ML16256A276
| ML16256A276 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 08/25/2016 |
| From: | Entergy Operations |
| To: | Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML16256A115 | List:
|
| References | |
| W3F1-2016-0053 | |
| Download: ML16256A276 (7) | |
Text
WSES-FSAR-UNIT-3 6.2C-1 Revision 10 (10/99)
APPENDIX 6.2C DECLASSIFICATION OF FAN COOLER DUCTWORK:
HEAT AND STEAM REMOVAL AND CONTAINMENT MIXING
WSES-FSAR-UNIT-3 6.2C-2 Revision 10 (10/99)
Objective After a Design Base Accident (DBA), the fan cooler ductwork may not survive if it does not meet the requirement of Safety Class II and Seismic Class I. This investigation is to illustrate the capability of the fan cooler system to carry out the function of containment heat and steam removal without the consideration of ductwork.
Assumptions The air steam mixture discharged from the fan cooler will be considered as submerged turbulent jet; the analytical treatment of the jet with regard to mixing and momentum transfer is based on the jet theories [1, 2, 3,]*. Furthermore, the containment spray enhances the mixing process by the wake action which will also be included in this analysis. Also assumed is a complete severance of the duct at the junction of the classified to nonclassifed ductwork following the fan exhaust.
Inputs [4]
Q
=
Fan cooler capacity after accident = 44000 CFM A
=
Discharge opening area = 8 x 8 = 64 ft2 Rf
=
Radius of containment space for unobstructed jet flow = 40 ft Rc
=
Primary containment radius = 70 ft Rd
=
Direct distance from the fan discharge to the containment wall = 98 ft Qw
=
Containment spray flow rate = 1750 gpm dw
=
Spray drop size = 700 Vw
=
Droplet terminal velocity = 8.36 fps Cd
=
Drag coefficient = 0.5
=
Angle between jet flow and spray flow = 45°
=
Spray coverage factor = 0.95 Analysis We can assume a round jet at the discharge even if the initial cross-section is square [3]. So we have:
ro
=
equivalent round jet radius, ft Since A
ro
=
2 thus ro
=
A ft
=
=
64 4 51
- Reference numbers
WSES-FSAR-UNIT-3 6.2C-3 Revision 10 (10/99)
We define:
xH
=
length of the initial region, distance along the jet axis from the discharge plane to the point beyond which the jet velocity on the axis begins to change.
xH can be calculated from [1]:
x r
H o
= 8 or xH
=
=
8 4 51 36 1 x
ft
. which is within the unobstructed zone.
Also we define:
veolictity jet initial o
U
=
axis jet the on velocity m
U
=
section cross jet entire the over averaged mass the on based velocity c
U
=
with:
°
°
=
A d
U A
d U
Uc A
A
2 where:
=
density U
=
velocity At the end of the initial region where the main region is assumed to begin, the universal velocity profile is valid and that leads to: [1, 2,]:
Uc
=
.52 Um In the initial region Um
=
Uo with fps; 11.46 60 x
64 44,000 A
Q o
U
=
=
=
accordingly, at the end of the initial region
WSES-FSAR-UNIT-3 6.2C-4 Revision 10 (10/99) fps.
5.96 11.46 x
0.52 c
U
=
=
Due to the fact that the momentum and heat content of the jet remain unchanged, the following relation is obtained for turbulent jet [1]:
T T
U U
c o
c o
=
also from the similarity of heat and mass transfer [1]:
X X
T T
c o
c o
=
where T
T T
o o
a
=
T T
T c
c a
=
X X
X o
o a
=
X X
X c
c a
=
with To = initial jet temperature Ta = ambient gas temperature Tc = mass averaged temperature over the jet cross-section Xo = initial concentration of certain species of the jet Xa = ambient concentration of the same species Xc = mass averaged concentration over the jet cross-section Tc and Xc are defined in a manner similar to Uc:
°
°
=
A A
c a
d U
a d
T U
T
°
°
=
A A
c A
d U
A d
X U
X
with T = temperature X = concentration We then conclude:
X X
U U
c o
c o
=
Since the containment atmosphere is made up of air and steam, the initial density of the jet differs from that of the surrounding medium by the effects of cooling and condensation through the cooler. The percentage decrease in density is found less than 15 percent which is based on the output from the containment analysis. This value represents approximately the initial steam concentration difference:
WSES-FSAR-UNIT-3 6.2C-5 Revision 10 (10/99)
X 0.15
=
the minus sign indicates defect. At the end of the initial region, one can find:
X
X U
U 0.52 c
o c
o
=
=
Within the free space zone, the concentration deficiency is down to half of what it was initially. This is true also for the temperature defect. The effect of containment spray is investigated next.
