ML20237K335
| ML20237K335 | |
| Person / Time | |
|---|---|
| Site: | Diablo Canyon  |
| Issue date: | 06/17/1987 |
| From: | Singh K, Soler A JOSEPH OAT CORP., PENNSYLVANIA, UNIV. OF, PHILADELPHIA, PA |
| To: | |
| References | |
| OLA-I-SC-008, OLA-I-SC-8, NUDOCS 8709040302 | |
| Download: ML20237K335 (21) | |
Text
Proc. of the Third Conf er ence on " Vibration in Nuclear Plant". - 1082, chgg "a British Nuclear Energy Society (1983)
.e l
DYl /.MIC CC"PLIi!G IU f. CLOSELY SPf CED '"h'D-CODY SYSTEM i
VIBR ATING IN A LIOUID MEMUK1: THC CASE OF FUEL RACKS *87 AUG 26 P4 :02 l
!..I.
SOLER
(,
Professor of Mechanical Engineering and Applied Mechanics University of Pennsylvania, Philadelphia, PA,1910 6l/7 7
K.P. SINGH g_[
Vice President Engineering, Joseph Oat Corporation, 2500 Broadway, Camden, NJ 08104 U.S.A.
i
SUMMARY
An approximate analysis of the effects of confined fluid on the mass and damping present in high density spent fuel storage racks is performed.
It is shown that inclusion of large displacement effects is required to yield realistic results for rack forces and pool floor slab forces.
The theory is developed for square cell geometries. and a simple two degree of freedom numerical example is presented to illustrate the effects.
NOMENCLATURE e
Characteristic dimension of gap (Fig. 2)
T' s
Triction Coefficient (Eq. 16) h Nominal gap between body 1 and body 2 (Fic. 2) h Cap in annulus i at time t. (Fig. 1) i K
Loss coefficient Kr Kinetic energy of the fluid set in motion L
Length of bodies 1 and 2 (dimension perpendicular tc the plane of motion) pi Hydrostatic pressure in cap 1.
Ori,QT2 Generali::ed forces corresponding to System Lagrangian in X and Y directions, respectively.
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. Vg!O {
Egyprter __
\\
0,,
k
+
I s
l r
l
]
i l
\\
t y.
I 1h
.h
Length co-ordinate in sap i.
Sg y
Displacement of body 1 (inner body) in X-direction (Fig.
2)
Displacement of body 1 (inner body) in Y-direction (Fig.
g2 2) l Displacement of body 2 in X-direction (Fig. 2)
V1 Displacement of body 2 in Y-direction (Fig. 2)
V2 Width of gap i at time t (Eq. 3) gg Velocity of body inner antf outer bodies, respectively.
(,i, t
Dimensionless width.of gap i eg Ratio of length to nominaal width of gap (Eq. 7) p Mass density of the fludX medium.
p INTRODUCTION Dynamic coupling between proximate th:riies vibrating in a fluid medium 1.is a well known phenomenon (1).
In the special case of a two body system executing planar motion where one body is ecmpletely enveloped by another,
(
Fritz [2] derived expressions for the virtual mass and the couplar.t inertial force und e r.ithr. ance :'.x m-the motions are of small amplitude.
Fritz's work has been the basis of the dynamic modelling of fluid coupling in much of the structural analysis performed in the nuclear industry (3).
Dong [4] gives a concise account of previously published work on dynamic coupling between closely spaced bodies executing small amplitude motions.
Unfortunately, the assumption of infinitesimal vibrations is rather untenable in many applications.
The case of
" poisoned"' fuel storage racks containing spent nuclear fuel is one such example.
The fuel rack dynamic coupling problem will be described in some detail since it provided the primary impetus for this study.
10 The term " poison" denotes a product containing the B isotope, used.
for capturing neutrons.
2.
A " poisoned" or high density storage rack is essentially an assemblage of cellular members of square cross sectional openings. Fuel storage racks are about 16' (4.88 m.) high and vertically submerged in fuel pools containing approximately 40' of water.
