The nuclear accidents like TMI, Chernobyl and Fukushima have imposed a
major challenge in front of a nuclear community to design advanced nuclear
reactors with enhanced safety and reliability. To ensure this, many advanced nuclear reactors adopt methodologies of passive
safety systems based on natural forces such as gravity. A typical design consists
of Isolation
Condensers (ICs) submerged in a Gravity
Driven Water Pool (GDWP). The IC consists of vertical tubes in which steam enters from
the steam drum. In a passive decay heat
removal system (PDHRS), the decay heat generated in
a reactor is transferred by natural circulation into a large water pool ( ̴
10000m³), namely the GDWP.
Considering the weak driving
forces in passive systems, which are based on natural circulation, careful
design of IC is necessary to facilitate the efficient decay heat removal. The objective of this study is to understand the two phase (vapor-liquid) flow and
the temperature fields generated by ICs in GDWP. Further, the effect of these
fields on the mixing, temperature stratification and the rate of heat transfer
have been investigated. An attempt has been made to design an efficient and
economical IC for the PDHRS which satisfies the design criterion of achieving
50% heat decay in less than 100s and the temperature stratification less than
0.2.

            The present work is in continuation of our earlier
work where the performance of small scales GDWPs (0.025 and 0.21m³) [Gandhi
et al. 2013a, 2013b] was investigated. Initially these GDWPs consist of a single
IC tube through which steam was passed. The heat transfer from the IC was concentrated
in a very limited zone of a water pool and resulted into non-uniform
temperature distribution which can be expressed in terms of extent of
stratification. The heat transfer rate can get compromised by such temperature
stratifications. Under these conditions, the fluid at the top of the pool
reaches the saturation temperature much earlier as compared to the time needed
for the case of homogeneous temperature distribution. The evaporation also
starts much earlier which may lead to over-pressurization of the reactor containment
building. In
order to reduce the thermal stratification, many modifications in the design of IC have been
proposed.

            The next step was to extend the knowledge gained from the
small scale investigation to the real size ( ̴ 10000m³) GDWP (ID
= 12m, OD = 50m and H_T = 5m). As a first attempt, the three
dimensional natural convection inside GDWP was examined by considering single heat source submerged
(s) at centre IC1 (HT area = 54.6m²). It has been
observed that, due to concentrated heat source (IC1) at centre, heat
transfer was also concentrated in a very small volume, which resulted into temperature
stratification which was quantified in terms of stratification number (S). The value of S varies from zero to one with zero
representing no stratification (complete mixing) and one representing complete stratification. The
value of S was found to be 0.87 for the IC1[Fig.2 case (1)] which
is far greater than the desired number of 0.2. In
order to reduce S, various modifications in the IC design have been incorporated, such
as (1) distributing the heat transfer area of IC among two and multiple ICs (2)
variation in the submergence of ICs (3) combined effect of distribution and
submergence (4) provision of passive elements such as draft tube around a heat
source (5) combination of multiple draft tubes and baffle at the top. The heat
source distribution into two ICs (IC2) of HT area 27.3m² each results in an enhancement in the
average circulation velocity by 35% and reduction in S by 12% as compared
to IC1 [Fig 2 case (2)]. The higher submergence (IC2s0.1) (0.1 m from bottom) of IC results in reduction in S by 17%
[Fig 2 case (3)]. In order to combine the benefits of (1) distribution and (2)
submergence of ICs, a new geometry (3) ICMs0.1 was considered which consists
of 36 ICs placed at a distance of 0.1m from bottom of the tank. The presence of
multiple ICs results into formation of multiple convective cells. The length of
natural circulation loop (and hence the mixing length) gets reduced because of the multiplicity
of convective cells. Thus the combination was found to result in 33%
reduction in S for ICMs0.1 [Fig.2 case
(4)]. In addition to these two parameters,
it was thought desirable to incorporate draft tubes and baffles. For this
purpose, two designs 'DF1' and 'BDF3' were considered (Fig 1). The DF1 design consists of a single
draft tube around the heat source whereas the BDF3 design consists of
three draft tubes along with a baffle at the top. Presence of draft tube (DF1)
gives directional motion from bottom to top (or top to bottom) and improves
mixing in the liquid phase and reduces S by 46%  [Fig.2 case (5)]. In addition, the combination
of three draft tubes and baffle (BDF3) prevents the accumulation of hot
fluid at the top by providing a flow path to it and results in 40% reduction in
stratfiication [Fig.2 case (6)]

