sample problems is to demonstrate the capabilities of the various program features. The sample problems do not necessarily reflect realistic

situations.

This input file (Fig. 5), which is at the end of TORAC, is written to a

file called INPUT if the TORAC program is executed without -the existence of a

file called INPUT. The test for this file.'is made automatically if the filesearch utility is available. If this is not the case, the user must change the

source program for the initial run only to write the input file rather than

reading from one in your local file space.

The sample problems appearing in this combined input file are (1) Tornado

at Exhaust, (2) Tornado at Intake, (3) Supply Blower Turned Off and On,

(4) Supply Blower Speed Reduced, (5) Control Damper Closing and Blower Speed

Reduced, (6) Material Transport (No Filter Plugging), (7) Material Transport

(Filter Plugging), (8) Entrainment, and (9) Deposition. Here we will provide

examples pertaining to material transport only.

The sample problems presented here demonstrate the following program

features using the system shown in Figs. 3 and 4.

* Material transport

* 1Filter plugging

* Entrainment

: Deposition

A tornado is simulated by specifying a pressure-time function at one or both

boundary nodes. This will be illustrated in the sample problems below. Up to

20 points can be used to define the assumed fluctuations in pressure that simulate the passing of a tornado. A blower is turned off by replacing the blower

with a damper having a known resistance characteristic. Blower characteristics

are changed during a run by substituting another blower curve at the time the

change occurs. A damper is closed or opened according to a given resistance

coefficient time function for that branch. These features can be made to occur

at different intervals during a run to depict a sequence of events. Material

41
BLOWER

DUCT VOLUME FILTER

DAMPER

DAMPER

Fig. 3.

TORAC sample problem ventilation system schematic.

DAMPER BLOWER DAMPER ROOM

DUCT DUCT

VOLUME VOLUME FILTER

(7) (8) (9)

DAMPER BLOWER STACK

Fig. 4.

Computer model of TORAC sample problem ventilation system.

42
i *

2 EXAMPLE PROBLEM!

3.

4 * RUN CONTROL 1

5 ST 0.0 .01

6 * PRINT/PLOT COt

7 3 1

8 * FRAME DESCRIP1

9 4 2 3

10 4 6 7

11 2 10 1

12 4 2 4

13 3 2 6

14 * RUN CONTROL 2

15 500

16 * BOUNDARY CONT;

17 1 2

18 * GEOMETRY AND

19 9 10

20 * BRANCH DATA

21 1 1 2

22 2 2 3

23 3 3 4

24 4 4 5

25 5 5 6

26 6 6 7

27 7 7 8

28 8 8 9

29 9 9 10

30 * BOUNDARY DATA

31 1

32 10

33 * CONTROL DAMPE;

34 1

35 0 1 4.(

36 * BLOWER CURVE

37 1

38 0 3 50.

39 * TORNADO PRESSL

40 1 5

41 0.0 0.0

42 16. -25.

43 * PARTICULATE FL

44 1 6 0.35

45 0.0 0.0

46 14. 0.1

47 * CONTROL DAMPE

48 1 4

49 0.0

50 150.

51 * BLOWER TURNED

52 1

53 0 50.

54 * ROOM DATA

55 4 10.

56 5 2.

57 6 2.

58 * FILTER MODEL

59 1 1

60 .8

61 0.0

62 a BLOWER CURVES

63 1 6

64 -100. 2.7

S (E.G. TORNADO AT EXHAUST)

030.

NTROL

rion~s

4 5 B 9

6 B 8

P

ROL

OMPONENT CONTROL

3 3

1000.

1000.

1000.

1000.

1000.

1000.

1000.

1000.

1000.

0 0 0

PLOT

I

I

OPTION NO. 2

2

2

2

2

2

2

2

1

V

B .

V

V

V

F

V

B

V

0

2

0

1

INSTRUCTIONS

)OOE-07 9

HANGE INSTRUCTIONS

2

iRE FUNCTION

10.

18.