Spent fuel assemblies, after their removal from the reactor core, are placed in these cellular locations for long term radioactive decay.
l I
3 Figure 1 shows a typical channelled BWR fuel assembly in a storage cell.
Curbs on fuel reprocessing have accentuated utilit'ies' need to use
- poisoned" storage racks, as opposed to open lattice constrt.ction employed' in the past.
Water in the pool acts to moderate the emitted neutrons and l
to transport the spent fuel decay heat.
However, in the event of an
)
earthquake, it also produces dynamic coupling between the fuel assembly and i
y y a,i p 7
r The cap between the fuei assembly and the cel.ular container around it.
the container is in the order of 0.006-0.008 m. on each side.
Fw example, th/ cells for BWR.ftel assemblies (approximately 0.133 m side dunension) gry typically mada 0.1524 m. nquare.
When subjected to a given ground motion, a fuel assembly is free to vibrate and local impacts with the storap cell cay occur. She magnitude of impact, of enurse, is a strong furietyn of the dynamic coupling between the vibrating fuel assembly and its seroundins, vibrating fuel cell.
A mM ' hde of luel vibrating in unison hnd impacting storage conthiners cc. yield a large overturning force on the stwage racks.
Ultimately, this laat must be borne by the pool I
floor slab, and its supporting structure. Moreover, in free-standing racks (unanchored to the floor), excessive rigid body displacement of the rack, and consequent inter-rack inpact are also areas of concern.
These considerations indicate the importance of modelling.the fuel assembly / cell dynamic coupling in an appropriate manner.
This is especially important.in L
~ operating plants, since strengthening of therir pool floor and support structure is all but impossible in most cases.
It is important to develop i
l l s seismic nodel that yields conservative results for floor slab forces, yet
) !
is not so conservative that unrealistically high flocr loads are obtained.
4.
2 ~ (s recognized that the velocity of water in the gap between the fuel apenbly and the storage cell will be three dimensional.
Howeve.", the exial component will be quite small since the length of the fuel assembly is an. order of magnitude greater than the characteristic gap dimension.
l Tans it is sufficient.y accurate to model the problem in two dimensions as Show in Figure 2.
The outer body of square cross sectional opening simulates a single storage cell, The fuel assembly is moo'elled as an i
unperforated square cross-section to simulate a channeled BWR fuel f
assembly.
It is Intuitively obvious that the effect of einstic deformation of the cell and channel walls on the f)uid tootion will be insignificant.
I Therefore, the wa.ls af ;tme. :tm bodder...sne.nssumed to be rigid.
For analysis, the inner body is labelled is body' 1, and the outer body ~ 'is labelled as body 2.
The fluid.4n M4m fwec TB M ~Ea Wim ~ sed,
$wo dimensfqnfd.NnotSii"' ondoey dare 4
^
sy ~ em QFaiidErdr the' T1uiFkinetiedktssum.
OR.
Lagrange's equations or motion are used to determd.ne the generalized force.
The
[
amplitude of oscillations of the inner body (body 1) is allowed to be
(
comparable in magnitude to the inter-body gap.
The resulting expression shcus that the dynamic coupling consists of a virtual mass, a coupling in';rtial mass of the type derived by Fritz, and an additional non-linear force which may be referred to as " fluid spring".
These three forces
. )
completoly characterize the fluid forces for large amplitude motion under 1rviscid conditions.,
Fluid damping due to duct flow type losus due to form drag can also be derived from force equilibrium, if,' the duct turnaround coefficients are knovn.
Expressions for equivalent damping, due l
to drag are also given her9 for the sakt of completeness.
L in the following section, the detailed analysis of the subject problem l
is Given.
The results of the analysis are illustrated by tret ting a typical numerical problem in some da. tail.
JThe ~ primary intent %f this i
inalhis is to demonstrate ~that accurate "detFri!H!M9tlFWl'89191TMs e re491r es inclusion or Lne eITe'dT"M"EM6fst Tre Targe'compafed'to hie '
I
~~
Cap betwe e"r"*T$s*1"EMXi'%fr$*cet1~~Ulifrs.- % illustrate the potential effects', e simple two degree of freedom model is subject 6d to a simulate'd j
3cismic event, and a comparison between small and lar,te displacement 1
(l 1
l 017 l
l
golutions is made to illustrate errors sustained in using the small disp 1'acement theory.
