1

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

INDIGENOUS RESEARCH AND DEVELOPMENT FORREACTOR SAFETY ASSESSMENT UNDER EXTREME

EVENTS AND STRATEGIC APPLICATIONS

Ram Kumar SinghReactor Safety Division

Dr. Ram Kumar Singh is the recipient of the DAE Homi Bhabha Science &

Technology Award for the year 2011

IntroductionIntroductionIntroductionIntroductionIntroduction

The relevant areas of nuclear reactor design and

development, reactor safety assessment and strategic

applications have been enabled through a systematic

indigenous research and development program over

the years. With focus on computational and

experimental structural mechanics, wave propagation

in solid and fluid media, fluid-structure interaction,

computational fluid dynamics and heat transfer various

thrust areas for the closed nuclear fuel cycle have been

addressed. Specific case studies of coupled fluid-

structure interaction analysis for TAPS-BWR core shroud

in case of the recirculation break and PWR HDR-v32

blowdown, shock / seismic wave propagation in solid

media for underground nuclear explosion events,

assessment of Indian nuclear power plants for extreme

events of tsunami and earthquakes and PHWR / AHWR

containment structural and thermal hydraulic safety

evaluation are presented in this article.

All the above identified problems involve multi-physics

coupling and multi-scale modeling and have been

addressed due to the rapid growth and development

in computer hardware and massive parallel high-

performance computers. The novel concepts of

computational mechanics and associated algorithms

in computational mathematics have enabled to explore

multi-physics problems that were earlier not

conceivable. A few examples under this category are

tracing the evolution of discontinuities in

heterogeneous materials, which may evolve at solid-

fluid and solid-solid boundaries, problems of phase

change and crack propagation and erosion in solid

structures due to hyper velocity impact. This

development has been further supplemented with

improvements in the experimental techniques with

measurement and verification of relevant parameters

at different length scales. A few examples in this

category are optical crack profiling, digital image

correlation and the acoustic emission techniques in

addition to the conventional sensors and

instrumentation. For large scale problems related to

weather forecasting, tsunami, earthquakes and

environmental modeling; the satellite imaging, Airborne

Lidar Terrain Mapper (ALTM) and GPS systems have

helped to improve the modeling capabilities, which has

provided the requisite support for tsunami warning

system.

Fluid-Structure Interaction Studies for ReactorFluid-Structure Interaction Studies for ReactorFluid-Structure Interaction Studies for ReactorFluid-Structure Interaction Studies for ReactorFluid-Structure Interaction Studies for Reactor

Components and WComponents and WComponents and WComponents and WComponents and Wave Propagation in Tave Propagation in Tave Propagation in Tave Propagation in Tave Propagation in Two Phasewo Phasewo Phasewo Phasewo Phase

MediaMediaMediaMediaMedia

The fluid-structure interaction problems are important

for various reactor safety issues with regard to PWR

core-barrel, BWR core shroud and PHWR core internal

safety evaluation resulting from internal postulated

blowdown events. Potential safety concerns were raised

by regulatory bodies regarding the 360 degrees

circumferential separation of TAPS-BWR core shroud

following LOCA. The material degradation accelerated

by crevices, residual stress, cold work, sensitisation, and

corrosive environment could be detrimental for

impulsive acoustic load due to pipe break. This might

either prevent full insertion of the control rods or open

2

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

a gap in the shroud large enough to preclude adequate

core cooling. Validation of in-house 3D finite element

code FLFLFLFLFLUSHELUSHELUSHELUSHELUSHEL for coupled fluid-structure interaction

transient analysis of light water reactor components in

case of sub-cooled and saturated blowdown accidents

has been carried out. Simulation of German HDR (Heiss-

Dampf Reaktor) v.32 LOCA experiment on a full scale

PWR model for single and two phase blowdown

problems were carried out with the implementation of

unified sub cooled and saturated critical flow models.

With the due considerations to the non-equilibrium

effects due to flashing for the rarefaction wave

propagation, acoustic load evaluation and structural

safety assessment of TAPS-BWR core shroud for

postulated Recirculation Line Break (RLB) were carried

out. This in-house code has also been used for the

evaluation of PHWR internal core components for the

postulated calandria tube / pressure tube failure

accidents.

For the acoustic wave propagation problems, the code

FLUSHEL accounts for the spatial and temporal variation

of acoustic speed in the dispersive two-phase media of

the light water coolant generated due to the postulated

blowdown. The in-house code has been coupled with

standard water steam property code WASP to compute

the acoustic speed in the two phase fluid domain during

the passage of rarefaction wave. The critical discharge

and pressure are computed by the unified Leung model

for both sub-cooled and saturated blowdowns. It has

been shown that for the case of stratified flow in a

vertical channel, the liquid gas plug behaves as gas

from compressibility point of view, and its mass is close

to that of the liquid, which could lead to excitation of

coupled fluid acoustic and core internal shell modes.