JNCTION

10.

15.

Z FUNCTION

4.OOOE-07 I

I.000E-06

OFF/ON INSTI

1.000E-09 1I

0.0

0.0

0.0

0.0

12. -25.

12. 0.1

60. 00

so. 4.OOOE-07 100.

RUCTIONS

so.

1.000E -06

2

10. 0

2.

2.

)ATA

10.

50.

50.

0.0 1.9 800. 1.8

Fig. 5.

Built-in TORAC input file.

43
65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

8B

89

90

91

92

93

94

95

96

97

98

99

100

I01

102

103

1000. 1.6 1300.

2 6

-200. 1.4 0.0

1000. 0.7 1400. 3 6

-100. 2.3 0.0

940. 1.3 1100.

* PRESSURES

0.0 -0.5

0.8 -0.2

" DEPOSITION COEFICIENTS

0 0 0 0 0.0

0 0 0 1 0.0

0 0 0 1 0.0

END OF INPUT FILE. ANYTHING

WHEN THIS FILE IS READ.

0.8

1.0

0.4

1.6

0.8

1400.

700.

1600.

770.

1200.

0.0

0.9

0.0

1.5

0.0

+1.1

-0.3

0.0

0.02

0.02

WRITTEN BEYOND THIS

1.0

0.4

0.9

0.0

POINT WILL BE IGNORED

REPLACE LINES 6 THRU 13 WITH ONE OF THE FOLLOWING OPTIONS

*,PRINT/PLOT CONTROL

. 2 1 1

* FRAME DESCRIPTIONS

4 2 3 4

4 6 7 8

4 2 4 6

3 2 6 8

* PRINT/PLOT CONTROL

3 1 1

* FRAME DESCRIPTIONS

4 2 3 4

4 6 7 8

2 10 t

4 2 4 6

3 2 6 8

* PRINT/PLOT CONTROLt

PLOT OPTION

5

9

8

U

m

m

M

m

m

5

9

8

PLOT OPTION

OPTION

NO.

NO.

PLOT NO.

1

104 *

105

106

107

108

109

110 TI

111 C

112

113 R

114 -

115

116

117

1t8

119

120

121

122

123

124

125

126

127

128

F;

HE

HAP

LUN

RAME

1

3

4

4

DESCRIPTIONS

6

3 4 5

4 5 6

4 5 6

7

7

m

m

FOLLOWING RUNS CAN

JGES INDICATED

BE MADE FROM THE ABOVE INPUT FILE BY.-MAKING THE

CHANGES TO "COMBINED INPUT FILE"

TORNADO AT EXHAUST (PLOT OPTION NO. 2) "AS IS"

TORNADO AT INTAKE (PLOT OPTION NO. 2)

LINE 32 - I TO 0 (CC 20)

LINE 31 - 0 TO i (CC 20)

SUPPLY BLOWER TURNED OFF AND ON (PLOT OPTION NO. 1)

LINE 5 - 030. TO 200.

LINE 32 - I TO 0 (CC 20)

LINE 53 - 0 TO 2 (CC 5)

SUPPLY BLOWER SPEED REDUCED (PLOT OPTION NO. 1)

Fig. 5.

Built-in TORAC input file (cont).

44
129 LINE.5 - 030. TO 200.

130 lINE. 32** I TO 0 .(CC 20)

131 LINE 38..- 0 TO 2 (CC 5)

132

133 CONTROL DAMPER CLOSING. (BRANCH 9) (PLOT OPTION NO. 1)

134 LINE5 - 030. TO 200..

135 L!NE.'32 I TO 0 (CC 20)

136 - LINE 35 - 0 TO 9 (CC 5)