Approximate Analysis of Duct Flow 6.
We consider the 2-D cross section shown in Figure 2.
Neglecting g
out-of-plane flow, and assuming small gap width hi compared to the characteristic length c,
permits the incompressible flow continuity equation to be written, in each portion of the duct, as (1) k1b~
au
=
.t hi which yields the solution for the local fluid velocity
( i. - i_ ) S i+Bi(t)
(2)
Ug=
3, 1
In terms of displacements Ui (t), Vi (t), i = 1, 2 shown in Figure 2, we define
?
1 = W (t) / h
'; i = 1, 2 (3)
Wi=Ui-V; t
i i
If h is defined as the nominal gap width around the. entire periphery, then the current gap widths in any portion of the cross section are given by the relations h,4
- h (1 E)
(4)
~
h,3
- h (1 I 1) I 2
2 1
Applying Eq2ation (2) to e m W m-,wz.d interpreting Si as eit,her x or y, i
i, = 1 Ui, i,= t v, yields i
3 2x/hp + B (t) g + D (t) ; u2 g /h ug=
y 2
~
(5) u3 = W y/h3 + B (t) i "4 * ~ W */h4 + B (t}
g 3
2 4
At corners, we require flow continuity in the local Si direction and impose the following conditions to determine B (t);
i hg ug (C/2) = h2 u2( /2) ;h2up(-h):
3 h U3 (c/2)
(6)
U (.C/2) u (c/2) e h3 U (,e/2); ha h3 u3(
/2) = ha a
g 4
where ui (C/2)denotesuievaluatedatS=hinregion1.
7.
The following final solutions are obtained for the approximate flow velocity distribution.
- pA yA j
2 1
- yjc, U3(S,t)
=
j
-c 2 (1-c )
(1-c )
y (7) vu vu 1
2 x j Up(S,t)
=
2 (1-c I Il~C2) l 2
i uu MW 2
1
=
+
Yj U3(s,t) c 2 (1+c )
(1+c1) y ana
I-UA)
V0
=
2 Ug'(S, t) x/
2 (1+c )
(1+c I 2
2 The kinetic energy of the fluid can be written in the form 4
U/2 h i (ci+S x
i S /c)
Sd L
(8)
=
i i
i"1 -h 2
where we have temporarily employed the notation ui = at+ $1 S /c and L is the length of the container. integrating yields i
4 2'
{.
Ph u.2 S
i g
f" 4,
2 1
- ^12 C.L i=1 (g)
After eliminating ai, $1 by inspection of Equation (7), we obtain-3 f " ~8 h 2+#
- 2 oc3 E
1 1
2 2
(10)
~
with 2
2 fl" 2
2
+
3 (1-c3)
(1-c I
2 (11) i -
/
2 2
t' '
- 2 *
+
i 2
2
,,, g }(
3 (1-c2)
(1-c3) t J.
(
4 2
S>t' ile form 4
[
EE Q gu b,,...f.. /c.. D.5,r' -u f
i f
)
1 = 1, 2 ft (B s. /
3 W.
r,', \\
t 1
1 2
1
/and obtain the formal results
' t' O) 3 f
pC 4
!Il
- \\
1 L
4h 1
1+4h I dW 1+
BW 2
y 2
/
~,
2+I#
oC 1
2 2
i sh Bw "1
BW "2
(12) 1 1
g
)h &
Q 3
3 f2
- m. p C 4
g B&
oC 2
2-g,BW g
L 4h 2
2,4h 2
BW 1
2 y
2 3
3&
B&
\\
oC 1
2+BW 2
2
' '8 h (%
1 2
2 l
8.