Normally the associated frequencies of acoustic cavity

and the submerged shell frequencies of interest are far

below compared to the resonance frequency due to

the oscillation occurring in the bubble which are in

kHz range. Thus only the total gas content per unit

volume of the fluid medium is important and not the

distribution of this gas content over bubbles of specific

size. So a typical density wave oscillation equation of

the form:

2

22 2

2

2

2 2

2 0

tC

C

tB

( ) (1)

can be simplified to acoustic wave equation of small

amplitude. This assumption is valid for the region within

the reactor vessel and the downcomer annulus where

bubbles of very small sizes compared to the

characteristic dimension of the reactor vessel and core

shroud may be present. The bubble oscillation

frequency is B

o

f o

p

R

32 (2)

In case of a one-dimensional vapour liquid plug the

oscillation frequency of the cavity is:

Oo

f

p

l

2 1 (3)

Where po is the stagnation pressure, pf is liquid density,

Ro is the bubble size, is ratio of specific heats for

vapour, is the void fraction of liquid vapour system

and l is the characteristic dimension of the acoustic

cavity. Normally Ro is of micron size for small vapour

nucleation sites. Thus l >>Ro and the pressure

oscillation frequency within the bubble is very large

(B>>o). The stratified sound speed is given as

 

C

C C

st

f g

g

f

f

g

1

12 2

(4)

With the above classical expression for the sound speed

in the two-phase medium, the acoustic wave

propagation can be described. If the interaction of

individual bubbles with the fluid and mutually through

the fluid has to be considered, the medium becomes

dispersive. The propagation of acoustic wave becomes

frequency dependant. However with vapour density

being very small compared to the liquid density

(pg<<pf), the sound speed in the two-phase medium

approaches the sound speed in vapour medium

(CstCg). This is based on the assumption of no inter-

phase mass or momentum transfer at the gas bubble

liquid interface. Thus within the reactor vessel and core

shroud downcomer annulus region, homogeneous

medium assumption is made after the passage of elastic

wave of amplitude (po-pso) at sonic speed in liquid

medium which is typically 1000m/s. Subsequently

after the passage of this elastic wave, the second wave

3

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

travels at a speed, which is two to three times less than

the elastic wave speed due to high compressibility of

the medium. Sudden density changes in case of

cavitations and resultant formation of bubbles calls for

non-linear analysis and has been implemented using a

bilinear fluid model with tension cut-off, which depends

on the saturation pressure.

The estimation of the critical flow for blow down due to

LOCA was carried out with systematic review of Burnell’s

model, Moody’s homogeneous equilibrium model and

Leung’s generalised equilibrium model. The adequacy of

Leung’s generalised model was established for the

prediction of sub-cooled and two-phase blow down

induced critical discharge for HDR-PWR and TAPS-BWR

problems respectively. It has been demonstrated that the

acoustic Helmholtz modes of the downcomer annulus

and the core shroud shell multi-lobe modes of TAPS-BWR

are well separated (Fig. 1). The transient dynamic response

of the core shroud shows that the acoustic load induced

stresses are within service level D limits of Section III NB of

ASME Boiler and Pressure vessel Code.

WWWWWave Propagation in Geogological Mediaave Propagation in Geogological Mediaave Propagation in Geogological Mediaave Propagation in Geogological Mediaave Propagation in Geogological Media

The indigenous development of in-house finite element

code SHOCKSHOCKSHOCKSHOCKSHOCK-3D-3D-3D-3D-3D, with strong capabilities for the three-

dimensional simulation of shock wave propagation and

coupled fluid-structure interaction analysis of

underground explosion induced gas cavity growth and

the resulting spall, fracture and crater simulation has

helped to strengthen Indian strategic programs. This

code has been used to simulate the near field

hydrodynamic and anelastic / inelastic features around

underground sources using equation of states in

different regimes. The study has been useful for wave

propagation and seismic signal analysis in rock/soil

media for near and far field regions. The work on US

Baneberry-1970 nuclear test 3D simulation could

successful explain the reported venting due to explosion

induced fault movement in the complex geological

strata. This 3D code development and subsequent

analysis gave requisite confidence for the Indian nuclear

test programme. These studies have been useful to

explain the effect of local geological formations on the

observations made during the tests and

have been cited for resolving critical

national security issues.