137

138 BLOWER SPEED REDUCED & DAMPER CLOSING (PLOT OPTION NO. 1)

139 LINE 5 - 030. TO 200.

140 LINE 32 1 TO 0 (CC 20)

141 LINEý35 -0 TO 9 (CC 5)

142 LINE 38*- 0 TO 2 (CC 5)

143

144 MATERIAL: TRANSPORT (PLOT OPTION NO. 3)

145 LINE 5 - 030. TO 200.

146 LINE.5 - 0 O TO 1 0 0

147 LINE 32 I TO 0 (CC 20)

148 LINE 26 - O TO I (CC 75)

149 LINE 55 - 0 TO I (CC 40)

.150

151 FILTER PLUGGING (PLOT OPTION NO. 3)

152 LINE 5 - 030. TO 200.

153 LINE 5 - 0 O TO 1 0 0

154 LINE 26 - 0 TO I .(CC 75)

155 LINE 32 - I TO 0 (CC 20)

156 ... LINE 55 - 0 TO I (CC 40)

157 LINE 61 - 0.0 TO 30.

158

Fig. 5.

Built-in TORAC input file (cont).

can be injected into any room or can be aerodynamically entrained and transported to the boundaries by the flow.. Aerosol depletion by sedimentation will

be calculated for ducts and rooms where specified. Filter plugging will occur

if the filter model used is assigned a plugging coefficient.

Problem No. 1 - Tornado at Exhaust

A pressure-time function dropping to a -25 in. w..g. (about 1 psi or

6200 Pa) is placed at the exhaust boundary, node No. 10 (Figs. 6--0).

Problem No. 2 - Tornado at-Intake

The same pressure-time function used in Problem No. 1 is reassigned to the

system intake boundary, node No. 1 (Figs. 11-15).

Problem 3 - Material Transport (No Filter Plugging)

Problem 3 involves the transport of material injected into the room at

node 4 and carried downstream by the normal operating flow of 1000 cfm. Most

of this material is trapped on the filter (Figs. 16-19).

45
X101

0.0

LEGEND

-0.2 -:=NODE 10

[= NODE 1

-0.4

-0.6

-0.8

-1.0

3'-1.2

• -1.4

-.8

-2.0

-2.2

-2.4

-2.6 L

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time (s)

Fig. 6.

Tornado at exhaust.

46
-2•0 -

-4.0 -

. -o 0

-10.0

-12.0

-14.0

-16.0 5.0 I0.0 15.0 20.0 25.0

Time (s)

Fig. 7.

Tornado at exhaust.

30.0

47
X10- 1

20D

LEGEND

0.0V= NODE 6 L Ii0 = NODE 7

+ = NODE 8

-0= NODE 9

-40.01

60.0

80.0

: -100.0 - 'I

d. -140.0

-160.0

-180.0

-200.0 -

-2o20.0

-240.0 I

0.0 5.0 10.0 15LO 20.0 25.0 30.1

Time(s)

Fig. 8.

Tornado at exhaust.

48
X10 3

4.0

352BRANCH

0 BRANCH 4

4n BRANCH 6

13 BRANCH81

3.0

2.5 1 5. I

2.0 -

1.5 10•- / - I'.1,

0.5 ~1

.0. '

-0.5

0.0~ 5.0 10.0 15.0. 20.0, 25.0 30.0

Time (s)

Fig. 9.

Tornado at exhaust.

49
x101

1.1

1O0=BRANCH 2

I+=BRANCH68

0.9-

0.8

0.7

.- 0.6

0.5

0.. 0.2

- 0.4

0.0

..... -I" ..... + .. + : .. • , "'+....... . ......- I.. ..

9e- IP 0.1 ,- 9 7

.- 0.2 I I I ' I I

0.0 5.0-. 10.0 15.0 20.0 25.0 30.0

Time (s)

Fig. 10.

Tornado at exhaust.

50
X10O

0.0

-0.2

-0.4

-0.6

-0.8

-- -1.0 I,

. -1.2

to-1.4

0,.

a_ -1.6

-1.8

-2.0

-2.2

-2.4

-2.6

I-. I

I

j

I

I.

I.

I

I.

*1

I.

I

I

I.I

I

I

i

I

I.,

I.