Using Equation'(11) to evaluate a4/6W
(
Qri as 1
1 permit,s us to finally write B19 L___n__-_-_-__________-_-_
- 1 2
1 2
+$
O
=m Wy+
6 1
2 1
2 ~T N
fy y
2 (13)
$ -2. 2
+$
W 2
2 W
W
~
N2+
6 2
1 1
2 2
1 Of2 " *2 where D
i = 1,2 (ga)
$f=h (1-c{2) 2 2
i 1 ' "2 3
~
L 1
1 "i*pC
+
(15) 2h 3 (1-c4) gy_g 2) i=2,j=1 2
j I
9 Equations (13) and (15) provide the contribution of the fluid in the conservative effects.f We gap to the system Lagrangian and j
clearly see the virtual mass effects in' the7eam g terms of Equation (13).
The coupled quadratic terms in the generalized velocities appear solely from the assumptica that 6 i need not be small compared to unity.
For small vibrations, with Ei-+ 0, then 4'i -* 0, and mi -+ 3 Pc3L/ - It 3" '"
h should be noted that the quadratic terms in Equation (13) do not behave as [3 c#
velocity squared damping terms,!but appear to behave more like no
'gp'rltyis!
This is easily seen by It is clear, there, that the teld T96aiiges sign / g c e casa with Wj = 0.
.only when G.2 changes'51gn;1 that is, no net energy is dissipated during a "
r* [ i
- j
' complete harmonic motion cycle.
10.
The usual small moh..ammalysis sincludes only the virtual mass effects; the effect of fluid friction can be shown to be negligible.
In our case, where large motions, relative to the nominal gap width h, are admissible, we need to compute additional contributions to Equation (13) which account for frictional forces and the turning losses.
The following approximate analysis is used to develoo the additional terms necessary to include dissipative effects.
11.
If the balance between pressure and frictional shear forces along any straight portion of the duct is considered, Reference 5 shows that the governing relation for the fluid pressure change due to shear stress is i
y f*p U.
U.
,9 P fl 1
1 BS h
h (16)'
=-2
=-
y g
g where f' is the friction loss factor defined by the relation i
f*
U U
g1 " 7 P i
i T
12.
Equation (10), written for each portion of the duct, can be integrated to' yield the pressure distribution in each region.
Note, however, that for I
arbitrary 2-D motions, proper attentian must be focussed on the local fluid flow direction in cach duct in order to ascertain the location or points of I
flow reversal.
The arbitrary time functions arising from the integration of Equation (16) are determined by applying corner pressure matching conditions.
From Figure 3, for 1, j combinations 1,2 : 2,3: 3,4' : 4,1,
(
t i
4
(
ecpirical equations for pressure loss due to abrupt turning of the flow may be written as:
P -3 ~P i
=Ey v
- 2V
=U.+U 2
m m
m 1
j (17) p where K is a loss coefficient.
For a sencral 2-D motion (W, h f 0), the pressure in each region is 13 2 (16) 1 and (17); contributions to the fully determined by using Equations
-generalized forces Qpi(Equation (13)), due to frictional and te,rting losses, are calculated from the expressions c/ 2 F
=L (P -P y) dy g
3 c/
(16) 2 F
=L (P -P) dx 4
2
-c,2 Note that the direct effect of shear forces is neglected in Equation (18).
14.
For the purpose of illustration, v,e restrict further damping computations to uni-directional motion, say W2 / 0.
It is clear that the plane x = 0 is a plane of symmetry for the fluid flow; for such a motion, the pressure distribution due to friction losses in regions 2, 1,
4 in Figure 2 are obtained from Equation (16) as p f*.4" S %. J.
.)
(
o 3
%fj P (x,t)
=
A2 (t)
- x
>,0 7
2 3
3e h tl-c I 2
(19) 2+
p f* y W
W Y
c 2
2
+
AI 8
Yd 2 P 3 (y, t) 4h 1
=
p f*
11 'x
$ 2 2
=
+A4 (t)
- x ), 0 P 4 (x,t) 2 h (1-c ) 3 3e 2
Using Equation (18) to compute F yields y
c/
3 2
p f* v CLW W
p 2
2 F
= 2L (P
-P 2) dx =
4 96
)
(20) 1 0
1 1
+
+ G44 2
(1+c )3 (1~'2)3 g
2 f
Using Equation (19), and Equation (7) in Equation (17)iat the cornens x e a
c/2*Y: I.c/2 yields:
g
'l i
821
2 2
(2-c I A ~^1 V
W2 "2 K
2 1
2
+ pU 1+
=
- 7 (1-c )g 3 (1~ C I E'
g 3
2 2
s
,(21) 7 2
2 A -A W
W (2+C2}
1 1
4
,u 2
2
_K
+ pf*
1+
0 p
(1+c )
3 (1+C2}
y A 'A 2
4 15.