Constitutive Models in Code SHOCKConstitutive Models in Code SHOCKConstitutive Models in Code SHOCKConstitutive Models in Code SHOCKConstitutive Models in Code SHOCK-3D-3D-3D-3D-3D

The fluid-structure interaction code SHOCKSHOCKSHOCKSHOCKSHOCK-----

3D3D3D3D3D with explicit transient formulation is

finite element based, where in the two field

problem of the rock media and explosion

induced gas cavity are coupled to analyze

the underground explosion problems. For

the explosion induced gas cavity non-

viscous hydrodynamic formulation based

fluid elements with limited overburden

pressure are used to correlate the pressure

(p) with volumetric strain (v) and specific

energy (E).

The constitutive model for the geological

medium due to Hoek and Brown (Int. J.

Rock Mech. Min. Sci, 34, 1998) for the

different rock strata accounts for the

confinement effect on the rock strength.

TAPS BWR Core Shroud Shell Modes

Acoustic Wave propagationin TAPS-BWR downcomerdue to Recirculation Break PWR-HDR V32 LOCA Benchmark –

Comparison of FLUSHEL Code withExperimental Data

Fig. 1: Coupled Two Phase Fluid-Structure Interaction for TAPS-BWRCore Shroud and HDR-v.32 Core Barrel for Blowdown Problems

4

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

Damage mechanics based failure models are used

depending on the strain levels for quasi-brittle and

ductile failures. The Hugoniot equation of state at high

shock pressures and hydrostatic data for different rock

media has been used in the present code. The loading

and unloading bulk modulii in the different regimes

such as the mean pressures corresponding to the

maximum tensile and compressive stresses of the rock

medium at zero confinement describing the Hugoniot

elastic limits, hydrostatic pressure range and high

pressure shock range are evaluated for different rock

media. The equation of state for the rock media is

represented as

Kvv)E (5)

Where p is the hydrodynamic pressure, the local bulk

modulus K(v), is obtained from Hugoniot equation of

state depending on the loading or unloading condition,

v is the volumetric strain, E is the specific energy and is the Gruneisen parameter which allows dissipation of

energy and is a function of volumetric strain.

The strain rate dependent model of the code SHOCK-

3D has been formulated with the modified form of

classical elasto-viscoplastic constitutive theory, which

accounts for strain-rate sensitivity with allowance for

progressive degradation of strength. In view of the

limitations of the classical elasto-plastic and elasto-

viscoplastic models to deal with rate and history

dependent problems for transient shock and dynamic

loadings, the visco-plastic strain rate is defined as a

function of elastic strain /stress rate. In addition the

damage due to the viscoplastic flow is monitored with

the help of a variable strength limit surface. The yield

surface defines the onset of viscoplastic flow and the

strength limit surface defines the initiation of material

degradation and these are represented with the help

of first and second stress invariants of deviatoric

stresses. A constant failure strain based criteria is used

in this model irrespective of the strain rate. Thus the

present viscoplastic constitutive model of the code

SHOCK-3D retains all the important features of rate

dependent inelastic behavior along with the equation

of state which characterize the rock behavior in the

different regimes of shock loading,

The overburden simulation is important for the accurate

simulation of transient problem of underground

explosion event since the rising mound is finally settled

due to fall back induced by gravity forces. This feature

is accounted with the simulation of the initial stress

field due to the overburden. Sommerfeld radiation

condition is used to simulate a non-reflecting boundary

to avoid any spurious reflection from the model

boundary with normal and tangential directions as n

and t respectively as follows.

n = cb vn (6)

t = cs vt (7)

Here n and t are normal and tangential stresses, vn

and vt are the normal and tangential components of

the particle velocity at the mesh boundary, ñ is the

medium density and cb and cs are the body wave and

shear wave velocities for the medium. These conditions

are applied sufficiently away from the source where

plane elastic wave conditions exist, in which case the

wave speeds are constant.

VVVVVenting Concept and Baneberryenting Concept and Baneberryenting Concept and Baneberryenting Concept and Baneberryenting Concept and Baneberry-1970 Event-1970 Event-1970 Event-1970 Event-1970 Event

Phenomenology SimulationPhenomenology SimulationPhenomenology SimulationPhenomenology SimulationPhenomenology Simulation

The US Baneberry-1970 event with a shot depth of 278

m, yield of 10 kT vented due to the establishment of a

fracture path owing to the presence of pre-existing

Baneberry fault and unfavorable combination of local

geological strata near the source. The classic example

with all the complex geological features has been

successfully simulated by three-dimensional finite

element code SHOCK-3D in the present work. All the

undesirable features namely the closeness of the fault

with the emplacement point, proximity of the hard

Paleozoic layer underneath the source near the fault

region on the west end and clay rich tuff layer on the

east end (Fig. 2) of the source formed the worst

combination leading to venting which is not expected

at such large scaled depth of burst ~129.3m/kT1/3.