I

I V V. I V I

F7 D

LEGEN

0.0 5.0 10.0 15.0

Time (s)

Fig. 11.

Tornado at intake.

20.0 25.0 30.0

51
-2.0 [ 16 ODE

-4.0 -

-6.0

. -8.0

3i

"- -10.0

In -12.0

-14.0

-16.0 -

-18.0 -

-20.0 -

-22.0

-24.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time(s)

Fig. 12.

Tornado at intake.

52
3e

axi0- 1

10.0

0.0

-10.0

-20.0

-30.0

,-40.0

-50.0

-60.0

-70.0

-80.0

0.0 5.0 10.0 15.0 20.0 25.0

Time (s)

Fig. 13.

Tornado at intake.

300

53
x1o 3

1.5

~. 0.0 iI

E

"5 -0.5 -

1.0oI'

-0.5

-2.0 I I I

0.0 5.0 10.0 15.0 20.0 25.0" 30.0

Time (s)

Fig. 14.

Tornado at intake.

54
2.01

0.0

-2.0 I

-- 4.0

- -6.0

Q)

LiL

a0~

0 1 .

S-10.0

"4• 4- "

0._

-12.0

-14.0

-16.0

la.o I • .. .

0.0 5.0 10.0 15.0

Time (s)

Fig. 15.

Tornado at intake.

200 25.0 30.0

55
1.0 --

. LEGEND i

BRANCH 6±

0.8

- 0.7

0.6

0.-

a,•

'0.5

0.-

0.4

0.23.

0.2

0.1- •

0.0 I I I I I II I I

0.0 20.0 '40.0.' 60.0 80.0 100.0 ý120.0 1400 160.0 '18QO -200.0

Time (s)

Fig. 16.

Material transport (no,filter plugging).

56
*1

.4

-4

XI0-2

1.4 i

1'.2

1.0

0.9

ES0.8 -

2 0.7

0.6 - = ii

0.5 -

0.4 i

0.3

0.2-

0.1

0.0

0.0., 20.0

V=NODE 3

-0 =NODE 4I

+ 10NDE'5ý

10

AV

40.0 60.0 80.0 100.0' 120.0 140.0 160.0 180.0 200.0

Time (s)

Fig. 17.

Mater i al transport (no filter plugging).

57
X10-3

6.5 I

6.0 IV=BRANCH 4

0 • ~BRANCH o= BRANCH 53

I+= BRANCH

5.5 -- ' . o= BRANCH

5.0

4.5-

4.0 I .

p3.5

4-_ 3.0 -'"•. •o_•_ I..'*

2.5

2.0

1.5 ~

1.0 I'

0.5 . 0.0, L-,.. -- .

0.0 20.0 40.0 60.0 800 100.0 120.0 140.0 160.0 180.0 200.0

: Time (s)

Fig. 18.

Material transport (no filter plugging).

58
x10-1

4.0 i .i

3.5 += BR

3.0

S2.5

-CI-t

Mf

0 2.0

iT

U)1.5

:,0.

/ .+""

1,4

0.0 1 /

0. . 0.0: 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Time (s)

Fig. 19.

Material transport-(no filter plugging).

'59
Problem 4 - Material Transport (Filter Plugging)

Problem 4 also involves the transport of material injected into the room

at node 4 and carried downstream by the normal operating flow of 1000 cfm. This

is the same condition as in problem No. 6, but the filter has been assigned a

plugging factor of 30 (Figs. 20--23.)

Problem 5 - Calculated Aerodynamic Entrainment

This sample problem illustrates the use of the calculated aerodynamic'

entrainment option for material transport initiation in a duct. The user

requirements and theory for this option are discussed above. For convenience,

we used the same system shown in^Figs. 3 and 4. The 100-ft-long duct connecting

the room at node 4 to the filter in branch 6 was modeled using two segments.