Solvir-g Equation (21) for and substituting in Equation (20) p yields the resulting velocity squared non-linear damping force as y=CiG.2)
F 2
2
~
~
2 4
(22) where I1*3C 2}
I4~3C2 +C2 3
2 2
pp CL ipf 1+
6+K ~
23 4
22 c (g2) 4II~C I
II~C I
4 2
2 4
L Dynamic Analysis
- 16. The simple dynamic model shown in Figure 4 is now considered as a vehicle to obtain numerical results which illustrate the effects of the K,
K are introduced representing the fluid coupling.
Linear springs I
o elastic stiffness coupling the structure to ground, lumped masses M, MO y
f representing the mass of the respective solid bodies, and non-linear elements F *,
F8 which act a:117 h. impact between the bodies occurs.
i 4
p h
Ther. if Y(t) represents a known ground motion, and relative co-ordinates U, 1
v are introduced by the relations
. _z,,-,r g
< - R' t ww-
~
t
,Ed U2 U+IIY2*V+I L
(23) ~
- > ~ ~ ~ ~ ~
~ ~
- }
, =., ( ( -
(
a.
~
3';a the equations of motion for the system shown in Figure 4 can be written as
- c L ';-
(Hy + H )
..U-m2 V
0-E U -F2 + F4' - MI Y 2
I (24) t s_
Ov+F'-F'-MO Y
- m2 U + (MO + m2) v = K 2
4 k
where the impact elements F ' (n4) = 0 if h4>0 4
F ' (h ) = 0 if h2>0 2
2 the fluid mass m2 is given as l
2 4
p pc y
1+
m2*
- 2 2
3 (1-c2) j I
and the fluid forces are 2
e up c p c
G =j Ch) W W
(26) 2 2
p 2
2 6
(1-c2 )2 i
l l
--- D
are assumed small, then it may be It is cicar that if the motions U, y 17argued -that conservative results arg obtained by including only the effect 2
Oc L and neglecting the effect of G.
of a constant' fluid mass However, if the effect of large motions is incorporated with respect to then more realistic results can be achieved, since it is nominal gap size, easily shown that increases in the fluid effects encompassed in G are larger than the increases in fluid mass.
To illustrate the fluid effects, equations (24) and (26) ar,e solved, 18.
using a modification of the for a given time history ground motion Y(t),
time history computer code presented in Reference 6.
Typical geometry and material values are assigned which are representative of a fully loaded fuel rack containing 169 cells simulated by a two degree of freedom dynamic that such a simple model is only for illustrative model.
Note, however, purposes; the authors have devcdoped a more realistic rack and. fuel assembly group model which uses thirty-two degrees of freedom to accurately j,
]
simulate potential for rack deformation, impact, and sliding under ' a l
realistic 3-D seismic event.
For the purpose of illustrating the effects l
of confined fluid, the following inptt data is used:
Rack Mass MO = 9368.8 Kg Fuel Assembly Mass (169 cells) My = 53586.1 Kg li e =.1524 m. : h = 7.9375 mm. ; L = 53 34 m 4
lj Ky = 60590.9 N/m. ;KO = 60590.9 x 10 N/m.
l,l f8= 0.025
- K =.9 I.
6 3
]'
p = 1019.P Vejf3 -x %9 eells =.1723 x 10 ggfm d
19.'To simulate the impact force on the cell walls, non-linear gap elements with stiffness 10 Ko are used.
These gap elements become active, l
when the hp or h4 approach value.01 h.
The seismic acceleration Y(t) used in the simulation is Y(t) = A sin D t where A =.5 g
= 10 Hertz O (t 4
.2 see (26)
I
= 5 Hertz t
>f
.2 see I
A =1.0 g A total event duration of 1 3 see. is assumed.