Fig 1: Schematic diagram for single Draft tube (DF1)
and three draft tubes with baffle (BDF3)

Fig 2: Effect of various designs on
stratification number (S) with time

(1) IC1; (2) IC2;
(3) IC2s0.1; (4) ICMs0.1; (5) DF1; (6) BDF3;

The above recommendations for the design of IC showed a huge
potential. However, desired level of mitigation of thermal stratification was still
not possible. In order to design an efficient and economical IC, we have explored
further possibilities to improve its performance. In all the above cases, the IC
tubes were vertical. The phenomenon of thermal stratification was more
pronounced in the presence of vertical
heat source. As the hot fluid rises upwards along the length of IC, temperature
difference (∆T)
between the IC and the nearby fluid decreaseswhich further reults in a decrease in heat transfer. Therefore, it
was thought desirable to undertsand the effect of tube inclination on the rate
of heat transfer and stratification. Initially, such an effect was investigated
in a small scale assembly and the optimim results were tested in large scale
GDWP ( ̴ 10000m³). Therefore, the effect of inclination
of IC tube (d = 7.1mm and H_t = 0.1m) was studied in a small GDWP (D =
0.25m and H_T = 0.2 m) (Fig. 3A) for seven values of inclination
angles (α) (α = 0⁰, 15⁰, 30⁰,
45⁰, 60⁰, 75⁰, 90⁰). As the angle
of inclination
of the heated tube increases, the component of the buoyancy force acting
normal to the tube becomes stronger which results in stronger flow in
span wise direction (Fig 4). The stronger spanwise
flow provides sufficient kinetic energy to overcome the adverse pressure gradients
near the tube periphery and leads to delay in the flow
separationFurther, it  results in enhanced heat transfer and reduction in
thermal stratification (Fig 3B).

Fig 3: (A) Schematic of small
GDWP with IC tube (B) Effect of inclination angle (α) on stratification
number (S) at t=100s.

Fig 4: Isotherms at different inclination
angles at t=100s along plane (P): (a) α=
0⁰; (b) α= 15⁰; (c) α= 30⁰;
(d) α=
45⁰; (e) α= 60⁰; (f) α= 75⁰;

Based on the abovementioned findings, an improved design of IC (Fig
5) has been proposed which consist of a bundle of 40 slightly inclined (α= 85⁰) tubes of varying length and placed near the bottom of tank. The
slight inclination of IC tubes prevents the occurrence of a condensation-induced
water hammer. It was found that the proposed design is capable of removing the
required amount of decay heat in a stipulated time and also get the
stratification number of 0.2.

            It was also thought desirable to investigate
uniformity of steam distribution in all the IC tubes. For this purpose, various
choices of header diameter, tube diameter and tube pitch were examined and more
than 95% uniformity has been ensured.

Fig 5: Schematic diagram for the spider shape IC

            In order to model
unsteady natural convection with thermal stratification, both single phase and
two phase 3D CFD simulations have been performed. For single phase simulations,
open source CFD code [OpenFoam-2.2] was used. In order to study
the effect of two phase flow (boiling of GDWP water at high steam temperatures
on condensation side), the commercial CFD code [FLUENT-13] was used. The two phase simulations have
been performed using mixture model based on Euler-Euler approach. In the range of parameters covered in this work, the value of Rayleigh
number (Ra) varied from 5× 10¹² to 7× 10¹³ which
implies the need of turbulence model. In order to model turbulence, Shear
Stress Transport (SST) k-ω model was used.

References:

a.          
M.S. Gandhi, J.B. Joshi, P.K. Vijayan, Study of two phase thermal
stratification in cylindrical vessels: CFD simulations and PIV measurement.
Chem. Eng. Sci. 98 (2013) 125-151.

b.          
M.S. Gandhi, J.B. Joshi, A.K. Nayak, P.K. Vijayan, Reduction in thermal stratification in two phase natural
convection in rectangular tanks: CFD simulations and PIV measurements. Chem. Eng. Sci. 100 (2013) 300-325.