Each segment contained a resistance lumped in a branch and a volume lumped at a

node. Duct entrainment should be specified at the latter nodes. For more accurate results, more segments should be used. In this version of TORAC, entrainment of beds of material in rooms or cells is treated in the same way as illustrated here. The following conditions were assumed and set up in the master

input file of TORAC. (See Fig. 5.)

1. Tornado of strength 50 in. w.g. simulated at exhaust node 10.

2. No material injection (transport initiation) in room 4 or elsewhere

using the user-specified option.

3. A total of 1 kg of contaminant material is subjected to entrainment in

the duct volume represented by node 5.

4. The contaminant material is assumed to consist of homogeneous,

monodisperse, spherical particles with aerodynamic diameter Dp = 100 -m

(10-4m) and bulk density p = 3 g/cm3 (3000 kg/m 3 ).

5. The contaminant material i.s distributed uniformly over the 27 by 50-ft

floor area of duct volume 5.

6. No deposition occurs in duct branches 4 or 5. (The volumes of these

branches were modeled by nodes 5 and 6, respectively.)

7. The filter efficiency was set at 0.8.

Our choice of material and surface loading for this example was somewhat arbitrary. Specific values are presented for illustrative purposes only. Based on

data for mixed-oxide fuel (PuO 2 powder size),1'16 a more realistic choice may be

mass median aerodynamic diameter equals 20 pm and density equals 10 g/cm3 . The

60
2.8, .1 ...

2.6 L=

2.4

2.2

2.0-

3i 1.8

w 1.6

P? 1.4

0-,

S1.0

1 ....

0.8

0.6

0.4

,0.2

0.0 I I I I

0.0 20.0 40.0, 60.0 80.0 1000, 120.0 140.0 160.1

Time (s)

Fig. 20.

Material transport (filter plugging).

61
'I

X10- 2

S1.4

1.3

Ii 1.2

1.0-

0- .9. -i

E i

,0.8 - i

.0.7 i

0.6-

OA i

S0.35-."

0.1

0.6

0.3 2i0"

0.2- ;

I"

0.1 - !

0.0 ' " - 0.0 20.0

.. \

\

SI I I

LEGENDI

0o= NODE 3

o0= NODE 4 + = NODE 5

1+6

I 'I ,.1 1 A A .4 -1 .:4

40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

Time (s)

Fig. 21.

Material transport (filter plugging).

20QO

62
X10- 3

6.5 I I I I I - I

6.0 V= B I

I O=B

I+:eD

, BI 5.5

5.0

4.5

- 4.0

C,)"B3.5

n- 3.0

" 2.5

2.0

1.5 *.

1.0 .:

~I i

0.5 - !" "• " -.-- . _

0.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0 1400 160

Time (s)

Fig. 22.

Material transport (filter plugging).

1.0, 180.0 200.0

63
XI0-1

LE

V=BR

O= BR

4- BR, 3.0 BR,

low

2.5

~/"

C-- ,,,8

20.

2 / .. "

,,.I / •-

1.5 /

o //

U) /

S1.0 -

•0.5 -4-1 / o . .... ' • ,.. 0 "

0.0

0.0 20.0 40.0 60.0 80.0 100.0 12Q0 140.0 160.C

Time (s)

Fig. 23.

Material transport (filter plugging).

64

180.0 200.0
3 theoretical density of PuO2 is about 11.5 g/cm The values used here may be .

representative of a more agglomerated material. The material loading of 27 g/m 2

(based on four surfaces) for duct volume 5 is about four times the loading of

7 g/m 2 for a very dusty surface. The latter material loading value is discussed

in.Ref. 1.

The tornado-induced nodal pressure-time histories for this example are sim..-

ilar in shape to those shown in Figs. 6-*8 except that they show more negative

peaks in gauge pressure because the tornado is more severe in the current

example. Thepeak negative gauge pressure for node 10 is -50 in. w.g. compared

with -25 in. w.g., which was shown in Fig. 6. On these figures, the symbols

T(50) and D(100) refer to the tornado strength of 50 in. w.g. and the particulate diameter of 100 um, respectively.