Here, the shock-induced slip along the pre-existing

fault plane has an important bearing on the

containment efficiency of this event. None of the earlier

reported 2D simulations (UCRL-52365-1977 &

5

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

Nuc. Tech. 46, Nov.1979) addressed the slip

phenomenon and the influence of variation in

geological strata in presence of the pre-existing

fault in a three dimensional framework. The Indian

simulation work despite the uncertainty of detail data

on the local geology demonstrated with precise

modeling of the composite geological strata and

fault system that a dip slip mechanism developed

for Baneberry event leading to final venting. This

was the first 3D simulation of Baneberry event (Fig. 3)

and it created a renewed interest amomg the

international community in such development. The vent

location prediction of 97 m south-west of source in

the simulation compared well with 90 m as noticed at

test site. Further the subsidence crater of 200 m dia

and 25-26 m depth also compared well with

the observed crater of 128 m dia and 24 m depth for

this event.

BANEBERRY-1970 EVENT

Fig. 2: Three-Dimensional Model with Layered rock Media, Fault, Source Location for 10kT Baneberry-1970 Event

Fig. 3: Maximum Principal Stress ( N/m2 ) at 0.1 sec and Resulting Vent Path for 10kTBaneberry Event

6

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

TTTTTsunami Wsunami Wsunami Wsunami Wsunami Wave Propagation and Run-up Evaluation forave Propagation and Run-up Evaluation forave Propagation and Run-up Evaluation forave Propagation and Run-up Evaluation forave Propagation and Run-up Evaluation for

Indian Coastal Nuclear PIndian Coastal Nuclear PIndian Coastal Nuclear PIndian Coastal Nuclear PIndian Coastal Nuclear Power Plantsower Plantsower Plantsower Plantsower Plants

The simulation of tsunami events with the indigenous

finite element code Tsunami Solution (TSUSOL)

developed immediately after the Sumatra-2004 tsunami

event has been used extensively for the study of

Sumatra-2004 and Makran-1945 events and other

subsequent events of tsunami wave generation, its

propagation and near shore wave run-up evaluation.

The predictions of the code for the tsunami wave arrival

time and the wave run up heights were noted to be in

good agreement with the post tsunami survey

observations reported for the different coastal regions

of the Indian Ocean for Dec 26 Sumatra earthquake

event.

TTTTTsunami In-house Code TSUSOLsunami In-house Code TSUSOLsunami In-house Code TSUSOLsunami In-house Code TSUSOLsunami In-house Code TSUSOL

In-house finite element code TSUSOL is a compressible

wave propagation code with due consideration to free

surface shallow water theory and acoustic wave

propagation below the free surface. The continuity and

momentum equations with velocity components vi are

expressed as

/t + (vi) = 0 (8)

Dvi / Dt = ij,j - gi (9)

For the tsunami wave propagation throughout the

whole 2D surface the normal surface tractions gradient

with surface normal n is defined as

p/n = -1/g 2p/t2 (10)

The Sommerfeld radiation boundary condition at the

non-reflecting boundary is

p/n = -1/c p/t (11)

For computation of fluid continuum coupling to the

seabed is obtained from

p/n = - vn/t, (12)

vn is the normal velocity at the seabed due to the

earthquake/subduction motion

The in-house studies have been effectively utilized for

design and implementation of early warning system

for coastal region of the country in addition to the site

evaluation of Indian nuclear coastal installations. The

in-house finite element code TSUSOL predictions of

wave arrival time, reflections from coastal regions and

run up were later confirmed by Jason satellite data.

(Fig. 4) The time signal analysis of the wave time history

(Fig. 5) from in-house finite element code TSUSOL

confirmed the reflections from Sri Lanka and various

other Indian islands. The reflected wave periods from

Sri Lanka computed as 4096 sec, 2560 sec and 1280

sec compare well with the spectral periods of 4380

sec, 2580 sec and 1320 sec respectively from the de-

tided data of National Institute of Oceanography (NIO)

tide gauge records for 2004 tsunami event.