The following five g
simulations are performed using the two degree of freedom model:
3 Remarks Case
)
Vibration in air; no fluid mass or damping ii i
i Vibration in fluid; small deflection model - 6 i 2
= 0 when calculating m2 and fluid damping effect 0
6 Vibration in fluid; large deflection model used i
3 G
l i
823 l
Q
l l
1 no fluid for computing fluid masseo ofrect f
damping Same as case 3 except fluid damping included l
4 I
Same as case 4, except f*, K reduced to 1% of 5
values used in case 4.
(
Discussion of Results of Simulation Runs 20.
The following table summarizes the results obtained from the five I
simulations.
Figures 5 and 7 show typical time histories of the rack I
The magnitude of the rack spring force range is a direct measure of the expected rack stress level at the rack base and the j
spring force.
subsequent loads transmitted to the pool floor slab through the rack feet g
(which are not modelled in our simple simulation).
TABLE 1_
l Summary of Results - Max. Force Range I
i Local Impact Force Fluid Damping RackSpringFogce Case Range from Gap ForceRagge l
Range (N x 10~ )
Springs (N x 10-6)
(N x 10~ )
1 I
1 2.678 12.005
(
2 2.228 9 599
.756
~
3 1.997 10.555 4
1.535 O.
1.503 5
1.766 7.499 li.852 l
Examination of the maximum force ranges shown in Table 1 produces the ;
anticipated results; namely, the inclusion of fluid damping coupled with g
large deflection effects significantly reduces the force range in the fuel l
Comparison of the results of case 4 with case 2 shows a reduction of rack.
31% in the rack force range by the inclusion of large deflection effects in l
the calculation of fluid mass and fluid damping.
The impacts with the cell wall are eliminated, thus eliminating the need for calculation of local impact effects en the rack cell wall.
The results of case 3 indicate that at least for this simulated seismic input, the inclusion of only large j
1 deflection effects in the fluid virtual mass and the complete neglect of i
fluid damping serves to reduce the force range in the rack.
The local f,
8 The stress range in the rack cell wall is increased in this case however.
i to draw any lasting conclusions from the case 3 results authors hesitate since a chenge in input seismic frequence content may very well reverse the conclusions inferred from this data.
I i
i I
I
l l
- 21.. The results obtained in case 5 m rit some further elaboration.
The reduction in fluid damping to 1% of the values used in case 4 is an attempt g
I to simulate the possible damping effect of unchannelled fuel assemblies, h
It is clear that the damping and virtual mass effects from an unchannelled fuel ' assembly should be substantially less since the confined fluid has more unobstructed area in which to flow as the fuel assembly moves relative to the cell wall.
In addition, there are substantial differences in the flow-field which should be considered in any analysis of unchannelled fuel.
Nevertheless, case 5 may give some indication of what might be expected if l
only unchannelled fuel assemblies are: in the rack.
Table 1 shows that the rack force range certainly increases over the results obtained in case 4; the rack force level is still substantially less than the results obtained for case 2.
Local impact with the rack cell wall occurs during the event although the impact range is less than that of case 2.
A somewhat surprising results, on first reading, is obtained for the maximum fluid damping force range.
Since the damping coefficients have been reduced, one might expect that the damping force range should also be reduced. However, we recall that the damping force is of the form C(6.)Slh (27)
Fd N
W is maximum when 6.a 0, and goes to zero as the gap closes.
C ( f_ )
achieves its largest value when the gap closes, and is relatively ' small when E.~ 0.
Examination of the detailed numerical output from the simulations show that the damping force exhibits a sharper and higher peak in case 5, compared to case 4, but the energy dissipation due to the fluid damping is higher in case 4.
The increased dissipation in case 4 precludes C (E ) from growing too large since the gap never becomes too small.
The effect of fluid damping on the rack spring force range is measured by the
(
dissipation level dur:xst. tac % 2ather than the peak value of the fluid damping force.
Thur, the expected result that a decrease in the effective fluid friction coefficient results in increased rack force level is obtained.
l 22.
Examination of the detailed tiae history of rack force level shows
(
that in air the rack essentially vibrates at its natural frequency of 41 l
Hertz with amplitudes modified by the local impact forces.