The results of sample Problem 5 are shown in Figs. 24--27. The volume flow

rates in four selected branches are, shown in Fig. 24. These flows were induced

by a tornado depressurization from 0 to -50 in. w.g. pressure between times

10 and 12 s, constant at -50 in. w.g. pressure from times 12 s to 16 s, and

back up to.0 in. w.g. pressure at time 18 s. A flow reversal occurs' in branches

4, 5, and 8 at about 18 s. The material concentration time histories for four

selected nodes are shown in Fig. 25. Aerodynamic entrainment of powder with

0p = 100 um and Pp =. 3 g/cm from thick beds may be expected for surface fricp

tion velocities exceeding a threshold value of about u.t= 21.7 cm/s. This corresponds to an air velocity of •about U = 374 cm/s (12.3 ft/s) and an airflow

rate of about Q =.3000 ft 3 /min through a duct with a cross section of 4 ft 2 . In

Fig. 24 for -branch .4, Q = 3000 -ft 3 /min is induced by the tornado,-.at about

t = 12 s.. At about this time, the aerosol concentration at node 5 jumps as a

3 spike to over 0.16.kg/mi (Fig. 25). If 1 kg of material were injected instantly

33

into the 200 ft3 volume of the duct segment represented .by node 5., we would expect an instantaneous spike in concentration to 0.18 kg/m3. The airborne mate-,

rial is convected into node 6 and partially collected on the 80% filter in.

..branch 6. The particulate flow rate is shown in Fig. 26. Figure 27 gives the

cumulative particulate mass on a filter or through each branch. The curves in

Fig. 27 represent the integral of their counterparts in Fig. ?6. At t = 30 s in

this example, Fig. 27 shows that about 0.92 kg of material was removed from

node 5 with about 0.15 kg surviving the filter. The net reduction in concen--

.tration ahead of the filter observed here is caused by -dilution and time delay

only as deposition was turned off. That is, before material can flow through

65
X1O-3

5.0 + D0= =BRANCH BRANCH 5

81

4.0

E

02.0

-1.0

LI

-2.0 1 1 1 1

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time (s)

Fig. 24.

Entrainment: T(50), D(100).

66
-10-I

L8

-1.6

1.4

1.2

ei¢

E

1.0

C 0.8

U

0.6

0.4

S0..2

,0.0

I I i i

I

ii.

I'

I'.

I'

I ~*

I'

I.'

I-

~NODE 4

+I= NODEI 6 0I= NODEI

I

I:

I:

I:

I U 17

0.0 5.0 10.0 15.0

Time (s)

20.0 25.0 30.0

Fig. 25.

Entrainment: T(50), D(100).

67
x10- 1

4.0

3.5 -

3.01-

N,

w

ar

,L0

0

2.5F

2.0[

*Ij

I.

I.

ii.

I'

I'.

I '.

i '.

i '.

i '

I ~

if

V

jf ~ j51

V= BRANCH 4

0 =BRANCH 5

1+ =BRANCH 6]

1.5 -

1.0 -

0.5[

0.0

-0.5

-9 qr la I- w

V7.

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time (s)

Fig. 26.

Entrainment: T(50), D(100).

68
x10.0 10.0 I ,I .1 .1

• LEGEND

9.0 - V= BRANCH 4

0= BRANCH 51

+ =BRANCH6

•:BRANCH 7

8.0

Je 7.0 /

6.0

5.0

"i" 4.0

I_ o -. -.

,0 . . ,• .

3.0-

20

10)

, .ig'. 27 ..

1.0 Et.On D(100:

-1.0_ 0 .0 5.0 10.0 15.0 20.0O 25.0 30.0 •":

Time (s)•

S Fig. :27. ,

. ; ,, ~Entrainment: T(50), D(IO0). •

• .... .. " • 6 9
branch 6 (filter), the concentration in node 6 (duct volume) must be built up by

material flow in branch 5 following entrainment in node 5. Deposition by sedimentation was turned off in this example for simplicity and clarity but could

have been turned on simultaneously with entrainment. Problem 6 shows that this

3 100-um, 3-g/cm material would have been substantially removed from suspension

if the deposition module had been turned on.