Fig. 4: JASON-1 Track 109 Satellite (altitude 1300 km) Record and TSUSOL Predictions for 2004 Java SumatraTsunami Event

7

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

For Kalpakkam, Tarapur and Vizag sites tsunami

evaluation, coordination with national agencies was

carried to obtain bathymetric and land morphology

data and source term evaluation was made for accurate

inundation and wave run-up modeling. Tsunami effects

for these specific nuclear power plant sites in terms of

wave height, run-up and the resulting inundation were

studied and confirmed with on-site observations of

Kalpakkam (Fig. 6) and Vizag sites in a National Round

Robin Analysis coordinated for site evaluation. The

tsunami height data has been generated for the present

and future prospective nuclear coastal facilities, which

is extremely useful for the site evaluation

and for evolving necessary up-gradation

measures.

Indian PHWR Nuclear Containment SafetyIndian PHWR Nuclear Containment SafetyIndian PHWR Nuclear Containment SafetyIndian PHWR Nuclear Containment SafetyIndian PHWR Nuclear Containment Safety

AssessmentAssessmentAssessmentAssessmentAssessment

The beyond design basis accidents of Three

Mile Island (1979) and Chernobyl (1986)

created interest among the nuclear

community for the safety assessment

studies related to the ultimate load

capacity of the nuclear containment

structures in addition to the release of

radioactivity to the environment due to

over-pressurization. The progression of the

severe accident recently at Fukushima

(2011) multiple nuclear plants has further

emphasized the need for the containment

integrity evaluation. For the containment structural

safety evaluation, BARC Containment (BARCOM) the

1:4 size Test Model of 540 MWe PHWR pre-stressed

concrete inner containment (Fig. 7) has been

constructed and commissioned at Tarapur. The Control

& Instrumentation building equipped with modern data

logging systems along with 1200 embedded and

surface type sensors, process parameter sensors and

camera systems have been integrated with BARCOM

for the mega size experiment. An International Round

Robin Analysis with eighteen participants during the

pre-test and post-test phases has been coordinated to

Fig. 6: Kalpakkam Site Tsunami Run up Measurement at Standard Locations and Inter-code Comparison

Fig. 5: Spectral Analysis of Tsunami Waves from TSUSOL Predictionsfor Sumatra-2004 Event and Comparison with NIO Tide Gauge Data

8

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

study the various failure modes of the model and the

evaluation of the ultimate load capacity have been

completed in different phases of the experiments to

benchmark the inelastic computer codes, constitutive

models and fracture mechanics models for the design

have been evaluated to address the related modelling

issues for inelastic code benchmarking for local and

global failure modes, which have been backed up with

extensive data collected during the Phase-III

experiments.

Fig. 7: BARCOM Test Model and Longitudinal & Shear Cracks around MAL & Embedded Sensor Response duringOver-Pressure Tests on July 23-24, 2011 (1.78 Pd) & Oct 02 2011 (1.68 Pd) and Numerical Simulation Results

Fig. 8: First Appearance of Crack in BARCOM Test Model during Over-Pressure Test Phase-III Experiment andverification with Soap Bubble Test & Optical Crack Profiling to identify Fracture Process Zone

basis and severe accident scenarios. This research

project with academic orientation is very relevant in

the present day context for country’s nuclear power

programme in the aftermath of Chernobyl-1986 and

recent Fukushima-2011 severe accident events.

BARCOM experimental program has achieved the

desired objectives to obtain the functional failure mode

through a systematic test program and has given the

requisite confidence for the Indian PHWR containment

integrity as demonstrated in this project. The results

from the various international round robin participantsFig. 9: Leakage Observed in BARCOM Over-Pressure Test

9

BARC NEWSLETTER

Founder’s Day Special Issue October 2013

endevours will be directed and focused towards

development of robust codes and its validation

through various standard problem and round robin

exercises for concurrent problems of multi-physics

nature, which will be addressed through in-house

experimental programs with improved instrumentation

techniques.

I sincerely acknowledge with thanks the significant

contributions made by a large number of colleagues

in Reactor Safety Division, collaborators from BARC,

AERB and NPCIL and other academic institutes

along with the participants of international / national

round robin exercises who have not only supported

these in-house efforts with their scientific and

technical inputs but also have been along with us to

evolve these technologies through a collective thinking

process.

The experiment demonstrated that even after functional

failure of primary containment, the leakage rates

through with tight cracks (Fig. 8) due to residual pre-

stresses are within controllable and manageable limits

and shielding cover is retained. Double containment

and related Engineered Safety Features further assist

in controlling the ground leakage and releases to the

environment. Margin against over-pressurization of

BARCOM has addressed important issues with regard

to containment safety and the resulting leakages due

to over-pressure (Fig. 9) under extreme events.

ConclusionsConclusionsConclusionsConclusionsConclusions

The indigeneous efforts to address multi-displinary

coupled problems relevant for various thrust areas of

reactor safety and strategic applications enabled

through in-house code development and experimental

programs have been presented in this article. Our future