Double Diffusive Natural Convection in a Nuclear Waste Repository
Yue Hao, John
J.
Nitao, Thomas A. Buscheck, and Yunwei Sun
L631, Lawrence Livermore National Laboratory, Livermore,
CA
94551
Abstract

In this study, we conduct a twodimensional numerical analysis of double diffusive natural convection in an
er?lplacement drift for a nuclear waste repository. Indrift heat and moisture transport is driven by combined thermal and
conlpositionalinduced buoyancy forces. Numerical results demonstrate buoyancydriven convective flow patterns and
configurations during both repository heatup and cooldown phases. It is also shown that bounda ry conditions, particularly
on the dripshield
surfnce, have strong impacts on the indrift convective flow and transport.
I. INTRODUCTION Stokes equations. The governing equations are expressed
in the following mass, momentum, energy, and vapor
It is recognized that natural convection plays an
concentration conservation forms:
important role in
many heat and mass transfer vrocesses.
In
ionisothermal appfications with binary fluid mixtures,
the interaction of natural heat convection
with.mass
transport of two components results in a complex flow
and transport phenomenon called double
diffusive
convection. Double diffusive convection, resulting from
buoyancy forces caused by temperature and
compositional gradients, is found in many naturalsystem
and engineering applications. For this reason it has
attracted considerable attention
[l, 21. One potential
example is related to the transport of heat and moisture
inside emplacement drifts in a nuclearwaste repository in
the unsaturated zone. After the emplacement of waste
packages, the radioactive heat of decay generates water
vapor due. to the evaporation of water in the adjoining
host rock, which migrates into the drift. Within the drift,
natural convection contributes to transport of water vapor
from hotter to cooler locations, where it may condense.
Continuity:
Momentum:
where
t,
p,
u,
p,
and
g
represent time, binary mixture
density, velocity, pressure, and body force, and
z
is the
viscous stress tensor,
in which
p
is fluid viscosity and the superscript
T
denotes
the transpose.
Energy:
In addition to affecting heat and mass transport, the
complicated flow patterns and structures induced by
(4)
combined thermaland compositional buoyancy effects
will influence evaporation and condensation on
engineered material surfaces within the drift. Because of
the potential for influencing the corrosion of drip shields
and waste packages, moisture condensation within drifts
is of concern for total system performance assessment of
the repository. Moreover, analyses of indrift heat and
moisture convection can
ljrovide a better understanding of
the basic physics of flow and transport phenomena inside
engineered tunnels. Recent CFD models that apply the
FLUENT code have been used to describe indrift flows,
with a focus on thermalinduced natural convection and
determining effective dispersion coefficients for models
predicting moisture transport and condensation
[3,4].
The .goal of this work is to investigate double
diffusive convection inside an emplacement drift, using a
NavierStokes model approach to examine and capture
the predominant convection modes.
with
T,
C,,,
k,
and
Q
as temperature, specific heat, thermal
conductivity, and heat generation term.
Vapor concentration (expressed as mass fraction) in a
I
vaporair mixture:
C, D,
and
R
are vapor mass fraction, binary diffusion
coefficient, and vapor source term, respectively.
For this study, the total pressure of the
airlvapor
mixture
p,
is assumed spatially uniform, and the binary
mixture obeys the ideal gas law. Based on these
conditions, the fluid density can be expressed as
,
.
11.
MATHEMATICAL FORMULATION
with
T
as temperature,
R
as universal gas constant,
My
as
In this study, natural heat and mass convection in an
molecular mass of water vapor and
MA
as molecular mass
.air/vapor binary system is considered, using Navier
of air.
If both temperature and vaporconcentration
variations are small, then the Boussinesq approximation is
applied with the fluid density simplified as
in which subscript
oo
denotes the reference state, and
BT
and
/Ic
are the thermal and concentration expansion
coefficients, respectively,
For thermal natural convection, we use the dimensionless
Rayleigh number
Ra,
=
TL3
and Prandtl number
For mass transfer, we use the corresponding Rayleigh
number
Ra,
=
g&AcL3
VD
and Schmidt number
Here AT, AC,
u,
a,
and L are temperature difference,
vaporconcentration difference, fluid kinematics viscosity,
thermal diffusivity, and length scale, respectively.
In order to compare the magnitudes of thermal and
compositionalinduced natural convections, the so called
"buoyancy ratio" is introduced by
[5],
The dominant driving buoyant force is determined by the
buoyancy ratio N. It is obvious that as N decreases,
thermal buoyancy effects will become dominant over
compositional effects. The
kw
turbulent model [6] is
used to account for turbulent flow effects for large
Rayleighnumber problems. The above governing
equations are solved by the NavierStokes module
implemented in the NUFT code
[7], which has been
validated against benchmark
problemS.
Ill.
RESULTS
AND
DISCUSSION
This study addresses both heat and vapor transport
within an emplacement drift (Fig la). As depicted in Fig.
I
b, the drip shield and waste package are lumped together
as a monolithic heat source that is impermeable with
respect to mass transport. We model a twodimensional
indrift flow domain (Fig. la), which is bounded by the
outer dripshield surface, upper invert surface, and
drift
wall surface above the invert. Due to the symmetry of the
problem, only half of the drift needs to be represented in
the numerical model (Fig. lb).
For the problem shown in Fig. 1, indrift flow and
transport processes are highly dependent on
thermal
hydrological conditions in the adjoining porous host rock.
Hence the key aspect of modeling of indrift flow is the
specification of boundary conditions on the interfaces
between the fieelopenflow system in the drift and the
porousflow system in the host rock. Ideally one would
determine these conditions by directly coupling
freelopen
flow with porous flow. However, this is beyond the scope
of the current study. For the purpose of this study, we
assign appropriate boundary conditions on the surfaces of
the drift wall, invert, and drip shield on the basis of results
fiom the Multiscale Thermohydrologic Model (MSTHM)
[8,9, 101. The MSTHM, which is based on porous
medium Darcyflow approximations, predicts the coupled
thermalhydrological conditions at both driftscale and
mountainscale. Fig. 2 plots the time history of the
representative driftwall temperature and vapor
concentration obtained fiom the MSTHM
LDTH
submodel simulations.
During the initial 50year preclosure ventilation
0
period, the heat generated by waste packages is removed
by forced convective cooling. After drift ventilation
ceases, the postclosure period begins and the driftwall
temperature abruptly rises (Fig. 2a) to well above the
local boiling point of water
(96°C). The vapor
concentration at the driftwall surfaces also sharply
increases along with temperatures (Fig. 2b). The
dryout
phase lasts over 1000 years until the drift wall cools down
to
96OC (Fig. 2b).
For simplicity, the temperature
Tdw, Tbvert, and Tds are
uniformly imposed along the driftwall surface, upper
invert surface, and dripshield surface (Fig. lb). In
addition, the surfaces of the drift wall and invert are
assumed to be permeable with constant vapor
concentrations
Cdw and ChVe,. In order to explore all the
possible flow patterns and convection modes inside the
drift, we investigate two possible conditions on the outer
dripshield surface with respect to mass transfer.
The simulated transient behavior discussed in the
following sections is not intended to be exactly
representative of a real repository system. The primary
purpose of this study is to illustrate the influence of
boundary conditions on double diffusive natural
convection within emplacement drifts, with a focus on the
interactionbetween the thermal and compositional
buoyancy forces. These simulations neglect phase change
(evaporation and condensation) within the
dnft.
Moreover, the transient aspects of the simulated behavior
are presented to illustrate the interaction between the
thermal and compositional buoyancy forces.