Problem 6 - Aerosol Depletion

This problem illustrates TORAC's capability to account for aerosol depletion by gravitational sedimentation. The user 'requirements and theory for this

subroutine are discussed above. As before, our model is shown schematically in

Figs. 3 and 4. In this version of TORAC, aerosol depletion is handled in the

same way for ducts and rooms. The following conditions were assumed and set up

in the TORAC master input (Fig. 5).

1. Tornado of strength 50 in. w.g. simulated at exhaust node 10.

2. From times t = 10 s to t = 16 s, a total of 0.4 kg of aerosol is

injected into the 1000-ft 3 -volume room represented by node 4.

3. No material is subject to entrainment anywhere.

4. The contaminant material is assumed to be composed of homogeneous,

monodisperse, spherical particles with aerodynamic diameter D = 10 Jrm

(O15m) and bulk density p = 3 g/cm3 (3000 kg/m 2 ). P

5. As the contaminant material is injected, it instantly forms a

homogeneous mixture with the air in room 4.

6. Deposition by sedimentation occurs, in the duct lengths represented by

volumes at nodes 5:and 6 only (and was not turned on for room 4).

7. The filter efficiency was set at 0.8.

In this example we illustrate the alternate user-input option for material

transport initiation as opposed to the other option, calculated aerodynamic

entrainment, which was illustrated in Problem 5. Material is injected at node 4

to simulate accident conditions there. Deposition occurs in the two downstream

duct segments. The choice of material characteristics for this example is

strictly hypothetical and, different from that discussed for Problem 5. (See

example Problem 5 above.) The same tornado pressure function described in

Problem 5 was used here. However, the material generation function goes from

0 kg/s at time t = 10 s to 0.1 kg/s at t = 12 s, stays constant until t = 14 s,

and returns to 0 kg/s at t = 16 s. (See Fig. 5.)

70
The results of sample Problem 6 are shown in Fig. 24 and Figs. 28--32.

That is, the tornado-induced airflow time histories are identical to those discussed for Problem 5. The material concentration histories for four selected

nodes are shown in Fig. 28. The aerosol concentration in room 4 begins to rise

immediately at t = 10 s because that is when material injection begins. As the

1000-ft 3 room 4 receives aerosol, the concentration goes up and peaks at

t = 16 s. Meanwhile, there is a delay while the particulate-laden air drawn out

of room 4 flows into duct volume 5. The dip in the concentration profiles at

about t = 17.5 s was caused by the flow reversal. Figure 29 also shows this

momentary flow reversal in particulate flow rate. The material accumulations

on the filter (branch 7) and passing through branches 4-6 are shown in Fig. 30.

Although 0.4 kg of aerosol is injected into room 4 during 10 < t < 16 s, the

accumulated aerosol mass flow passing through branch 4 at t = 30 s is only about

0.143 kg. This is because fresh air from branch 3 is diluting the mixture in

room 4 continually. By t = 120 s, the accumulation of mass through branch 4 is

about 0.34 kg, and the concentration in node 4 is down to about 0.0012 kg/m3

(not shown in Fig. 30). The effect of deposition can be observed by comparing

Fig.. 30 with Figs. 31 and 32. Figure 31 was run for the same conditions as

Figs. 28-30 except that deposition in branches 4 and 5 was shut off. The

reduction in accumulation of 10-pm material in branches 5--7 in Fig. 30 from

Fig. 31 is relatively small. However, material losses resulting from sedimentation in these branches are more pronounced in Fig. 32. The results shown in

Fig. 32 were obtained for the same conditions as for Figs. 28-30 except that

the material size was input as 100 lim instead of 10 im. Figure 32 should be

compared with Figs. 30 and 31.