Although not shom1 here in the results, during the 1 3 second. time of the event, vibration in air results in a total of twenty-two impacts with the outer s
cell walls.
With the additional of fluid mass, the graphs show that the l
rack essentially vibrates at the forcing frequency of either 10 or 5 Hertz.
l The addition of fluid mass effects in cases 2-5 reduces the number of
(
impacts to a total of three during the time span of the event.
1 CONCLUSIONS i
23.
It has been demonstrated that in high density fuel racks containing channelled fuel assemblies, large displacement effects coupled with the l
inclusion of fluid damping results in a significant decrease in rack force-range and possibly the complete elimination of local, impacts between rack
}
cell and fuel assembly.
It has also been shown ithat an approximate '
analysis of the large displacement effect is easily implemented into a time
)
j history lumped mass analysis.
In a 3-D motion cross coupling effects between the two on-plane motions will occur in the inertial. terms due to
)
1 1
f 825
4 g urge displacements although not carried out in detail herein, similar
,coss coupling in the fluid damping terms is expected.
.p, experimental; work is currently planned to verify the analysis esented here. e Once the analysis 'has -been - matched with experiment for both channellePaYd unchan~n~BTled*MiM%4ec6FatsN55c5616n*oI fiuid Msoping effects shotil,HMiim'eNe analysis 'of ~liisli" density fuei storage,cgdB~~ feature ~ of ~the 3-D
~ isamic ac d
racNE REFERENCES 1.
Sharp G R and Wenzel W A.
" Hydrodynamic Mass Matrix for a Multibodies System", Journal. of Engineering for Industry, Trans. of the ASME, pp.
611-618, May 1974.
2.
Fritz R J.
"Effect of. Liquids on the Dynamic Motions of Immersed Solids", Journal of Engineering for Industry, Trans. of the ASME, February 1972, pp. 167-.173.
3.
Stokey W F and Scavuzzo R J.
" Normal Mode Solution of Fluid-Coupled Concentric Cylindrical Vessels", Trans. 'of the ASME, Vol.100, Journal of Pressure Vessel Technology, pp. 350-353, November 1978.
4.
Dong R G.
" Size Effect in Damping Caused by Water Submersion", AICE, Journal of the Structural Division, May 1979,.pp, 847-857 5.
Li W H and Lam S H.
Principles of Fluid Mechanics, Addison Wesley, 19614, pp. 273-278.
6.
Levy S and Wilkinson 3 Y A % Component Element Method in Dynamics, McGraw Hill, 1976, Chapter 3 s
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l-
PRESENTATION AND DISCUSSION In presentins'the paper Dr. SOLER gaid that it dealt with work'Grising from
. a. seismic analysis and qualification of high density. -spent fuel s t.orage racks.
He' defined L the problem and gave an outline of the model adopted with the assumption.of no axial vibration.. He discussed the derivation of fluid velocity - field -and.the calculation ~ of fluid kinetic energy and damping forces.
He gave a numerical example-and discussed the results.
Dr.' J.D. DUTHIE (UKAEA) noted that the force transmitted Lto the support was reduced by.the inclusion of large added mass terms'and asked why that was.
j Dr. SOLER discussed'this in the terms of theLway the damping built-up and the analysis which included all the -large deflection ' effects : as compared with the case which only included the small mass effects.' The force in the rack. spring was 30% less for the former.
Mr.'DUTHIE thought they would be.
about ' the same. He then: asked-if Dr. SOLER had any feel for how shortL the; length of the axial contact needs to be bafore the assumption of no axial fluid velocity breaks down..
He thought this would reduce the very large values of added mass.
Dr..SOLER said he would expect that the inclusion of-axial terms would reduce the 30% result to maybe 20% because the flow would split i.e. the present results probably gave an upper boundary.
Dr. D.E.
HOBSON - (CEGB) said that he would expect that at the ends of -the storage racks the high fluid pressures predicted would not be realised.due to axial movement and this would induce a pressure distribution which was very non-uniform in the axial direction..
This would introduce close distortion of the element, bending and axial motion.- Dr.~SOLER agreed.
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