B.
Containment Spray The interaction between the jet and the spray is studied here. Defining N = drop number density N can be found by the continuity relation between spray flow rate and pump rate:
w Q
2 c
R w
V w
d 6
N
=
or
2 3
6 c
w w
w R
V d
Q N =
0.95 x
70 x
8.36 x
3.28 x
10 x
700 6
60
/
0.13368 x
1750 2
3 6
=
= 5032 drops/ft3 The interaction between the jet and the droplet motion can be found through the momentum exchange; the momentum flux gain by the jet in the transverse direction must be equal to the total drag force to the droplets in the same direction. The result is [2]:
(
)
=
4 d
N Cos V
2 C
V 2
w 2
w d
2s fps 0.427 45 cos x
8.36 x
1/2 4
2 3.28 x
6 10 x
700 x
5032 x
2 0.5 s
V
=
°
=
where
WSES-FSAR-UNIT-3 6.2C-6 Revision 10 (10/99)
Vs = transverse velocity gain by the jet However, the momentum transfer is dissipative, namely, it contributes to the mixing of the jet with its surrounding through the wake of the drop. Vs represents approximately the turbulence fluctuation supplied to the jet by the spray.
=
V V
fps s
s 2
0 427 where
=
Vs 2
turbulence fluctuation in the jet contributed by the spray; we also define:
=
2 transverse turbulence fluctuation of the jet; it is observed that [1]:
V Um 2
01.
In the initial region, Um = Uo therefore fps 1.15 11.46 x
0.1 V 2
=
The ratio of the turbulence fluctuation due to spray to that due to the jet alone is
=
Vs 2
0 427 0 37 2
Thus, the spray increases the mixing rate about 37 percent. At this point, it is felt that the mixing in the main region of the jet should also be considered since it can extend beyond the initial region. If the jet can reach to containment wall directly, the jet center velocity is found to be [1]:
d ro o
m R
U U
4.
12
=
or Um = 12.4 x 4.51 x 11.46/98 = 6.54 fps the turbulence fluctuation is
=
V x
fps 2
0 1 6 54 0 654 and the ratio of fluctuations 0.652 0.6545 0.427
V
s V
2 2
=
The spray can increase the mixing rate by 65.2 percent at this distance. Without the spray, the concentration ratio is
WSES-FSAR-UNIT-3 6.2C-7 Revision 10 (10/99) 0.285 U
m 0.5U U
U
o o
c o
c
=
=
=
with the spray, the concentration ratio can be reduced to:
0.653 1
0.285 V
s V
1 spray no o
c
o
c
2
+
=
+
2
= 0.172 or
(
)
0.03 0.026 0.15 x
0.172 c
=
we can conclude that the concentration difference is reduced below 3 percent. This situation should be considered sufficiently mixed.
Conclusion The fan cooler without ductwork will assure adequate mixing in association with the spray inside the containment. Interference between the fan cooler discharge and solid object in its path will result in further enhancement of mixing through wake action. Any form of natural circulation within the containment will also increase the mixing process. The arrangement of the fan cooler discharge without ductwork ring headers and the strength of the jet will assure the ejected cool air to be mixed well with the ambient air before it is drawn in the cooler inlet. We can conclude that the fan cooler will perform the heat and steam removal functions as designed.
References 1.
Abramovich, G.N., "The Theory of Turbulent Jets", MIT Press, 1963 2.
Schlichting, H., "Boundary Layer Theory," Mc Graw Hill, 1968.
3.
duPlessis, M.P., Wang, R.L. and Kahawita, R.,"Investigation of the Near-Region of a Square Jet," Journal of Fluid Engineering, Trans. ASME, Vol. 96, 1974.
4.
Drawings [LOU-1564] G-146, G-854, G-855, G-856 (6/15/76).