X. SUMMARY

To insure that nuclear facilities can withstand postulated accidents,

.regulatory agencies have the responsibility of reviewing proposed facility

designs. The degree of conservatism and the related risk assessment also must

be evaluated for these accident conditions. The nature of the hazardous

material involved and the potential for accidents require designers and

analysts to have methods and supportive experimental data for a systematic

approach to estimating accident effects.

Assessment of the environmental consequences of an accident ultimately

involves calculating atmospheric dispersion and radioactive dosage estimates

71
1.2

I.1

1.0

0.9

0.8

E

- 0.7

o 0.6. .2

w 0.5 U

C

0.4

0.3

0.2

0.1

0.0

10.0 15.0 20.0

Time (s)

Fig. 28.

Deposition: T(50), D(10).

30.0.

72
X -10-2 II. . ....

2.2 LEGEND

2 =BRANCH4

o = BRANCH 51 + =BRANCH

2.0 BRANCH

1.8

1.6

1.4

"" 1.2 -

X 1.0

2_0.8

0. •" 0.6- /'. .:'.J /...--

0.

0 . -4 ..... +. ... . ..... Ir

0.01 -,

-0.24

-0.4 I I I J

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time (s)

Fig. 29.

Deposition: T(50), D(10).

73
X10-6 .1.6

1.2

M 1.0

0.8- ,

0

0.6

~*.1.0

o 

/

. 0.4

C) 

.

0.2 04

0.0 "-- . -'- -- I ~ I

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time (s)

Fig. 30.

Deposition: T(50), D(10).

74
x io1.6

1.4

- 1.2

0

E- 1.0

0.

b-

•' 0.8

a)

iz

C

0

0 0.6

a) 0.4

0.2

0.0

0.0 5.0 10.0 15.0 20.0 25.0

Time (s)

30.0

Injection:

Fig. 31.

no deposition, T(50).

75
XT0- 1

1.6

LEGEND

V= BRANCH 4

0 = BRANCH 5

O 1 = 

= BRANCH 6 BRANCH 7

1.2

0

-. 8

,•1.o

i0

,0.8

0.,t°

C

0

(I0

0.6

D(

O._4

0.2

0.0 = = _.I ..-... ,_""• •,,:._ _.'"•• .:''

0.0 5.0 10.0 15.0 20.0 25.0 30.0

rime (s)

Fig. 32.

Deposition: T(50), D(1O0).

76
for the surrounding. popul ati on. Some uncertainty'. lies in the, estimate of the

nuclear facility source term to be used -for atmospheric dispersion. In current

safety analyses, some .conservative assumptions are applied to assess worst

cases. Such assumptions are made to assure that the consequences are not underestimated. The, current program is intended to improve on our abilityAto more

accurately estimate nuclear facility-source terms., Thus, we have undertaken a

fuel cycle facility safety. analysis program. to provide user-oriented tools for

making better estimates of accident-induced release or source-term characteristics at a nuclear facility's atmospheric boundaries. 1' 2 These tools are intended to be an improvement over current safety analysis review techniques. The

scope of the program is.limited to only accident-induced material movement within a nuclear facility.

This report..is a summary of .material transport modeling procedures developed to support a f amily: of accideit analysis :computer codes. The calculation

procedures include, transport initiation, convection, interaction, depletion, and

filtration. Except for material interaction, these procedures'-are bei.ng used in

modular form in TORAC, EXPAC, and FIRAC. This family of codes was developed to

provide improved methods of tornado, explosion, and fire accident consequence

assessment capability, respectively, for the nuclear industry. The codes were

designed to estimate accident-induced gas-dynamic, thermal, and material transport transient phenomena in nuclear fuel cycle facility ventilation systems.

However, they are applicable to other facilities as well. Results from sample

problems using TORAC have been provided to illustrate current material transport

capabilities in a simple .system under tornado-induced accident conditions. Some

suggestions for future improvements to some of these material transport models

als6o were discussed.,

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82
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